Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,2,Mod(106,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("285.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.i (of order \(3\), 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: | \(2.27573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 2x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.121 |
Dual form | 285.2.i.d.106.2 |
$q$-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 \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.207107 | + | 0.358719i | 0.146447 | + | 0.253653i | 0.929912 | − | 0.367783i | \(-0.119883\pi\) |
−0.783465 | + | 0.621436i | \(0.786550\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.914214 | − | 1.58346i | 0.457107 | − | 0.791732i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −0.207107 | + | 0.358719i | −0.0845510 | + | 0.146447i | ||||
\(7\) | 1.82843 | 0.691080 | 0.345540 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345540 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.207107 | + | 0.358719i | −0.0654929 | + | 0.113437i | ||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 1.82843 | 0.527821 | ||||||||
\(13\) | 0.914214 | − | 1.58346i | 0.253557 | − | 0.439174i | −0.710945 | − | 0.703247i | \(-0.751733\pi\) |
0.964503 | + | 0.264073i | \(0.0850661\pi\) | |||||||
\(14\) | 0.378680 | + | 0.655892i | 0.101206 | + | 0.175295i | ||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 0.585786 | + | 1.01461i | 0.142074 | + | 0.246080i | 0.928278 | − | 0.371888i | \(-0.121290\pi\) |
−0.786203 | + | 0.617968i | \(0.787956\pi\) | |||||||
\(18\) | −0.414214 | −0.0976311 | ||||||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | 0.914214 | + | 1.58346i | 0.199498 | + | 0.345540i | ||||
\(22\) | −0.585786 | − | 1.01461i | −0.124890 | − | 0.216316i | ||||
\(23\) | 0.414214 | − | 0.717439i | 0.0863695 | − | 0.149596i | −0.819604 | − | 0.572930i | \(-0.805807\pi\) |
0.905974 | + | 0.423333i | \(0.139140\pi\) | |||||||
\(24\) | 0.792893 | + | 1.37333i | 0.161849 | + | 0.280330i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.757359 | 0.148530 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.67157 | − | 2.89525i | 0.315898 | − | 0.547151i | ||||
\(29\) | −4.82843 | + | 8.36308i | −0.896616 | + | 1.55299i | −0.0648251 | + | 0.997897i | \(0.520649\pi\) |
−0.831791 | + | 0.555089i | \(0.812684\pi\) | |||||||
\(30\) | −0.414214 | −0.0756247 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | 2.20711 | − | 3.82282i | 0.390165 | − | 0.675786i | ||||
\(33\) | −1.41421 | − | 2.44949i | −0.246183 | − | 0.426401i | ||||
\(34\) | −0.242641 | + | 0.420266i | −0.0416125 | + | 0.0720750i | ||||
\(35\) | 0.914214 | + | 1.58346i | 0.154530 | + | 0.267654i | ||||
\(36\) | 0.914214 | + | 1.58346i | 0.152369 | + | 0.263911i | ||||
\(37\) | −2.17157 | −0.357004 | −0.178502 | − | 0.983940i | \(-0.557125\pi\) | ||||
−0.178502 | + | 0.983940i | \(0.557125\pi\) | |||||||
\(38\) | 0.207107 | + | 1.79360i | 0.0335972 | + | 0.290960i | ||||
\(39\) | 1.82843 | 0.292783 | ||||||||
\(40\) | 0.792893 | + | 1.37333i | 0.125367 | + | 0.217143i | ||||
\(41\) | −1.41421 | − | 2.44949i | −0.220863 | − | 0.382546i | 0.734207 | − | 0.678925i | \(-0.237554\pi\) |
−0.955070 | + | 0.296379i | \(0.904221\pi\) | |||||||
\(42\) | −0.378680 | + | 0.655892i | −0.0584315 | + | 0.101206i | ||||
\(43\) | −3.91421 | − | 6.77962i | −0.596912 | − | 1.03388i | −0.993274 | − | 0.115788i | \(-0.963061\pi\) |
0.396362 | − | 0.918094i | \(-0.370273\pi\) | |||||||
\(44\) | −2.58579 | + | 4.47871i | −0.389822 | + | 0.675191i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0.343146 | 0.0505941 | ||||||||
\(47\) | 1.58579 | − | 2.74666i | 0.231311 | − | 0.400642i | −0.726883 | − | 0.686761i | \(-0.759032\pi\) |
0.958194 | + | 0.286119i | \(0.0923653\pi\) | |||||||
\(48\) | 1.50000 | − | 2.59808i | 0.216506 | − | 0.375000i | ||||
\(49\) | −3.65685 | −0.522408 | ||||||||
\(50\) | −0.414214 | −0.0585786 | ||||||||
\(51\) | −0.585786 | + | 1.01461i | −0.0820265 | + | 0.142074i | ||||
\(52\) | −1.67157 | − | 2.89525i | −0.231805 | − | 0.401499i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | −0.207107 | − | 0.358719i | −0.0281837 | − | 0.0488155i | ||||
\(55\) | −1.41421 | − | 2.44949i | −0.190693 | − | 0.330289i | ||||
\(56\) | 2.89949 | 0.387461 | ||||||||
\(57\) | 0.500000 | + | 4.33013i | 0.0662266 | + | 0.573539i | ||||
\(58\) | −4.00000 | −0.525226 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0.914214 | + | 1.58346i | 0.118024 | + | 0.204424i | ||||
\(61\) | 4.15685 | − | 7.19988i | 0.532231 | − | 0.921851i | −0.467061 | − | 0.884225i | \(-0.654687\pi\) |
0.999292 | − | 0.0376256i | \(-0.0119794\pi\) | |||||||
\(62\) | −1.03553 | − | 1.79360i | −0.131513 | − | 0.227787i | ||||
\(63\) | −0.914214 | + | 1.58346i | −0.115180 | + | 0.199498i | ||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 1.82843 | 0.226788 | ||||||||
\(66\) | 0.585786 | − | 1.01461i | 0.0721053 | − | 0.124890i | ||||
\(67\) | −2.74264 | + | 4.75039i | −0.335067 | + | 0.580353i | −0.983498 | − | 0.180921i | \(-0.942092\pi\) |
0.648431 | + | 0.761274i | \(0.275426\pi\) | |||||||
\(68\) | 2.14214 | 0.259772 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | −0.378680 | + | 0.655892i | −0.0452609 | + | 0.0783941i | ||||
\(71\) | −5.00000 | − | 8.66025i | −0.593391 | − | 1.02778i | −0.993772 | − | 0.111434i | \(-0.964456\pi\) |
0.400381 | − | 0.916349i | \(-0.368878\pi\) | |||||||
\(72\) | −0.792893 | + | 1.37333i | −0.0934434 | + | 0.161849i | ||||
\(73\) | −4.74264 | − | 8.21449i | −0.555084 | − | 0.961434i | −0.997897 | − | 0.0648198i | \(-0.979353\pi\) |
0.442813 | − | 0.896614i | \(-0.353981\pi\) | |||||||
\(74\) | −0.449747 | − | 0.778985i | −0.0522821 | − | 0.0905552i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 6.39949 | − | 4.75039i | 0.734072 | − | 0.544907i | ||||
\(77\) | −5.17157 | −0.589355 | ||||||||
\(78\) | 0.378680 | + | 0.655892i | 0.0428770 | + | 0.0742652i | ||||
\(79\) | 1.67157 | + | 2.89525i | 0.188067 | + | 0.325741i | 0.944606 | − | 0.328208i | \(-0.106445\pi\) |
−0.756539 | + | 0.653949i | \(0.773111\pi\) | |||||||
\(80\) | 1.50000 | − | 2.59808i | 0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.585786 | − | 1.01461i | 0.0646893 | − | 0.112045i | ||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 3.34315 | 0.364767 | ||||||||
\(85\) | −0.585786 | + | 1.01461i | −0.0635375 | + | 0.110050i | ||||
\(86\) | 1.62132 | − | 2.80821i | 0.174831 | − | 0.302817i | ||||
\(87\) | −9.65685 | −1.03532 | ||||||||
\(88\) | −4.48528 | −0.478133 | ||||||||
\(89\) | −6.24264 | + | 10.8126i | −0.661719 | + | 1.14613i | 0.318445 | + | 0.947941i | \(0.396839\pi\) |
−0.980164 | + | 0.198189i | \(0.936494\pi\) | |||||||
\(90\) | −0.207107 | − | 0.358719i | −0.0218310 | − | 0.0378124i | ||||
\(91\) | 1.67157 | − | 2.89525i | 0.175228 | − | 0.303505i | ||||
\(92\) | −0.757359 | − | 1.31178i | −0.0789602 | − | 0.136763i | ||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | 1.31371 | 0.135499 | ||||||||
\(95\) | 0.500000 | + | 4.33013i | 0.0512989 | + | 0.444262i | ||||
\(96\) | 4.41421 | 0.450524 | ||||||||
\(97\) | 3.00000 | + | 5.19615i | 0.304604 | + | 0.527589i | 0.977173 | − | 0.212445i | \(-0.0681426\pi\) |
−0.672569 | + | 0.740034i | \(0.734809\pi\) | |||||||
\(98\) | −0.757359 | − | 1.31178i | −0.0765048 | − | 0.132510i | ||||
\(99\) | 1.41421 | − | 2.44949i | 0.142134 | − | 0.246183i | ||||
\(100\) | 0.914214 | + | 1.58346i | 0.0914214 | + | 0.158346i | ||||
\(101\) | −6.07107 | + | 10.5154i | −0.604094 | + | 1.04632i | 0.388100 | + | 0.921617i | \(0.373131\pi\) |
−0.992194 | + | 0.124704i | \(0.960202\pi\) | |||||||
\(102\) | −0.485281 | −0.0480500 | ||||||||
\(103\) | 9.82843 | 0.968424 | 0.484212 | − | 0.874951i | \(-0.339106\pi\) | ||||
0.484212 | + | 0.874951i | \(0.339106\pi\) | |||||||
\(104\) | 1.44975 | − | 2.51104i | 0.142159 | − | 0.246227i | ||||
\(105\) | −0.914214 | + | 1.58346i | −0.0892181 | + | 0.154530i | ||||
\(106\) | 0.828427 | 0.0804640 | ||||||||
\(107\) | 14.0000 | 1.35343 | 0.676716 | − | 0.736245i | \(-0.263403\pi\) | ||||
0.676716 | + | 0.736245i | \(0.263403\pi\) | |||||||
\(108\) | −0.914214 | + | 1.58346i | −0.0879702 | + | 0.152369i | ||||
\(109\) | 8.65685 | + | 14.9941i | 0.829176 | + | 1.43618i | 0.898685 | + | 0.438594i | \(0.144523\pi\) |
−0.0695090 | + | 0.997581i | \(0.522143\pi\) | |||||||
\(110\) | 0.585786 | − | 1.01461i | 0.0558525 | − | 0.0967394i | ||||
\(111\) | −1.08579 | − | 1.88064i | −0.103058 | − | 0.178502i | ||||
\(112\) | −2.74264 | − | 4.75039i | −0.259155 | − | 0.448870i | ||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | −1.44975 | + | 1.07616i | −0.135781 | + | 0.100791i | ||||
\(115\) | 0.828427 | 0.0772512 | ||||||||
\(116\) | 8.82843 | + | 15.2913i | 0.819699 | + | 1.41976i | ||||
\(117\) | 0.914214 | + | 1.58346i | 0.0845191 | + | 0.146391i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.07107 | + | 1.85514i | 0.0981846 | + | 0.170061i | ||||
\(120\) | −0.792893 | + | 1.37333i | −0.0723809 | + | 0.125367i | ||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 3.44365 | 0.311773 | ||||||||
\(123\) | 1.41421 | − | 2.44949i | 0.127515 | − | 0.220863i | ||||
\(124\) | −4.57107 | + | 7.91732i | −0.410494 | + | 0.710996i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.757359 | −0.0674709 | ||||||||
\(127\) | −6.48528 | + | 11.2328i | −0.575476 | + | 0.996753i | 0.420514 | + | 0.907286i | \(0.361850\pi\) |
−0.995990 | + | 0.0894671i | \(0.971484\pi\) | |||||||
\(128\) | −5.27817 | − | 9.14207i | −0.466529 | − | 0.808052i | ||||
\(129\) | 3.91421 | − | 6.77962i | 0.344627 | − | 0.596912i | ||||
\(130\) | 0.378680 | + | 0.655892i | 0.0332124 | + | 0.0575256i | ||||
\(131\) | −3.24264 | − | 5.61642i | −0.283311 | − | 0.490709i | 0.688887 | − | 0.724868i | \(-0.258099\pi\) |
−0.972198 | + | 0.234160i | \(0.924766\pi\) | |||||||
\(132\) | −5.17157 | −0.450128 | ||||||||
\(133\) | 7.31371 | + | 3.16693i | 0.634179 | + | 0.274608i | ||||
\(134\) | −2.27208 | −0.196278 | ||||||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 0.928932 | + | 1.60896i | 0.0796553 | + | 0.137967i | ||||
\(137\) | 5.24264 | − | 9.08052i | 0.447909 | − | 0.775801i | −0.550341 | − | 0.834940i | \(-0.685502\pi\) |
0.998250 | + | 0.0591390i | \(0.0188355\pi\) | |||||||
\(138\) | 0.171573 | + | 0.297173i | 0.0146053 | + | 0.0252970i | ||||
\(139\) | 8.15685 | − | 14.1281i | 0.691855 | − | 1.19833i | −0.279374 | − | 0.960182i | \(-0.590127\pi\) |
0.971229 | − | 0.238146i | \(-0.0765398\pi\) | |||||||
\(140\) | 3.34315 | 0.282547 | ||||||||
\(141\) | 3.17157 | 0.267095 | ||||||||
\(142\) | 2.07107 | − | 3.58719i | 0.173800 | − | 0.301031i | ||||
\(143\) | −2.58579 | + | 4.47871i | −0.216234 | + | 0.374529i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −9.65685 | −0.801958 | ||||||||
\(146\) | 1.96447 | − | 3.40256i | 0.162580 | − | 0.281597i | ||||
\(147\) | −1.82843 | − | 3.16693i | −0.150806 | − | 0.261204i | ||||
\(148\) | −1.98528 | + | 3.43861i | −0.163189 | + | 0.282652i | ||||
\(149\) | 0.585786 | + | 1.01461i | 0.0479895 | + | 0.0831202i | 0.889022 | − | 0.457864i | \(-0.151385\pi\) |
−0.841033 | + | 0.540984i | \(0.818052\pi\) | |||||||
\(150\) | −0.207107 | − | 0.358719i | −0.0169102 | − | 0.0292893i | ||||
\(151\) | 10.3431 | 0.841713 | 0.420857 | − | 0.907127i | \(-0.361730\pi\) | ||||
0.420857 | + | 0.907127i | \(0.361730\pi\) | |||||||
\(152\) | 6.34315 | + | 2.74666i | 0.514497 | + | 0.222784i | ||||
\(153\) | −1.17157 | −0.0947161 | ||||||||
\(154\) | −1.07107 | − | 1.85514i | −0.0863091 | − | 0.149492i | ||||
\(155\) | −2.50000 | − | 4.33013i | −0.200805 | − | 0.347804i | ||||
\(156\) | 1.67157 | − | 2.89525i | 0.133833 | − | 0.231805i | ||||
\(157\) | 9.91421 | + | 17.1719i | 0.791240 | + | 1.37047i | 0.925199 | + | 0.379482i | \(0.123898\pi\) |
−0.133959 | + | 0.990987i | \(0.542769\pi\) | |||||||
\(158\) | −0.692388 | + | 1.19925i | −0.0550834 | + | 0.0954073i | ||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 4.41421 | 0.348974 | ||||||||
\(161\) | 0.757359 | − | 1.31178i | 0.0596883 | − | 0.103383i | ||||
\(162\) | 0.207107 | − | 0.358719i | 0.0162718 | − | 0.0281837i | ||||
\(163\) | 15.1421 | 1.18602 | 0.593012 | − | 0.805194i | \(-0.297939\pi\) | ||||
0.593012 | + | 0.805194i | \(0.297939\pi\) | |||||||
\(164\) | −5.17157 | −0.403832 | ||||||||
\(165\) | 1.41421 | − | 2.44949i | 0.110096 | − | 0.190693i | ||||
\(166\) | −1.65685 | − | 2.86976i | −0.128597 | − | 0.222736i | ||||
\(167\) | 12.4853 | − | 21.6251i | 0.966140 | − | 1.67340i | 0.259620 | − | 0.965711i | \(-0.416403\pi\) |
0.706520 | − | 0.707693i | \(-0.250264\pi\) | |||||||
\(168\) | 1.44975 | + | 2.51104i | 0.111850 | + | 0.193731i | ||||
\(169\) | 4.82843 | + | 8.36308i | 0.371417 | + | 0.643314i | ||||
\(170\) | −0.485281 | −0.0372194 | ||||||||
\(171\) | −3.50000 | + | 2.59808i | −0.267652 | + | 0.198680i | ||||
\(172\) | −14.3137 | −1.09141 | ||||||||
\(173\) | −3.65685 | − | 6.33386i | −0.278025 | − | 0.481554i | 0.692868 | − | 0.721064i | \(-0.256347\pi\) |
−0.970894 | + | 0.239510i | \(0.923013\pi\) | |||||||
\(174\) | −2.00000 | − | 3.46410i | −0.151620 | − | 0.262613i | ||||
\(175\) | −0.914214 | + | 1.58346i | −0.0691080 | + | 0.119699i | ||||
\(176\) | 4.24264 | + | 7.34847i | 0.319801 | + | 0.553912i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.17157 | −0.387626 | ||||||||
\(179\) | 16.1421 | 1.20652 | 0.603260 | − | 0.797545i | \(-0.293868\pi\) | ||||
0.603260 | + | 0.797545i | \(0.293868\pi\) | |||||||
\(180\) | −0.914214 | + | 1.58346i | −0.0681415 | + | 0.118024i | ||||
\(181\) | −12.6569 | + | 21.9223i | −0.940777 | + | 1.62947i | −0.176782 | + | 0.984250i | \(0.556569\pi\) |
−0.763994 | + | 0.645223i | \(0.776765\pi\) | |||||||
\(182\) | 1.38478 | 0.102646 | ||||||||
\(183\) | 8.31371 | 0.614567 | ||||||||
\(184\) | 0.656854 | − | 1.13770i | 0.0484239 | − | 0.0838727i | ||||
\(185\) | −1.08579 | − | 1.88064i | −0.0798286 | − | 0.138267i | ||||
\(186\) | 1.03553 | − | 1.79360i | 0.0759290 | − | 0.131513i | ||||
\(187\) | −1.65685 | − | 2.86976i | −0.121161 | − | 0.209857i | ||||
\(188\) | −2.89949 | − | 5.02207i | −0.211467 | − | 0.366272i | ||||
\(189\) | −1.82843 | −0.132999 | ||||||||
\(190\) | −1.44975 | + | 1.07616i | −0.105176 | + | 0.0780727i | ||||
\(191\) | −16.8284 | −1.21766 | −0.608831 | − | 0.793300i | \(-0.708361\pi\) | ||||
−0.608831 | + | 0.793300i | \(0.708361\pi\) | |||||||
\(192\) | −2.08579 | − | 3.61269i | −0.150529 | − | 0.260723i | ||||
\(193\) | 12.3995 | + | 21.4766i | 0.892535 | + | 1.54592i | 0.836826 | + | 0.547469i | \(0.184409\pi\) |
0.0557094 | + | 0.998447i | \(0.482258\pi\) | |||||||
\(194\) | −1.24264 | + | 2.15232i | −0.0892164 | + | 0.154527i | ||||
\(195\) | 0.914214 | + | 1.58346i | 0.0654682 | + | 0.113394i | ||||
\(196\) | −3.34315 | + | 5.79050i | −0.238796 | + | 0.413607i | ||||
\(197\) | 17.6569 | 1.25800 | 0.628999 | − | 0.777406i | \(-0.283465\pi\) | ||||
0.628999 | + | 0.777406i | \(0.283465\pi\) | |||||||
\(198\) | 1.17157 | 0.0832601 | ||||||||
\(199\) | 8.50000 | − | 14.7224i | 0.602549 | − | 1.04365i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) |
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | −0.792893 | + | 1.37333i | −0.0560660 | + | 0.0971092i | ||||
\(201\) | −5.48528 | −0.386902 | ||||||||
\(202\) | −5.02944 | −0.353870 | ||||||||
\(203\) | −8.82843 | + | 15.2913i | −0.619634 | + | 1.07324i | ||||
\(204\) | 1.07107 | + | 1.85514i | 0.0749897 | + | 0.129886i | ||||
\(205\) | 1.41421 | − | 2.44949i | 0.0987730 | − | 0.171080i | ||||
\(206\) | 2.03553 | + | 3.52565i | 0.141822 | + | 0.245644i | ||||
\(207\) | 0.414214 | + | 0.717439i | 0.0287898 | + | 0.0498655i | ||||
\(208\) | −5.48528 | −0.380336 | ||||||||
\(209\) | −11.3137 | − | 4.89898i | −0.782586 | − | 0.338869i | ||||
\(210\) | −0.757359 | −0.0522628 | ||||||||
\(211\) | 0.156854 | + | 0.271680i | 0.0107983 | + | 0.0187032i | 0.871374 | − | 0.490619i | \(-0.163229\pi\) |
−0.860576 | + | 0.509322i | \(0.829896\pi\) | |||||||
\(212\) | −1.82843 | − | 3.16693i | −0.125577 | − | 0.217506i | ||||
\(213\) | 5.00000 | − | 8.66025i | 0.342594 | − | 0.593391i | ||||
\(214\) | 2.89949 | + | 5.02207i | 0.198205 | + | 0.343302i | ||||
\(215\) | 3.91421 | − | 6.77962i | 0.266947 | − | 0.462366i | ||||
\(216\) | −1.58579 | −0.107899 | ||||||||
\(217\) | −9.14214 | −0.620609 | ||||||||
\(218\) | −3.58579 | + | 6.21076i | −0.242860 | + | 0.420646i | ||||
\(219\) | 4.74264 | − | 8.21449i | 0.320478 | − | 0.555084i | ||||
\(220\) | −5.17157 | −0.348667 | ||||||||
\(221\) | 2.14214 | 0.144096 | ||||||||
\(222\) | 0.449747 | − | 0.778985i | 0.0301851 | − | 0.0522821i | ||||
\(223\) | −2.91421 | − | 5.04757i | −0.195150 | − | 0.338010i | 0.751800 | − | 0.659392i | \(-0.229186\pi\) |
−0.946950 | + | 0.321382i | \(0.895853\pi\) | |||||||
\(224\) | 4.03553 | − | 6.98975i | 0.269635 | − | 0.467022i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 0.828427 | + | 1.43488i | 0.0551062 | + | 0.0954467i | ||||
\(227\) | −18.9706 | −1.25912 | −0.629560 | − | 0.776952i | \(-0.716765\pi\) | ||||
−0.629560 | + | 0.776952i | \(0.716765\pi\) | |||||||
\(228\) | 7.31371 | + | 3.16693i | 0.484362 | + | 0.209735i | ||||
\(229\) | −4.65685 | −0.307734 | −0.153867 | − | 0.988092i | \(-0.549173\pi\) | ||||
−0.153867 | + | 0.988092i | \(0.549173\pi\) | |||||||
\(230\) | 0.171573 | + | 0.297173i | 0.0113132 | + | 0.0195950i | ||||
\(231\) | −2.58579 | − | 4.47871i | −0.170132 | − | 0.294678i | ||||
\(232\) | −7.65685 | + | 13.2621i | −0.502697 | + | 0.870697i | ||||
\(233\) | 12.6569 | + | 21.9223i | 0.829178 | + | 1.43618i | 0.898684 | + | 0.438597i | \(0.144524\pi\) |
−0.0695057 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(234\) | −0.378680 | + | 0.655892i | −0.0247551 | + | 0.0428770i | ||||
\(235\) | 3.17157 | 0.206891 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.67157 | + | 2.89525i | −0.108580 | + | 0.188067i | ||||
\(238\) | −0.443651 | + | 0.768426i | −0.0287576 | + | 0.0498096i | ||||
\(239\) | −24.6274 | −1.59302 | −0.796508 | − | 0.604629i | \(-0.793322\pi\) | ||||
−0.796508 | + | 0.604629i | \(0.793322\pi\) | |||||||
\(240\) | 3.00000 | 0.193649 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | −0.621320 | − | 1.07616i | −0.0399400 | − | 0.0691781i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −7.60051 | − | 13.1645i | −0.486572 | − | 0.842768i | ||||
\(245\) | −1.82843 | − | 3.16693i | −0.116814 | − | 0.202328i | ||||
\(246\) | 1.17157 | 0.0746968 | ||||||||
\(247\) | 6.39949 | − | 4.75039i | 0.407190 | − | 0.302260i | ||||
\(248\) | −7.92893 | −0.503488 | ||||||||
\(249\) | −4.00000 | − | 6.92820i | −0.253490 | − | 0.439057i | ||||
\(250\) | −0.207107 | − | 0.358719i | −0.0130986 | − | 0.0226874i | ||||
\(251\) | 8.17157 | − | 14.1536i | 0.515785 | − | 0.893366i | −0.484047 | − | 0.875042i | \(-0.660834\pi\) |
0.999832 | − | 0.0183240i | \(-0.00583304\pi\) | |||||||
\(252\) | 1.67157 | + | 2.89525i | 0.105299 | + | 0.182384i | ||||
\(253\) | −1.17157 | + | 2.02922i | −0.0736562 | + | 0.127576i | ||||
\(254\) | −5.37258 | −0.337106 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | 8.41421 | − | 14.5738i | 0.524864 | − | 0.909091i | −0.474717 | − | 0.880139i | \(-0.657449\pi\) |
0.999581 | − | 0.0289528i | \(-0.00921724\pi\) | |||||||
\(258\) | 3.24264 | 0.201878 | ||||||||
\(259\) | −3.97056 | −0.246719 | ||||||||
\(260\) | 1.67157 | − | 2.89525i | 0.103667 | − | 0.179556i | ||||
\(261\) | −4.82843 | − | 8.36308i | −0.298872 | − | 0.517662i | ||||
\(262\) | 1.34315 | − | 2.32640i | 0.0829798 | − | 0.143725i | ||||
\(263\) | −12.8995 | − | 22.3426i | −0.795417 | − | 1.37770i | −0.922574 | − | 0.385820i | \(-0.873919\pi\) |
0.127157 | − | 0.991883i | \(-0.459415\pi\) | |||||||
\(264\) | −2.24264 | − | 3.88437i | −0.138025 | − | 0.239066i | ||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0.378680 | + | 3.27946i | 0.0232183 | + | 0.201077i | ||||
\(267\) | −12.4853 | −0.764087 | ||||||||
\(268\) | 5.01472 | + | 8.68575i | 0.306323 | + | 0.530566i | ||||
\(269\) | −0.828427 | − | 1.43488i | −0.0505101 | − | 0.0874860i | 0.839665 | − | 0.543105i | \(-0.182751\pi\) |
−0.890175 | + | 0.455619i | \(0.849418\pi\) | |||||||
\(270\) | 0.207107 | − | 0.358719i | 0.0126041 | − | 0.0218310i | ||||
\(271\) | −6.82843 | − | 11.8272i | −0.414797 | − | 0.718450i | 0.580610 | − | 0.814182i | \(-0.302814\pi\) |
−0.995407 | + | 0.0957318i | \(0.969481\pi\) | |||||||
\(272\) | 1.75736 | − | 3.04384i | 0.106556 | − | 0.184560i | ||||
\(273\) | 3.34315 | 0.202336 | ||||||||
\(274\) | 4.34315 | 0.262379 | ||||||||
\(275\) | 1.41421 | − | 2.44949i | 0.0852803 | − | 0.147710i | ||||
\(276\) | 0.757359 | − | 1.31178i | 0.0455877 | − | 0.0789602i | ||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 6.75736 | 0.405279 | ||||||||
\(279\) | 2.50000 | − | 4.33013i | 0.149671 | − | 0.259238i | ||||
\(280\) | 1.44975 | + | 2.51104i | 0.0866390 | + | 0.150063i | ||||
\(281\) | 3.48528 | − | 6.03668i | 0.207914 | − | 0.360118i | −0.743143 | − | 0.669133i | \(-0.766666\pi\) |
0.951057 | + | 0.309014i | \(0.0999991\pi\) | |||||||
\(282\) | 0.656854 | + | 1.13770i | 0.0391151 | + | 0.0677493i | ||||
\(283\) | 10.4853 | + | 18.1610i | 0.623285 | + | 1.07956i | 0.988870 | + | 0.148784i | \(0.0475358\pi\) |
−0.365584 | + | 0.930778i | \(0.619131\pi\) | |||||||
\(284\) | −18.2843 | −1.08497 | ||||||||
\(285\) | −3.50000 | + | 2.59808i | −0.207322 | + | 0.153897i | ||||
\(286\) | −2.14214 | −0.126667 | ||||||||
\(287\) | −2.58579 | − | 4.47871i | −0.152634 | − | 0.264370i | ||||
\(288\) | 2.20711 | + | 3.82282i | 0.130055 | + | 0.225262i | ||||
\(289\) | 7.81371 | − | 13.5337i | 0.459630 | − | 0.796102i | ||||
\(290\) | −2.00000 | − | 3.46410i | −0.117444 | − | 0.203419i | ||||
\(291\) | −3.00000 | + | 5.19615i | −0.175863 | + | 0.304604i | ||||
\(292\) | −17.3431 | −1.01493 | ||||||||
\(293\) | −5.31371 | −0.310430 | −0.155215 | − | 0.987881i | \(-0.549607\pi\) | ||||
−0.155215 | + | 0.987881i | \(0.549607\pi\) | |||||||
\(294\) | 0.757359 | − | 1.31178i | 0.0441701 | − | 0.0765048i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.44365 | −0.200158 | ||||||||
\(297\) | 2.82843 | 0.164122 | ||||||||
\(298\) | −0.242641 | + | 0.420266i | −0.0140558 | + | 0.0243454i | ||||
\(299\) | −0.757359 | − | 1.31178i | −0.0437992 | − | 0.0758625i | ||||
\(300\) | −0.914214 | + | 1.58346i | −0.0527821 | + | 0.0914214i | ||||
\(301\) | −7.15685 | − | 12.3960i | −0.412514 | − | 0.714496i | ||||
\(302\) | 2.14214 | + | 3.71029i | 0.123266 | + | 0.213503i | ||||
\(303\) | −12.1421 | −0.697547 | ||||||||
\(304\) | −1.50000 | − | 12.9904i | −0.0860309 | − | 0.745049i | ||||
\(305\) | 8.31371 | 0.476042 | ||||||||
\(306\) | −0.242641 | − | 0.420266i | −0.0138708 | − | 0.0240250i | ||||
\(307\) | 8.82843 | + | 15.2913i | 0.503865 | + | 0.872720i | 0.999990 | + | 0.00446862i | \(0.00142241\pi\) |
−0.496125 | + | 0.868251i | \(0.665244\pi\) | |||||||
\(308\) | −4.72792 | + | 8.18900i | −0.269398 | + | 0.466612i | ||||
\(309\) | 4.91421 | + | 8.51167i | 0.279560 | + | 0.484212i | ||||
\(310\) | 1.03553 | − | 1.79360i | 0.0588144 | − | 0.101869i | ||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 2.89949 | 0.164152 | ||||||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | −4.10660 | + | 7.11284i | −0.231749 | + | 0.401401i | ||||
\(315\) | −1.82843 | −0.103020 | ||||||||
\(316\) | 6.11270 | 0.343866 | ||||||||
\(317\) | −2.65685 | + | 4.60181i | −0.149224 | + | 0.258463i | −0.930941 | − | 0.365170i | \(-0.881011\pi\) |
0.781717 | + | 0.623633i | \(0.214344\pi\) | |||||||
\(318\) | 0.414214 | + | 0.717439i | 0.0232279 | + | 0.0402320i | ||||
\(319\) | 13.6569 | − | 23.6544i | 0.764637 | − | 1.32439i | ||||
\(320\) | −2.08579 | − | 3.61269i | −0.116599 | − | 0.201955i | ||||
\(321\) | 7.00000 | + | 12.1244i | 0.390702 | + | 0.676716i | ||||
\(322\) | 0.627417 | 0.0349646 | ||||||||
\(323\) | 0.585786 | + | 5.07306i | 0.0325940 | + | 0.282273i | ||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0.914214 | + | 1.58346i | 0.0507114 | + | 0.0878348i | ||||
\(326\) | 3.13604 | + | 5.43178i | 0.173689 | + | 0.300838i | ||||
\(327\) | −8.65685 | + | 14.9941i | −0.478725 | + | 0.829176i | ||||
\(328\) | −2.24264 | − | 3.88437i | −0.123829 | − | 0.214478i | ||||
\(329\) | 2.89949 | − | 5.02207i | 0.159854 | − | 0.276876i | ||||
\(330\) | 1.17157 | 0.0644930 | ||||||||
\(331\) | −5.34315 | −0.293686 | −0.146843 | − | 0.989160i | \(-0.546911\pi\) | ||||
−0.146843 | + | 0.989160i | \(0.546911\pi\) | |||||||
\(332\) | −7.31371 | + | 12.6677i | −0.401392 | + | 0.695231i | ||||
\(333\) | 1.08579 | − | 1.88064i | 0.0595007 | − | 0.103058i | ||||
\(334\) | 10.3431 | 0.565952 | ||||||||
\(335\) | −5.48528 | −0.299693 | ||||||||
\(336\) | 2.74264 | − | 4.75039i | 0.149623 | − | 0.259155i | ||||
\(337\) | −8.74264 | − | 15.1427i | −0.476242 | − | 0.824875i | 0.523387 | − | 0.852095i | \(-0.324668\pi\) |
−0.999629 | + | 0.0272195i | \(0.991335\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | 2.00000 | + | 3.46410i | 0.108625 | + | 0.188144i | ||||
\(340\) | 1.07107 | + | 1.85514i | 0.0580868 | + | 0.100609i | ||||
\(341\) | 14.1421 | 0.765840 | ||||||||
\(342\) | −1.65685 | − | 0.717439i | −0.0895924 | − | 0.0387947i | ||||
\(343\) | −19.4853 | −1.05211 | ||||||||
\(344\) | −6.20711 | − | 10.7510i | −0.334665 | − | 0.579656i | ||||
\(345\) | 0.414214 | + | 0.717439i | 0.0223005 | + | 0.0386256i | ||||
\(346\) | 1.51472 | − | 2.62357i | 0.0814318 | − | 0.141044i | ||||
\(347\) | 17.7279 | + | 30.7057i | 0.951685 | + | 1.64837i | 0.741779 | + | 0.670645i | \(0.233982\pi\) |
0.209906 | + | 0.977722i | \(0.432684\pi\) | |||||||
\(348\) | −8.82843 | + | 15.2913i | −0.473253 | + | 0.819699i | ||||
\(349\) | −31.6274 | −1.69298 | −0.846488 | − | 0.532407i | \(-0.821288\pi\) | ||||
−0.846488 | + | 0.532407i | \(0.821288\pi\) | |||||||
\(350\) | −0.757359 | −0.0404826 | ||||||||
\(351\) | −0.914214 | + | 1.58346i | −0.0487971 | + | 0.0845191i | ||||
\(352\) | −6.24264 | + | 10.8126i | −0.332734 | + | 0.576312i | ||||
\(353\) | −1.31371 | −0.0699216 | −0.0349608 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349608 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | − | 8.66025i | 0.265372 | − | 0.459639i | ||||
\(356\) | 11.4142 | + | 19.7700i | 0.604952 | + | 1.04781i | ||||
\(357\) | −1.07107 | + | 1.85514i | −0.0566869 | + | 0.0981846i | ||||
\(358\) | 3.34315 | + | 5.79050i | 0.176691 | + | 0.306037i | ||||
\(359\) | −4.58579 | − | 7.94282i | −0.242029 | − | 0.419206i | 0.719263 | − | 0.694737i | \(-0.244479\pi\) |
−0.961292 | + | 0.275532i | \(0.911146\pi\) | |||||||
\(360\) | −1.58579 | −0.0835783 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −10.4853 | −0.551094 | ||||||||
\(363\) | −1.50000 | − | 2.59808i | −0.0787296 | − | 0.136364i | ||||
\(364\) | −3.05635 | − | 5.29375i | −0.160196 | − | 0.277468i | ||||
\(365\) | 4.74264 | − | 8.21449i | 0.248241 | − | 0.429966i | ||||
\(366\) | 1.72183 | + | 2.98229i | 0.0900013 | + | 0.155887i | ||||
\(367\) | 17.0563 | − | 29.5425i | 0.890334 | − | 1.54210i | 0.0508591 | − | 0.998706i | \(-0.483804\pi\) |
0.839475 | − | 0.543398i | \(-0.182863\pi\) | |||||||
\(368\) | −2.48528 | −0.129554 | ||||||||
\(369\) | 2.82843 | 0.147242 | ||||||||
\(370\) | 0.449747 | − | 0.778985i | 0.0233813 | − | 0.0404975i | ||||
\(371\) | 1.82843 | − | 3.16693i | 0.0949272 | − | 0.164419i | ||||
\(372\) | −9.14214 | −0.473998 | ||||||||
\(373\) | −11.6569 | −0.603569 | −0.301785 | − | 0.953376i | \(-0.597582\pi\) | ||||
−0.301785 | + | 0.953376i | \(0.597582\pi\) | |||||||
\(374\) | 0.686292 | − | 1.18869i | 0.0354873 | − | 0.0614658i | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 2.51472 | − | 4.35562i | 0.129687 | − | 0.224624i | ||||
\(377\) | 8.82843 | + | 15.2913i | 0.454687 | + | 0.787541i | ||||
\(378\) | −0.378680 | − | 0.655892i | −0.0194772 | − | 0.0337355i | ||||
\(379\) | 1.68629 | 0.0866190 | 0.0433095 | − | 0.999062i | \(-0.486210\pi\) | ||||
0.0433095 | + | 0.999062i | \(0.486210\pi\) | |||||||
\(380\) | 7.31371 | + | 3.16693i | 0.375185 | + | 0.162460i | ||||
\(381\) | −12.9706 | −0.664502 | ||||||||
\(382\) | −3.48528 | − | 6.03668i | −0.178323 | − | 0.308864i | ||||
\(383\) | 16.9706 | + | 29.3939i | 0.867155 | + | 1.50196i | 0.864891 | + | 0.501960i | \(0.167387\pi\) |
0.00226413 | + | 0.999997i | \(0.499279\pi\) | |||||||
\(384\) | 5.27817 | − | 9.14207i | 0.269351 | − | 0.466529i | ||||
\(385\) | −2.58579 | − | 4.47871i | −0.131784 | − | 0.228256i | ||||
\(386\) | −5.13604 | + | 8.89588i | −0.261418 | + | 0.452788i | ||||
\(387\) | 7.82843 | 0.397941 | ||||||||
\(388\) | 10.9706 | 0.556946 | ||||||||
\(389\) | 7.72792 | − | 13.3852i | 0.391821 | − | 0.678654i | −0.600869 | − | 0.799348i | \(-0.705179\pi\) |
0.992690 | + | 0.120694i | \(0.0385118\pi\) | |||||||
\(390\) | −0.378680 | + | 0.655892i | −0.0191752 | + | 0.0332124i | ||||
\(391\) | 0.970563 | 0.0490835 | ||||||||
\(392\) | −5.79899 | −0.292893 | ||||||||
\(393\) | 3.24264 | − | 5.61642i | 0.163570 | − | 0.283311i | ||||
\(394\) | 3.65685 | + | 6.33386i | 0.184230 | + | 0.319095i | ||||
\(395\) | −1.67157 | + | 2.89525i | −0.0841060 | + | 0.145676i | ||||
\(396\) | −2.58579 | − | 4.47871i | −0.129941 | − | 0.225064i | ||||
\(397\) | 11.9142 | + | 20.6360i | 0.597957 | + | 1.03569i | 0.993122 | + | 0.117082i | \(0.0373541\pi\) |
−0.395165 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(398\) | 7.04163 | 0.352965 | ||||||||
\(399\) | 0.914214 | + | 7.91732i | 0.0457679 | + | 0.396362i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 11.3137 | + | 19.5959i | 0.564980 | + | 0.978573i | 0.997052 | + | 0.0767343i | \(0.0244493\pi\) |
−0.432072 | + | 0.901839i | \(0.642217\pi\) | |||||||
\(402\) | −1.13604 | − | 1.96768i | −0.0566605 | − | 0.0981388i | ||||
\(403\) | −4.57107 | + | 7.91732i | −0.227701 | + | 0.394390i | ||||
\(404\) | 11.1005 | + | 19.2266i | 0.552271 | + | 0.956561i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | −7.31371 | −0.362973 | ||||||||
\(407\) | 6.14214 | 0.304454 | ||||||||
\(408\) | −0.928932 | + | 1.60896i | −0.0459890 | + | 0.0796553i | ||||
\(409\) | −3.00000 | + | 5.19615i | −0.148340 | + | 0.256933i | −0.930614 | − | 0.366002i | \(-0.880726\pi\) |
0.782274 | + | 0.622935i | \(0.214060\pi\) | |||||||
\(410\) | 1.17157 | 0.0578599 | ||||||||
\(411\) | 10.4853 | 0.517201 | ||||||||
\(412\) | 8.98528 | − | 15.5630i | 0.442673 | − | 0.766732i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.171573 | + | 0.297173i | −0.00843235 | + | 0.0146053i | ||||
\(415\) | −4.00000 | − | 6.92820i | −0.196352 | − | 0.340092i | ||||
\(416\) | −4.03553 | − | 6.98975i | −0.197858 | − | 0.342701i | ||||
\(417\) | 16.3137 | 0.798886 | ||||||||
\(418\) | −0.585786 | − | 5.07306i | −0.0286518 | − | 0.248131i | ||||
\(419\) | 3.31371 | 0.161885 | 0.0809426 | − | 0.996719i | \(-0.474207\pi\) | ||||
0.0809426 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(420\) | 1.67157 | + | 2.89525i | 0.0815644 | + | 0.141274i | ||||
\(421\) | 3.82843 | + | 6.63103i | 0.186586 | + | 0.323177i | 0.944110 | − | 0.329631i | \(-0.106924\pi\) |
−0.757524 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(422\) | −0.0649712 | + | 0.112533i | −0.00316275 | + | 0.00547804i | ||||
\(423\) | 1.58579 | + | 2.74666i | 0.0771036 | + | 0.133547i | ||||
\(424\) | 1.58579 | − | 2.74666i | 0.0770126 | − | 0.133390i | ||||
\(425\) | −1.17157 | −0.0568296 | ||||||||
\(426\) | 4.14214 | 0.200687 | ||||||||
\(427\) | 7.60051 | − | 13.1645i | 0.367814 | − | 0.637073i | ||||
\(428\) | 12.7990 | − | 22.1685i | 0.618663 | − | 1.07155i | ||||
\(429\) | −5.17157 | −0.249686 | ||||||||
\(430\) | 3.24264 | 0.156374 | ||||||||
\(431\) | 1.24264 | − | 2.15232i | 0.0598559 | − | 0.103673i | −0.834545 | − | 0.550940i | \(-0.814269\pi\) |
0.894401 | + | 0.447267i | \(0.147603\pi\) | |||||||
\(432\) | 1.50000 | + | 2.59808i | 0.0721688 | + | 0.125000i | ||||
\(433\) | 19.9142 | − | 34.4924i | 0.957016 | − | 1.65760i | 0.227330 | − | 0.973818i | \(-0.427000\pi\) |
0.729686 | − | 0.683783i | \(-0.239666\pi\) | |||||||
\(434\) | −1.89340 | − | 3.27946i | −0.0908860 | − | 0.157419i | ||||
\(435\) | −4.82843 | − | 8.36308i | −0.231505 | − | 0.400979i | ||||
\(436\) | 31.6569 | 1.51609 | ||||||||
\(437\) | 2.89949 | − | 2.15232i | 0.138702 | − | 0.102959i | ||||
\(438\) | 3.92893 | 0.187732 | ||||||||
\(439\) | −8.50000 | − | 14.7224i | −0.405683 | − | 0.702663i | 0.588718 | − | 0.808339i | \(-0.299633\pi\) |
−0.994401 | + | 0.105675i | \(0.966300\pi\) | |||||||
\(440\) | −2.24264 | − | 3.88437i | −0.106914 | − | 0.185180i | ||||
\(441\) | 1.82843 | − | 3.16693i | 0.0870680 | − | 0.150806i | ||||
\(442\) | 0.443651 | + | 0.768426i | 0.0211023 | + | 0.0365503i | ||||
\(443\) | −9.07107 | + | 15.7116i | −0.430979 | + | 0.746478i | −0.996958 | − | 0.0779417i | \(-0.975165\pi\) |
0.565978 | + | 0.824420i | \(0.308499\pi\) | |||||||
\(444\) | −3.97056 | −0.188435 | ||||||||
\(445\) | −12.4853 | −0.591859 | ||||||||
\(446\) | 1.20711 | − | 2.09077i | 0.0571582 | − | 0.0990008i | ||||
\(447\) | −0.585786 | + | 1.01461i | −0.0277067 | + | 0.0479895i | ||||
\(448\) | −7.62742 | −0.360362 | ||||||||
\(449\) | 13.1716 | 0.621605 | 0.310802 | − | 0.950475i | \(-0.399402\pi\) | ||||
0.310802 | + | 0.950475i | \(0.399402\pi\) | |||||||
\(450\) | 0.207107 | − | 0.358719i | 0.00976311 | − | 0.0169102i | ||||
\(451\) | 4.00000 | + | 6.92820i | 0.188353 | + | 0.326236i | ||||
\(452\) | 3.65685 | − | 6.33386i | 0.172004 | − | 0.297920i | ||||
\(453\) | 5.17157 | + | 8.95743i | 0.242982 | + | 0.420857i | ||||
\(454\) | −3.92893 | − | 6.80511i | −0.184394 | − | 0.319380i | ||||
\(455\) | 3.34315 | 0.156729 | ||||||||
\(456\) | 0.792893 | + | 6.86666i | 0.0371306 | + | 0.321561i | ||||
\(457\) | −4.17157 | −0.195138 | −0.0975690 | − | 0.995229i | \(-0.531107\pi\) | ||||
−0.0975690 | + | 0.995229i | \(0.531107\pi\) | |||||||
\(458\) | −0.964466 | − | 1.67050i | −0.0450665 | − | 0.0780575i | ||||
\(459\) | −0.585786 | − | 1.01461i | −0.0273422 | − | 0.0473580i | ||||
\(460\) | 0.757359 | − | 1.31178i | 0.0353121 | − | 0.0611623i | ||||
\(461\) | −15.0711 | − | 26.1039i | −0.701930 | − | 1.21578i | −0.967788 | − | 0.251766i | \(-0.918989\pi\) |
0.265859 | − | 0.964012i | \(-0.414345\pi\) | |||||||
\(462\) | 1.07107 | − | 1.85514i | 0.0498306 | − | 0.0863091i | ||||
\(463\) | −22.7990 | −1.05956 | −0.529779 | − | 0.848135i | \(-0.677725\pi\) | ||||
−0.529779 | + | 0.848135i | \(0.677725\pi\) | |||||||
\(464\) | 28.9706 | 1.34492 | ||||||||
\(465\) | 2.50000 | − | 4.33013i | 0.115935 | − | 0.200805i | ||||
\(466\) | −5.24264 | + | 9.08052i | −0.242861 | + | 0.420647i | ||||
\(467\) | 23.7990 | 1.10129 | 0.550643 | − | 0.834741i | \(-0.314383\pi\) | ||||
0.550643 | + | 0.834741i | \(0.314383\pi\) | |||||||
\(468\) | 3.34315 | 0.154537 | ||||||||
\(469\) | −5.01472 | + | 8.68575i | −0.231558 | + | 0.401071i | ||||
\(470\) | 0.656854 | + | 1.13770i | 0.0302984 | + | 0.0524784i | ||||
\(471\) | −9.91421 | + | 17.1719i | −0.456823 | + | 0.791240i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0711 | + | 19.1757i | 0.509048 | + | 0.881697i | ||||
\(474\) | −1.38478 | −0.0636049 | ||||||||
\(475\) | −3.50000 | + | 2.59808i | −0.160591 | + | 0.119208i | ||||
\(476\) | 3.91674 | 0.179523 | ||||||||
\(477\) | 1.00000 | + | 1.73205i | 0.0457869 | + | 0.0793052i | ||||
\(478\) | −5.10051 | − | 8.83433i | −0.233292 | − | 0.404073i | ||||
\(479\) | −1.24264 | + | 2.15232i | −0.0567777 | + | 0.0983419i | −0.893017 | − | 0.450022i | \(-0.851416\pi\) |
0.836240 | + | 0.548364i | \(0.184749\pi\) | |||||||
\(480\) | 2.20711 | + | 3.82282i | 0.100740 | + | 0.174487i | ||||
\(481\) | −1.98528 | + | 3.43861i | −0.0905210 | + | 0.156787i | ||||
\(482\) | −2.07107 | −0.0943346 | ||||||||
\(483\) | 1.51472 | 0.0689221 | ||||||||
\(484\) | −2.74264 | + | 4.75039i | −0.124665 | + | 0.215927i | ||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 0.414214 | 0.0187891 | ||||||||
\(487\) | −6.34315 | −0.287435 | −0.143718 | − | 0.989619i | \(-0.545906\pi\) | ||||
−0.143718 | + | 0.989619i | \(0.545906\pi\) | |||||||
\(488\) | 6.59188 | − | 11.4175i | 0.298401 | − | 0.516845i | ||||
\(489\) | 7.57107 | + | 13.1135i | 0.342376 | + | 0.593012i | ||||
\(490\) | 0.757359 | − | 1.31178i | 0.0342140 | − | 0.0592604i | ||||
\(491\) | −11.8284 | − | 20.4874i | −0.533809 | − | 0.924585i | −0.999220 | − | 0.0394901i | \(-0.987427\pi\) |
0.465411 | − | 0.885095i | \(-0.345907\pi\) | |||||||
\(492\) | −2.58579 | − | 4.47871i | −0.116576 | − | 0.201916i | ||||
\(493\) | −11.3137 | −0.509544 | ||||||||
\(494\) | 3.02944 | + | 1.31178i | 0.136301 | + | 0.0590200i | ||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 7.50000 | + | 12.9904i | 0.336760 | + | 0.583285i | ||||
\(497\) | −9.14214 | − | 15.8346i | −0.410081 | − | 0.710281i | ||||
\(498\) | 1.65685 | − | 2.86976i | 0.0742454 | − | 0.128597i | ||||
\(499\) | 3.67157 | + | 6.35935i | 0.164362 | + | 0.284684i | 0.936429 | − | 0.350858i | \(-0.114110\pi\) |
−0.772066 | + | 0.635542i | \(0.780777\pi\) | |||||||
\(500\) | −0.914214 | + | 1.58346i | −0.0408849 | + | 0.0708147i | ||||
\(501\) | 24.9706 | 1.11560 | ||||||||
\(502\) | 6.76955 | 0.302140 | ||||||||
\(503\) | −6.92893 | + | 12.0013i | −0.308946 | + | 0.535110i | −0.978132 | − | 0.207985i | \(-0.933310\pi\) |
0.669186 | + | 0.743095i | \(0.266643\pi\) | |||||||
\(504\) | −1.44975 | + | 2.51104i | −0.0645769 | + | 0.111850i | ||||
\(505\) | −12.1421 | −0.540318 | ||||||||
\(506\) | −0.970563 | −0.0431468 | ||||||||
\(507\) | −4.82843 | + | 8.36308i | −0.214438 | + | 0.371417i | ||||
\(508\) | 11.8579 | + | 20.5384i | 0.526108 | + | 0.911245i | ||||
\(509\) | −16.5563 | + | 28.6764i | −0.733847 | + | 1.27106i | 0.221380 | + | 0.975188i | \(0.428944\pi\) |
−0.955227 | + | 0.295873i | \(0.904389\pi\) | |||||||
\(510\) | −0.242641 | − | 0.420266i | −0.0107443 | − | 0.0186097i | ||||
\(511\) | −8.67157 | − | 15.0196i | −0.383608 | − | 0.664428i | ||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | −4.00000 | − | 1.73205i | −0.176604 | − | 0.0764719i | ||||
\(514\) | 6.97056 | 0.307458 | ||||||||
\(515\) | 4.91421 | + | 8.51167i | 0.216546 | + | 0.375069i | ||||
\(516\) | −7.15685 | − | 12.3960i | −0.315063 | − | 0.545705i | ||||
\(517\) | −4.48528 | + | 7.76874i | −0.197262 | + | 0.341669i | ||||
\(518\) | −0.822330 | − | 1.42432i | −0.0361311 | − | 0.0625809i | ||||
\(519\) | 3.65685 | − | 6.33386i | 0.160518 | − | 0.278025i | ||||
\(520\) | 2.89949 | 0.127151 | ||||||||
\(521\) | 6.34315 | 0.277898 | 0.138949 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138949 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(522\) | 2.00000 | − | 3.46410i | 0.0875376 | − | 0.151620i | ||||
\(523\) | 14.8848 | − | 25.7812i | 0.650866 | − | 1.12733i | −0.332047 | − | 0.943263i | \(-0.607739\pi\) |
0.982913 | − | 0.184070i | \(-0.0589273\pi\) | |||||||
\(524\) | −11.8579 | −0.518013 | ||||||||
\(525\) | −1.82843 | −0.0797991 | ||||||||
\(526\) | 5.34315 | − | 9.25460i | 0.232972 | − | 0.403520i | ||||
\(527\) | −2.92893 | − | 5.07306i | −0.127586 | − | 0.220986i | ||||
\(528\) | −4.24264 | + | 7.34847i | −0.184637 | + | 0.319801i | ||||
\(529\) | 11.1569 | + | 19.3242i | 0.485081 | + | 0.840184i | ||||
\(530\) | 0.414214 | + | 0.717439i | 0.0179923 | + | 0.0311636i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.7010 | − | 8.68575i | 0.507303 | − | 0.376575i | ||||
\(533\) | −5.17157 | −0.224006 | ||||||||
\(534\) | −2.58579 | − | 4.47871i | −0.111898 | − | 0.193813i | ||||
\(535\) | 7.00000 | + | 12.1244i | 0.302636 | + | 0.524182i | ||||
\(536\) | −4.34924 | + | 7.53311i | −0.187859 | + | 0.325381i | ||||
\(537\) | 8.07107 | + | 13.9795i | 0.348292 | + | 0.603260i | ||||
\(538\) | 0.343146 | − | 0.594346i | 0.0147941 | − | 0.0256241i | ||||
\(539\) | 10.3431 | 0.445511 | ||||||||
\(540\) | −1.82843 | −0.0786830 | ||||||||
\(541\) | −8.15685 | + | 14.1281i | −0.350691 | + | 0.607414i | −0.986371 | − | 0.164539i | \(-0.947386\pi\) |
0.635680 | + | 0.771953i | \(0.280720\pi\) | |||||||
\(542\) | 2.82843 | − | 4.89898i | 0.121491 | − | 0.210429i | ||||
\(543\) | −25.3137 | −1.08632 | ||||||||
\(544\) | 5.17157 | 0.221729 | ||||||||
\(545\) | −8.65685 | + | 14.9941i | −0.370819 | + | 0.642277i | ||||
\(546\) | 0.692388 | + | 1.19925i | 0.0296315 | + | 0.0513232i | ||||
\(547\) | 6.57107 | − | 11.3814i | 0.280959 | − | 0.486635i | −0.690663 | − | 0.723177i | \(-0.742681\pi\) |
0.971621 | + | 0.236543i | \(0.0760143\pi\) | |||||||
\(548\) | −9.58579 | − | 16.6031i | −0.409485 | − | 0.709248i | ||||
\(549\) | 4.15685 | + | 7.19988i | 0.177410 | + | 0.307284i | ||||
\(550\) | 1.17157 | 0.0499560 | ||||||||
\(551\) | −33.7990 | + | 25.0892i | −1.43989 | + | 1.06884i | ||||
\(552\) | 1.31371 | 0.0559151 | ||||||||
\(553\) | 3.05635 | + | 5.29375i | 0.129969 | + | 0.225113i | ||||
\(554\) | 1.24264 | + | 2.15232i | 0.0527947 | + | 0.0914432i | ||||
\(555\) | 1.08579 | − | 1.88064i | 0.0460891 | − | 0.0798286i | ||||
\(556\) | −14.9142 | − | 25.8322i | −0.632504 | − | 1.09553i | ||||
\(557\) | 4.51472 | − | 7.81972i | 0.191295 | − | 0.331332i | −0.754385 | − | 0.656432i | \(-0.772065\pi\) |
0.945680 | + | 0.325100i | \(0.105398\pi\) | |||||||
\(558\) | 2.07107 | 0.0876753 | ||||||||
\(559\) | −14.3137 | −0.605405 | ||||||||
\(560\) | 2.74264 | − | 4.75039i | 0.115898 | − | 0.200741i | ||||
\(561\) | 1.65685 | − | 2.86976i | 0.0699524 | − | 0.121161i | ||||
\(562\) | 2.88730 | 0.121793 | ||||||||
\(563\) | −12.1421 | −0.511730 | −0.255865 | − | 0.966713i | \(-0.582360\pi\) | ||||
−0.255865 | + | 0.966713i | \(0.582360\pi\) | |||||||
\(564\) | 2.89949 | − | 5.02207i | 0.122091 | − | 0.211467i | ||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | −4.34315 | + | 7.52255i | −0.182556 | + | 0.316196i | ||||
\(567\) | −0.914214 | − | 1.58346i | −0.0383934 | − | 0.0664993i | ||||
\(568\) | −7.92893 | − | 13.7333i | −0.332691 | − | 0.576237i | ||||
\(569\) | 4.97056 | 0.208377 | 0.104188 | − | 0.994558i | \(-0.466776\pi\) | ||||
0.104188 | + | 0.994558i | \(0.466776\pi\) | |||||||
\(570\) | −1.65685 | − | 0.717439i | −0.0693980 | − | 0.0300502i | ||||
\(571\) | 14.3137 | 0.599010 | 0.299505 | − | 0.954095i | \(-0.403178\pi\) | ||||
0.299505 | + | 0.954095i | \(0.403178\pi\) | |||||||
\(572\) | 4.72792 | + | 8.18900i | 0.197684 | + | 0.342399i | ||||
\(573\) | −8.41421 | − | 14.5738i | −0.351509 | − | 0.608831i | ||||
\(574\) | 1.07107 | − | 1.85514i | 0.0447055 | − | 0.0774322i | ||||
\(575\) | 0.414214 | + | 0.717439i | 0.0172739 | + | 0.0299193i | ||||
\(576\) | 2.08579 | − | 3.61269i | 0.0869078 | − | 0.150529i | ||||
\(577\) | −36.3431 | −1.51298 | −0.756492 | − | 0.654002i | \(-0.773089\pi\) | ||||
−0.756492 | + | 0.654002i | \(0.773089\pi\) | |||||||
\(578\) | 6.47309 | 0.269245 | ||||||||
\(579\) | −12.3995 | + | 21.4766i | −0.515305 | + | 0.892535i | ||||
\(580\) | −8.82843 | + | 15.2913i | −0.366580 | + | 0.634936i | ||||
\(581\) | −14.6274 | −0.606848 | ||||||||
\(582\) | −2.48528 | −0.103018 | ||||||||
\(583\) | −2.82843 | + | 4.89898i | −0.117141 | + | 0.202895i | ||||
\(584\) | −7.52082 | − | 13.0264i | −0.311214 | − | 0.539038i | ||||
\(585\) | −0.914214 | + | 1.58346i | −0.0377981 | + | 0.0654682i | ||||
\(586\) | −1.10051 | − | 1.90613i | −0.0454614 | − | 0.0787415i | ||||
\(587\) | −5.31371 | − | 9.20361i | −0.219320 | − | 0.379874i | 0.735280 | − | 0.677763i | \(-0.237051\pi\) |
−0.954600 | + | 0.297890i | \(0.903717\pi\) | |||||||
\(588\) | −6.68629 | −0.275738 | ||||||||
\(589\) | −20.0000 | − | 8.66025i | −0.824086 | − | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.82843 | + | 15.2913i | 0.363153 | + | 0.628999i | ||||
\(592\) | 3.25736 | + | 5.64191i | 0.133877 | + | 0.231881i | ||||
\(593\) | 4.92893 | − | 8.53716i | 0.202407 | − | 0.350579i | −0.746896 | − | 0.664940i | \(-0.768457\pi\) |
0.949303 | + | 0.314361i | \(0.101790\pi\) | |||||||
\(594\) | 0.585786 | + | 1.01461i | 0.0240351 | + | 0.0416300i | ||||
\(595\) | −1.07107 | + | 1.85514i | −0.0439095 | + | 0.0760535i | ||||
\(596\) | 2.14214 | 0.0877453 | ||||||||
\(597\) | 17.0000 | 0.695764 | ||||||||
\(598\) | 0.313708 | − | 0.543359i | 0.0128285 | − | 0.0222196i | ||||
\(599\) | 8.48528 | − | 14.6969i | 0.346699 | − | 0.600501i | −0.638962 | − | 0.769238i | \(-0.720636\pi\) |
0.985661 | + | 0.168738i | \(0.0539691\pi\) | |||||||
\(600\) | −1.58579 | −0.0647395 | ||||||||
\(601\) | −35.3431 | −1.44168 | −0.720838 | − | 0.693103i | \(-0.756243\pi\) | ||||
−0.720838 | + | 0.693103i | \(0.756243\pi\) | |||||||
\(602\) | 2.96447 | − | 5.13461i | 0.120823 | − | 0.209271i | ||||
\(603\) | −2.74264 | − | 4.75039i | −0.111689 | − | 0.193451i | ||||
\(604\) | 9.45584 | − | 16.3780i | 0.384753 | − | 0.666411i | ||||
\(605\) | −1.50000 | − | 2.59808i | −0.0609837 | − | 0.105627i | ||||
\(606\) | −2.51472 | − | 4.35562i | −0.102153 | − | 0.176935i | ||||
\(607\) | −6.17157 | −0.250496 | −0.125248 | − | 0.992125i | \(-0.539973\pi\) | ||||
−0.125248 | + | 0.992125i | \(0.539973\pi\) | |||||||
\(608\) | 15.4497 | − | 11.4685i | 0.626570 | − | 0.465108i | ||||
\(609\) | −17.6569 | −0.715492 | ||||||||
\(610\) | 1.72183 | + | 2.98229i | 0.0697147 | + | 0.120749i | ||||
\(611\) | −2.89949 | − | 5.02207i | −0.117301 | − | 0.203171i | ||||
\(612\) | −1.07107 | + | 1.85514i | −0.0432954 | + | 0.0749897i | ||||
\(613\) | −16.7990 | − | 29.0967i | −0.678505 | − | 1.17520i | −0.975431 | − | 0.220304i | \(-0.929295\pi\) |
0.296926 | − | 0.954900i | \(-0.404038\pi\) | |||||||
\(614\) | −3.65685 | + | 6.33386i | −0.147579 | + | 0.255614i | ||||
\(615\) | 2.82843 | 0.114053 | ||||||||
\(616\) | −8.20101 | −0.330428 | ||||||||
\(617\) | −12.8284 | + | 22.2195i | −0.516453 | + | 0.894523i | 0.483364 | + | 0.875419i | \(0.339415\pi\) |
−0.999818 | + | 0.0191037i | \(0.993919\pi\) | |||||||
\(618\) | −2.03553 | + | 3.52565i | −0.0818812 | + | 0.141822i | ||||
\(619\) | 15.6863 | 0.630485 | 0.315243 | − | 0.949011i | \(-0.397914\pi\) | ||||
0.315243 | + | 0.949011i | \(0.397914\pi\) | |||||||
\(620\) | −9.14214 | −0.367157 | ||||||||
\(621\) | −0.414214 | + | 0.717439i | −0.0166218 | + | 0.0287898i | ||||
\(622\) | −0.828427 | − | 1.43488i | −0.0332169 | − | 0.0575334i | ||||
\(623\) | −11.4142 | + | 19.7700i | −0.457301 | + | 0.792068i | ||||
\(624\) | −2.74264 | − | 4.75039i | −0.109793 | − | 0.190168i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 2.48528 | 0.0993318 | ||||||||
\(627\) | −1.41421 | − | 12.2474i | −0.0564782 | − | 0.489116i | ||||
\(628\) | 36.2548 | 1.44673 | ||||||||
\(629\) | −1.27208 | − | 2.20330i | −0.0507211 | − | 0.0878515i | ||||
\(630\) | −0.378680 | − | 0.655892i | −0.0150870 | − | 0.0261314i | ||||
\(631\) | 6.64214 | − | 11.5045i | 0.264419 | − | 0.457988i | −0.702992 | − | 0.711198i | \(-0.748153\pi\) |
0.967411 | + | 0.253210i | \(0.0814864\pi\) | |||||||
\(632\) | 2.65076 | + | 4.59125i | 0.105441 | + | 0.182630i | ||||
\(633\) | −0.156854 | + | 0.271680i | −0.00623440 | + | 0.0107983i | ||||
\(634\) | −2.20101 | −0.0874133 | ||||||||
\(635\) | −12.9706 | −0.514721 | ||||||||
\(636\) | 1.82843 | − | 3.16693i | 0.0725019 | − | 0.125577i | ||||
\(637\) | −3.34315 | + | 5.79050i | −0.132460 | + | 0.229428i | ||||
\(638\) | 11.3137 | 0.447914 | ||||||||
\(639\) | 10.0000 | 0.395594 | ||||||||
\(640\) | 5.27817 | − | 9.14207i | 0.208638 | − | 0.361372i | ||||
\(641\) | −14.0711 | − | 24.3718i | −0.555774 | − | 0.962628i | −0.997843 | − | 0.0656474i | \(-0.979089\pi\) |
0.442069 | − | 0.896981i | \(-0.354245\pi\) | |||||||
\(642\) | −2.89949 | + | 5.02207i | −0.114434 | + | 0.198205i | ||||
\(643\) | −2.91421 | − | 5.04757i | −0.114925 | − | 0.199057i | 0.802825 | − | 0.596215i | \(-0.203330\pi\) |
−0.917750 | + | 0.397159i | \(0.869996\pi\) | |||||||
\(644\) | −1.38478 | − | 2.39850i | −0.0545678 | − | 0.0945143i | ||||
\(645\) | 7.82843 | 0.308244 | ||||||||
\(646\) | −1.69848 | + | 1.26080i | −0.0668260 | + | 0.0496054i | ||||
\(647\) | −32.2843 | −1.26923 | −0.634613 | − | 0.772830i | \(-0.718840\pi\) | ||||
−0.634613 | + | 0.772830i | \(0.718840\pi\) | |||||||
\(648\) | −0.792893 | − | 1.37333i | −0.0311478 | − | 0.0539496i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.378680 | + | 0.655892i | −0.0148530 | + | 0.0257262i | ||||
\(651\) | −4.57107 | − | 7.91732i | −0.179154 | − | 0.310304i | ||||
\(652\) | 13.8431 | − | 23.9770i | 0.542139 | − | 0.939013i | ||||
\(653\) | 39.9411 | 1.56302 | 0.781509 | − | 0.623895i | \(-0.214451\pi\) | ||||
0.781509 | + | 0.623895i | \(0.214451\pi\) | |||||||
\(654\) | −7.17157 | −0.280431 | ||||||||
\(655\) | 3.24264 | − | 5.61642i | 0.126700 | − | 0.219452i | ||||
\(656\) | −4.24264 | + | 7.34847i | −0.165647 | + | 0.286910i | ||||
\(657\) | 9.48528 | 0.370056 | ||||||||
\(658\) | 2.40202 | 0.0936405 | ||||||||
\(659\) | −3.75736 | + | 6.50794i | −0.146366 | + | 0.253513i | −0.929882 | − | 0.367859i | \(-0.880091\pi\) |
0.783516 | + | 0.621372i | \(0.213424\pi\) | |||||||
\(660\) | −2.58579 | − | 4.47871i | −0.100652 | − | 0.174334i | ||||
\(661\) | 3.48528 | − | 6.03668i | 0.135562 | − | 0.234800i | −0.790250 | − | 0.612784i | \(-0.790049\pi\) |
0.925812 | + | 0.377985i | \(0.123383\pi\) | |||||||
\(662\) | −1.10660 | − | 1.91669i | −0.0430093 | − | 0.0744943i | ||||
\(663\) | 1.07107 | + | 1.85514i | 0.0415968 | + | 0.0720478i | ||||
\(664\) | −12.6863 | −0.492324 | ||||||||
\(665\) | 0.914214 | + | 7.91732i | 0.0354517 | + | 0.307021i | ||||
\(666\) | 0.899495 | 0.0348547 | ||||||||
\(667\) | 4.00000 | + | 6.92820i | 0.154881 | + | 0.268261i | ||||
\(668\) | −22.8284 | − | 39.5400i | −0.883258 | − | 1.52985i | ||||
\(669\) | 2.91421 | − | 5.04757i | 0.112670 | − | 0.195150i | ||||
\(670\) | −1.13604 | − | 1.96768i | −0.0438890 | − | 0.0760180i | ||||
\(671\) | −11.7574 | + | 20.3643i | −0.453888 | + | 0.786157i | ||||
\(672\) | 8.07107 | 0.311348 | ||||||||
\(673\) | −23.8284 | −0.918518 | −0.459259 | − | 0.888302i | \(-0.651885\pi\) | ||||
−0.459259 | + | 0.888302i | \(0.651885\pi\) | |||||||
\(674\) | 3.62132 | − | 6.27231i | 0.139488 | − | 0.241600i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 17.6569 | 0.679110 | ||||||||
\(677\) | −23.4558 | −0.901481 | −0.450741 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450741 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(678\) | −0.828427 | + | 1.43488i | −0.0318156 | + | 0.0551062i | ||||
\(679\) | 5.48528 | + | 9.50079i | 0.210506 | + | 0.364607i | ||||
\(680\) | −0.928932 | + | 1.60896i | −0.0356229 | + | 0.0617007i | ||||
\(681\) | −9.48528 | − | 16.4290i | −0.363477 | − | 0.629560i | ||||
\(682\) | 2.92893 | + | 5.07306i | 0.112155 | + | 0.194257i | ||||
\(683\) | 44.1421 | 1.68905 | 0.844526 | − | 0.535515i | \(-0.179882\pi\) | ||||
0.844526 | + | 0.535515i | \(0.179882\pi\) | |||||||
\(684\) | 0.914214 | + | 7.91732i | 0.0349558 | + | 0.302726i | ||||
\(685\) | 10.4853 | 0.400622 | ||||||||
\(686\) | −4.03553 | − | 6.98975i | −0.154077 | − | 0.266870i | ||||
\(687\) | −2.32843 | − | 4.03295i | −0.0888350 | − | 0.153867i | ||||
\(688\) | −11.7426 | + | 20.3389i | −0.447684 | + | 0.775411i | ||||
\(689\) | −1.82843 | − | 3.16693i | −0.0696575 | − | 0.120650i | ||||
\(690\) | −0.171573 | + | 0.297173i | −0.00653167 | + | 0.0113132i | ||||
\(691\) | 31.3137 | 1.19123 | 0.595615 | − | 0.803270i | \(-0.296908\pi\) | ||||
0.595615 | + | 0.803270i | \(0.296908\pi\) | |||||||
\(692\) | −13.3726 | −0.508349 | ||||||||
\(693\) | 2.58579 | − | 4.47871i | 0.0982259 | − | 0.170132i | ||||
\(694\) | −7.34315 | + | 12.7187i | −0.278742 | + | 0.482795i | ||||
\(695\) | 16.3137 | 0.618814 | ||||||||
\(696\) | −15.3137 | −0.580465 | ||||||||
\(697\) | 1.65685 | − | 2.86976i | 0.0627578 | − | 0.108700i | ||||
\(698\) | −6.55025 | − | 11.3454i | −0.247931 | − | 0.429429i | ||||
\(699\) | −12.6569 | + | 21.9223i | −0.478726 | + | 0.829178i | ||||
\(700\) | 1.67157 | + | 2.89525i | 0.0631795 | + | 0.109430i | ||||
\(701\) | −16.0711 | − | 27.8359i | −0.606996 | − | 1.05135i | −0.991733 | − | 0.128321i | \(-0.959041\pi\) |
0.384737 | − | 0.923026i | \(-0.374292\pi\) | |||||||
\(702\) | −0.757359 | −0.0285847 | ||||||||
\(703\) | −8.68629 | − | 3.76127i | −0.327610 | − | 0.141859i | ||||
\(704\) | 11.7990 | 0.444691 | ||||||||
\(705\) | 1.58579 | + | 2.74666i | 0.0597242 | + | 0.103445i | ||||
\(706\) | −0.272078 | − | 0.471253i | −0.0102398 | − | 0.0177358i | ||||
\(707\) | −11.1005 | + | 19.2266i | −0.417477 | + | 0.723092i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8137 | + | 27.3901i | −0.593896 | + | 1.02866i | 0.399805 | + | 0.916600i | \(0.369078\pi\) |
−0.993702 | + | 0.112058i | \(0.964256\pi\) | |||||||
\(710\) | 4.14214 | 0.155452 | ||||||||
\(711\) | −3.34315 | −0.125378 | ||||||||
\(712\) | −9.89949 | + | 17.1464i | −0.370999 | + | 0.642590i | ||||
\(713\) | −2.07107 | + | 3.58719i | −0.0775621 | + | 0.134341i | ||||
\(714\) | −0.887302 | −0.0332064 | ||||||||
\(715\) | −5.17157 | −0.193406 | ||||||||
\(716\) | 14.7574 | − | 25.5605i | 0.551508 | − | 0.955241i | ||||
\(717\) | −12.3137 | − | 21.3280i | −0.459864 | − | 0.796508i | ||||
\(718\) | 1.89949 | − | 3.29002i | 0.0708885 | − | 0.122783i | ||||
\(719\) | 11.5858 | + | 20.0672i | 0.432077 | + | 0.748379i | 0.997052 | − | 0.0767288i | \(-0.0244476\pi\) |
−0.564975 | + | 0.825108i | \(0.691114\pi\) | |||||||
\(720\) | 1.50000 | + | 2.59808i | 0.0559017 | + | 0.0968246i | ||||
\(721\) | 17.9706 | 0.669259 | ||||||||
\(722\) | −2.27817 | + | 7.53311i | −0.0847849 | + | 0.280353i | ||||
\(723\) | −5.00000 | −0.185952 | ||||||||
\(724\) | 23.1421 | + | 40.0834i | 0.860071 | + | 1.48969i | ||||
\(725\) | −4.82843 | − | 8.36308i | −0.179323 | − | 0.310597i | ||||
\(726\) | 0.621320 | − | 1.07616i | 0.0230594 | − | 0.0399400i | ||||
\(727\) | −18.0858 | − | 31.3255i | −0.670765 | − | 1.16180i | −0.977688 | − | 0.210064i | \(-0.932633\pi\) |
0.306923 | − | 0.951734i | \(-0.400701\pi\) | |||||||
\(728\) | 2.65076 | − | 4.59125i | 0.0982436 | − | 0.170163i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.92893 | 0.145416 | ||||||||
\(731\) | 4.58579 | − | 7.94282i | 0.169611 | − | 0.293776i | ||||
\(732\) | 7.60051 | − | 13.1645i | 0.280923 | − | 0.486572i | ||||
\(733\) | 3.65685 | 0.135069 | 0.0675345 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675345 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(734\) | 14.1299 | 0.521546 | ||||||||
\(735\) | 1.82843 | − | 3.16693i | 0.0674426 | − | 0.116814i | ||||
\(736\) | −1.82843 | − | 3.16693i | −0.0673967 | − | 0.116735i | ||||
\(737\) | 7.75736 | − | 13.4361i | 0.285746 | − | 0.494927i | ||||
\(738\) | 0.585786 | + | 1.01461i | 0.0215631 | + | 0.0373484i | ||||
\(739\) | 20.8137 | + | 36.0504i | 0.765645 | + | 1.32614i | 0.939905 | + | 0.341436i | \(0.110913\pi\) |
−0.174260 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(740\) | −3.97056 | −0.145961 | ||||||||
\(741\) | 7.31371 | + | 3.16693i | 0.268676 | + | 0.116340i | ||||
\(742\) | 1.51472 | 0.0556071 | ||||||||
\(743\) | −17.0711 | − | 29.5680i | −0.626277 | − | 1.08474i | −0.988292 | − | 0.152571i | \(-0.951245\pi\) |
0.362016 | − | 0.932172i | \(-0.382089\pi\) | |||||||
\(744\) | −3.96447 | − | 6.86666i | −0.145344 | − | 0.251744i | ||||
\(745\) | −0.585786 | + | 1.01461i | −0.0214616 | + | 0.0371725i | ||||
\(746\) | −2.41421 | − | 4.18154i | −0.0883906 | − | 0.153097i | ||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | −6.05887 | −0.221534 | ||||||||
\(749\) | 25.5980 | 0.935330 | ||||||||
\(750\) | 0.207107 | − | 0.358719i | 0.00756247 | − | 0.0130986i | ||||
\(751\) | −13.1569 | + | 22.7883i | −0.480100 | + | 0.831558i | −0.999739 | − | 0.0228276i | \(-0.992733\pi\) |
0.519639 | + | 0.854386i | \(0.326066\pi\) | |||||||
\(752\) | −9.51472 | −0.346966 | ||||||||
\(753\) | 16.3431 | 0.595577 | ||||||||
\(754\) | −3.65685 | + | 6.33386i | −0.133175 | + | 0.230665i | ||||
\(755\) | 5.17157 | + | 8.95743i | 0.188213 | + | 0.325994i | ||||
\(756\) | −1.67157 | + | 2.89525i | −0.0607945 | + | 0.105299i | ||||
\(757\) | 16.5711 | + | 28.7019i | 0.602286 | + | 1.04319i | 0.992474 | + | 0.122454i | \(0.0390765\pi\) |
−0.390188 | + | 0.920735i | \(0.627590\pi\) | |||||||
\(758\) | 0.349242 | + | 0.604906i | 0.0126851 | + | 0.0219712i | ||||
\(759\) | −2.34315 | −0.0850508 | ||||||||
\(760\) | 0.792893 | + | 6.86666i | 0.0287613 | + | 0.249080i | ||||
\(761\) | 51.5980 | 1.87043 | 0.935213 | − | 0.354087i | \(-0.115208\pi\) | ||||
0.935213 | + | 0.354087i | \(0.115208\pi\) | |||||||
\(762\) | −2.68629 | − | 4.65279i | −0.0973141 | − | 0.168553i | ||||
\(763\) | 15.8284 | + | 27.4156i | 0.573028 | + | 0.992513i | ||||
\(764\) | −15.3848 | + | 26.6472i | −0.556602 | + | 0.964062i | ||||
\(765\) | −0.585786 | − | 1.01461i | −0.0211792 | − | 0.0366834i | ||||
\(766\) | −7.02944 | + | 12.1753i | −0.253984 | + | 0.439913i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.97056 | −0.143275 | ||||||||
\(769\) | −7.15685 | + | 12.3960i | −0.258083 | + | 0.447012i | −0.965728 | − | 0.259555i | \(-0.916424\pi\) |
0.707646 | + | 0.706568i | \(0.249757\pi\) | |||||||
\(770\) | 1.07107 | − | 1.85514i | 0.0385986 | − | 0.0668547i |