Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(89,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bo (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.8 | ||
Root | \(2.11423 + 0.728019i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.89 |
Dual form | 630.2.bo.b.269.8 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.11423 | + | 0.728019i | 0.945515 | + | 0.325580i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30608 | − | 1.29693i | 0.871614 | − | 0.490192i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.68760 | − | 1.46697i | 0.533666 | − | 0.463897i | ||||
\(11\) | 1.11120 | − | 0.641550i | 0.335038 | − | 0.193435i | −0.323037 | − | 0.946386i | \(-0.604704\pi\) |
0.658076 | + | 0.752952i | \(0.271371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.14864 | −1.70533 | −0.852663 | − | 0.522462i | \(-0.825014\pi\) | ||||
−0.852663 | + | 0.522462i | \(0.825014\pi\) | |||||||
\(14\) | 0.0298666 | − | 2.64558i | 0.00798219 | − | 0.707062i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 5.64871 | − | 3.26128i | 1.37001 | − | 0.790977i | 0.379084 | − | 0.925362i | \(-0.376239\pi\) |
0.990929 | + | 0.134385i | \(0.0429059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.22868 | + | 3.01878i | 1.19954 | + | 0.692555i | 0.960453 | − | 0.278443i | \(-0.0898183\pi\) |
0.239088 | + | 0.970998i | \(0.423152\pi\) | |||||||
\(20\) | −0.426635 | − | 2.19499i | −0.0953985 | − | 0.490815i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.28310i | − | 0.273558i | ||||||
\(23\) | 1.43958 | − | 2.49343i | 0.300174 | − | 0.519917i | −0.676001 | − | 0.736901i | \(-0.736289\pi\) |
0.976175 | + | 0.216984i | \(0.0696219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.93998 | + | 3.07840i | 0.787996 | + | 0.615681i | ||||
\(26\) | −3.07432 | + | 5.32488i | −0.602923 | + | 1.04429i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.27621 | − | 1.34866i | −0.430163 | − | 0.254872i | ||||
\(29\) | 1.35052i | 0.250785i | 0.992107 | + | 0.125393i | \(0.0400191\pi\) | ||||
−0.992107 | + | 0.125393i | \(0.959981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.49558 | + | 4.32758i | −1.34625 | + | 0.777255i | −0.987716 | − | 0.156263i | \(-0.950055\pi\) |
−0.358530 | + | 0.933518i | \(0.616722\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.52257i | − | 1.11861i | ||||||
\(35\) | 5.81977 | − | 1.06314i | 0.983721 | − | 0.179704i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.25652 | − | 4.76690i | −1.35736 | − | 0.783674i | −0.368095 | − | 0.929788i | \(-0.619990\pi\) |
−0.989268 | + | 0.146114i | \(0.953323\pi\) | |||||||
\(38\) | 5.22868 | − | 3.01878i | 0.848203 | − | 0.489710i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.11423 | − | 0.728019i | −0.334290 | − | 0.115110i | ||||
\(41\) | 8.71759 | 1.36146 | 0.680730 | − | 0.732535i | \(-0.261663\pi\) | ||||
0.680730 | + | 0.732535i | \(0.261663\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.35859i | − | 0.817177i | −0.912719 | − | 0.408588i | \(-0.866021\pi\) | ||
0.912719 | − | 0.408588i | \(-0.133979\pi\) | |||||||
\(44\) | −1.11120 | − | 0.641550i | −0.167519 | − | 0.0967173i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.43958 | − | 2.49343i | −0.212255 | − | 0.367637i | ||||
\(47\) | −0.698165 | − | 0.403086i | −0.101838 | − | 0.0587961i | 0.448216 | − | 0.893925i | \(-0.352060\pi\) |
−0.550054 | + | 0.835129i | \(0.685393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.63597 | − | 5.98162i | 0.519424 | − | 0.854517i | ||||
\(50\) | 4.63597 | − | 1.87292i | 0.655625 | − | 0.264871i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.07432 | + | 5.32488i | 0.426331 | + | 0.738427i | ||||
\(53\) | −3.33413 | − | 5.77488i | −0.457978 | − | 0.793241i | 0.540876 | − | 0.841102i | \(-0.318093\pi\) |
−0.998854 | + | 0.0478611i | \(0.984760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.81639 | − | 0.547415i | 0.379762 | − | 0.0738134i | ||||
\(56\) | −2.30608 | + | 1.29693i | −0.308162 | + | 0.173309i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.16959 | + | 0.675260i | 0.153574 | + | 0.0886660i | ||||
\(59\) | −0.798110 | − | 1.38237i | −0.103905 | − | 0.179969i | 0.809385 | − | 0.587278i | \(-0.199800\pi\) |
−0.913290 | + | 0.407309i | \(0.866467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50239 | − | 3.17681i | −0.704509 | − | 0.406748i | 0.104516 | − | 0.994523i | \(-0.466671\pi\) |
−0.809025 | + | 0.587775i | \(0.800004\pi\) | |||||||
\(62\) | 8.65515i | 1.09921i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.9997 | − | 4.47632i | −1.61241 | − | 0.555219i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.67188 | + | 2.69731i | −0.570761 | + | 0.329529i | −0.757453 | − | 0.652889i | \(-0.773557\pi\) |
0.186692 | + | 0.982418i | \(0.440223\pi\) | |||||||
\(68\) | −5.64871 | − | 3.26128i | −0.685006 | − | 0.395489i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.98918 | − | 5.57164i | 0.237752 | − | 0.665938i | ||||
\(71\) | 15.6787i | 1.86072i | 0.366650 | + | 0.930359i | \(0.380505\pi\) | ||||
−0.366650 | + | 0.930359i | \(0.619495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.20837 | + | 10.7532i | 0.726635 | + | 1.25857i | 0.958298 | + | 0.285772i | \(0.0922501\pi\) |
−0.231663 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(74\) | −8.25652 | + | 4.76690i | −0.959801 | + | 0.554141i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.03756i | − | 0.692555i | ||||||
\(77\) | 1.73046 | − | 2.92060i | 0.197204 | − | 0.332834i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.59093 | + | 9.68377i | −0.629028 | + | 1.08951i | 0.358719 | + | 0.933446i | \(0.383214\pi\) |
−0.987747 | + | 0.156064i | \(0.950120\pi\) | |||||||
\(80\) | −1.68760 | + | 1.46697i | −0.188679 | + | 0.164012i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.35880 | − | 7.54966i | 0.481349 | − | 0.833720i | ||||
\(83\) | 3.74493i | 0.411059i | 0.978651 | + | 0.205530i | \(0.0658917\pi\) | ||||
−0.978651 | + | 0.205530i | \(0.934108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.3170 | − | 2.78275i | 1.55289 | − | 0.301832i | ||||
\(86\) | −4.64067 | − | 2.67929i | −0.500417 | − | 0.288916i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.11120 | + | 0.641550i | −0.118454 | + | 0.0683894i | ||||
\(89\) | 1.81971 | − | 3.15183i | 0.192889 | − | 0.334093i | −0.753318 | − | 0.657657i | \(-0.771548\pi\) |
0.946206 | + | 0.323564i | \(0.104881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.1792 | + | 7.97433i | −1.48639 | + | 0.835937i | ||||
\(92\) | −2.87917 | −0.300174 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.698165 | + | 0.403086i | −0.0720102 | + | 0.0415751i | ||||
\(95\) | 8.85692 | + | 10.1890i | 0.908701 | + | 1.04537i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.76818 | 0.890274 | 0.445137 | − | 0.895463i | \(-0.353155\pi\) | ||||
0.445137 | + | 0.895463i | \(0.353155\pi\) | |||||||
\(98\) | −3.36225 | − | 6.13965i | −0.339639 | − | 0.620198i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.695987 | − | 4.95132i | 0.0695987 | − | 0.495132i | ||||
\(101\) | 0.853270 | + | 1.47791i | 0.0849035 | + | 0.147057i | 0.905350 | − | 0.424666i | \(-0.139608\pi\) |
−0.820447 | + | 0.571723i | \(0.806275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.18220 | + | 8.97583i | −0.510617 | + | 0.884415i | 0.489307 | + | 0.872112i | \(0.337250\pi\) |
−0.999924 | + | 0.0123035i | \(0.996084\pi\) | |||||||
\(104\) | 6.14864 | 0.602923 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.66826 | −0.647679 | ||||||||
\(107\) | −5.75680 | + | 9.97106i | −0.556531 | + | 0.963939i | 0.441252 | + | 0.897383i | \(0.354534\pi\) |
−0.997783 | + | 0.0665560i | \(0.978799\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0.934120 | − | 2.71277i | 0.0890649 | − | 0.258653i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0298666 | + | 2.64558i | −0.00282213 | + | 0.249984i | ||||
\(113\) | −13.3875 | −1.25939 | −0.629695 | − | 0.776843i | \(-0.716820\pi\) | ||||
−0.629695 | + | 0.776843i | \(0.716820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.85888 | − | 4.22366i | 0.453093 | − | 0.393858i | ||||
\(116\) | 1.16959 | − | 0.675260i | 0.108593 | − | 0.0626963i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.59622 | −0.146944 | ||||||||
\(119\) | 8.79670 | − | 14.8467i | 0.806392 | − | 1.36100i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.67683 | + | 8.10050i | −0.425166 | + | 0.736409i | ||||
\(122\) | −5.50239 | + | 3.17681i | −0.498163 | + | 0.287615i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.49558 | + | 4.32758i | 0.673123 | + | 0.388628i | ||||
\(125\) | 6.08890 | + | 9.37685i | 0.544608 | + | 0.838691i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65313i | 0.501634i | 0.968035 | + | 0.250817i | \(0.0806992\pi\) | ||||
−0.968035 | + | 0.250817i | \(0.919301\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.3764 | + | 9.01988i | −0.910074 | + | 0.791096i | ||||
\(131\) | −6.23366 | + | 10.7970i | −0.544638 | + | 0.943340i | 0.453992 | + | 0.891006i | \(0.349999\pi\) |
−0.998630 | + | 0.0523344i | \(0.983334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.9729 | + | 0.180321i | 1.38502 | + | 0.0156358i | ||||
\(134\) | 5.39463i | 0.466025i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.64871 | + | 3.26128i | −0.484373 | + | 0.279653i | ||||
\(137\) | −0.0254843 | − | 0.0441401i | −0.00217727 | − | 0.00377114i | 0.864935 | − | 0.501884i | \(-0.167360\pi\) |
−0.867112 | + | 0.498113i | \(0.834026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.05069i | − | 0.0891184i | −0.999007 | − | 0.0445592i | \(-0.985812\pi\) | ||
0.999007 | − | 0.0445592i | \(-0.0141883\pi\) | |||||||
\(140\) | −3.83059 | − | 4.50850i | −0.323744 | − | 0.381038i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.5781 | + | 7.83934i | 1.13945 | + | 0.657863i | ||||
\(143\) | −6.83235 | + | 3.94466i | −0.571350 | + | 0.329869i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.983204 | + | 2.85532i | −0.0816506 | + | 0.237121i | ||||
\(146\) | 12.4167 | 1.02762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.53381i | 0.783674i | ||||||||
\(149\) | −7.12137 | − | 4.11153i | −0.583406 | − | 0.336829i | 0.179080 | − | 0.983835i | \(-0.442688\pi\) |
−0.762486 | + | 0.647005i | \(0.776021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.13357 | + | 3.69546i | 0.173628 | + | 0.300732i | 0.939686 | − | 0.342040i | \(-0.111118\pi\) |
−0.766058 | + | 0.642772i | \(0.777784\pi\) | |||||||
\(152\) | −5.22868 | − | 3.01878i | −0.424102 | − | 0.244855i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.66409 | − | 2.95892i | −0.134096 | − | 0.238437i | ||||
\(155\) | −18.9980 | + | 3.69259i | −1.52595 | + | 0.296596i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.41601 | − | 4.18466i | −0.192819 | − | 0.333972i | 0.753364 | − | 0.657603i | \(-0.228430\pi\) |
−0.946183 | + | 0.323631i | \(0.895096\pi\) | |||||||
\(158\) | 5.59093 | + | 9.68377i | 0.444790 | + | 0.770399i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.426635 | + | 2.19499i | 0.0337285 | + | 0.173529i | ||||
\(161\) | 0.0859910 | − | 7.61708i | 0.00677704 | − | 0.600310i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.31256 | − | 5.37661i | −0.729416 | − | 0.421128i | 0.0887927 | − | 0.996050i | \(-0.471699\pi\) |
−0.818208 | + | 0.574922i | \(0.805032\pi\) | |||||||
\(164\) | −4.35880 | − | 7.54966i | −0.340365 | − | 0.589529i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.24320 | + | 1.87246i | 0.251721 | + | 0.145331i | ||||
\(167\) | − | 18.9267i | − | 1.46459i | −0.680988 | − | 0.732295i | \(-0.738449\pi\) | ||
0.680988 | − | 0.732295i | \(-0.261551\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.8057 | 1.90813 | ||||||||
\(170\) | 4.74855 | − | 13.7902i | 0.364197 | − | 1.05766i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.64067 | + | 2.67929i | −0.353848 | + | 0.204294i | ||||
\(173\) | 10.2568 | + | 5.92176i | 0.779810 | + | 0.450223i | 0.836363 | − | 0.548176i | \(-0.184678\pi\) |
−0.0565531 | + | 0.998400i | \(0.518011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0783 | + | 1.98917i | 0.988630 | + | 0.150367i | ||||
\(176\) | 1.28310i | 0.0967173i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.81971 | − | 3.15183i | −0.136393 | − | 0.236239i | ||||
\(179\) | −3.27843 | + | 1.89280i | −0.245041 | + | 0.141475i | −0.617492 | − | 0.786577i | \(-0.711851\pi\) |
0.372450 | + | 0.928052i | \(0.378518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.0033i | − | 1.41251i | −0.707960 | − | 0.706253i | \(-0.750384\pi\) | ||
0.707960 | − | 0.706253i | \(-0.249616\pi\) | |||||||
\(182\) | −0.183639 | + | 16.2667i | −0.0136122 | + | 1.20577i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.43958 | + | 2.49343i | −0.106128 | + | 0.183818i | ||||
\(185\) | −13.9858 | − | 16.0893i | −1.02826 | − | 1.18291i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.18455 | − | 7.24785i | 0.306005 | − | 0.530016i | ||||
\(188\) | 0.806172i | 0.0587961i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.2524 | − | 2.57583i | 0.961428 | − | 0.186871i | ||||
\(191\) | −2.44949 | − | 1.41421i | −0.177239 | − | 0.102329i | 0.408756 | − | 0.912644i | \(-0.365963\pi\) |
−0.585995 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.06479 | + | 1.76946i | −0.220608 | + | 0.127368i | −0.606232 | − | 0.795288i | \(-0.707320\pi\) |
0.385623 | + | 0.922656i | \(0.373986\pi\) | |||||||
\(194\) | 4.38409 | − | 7.59347i | 0.314759 | − | 0.545179i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99822 | − | 0.158029i | −0.499873 | − | 0.0112878i | ||||
\(197\) | 2.36728 | 0.168662 | 0.0843308 | − | 0.996438i | \(-0.473125\pi\) | ||||
0.0843308 | + | 0.996438i | \(0.473125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | + | 1.73205i | −0.212664 | + | 0.122782i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | −3.93998 | − | 3.07840i | −0.278599 | − | 0.217676i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.70654 | 0.120072 | ||||||||
\(203\) | 1.75153 | + | 3.11440i | 0.122933 | + | 0.218588i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.4310 | + | 6.34657i | 1.28728 | + | 0.443264i | ||||
\(206\) | 5.18220 | + | 8.97583i | 0.361061 | + | 0.625376i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.07432 | − | 5.32488i | 0.213166 | − | 0.369214i | ||||
\(209\) | 7.74679 | 0.535856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3620 | −0.988721 | −0.494361 | − | 0.869257i | \(-0.664598\pi\) | ||||
−0.494361 | + | 0.869257i | \(0.664598\pi\) | |||||||
\(212\) | −3.33413 | + | 5.77488i | −0.228989 | + | 0.396621i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.75680 | + | 9.97106i | 0.393527 | + | 0.681608i | ||||
\(215\) | 3.90115 | − | 11.3293i | 0.266056 | − | 0.772653i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.6728 | + | 19.7009i | −0.792403 | + | 1.33739i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.88227 | − | 2.16536i | −0.126903 | − | 0.145988i | ||||
\(221\) | −34.7319 | + | 20.0524i | −2.33632 | + | 1.34887i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5975 | 0.910557 | 0.455279 | − | 0.890349i | \(-0.349540\pi\) | ||||
0.455279 | + | 0.890349i | \(0.349540\pi\) | |||||||
\(224\) | 2.27621 | + | 1.34866i | 0.152086 | + | 0.0901109i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.69375 | + | 11.5939i | −0.445261 | + | 0.771215i | ||||
\(227\) | 10.7006 | − | 6.17797i | 0.710221 | − | 0.410046i | −0.100922 | − | 0.994894i | \(-0.532179\pi\) |
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.09008 | − | 1.20671i | −0.138116 | − | 0.0797414i | 0.429350 | − | 0.903138i | \(-0.358743\pi\) |
−0.567466 | + | 0.823397i | \(0.692076\pi\) | |||||||
\(230\) | −1.22835 | − | 6.31975i | −0.0809952 | − | 0.416712i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.35052i | − | 0.0886660i | ||||||
\(233\) | −6.43780 | + | 11.1506i | −0.421754 | + | 0.730500i | −0.996111 | − | 0.0881051i | \(-0.971919\pi\) |
0.574357 | + | 0.818605i | \(0.305252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.18263 | − | 1.36050i | −0.0771464 | − | 0.0887489i | ||||
\(236\) | −0.798110 | + | 1.38237i | −0.0519525 | + | 0.0899844i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.45929 | − | 15.0415i | −0.548334 | − | 0.974997i | ||||
\(239\) | 27.2546i | 1.76296i | 0.472226 | + | 0.881478i | \(0.343451\pi\) | ||||
−0.472226 | + | 0.881478i | \(0.656549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.26690 | − | 1.30880i | 0.146024 | − | 0.0843070i | −0.425208 | − | 0.905096i | \(-0.639799\pi\) |
0.571232 | + | 0.820789i | \(0.306466\pi\) | |||||||
\(242\) | 4.67683 | + | 8.10050i | 0.300638 | + | 0.520720i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.35361i | 0.406748i | ||||||||
\(245\) | 12.0420 | − | 9.99950i | 0.769336 | − | 0.638844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.1492 | − | 18.5614i | −2.04561 | − | 1.18103i | ||||
\(248\) | 7.49558 | − | 4.32758i | 0.475970 | − | 0.274801i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.1650 | − | 0.584722i | 0.706139 | − | 0.0369811i | ||||
\(251\) | 26.7173 | 1.68638 | 0.843190 | − | 0.537615i | \(-0.180675\pi\) | ||||
0.843190 | + | 0.537615i | \(0.180675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.69426i | − | 0.232256i | ||||||
\(254\) | 4.89575 | + | 2.82656i | 0.307187 | + | 0.177354i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.14632 | − | 5.28063i | −0.570532 | − | 0.329397i | 0.186830 | − | 0.982392i | \(-0.440179\pi\) |
−0.757362 | + | 0.652996i | \(0.773512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.2225 | − | 0.284743i | −1.56725 | − | 0.0176930i | ||||
\(260\) | 2.62322 | + | 13.4962i | 0.162685 | + | 0.836999i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.23366 | + | 10.7970i | 0.385117 | + | 0.667042i | ||||
\(263\) | −4.16587 | − | 7.21550i | −0.256879 | − | 0.444927i | 0.708526 | − | 0.705685i | \(-0.249361\pi\) |
−0.965404 | + | 0.260759i | \(0.916027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.84491 | − | 14.6368i | −0.174762 | − | 0.899130i | ||||
\(266\) | 8.14259 | − | 13.7427i | 0.499254 | − | 0.842621i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.67188 | + | 2.69731i | 0.285381 | + | 0.164765i | ||||
\(269\) | −7.14171 | − | 12.3698i | −0.435438 | − | 0.754201i | 0.561893 | − | 0.827210i | \(-0.310073\pi\) |
−0.997331 | + | 0.0730091i | \(0.976740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.58566 | − | 3.80223i | −0.400050 | − | 0.230969i | 0.286456 | − | 0.958094i | \(-0.407523\pi\) |
−0.686506 | + | 0.727125i | \(0.740856\pi\) | |||||||
\(272\) | 6.52257i | 0.395489i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0509686 | −0.00307912 | ||||||||
\(275\) | 6.35304 | + | 0.893021i | 0.383103 | + | 0.0538512i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4270 | − | 6.02002i | 0.626497 | − | 0.361708i | −0.152897 | − | 0.988242i | \(-0.548860\pi\) |
0.779394 | + | 0.626534i | \(0.215527\pi\) | |||||||
\(278\) | −0.909924 | − | 0.525345i | −0.0545736 | − | 0.0315081i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.81977 | + | 1.06314i | −0.347798 | + | 0.0635348i | ||||
\(281\) | − | 12.7879i | − | 0.762861i | −0.924397 | − | 0.381431i | \(-0.875431\pi\) | ||
0.924397 | − | 0.381431i | \(-0.124569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.77607 | − | 13.4685i | −0.462239 | − | 0.800622i | 0.536833 | − | 0.843689i | \(-0.319621\pi\) |
−0.999072 | + | 0.0430666i | \(0.986287\pi\) | |||||||
\(284\) | 13.5781 | − | 7.83934i | 0.805715 | − | 0.465180i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.88931i | 0.466505i | ||||||||
\(287\) | 20.1034 | − | 11.3061i | 1.18667 | − | 0.667376i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7719 | − | 22.1216i | 0.751290 | − | 1.30127i | ||||
\(290\) | 1.98118 | + | 2.27914i | 0.116339 | + | 0.133836i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.20837 | − | 10.7532i | 0.363317 | − | 0.629284i | ||||
\(293\) | 11.5536i | 0.674967i | 0.941331 | + | 0.337483i | \(0.109576\pi\) | ||||
−0.941331 | + | 0.337483i | \(0.890424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.681003 | − | 3.50369i | −0.0396495 | − | 0.203993i | ||||
\(296\) | 8.25652 | + | 4.76690i | 0.479900 | + | 0.277071i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.12137 | + | 4.11153i | −0.412530 | + | 0.238174i | ||||
\(299\) | −8.85148 | + | 15.3312i | −0.511894 | + | 0.886627i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.94969 | − | 12.3573i | −0.400573 | − | 0.712263i | ||||
\(302\) | 4.26715 | 0.245547 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.22868 | + | 3.01878i | −0.299885 | + | 0.173139i | ||||
\(305\) | −9.32057 | − | 10.7224i | −0.533694 | − | 0.613961i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57617 | 0.147030 | 0.0735150 | − | 0.997294i | \(-0.476578\pi\) | ||||
0.0735150 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(308\) | −3.39455 | − | 0.0383219i | −0.193422 | − | 0.00218359i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.30111 | + | 18.2990i | −0.357879 | + | 1.03931i | ||||
\(311\) | 12.3570 | + | 21.4030i | 0.700702 | + | 1.21365i | 0.968220 | + | 0.250098i | \(0.0804629\pi\) |
−0.267519 | + | 0.963553i | \(0.586204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.50087 | + | 7.79573i | −0.254404 | + | 0.440641i | −0.964733 | − | 0.263229i | \(-0.915213\pi\) |
0.710329 | + | 0.703869i | \(0.248546\pi\) | |||||||
\(314\) | −4.83203 | −0.272687 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.1819 | 0.629028 | ||||||||
\(317\) | 11.9529 | − | 20.7031i | 0.671344 | − | 1.16280i | −0.306180 | − | 0.951974i | \(-0.599051\pi\) |
0.977523 | − | 0.210828i | \(-0.0676158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.866426 | + | 1.50069i | 0.0485106 | + | 0.0840227i | ||||
\(320\) | 2.11423 | + | 0.728019i | 0.118189 | + | 0.0406975i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.55359 | − | 3.88301i | −0.365217 | − | 0.216392i | ||||
\(323\) | 39.3804 | 2.19118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.2255 | − | 18.9280i | −1.34379 | − | 1.04994i | ||||
\(326\) | −9.31256 | + | 5.37661i | −0.515775 | + | 0.297783i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.71759 | −0.481349 | ||||||||
\(329\) | −2.13279 | − | 0.0240776i | −0.117585 | − | 0.00132744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.18364 | + | 3.78217i | −0.120024 | + | 0.207887i | −0.919777 | − | 0.392442i | \(-0.871630\pi\) |
0.799753 | + | 0.600329i | \(0.204964\pi\) | |||||||
\(332\) | 3.24320 | − | 1.87246i | 0.177994 | − | 0.102765i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.3910 | − | 9.46334i | −0.896874 | − | 0.517811i | ||||
\(335\) | −11.8412 | + | 2.30154i | −0.646951 | + | 0.125746i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.5159i | − | 1.06310i | −0.847028 | − | 0.531549i | \(-0.821610\pi\) | ||
0.847028 | − | 0.531549i | \(-0.178390\pi\) | |||||||
\(338\) | 12.4029 | − | 21.4824i | 0.674627 | − | 1.16849i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.56842 | − | 11.0075i | −0.518920 | − | 0.596964i | ||||
\(341\) | −5.55271 | + | 9.61758i | −0.300696 | + | 0.520821i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.627092 | − | 18.5096i | 0.0338598 | − | 0.999427i | ||||
\(344\) | 5.35859i | 0.288916i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2568 | − | 5.92176i | 0.551409 | − | 0.318356i | ||||
\(347\) | −13.4574 | − | 23.3088i | −0.722429 | − | 1.25128i | −0.960024 | − | 0.279919i | \(-0.909692\pi\) |
0.237595 | − | 0.971364i | \(-0.423641\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.3821i | − | 0.555741i | −0.960619 | − | 0.277870i | \(-0.910371\pi\) | ||
0.960619 | − | 0.277870i | \(-0.0896286\pi\) | |||||||
\(350\) | 8.26185 | − | 10.3316i | 0.441614 | − | 0.552247i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.11120 | + | 0.641550i | 0.0592270 | + | 0.0341947i | ||||
\(353\) | 0.146316 | − | 0.0844756i | 0.00778761 | − | 0.00449618i | −0.496101 | − | 0.868265i | \(-0.665235\pi\) |
0.503889 | + | 0.863769i | \(0.331902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4144 | + | 33.1484i | −0.605812 | + | 1.75934i | ||||
\(356\) | −3.63941 | −0.192889 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.78561i | 0.200075i | ||||||||
\(359\) | −32.6198 | − | 18.8330i | −1.72161 | − | 0.993970i | −0.915631 | − | 0.402021i | \(-0.868308\pi\) |
−0.805975 | − | 0.591949i | \(-0.798359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72604 | + | 15.1139i | 0.459265 | + | 0.795471i | ||||
\(362\) | −16.4574 | − | 9.50166i | −0.864979 | − | 0.499396i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.9956 | + | 8.29240i | 0.733568 | + | 0.434640i | ||||
\(365\) | 5.29741 | + | 27.2546i | 0.277279 | + | 1.42657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.57787 | + | 13.1253i | 0.395562 | + | 0.685133i | 0.993173 | − | 0.116653i | \(-0.0372166\pi\) |
−0.597611 | + | 0.801786i | \(0.703883\pi\) | |||||||
\(368\) | 1.43958 | + | 2.49343i | 0.0750435 | + | 0.129979i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.9266 | + | 4.06745i | −1.08792 | + | 0.211457i | ||||
\(371\) | −15.1784 | − | 8.99319i | −0.788021 | − | 0.466903i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4270 | + | 6.02002i | 0.539889 | + | 0.311705i | 0.745034 | − | 0.667027i | \(-0.232433\pi\) |
−0.205145 | + | 0.978732i | \(0.565767\pi\) | |||||||
\(374\) | −4.18455 | − | 7.24785i | −0.216378 | − | 0.374778i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.698165 | + | 0.403086i | 0.0360051 | + | 0.0207876i | ||||
\(377\) | − | 8.30386i | − | 0.427671i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0918 | 0.929312 | 0.464656 | − | 0.885491i | \(-0.346178\pi\) | ||||
0.464656 | + | 0.885491i | \(0.346178\pi\) | |||||||
\(380\) | 4.39545 | − | 12.7648i | 0.225482 | − | 0.654821i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.44949 | + | 1.41421i | −0.125327 | + | 0.0723575i | ||||
\(383\) | 25.2480 | + | 14.5769i | 1.29011 | + | 0.744846i | 0.978674 | − | 0.205421i | \(-0.0658565\pi\) |
0.311437 | + | 0.950267i | \(0.399190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.78485 | − | 4.91503i | 0.294823 | − | 0.250493i | ||||
\(386\) | 3.53892i | 0.180126i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.38409 | − | 7.59347i | −0.222568 | − | 0.385500i | ||||
\(389\) | 17.0297 | − | 9.83207i | 0.863438 | − | 0.498506i | −0.00172432 | − | 0.999999i | \(-0.500549\pi\) |
0.865162 | + | 0.501493i | \(0.167216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.7796i | − | 0.949723i | ||||||
\(392\) | −3.63597 | + | 5.98162i | −0.183644 | + | 0.302117i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.18364 | − | 2.05012i | 0.0596309 | − | 0.103284i | ||||
\(395\) | −18.8705 | + | 16.4035i | −0.949478 | + | 0.825348i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.84227 | + | 4.92295i | −0.142649 | + | 0.247076i | −0.928493 | − | 0.371349i | \(-0.878895\pi\) |
0.785844 | + | 0.618425i | \(0.212229\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.63597 | + | 1.87292i | −0.231798 | + | 0.0936460i | ||||
\(401\) | −8.84787 | − | 5.10832i | −0.441842 | − | 0.255097i | 0.262537 | − | 0.964922i | \(-0.415441\pi\) |
−0.704378 | + | 0.709825i | \(0.748774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.0876 | − | 26.6087i | 2.29579 | − | 1.32547i | ||||
\(404\) | 0.853270 | − | 1.47791i | 0.0424518 | − | 0.0735286i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.57291 | + | 0.0403355i | 0.177321 | + | 0.00200182i | ||||
\(407\) | −12.2328 | −0.606359 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0969 | − | 6.98414i | 0.598153 | − | 0.345344i | −0.170162 | − | 0.985416i | \(-0.554429\pi\) |
0.768314 | + | 0.640073i | \(0.221096\pi\) | |||||||
\(410\) | 14.7118 | − | 12.7885i | 0.726565 | − | 0.631577i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.3644 | 0.510617 | ||||||||
\(413\) | −3.63333 | − | 2.15275i | −0.178784 | − | 0.105930i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.72638 | + | 7.91766i | −0.133833 | + | 0.388663i | ||||
\(416\) | −3.07432 | − | 5.32488i | −0.150731 | − | 0.261074i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.87339 | − | 6.70891i | 0.189454 | − | 0.328144i | ||||
\(419\) | 11.3181 | 0.552924 | 0.276462 | − | 0.961025i | \(-0.410838\pi\) | ||||
0.276462 | + | 0.961025i | \(0.410838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9099 | −0.677928 | −0.338964 | − | 0.940799i | \(-0.610077\pi\) | ||||
−0.338964 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(422\) | −7.18100 | + | 12.4379i | −0.349566 | + | 0.605466i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.33413 | + | 5.77488i | 0.161920 | + | 0.280453i | ||||
\(425\) | 32.2953 | + | 4.53962i | 1.56655 | + | 0.220204i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.8090 | − | 0.189761i | −0.813445 | − | 0.00918318i | ||||
\(428\) | 11.5136 | 0.556531 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.86090 | − | 9.04315i | −0.379086 | − | 0.436099i | ||||
\(431\) | 22.5947 | − | 13.0451i | 1.08835 | − | 0.628359i | 0.155213 | − | 0.987881i | \(-0.450394\pi\) |
0.933137 | + | 0.359522i | \(0.117060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.42614 | −0.404935 | −0.202467 | − | 0.979289i | \(-0.564896\pi\) | ||||
−0.202467 | + | 0.979289i | \(0.564896\pi\) | |||||||
\(434\) | 11.2251 | + | 19.9594i | 0.538822 | + | 0.958083i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 15.0542 | − | 8.69157i | 0.720142 | − | 0.415774i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9529 | − | 13.8292i | −1.14321 | − | 0.660033i | −0.195987 | − | 0.980606i | \(-0.562791\pi\) |
−0.947224 | + | 0.320573i | \(0.896125\pi\) | |||||||
\(440\) | −2.81639 | + | 0.547415i | −0.134266 | + | 0.0260970i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 40.1049i | 1.90759i | ||||||||
\(443\) | 1.17861 | − | 2.04142i | 0.0559975 | − | 0.0969906i | −0.836668 | − | 0.547711i | \(-0.815499\pi\) |
0.892665 | + | 0.450720i | \(0.148833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.14187 | − | 5.33892i | 0.291153 | − | 0.253089i | ||||
\(446\) | 6.79876 | − | 11.7758i | 0.321931 | − | 0.557600i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.30608 | − | 1.29693i | 0.108952 | − | 0.0612740i | ||||
\(449\) | − | 12.8021i | − | 0.604169i | −0.953281 | − | 0.302084i | \(-0.902318\pi\) | ||
0.953281 | − | 0.302084i | \(-0.0976824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.68696 | − | 5.59277i | 0.456141 | − | 0.263353i | ||||
\(452\) | 6.69375 | + | 11.5939i | 0.314847 | + | 0.545332i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 12.3559i | − | 0.579893i | ||||||
\(455\) | −35.7837 | + | 6.53687i | −1.67756 | + | 0.306453i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.8989 | − | 17.2621i | −1.39861 | − | 0.807488i | −0.404363 | − | 0.914599i | \(-0.632507\pi\) |
−0.994247 | + | 0.107111i | \(0.965840\pi\) | |||||||
\(458\) | −2.09008 | + | 1.20671i | −0.0976628 | + | 0.0563857i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.08724 | − | 2.09609i | −0.283819 | − | 0.0977306i | ||||
\(461\) | 20.2692 | 0.944032 | 0.472016 | − | 0.881590i | \(-0.343526\pi\) | ||||
0.472016 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1246i | 0.609952i | 0.952360 | + | 0.304976i | \(0.0986485\pi\) | ||||
−0.952360 | + | 0.304976i | \(0.901352\pi\) | |||||||
\(464\) | −1.16959 | − | 0.675260i | −0.0542966 | − | 0.0313482i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.43780 | + | 11.1506i | 0.298225 | + | 0.516541i | ||||
\(467\) | −1.32647 | − | 0.765836i | −0.0613816 | − | 0.0354387i | 0.468995 | − | 0.883201i | \(-0.344616\pi\) |
−0.530377 | + | 0.847762i | \(0.677950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.27550 | + | 12.2793i | −0.335951 | + | 0.567005i | ||||
\(470\) | −1.76954 | + | 0.343941i | −0.0816228 | + | 0.0158648i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.798110 | + | 1.38237i | 0.0367360 | + | 0.0636286i | ||||
\(473\) | −3.43780 | − | 5.95444i | −0.158070 | − | 0.273786i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3079 | + | 27.9899i | 0.518840 | + | 1.28426i | ||||
\(476\) | −17.2560 | − | 0.194807i | −0.790927 | − | 0.00892896i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.6032 | + | 13.6273i | 1.07959 | + | 0.623299i | ||||
\(479\) | 14.6585 | + | 25.3893i | 0.669764 | + | 1.16007i | 0.977970 | + | 0.208746i | \(0.0669382\pi\) |
−0.308205 | + | 0.951320i | \(0.599728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.7663 | + | 29.3100i | 2.31475 | + | 1.33642i | ||||
\(482\) | − | 2.61759i | − | 0.119228i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.35366 | 0.425166 | ||||||||
\(485\) | 18.5380 | + | 6.38340i | 0.841767 | + | 0.289855i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.09743 | − | 4.09770i | 0.321615 | − | 0.185685i | −0.330497 | − | 0.943807i | \(-0.607216\pi\) |
0.652112 | + | 0.758122i | \(0.273883\pi\) | |||||||
\(488\) | 5.50239 | + | 3.17681i | 0.249082 | + | 0.143807i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.63881 | − | 15.4284i | −0.119209 | − | 0.696986i | ||||
\(491\) | − | 40.4383i | − | 1.82495i | −0.409129 | − | 0.912477i | \(-0.634167\pi\) | ||
0.409129 | − | 0.912477i | \(-0.365833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.40443 | + | 7.62869i | 0.198366 | + | 0.343579i | ||||
\(494\) | −32.1492 | + | 18.5614i | −1.44646 | + | 0.835116i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.65515i | − | 0.388628i | ||||||
\(497\) | 20.3341 | + | 36.1562i | 0.912109 | + | 1.62183i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.72450 | + | 15.1113i | −0.390562 | + | 0.676474i | −0.992524 | − | 0.122051i | \(-0.961053\pi\) |
0.601961 | + | 0.798525i | \(0.294386\pi\) | |||||||
\(500\) | 5.07614 | − | 9.96157i | 0.227012 | − | 0.445495i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.3586 | − | 23.1379i | 0.596226 | − | 1.03269i | ||||
\(503\) | 1.91949i | 0.0855860i | 0.999084 | + | 0.0427930i | \(0.0136256\pi\) | ||||
−0.999084 | + | 0.0427930i | \(0.986374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.728069 | + | 3.74584i | 0.0323987 | + | 0.166688i | ||||
\(506\) | −3.19932 | − | 1.84713i | −0.142227 | − | 0.0821149i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.89575 | − | 2.82656i | 0.217214 | − | 0.125408i | ||||
\(509\) | −5.54549 | + | 9.60508i | −0.245800 | + | 0.425737i | −0.962356 | − | 0.271792i | \(-0.912384\pi\) |
0.716556 | + | 0.697529i | \(0.245717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2631 | + | 16.7459i | 1.25029 | + | 0.740796i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.14632 | + | 5.28063i | −0.403427 | + | 0.232919i | ||||
\(515\) | −17.4910 | + | 15.2043i | −0.770744 | + | 0.669981i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.03440 | −0.0454928 | ||||||||
\(518\) | −12.8578 | + | 21.7009i | −0.564941 | + | 0.953484i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.9997 | + | 4.47632i | 0.570073 | + | 0.196300i | ||||
\(521\) | −19.8706 | − | 34.4168i | −0.870546 | − | 1.50783i | −0.861433 | − | 0.507871i | \(-0.830433\pi\) |
−0.00911254 | − | 0.999958i | \(-0.502901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.6404 | + | 27.0900i | −0.683907 | + | 1.18456i | 0.289872 | + | 0.957065i | \(0.406387\pi\) |
−0.973779 | + | 0.227496i | \(0.926946\pi\) | |||||||
\(524\) | 12.4673 | 0.544638 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.33174 | −0.363281 | ||||||||
\(527\) | −28.2269 | + | 48.8904i | −1.22958 | + | 2.12970i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.35519 | + | 12.7396i | 0.319791 | + | 0.553894i | ||||
\(530\) | −14.0983 | − | 4.85462i | −0.612390 | − | 0.210871i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.83026 | − | 13.9231i | −0.339485 | − | 0.603641i | ||||
\(533\) | −53.6013 | −2.32173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4303 | + | 16.8901i | −0.840047 | + | 0.730223i | ||||
\(536\) | 4.67188 | − | 2.69731i | 0.201795 | − | 0.116506i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.2834 | −0.615802 | ||||||||
\(539\) | 0.202767 | − | 8.97941i | 0.00873380 | − | 0.386771i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3987 | − | 21.4752i | 0.533061 | − | 0.923290i | −0.466193 | − | 0.884683i | \(-0.654375\pi\) |
0.999254 | − | 0.0386065i | \(-0.0122919\pi\) | |||||||
\(542\) | −6.58566 | + | 3.80223i | −0.282878 | + | 0.163320i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.64871 | + | 3.26128i | 0.242186 | + | 0.139826i | ||||
\(545\) | −0.853270 | − | 4.38998i | −0.0365501 | − | 0.188046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.5380i | 1.73328i | 0.498934 | + | 0.866640i | \(0.333725\pi\) | ||||
−0.498934 | + | 0.866640i | \(0.666275\pi\) | |||||||
\(548\) | −0.0254843 | + | 0.0441401i | −0.00108863 | + | 0.00188557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.94990 | − | 5.05538i | 0.168424 | − | 0.215562i | ||||
\(551\) | −4.07692 | + | 7.06144i | −0.173683 | + | 0.300827i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.333964 | + | 29.5825i | −0.0142016 | + | 1.25798i | ||||
\(554\) | − | 12.0400i | − | 0.511532i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.909924 | + | 0.525345i | −0.0385894 | + | 0.0222796i | ||||
\(557\) | −11.8732 | − | 20.5650i | −0.503084 | − | 0.871367i | −0.999994 | − | 0.00356477i | \(-0.998865\pi\) |
0.496910 | − | 0.867802i | \(-0.334468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9480i | 1.39355i | ||||||||
\(560\) | −1.98918 | + | 5.57164i | −0.0840581 | + | 0.235445i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.0746 | − | 6.39394i | −0.467155 | − | 0.269712i | ||||
\(563\) | −7.29944 | + | 4.21434i | −0.307635 | + | 0.177613i | −0.645868 | − | 0.763449i | \(-0.723504\pi\) |
0.338233 | + | 0.941062i | \(0.390171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.3043 | − | 9.74634i | −1.19077 | − | 0.410032i | ||||
\(566\) | −15.5521 | −0.653705 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 15.6787i | − | 0.657863i | ||||||
\(569\) | 20.3139 | + | 11.7283i | 0.851605 | + | 0.491674i | 0.861192 | − | 0.508280i | \(-0.169718\pi\) |
−0.00958727 | + | 0.999954i | \(0.503052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.67946 | − | 13.3012i | −0.321376 | − | 0.556639i | 0.659397 | − | 0.751795i | \(-0.270812\pi\) |
−0.980772 | + | 0.195157i | \(0.937479\pi\) | |||||||
\(572\) | 6.83235 | + | 3.94466i | 0.285675 | + | 0.164934i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.260365 | − | 23.0631i | 0.0108674 | − | 0.962636i | ||||
\(575\) | 13.3477 | − | 5.39245i | 0.556639 | − | 0.224881i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.12041 | + | 12.3329i | 0.296426 | + | 0.513426i | 0.975316 | − | 0.220815i | \(-0.0708717\pi\) |
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(578\) | −12.7719 | − | 22.1216i | −0.531242 | − | 0.920139i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.96438 | − | 0.576179i | 0.123089 | − | 0.0239245i | ||||
\(581\) | 4.85690 | + | 8.63609i | 0.201498 | + | 0.358285i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.40975 | − | 4.27802i | −0.306881 | − | 0.177178i | ||||
\(584\) | −6.20837 | − | 10.7532i | −0.256904 | − | 0.444971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0057 | + | 5.77679i | 0.413331 | + | 0.238637i | ||||
\(587\) | − | 12.5249i | − | 0.516958i | −0.966017 | − | 0.258479i | \(-0.916779\pi\) | ||
0.966017 | − | 0.258479i | \(-0.0832212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.2560 | −2.15317 | ||||||||
\(590\) | −3.37478 | − | 1.16208i | −0.138938 | − | 0.0478420i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.25652 | − | 4.76690i | 0.339341 | − | 0.195919i | ||||
\(593\) | −12.7436 | − | 7.35750i | −0.523316 | − | 0.302136i | 0.214975 | − | 0.976620i | \(-0.431033\pi\) |
−0.738290 | + | 0.674483i | \(0.764366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.4070 | − | 24.9853i | 1.20557 | − | 1.02430i | ||||
\(596\) | 8.22305i | 0.336829i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.85148 | + | 15.3312i | 0.361964 | + | 0.626940i | ||||
\(599\) | 23.9304 | − | 13.8162i | 0.977769 | − | 0.564515i | 0.0761732 | − | 0.997095i | \(-0.475730\pi\) |
0.901596 | + | 0.432579i | \(0.142396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.82137i | − | 0.359831i | −0.983682 | − | 0.179916i | \(-0.942418\pi\) | ||
0.983682 | − | 0.179916i | \(-0.0575825\pi\) | |||||||
\(602\) | −14.1766 | − | 0.160043i | −0.577794 | − | 0.00652286i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.13357 | − | 3.69546i | 0.0868139 | − | 0.150366i | ||||
\(605\) | −15.7852 | + | 13.7215i | −0.641761 | + | 0.557860i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2677 | − | 22.9803i | 0.538519 | − | 0.932743i | −0.460465 | − | 0.887678i | \(-0.652317\pi\) |
0.998984 | − | 0.0450649i | \(-0.0143495\pi\) | |||||||
\(608\) | 6.03756i | 0.244855i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.9461 | + | 2.71067i | −0.564662 | + | 0.109752i | ||||
\(611\) | 4.29276 | + | 2.47843i | 0.173667 | + | 0.100266i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.791273 | + | 0.456842i | −0.0319592 | + | 0.0184517i | −0.515894 | − | 0.856652i | \(-0.672540\pi\) |
0.483935 | + | 0.875104i | \(0.339207\pi\) | |||||||
\(614\) | 1.28809 | − | 2.23103i | 0.0519830 | − | 0.0900371i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.73046 | + | 2.92060i | −0.0697223 | + | 0.117674i | ||||
\(617\) | 35.0558 | 1.41129 | 0.705646 | − | 0.708565i | \(-0.250657\pi\) | ||||
0.705646 | + | 0.708565i | \(0.250657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5382 | − | 9.54835i | 0.664727 | − | 0.383781i | −0.129348 | − | 0.991599i | \(-0.541289\pi\) |
0.794076 | + | 0.607819i | \(0.207955\pi\) | |||||||
\(620\) | 12.6969 | + | 14.6064i | 0.509918 | + | 0.586608i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.7140 | 0.990942 | ||||||||
\(623\) | 0.108697 | − | 9.62837i | 0.00435485 | − | 0.385753i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.04685 | + | 24.2577i | 0.241874 | + | 0.970308i | ||||
\(626\) | 4.50087 | + | 7.79573i | 0.179891 | + | 0.311580i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.41601 | + | 4.18466i | −0.0964095 | + | 0.166986i | ||||
\(629\) | −62.1849 | −2.47947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5350 | 0.857296 | 0.428648 | − | 0.903472i | \(-0.358990\pi\) | ||||
0.428648 | + | 0.903472i | \(0.358990\pi\) | |||||||
\(632\) | 5.59093 | − | 9.68377i | 0.222395 | − | 0.385200i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9529 | − | 20.7031i | −0.474712 | − | 0.822225i | ||||
\(635\) | −4.11558 | + | 11.9520i | −0.163322 | + | 0.474302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.3562 | + | 36.7788i | −0.885786 | + | 1.45723i | ||||
\(638\) | 1.73285 | 0.0686043 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.68760 | − | 1.46697i | 0.0667082 | − | 0.0579872i | ||||
\(641\) | 28.6767 | − | 16.5565i | 1.13266 | − | 0.653943i | 0.188060 | − | 0.982158i | \(-0.439780\pi\) |
0.944603 | + | 0.328214i | \(0.106447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.31191 | 0.130609 | 0.0653044 | − | 0.997865i | \(-0.479198\pi\) | ||||
0.0653044 | + | 0.997865i | \(0.479198\pi\) | |||||||
\(644\) | −6.63958 | + | 3.73407i | −0.261636 | + | 0.147143i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.6902 | − | 34.1044i | 0.774700 | − | 1.34182i | ||||
\(647\) | −20.2077 | + | 11.6669i | −0.794447 | + | 0.458674i | −0.841526 | − | 0.540217i | \(-0.818342\pi\) |
0.0470789 | + | 0.998891i | \(0.485009\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.77371 | − | 1.02405i | −0.0696244 | − | 0.0401977i | ||||
\(650\) | −28.5049 | + | 11.5159i | −1.11805 | + | 0.451691i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.7532i | 0.421128i | ||||||||
\(653\) | −8.73019 | + | 15.1211i | −0.341639 | + | 0.591735i | −0.984737 | − | 0.174048i | \(-0.944315\pi\) |
0.643099 | + | 0.765783i | \(0.277649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.0399 | + | 18.2892i | −0.822095 | + | 0.714619i | ||||
\(656\) | −4.35880 | + | 7.54966i | −0.170182 | + | 0.294765i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.08725 | + | 1.83501i | −0.0423854 | + | 0.0715363i | ||||
\(659\) | 1.29864i | 0.0505877i | 0.999680 | + | 0.0252939i | \(0.00805215\pi\) | ||||
−0.999680 | + | 0.0252939i | \(0.991948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.39869 | − | 2.53959i | 0.171089 | − | 0.0987785i | −0.412010 | − | 0.911179i | \(-0.635173\pi\) |
0.583099 | + | 0.812401i | \(0.301840\pi\) | |||||||
\(662\) | 2.18364 | + | 3.78217i | 0.0848695 | + | 0.146998i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.74493i | − | 0.145331i | ||||||
\(665\) | 33.6391 | + | 12.0098i | 1.30447 | + | 0.465719i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.36743 | + | 1.94419i | 0.130387 | + | 0.0752793i | ||||
\(668\) | −16.3910 | + | 9.46334i | −0.634186 | + | 0.366147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.92739 | + | 11.4055i | −0.151728 | + | 0.440633i | ||||
\(671\) | −8.15232 | −0.314717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.4124i | − | 0.709747i | −0.934914 | − | 0.354873i | \(-0.884524\pi\) | ||
0.934914 | − | 0.354873i | \(-0.115476\pi\) | |||||||
\(674\) | −16.9012 | − | 9.75794i | −0.651012 | − | 0.375862i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4029 | − | 21.4824i | −0.477033 | − | 0.826246i | ||||
\(677\) | −35.7491 | − | 20.6397i | −1.37395 | − | 0.793250i | −0.382526 | − | 0.923945i | \(-0.624946\pi\) |
−0.991423 | + | 0.130695i | \(0.958279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2201 | − | 11.3717i | 0.775976 | − | 0.436405i | ||||
\(680\) | −14.3170 | + | 2.78275i | −0.549031 | + | 0.106714i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.55271 | + | 9.61758i | 0.212624 | + | 0.368276i | ||||
\(683\) | 11.4896 | + | 19.9007i | 0.439639 | + | 0.761477i | 0.997662 | − | 0.0683485i | \(-0.0217730\pi\) |
−0.558022 | + | 0.829826i | \(0.688440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0217450 | − | 0.111876i | −0.000830833 | − | 0.00427454i | ||||
\(686\) | −15.7163 | − | 9.79790i | −0.600050 | − | 0.374085i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.64067 | + | 2.67929i | 0.176924 | + | 0.102147i | ||||
\(689\) | 20.5004 | + | 35.5077i | 0.781001 | + | 1.35273i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0048 | + | 6.35361i | 0.418642 | + | 0.241703i | 0.694496 | − | 0.719497i | \(-0.255627\pi\) |
−0.275854 | + | 0.961199i | \(0.588961\pi\) | |||||||
\(692\) | − | 11.8435i | − | 0.450223i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.9147 | −1.02167 | ||||||||
\(695\) | 0.764922 | − | 2.22141i | 0.0290151 | − | 0.0842627i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.2431 | − | 28.4305i | 1.86522 | − | 1.07688i | ||||
\(698\) | −8.99116 | − | 5.19105i | −0.340320 | − | 0.196484i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.81650 | − | 12.3208i | −0.182047 | − | 0.465681i | ||||
\(701\) | − | 26.5441i | − | 1.00256i | −0.865286 | − | 0.501279i | \(-0.832863\pi\) | ||
0.865286 | − | 0.501279i | \(-0.167137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.7804 | − | 49.8492i | −1.08548 | − | 1.88010i | ||||
\(704\) | 1.11120 | − | 0.641550i | 0.0418798 | − | 0.0241793i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.168951i | − | 0.00635856i | ||||||
\(707\) | 3.88444 | + | 2.30154i | 0.146089 | + | 0.0865582i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.1766 | + | 36.6789i | −0.795303 | + | 1.37751i | 0.127343 | + | 0.991859i | \(0.459355\pi\) |
−0.922646 | + | 0.385647i | \(0.873978\pi\) | |||||||
\(710\) | 23.0002 | + | 26.4594i | 0.863182 | + | 0.993002i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.81971 | + | 3.15183i | −0.0681964 | + | 0.118120i | ||||
\(713\) | 24.9196i | 0.933248i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.3170 | + | 3.36586i | −0.647618 | + | 0.125876i | ||||
\(716\) | 3.27843 | + | 1.89280i | 0.122521 | + | 0.0707374i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.6198 | + | 18.8330i | −1.21736 | + | 0.702843i | ||||
\(719\) | 11.9507 | − | 20.6992i | 0.445686 | − | 0.771951i | −0.552413 | − | 0.833570i | \(-0.686293\pi\) |
0.998100 | + | 0.0616189i | \(0.0196263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.309550 | + | 27.4199i | −0.0115282 | + | 1.02117i | ||||
\(722\) | 17.4521 | 0.649499 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.4574 | + | 9.50166i | −0.611633 | + | 0.353126i | ||||
\(725\) | −4.15745 | + | 5.32102i | −0.154404 | + | 0.197618i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4529 | 0.832731 | 0.416365 | − | 0.909197i | \(-0.363304\pi\) | ||||
0.416365 | + | 0.909197i | \(0.363304\pi\) | |||||||
\(728\) | 14.1792 | − | 7.97433i | 0.525517 | − | 0.295548i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.2519 | + | 9.03962i | 0.971627 | + | 0.334571i | ||||
\(731\) | −17.4759 | − | 30.2691i | −0.646368 | − | 1.11954i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.7725 | + | 23.8547i | −0.508700 | + | 0.881094i | 0.491249 | + | 0.871019i | \(0.336540\pi\) |
−0.999949 | + | 0.0100750i | \(0.996793\pi\) | |||||||
\(734\) | 15.1557 | 0.559409 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.87917 | 0.106128 | ||||||||
\(737\) | −3.46092 | + | 5.99449i | −0.127485 | + | 0.220810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5456 | − | 26.9258i | −0.571856 | − | 0.990483i | −0.996375 | − | 0.0850646i | \(-0.972890\pi\) |
0.424520 | − | 0.905419i | \(-0.360443\pi\) | |||||||
\(740\) | −6.94079 | + | 20.1567i | −0.255148 | + | 0.740975i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.3775 | + | 8.64824i | −0.564526 | + | 0.317487i | ||||
\(743\) | −1.12610 | −0.0413127 | −0.0206564 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206564 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0630 | − | 13.8772i | −0.441954 | − | 0.508422i | ||||
\(746\) | 10.4270 | − | 6.02002i | 0.381759 | − | 0.220409i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.36910 | −0.306005 | ||||||||
\(749\) | −0.343872 | + | 30.4602i | −0.0125648 | + | 1.11299i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.77108 | − | 8.26375i | 0.174099 | − | 0.301549i | −0.765750 | − | 0.643138i | \(-0.777632\pi\) |
0.939849 | + | 0.341590i | \(0.110965\pi\) | |||||||
\(752\) | 0.698165 | − | 0.403086i | 0.0254595 | − | 0.0146990i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.19135 | − | 4.15193i | −0.261894 | − | 0.151204i | ||||
\(755\) | 1.82051 | + | 9.36635i | 0.0662553 | + | 0.340876i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.1687i | − | 1.20554i | −0.797917 | − | 0.602768i | \(-0.794065\pi\) | ||
0.797917 | − | 0.602768i | \(-0.205935\pi\) | |||||||
\(758\) | 9.04589 | − | 15.6679i | 0.328562 | − | 0.569085i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.85692 | − | 10.1890i | −0.321274 | − | 0.369593i | ||||
\(761\) | −2.17122 | + | 3.76067i | −0.0787068 | + | 0.136324i | −0.902692 | − | 0.430287i | \(-0.858412\pi\) |
0.823985 | + | 0.566611i | \(0.191746\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.55242 | − | 2.69731i | −0.164809 | − | 0.0976493i | ||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.2480 | − | 14.5769i | 0.912246 | − | 0.526685i | ||||
\(767\) | 4.90729 | + | 8.49967i | 0.177192 | + | 0.306905i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.1795i | 1.66528i | 0.553818 | + | 0.832638i | \(0.313170\pi\) | ||||
−0.553818 | + | 0.832638i | \(0.686830\pi\) | |||||||
\(770\) | −1.36412 | − | 7.46735i | −0.0491593 | − | 0.269104i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.06479 | + | 1.76946i | 0.110304 | + | 0.0636842i | ||||
\(773\) | −15.5663 | + | 8.98723i | −0.559883 | + | 0.323248i | −0.753098 | − | 0.657908i | \(-0.771442\pi\) |
0.193216 | + | 0.981156i | \(0.438108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.8544 | − | 6.02387i | −1.53938 | − | 0.216384i | ||||
\(776\) | −8.76818 | −0.314759 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 19.6641i | − | 0.704994i | ||||||
\(779\) | 45.5815 | + | 26.3165i | 1.63313 | + | 0.942886i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0587 | + | 17.4221i | 0.359927 | + | 0.623412i | ||||
\(782\) | −16.2636 | − | 9.38978i | −0.581584 | − | 0.335778i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.36225 | + | 6.13965i | 0.120080 | + | 0.219273i | ||||
\(785\) | −2.06151 | − | 10.6063i | −0.0735785 | − | 0.378554i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.92087 | + | 11.9873i | 0.246702 | + | 0.427301i | 0.962609 | − | 0.270895i | \(-0.0873197\pi\) |
−0.715907 | + | 0.698196i | \(0.753986\pi\) | |||||||
\(788\) | −1.18364 | − | 2.05012i | −0.0421654 | − | 0.0730326i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.77057 | + | 24.5441i | 0.169729 | + | 0.873239i | ||||
\(791\) | −30.8726 | + | 17.3626i | −1.09770 | + | 0.617342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.8322 | + | 19.5330i | 1.20142 | + | 0.693638i | ||||
\(794\) | 2.84227 | + | 4.92295i | 0.100868 | + | 0.174709i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | + | 1.73205i | 0.106332 | + | 0.0613909i | ||||
\(797\) | 7.46138i | 0.264296i | 0.991230 | + | 0.132148i | \(0.0421874\pi\) | ||||
−0.991230 | + | 0.132148i | \(0.957813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.25831 | −0.186026 | ||||||||
\(800\) | −0.695987 | + | 4.95132i | −0.0246069 | + | 0.175056i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.84787 | + | 5.10832i | −0.312429 | + | 0.180381i | ||||
\(803\) | 13.7974 | + | 7.96596i | 0.486901 | + | 0.281113i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.72718 | − | 16.0417i | 0.201857 | − | 0.565395i | ||||
\(806\) | − | 53.2174i | − | 1.87450i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.853270 | − | 1.47791i | −0.0300179 | − | 0.0519926i | ||||
\(809\) | 1.28750 | − | 0.743340i | 0.0452662 | − | 0.0261344i | −0.477196 | − | 0.878797i | \(-0.658347\pi\) |
0.522462 | + | 0.852662i | \(0.325014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5494i | 1.10785i | 0.832567 | + | 0.553925i | \(0.186871\pi\) | ||||
−0.832567 | + | 0.553925i | \(0.813129\pi\) | |||||||
\(812\) | 1.82139 | − | 3.07407i | 0.0639182 | − | 0.107879i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.11641 | + | 10.5939i | −0.214380 | + | 0.371317i | ||||
\(815\) | −15.7747 | − | 18.1471i | −0.552562 | − | 0.635666i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.1764 | − | 28.0183i | 0.565940 | − | 0.980237i | ||||
\(818\) | − | 13.9683i | − | 0.488390i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.71923 | − | 19.1350i | −0.129881 | − | 0.668224i | ||||
\(821\) | 27.5430 | + | 15.9020i | 0.961257 | + | 0.554982i | 0.896560 | − | 0.442923i | \(-0.146058\pi\) |
0.0646976 | + | 0.997905i | \(0.479392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.7287 | + | 18.3186i | −1.10599 | + | 0.638545i | −0.937788 | − | 0.347207i | \(-0.887130\pi\) |
−0.168204 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(824\) | 5.18220 | − | 8.97583i | 0.180530 | − | 0.312688i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.68100 | + | 2.07018i | −0.128078 | + | 0.0720308i | ||||
\(827\) | 21.9864 | 0.764541 | 0.382271 | − | 0.924050i | \(-0.375142\pi\) | ||||
0.382271 | + | 0.924050i | \(0.375142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.0498 | + | 12.1531i | −0.731090 | + | 0.422095i | −0.818821 | − | 0.574049i | \(-0.805372\pi\) |
0.0877305 | + | 0.996144i | \(0.472039\pi\) | |||||||
\(830\) | 5.49370 | + | 6.31994i | 0.190689 | + | 0.219368i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.14864 | −0.213166 | ||||||||
\(833\) | 1.03076 | − | 45.6463i | 0.0357136 | − | 1.58155i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7790 | − | 40.0154i | 0.476841 | − | 1.38479i | ||||
\(836\) | −3.87339 | − | 6.70891i | −0.133964 | − | 0.232033i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.65904 | − | 9.80175i | 0.195488 | − | 0.338596i | ||||
\(839\) | −27.3914 | −0.945655 | −0.472827 | − | 0.881155i | \(-0.656767\pi\) | ||||
−0.472827 | + | 0.881155i | \(0.656767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1761 | 0.937107 | ||||||||
\(842\) | −6.95496 | + | 12.0463i | −0.239684 | + | 0.415145i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.18100 | + | 12.4379i | 0.247180 | + | 0.428129i | ||||
\(845\) | 52.4452 | + | 18.0590i | 1.80417 | + | 0.621250i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.279362 | + | 24.7459i | −0.00959899 | + | 0.850278i | ||||
\(848\) | 6.66826 | 0.228989 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.0791 | − | 25.6988i | 0.688707 | − | 0.881460i | ||||
\(851\) | −23.7719 | + | 13.7247i | −0.814890 | + | 0.470477i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.6073 | −0.774060 | −0.387030 | − | 0.922067i | \(-0.626499\pi\) | ||||
−0.387030 | + | 0.922067i | \(0.626499\pi\) | |||||||
\(854\) | −8.56884 | + | 14.4622i | −0.293220 | + | 0.494885i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.75680 | − | 9.97106i | 0.196763 | − | 0.340804i | ||||
\(857\) | 41.4461 | − | 23.9289i | 1.41577 | − | 0.817396i | 0.419848 | − | 0.907595i | \(-0.362083\pi\) |
0.995924 | + | 0.0901984i | \(0.0287501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5770 | + | 24.0045i | 1.41859 | + | 0.819022i | 0.996175 | − | 0.0873810i | \(-0.0278498\pi\) |
0.422413 | + | 0.906403i | \(0.361183\pi\) | |||||||
\(860\) | −11.7620 | + | 2.28616i | −0.401082 | + | 0.0779574i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26.0901i | − | 0.888634i | ||||||
\(863\) | 23.7785 | − | 41.1855i | 0.809428 | − | 1.40197i | −0.103832 | − | 0.994595i | \(-0.533110\pi\) |
0.913260 | − | 0.407376i | \(-0.133556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.3741 | + | 19.9871i | 0.590738 | + | 0.679583i | ||||
\(866\) | −4.21307 | + | 7.29726i | −0.143166 | + | 0.247971i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.8979 | + | 0.258500i | 0.777206 | + | 0.00877406i | ||||
\(869\) | 14.3474i | 0.486703i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.7257 | − | 16.5848i | 0.973334 | − | 0.561955i | ||||
\(872\) | 1.00000 | + | 1.73205i | 0.0338643 | + | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17.3831i | − | 0.587993i | ||||||
\(875\) | 26.2025 | + | 13.7269i | 0.885808 | + | 0.464052i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.0433 | − | 18.5002i | −1.08202 | − | 0.624707i | −0.150583 | − | 0.988597i | \(-0.548115\pi\) |
−0.931442 | + | 0.363890i | \(0.881448\pi\) | |||||||
\(878\) | −23.9529 | + | 13.8292i | −0.808372 | + | 0.466714i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.934120 | + | 2.71277i | −0.0314892 | + | 0.0914476i | ||||
\(881\) | 5.97213 | 0.201206 | 0.100603 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100603 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0589i | 0.372163i | 0.982534 | + | 0.186081i | \(0.0595788\pi\) | ||||
−0.982534 | + | 0.186081i | \(0.940421\pi\) | |||||||
\(884\) | 34.7319 | + | 20.0524i | 1.16816 | + | 0.674437i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.17861 | − | 2.04142i | −0.0395962 | − | 0.0685827i | ||||
\(887\) | 5.15346 | + | 2.97535i | 0.173036 | + | 0.0999026i | 0.584017 | − | 0.811742i | \(-0.301480\pi\) |
−0.410980 | + | 0.911644i | \(0.634814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.33169 | + | 13.0365i | 0.245897 | + | 0.437231i | ||||
\(890\) | −1.55270 | − | 7.98848i | −0.0520467 | − | 0.267774i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.79876 | − | 11.7758i | −0.227639 | − | 0.394283i | ||||
\(893\) | −2.43365 | − | 4.21521i | −0.0814391 | − | 0.141057i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.30937 | + | 1.61507i | −0.277752 | + | 0.0539859i | ||||
\(896\) | 0.0298666 | − | 2.64558i | 0.000997774 | − | 0.0883827i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0869 | − | 6.40105i | −0.369976 | − | 0.213606i | ||||
\(899\) | −5.84448 | − | 10.1229i | −0.194924 | − | 0.337619i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.6671 | − | 21.7471i | −1.25487 | − | 0.724500i | ||||
\(902\) | − | 11.1855i | − | 0.372438i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.3875 | 0.445261 | ||||||||
\(905\) | 13.8348 | − | 40.1775i | 0.459883 | − | 1.33554i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.9037 | + | 27.6572i | −1.59062 | + | 0.918343i | −0.597415 | + | 0.801932i | \(0.703805\pi\) |
−0.993201 | + | 0.116411i | \(0.962861\pi\) | |||||||
\(908\) | −10.7006 | − | 6.17797i | −0.355110 | − | 0.205023i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.2307 | + | 34.2580i | −0.405445 | + | 1.13564i | ||||
\(911\) | − | 35.2080i | − | 1.16649i | −0.812295 | − | 0.583246i | \(-0.801782\pi\) | ||
0.812295 | − | 0.583246i | \(-0.198218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.40256 | + | 4.16135i | 0.0795131 | + | 0.137721i | ||||
\(914\) | −29.8989 | + | 17.2621i | −0.988966 | + | 0.570980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.41341i | 0.0797414i | ||||||||
\(917\) | −0.372357 | + | 32.9833i | −0.0122963 | + | 1.08921i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4437 | − | 44.0698i | 0.839311 | − | 1.45373i | −0.0511601 | − | 0.998690i | \(-0.516292\pi\) |
0.890471 | − | 0.455039i | \(-0.150375\pi\) | |||||||
\(920\) | −4.85888 | + | 4.22366i | −0.160193 | + | 0.139250i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.1346 | − | 17.5537i | 0.333766 | − | 0.578099i | ||||
\(923\) | − | 96.4026i | − | 3.17313i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8560 | − | 44.1984i | −0.587103 | − | 1.45323i | ||||
\(926\) | 11.3662 | + | 6.56230i | 0.373518 | + | 0.215651i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.16959 | + | 0.675260i | −0.0383935 | + | 0.0221665i | ||||
\(929\) | 29.8405 | − | 51.6853i | 0.979036 | − | 1.69574i | 0.313118 | − | 0.949714i | \(-0.398627\pi\) |
0.665918 | − | 0.746025i | \(-0.268040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.0685 | − | 20.2998i | 1.21487 | − | 0.665298i | ||||
\(932\) | 12.8756 | 0.421754 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.32647 | + | 0.765836i | −0.0434033 | + | 0.0250589i | ||||
\(935\) | 14.1237 | − | 12.2772i | 0.461894 | − | 0.401509i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.2579 | −0.792471 | −0.396235 | − | 0.918149i | \(-0.629684\pi\) | ||||
−0.396235 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(938\) | 6.99643 | + | 12.4404i | 0.228442 | + | 0.406194i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.586908 | + | 1.70444i | −0.0191428 | + | 0.0555926i | ||||
\(941\) | 15.0539 | + | 26.0742i | 0.490744 | + | 0.849994i | 0.999943 | − | 0.0106549i | \(-0.00339164\pi\) |
−0.509199 | + | 0.860649i | \(0.670058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.5497 | − | 21.7367i | 0.408675 | − | 0.707845i | ||||
\(944\) | 1.59622 | 0.0519525 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.87560 | −0.223545 | ||||||||
\(947\) | −23.0812 | + | 39.9779i | −0.750039 | + | 1.29911i | 0.197764 | + | 0.980250i | \(0.436632\pi\) |
−0.947803 | + | 0.318857i | \(0.896701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.1730 | − | 66.1176i | −1.23915 | − | 2.14627i | ||||
\(950\) | 29.8939 | + | 4.20206i | 0.969886 | + | 0.136333i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.79670 | + | 14.8467i | −0.285103 | + | 0.481185i | ||||
\(953\) | −23.7121 | −0.768110 | −0.384055 | − | 0.923310i | \(-0.625473\pi\) | ||||
−0.384055 | + | 0.923310i | \(0.625473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.14922 | − | 4.77325i | −0.134266 | − | 0.154459i | ||||
\(956\) | 23.6032 | − | 13.6273i | 0.763382 | − | 0.440739i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.3170 | 0.947190 | ||||||||
\(959\) | −0.116015 | − | 0.0687391i | −0.00374632 | − | 0.00221970i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9558 | − | 38.0286i | 0.708252 | − | 1.22673i | ||||
\(962\) | 50.7663 | − | 29.3100i | 1.63677 | − | 0.944991i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.26690 | − | 1.30880i | −0.0730120 | − | 0.0421535i | ||||
\(965\) | −7.76789 | + | 1.50983i | −0.250057 | + | 0.0486030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 0.0922780i | − | 0.00296746i | −0.999999 | − | 0.00148373i | \(-0.999528\pi\) | ||
0.999999 | − | 0.00148373i | \(-0.000472286\pi\) | |||||||
\(968\) | 4.67683 | − | 8.10050i | 0.150319 | − | 0.260360i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.7972 | − | 12.8627i | 0.475109 | − | 0.412996i | ||||
\(971\) | 19.8502 | − | 34.3816i | 0.637024 | − | 1.10336i | −0.349058 | − | 0.937101i | \(-0.613498\pi\) |
0.986082 | − | 0.166257i | \(-0.0531683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.36267 | − | 2.42297i | −0.0436851 | − | 0.0776769i | ||||
\(974\) | − | 8.19540i | − | 0.262598i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.50239 | − | 3.17681i | 0.176127 | − | 0.101687i | ||||
\(977\) | 18.4035 | + | 31.8758i | 0.588779 | + | 1.01980i | 0.994393 | + | 0.105751i | \(0.0337246\pi\) |
−0.405613 | + | 0.914045i | \(0.632942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.66973i | − | 0.149245i | ||||||
\(980\) | −14.6808 | − | 5.42894i | −0.468962 | − | 0.173421i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.0206 | − | 20.2191i | −1.11755 | − | 0.645218i | ||||
\(983\) | 54.1899 | − | 31.2865i | 1.72839 | − | 0.997885i | 0.831693 | − | 0.555235i | \(-0.187372\pi\) |
0.896694 | − | 0.442650i | \(-0.145962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00498 | + | 1.72342i | 0.159472 | + | 0.0549128i | ||||
\(986\) | 8.80886 | 0.280531 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 37.1227i | 1.18103i | ||||||||
\(989\) | −13.3613 | − | 7.71414i | −0.424864 | − | 0.245295i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4019 | + | 30.1410i | 0.552791 | + | 0.957462i | 0.998072 | + | 0.0620708i | \(0.0197704\pi\) |
−0.445281 | + | 0.895391i | \(0.646896\pi\) | |||||||
\(992\) | −7.49558 | − | 4.32758i | −0.237985 | − | 0.137401i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 41.4793 | + | 0.468269i | 1.31564 | + | 0.0148526i | ||||
\(995\) | −7.60367 | + | 1.47791i | −0.241053 | + | 0.0468528i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4316 | + | 42.3167i | 0.773755 | + | 1.34018i | 0.935492 | + | 0.353349i | \(0.114957\pi\) |
−0.161736 | + | 0.986834i | \(0.551709\pi\) | |||||||
\(998\) | 8.72450 | + | 15.1113i | 0.276169 | + | 0.478339i | ||||
\(999\) | 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 | 630.2.bo.b.89.8 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.a.89.1 | ✓ | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1601.10 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1601.7 | 32 | |||
5.4 | even | 2 | 630.2.bo.a.89.3 | yes | 16 | ||
7.2 | even | 3 | 4410.2.d.a.4409.7 | 16 | |||
7.3 | odd | 6 | inner | 630.2.bo.b.269.6 | yes | 16 | |
7.5 | odd | 6 | 4410.2.d.a.4409.10 | 16 | |||
15.2 | even | 4 | 3150.2.bf.f.1601.8 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1601.9 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.b.89.6 | yes | 16 | |
21.2 | odd | 6 | 4410.2.d.b.4409.10 | 16 | |||
21.5 | even | 6 | 4410.2.d.b.4409.7 | 16 | |||
21.17 | even | 6 | 630.2.bo.a.269.3 | yes | 16 | ||
35.3 | even | 12 | 3150.2.bf.f.1151.9 | 32 | |||
35.9 | even | 6 | 4410.2.d.b.4409.8 | 16 | |||
35.17 | even | 12 | 3150.2.bf.f.1151.8 | 32 | |||
35.19 | odd | 6 | 4410.2.d.b.4409.9 | 16 | |||
35.24 | odd | 6 | 630.2.bo.a.269.1 | yes | 16 | ||
105.17 | odd | 12 | 3150.2.bf.f.1151.10 | 32 | |||
105.38 | odd | 12 | 3150.2.bf.f.1151.7 | 32 | |||
105.44 | odd | 6 | 4410.2.d.a.4409.9 | 16 | |||
105.59 | even | 6 | inner | 630.2.bo.b.269.8 | yes | 16 | |
105.89 | even | 6 | 4410.2.d.a.4409.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.1 | ✓ | 16 | 3.2 | odd | 2 | ||
630.2.bo.a.89.3 | yes | 16 | 5.4 | even | 2 | ||
630.2.bo.a.269.1 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bo.a.269.3 | yes | 16 | 21.17 | even | 6 | ||
630.2.bo.b.89.6 | yes | 16 | 15.14 | odd | 2 | inner | |
630.2.bo.b.89.8 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.b.269.6 | yes | 16 | 7.3 | odd | 6 | inner | |
630.2.bo.b.269.8 | yes | 16 | 105.59 | even | 6 | inner | |
3150.2.bf.f.1151.7 | 32 | 105.38 | odd | 12 | |||
3150.2.bf.f.1151.8 | 32 | 35.17 | even | 12 | |||
3150.2.bf.f.1151.9 | 32 | 35.3 | even | 12 | |||
3150.2.bf.f.1151.10 | 32 | 105.17 | odd | 12 | |||
3150.2.bf.f.1601.7 | 32 | 5.3 | odd | 4 | |||
3150.2.bf.f.1601.8 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1601.9 | 32 | 15.8 | even | 4 | |||
3150.2.bf.f.1601.10 | 32 | 5.2 | odd | 4 | |||
4410.2.d.a.4409.7 | 16 | 7.2 | even | 3 | |||
4410.2.d.a.4409.8 | 16 | 105.89 | even | 6 | |||
4410.2.d.a.4409.9 | 16 | 105.44 | odd | 6 | |||
4410.2.d.a.4409.10 | 16 | 7.5 | odd | 6 | |||
4410.2.d.b.4409.7 | 16 | 21.5 | even | 6 | |||
4410.2.d.b.4409.8 | 16 | 35.9 | even | 6 | |||
4410.2.d.b.4409.9 | 16 | 35.19 | odd | 6 | |||
4410.2.d.b.4409.10 | 16 | 21.2 | odd | 6 |