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 | 89.6 | ||
Root | \(1.68760 + 1.46697i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.89 |
Dual form | 630.2.bo.b.269.6 |
$q$-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 | ||||
\(5\) | 1.68760 | + | 1.46697i | 0.754718 | + | 0.656050i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.30608 | + | 1.29693i | −0.871614 | + | 0.490192i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.11423 | − | 0.728019i | 0.668580 | − | 0.230220i | ||||
\(11\) | −1.11120 | + | 0.641550i | −0.335038 | + | 0.193435i | −0.658076 | − | 0.752952i | \(-0.728629\pi\) |
0.323037 | + | 0.946386i | \(0.395296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.14864 | 1.70533 | 0.852663 | − | 0.522462i | \(-0.174986\pi\) | ||||
0.852663 | + | 0.522462i | \(0.174986\pi\) | |||||||
\(14\) | −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 | ||||||||
\(25\) | 0.695987 | + | 4.95132i | 0.139197 | + | 0.990265i | ||||
\(26\) | 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 | \(-0.959981\pi\) | ||
0.992107 | − | 0.125393i | \(-0.0400191\pi\) | |||||||
\(30\) | 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 | ||||||
\(35\) | −5.79429 | − | 1.19425i | −0.979413 | − | 0.201866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.25652 | + | 4.76690i | 1.35736 | + | 0.783674i | 0.989268 | − | 0.146114i | \(-0.0466766\pi\) |
0.368095 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(38\) | 5.22868 | − | 3.01878i | 0.848203 | − | 0.489710i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.68760 | − | 1.46697i | −0.266833 | − | 0.231949i | ||||
\(41\) | −8.71759 | −1.36146 | −0.680730 | − | 0.732535i | \(-0.738337\pi\) | ||||
−0.680730 | + | 0.732535i | \(0.738337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.35859i | 0.817177i | 0.912719 | + | 0.408588i | \(0.133979\pi\) | ||||
−0.912719 | + | 0.408588i | \(0.866021\pi\) | |||||||
\(44\) | 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 | 0.913290 | − | 0.407309i | \(-0.133533\pi\) |
−0.809385 | + | 0.587278i | \(0.800200\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 10.3764 | + | 9.01988i | 1.28704 | + | 1.11878i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.67188 | − | 2.69731i | 0.570761 | − | 0.329529i | −0.186692 | − | 0.982418i | \(-0.559777\pi\) |
0.757453 | + | 0.652889i | \(0.226443\pi\) | |||||||
\(68\) | −5.64871 | − | 3.26128i | −0.685006 | − | 0.395489i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.93140 | + | 4.42087i | −0.469892 | + | 0.528395i | ||||
\(71\) | − | 15.6787i | − | 1.86072i | −0.366650 | − | 0.930359i | \(-0.619495\pi\) | ||
0.366650 | − | 0.930359i | \(-0.380505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.20837 | − | 10.7532i | −0.726635 | − | 1.25857i | −0.958298 | − | 0.285772i | \(-0.907750\pi\) |
0.231663 | − | 0.972796i | \(-0.425583\pi\) | |||||||
\(74\) | 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 | \(0.950120\pi\) | |||||||
\(80\) | −2.11423 | + | 0.728019i | −0.236379 | + | 0.0813949i | ||||
\(81\) | 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 | −0.946206 | − | 0.323564i | \(-0.895119\pi\) |
0.753318 | + | 0.657657i | \(0.228452\pi\) | |||||||
\(90\) | 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 | ||||
\(95\) | 4.39545 | + | 12.7648i | 0.450964 | + | 1.30964i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.76818 | −0.890274 | −0.445137 | − | 0.895463i | \(-0.646845\pi\) | ||||
−0.445137 | + | 0.895463i | \(0.646845\pi\) | |||||||
\(98\) | −3.36225 | − | 6.13965i | −0.339639 | − | 0.620198i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.93998 | − | 3.07840i | 0.393998 | − | 0.307840i | ||||
\(101\) | −0.853270 | − | 1.47791i | −0.0849035 | − | 0.147057i | 0.820447 | − | 0.571723i | \(-0.193725\pi\) |
−0.905350 | + | 0.424666i | \(0.860392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.18220 | − | 8.97583i | 0.510617 | − | 0.884415i | −0.489307 | − | 0.872112i | \(-0.662750\pi\) |
0.999924 | − | 0.0123035i | \(-0.00391643\pi\) | |||||||
\(104\) | −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 | \(0.863869\pi\) | |||||||
\(110\) | −1.88227 | + | 2.16536i | −0.179468 | + | 0.206459i | ||||
\(111\) | 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 | ||||||||
\(115\) | 6.08724 | − | 2.09609i | 0.567638 | − | 0.195461i | ||||
\(116\) | −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 | \(-0.919301\pi\) | ||
0.968035 | − | 0.250817i | \(-0.0806992\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.9997 | − | 4.47632i | 1.14015 | − | 0.392599i | ||||
\(131\) | 6.23366 | − | 10.7970i | 0.544638 | − | 0.943340i | −0.453992 | − | 0.891006i | \(-0.650001\pi\) |
0.998630 | − | 0.0523344i | \(-0.0166662\pi\) | |||||||
\(132\) | 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 | \(-0.0141883\pi\) | |||||||
\(140\) | 1.86289 | + | 5.61513i | 0.157443 | + | 0.474565i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.5781 | − | 7.83934i | −1.13945 | − | 0.657863i | ||||
\(143\) | −6.83235 | + | 3.94466i | −0.571350 | + | 0.329869i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.98118 | − | 2.27914i | 0.164528 | − | 0.189272i | ||||
\(146\) | −12.4167 | −1.02762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.53381i | − | 0.783674i | ||||||
\(149\) | 7.12137 | + | 4.11153i | 0.583406 | + | 0.336829i | 0.762486 | − | 0.647005i | \(-0.223979\pi\) |
−0.179080 | + | 0.983835i | \(0.557312\pi\) | |||||||
\(150\) | 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 | 0.946183 | − | 0.323631i | \(-0.104904\pi\) |
−0.753364 | + | 0.657603i | \(0.771570\pi\) | |||||||
\(158\) | 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 | 0.818208 | − | 0.574922i | \(-0.194968\pi\) |
−0.0887927 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(164\) | 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 | ||||||||
\(170\) | 9.56842 | − | 11.0075i | 0.733864 | − | 0.844235i | ||||
\(171\) | 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 | ||||||||
\(175\) | −8.02650 | − | 10.5155i | −0.606746 | − | 0.794896i | ||||
\(176\) | − | 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 | −0.372450 | − | 0.928052i | \(-0.621482\pi\) |
0.617492 | + | 0.786577i | \(0.288149\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | 6.94079 | + | 20.1567i | 0.510297 | + | 1.48195i | ||||
\(186\) | 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 | 0.585995 | − | 0.810315i | \(-0.300704\pi\) |
−0.408756 | + | 0.912644i | \(0.634037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.06479 | − | 1.76946i | 0.220608 | − | 0.127368i | −0.385623 | − | 0.922656i | \(-0.626014\pi\) |
0.606232 | + | 0.795288i | \(0.292680\pi\) | |||||||
\(194\) | −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 | \(0.372515\pi\) | |||||||
\(200\) | −0.695987 | − | 4.95132i | −0.0492137 | − | 0.350111i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.70654 | −0.120072 | ||||||||
\(203\) | 1.75153 | + | 3.11440i | 0.122933 | + | 0.218588i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.7118 | − | 12.7885i | −1.02752 | − | 0.893185i | ||||
\(206\) | −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 | ||||
\(215\) | −7.86090 | + | 9.04315i | −0.536109 | + | 0.616738i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.6728 | − | 19.7009i | 0.792403 | − | 1.33739i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.934120 | + | 2.71277i | 0.0629784 | + | 0.182895i | ||||
\(221\) | 34.7319 | − | 20.0524i | 2.33632 | − | 1.34887i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5975 | −0.910557 | −0.455279 | − | 0.890349i | \(-0.650460\pi\) | ||||
−0.455279 | + | 0.890349i | \(0.650460\pi\) | |||||||
\(224\) | −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 | ||||||||
\(235\) | −0.586908 | − | 1.70444i | −0.0382857 | − | 0.111185i | ||||
\(236\) | 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 | \(-0.656549\pi\) | ||
0.472226 | − | 0.881478i | \(-0.343451\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 14.9109 | − | 4.76072i | 0.952624 | − | 0.304151i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.1492 | + | 18.5614i | 2.04561 | + | 1.18103i | ||||
\(248\) | 7.49558 | − | 4.32758i | 0.475970 | − | 0.274801i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.07614 | + | 9.96157i | 0.321043 | + | 0.630025i | ||||
\(251\) | −26.7173 | −1.68638 | −0.843190 | − | 0.537615i | \(-0.819325\pi\) | ||||
−0.843190 | + | 0.537615i | \(0.819325\pi\) | |||||||
\(252\) | 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 | 0.997331 | − | 0.0730091i | \(-0.0232602\pi\) |
−0.561893 | + | 0.827210i | \(0.689927\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −3.94990 | − | 5.05538i | −0.238188 | − | 0.304851i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4270 | + | 6.02002i | −0.626497 | + | 0.361708i | −0.779394 | − | 0.626534i | \(-0.784473\pi\) |
0.152897 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(278\) | −0.909924 | − | 0.525345i | −0.0545736 | − | 0.0315081i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.79429 | + | 1.19425i | 0.346275 | + | 0.0713704i | ||||
\(281\) | 12.7879i | 0.762861i | 0.924397 | + | 0.381431i | \(0.124569\pi\) | ||||
−0.924397 | + | 0.381431i | \(0.875431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.77607 | + | 13.4685i | 0.462239 | + | 0.800622i | 0.999072 | − | 0.0430666i | \(-0.0137128\pi\) |
−0.536833 | + | 0.843689i | \(0.680379\pi\) | |||||||
\(284\) | −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 | ||||
\(290\) | −0.983204 | − | 2.85532i | −0.0577357 | − | 0.167670i | ||||
\(291\) | 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 | ||||
\(305\) | −4.62555 | − | 13.4330i | −0.264858 | − | 0.769173i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.57617 | −0.147030 | −0.0735150 | − | 0.997294i | \(-0.523422\pi\) | ||||
−0.0735150 | + | 0.997294i | \(0.523422\pi\) | |||||||
\(308\) | −3.39455 | − | 0.0383219i | −0.193422 | − | 0.00218359i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.6969 | + | 14.6064i | −0.721133 | + | 0.829590i | ||||
\(311\) | −12.3570 | − | 21.4030i | −0.700702 | − | 1.21365i | −0.968220 | − | 0.250098i | \(-0.919537\pi\) |
0.267519 | − | 0.963553i | \(-0.413796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50087 | − | 7.79573i | 0.254404 | − | 0.440641i | −0.710329 | − | 0.703869i | \(-0.751454\pi\) |
0.964733 | + | 0.263229i | \(0.0847874\pi\) | |||||||
\(314\) | 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 | ||||
\(320\) | 1.68760 | + | 1.46697i | 0.0943397 | + | 0.0820062i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.55359 | + | 3.88301i | 0.365217 | + | 0.216392i | ||||
\(323\) | 39.3804 | 2.19118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.27937 | + | 30.4439i | 0.237377 | + | 1.68872i | ||||
\(326\) | 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 | \(0.178390\pi\) | ||||
−0.847028 | + | 0.531549i | \(0.821610\pi\) | |||||||
\(338\) | 12.4029 | − | 21.4824i | 0.674627 | − | 1.16849i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.74855 | − | 13.7902i | −0.257526 | − | 0.747881i | ||||
\(341\) | 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 | \(-0.0896286\pi\) | |||||||
\(350\) | −13.1199 | + | 1.69341i | −0.701289 | + | 0.0905167i | ||||
\(351\) | 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 | ||||||||
\(355\) | 23.0002 | − | 26.4594i | 1.22072 | − | 1.40432i | ||||
\(356\) | 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 | \(0.131692\pi\) |
0.805975 | + | 0.591949i | \(0.201641\pi\) | |||||||
\(360\) | 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 | 0.597611 | − | 0.801786i | \(-0.296117\pi\) |
−0.993173 | + | 0.116653i | \(0.962783\pi\) | |||||||
\(368\) | 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 | 0.205145 | − | 0.978732i | \(-0.434233\pi\) |
−0.745034 | + | 0.667027i | \(0.767567\pi\) | |||||||
\(374\) | 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 | \(0.346178\pi\) | |||||||
\(380\) | 8.85692 | − | 10.1890i | 0.454351 | − | 0.522684i | ||||
\(381\) | 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 | ||||||||
\(385\) | 7.20477 | − | 2.39027i | 0.367189 | − | 0.121819i | ||||
\(386\) | − | 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 | −0.865162 | − | 0.501493i | \(-0.832784\pi\) |
0.00172432 | + | 0.999999i | \(0.499451\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | −23.6411 | + | 8.14060i | −1.18951 | + | 0.409598i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.84227 | − | 4.92295i | 0.142649 | − | 0.247076i | −0.785844 | − | 0.618425i | \(-0.787771\pi\) |
0.928493 | + | 0.371349i | \(0.121105\pi\) | |||||||
\(398\) | 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 | 0.704378 | − | 0.709825i | \(-0.251226\pi\) |
−0.262537 | + | 0.964922i | \(0.584559\pi\) | |||||||
\(402\) | 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 | \(0.221096\pi\) | |||||||
\(410\) | −18.4310 | + | 6.34657i | −0.910244 | + | 0.313435i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.3644 | −0.510617 | ||||||||
\(413\) | −3.63333 | − | 2.15275i | −0.178784 | − | 0.105930i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.49370 | + | 6.31994i | −0.269675 | + | 0.310234i | ||||
\(416\) | 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 | \(-0.589162\pi\) | ||||
−0.276462 | + | 0.961025i | \(0.589162\pi\) | |||||||
\(420\) | 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 | ||||
\(425\) | 20.0791 | + | 25.6988i | 0.973979 | + | 1.24657i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.8090 | + | 0.189761i | 0.813445 | + | 0.00918318i | ||||
\(428\) | 11.5136 | 0.556531 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.90115 | + | 11.3293i | 0.188130 | + | 0.546348i | ||||
\(431\) | −22.5947 | + | 13.0451i | −1.08835 | + | 0.628359i | −0.933137 | − | 0.359522i | \(-0.882940\pi\) |
−0.155213 | + | 0.987881i | \(0.549606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.42614 | 0.404935 | 0.202467 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202467 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(434\) | −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 | ||||||||
\(445\) | −7.69458 | + | 2.64956i | −0.364758 | + | 0.125601i | ||||
\(446\) | −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 | \(0.0976824\pi\) | ||||
−0.953281 | + | 0.302084i | \(0.902318\pi\) | |||||||
\(450\) | 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 | ||||||
\(455\) | −35.6270 | − | 7.34304i | −1.67022 | − | 0.344247i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.8989 | + | 17.2621i | 1.39861 | + | 0.807488i | 0.994247 | − | 0.107111i | \(-0.0341601\pi\) |
0.404363 | + | 0.914599i | \(0.367493\pi\) | |||||||
\(458\) | −2.09008 | + | 1.20671i | −0.0976628 | + | 0.0563857i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.85888 | − | 4.22366i | −0.226547 | − | 0.196929i | ||||
\(461\) | −20.2692 | −0.944032 | −0.472016 | − | 0.881590i | \(-0.656474\pi\) | ||||
−0.472016 | + | 0.881590i | \(0.656474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.1246i | − | 0.609952i | −0.952360 | − | 0.304976i | \(-0.901352\pi\) | ||
0.952360 | − | 0.304976i | \(-0.0986485\pi\) | |||||||
\(464\) | 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 | \(-0.933062\pi\) |
0.308205 | − | 0.951320i | \(-0.400272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.7663 | + | 29.3100i | 2.31475 | + | 1.33642i | ||||
\(482\) | − | 2.61759i | − | 0.119228i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.35366 | 0.425166 | ||||||||
\(485\) | −14.7972 | − | 12.8627i | −0.671905 | − | 0.584064i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.09743 | + | 4.09770i | −0.321615 | + | 0.185685i | −0.652112 | − | 0.758122i | \(-0.726117\pi\) |
0.330497 | + | 0.943807i | \(0.392784\pi\) | |||||||
\(488\) | 5.50239 | + | 3.17681i | 0.249082 | + | 0.143807i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.33256 | − | 15.2936i | 0.150550 | − | 0.690894i | ||||
\(491\) | 40.4383i | 1.82495i | 0.409129 | + | 0.912477i | \(0.365833\pi\) | ||||
−0.409129 | + | 0.912477i | \(0.634167\pi\) | |||||||
\(492\) | 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 | \(0.294386\pi\) | |||||||
\(500\) | 11.1650 | + | 0.584722i | 0.499316 | + | 0.0261496i | ||||
\(501\) | 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 | −0.716556 | − | 0.697529i | \(-0.754283\pi\) |
0.962356 | + | 0.271792i | \(0.0876161\pi\) | |||||||
\(510\) | 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 | ||||
\(515\) | 21.9128 | − | 7.54547i | 0.965592 | − | 0.332493i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.03440 | 0.0454928 | ||||||||
\(518\) | −12.8578 | + | 21.7009i | −0.564941 | + | 0.953484i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.3764 | − | 9.01988i | −0.455037 | − | 0.395548i | ||||
\(521\) | 19.8706 | + | 34.4168i | 0.870546 | + | 1.50783i | 0.861433 | + | 0.507871i | \(0.169567\pi\) |
0.00911254 | + | 0.999958i | \(0.497099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6404 | − | 27.0900i | 0.683907 | − | 1.18456i | −0.289872 | − | 0.957065i | \(-0.593613\pi\) |
0.973779 | − | 0.227496i | \(-0.0730538\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −11.2534 | − | 9.78215i | −0.488815 | − | 0.424909i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.83026 | + | 13.9231i | 0.339485 | + | 0.603641i | ||||
\(533\) | −53.6013 | −2.32173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.3424 | + | 8.38211i | −1.05242 | + | 0.362390i | ||||
\(536\) | −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 | \(-0.666275\pi\) | ||
0.498934 | − | 0.866640i | \(-0.333725\pi\) | |||||||
\(548\) | −0.0254843 | + | 0.0441401i | −0.00108863 | + | 0.00188557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.35304 | + | 0.893021i | −0.270895 | + | 0.0380785i | ||||
\(551\) | 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 | ||||||||
\(560\) | 3.93140 | − | 4.42087i | 0.166132 | − | 0.186816i | ||||
\(561\) | 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 | ||||||||
\(565\) | −22.5927 | − | 19.6391i | −0.950483 | − | 0.826222i | ||||
\(566\) | 15.5521 | 0.653705 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.6787i | 0.657863i | ||||||||
\(569\) | −20.3139 | − | 11.7283i | −0.851605 | − | 0.491674i | 0.00958727 | − | 0.999954i | \(-0.496948\pi\) |
−0.861192 | + | 0.508280i | \(0.830282\pi\) | |||||||
\(570\) | 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 | 0.678889 | − | 0.734241i | \(-0.262462\pi\) |
−0.975316 | + | 0.220815i | \(0.929128\pi\) | |||||||
\(578\) | −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 | ||||||||
\(590\) | 2.69378 | + | 2.34161i | 0.110901 | + | 0.0964025i | ||||
\(591\) | 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 | ||||||||
\(595\) | −36.6250 | + | 12.1508i | −1.50148 | + | 0.498135i | ||||
\(596\) | − | 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 | −0.901596 | − | 0.432579i | \(-0.857604\pi\) |
−0.0761732 | + | 0.997095i | \(0.524270\pi\) | |||||||
\(600\) | 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 | ||||
\(605\) | −19.7758 | + | 6.80963i | −0.804002 | + | 0.276851i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.2677 | + | 22.9803i | −0.538519 | + | 0.932743i | 0.460465 | + | 0.887678i | \(0.347683\pi\) |
−0.998984 | + | 0.0450649i | \(0.985651\pi\) | |||||||
\(608\) | 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 | −0.483935 | − | 0.875104i | \(-0.660793\pi\) |
0.515894 | + | 0.856652i | \(0.327460\pi\) | |||||||
\(614\) | −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 | \(0.207955\pi\) | |||||||
\(620\) | 6.30111 | + | 18.2990i | 0.253059 | + | 0.734906i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.7140 | −0.990942 | ||||||||
\(623\) | 0.108697 | − | 9.62837i | 0.00435485 | − | 0.385753i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0312 | + | 6.89212i | −0.961248 | + | 0.275685i | ||||
\(626\) | −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 | ||||
\(635\) | 8.29298 | − | 9.54022i | 0.329097 | − | 0.378592i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3562 | − | 36.7788i | 0.885786 | − | 1.45723i | ||||
\(638\) | 1.73285 | 0.0686043 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.11423 | − | 0.728019i | 0.0835725 | − | 0.0287775i | ||||
\(641\) | −28.6767 | + | 16.5565i | −1.13266 | + | 0.653943i | −0.944603 | − | 0.328214i | \(-0.893553\pi\) |
−0.188060 | + | 0.982158i | \(0.560220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.31191 | −0.130609 | −0.0653044 | − | 0.997865i | \(-0.520802\pi\) | ||||
−0.0653044 | + | 0.997865i | \(0.520802\pi\) | |||||||
\(644\) | 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 | ||||||||
\(655\) | 26.3589 | − | 9.07644i | 1.02993 | − | 0.354646i | ||||
\(656\) | 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 | \(-0.991948\pi\) | ||
0.999680 | − | 0.0252939i | \(-0.00805215\pi\) | |||||||
\(660\) | 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 | ||||||
\(665\) | −26.6913 | − | 23.7360i | −1.03504 | − | 0.920444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.36743 | − | 1.94419i | −0.130387 | − | 0.0752793i | ||||
\(668\) | −16.3910 | + | 9.46334i | −0.634186 | + | 0.366147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.91377 | − | 9.10397i | 0.305735 | − | 0.351717i | ||||
\(671\) | 8.15232 | 0.314717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4124i | 0.709747i | 0.934914 | + | 0.354873i | \(0.115476\pi\) | ||||
−0.934914 | + | 0.354873i | \(0.884524\pi\) | |||||||
\(674\) | 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 | ||||||||
\(695\) | 1.54133 | − | 1.77314i | 0.0584661 | − | 0.0672592i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.2431 | + | 28.4305i | −1.86522 | + | 1.07688i | ||||
\(698\) | −8.99116 | − | 5.19105i | −0.340320 | − | 0.196484i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.09342 | + | 12.2089i | −0.192513 | + | 0.461453i | ||||
\(701\) | 26.5441i | 1.00256i | 0.865286 | + | 0.501279i | \(0.167137\pi\) | ||||
−0.865286 | + | 0.501279i | \(0.832863\pi\) | |||||||
\(702\) | 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 | \(0.873978\pi\) | |||||||
\(710\) | −11.4144 | − | 33.1484i | −0.428374 | − | 1.24404i | ||||
\(711\) | 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 | −0.998100 | − | 0.0616189i | \(-0.980374\pi\) |
0.552413 | + | 0.833570i | \(0.313707\pi\) | |||||||
\(720\) | 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 | ||||
\(725\) | 6.68686 | − | 0.939945i | 0.248344 | − | 0.0349087i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.4529 | −0.832731 | −0.416365 | − | 0.909197i | \(-0.636696\pi\) | ||||
−0.416365 | + | 0.909197i | \(0.636696\pi\) | |||||||
\(728\) | 14.1792 | − | 7.97433i | 0.525517 | − | 0.295548i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.9545 | − | 18.2150i | −0.775560 | − | 0.674168i | ||||
\(731\) | 17.4759 | + | 30.2691i | 0.646368 | + | 1.11954i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7725 | − | 23.8547i | 0.508700 | − | 0.881094i | −0.491249 | − | 0.871019i | \(-0.663460\pi\) |
0.999949 | − | 0.0100750i | \(-0.00320702\pi\) | |||||||
\(734\) | −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 | \(-0.360443\pi\) | |||||||
\(740\) | 13.9858 | − | 16.0893i | 0.514129 | − | 0.591453i | ||||
\(741\) | 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 | ||||||||
\(745\) | 5.98654 | + | 17.3855i | 0.219330 | + | 0.636954i | ||||
\(746\) | −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 | \(0.205935\pi\) | ||||
−0.797917 | + | 0.602768i | \(0.794065\pi\) | |||||||
\(758\) | 9.04589 | − | 15.6679i | 0.328562 | − | 0.569085i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.39545 | − | 12.7648i | −0.159440 | − | 0.463028i | ||||
\(761\) | 2.17122 | − | 3.76067i | 0.0787068 | − | 0.136324i | −0.823985 | − | 0.566611i | \(-0.808254\pi\) |
0.902692 | + | 0.430287i | \(0.141588\pi\) | |||||||
\(762\) | 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 | \(0.686830\pi\) | |||||||
\(770\) | 1.53235 | − | 7.43465i | 0.0552220 | − | 0.267926i | ||||
\(771\) | 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 | ||||||||
\(775\) | −26.6441 | − | 34.1011i | −0.957083 | − | 1.22495i | ||||
\(776\) | 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 | 0.715907 | − | 0.698196i | \(-0.246014\pi\) |
−0.962609 | + | 0.270895i | \(0.912680\pi\) | |||||||
\(788\) | −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 | ||||||||
\(800\) | −3.93998 | + | 3.07840i | −0.139299 | + | 0.108838i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.84787 | − | 5.10832i | 0.312429 | − | 0.180381i | ||||
\(803\) | 13.7974 | + | 7.96596i | 0.486901 | + | 0.281113i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.3192 | + | 12.7284i | −0.398948 | + | 0.448618i | ||||
\(806\) | 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 | −0.522462 | − | 0.852662i | \(-0.674986\pi\) |
0.477196 | + | 0.878797i | \(0.341653\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | 7.82854 | + | 22.7348i | 0.274222 | + | 0.796366i | ||||
\(816\) | 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 | −0.0646976 | − | 0.997905i | \(-0.520608\pi\) |
−0.896560 | + | 0.442923i | \(0.853942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.7287 | − | 18.3186i | 1.10599 | − | 0.638545i | 0.168204 | − | 0.985752i | \(-0.446203\pi\) |
0.937788 | + | 0.347207i | \(0.112870\pi\) | |||||||
\(824\) | −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 | \(0.472039\pi\) | |||||||
\(830\) | 2.72638 | + | 7.91766i | 0.0946339 | + | 0.274826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.14864 | 0.213166 | ||||||||
\(833\) | 1.03076 | − | 45.6463i | 0.0357136 | − | 1.58155i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7649 | − | 31.9406i | 0.960844 | − | 1.10535i | ||||
\(836\) | 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 | \(-0.343233\pi\) | ||||
0.472827 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(840\) | 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 | ||||
\(845\) | 41.8622 | + | 36.3893i | 1.44010 | + | 1.25183i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.279362 | − | 24.7459i | 0.00959899 | − | 0.850278i | ||||
\(848\) | 6.66826 | 0.228989 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.2953 | − | 4.53962i | 1.10772 | − | 0.155708i | ||||
\(851\) | 23.7719 | − | 13.7247i | 0.814890 | − | 0.470477i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6073 | 0.774060 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(854\) | 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 | ||||||||
\(865\) | 8.62231 | + | 25.0400i | 0.293167 | + | 0.851386i | ||||
\(866\) | 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 | ||||||
\(875\) | 1.88039 | − | 29.5206i | 0.0635689 | − | 0.997977i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0433 | + | 18.5002i | 1.08202 | + | 0.624707i | 0.931442 | − | 0.363890i | \(-0.118552\pi\) |
0.150583 | + | 0.988597i | \(0.451885\pi\) | |||||||
\(878\) | −23.9529 | + | 13.8292i | −0.808372 | + | 0.466714i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.88227 | − | 2.16536i | 0.0634513 | − | 0.0729942i | ||||
\(881\) | −5.97213 | −0.201206 | −0.100603 | − | 0.994927i | \(-0.532077\pi\) | ||||
−0.100603 | + | 0.994927i | \(0.532077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11.0589i | − | 0.372163i | −0.982534 | − | 0.186081i | \(-0.940421\pi\) | ||
0.982534 | − | 0.186081i | \(-0.0595788\pi\) | |||||||
\(884\) | −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 | ||||||||
\(905\) | 27.8773 | − | 32.0700i | 0.926674 | − | 1.06604i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.9037 | − | 27.6572i | 1.59062 | − | 0.918343i | 0.597415 | − | 0.801932i | \(-0.296195\pi\) |
0.993201 | − | 0.116411i | \(-0.0371388\pi\) | |||||||
\(908\) | −10.7006 | − | 6.17797i | −0.355110 | − | 0.205023i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.1727 | + | 27.1823i | −0.801319 | + | 0.901086i | ||||
\(911\) | 35.2080i | 1.16649i | 0.812295 | + | 0.583246i | \(0.198218\pi\) | ||||
−0.812295 | + | 0.583246i | \(0.801782\pi\) | |||||||
\(912\) | 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 | \(-0.150375\pi\) | |||||||
\(920\) | −6.08724 | + | 2.09609i | −0.200690 | + | 0.0691060i | ||||
\(921\) | 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 | \(0.601373\pi\) |
−0.665918 | + | 0.746025i | \(0.731960\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | −17.6942 | + | 6.09286i | −0.578664 | + | 0.199258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2579 | 0.792471 | 0.396235 | − | 0.918149i | \(-0.370316\pi\) | ||||
0.396235 | + | 0.918149i | \(0.370316\pi\) | |||||||
\(938\) | 6.99643 | + | 12.4404i | 0.228442 | + | 0.406194i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.18263 | + | 1.36050i | −0.0385732 | + | 0.0443745i | ||||
\(941\) | −15.0539 | − | 26.0742i | −0.490744 | − | 0.849994i | 0.509199 | − | 0.860649i | \(-0.329942\pi\) |
−0.999943 | + | 0.0106549i | \(0.996608\pi\) | |||||||
\(942\) | 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 | ||||
\(950\) | 18.5860 | + | 23.7878i | 0.603011 | + | 0.771779i | ||||
\(951\) | 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 | ||||||||
\(955\) | 2.05915 | + | 5.97996i | 0.0666324 | + | 0.193507i | ||||
\(956\) | −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 | \(0.000472286\pi\) | ||||
−0.999999 | + | 0.00148373i | \(0.999528\pi\) | |||||||
\(968\) | 4.67683 | − | 8.10050i | 0.150319 | − | 0.260360i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.5380 | + | 6.38340i | −0.595219 | + | 0.204959i | ||||
\(971\) | −19.8502 | + | 34.3816i | −0.637024 | + | 1.10336i | 0.349058 | + | 0.937101i | \(0.386502\pi\) |
−0.986082 | + | 0.166257i | \(0.946832\pi\) | |||||||
\(972\) | 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 | ||||||
\(980\) | −11.5784 | − | 10.5329i | −0.369857 | − | 0.336460i | ||||
\(981\) | 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 | ||||||||
\(985\) | 3.99502 | + | 3.47273i | 0.127292 | + | 0.110650i | ||||
\(986\) | −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 | \(-0.885043\pi\) |
0.161736 | − | 0.986834i | \(-0.448291\pi\) | |||||||
\(998\) | 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.89.6 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.a.89.3 | yes | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1601.9 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1601.8 | 32 | |||
5.4 | even | 2 | 630.2.bo.a.89.1 | ✓ | 16 | ||
7.2 | even | 3 | 4410.2.d.a.4409.9 | 16 | |||
7.3 | odd | 6 | inner | 630.2.bo.b.269.8 | yes | 16 | |
7.5 | odd | 6 | 4410.2.d.a.4409.8 | 16 | |||
15.2 | even | 4 | 3150.2.bf.f.1601.7 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1601.10 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.b.89.8 | yes | 16 | |
21.2 | odd | 6 | 4410.2.d.b.4409.8 | 16 | |||
21.5 | even | 6 | 4410.2.d.b.4409.9 | 16 | |||
21.17 | even | 6 | 630.2.bo.a.269.1 | yes | 16 | ||
35.3 | even | 12 | 3150.2.bf.f.1151.10 | 32 | |||
35.9 | even | 6 | 4410.2.d.b.4409.10 | 16 | |||
35.17 | even | 12 | 3150.2.bf.f.1151.7 | 32 | |||
35.19 | odd | 6 | 4410.2.d.b.4409.7 | 16 | |||
35.24 | odd | 6 | 630.2.bo.a.269.3 | yes | 16 | ||
105.17 | odd | 12 | 3150.2.bf.f.1151.9 | 32 | |||
105.38 | odd | 12 | 3150.2.bf.f.1151.8 | 32 | |||
105.44 | odd | 6 | 4410.2.d.a.4409.7 | 16 | |||
105.59 | even | 6 | inner | 630.2.bo.b.269.6 | yes | 16 | |
105.89 | even | 6 | 4410.2.d.a.4409.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.1 | ✓ | 16 | 5.4 | even | 2 | ||
630.2.bo.a.89.3 | yes | 16 | 3.2 | odd | 2 | ||
630.2.bo.a.269.1 | yes | 16 | 21.17 | even | 6 | ||
630.2.bo.a.269.3 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bo.b.89.6 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.b.89.8 | yes | 16 | 15.14 | odd | 2 | inner | |
630.2.bo.b.269.6 | yes | 16 | 105.59 | even | 6 | inner | |
630.2.bo.b.269.8 | yes | 16 | 7.3 | odd | 6 | inner | |
3150.2.bf.f.1151.7 | 32 | 35.17 | even | 12 | |||
3150.2.bf.f.1151.8 | 32 | 105.38 | odd | 12 | |||
3150.2.bf.f.1151.9 | 32 | 105.17 | odd | 12 | |||
3150.2.bf.f.1151.10 | 32 | 35.3 | even | 12 | |||
3150.2.bf.f.1601.7 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1601.8 | 32 | 5.3 | odd | 4 | |||
3150.2.bf.f.1601.9 | 32 | 5.2 | odd | 4 | |||
3150.2.bf.f.1601.10 | 32 | 15.8 | even | 4 | |||
4410.2.d.a.4409.7 | 16 | 105.44 | odd | 6 | |||
4410.2.d.a.4409.8 | 16 | 7.5 | odd | 6 | |||
4410.2.d.a.4409.9 | 16 | 7.2 | even | 3 | |||
4410.2.d.a.4409.10 | 16 | 105.89 | even | 6 | |||
4410.2.d.b.4409.7 | 16 | 35.19 | odd | 6 | |||
4410.2.d.b.4409.8 | 16 | 21.2 | odd | 6 | |||
4410.2.d.b.4409.9 | 16 | 21.5 | even | 6 | |||
4410.2.d.b.4409.10 | 16 | 35.9 | even | 6 |