Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 748.7 | ||
Character | \(\chi\) | \(=\) | 819.748 |
Dual form | 819.2.fm.e.496.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11902 | − | 0.567791i | 1.49838 | − | 0.401489i | 0.585820 | − | 0.810441i | \(-0.300773\pi\) |
0.912556 | + | 0.408953i | \(0.134106\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.43582 | − | 1.40632i | 1.21791 | − | 0.703161i | ||||
\(5\) | 3.00219 | − | 3.00219i | 1.34262 | − | 1.34262i | 0.449179 | − | 0.893442i | \(-0.351717\pi\) |
0.893442 | − | 0.449179i | \(-0.148283\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60148 | − | 0.481982i | −0.983267 | − | 0.182172i | ||||
\(8\) | 1.26060 | − | 1.26060i | 0.445690 | − | 0.445690i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.65710 | − | 8.06633i | 1.47270 | − | 2.55080i | ||||
\(11\) | 0.698323 | + | 2.60618i | 0.210552 | + | 0.785792i | 0.987685 | + | 0.156455i | \(0.0500068\pi\) |
−0.777133 | + | 0.629337i | \(0.783327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.373866 | − | 3.58612i | 0.103692 | − | 0.994609i | ||||
\(14\) | −5.78626 | + | 0.455764i | −1.54644 | + | 0.121808i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.857159 | + | 1.48464i | −0.214290 | + | 0.371161i | ||||
\(17\) | −0.599399 | − | 1.03819i | −0.145376 | − | 0.251798i | 0.784137 | − | 0.620587i | \(-0.213106\pi\) |
−0.929513 | + | 0.368789i | \(0.879772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.89568 | + | 0.507945i | 0.434898 | + | 0.116531i | 0.469624 | − | 0.882866i | \(-0.344389\pi\) |
−0.0347266 | + | 0.999397i | \(0.511056\pi\) | |||||||
\(20\) | 3.09075 | − | 11.5349i | 0.691114 | − | 2.57927i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.95953 | + | 5.12605i | 0.630973 | + | 1.09288i | ||||
\(23\) | 4.65282 | + | 2.68631i | 0.970181 | + | 0.560134i | 0.899291 | − | 0.437350i | \(-0.144083\pi\) |
0.0708893 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 13.0263i | − | 2.60526i | ||||||
\(26\) | −1.24393 | − | 7.81134i | −0.243955 | − | 1.53193i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.01456 | + | 2.48450i | −1.32563 | + | 0.469526i | ||||
\(29\) | −1.47928 | + | 2.56220i | −0.274696 | + | 0.475788i | −0.970058 | − | 0.242872i | \(-0.921911\pi\) |
0.695362 | + | 0.718659i | \(0.255244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.36721 | + | 3.36721i | −0.604768 | + | 0.604768i | −0.941574 | − | 0.336806i | \(-0.890653\pi\) |
0.336806 | + | 0.941574i | \(0.390653\pi\) | |||||||
\(32\) | −1.89620 | + | 7.07671i | −0.335204 | + | 1.25100i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.85961 | − | 1.85961i | −0.318921 | − | 0.318921i | ||||
\(35\) | −9.25714 | + | 6.36314i | −1.56474 | + | 1.07557i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.03769 | − | 3.87273i | −0.170596 | − | 0.636673i | −0.997260 | − | 0.0739770i | \(-0.976431\pi\) |
0.826664 | − | 0.562696i | \(-0.190236\pi\) | |||||||
\(38\) | 4.30539 | 0.698426 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 7.56914i | − | 1.19679i | ||||||
\(41\) | 1.42770 | + | 5.32825i | 0.222969 | + | 0.832133i | 0.983208 | + | 0.182489i | \(0.0584154\pi\) |
−0.760239 | + | 0.649644i | \(0.774918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.78317 | + | 5.64832i | −1.49192 | + | 0.861360i | −0.999957 | − | 0.00925580i | \(-0.997054\pi\) |
−0.491963 | + | 0.870616i | \(0.663720\pi\) | |||||||
\(44\) | 5.36612 | + | 5.36612i | 0.808973 | + | 0.808973i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.3847 | + | 3.05052i | 1.67858 | + | 0.449775i | ||||
\(47\) | 2.97828 | + | 2.97828i | 0.434427 | + | 0.434427i | 0.890131 | − | 0.455704i | \(-0.150613\pi\) |
−0.455704 | + | 0.890131i | \(0.650613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.53539 | + | 2.50773i | 0.933627 | + | 0.358248i | ||||
\(50\) | −7.39621 | − | 27.6030i | −1.04598 | − | 3.90366i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.13256 | − | 9.26092i | −0.573084 | − | 1.28426i | ||||
\(53\) | 11.0603 | 1.51925 | 0.759627 | − | 0.650359i | \(-0.225382\pi\) | ||||
0.759627 | + | 0.650359i | \(0.225382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.92075 | + | 5.72775i | 1.33771 | + | 0.772329i | ||||
\(56\) | −3.88702 | + | 2.67184i | −0.519424 | + | 0.357040i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.67985 | + | 6.26927i | −0.220575 | + | 0.823196i | ||||
\(59\) | 3.14721 | − | 11.7455i | 0.409731 | − | 1.52914i | −0.385428 | − | 0.922738i | \(-0.625946\pi\) |
0.795160 | − | 0.606400i | \(-0.207387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55683 | + | 2.63089i | −0.583442 | + | 0.336851i | −0.762500 | − | 0.646988i | \(-0.776028\pi\) |
0.179058 | + | 0.983839i | \(0.442695\pi\) | |||||||
\(62\) | −5.22332 | + | 9.04706i | −0.663362 | + | 1.14898i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.6437i | 1.58046i | ||||||||
\(65\) | −9.64379 | − | 11.8886i | −1.19616 | − | 1.47460i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.15530 | − | 1.11341i | 0.507651 | − | 0.136025i | 0.00410235 | − | 0.999992i | \(-0.498694\pi\) |
0.503549 | + | 0.863967i | \(0.332028\pi\) | |||||||
\(68\) | −2.92006 | − | 1.68590i | −0.354109 | − | 0.204445i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.0032 | + | 18.7397i | −1.91274 | + | 2.23983i | ||||
\(71\) | −0.800761 | + | 2.98848i | −0.0950329 | + | 0.354668i | −0.997024 | − | 0.0770861i | \(-0.975438\pi\) |
0.901992 | + | 0.431754i | \(0.142105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.78407 | + | 4.78407i | 0.559933 | + | 0.559933i | 0.929288 | − | 0.369355i | \(-0.120421\pi\) |
−0.369355 | + | 0.929288i | \(0.620421\pi\) | |||||||
\(74\) | −4.39780 | − | 7.61721i | −0.511234 | − | 0.885483i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.33186 | − | 1.42867i | 0.611607 | − | 0.163879i | ||||
\(77\) | −0.560542 | − | 7.11650i | −0.0638797 | − | 0.811000i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.16895 | −0.131517 | −0.0657584 | − | 0.997836i | \(-0.520947\pi\) | ||||
−0.0657584 | + | 0.997836i | \(0.520947\pi\) | |||||||
\(80\) | 1.88383 | + | 7.03054i | 0.210618 | + | 0.786038i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.05066 | + | 10.4801i | 0.668184 | + | 1.15733i | ||||
\(83\) | 3.24002 | − | 3.24002i | 0.355639 | − | 0.355639i | −0.506564 | − | 0.862202i | \(-0.669085\pi\) |
0.862202 | + | 0.506564i | \(0.169085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.91635 | − | 1.31733i | −0.533253 | − | 0.142885i | ||||
\(86\) | −17.5237 | + | 17.5237i | −1.88963 | + | 1.88963i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.16566 | + | 2.40505i | 0.444061 | + | 0.256379i | ||||
\(89\) | −4.80209 | + | 1.28672i | −0.509020 | + | 0.136392i | −0.504183 | − | 0.863597i | \(-0.668206\pi\) |
−0.00483713 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70105 | + | 9.14901i | −0.283147 | + | 0.959077i | ||||
\(92\) | 15.1113 | 1.57546 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00209 | + | 4.62001i | 0.825352 | + | 0.476517i | ||||
\(95\) | 7.21613 | − | 4.16623i | 0.740359 | − | 0.427447i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7483 | − | 3.95180i | −1.49746 | − | 0.401244i | −0.585214 | − | 0.810879i | \(-0.698990\pi\) |
−0.912250 | + | 0.409634i | \(0.865656\pi\) | |||||||
\(98\) | 15.2725 | + | 1.60321i | 1.54276 | + | 0.161949i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.3192 | − | 31.7298i | −1.83192 | − | 3.17298i | ||||
\(101\) | 0.803086 | − | 1.39099i | 0.0799101 | − | 0.138408i | −0.823301 | − | 0.567605i | \(-0.807870\pi\) |
0.903211 | + | 0.429197i | \(0.141203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4997 | −1.42870 | −0.714351 | − | 0.699787i | \(-0.753278\pi\) | ||||
−0.714351 | + | 0.699787i | \(0.753278\pi\) | |||||||
\(104\) | −4.04937 | − | 4.99196i | −0.397073 | − | 0.489502i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 23.4371 | − | 6.27995i | 2.27641 | − | 0.609963i | ||||
\(107\) | −1.91021 | + | 3.30858i | −0.184667 | + | 0.319852i | −0.943464 | − | 0.331475i | \(-0.892454\pi\) |
0.758797 | + | 0.651327i | \(0.225787\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.59246 | + | 9.59246i | 0.918791 | + | 0.918791i | 0.996942 | − | 0.0781507i | \(-0.0249015\pi\) |
−0.0781507 | + | 0.996942i | \(0.524902\pi\) | |||||||
\(110\) | 24.2745 | + | 6.50432i | 2.31448 | + | 0.620163i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.94545 | − | 3.44913i | 0.278319 | − | 0.325912i | ||||
\(113\) | 1.57880 | + | 2.73457i | 0.148521 | + | 0.257247i | 0.930681 | − | 0.365831i | \(-0.119215\pi\) |
−0.782160 | + | 0.623078i | \(0.785882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.0335 | − | 5.90385i | 2.05463 | − | 0.550537i | ||||
\(116\) | 8.32140i | 0.772623i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 26.6760i | − | 2.45573i | ||||||
\(119\) | 1.05893 | + | 2.98973i | 0.0970724 | + | 0.274068i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.22177 | − | 1.86009i | 0.292888 | − | 0.169099i | ||||
\(122\) | −8.16224 | + | 8.16224i | −0.738974 | + | 0.738974i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.46654 | + | 12.9373i | −0.311304 | + | 1.16180i | ||||
\(125\) | −24.0965 | − | 24.0965i | −2.15526 | − | 2.15526i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.77265 | + | 3.33284i | 0.512240 | + | 0.295742i | 0.733754 | − | 0.679415i | \(-0.237767\pi\) |
−0.221514 | + | 0.975157i | \(0.571100\pi\) | |||||||
\(128\) | 3.38658 | + | 12.6389i | 0.299335 | + | 1.11713i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −27.1857 | − | 19.7166i | −2.38434 | − | 1.72926i | ||||
\(131\) | 9.80212i | 0.856415i | 0.903680 | + | 0.428207i | \(0.140855\pi\) | ||||
−0.903680 | + | 0.428207i | \(0.859145\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68674 | − | 2.23509i | −0.406392 | − | 0.193807i | ||||
\(134\) | 8.17300 | − | 4.71868i | 0.706039 | − | 0.407632i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.06435 | − | 0.553140i | −0.177016 | − | 0.0474314i | ||||
\(137\) | −6.48757 | − | 1.73834i | −0.554271 | − | 0.148516i | −0.0291978 | − | 0.999574i | \(-0.509295\pi\) |
−0.525073 | + | 0.851057i | \(0.675962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.304839 | + | 0.175999i | −0.0258561 | + | 0.0149280i | −0.512872 | − | 0.858465i | \(-0.671419\pi\) |
0.487016 | + | 0.873393i | \(0.338085\pi\) | |||||||
\(140\) | −13.6001 | + | 28.5180i | −1.14942 | + | 2.41021i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.78733i | 0.569580i | ||||||||
\(143\) | 9.60714 | − | 1.52991i | 0.803389 | − | 0.127937i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.25111 | + | 12.1333i | 0.269990 | + | 1.00762i | ||||
\(146\) | 12.8539 | + | 7.42121i | 1.06380 | + | 0.614184i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.97395 | − | 7.97395i | −0.655455 | − | 0.655455i | ||||
\(149\) | −3.05452 | + | 11.3996i | −0.250236 | + | 0.933892i | 0.720443 | + | 0.693514i | \(0.243938\pi\) |
−0.970679 | + | 0.240379i | \(0.922728\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2745 | + | 12.2745i | −0.998884 | + | 0.998884i | −0.999999 | − | 0.00111530i | \(-0.999645\pi\) |
0.00111530 | + | 0.999999i | \(0.499645\pi\) | |||||||
\(152\) | 3.03001 | − | 1.74938i | 0.245766 | − | 0.141893i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.22848 | − | 14.7618i | −0.421323 | − | 1.18954i | ||||
\(155\) | 20.2180i | 1.62395i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.41109i | − | 0.352043i | −0.984386 | − | 0.176022i | \(-0.943677\pi\) | ||
0.984386 | − | 0.176022i | \(-0.0563228\pi\) | |||||||
\(158\) | −2.47702 | + | 0.663716i | −0.197061 | + | 0.0528024i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.5529 | + | 26.9384i | 1.22956 | + | 2.12967i | ||||
\(161\) | −10.8095 | − | 9.23095i | −0.851905 | − | 0.727501i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.610931 | − | 0.163698i | −0.0478518 | − | 0.0128219i | 0.234814 | − | 0.972040i | \(-0.424552\pi\) |
−0.282666 | + | 0.959219i | \(0.591219\pi\) | |||||||
\(164\) | 10.9709 | + | 10.9709i | 0.856680 | + | 0.856680i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.02603 | − | 8.70534i | 0.390096 | − | 0.675665i | ||||
\(167\) | 16.3769 | − | 4.38817i | 1.26728 | − | 0.339567i | 0.438292 | − | 0.898833i | \(-0.355584\pi\) |
0.828988 | + | 0.559266i | \(0.188917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7204 | − | 2.68145i | −0.978496 | − | 0.206266i | ||||
\(170\) | −11.1658 | −0.856380 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.8867 | + | 27.5166i | −1.21135 | + | 2.09812i | ||||
\(173\) | −4.60670 | − | 7.97903i | −0.350241 | − | 0.606634i | 0.636051 | − | 0.771647i | \(-0.280567\pi\) |
−0.986291 | + | 0.165013i | \(0.947234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.27845 | + | 33.8877i | −0.474606 | + | 2.56167i | ||||
\(176\) | −4.46782 | − | 1.19715i | −0.336774 | − | 0.0902384i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.44515 | + | 5.45316i | −0.707944 | + | 0.408732i | ||||
\(179\) | −2.35631 | − | 1.36042i | −0.176119 | − | 0.101682i | 0.409349 | − | 0.912378i | \(-0.365756\pi\) |
−0.585468 | + | 0.810696i | \(0.699089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4525 | −1.14858 | −0.574288 | − | 0.818653i | \(-0.694721\pi\) | ||||
−0.574288 | + | 0.818653i | \(0.694721\pi\) | |||||||
\(182\) | −0.528864 | + | 20.9206i | −0.0392020 | + | 1.55074i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.25172 | − | 2.47899i | 0.682046 | − | 0.182754i | ||||
\(185\) | −14.7420 | − | 8.51132i | −1.08386 | − | 0.625765i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.28713 | − | 2.28713i | 0.167252 | − | 0.167252i | ||||
\(188\) | 11.4430 | + | 3.06614i | 0.834566 | + | 0.223621i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.9256 | − | 12.9256i | 0.937721 | − | 0.937721i | ||||
\(191\) | −1.63770 | − | 2.83658i | −0.118500 | − | 0.205248i | 0.800673 | − | 0.599101i | \(-0.204475\pi\) |
−0.919173 | + | 0.393853i | \(0.871142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.44447 | − | 20.3190i | −0.391901 | − | 1.46260i | −0.826995 | − | 0.562210i | \(-0.809951\pi\) |
0.435093 | − | 0.900385i | \(-0.356715\pi\) | |||||||
\(194\) | −33.4958 | −2.40486 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.4457 | − | 3.08247i | 1.38898 | − | 0.220176i | ||||
\(197\) | −20.1959 | + | 5.41149i | −1.43890 | + | 0.385553i | −0.892149 | − | 0.451741i | \(-0.850803\pi\) |
−0.546753 | + | 0.837294i | \(0.684136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4685 | − | 21.5960i | −0.883867 | − | 1.53090i | −0.847007 | − | 0.531582i | \(-0.821598\pi\) |
−0.0368601 | − | 0.999320i | \(-0.511736\pi\) | |||||||
\(200\) | −16.4210 | − | 16.4210i | −1.16114 | − | 1.16114i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.911969 | − | 3.40352i | 0.0641659 | − | 0.239471i | ||||
\(203\) | 5.08326 | − | 5.95251i | 0.356775 | − | 0.417784i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2827 | + | 11.7102i | 1.41660 | + | 0.817876i | ||||
\(206\) | −30.7253 | + | 8.23282i | −2.14073 | + | 0.573608i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00364 | + | 3.62893i | 0.346940 | + | 0.251621i | ||||
\(209\) | 5.29518i | 0.366275i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.46157 | − | 9.45972i | 0.375990 | − | 0.651234i | −0.614485 | − | 0.788929i | \(-0.710636\pi\) |
0.990475 | + | 0.137695i | \(0.0439694\pi\) | |||||||
\(212\) | 26.9410 | − | 15.5544i | 1.85032 | − | 1.06828i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.16919 | + | 8.09554i | −0.148283 | + | 0.553400i | ||||
\(215\) | −12.4136 | + | 46.3283i | −0.846602 | + | 3.15956i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3827 | − | 7.13678i | 0.704820 | − | 0.484476i | ||||
\(218\) | 25.7731 | + | 14.8801i | 1.74558 | + | 1.00781i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 32.2202 | 2.17229 | ||||||||
\(221\) | −3.94716 | + | 1.76137i | −0.265515 | + | 0.118483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.99267 | − | 14.9009i | −0.267369 | − | 0.997835i | −0.960784 | − | 0.277297i | \(-0.910561\pi\) |
0.693415 | − | 0.720538i | \(-0.256105\pi\) | |||||||
\(224\) | 8.34376 | − | 17.4960i | 0.557491 | − | 1.16900i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.89819 | + | 4.89819i | 0.325823 | + | 0.325823i | ||||
\(227\) | 18.6556 | + | 4.99875i | 1.23822 | + | 0.331779i | 0.817773 | − | 0.575541i | \(-0.195208\pi\) |
0.420442 | + | 0.907319i | \(0.361875\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6136 | + | 12.6136i | 0.833528 | + | 0.833528i | 0.987998 | − | 0.154470i | \(-0.0493669\pi\) |
−0.154470 | + | 0.987998i | \(0.549367\pi\) | |||||||
\(230\) | 43.3373 | − | 25.0208i | 2.85758 | − | 1.64982i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.36512 | + | 5.09470i | 0.0896245 | + | 0.334483i | ||||
\(233\) | − | 24.9418i | − | 1.63399i | −0.576643 | − | 0.816996i | \(-0.695638\pi\) | ||
0.576643 | − | 0.816996i | \(-0.304362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8827 | 1.16654 | ||||||||
\(236\) | −8.85197 | − | 33.0360i | −0.576214 | − | 2.15046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.94145 | + | 5.73405i | 0.255486 | + | 0.371683i | ||||
\(239\) | 4.67931 | + | 4.67931i | 0.302680 | + | 0.302680i | 0.842061 | − | 0.539382i | \(-0.181342\pi\) |
−0.539382 | + | 0.842061i | \(0.681342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.169033 | + | 0.630839i | −0.0108884 | + | 0.0406359i | −0.971156 | − | 0.238444i | \(-0.923363\pi\) |
0.960268 | + | 0.279080i | \(0.0900294\pi\) | |||||||
\(242\) | 5.77086 | − | 5.77086i | 0.370965 | − | 0.370965i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.39975 | + | 12.8167i | −0.473721 | + | 0.820508i | ||||
\(245\) | 27.1492 | − | 12.0918i | 1.73450 | − | 0.772516i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.53028 | − | 6.60821i | 0.160998 | − | 0.420470i | ||||
\(248\) | 8.48941i | 0.539078i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −64.7428 | − | 37.3793i | −4.09470 | − | 2.36407i | ||||
\(251\) | −9.89477 | − | 17.1382i | −0.624552 | − | 1.08176i | −0.988627 | − | 0.150386i | \(-0.951948\pi\) |
0.364075 | − | 0.931370i | \(-0.381385\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.75182 | + | 14.0020i | −0.235875 | + | 0.880298i | ||||
\(254\) | 14.1247 | + | 3.78471i | 0.886265 | + | 0.237474i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.70879 | + | 2.95971i | 0.106799 | + | 0.184982i | ||||
\(257\) | 7.97194 | − | 13.8078i | 0.497276 | − | 0.861307i | −0.502719 | − | 0.864450i | \(-0.667667\pi\) |
0.999995 | + | 0.00314245i | \(0.00100027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.832955 | + | 10.5750i | 0.0517573 | + | 0.657097i | ||||
\(260\) | −40.2098 | − | 15.3963i | −2.49371 | − | 0.954838i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.56555 | + | 20.7709i | 0.343841 | + | 1.28323i | ||||
\(263\) | 0.217727 | − | 0.377114i | 0.0134256 | − | 0.0232538i | −0.859235 | − | 0.511582i | \(-0.829060\pi\) |
0.872660 | + | 0.488328i | \(0.162393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.2052 | − | 33.2052i | 2.03978 | − | 2.03978i | ||||
\(266\) | −11.2004 | − | 2.07512i | −0.686739 | − | 0.127234i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.55576 | − | 8.55576i | 0.522626 | − | 0.522626i | ||||
\(269\) | −14.2630 | + | 8.23477i | −0.869633 | + | 0.502083i | −0.867226 | − | 0.497914i | \(-0.834099\pi\) |
−0.00240680 | + | 0.999997i | \(0.500766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4966 | + | 6.02794i | −1.36657 | + | 0.366171i | −0.866224 | − | 0.499655i | \(-0.833460\pi\) |
−0.500345 | + | 0.865826i | \(0.666793\pi\) | |||||||
\(272\) | 2.05512 | 0.124610 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7343 | −0.890133 | ||||||||
\(275\) | 33.9489 | − | 9.09658i | 2.04719 | − | 0.548544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.08167 | − | 4.08860i | 0.425496 | − | 0.245660i | −0.271930 | − | 0.962317i | \(-0.587662\pi\) |
0.697426 | + | 0.716657i | \(0.254329\pi\) | |||||||
\(278\) | −0.546031 | + | 0.546031i | −0.0327488 | + | 0.0327488i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.64819 | + | 19.6909i | −0.218021 | + | 1.17676i | ||||
\(281\) | −3.14177 | + | 3.14177i | −0.187422 | + | 0.187422i | −0.794581 | − | 0.607159i | \(-0.792309\pi\) |
0.607159 | + | 0.794581i | \(0.292309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.35147 | − | 11.0011i | 0.377555 | − | 0.653945i | −0.613151 | − | 0.789966i | \(-0.710098\pi\) |
0.990706 | + | 0.136021i | \(0.0434314\pi\) | |||||||
\(284\) | 2.25226 | + | 8.40554i | 0.133647 | + | 0.498777i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.4891 | − | 8.69675i | 1.15241 | − | 0.514250i | ||||
\(287\) | −1.14601 | − | 14.5495i | −0.0676469 | − | 0.858827i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.78144 | − | 13.4779i | 0.457732 | − | 0.792815i | ||||
\(290\) | 13.7783 | + | 23.8648i | 0.809092 | + | 1.40139i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.3811 | + | 4.92520i | 1.07567 | + | 0.288226i | ||||
\(293\) | 1.47718 | − | 5.51290i | 0.0862977 | − | 0.322067i | −0.909259 | − | 0.416231i | \(-0.863351\pi\) |
0.995557 | + | 0.0941633i | \(0.0300176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.8138 | − | 44.7109i | −1.50294 | − | 2.60317i | ||||
\(296\) | −6.19009 | − | 3.57385i | −0.359792 | − | 0.207726i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.8904i | 1.49979i | ||||||||
\(299\) | 11.3729 | − | 15.6812i | 0.657714 | − | 0.906870i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.1731 | − | 9.97867i | 1.62387 | − | 0.575161i | ||||
\(302\) | −19.0406 | + | 32.9793i | −1.09566 | + | 1.89774i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.37901 | + | 2.37901i | −0.136446 | + | 0.136446i | ||||
\(305\) | −5.78205 | + | 21.5789i | −0.331079 | + | 1.23560i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2283 | + | 10.2283i | 0.583760 | + | 0.583760i | 0.935934 | − | 0.352174i | \(-0.114558\pi\) |
−0.352174 | + | 0.935934i | \(0.614558\pi\) | |||||||
\(308\) | −11.3735 | − | 16.5462i | −0.648064 | − | 0.942808i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.4796 | + | 42.8424i | 0.651997 | + | 2.43328i | ||||
\(311\) | −14.6147 | −0.828724 | −0.414362 | − | 0.910112i | \(-0.635995\pi\) | ||||
−0.414362 | + | 0.910112i | \(0.635995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9984i | 1.01733i | 0.860965 | + | 0.508665i | \(0.169861\pi\) | ||||
−0.860965 | + | 0.508665i | \(0.830139\pi\) | |||||||
\(314\) | −2.50457 | − | 9.34720i | −0.141341 | − | 0.527493i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.84734 | + | 1.64392i | −0.160176 | + | 0.0924775i | ||||
\(317\) | 12.0835 | + | 12.0835i | 0.678674 | + | 0.678674i | 0.959700 | − | 0.281026i | \(-0.0906747\pi\) |
−0.281026 | + | 0.959700i | \(0.590675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.71056 | − | 2.06604i | −0.431708 | − | 0.115676i | ||||
\(320\) | 37.9588 | + | 37.9588i | 2.12196 | + | 2.12196i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.1468 | − | 13.4231i | −1.56856 | − | 0.748040i | ||||
\(323\) | −0.608923 | − | 2.27253i | −0.0338814 | − | 0.126447i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −46.7138 | − | 4.87009i | −2.59122 | − | 0.270144i | ||||
\(326\) | −1.38752 | −0.0768478 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.51656 | + | 4.91704i | 0.470248 | + | 0.271498i | ||||
\(329\) | −6.31246 | − | 9.18341i | −0.348017 | − | 0.506298i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.57122 | − | 9.59594i | 0.141327 | − | 0.527441i | −0.858564 | − | 0.512706i | \(-0.828643\pi\) |
0.999891 | − | 0.0147345i | \(-0.00469030\pi\) | |||||||
\(332\) | 3.33560 | − | 12.4486i | 0.183065 | − | 0.683208i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.2114 | − | 18.5973i | 1.76253 | − | 1.01760i | ||||
\(335\) | 9.13234 | − | 15.8177i | 0.498953 | − | 0.864212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.44780i | 0.351234i | 0.984459 | + | 0.175617i | \(0.0561920\pi\) | ||||
−0.984459 | + | 0.175617i | \(0.943808\pi\) | |||||||
\(338\) | −28.4774 | + | 1.54049i | −1.54897 | + | 0.0837915i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.8280 | + | 3.70519i | −0.749926 | + | 0.200942i | ||||
\(341\) | −11.1269 | − | 6.42414i | −0.602558 | − | 0.347887i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7930 | − | 9.67375i | −0.852741 | − | 0.522334i | ||||
\(344\) | −5.21241 | + | 19.4530i | −0.281034 | + | 1.04883i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2921 | − | 14.2921i | −0.768349 | − | 0.768349i | ||||
\(347\) | −6.00501 | − | 10.4010i | −0.322366 | − | 0.558354i | 0.658610 | − | 0.752484i | \(-0.271145\pi\) |
−0.980976 | + | 0.194131i | \(0.937811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5954 | − | 6.59031i | 1.31656 | − | 0.352771i | 0.468872 | − | 0.883266i | \(-0.344661\pi\) |
0.847688 | + | 0.530495i | \(0.177994\pi\) | |||||||
\(350\) | 5.93692 | + | 75.3736i | 0.317342 | + | 4.02889i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.7673 | −1.05360 | ||||||||
\(353\) | −2.43053 | − | 9.07084i | −0.129364 | − | 0.482792i | 0.870594 | − | 0.492003i | \(-0.163735\pi\) |
−0.999958 | + | 0.00921021i | \(0.997068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.56796 | + | 11.3760i | 0.348591 | + | 0.603777i | ||||
\(356\) | −9.88750 | + | 9.88750i | −0.524036 | + | 0.524036i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.76551 | − | 1.54486i | −0.304716 | − | 0.0816485i | ||||
\(359\) | 16.2790 | − | 16.2790i | 0.859171 | − | 0.859171i | −0.132070 | − | 0.991240i | \(-0.542162\pi\) |
0.991240 | + | 0.132070i | \(0.0421622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1189 | − | 7.57420i | −0.690469 | − | 0.398642i | ||||
\(362\) | −32.7442 | + | 8.77379i | −1.72100 | + | 0.461140i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.28718 | + | 26.0839i | 0.329538 | + | 1.36717i | ||||
\(365\) | 28.7254 | 1.50356 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6200 | + | 11.3276i | 1.02416 | + | 0.591297i | 0.915305 | − | 0.402761i | \(-0.131949\pi\) |
0.108851 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(368\) | −7.97642 | + | 4.60519i | −0.415799 | + | 0.240062i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −36.0714 | − | 9.66529i | −1.87526 | − | 0.502475i | ||||
\(371\) | −28.7732 | − | 5.33088i | −1.49383 | − | 0.276766i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0535 | + | 19.1453i | 0.572330 | + | 0.991305i | 0.996326 | + | 0.0856409i | \(0.0272938\pi\) |
−0.423996 | + | 0.905664i | \(0.639373\pi\) | |||||||
\(374\) | 3.54787 | − | 6.14510i | 0.183456 | − | 0.317755i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.50885 | 0.387240 | ||||||||
\(377\) | 8.63527 | + | 6.26280i | 0.444739 | + | 0.322551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03041 | + | 0.276097i | −0.0529284 | + | 0.0141821i | −0.285186 | − | 0.958472i | \(-0.592055\pi\) |
0.232258 | + | 0.972654i | \(0.425389\pi\) | |||||||
\(380\) | 11.7181 | − | 20.2964i | 0.601128 | − | 1.04118i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.08092 | − | 5.08092i | −0.259962 | − | 0.259962i | ||||
\(383\) | −12.0580 | − | 3.23092i | −0.616133 | − | 0.165092i | −0.0627635 | − | 0.998028i | \(-0.519991\pi\) |
−0.553369 | + | 0.832936i | \(0.686658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.0479 | − | 19.6822i | −1.17463 | − | 1.00310i | ||||
\(386\) | −23.0739 | − | 39.9652i | −1.17443 | − | 2.03417i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −41.4818 | + | 11.1150i | −2.10592 | + | 0.564279i | ||||
\(389\) | − | 19.0137i | − | 0.964031i | −0.876163 | − | 0.482015i | \(-0.839905\pi\) | ||
0.876163 | − | 0.482015i | \(-0.160095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.44068i | − | 0.325719i | ||||||
\(392\) | 11.3998 | − | 5.07727i | 0.575775 | − | 0.256441i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.7231 | + | 22.9341i | −2.00122 | + | 1.15541i | ||||
\(395\) | −3.50940 | + | 3.50940i | −0.176577 | + | 0.176577i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.702815 | + | 2.62294i | −0.0352733 | + | 0.131642i | −0.981317 | − | 0.192397i | \(-0.938374\pi\) |
0.946044 | + | 0.324038i | \(0.105041\pi\) | |||||||
\(398\) | −38.6830 | − | 38.6830i | −1.93900 | − | 1.93900i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.3394 | + | 11.1656i | 0.966970 | + | 0.558281i | ||||
\(401\) | −0.821135 | − | 3.06452i | −0.0410055 | − | 0.153035i | 0.942388 | − | 0.334523i | \(-0.108575\pi\) |
−0.983393 | + | 0.181488i | \(0.941909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8163 | + | 13.3341i | 0.538799 | + | 0.664218i | ||||
\(404\) | − | 4.51759i | − | 0.224759i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.39177 | − | 15.4997i | 0.366847 | − | 0.769239i | ||||
\(407\) | 9.36838 | − | 5.40884i | 0.464373 | − | 0.268106i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.97815 | − | 0.797992i | −0.147260 | − | 0.0394582i | 0.184436 | − | 0.982845i | \(-0.440954\pi\) |
−0.331696 | + | 0.943386i | \(0.607621\pi\) | |||||||
\(410\) | 49.6284 | + | 13.2979i | 2.45097 | + | 0.656735i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −35.3188 | + | 20.3913i | −1.74003 | + | 1.00461i | ||||
\(413\) | −13.8485 | + | 29.0389i | −0.681442 | + | 1.42891i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 19.4543i | − | 0.954976i | ||||||
\(416\) | 24.6690 | + | 9.44572i | 1.20950 | + | 0.463115i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.00655 | + | 11.2206i | 0.147055 | + | 0.548818i | ||||
\(419\) | 29.0623 | + | 16.7791i | 1.41979 | + | 0.819715i | 0.996280 | − | 0.0861779i | \(-0.0274653\pi\) |
0.423508 | + | 0.905893i | \(0.360799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2634 | + | 18.2634i | 0.890104 | + | 0.890104i | 0.994532 | − | 0.104429i | \(-0.0333014\pi\) |
−0.104429 | + | 0.994532i | \(0.533301\pi\) | |||||||
\(422\) | 6.20205 | − | 23.1464i | 0.301911 | − | 1.12675i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.9427 | − | 13.9427i | 0.677116 | − | 0.677116i | ||||
\(425\) | −13.5238 | + | 7.80795i | −0.655999 | + | 0.378741i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1225 | − | 4.64789i | 0.635044 | − | 0.224927i | ||||
\(428\) | 10.7455i | 0.519402i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 105.219i | 5.07411i | ||||||||
\(431\) | 16.9380 | − | 4.53851i | 0.815873 | − | 0.218612i | 0.173331 | − | 0.984864i | \(-0.444547\pi\) |
0.642541 | + | 0.766251i | \(0.277880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6656 | − | 30.5978i | −0.848957 | − | 1.47044i | −0.882140 | − | 0.470987i | \(-0.843898\pi\) |
0.0331835 | − | 0.999449i | \(-0.489435\pi\) | |||||||
\(434\) | 17.9489 | − | 21.0182i | 0.861574 | − | 1.00890i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36.8556 | + | 9.87543i | 1.76506 | + | 0.472947i | ||||
\(437\) | 7.45575 | + | 7.45575i | 0.356657 | + | 0.356657i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.35887 | + | 16.2100i | −0.446674 | + | 0.773663i | −0.998167 | − | 0.0605168i | \(-0.980725\pi\) |
0.551493 | + | 0.834180i | \(0.314058\pi\) | |||||||
\(440\) | 19.7265 | − | 5.28570i | 0.940425 | − | 0.251986i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.36404 | + | 5.97354i | −0.350272 | + | 0.284133i | ||||
\(443\) | −30.4948 | −1.44885 | −0.724426 | − | 0.689353i | \(-0.757895\pi\) | ||||
−0.724426 | + | 0.689353i | \(0.757895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5538 | + | 18.2798i | −0.500299 | + | 0.866544i | ||||
\(446\) | −16.9211 | − | 29.3083i | −0.801239 | − | 1.38779i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.09404 | − | 32.8924i | 0.287917 | − | 1.55402i | ||||
\(449\) | 19.0888 | + | 5.11484i | 0.900859 | + | 0.241384i | 0.679385 | − | 0.733782i | \(-0.262247\pi\) |
0.221474 | + | 0.975166i | \(0.428913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8894 | + | 7.44168i | −0.606937 | + | 0.350415i | ||||
\(452\) | 7.69138 | + | 4.44062i | 0.361772 | + | 0.208869i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 42.3699 | 1.98852 | ||||||||
\(455\) | 19.3580 | + | 35.5761i | 0.907517 | + | 1.66784i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.87442 | − | 2.10994i | 0.368350 | − | 0.0986990i | −0.0698958 | − | 0.997554i | \(-0.522267\pi\) |
0.438246 | + | 0.898855i | \(0.355600\pi\) | |||||||
\(458\) | 33.8903 | + | 19.5666i | 1.58359 | + | 0.914286i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 45.3669 | − | 45.3669i | 2.11524 | − | 2.11524i | ||||
\(461\) | −32.2015 | − | 8.62836i | −1.49977 | − | 0.401863i | −0.586748 | − | 0.809769i | \(-0.699592\pi\) |
−0.913024 | + | 0.407907i | \(0.866259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.66118 | − | 1.66118i | 0.0772018 | − | 0.0772018i | −0.667452 | − | 0.744653i | \(-0.732615\pi\) |
0.744653 | + | 0.667452i | \(0.232615\pi\) | |||||||
\(464\) | −2.53596 | − | 4.39242i | −0.117729 | − | 0.203913i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.1617 | − | 52.8523i | −0.656029 | − | 2.44833i | ||||
\(467\) | 12.2930 | 0.568854 | 0.284427 | − | 0.958698i | \(-0.408197\pi\) | ||||
0.284427 | + | 0.958698i | \(0.408197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3466 | + | 0.893731i | −0.523936 | + | 0.0412687i | ||||
\(470\) | 37.8939 | − | 10.1537i | 1.74792 | − | 0.468353i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.8391 | − | 18.7738i | −0.498908 | − | 0.864135i | ||||
\(473\) | −21.5523 | − | 21.5523i | −0.990978 | − | 0.990978i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.61664 | − | 24.6937i | 0.303592 | − | 1.13302i | ||||
\(476\) | 6.78390 | + | 5.79324i | 0.310939 | + | 0.265533i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.5724 | + | 7.25871i | 0.575050 | + | 0.332005i | ||||
\(479\) | −22.8035 | + | 6.11018i | −1.04192 | + | 0.279181i | −0.738908 | − | 0.673806i | \(-0.764658\pi\) |
−0.303010 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.2760 | + | 2.27341i | −0.650930 | + | 0.103659i | ||||
\(482\) | 1.43274i | 0.0652594i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.23177 | − | 9.06169i | 0.237808 | − | 0.411895i | ||||
\(485\) | −56.1413 | + | 32.4132i | −2.54925 | + | 1.47181i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.73616 | + | 10.2115i | −0.123987 | + | 0.462726i | −0.999802 | − | 0.0199217i | \(-0.993658\pi\) |
0.875814 | + | 0.482648i | \(0.160325\pi\) | |||||||
\(488\) | −2.42785 | + | 9.06085i | −0.109903 | + | 0.410165i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 50.6641 | − | 41.0378i | 2.28877 | − | 1.85390i | ||||
\(491\) | −9.46863 | − | 5.46672i | −0.427313 | − | 0.246710i | 0.270888 | − | 0.962611i | \(-0.412683\pi\) |
−0.698201 | + | 0.715901i | \(0.746016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.54672 | 0.159736 | ||||||||
\(494\) | 1.60964 | − | 15.4396i | 0.0724210 | − | 0.694661i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.11287 | − | 7.88533i | −0.0948705 | − | 0.354062i | ||||
\(497\) | 3.52356 | − | 7.38852i | 0.158053 | − | 0.331420i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1483 | − | 21.1483i | −0.946727 | − | 0.946727i | 0.0519238 | − | 0.998651i | \(-0.483465\pi\) |
−0.998651 | + | 0.0519238i | \(0.983465\pi\) | |||||||
\(500\) | −92.5823 | − | 24.8073i | −4.14041 | − | 1.10942i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.6982 | − | 30.6982i | −1.37013 | − | 1.37013i | ||||
\(503\) | 6.00891 | − | 3.46924i | 0.267924 | − | 0.154686i | −0.360020 | − | 0.932945i | \(-0.617230\pi\) |
0.627944 | + | 0.778259i | \(0.283897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.76499 | − | 6.58703i | −0.0785409 | − | 0.293119i | ||||
\(506\) | 31.8008i | 1.41372i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.7482 | 0.831817 | ||||||||
\(509\) | 2.48325 | + | 9.26762i | 0.110068 | + | 0.410780i | 0.998871 | − | 0.0475103i | \(-0.0151287\pi\) |
−0.888803 | + | 0.458290i | \(0.848462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1398 | − | 14.7515i | −0.448560 | − | 0.652568i | ||||
\(512\) | −13.2032 | − | 13.2032i | −0.583504 | − | 0.583504i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.05279 | − | 33.7855i | 0.399301 | − | 1.49021i | ||||
\(515\) | −43.5310 | + | 43.5310i | −1.91821 | + | 1.91821i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.68213 | + | 9.84174i | −0.249900 | + | 0.432839i | ||||
\(518\) | 7.76942 | + | 21.9357i | 0.341369 | + | 0.963798i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −27.1438 | − | 2.82984i | −1.19033 | − | 0.124097i | ||||
\(521\) | − | 17.8193i | − | 0.780676i | −0.920672 | − | 0.390338i | \(-0.872358\pi\) | ||
0.920672 | − | 0.390338i | \(-0.127642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.40070 | + | 3.69545i | 0.279883 | + | 0.161591i | 0.633370 | − | 0.773849i | \(-0.281671\pi\) |
−0.353487 | + | 0.935439i | \(0.615004\pi\) | |||||||
\(524\) | 13.7849 | + | 23.8762i | 0.602198 | + | 1.04304i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.247246 | − | 0.922736i | 0.0107805 | − | 0.0402332i | ||||
\(527\) | 5.51410 | + | 1.47750i | 0.240198 | + | 0.0643608i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.93251 | + | 5.07925i | 0.127500 | + | 0.220837i | ||||
\(530\) | 51.5090 | − | 89.2163i | 2.23741 | − | 3.87531i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.5593 | + | 1.14679i | −0.631227 | + | 0.0497196i | ||||
\(533\) | 19.6415 | − | 3.12785i | 0.850767 | − | 0.135482i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.19817 | + | 15.6678i | 0.181503 | + | 0.677377i | ||||
\(536\) | 3.83461 | − | 6.64175i | 0.165630 | − | 0.286880i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.5481 | + | 25.5481i | −1.10146 | + | 1.10146i | ||||
\(539\) | −1.97179 | + | 18.7836i | −0.0849308 | + | 0.809067i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3442 | + | 17.3442i | −0.745687 | + | 0.745687i | −0.973666 | − | 0.227979i | \(-0.926788\pi\) |
0.227979 | + | 0.973666i | \(0.426788\pi\) | |||||||
\(542\) | −44.2481 | + | 25.5467i | −1.90062 | + | 1.09732i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.48354 | − | 2.27316i | 0.363729 | − | 0.0974608i | ||||
\(545\) | 57.5968 | 2.46718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8037 | 1.14604 | 0.573022 | − | 0.819540i | \(-0.305771\pi\) | ||||
0.573022 | + | 0.819540i | \(0.305771\pi\) | |||||||
\(548\) | −18.2472 | + | 4.88933i | −0.779483 | + | 0.208862i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 66.7735 | − | 38.5517i | 2.84723 | − | 1.64385i | ||||
\(551\) | −4.10570 | + | 4.10570i | −0.174909 | + | 0.174909i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.04099 | + | 0.563411i | 0.129316 | + | 0.0239587i | ||||
\(554\) | 12.6847 | − | 12.6847i | 0.538923 | − | 0.538923i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.495023 | + | 0.857405i | −0.0209936 | + | 0.0363621i | ||||
\(557\) | 3.42508 | + | 12.7826i | 0.145125 | + | 0.541615i | 0.999750 | + | 0.0223686i | \(0.00712072\pi\) |
−0.854624 | + | 0.519247i | \(0.826213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5979 | + | 37.1953i | 0.702017 | + | 1.57319i | ||||
\(560\) | −1.51214 | − | 19.1978i | −0.0638997 | − | 0.811254i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.87361 | + | 8.44134i | −0.205581 | + | 0.356077i | ||||
\(563\) | 8.52959 | + | 14.7737i | 0.359479 | + | 0.622636i | 0.987874 | − | 0.155258i | \(-0.0496210\pi\) |
−0.628395 | + | 0.777895i | \(0.716288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9496 | + | 3.46983i | 0.544793 | + | 0.145977i | ||||
\(566\) | 7.21260 | − | 26.9178i | 0.303168 | − | 1.13144i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.75784 | + | 4.77673i | 0.115717 | + | 0.200427i | ||||
\(569\) | 26.6276 | + | 15.3735i | 1.11629 | + | 0.644489i | 0.940450 | − | 0.339931i | \(-0.110404\pi\) |
0.175837 | + | 0.984419i | \(0.443737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.14822i | − | 0.173598i | −0.996226 | − | 0.0867988i | \(-0.972336\pi\) | ||
0.996226 | − | 0.0867988i | \(-0.0276637\pi\) | |||||||
\(572\) | 21.2497 | − | 17.2373i | 0.888496 | − | 0.720728i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.6895 | − | 30.1799i | −0.446170 | − | 1.25969i | ||||
\(575\) | 34.9927 | − | 60.6091i | 1.45930 | − | 2.52757i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.22860 | − | 8.22860i | 0.342561 | − | 0.342561i | −0.514768 | − | 0.857329i | \(-0.672122\pi\) |
0.857329 | + | 0.514768i | \(0.172122\pi\) | |||||||
\(578\) | 8.83646 | − | 32.9781i | 0.367548 | − | 1.37171i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.9824 | + | 24.9824i | 1.03734 | + | 1.03734i | ||||
\(581\) | −9.99049 | + | 6.86722i | −0.414475 | + | 0.284900i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.72369 | + | 28.8252i | 0.319883 | + | 1.19382i | ||||
\(584\) | 12.0616 | 0.499113 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 12.5207i | − | 0.517225i | ||||||
\(587\) | −2.86420 | − | 10.6893i | −0.118218 | − | 0.441196i | 0.881289 | − | 0.472577i | \(-0.156676\pi\) |
−0.999508 | + | 0.0313808i | \(0.990010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.09348 | + | 4.67278i | −0.333486 | + | 0.192538i | ||||
\(590\) | −80.0865 | − | 80.0865i | −3.29711 | − | 3.29711i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.63909 | + | 1.77894i | 0.272865 | + | 0.0731139i | ||||
\(593\) | 9.97769 | + | 9.97769i | 0.409734 | + | 0.409734i | 0.881646 | − | 0.471911i | \(-0.156436\pi\) |
−0.471911 | + | 0.881646i | \(0.656436\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.1549 | + | 5.79661i | 0.498301 | + | 0.237638i | ||||
\(596\) | 8.59127 | + | 32.0631i | 0.351912 | + | 1.31335i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.1959 | − | 39.6864i | 0.621406 | − | 1.62290i | ||||
\(599\) | −34.7079 | −1.41813 | −0.709063 | − | 0.705145i | \(-0.750882\pi\) | ||||
−0.709063 | + | 0.705145i | \(0.750882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2636 | − | 6.50302i | −0.459450 | − | 0.265264i | 0.252363 | − | 0.967633i | \(-0.418792\pi\) |
−0.711813 | + | 0.702369i | \(0.752126\pi\) | |||||||
\(602\) | 54.0337 | − | 37.1414i | 2.20225 | − | 1.51377i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.6366 | + | 47.1604i | −0.514175 | + | 1.91893i | ||||
\(605\) | 4.08802 | − | 15.2567i | 0.166202 | − | 0.620273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9672 | − | 10.9507i | 0.769856 | − | 0.444477i | −0.0629670 | − | 0.998016i | \(-0.520056\pi\) |
0.832823 | + | 0.553539i | \(0.186723\pi\) | |||||||
\(608\) | −7.18915 | + | 12.4520i | −0.291559 | + | 0.504994i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 49.0092i | 1.98432i | ||||||||
\(611\) | 11.7939 | − | 9.56698i | 0.477132 | − | 0.387039i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3087 | + | 2.76221i | −0.416365 | + | 0.111565i | −0.460919 | − | 0.887442i | \(-0.652480\pi\) |
0.0445537 | + | 0.999007i | \(0.485813\pi\) | |||||||
\(614\) | 27.4815 | + | 15.8665i | 1.10906 | + | 0.640319i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.67769 | − | 8.26445i | −0.389925 | − | 0.332984i | ||||
\(617\) | −5.78797 | + | 21.6010i | −0.233015 | + | 0.869624i | 0.746019 | + | 0.665925i | \(0.231963\pi\) |
−0.979034 | + | 0.203699i | \(0.934704\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50453 | + | 5.50453i | 0.221246 | + | 0.221246i | 0.809023 | − | 0.587777i | \(-0.199997\pi\) |
−0.587777 | + | 0.809023i | \(0.699997\pi\) | |||||||
\(620\) | 28.4330 | + | 49.2474i | 1.14190 | + | 1.97782i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.9689 | + | 8.29810i | −1.24174 | + | 0.332723i | ||||
\(623\) | 13.1127 | − | 1.03284i | 0.525349 | − | 0.0413800i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −79.5531 | −3.18213 | ||||||||
\(626\) | 10.2193 | + | 38.1390i | 0.408446 | + | 1.52434i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.20341 | − | 10.7446i | −0.247543 | − | 0.428757i | ||||
\(629\) | −3.39863 | + | 3.39863i | −0.135512 | + | 0.135512i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7278 | − | 5.55399i | −0.825160 | − | 0.221101i | −0.178559 | − | 0.983929i | \(-0.557143\pi\) |
−0.646601 | + | 0.762828i | \(0.723810\pi\) | |||||||
\(632\) | −1.47358 | + | 1.47358i | −0.0586157 | + | 0.0586157i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.4660 | + | 18.7442i | 1.28939 | + | 0.744429i | ||||
\(635\) | 27.3364 | − | 7.32477i | 1.08481 | − | 0.290675i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.4364 | − | 22.4991i | 0.453126 | − | 0.891447i | ||||
\(638\) | −17.5119 | −0.693304 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.1116 | + | 27.7772i | 1.90178 | + | 1.09799i | ||||
\(641\) | 40.6530 | − | 23.4710i | 1.60570 | − | 0.927050i | 0.615379 | − | 0.788231i | \(-0.289003\pi\) |
0.990318 | − | 0.138818i | \(-0.0443304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.4152 | − | 6.00613i | −0.883968 | − | 0.236859i | −0.211850 | − | 0.977302i | \(-0.567949\pi\) |
−0.672118 | + | 0.740444i | \(0.734615\pi\) | |||||||
\(644\) | −39.3116 | − | 7.28336i | −1.54910 | − | 0.287005i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.58064 | − | 4.46981i | −0.101534 | − | 0.175862i | ||||
\(647\) | −6.98028 | + | 12.0902i | −0.274423 | + | 0.475315i | −0.969989 | − | 0.243147i | \(-0.921820\pi\) |
0.695566 | + | 0.718462i | \(0.255154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.8087 | 1.28786 | ||||||||
\(650\) | −101.753 | + | 16.2038i | −3.99108 | + | 0.635567i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.71833 | + | 0.460426i | −0.0672951 | + | 0.0180317i | ||||
\(653\) | 13.4921 | − | 23.3689i | 0.527985 | − | 0.914497i | −0.471483 | − | 0.881875i | \(-0.656281\pi\) |
0.999468 | − | 0.0326216i | \(-0.0103856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.4278 | + | 29.4278i | 1.14984 | + | 1.14984i | ||||
\(656\) | −9.13431 | − | 2.44753i | −0.356635 | − | 0.0955601i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.5905 | − | 15.8757i | −0.724733 | − | 0.618900i | ||||
\(659\) | −2.76889 | − | 4.79586i | −0.107861 | − | 0.186820i | 0.807043 | − | 0.590493i | \(-0.201067\pi\) |
−0.914903 | + | 0.403673i | \(0.867733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.8331 | + | 9.86941i | −1.43264 | + | 0.383875i | −0.889951 | − | 0.456057i | \(-0.849261\pi\) |
−0.542692 | + | 0.839932i | \(0.682595\pi\) | |||||||
\(662\) | − | 21.7939i | − | 0.847046i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.16876i | − | 0.317009i | ||||||
\(665\) | −20.7807 | + | 7.36032i | −0.805839 | + | 0.285421i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7657 | + | 7.94763i | −0.533010 | + | 0.307733i | ||||
\(668\) | 33.7200 | − | 33.7200i | 1.30466 | − | 1.30466i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.3705 | − | 38.7033i | 0.400648 | − | 1.49524i | ||||
\(671\) | −10.0387 | − | 10.0387i | −0.387540 | − | 0.387540i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.72219 | + | 3.30371i | 0.220574 | + | 0.127349i | 0.606216 | − | 0.795300i | \(-0.292687\pi\) |
−0.385642 | + | 0.922649i | \(0.626020\pi\) | |||||||
\(674\) | 3.66100 | + | 13.6630i | 0.141016 | + | 0.526281i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.7557 | + | 11.3575i | −1.33676 | + | 0.436827i | ||||
\(677\) | 21.3320i | 0.819855i | 0.912118 | + | 0.409928i | \(0.134446\pi\) | ||||
−0.912118 | + | 0.409928i | \(0.865554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.4627 | + | 17.3889i | 1.39931 | + | 0.667326i | ||||
\(680\) | −7.85819 | + | 4.53693i | −0.301348 | + | 0.173983i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.2258 | − | 7.29513i | −1.04253 | − | 0.279345i | ||||
\(683\) | 1.32430 | + | 0.354846i | 0.0506730 | + | 0.0135778i | 0.284067 | − | 0.958805i | \(-0.408316\pi\) |
−0.233393 | + | 0.972382i | \(0.574983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.6958 | + | 14.2581i | −0.943576 | + | 0.544774i | ||||
\(686\) | −38.9584 | − | 11.5318i | −1.48744 | − | 0.440286i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 19.3660i | − | 0.738323i | ||||||
\(689\) | 4.13508 | − | 39.6636i | 0.157534 | − | 1.51106i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.87327 | − | 33.1155i | −0.337555 | − | 1.25977i | −0.901072 | − | 0.433669i | \(-0.857219\pi\) |
0.563517 | − | 0.826104i | \(-0.309448\pi\) | |||||||
\(692\) | −22.4422 | − | 12.9570i | −0.853124 | − | 0.492551i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6303 | − | 18.6303i | −0.707197 | − | 0.707197i | ||||
\(695\) | −0.386803 | + | 1.44357i | −0.0146723 | + | 0.0547577i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.67597 | − | 4.67597i | 0.177115 | − | 0.177115i | ||||
\(698\) | 48.3762 | − | 27.9300i | 1.83107 | − | 1.05717i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 32.3638 | + | 91.3738i | 1.22324 | + | 3.45361i | ||||
\(701\) | 42.5906i | 1.60862i | 0.594208 | + | 0.804312i | \(0.297466\pi\) | ||||
−0.594208 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.86853i | − | 0.296767i | ||||||
\(704\) | −32.9518 | + | 8.82940i | −1.24192 | + | 0.332771i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.3007 | − | 17.8413i | −0.387671 | − | 0.671466i | ||||
\(707\) | −2.75964 | + | 3.23155i | −0.103787 | + | 0.121535i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3239 | + | 10.0009i | 1.40173 | + | 0.375592i | 0.878965 | − | 0.476886i | \(-0.158234\pi\) |
0.522764 | + | 0.852478i | \(0.324901\pi\) | |||||||
\(710\) | 20.3769 | + | 20.3769i | 0.764730 | + | 0.764730i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.43148 | + | 7.67556i | −0.166077 | + | 0.287654i | ||||
\(713\) | −24.7124 | + | 6.62166i | −0.925486 | + | 0.247983i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.2494 | − | 33.4355i | 0.906876 | − | 1.25042i | ||||
\(716\) | −7.65273 | −0.285996 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.2525 | − | 43.7385i | 0.942413 | − | 1.63231i | ||||
\(719\) | 25.0297 | + | 43.3527i | 0.933450 | + | 1.61678i | 0.777375 | + | 0.629038i | \(0.216551\pi\) |
0.156076 | + | 0.987745i | \(0.450116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.7208 | + | 6.98862i | 1.40480 | + | 0.260270i | ||||
\(722\) | −32.0998 | − | 8.60112i | −1.19463 | − | 0.320101i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −37.6396 | + | 21.7312i | −1.39886 | + | 0.807634i | ||||
\(725\) | 33.3759 | + | 19.2696i | 1.23955 | + | 0.715655i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.22923 | −0.193941 | −0.0969707 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969707 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(728\) | 8.12831 | + | 14.9382i | 0.301255 | + | 0.553647i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 60.8698 | − | 16.3100i | 2.25289 | − | 0.603661i | ||||
\(731\) | 11.7280 | + | 6.77119i | 0.433777 | + | 0.250442i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0406 | − | 10.0406i | 0.370858 | − | 0.370858i | −0.496932 | − | 0.867790i | \(-0.665540\pi\) |
0.867790 | + | 0.496932i | \(0.165540\pi\) | |||||||
\(734\) | 48.0070 | + | 12.8634i | 1.77197 | + | 0.474798i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.8329 | + | 27.8329i | −1.02593 | + | 1.02593i | ||||
\(737\) | 5.80349 | + | 10.0519i | 0.213774 | + | 0.370268i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.48318 | − | 5.53532i | −0.0545598 | − | 0.203620i | 0.933265 | − | 0.359187i | \(-0.116946\pi\) |
−0.987825 | + | 0.155567i | \(0.950279\pi\) | |||||||
\(740\) | −47.8786 | −1.76005 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −63.9979 | + | 5.04090i | −2.34944 | + | 0.185057i | ||||
\(743\) | −0.617584 | + | 0.165481i | −0.0226569 | + | 0.00607091i | −0.270130 | − | 0.962824i | \(-0.587067\pi\) |
0.247473 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0536 | + | 43.3941i | 0.917892 | + | 1.58984i | ||||
\(746\) | 34.2932 | + | 34.2932i | 1.25556 | + | 1.25556i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.35460 | − | 8.78749i | 0.0860928 | − | 0.321303i | ||||
\(749\) | 6.56404 | − | 7.68650i | 0.239845 | − | 0.280859i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0888 | − | 12.7530i | −0.806031 | − | 0.465362i | 0.0395448 | − | 0.999218i | \(-0.487409\pi\) |
−0.845576 | + | 0.533856i | \(0.820743\pi\) | |||||||
\(752\) | −6.97454 | + | 1.86882i | −0.254335 | + | 0.0681490i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.8543 | + | 8.36799i | 0.795887 | + | 0.304744i | ||||
\(755\) | 73.7008i | 2.68225i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.06785 | − | 13.9739i | 0.293231 | − | 0.507891i | −0.681341 | − | 0.731966i | \(-0.738603\pi\) |
0.974572 | + | 0.224075i | \(0.0719362\pi\) | |||||||
\(758\) | −2.02669 | + | 1.17011i | −0.0736127 | + | 0.0425003i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.84470 | − | 14.3486i | 0.139462 | − | 0.520479i | ||||
\(761\) | −6.42639 | + | 23.9836i | −0.232957 | + | 0.869406i | 0.746103 | + | 0.665831i | \(0.231923\pi\) |
−0.979059 | + | 0.203575i | \(0.934744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.3312 | − | 29.5780i | −0.736038 | − | 1.07079i | ||||
\(764\) | −7.97831 | − | 4.60628i | −0.288645 | − | 0.166649i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.3856 | −0.989481 | ||||||||
\(767\) | −40.9442 | − | 15.6775i | −1.47841 | − | 0.566082i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.09729 | + | 11.5592i | 0.111691 | + | 0.416837i | 0.999018 | − | 0.0443040i | \(-0.0141070\pi\) |
−0.887327 | + | 0.461141i | \(0.847440\pi\) | |||||||
\(770\) | −60.0145 | − | 28.6207i | −2.16277 | − | 1.03142i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41.8368 | − | 41.8368i | −1.50574 | − | 1.50574i | ||||
\(773\) | 1.00730 | + | 0.269904i | 0.0362299 | + | 0.00970777i | 0.276888 | − | 0.960902i | \(-0.410697\pi\) |
−0.240659 | + | 0.970610i | \(0.577363\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.8623 | + | 43.8623i | 1.57558 | + | 1.57558i | ||||
\(776\) | −23.5734 | + | 13.6101i | −0.846235 | + | 0.488574i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.7958 | − | 40.2904i | −0.387047 | − | 1.44448i | ||||
\(779\) | 10.8258i | 0.387875i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.34771 | −0.298704 | ||||||||
\(782\) | −3.65696 | − | 13.6480i | −0.130773 | − | 0.488050i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.32495 | + | 7.55319i | −0.333034 | + | 0.269757i | ||||
\(785\) | −13.2429 | − | 13.2429i | −0.472660 | − | 0.472660i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4106 | + | 46.3169i | −0.442389 | + | 1.65102i | 0.280349 | + | 0.959898i | \(0.409550\pi\) |
−0.722738 | + | 0.691122i | \(0.757117\pi\) | |||||||
\(788\) | −41.5834 | + | 41.5834i | −1.48135 | + | 1.48135i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.44390 | + | 9.42910i | −0.193685 | + | 0.335472i | ||||
\(791\) | −2.78921 | − | 7.87488i | −0.0991730 | − | 0.279999i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.73102 | + | 17.3249i | 0.274537 | + | 0.615226i | ||||
\(794\) | 5.95712i | 0.211410i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −60.7420 | − | 35.0694i | −2.15294 | − | 1.24300i | ||||
\(797\) | −22.8940 | − | 39.6535i | −0.810946 | − | 1.40460i | −0.912203 | − | 0.409739i | \(-0.865620\pi\) |
0.101257 | − | 0.994860i | \(-0.467713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.30684 | − | 4.87720i | 0.0462327 | − | 0.172543i | ||||
\(800\) | 92.1834 | + | 24.7005i | 3.25917 | + | 0.873293i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.48001 | − | 6.02755i | −0.122883 | − | 0.212840i | ||||
\(803\) | −9.12732 | + | 15.8090i | −0.322096 | + | 0.557887i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60.1652 | + | 4.73901i | −2.12054 | + | 0.167028i | ||||
\(806\) | 30.4910 | + | 22.1138i | 1.07400 | + | 0.778926i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.741108 | − | 2.76585i | −0.0260721 | − | 0.0973023i | ||||
\(809\) | 14.8591 | − | 25.7367i | 0.522418 | − | 0.904855i | −0.477241 | − | 0.878772i | \(-0.658363\pi\) |
0.999660 | − | 0.0260831i | \(-0.00830344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.3752 | + | 34.3752i | −1.20708 | + | 1.20708i | −0.235107 | + | 0.971970i | \(0.575544\pi\) |
−0.971970 | + | 0.235107i | \(0.924456\pi\) | |||||||
\(812\) | 4.01077 | − | 21.6480i | 0.140750 | − | 0.759694i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.7807 | − | 16.7807i | 0.588164 | − | 0.588164i | ||||
\(815\) | −2.32559 | + | 1.34268i | −0.0814617 | + | 0.0470319i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.4148 | + | 5.73807i | −0.749207 | + | 0.200750i | ||||
\(818\) | −6.76385 | −0.236493 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 65.8733 | 2.30039 | ||||||||
\(821\) | 30.4555 | − | 8.16053i | 1.06291 | − | 0.284805i | 0.315330 | − | 0.948982i | \(-0.397885\pi\) |
0.747575 | + | 0.664177i | \(0.231218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.78884 | + | 1.03279i | −0.0623550 | + | 0.0360007i | −0.530853 | − | 0.847464i | \(-0.678129\pi\) |
0.468498 | + | 0.883464i | \(0.344795\pi\) | |||||||
\(824\) | −18.2784 | + | 18.2784i | −0.636758 | + | 0.636758i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.8574 | + | 69.3971i | −0.447365 | + | 2.41463i | ||||
\(827\) | −15.5395 | + | 15.5395i | −0.540360 | + | 0.540360i | −0.923634 | − | 0.383275i | \(-0.874796\pi\) |
0.383275 | + | 0.923634i | \(0.374796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.58600 | + | 13.1393i | −0.263473 | + | 0.456348i | −0.967162 | − | 0.254159i | \(-0.918201\pi\) |
0.703690 | + | 0.710508i | \(0.251535\pi\) | |||||||
\(830\) | −11.0460 | − | 41.2242i | −0.383412 | − | 1.43091i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 45.3418 | + | 4.72706i | 1.57194 | + | 0.163881i | ||||
\(833\) | −1.31380 | − | 8.28810i | −0.0455205 | − | 0.287166i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.9924 | − | 62.3406i | 1.24557 | − | 2.15739i | ||||
\(836\) | 7.44673 | + | 12.8981i | 0.257550 | + | 0.446091i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 71.1108 | + | 19.0541i | 2.45648 | + | 0.658212i | ||||
\(839\) | −14.3405 | + | 53.5194i | −0.495088 | + | 1.84769i | 0.0344471 | + | 0.999407i | \(0.489033\pi\) |
−0.529535 | + | 0.848288i | \(0.677634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1234 | + | 17.5343i | 0.349084 | + | 0.604631i | ||||
\(842\) | 49.0703 | + | 28.3308i | 1.69108 | + | 0.976343i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 30.7229i | − | 1.05753i | ||||||
\(845\) | −46.2395 | + | 30.1390i | −1.59069 | + | 1.03681i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.27789 | + | 3.28615i | −0.318792 | + | 0.112913i | ||||
\(848\) | −9.48046 | + | 16.4206i | −0.325560 | + | 0.563887i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.2239 | + | 24.2239i | −0.830873 | + | 0.830873i | ||||
\(851\) | 5.57514 | − | 20.8067i | 0.191113 | − | 0.713244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.2556 | + | 31.2556i | 1.07017 | + | 1.07017i | 0.997345 | + | 0.0728280i | \(0.0232024\pi\) |
0.0728280 | + | 0.997345i | \(0.476798\pi\) | |||||||
\(854\) | 25.1679 | − | 17.2998i | 0.861229 | − | 0.591988i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.76279 | + | 6.57881i | 0.0602508 | + | 0.224859i | ||||
\(857\) | −4.67560 | −0.159715 | −0.0798577 | − | 0.996806i | \(-0.525447\pi\) | ||||
−0.0798577 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.70689i | − | 0.160597i | −0.996771 | − | 0.0802986i | \(-0.974413\pi\) | ||
0.996771 | − | 0.0802986i | \(-0.0255874\pi\) | |||||||
\(860\) | 34.9151 | + | 130.305i | 1.19060 | + | 4.44337i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.3150 | − | 19.2344i | 1.13471 | − | 0.655127i | ||||
\(863\) | 31.1015 | + | 31.1015i | 1.05871 | + | 1.05871i | 0.998166 | + | 0.0605431i | \(0.0192833\pi\) |
0.0605431 | + | 0.998166i | \(0.480717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.7848 | − | 10.1244i | −1.28472 | − | 0.344240i | ||||
\(866\) | −54.8070 | − | 54.8070i | −1.86242 | − | 1.86242i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.2537 | − | 31.9853i | 0.517743 | − | 1.08565i | ||||
\(869\) | −0.816302 | − | 3.04648i | −0.0276912 | − | 0.103345i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.43929 | − | 15.3177i | −0.0826522 | − | 0.519019i | ||||
\(872\) | 24.1845 | 0.818992 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.0322 | + | 11.5656i | 0.677599 | + | 0.391212i | ||||
\(875\) | 51.0725 | + | 74.3007i | 1.72657 | + | 2.51182i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.66722 | − | 24.8824i | 0.225136 | − | 0.840220i | −0.757214 | − | 0.653167i | \(-0.773440\pi\) |
0.982350 | − | 0.187052i | \(-0.0598934\pi\) | |||||||
\(878\) | −10.6278 | + | 39.6633i | −0.358669 | + | 1.33857i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.0073 | + | 9.81918i | −0.573316 | + | 0.331004i | ||||
\(881\) | −9.58023 | + | 16.5935i | −0.322766 | + | 0.559048i | −0.981058 | − | 0.193716i | \(-0.937946\pi\) |
0.658291 | + | 0.752763i | \(0.271279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.19989i | − | 0.275948i | −0.990436 | − | 0.137974i | \(-0.955941\pi\) | ||
0.990436 | − | 0.137974i | \(-0.0440591\pi\) | |||||||
\(884\) | −7.13753 | + | 9.84137i | −0.240061 | + | 0.331001i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −64.6192 | + | 17.3147i | −2.17092 | + | 0.581697i | ||||
\(887\) | −3.31720 | − | 1.91519i | −0.111381 | − | 0.0643057i | 0.443275 | − | 0.896386i | \(-0.353817\pi\) |
−0.554655 | + | 0.832080i | \(0.687150\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.4111 | − | 11.4526i | −0.449792 | − | 0.384109i | ||||
\(890\) | −11.9847 | + | 44.7276i | −0.401729 | + | 1.49927i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.6808 | − | 30.6808i | −1.02727 | − | 1.02727i | ||||
\(893\) | 4.13305 | + | 7.15866i | 0.138307 | + | 0.239555i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.1583 | + | 2.98986i | −0.372982 | + | 0.0999401i | ||||
\(896\) | −2.71840 | − | 34.5121i | −0.0908154 | − | 1.15297i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43.3539 | 1.44674 | ||||||||
\(899\) | −3.64639 | − | 13.6085i | −0.121614 | − | 0.453869i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.62955 | − | 11.4827i | −0.220862 | − | 0.382545i | ||||
\(902\) | −23.0876 | + | 23.0876i | −0.768732 | + | 0.768732i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.43745 | + | 1.45696i | 0.180847 | + | 0.0484578i | ||||
\(905\) | −46.3914 | + | 46.3914i | −1.54210 | + | 1.54210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5418 | + | 15.3239i | 0.881305 | + | 0.508821i | 0.871088 | − | 0.491126i | \(-0.163415\pi\) |
0.0102163 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(908\) | 52.4716 | − | 14.0597i | 1.74133 | − | 0.466588i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 61.2199 | + | 64.3954i | 2.02942 | + | 2.13469i | ||||
\(911\) | 17.6785 | 0.585714 | 0.292857 | − | 0.956156i | \(-0.405394\pi\) | ||||
0.292857 | + | 0.956156i | \(0.405394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7067 | + | 6.18149i | 0.354339 | + | 0.204578i | ||||
\(914\) | 15.4881 | − | 8.94204i | 0.512300 | − | 0.295776i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48.4631 | + | 12.9857i | 1.60127 | + | 0.429058i | ||||
\(917\) | 4.72445 | − | 25.5000i | 0.156015 | − | 0.842084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.76666 | + | 11.7202i | 0.223212 | + | 0.386614i | 0.955781 | − | 0.294078i | \(-0.0950126\pi\) |
−0.732570 | + | 0.680692i | \(0.761679\pi\) | |||||||
\(920\) | 20.3330 | − | 35.2178i | 0.670360 | − | 1.16110i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −73.1348 | −2.40856 | ||||||||
\(923\) | 10.4177 | + | 3.98892i | 0.342902 | + | 0.131297i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.4474 | + | 13.5173i | −1.65870 | + | 0.444447i | ||||
\(926\) | 2.57688 | − | 4.46329i | 0.0846816 | − | 0.146673i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.3269 | − | 15.3269i | −0.503130 | − | 0.503130i | ||||
\(929\) | 48.9198 | + | 13.1080i | 1.60501 | + | 0.430060i | 0.946549 | − | 0.322559i | \(-0.104543\pi\) |
0.658456 | + | 0.752619i | \(0.271210\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1152 | + | 8.07346i | 0.364285 | + | 0.264597i | ||||
\(932\) | −35.0762 | − | 60.7538i | −1.14896 | − | 1.99006i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.0492 | − | 6.97987i | 0.852357 | − | 0.228388i | ||||
\(935\) | − | 13.7328i | − | 0.449111i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.1481i | − | 0.788885i | −0.918921 | − | 0.394443i | \(-0.870938\pi\) | ||
0.918921 | − | 0.394443i | \(-0.129062\pi\) | |||||||
\(938\) | −23.5362 | + | 8.33631i | −0.768484 | + | 0.272190i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 43.5592 | − | 25.1489i | 1.42074 | − | 0.820267i | ||||
\(941\) | −11.0345 | + | 11.0345i | −0.359716 | + | 0.359716i | −0.863708 | − | 0.503992i | \(-0.831864\pi\) |
0.503992 | + | 0.863708i | \(0.331864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.67049 | + | 28.6266i | −0.249785 | + | 0.932212i | ||||
\(944\) | 14.7403 | + | 14.7403i | 0.479755 | + | 0.479755i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −57.9071 | − | 33.4327i | −1.88272 | − | 1.08699i | ||||
\(947\) | 6.74864 | + | 25.1863i | 0.219301 | + | 0.818444i | 0.984608 | + | 0.174778i | \(0.0559207\pi\) |
−0.765307 | + | 0.643666i | \(0.777413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9448 | − | 15.3676i | 0.614976 | − | 0.498855i | ||||
\(950\) | − | 56.0833i | − | 1.81958i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.10375 | + | 2.43396i | 0.165413 | + | 0.0788851i | ||||
\(953\) | −2.70119 | + | 1.55953i | −0.0875001 | + | 0.0505182i | −0.543112 | − | 0.839661i | \(-0.682754\pi\) |
0.455612 | + | 0.890179i | \(0.349421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.4327 | − | 3.59927i | −0.434671 | − | 0.116470i | ||||
\(956\) | 17.9786 | + | 4.81735i | 0.581470 | + | 0.155804i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.8518 | + | 25.8952i | −1.44910 | + | 0.836636i | ||||
\(959\) | 16.0394 | + | 7.64915i | 0.517940 | + | 0.247004i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.32384i | 0.268511i | ||||||||
\(962\) | −28.9604 | + | 12.9232i | −0.933720 | + | 0.416661i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.475429 | + | 1.77433i | 0.0153126 | + | 0.0571472i | ||||
\(965\) | −77.3469 | − | 44.6563i | −2.48989 | − | 1.43754i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4152 | + | 10.4152i | 0.334930 | + | 0.334930i | 0.854455 | − | 0.519525i | \(-0.173891\pi\) |
−0.519525 | + | 0.854455i | \(0.673891\pi\) | |||||||
\(968\) | 1.71654 | − | 6.40620i | 0.0551715 | − | 0.205903i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −100.561 | + | 100.561i | −3.22881 | + | 3.22881i | ||||
\(971\) | 17.7603 | − | 10.2539i | 0.569955 | − | 0.329064i | −0.187176 | − | 0.982326i | \(-0.559934\pi\) |
0.757131 | + | 0.653263i | \(0.226600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.877861 | − | 0.310931i | 0.0281429 | − | 0.00996798i | ||||
\(974\) | 23.1919i | 0.743117i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 9.02035i | − | 0.288734i | ||||||
\(977\) | −21.0235 | + | 5.63323i | −0.672601 | + | 0.180223i | −0.578926 | − | 0.815380i | \(-0.696528\pi\) |
−0.0936748 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.70682 | − | 11.6166i | −0.214351 | − | 0.371267i | ||||
\(980\) | 49.1256 | − | 67.6339i | 1.56926 | − | 2.16049i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.1682 | − | 6.20790i | −0.739327 | − | 0.198102i | ||||
\(983\) | 4.97085 | + | 4.97085i | 0.158546 | + | 0.158546i | 0.781922 | − | 0.623376i | \(-0.214240\pi\) |
−0.623376 | + | 0.781922i | \(0.714240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.3858 | + | 76.8784i | −1.41425 | + | 2.44955i | ||||
\(986\) | 7.51559 | − | 2.01380i | 0.239345 | − | 0.0641323i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.12997 | − | 19.6548i | −0.0995775 | − | 0.625303i | ||||
\(989\) | −60.6925 | −1.92991 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0062 | + | 27.7236i | −0.508454 | + | 0.880668i | 0.491498 | + | 0.870879i | \(0.336449\pi\) |
−0.999952 | + | 0.00978927i | \(0.996884\pi\) | |||||||
\(992\) | −17.4438 | − | 30.2136i | −0.553843 | − | 0.959283i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.27137 | − | 17.6571i | 0.103762 | − | 0.560049i | ||||
\(995\) | −102.268 | − | 27.4027i | −3.24212 | − | 0.868723i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.9153 | − | 22.4677i | 1.23246 | − | 0.711561i | 0.264917 | − | 0.964271i | \(-0.414655\pi\) |
0.967542 | + | 0.252711i | \(0.0813220\pi\) | |||||||
\(998\) | −56.8215 | − | 32.8059i | −1.79865 | − | 1.03845i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.fm.e.748.7 | 32 | ||
3.2 | odd | 2 | 273.2.by.d.202.2 | yes | 32 | ||
7.6 | odd | 2 | 819.2.fm.f.748.7 | 32 | |||
13.2 | odd | 12 | 819.2.fm.f.496.7 | 32 | |||
21.20 | even | 2 | 273.2.by.c.202.2 | ✓ | 32 | ||
39.2 | even | 12 | 273.2.by.c.223.2 | yes | 32 | ||
91.41 | even | 12 | inner | 819.2.fm.e.496.7 | 32 | ||
273.41 | odd | 12 | 273.2.by.d.223.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.by.c.202.2 | ✓ | 32 | 21.20 | even | 2 | ||
273.2.by.c.223.2 | yes | 32 | 39.2 | even | 12 | ||
273.2.by.d.202.2 | yes | 32 | 3.2 | odd | 2 | ||
273.2.by.d.223.2 | yes | 32 | 273.41 | odd | 12 | ||
819.2.fm.e.496.7 | 32 | 91.41 | even | 12 | inner | ||
819.2.fm.e.748.7 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fm.f.496.7 | 32 | 13.2 | odd | 12 | |||
819.2.fm.f.748.7 | 32 | 7.6 | odd | 2 |