Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [650,2,Mod(193,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.w (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.19027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 357.2 | ||
Root | \(0.500000 + 1.56488i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.357 |
Dual form | 650.2.w.d.193.2 |
$q$-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 \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{12}\right)\) |
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 | ||||
\(3\) | 0.849429 | + | 3.17011i | 0.490418 | + | 1.83026i | 0.554314 | + | 0.832308i | \(0.312981\pi\) |
−0.0638964 | + | 0.997957i | \(0.520353\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.17011 | + | 0.849429i | 1.29419 | + | 0.346778i | ||||
\(7\) | −0.344430 | + | 0.198857i | −0.130182 | + | 0.0751609i | −0.563677 | − | 0.825995i | \(-0.690614\pi\) |
0.433494 | + | 0.901156i | \(0.357280\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −6.72999 | + | 3.88556i | −2.24333 | + | 1.29519i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.33728 | + | 1.43012i | −1.60925 | + | 0.431197i | −0.947819 | − | 0.318809i | \(-0.896717\pi\) |
−0.661431 | + | 0.750006i | \(0.730051\pi\) | |||||||
\(12\) | 2.32068 | − | 2.32068i | 0.669923 | − | 0.669923i | ||||
\(13\) | −2.73499 | + | 2.34943i | −0.758551 | + | 0.651614i | ||||
\(14\) | 0.397714i | 0.106294i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.10523 | + | 0.564094i | 0.510593 | + | 0.136813i | 0.504912 | − | 0.863171i | \(-0.331525\pi\) |
0.00568097 | + | 0.999984i | \(0.498192\pi\) | |||||||
\(18\) | 7.77113i | 1.83167i | ||||||||
\(19\) | −0.507152 | + | 1.89272i | −0.116349 | + | 0.434219i | −0.999384 | − | 0.0350870i | \(-0.988829\pi\) |
0.883036 | + | 0.469306i | \(0.155496\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.922968 | − | 0.922968i | −0.201408 | − | 0.201408i | ||||
\(22\) | −1.43012 | + | 5.33728i | −0.304903 | + | 1.13791i | ||||
\(23\) | 5.75159 | − | 1.54113i | 1.19929 | − | 0.321349i | 0.396738 | − | 0.917932i | \(-0.370142\pi\) |
0.802551 | + | 0.596583i | \(0.203475\pi\) | |||||||
\(24\) | −0.849429 | − | 3.17011i | −0.173389 | − | 0.647096i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.667168 | + | 3.54329i | 0.130842 | + | 0.694896i | ||||
\(27\) | −11.0723 | − | 11.0723i | −2.13086 | − | 2.13086i | ||||
\(28\) | 0.344430 | + | 0.198857i | 0.0650912 | + | 0.0375804i | ||||
\(29\) | 3.96205 | + | 2.28749i | 0.735733 | + | 0.424776i | 0.820516 | − | 0.571624i | \(-0.193686\pi\) |
−0.0847826 | + | 0.996399i | \(0.527020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49794 | − | 2.49794i | 0.448644 | − | 0.448644i | −0.446260 | − | 0.894904i | \(-0.647244\pi\) |
0.894904 | + | 0.446260i | \(0.147244\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −9.06727 | − | 15.7050i | −1.57841 | − | 2.73389i | ||||
\(34\) | 1.54113 | − | 1.54113i | 0.264302 | − | 0.264302i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.72999 | + | 3.88556i | 1.12167 | + | 0.647594i | ||||
\(37\) | 2.77661 | + | 1.60307i | 0.456471 | + | 0.263544i | 0.710559 | − | 0.703637i | \(-0.248442\pi\) |
−0.254088 | + | 0.967181i | \(0.581775\pi\) | |||||||
\(38\) | 1.38556 | + | 1.38556i | 0.224768 | + | 0.224768i | ||||
\(39\) | −9.77113 | − | 6.67456i | −1.56463 | − | 1.06878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.28749 | + | 8.53702i | 0.357246 | + | 1.33326i | 0.877635 | + | 0.479330i | \(0.159120\pi\) |
−0.520389 | + | 0.853929i | \(0.674213\pi\) | |||||||
\(42\) | −1.26080 | + | 0.337830i | −0.194545 | + | 0.0521282i | ||||
\(43\) | 1.85658 | − | 6.92885i | 0.283126 | − | 1.05664i | −0.667072 | − | 0.744993i | \(-0.732453\pi\) |
0.950198 | − | 0.311647i | \(-0.100881\pi\) | |||||||
\(44\) | 3.90716 | + | 3.90716i | 0.589026 | + | 0.589026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.54113 | − | 5.75159i | 0.227228 | − | 0.848026i | ||||
\(47\) | 11.8102i | 1.72270i | 0.508016 | + | 0.861348i | \(0.330379\pi\) | ||||
−0.508016 | + | 0.861348i | \(0.669621\pi\) | |||||||
\(48\) | −3.17011 | − | 0.849429i | −0.457566 | − | 0.122604i | ||||
\(49\) | −3.42091 | + | 5.92519i | −0.488702 | + | 0.846456i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.15296i | 1.00162i | ||||||||
\(52\) | 3.40216 | + | 1.19386i | 0.471795 | + | 0.165558i | ||||
\(53\) | 5.86397 | − | 5.86397i | 0.805478 | − | 0.805478i | −0.178468 | − | 0.983946i | \(-0.557114\pi\) |
0.983946 | + | 0.178468i | \(0.0571140\pi\) | |||||||
\(54\) | −15.1250 | + | 4.05273i | −2.05825 | + | 0.551507i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.344430 | − | 0.198857i | 0.0460265 | − | 0.0265734i | ||||
\(57\) | −6.43091 | −0.851795 | ||||||||
\(58\) | 3.96205 | − | 2.28749i | 0.520242 | − | 0.300362i | ||||
\(59\) | −6.38556 | − | 1.71101i | −0.831330 | − | 0.222754i | −0.182036 | − | 0.983292i | \(-0.558269\pi\) |
−0.649294 | + | 0.760538i | \(0.724935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.72490 | + | 6.45171i | 0.476924 | + | 0.826057i | 0.999650 | − | 0.0264434i | \(-0.00841819\pi\) |
−0.522726 | + | 0.852501i | \(0.675085\pi\) | |||||||
\(62\) | −0.914311 | − | 3.41225i | −0.116118 | − | 0.433357i | ||||
\(63\) | 1.54534 | − | 2.67661i | 0.194695 | − | 0.337222i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −18.1345 | −2.23221 | ||||||||
\(67\) | 0.621825 | − | 1.07703i | 0.0759680 | − | 0.131580i | −0.825539 | − | 0.564345i | \(-0.809129\pi\) |
0.901507 | + | 0.432765i | \(0.142462\pi\) | |||||||
\(68\) | −0.564094 | − | 2.10523i | −0.0684065 | − | 0.255296i | ||||
\(69\) | 9.77113 | + | 16.9241i | 1.17631 | + | 2.03742i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.96205 | − | 2.66932i | −1.18228 | − | 0.316790i | −0.386448 | − | 0.922311i | \(-0.626298\pi\) |
−0.795829 | + | 0.605521i | \(0.792965\pi\) | |||||||
\(72\) | 6.72999 | − | 3.88556i | 0.793137 | − | 0.457918i | ||||
\(73\) | −1.92362 | −0.225142 | −0.112571 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112571 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(74\) | 2.77661 | − | 1.60307i | 0.322774 | − | 0.186354i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.89272 | − | 0.507152i | 0.217109 | − | 0.0581743i | ||||
\(77\) | 1.55393 | − | 1.55393i | 0.177087 | − | 0.177087i | ||||
\(78\) | −10.6659 | + | 5.12477i | −1.20768 | + | 0.580266i | ||||
\(79\) | − | 9.33180i | − | 1.04991i | −0.851130 | − | 0.524955i | \(-0.824082\pi\) | ||
0.851130 | − | 0.524955i | \(-0.175918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.0385 | − | 24.3154i | 1.55984 | − | 2.70172i | ||||
\(82\) | 8.53702 | + | 2.28749i | 0.942756 | + | 0.252611i | ||||
\(83\) | 6.90343i | 0.757750i | 0.925448 | + | 0.378875i | \(0.123689\pi\) | ||||
−0.925448 | + | 0.378875i | \(0.876311\pi\) | |||||||
\(84\) | −0.337830 | + | 1.26080i | −0.0368602 | + | 0.137564i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.07227 | − | 5.07227i | −0.546957 | − | 0.546957i | ||||
\(87\) | −3.88612 | + | 14.5032i | −0.416635 | + | 1.55490i | ||||
\(88\) | 5.33728 | − | 1.43012i | 0.568956 | − | 0.152451i | ||||
\(89\) | −1.88556 | − | 7.03702i | −0.199869 | − | 0.745923i | −0.990952 | − | 0.134214i | \(-0.957149\pi\) |
0.791083 | − | 0.611709i | \(-0.209518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.474815 | − | 1.35309i | 0.0497741 | − | 0.141842i | ||||
\(92\) | −4.21046 | − | 4.21046i | −0.438970 | − | 0.438970i | ||||
\(93\) | 10.0406 | + | 5.79693i | 1.04116 | + | 0.601114i | ||||
\(94\) | 10.2279 | + | 5.90510i | 1.05493 | + | 0.609065i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.32068 | + | 2.32068i | −0.236854 | + | 0.236854i | ||||
\(97\) | 2.07203 | + | 3.58887i | 0.210383 | + | 0.364394i | 0.951834 | − | 0.306612i | \(-0.0991955\pi\) |
−0.741451 | + | 0.671007i | \(0.765862\pi\) | |||||||
\(98\) | 3.42091 | + | 5.92519i | 0.345564 | + | 0.598535i | ||||
\(99\) | 30.3630 | − | 30.3630i | 3.05160 | − | 3.05160i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.21761 | + | 4.74444i | 0.817683 | + | 0.472089i | 0.849617 | − | 0.527401i | \(-0.176833\pi\) |
−0.0319341 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(102\) | 6.19465 | + | 3.57648i | 0.613361 | + | 0.354124i | ||||
\(103\) | −3.97420 | − | 3.97420i | −0.391589 | − | 0.391589i | 0.483664 | − | 0.875254i | \(-0.339306\pi\) |
−0.875254 | + | 0.483664i | \(0.839306\pi\) | |||||||
\(104\) | 2.73499 | − | 2.34943i | 0.268188 | − | 0.230380i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.14636 | − | 8.01033i | −0.208473 | − | 0.778032i | ||||
\(107\) | 10.1890 | − | 2.73013i | 0.985008 | − | 0.263932i | 0.269856 | − | 0.962901i | \(-0.413024\pi\) |
0.715152 | + | 0.698969i | \(0.246357\pi\) | |||||||
\(108\) | −4.05273 | + | 15.1250i | −0.389974 | + | 1.45540i | ||||
\(109\) | −4.56067 | − | 4.56067i | −0.436833 | − | 0.436833i | 0.454112 | − | 0.890945i | \(-0.349957\pi\) |
−0.890945 | + | 0.454112i | \(0.849957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.72339 | + | 10.1638i | −0.258493 | + | 0.964709i | ||||
\(112\) | − | 0.397714i | − | 0.0375804i | ||||||
\(113\) | 16.9477 | + | 4.54113i | 1.59431 | + | 0.427194i | 0.943318 | − | 0.331891i | \(-0.107687\pi\) |
0.650992 | + | 0.759085i | \(0.274353\pi\) | |||||||
\(114\) | −3.21545 | + | 5.56933i | −0.301155 | + | 0.521616i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.57498i | − | 0.424776i | ||||||
\(117\) | 9.27763 | − | 26.4386i | 0.857717 | − | 2.44425i | ||||
\(118\) | −4.67456 | + | 4.67456i | −0.430328 | + | 0.430328i | ||||
\(119\) | −0.837279 | + | 0.224348i | −0.0767532 | + | 0.0205660i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.9150 | − | 9.76589i | 1.53773 | − | 0.887808i | ||||
\(122\) | 7.44980 | 0.674473 | ||||||||
\(123\) | −25.1202 | + | 14.5032i | −2.26502 | + | 1.30771i | ||||
\(124\) | −3.41225 | − | 0.914311i | −0.306430 | − | 0.0821075i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.54534 | − | 2.67661i | −0.137670 | − | 0.238452i | ||||
\(127\) | 0.323386 | + | 1.20689i | 0.0286959 | + | 0.107095i | 0.978788 | − | 0.204874i | \(-0.0656784\pi\) |
−0.950092 | + | 0.311968i | \(0.899012\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 23.5423 | 2.07278 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2927 | 0.899279 | 0.449640 | − | 0.893210i | \(-0.351552\pi\) | ||||
0.449640 | + | 0.893210i | \(0.351552\pi\) | |||||||
\(132\) | −9.06727 | + | 15.7050i | −0.789205 | + | 1.36694i | ||||
\(133\) | −0.201701 | − | 0.752760i | −0.0174897 | − | 0.0652726i | ||||
\(134\) | −0.621825 | − | 1.07703i | −0.0537175 | − | 0.0930414i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.10523 | − | 0.564094i | −0.180522 | − | 0.0483707i | ||||
\(137\) | 5.35364 | − | 3.09092i | 0.457392 | − | 0.264076i | −0.253555 | − | 0.967321i | \(-0.581600\pi\) |
0.710947 | + | 0.703245i | \(0.248267\pi\) | |||||||
\(138\) | 19.5423 | 1.66355 | ||||||||
\(139\) | −17.5740 | + | 10.1464i | −1.49061 | + | 0.860603i | −0.999942 | − | 0.0107445i | \(-0.996580\pi\) |
−0.490666 | + | 0.871348i | \(0.663247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −37.4397 | + | 10.0319i | −3.15299 | + | 0.844841i | ||||
\(142\) | −7.29272 | + | 7.29272i | −0.611992 | + | 0.611992i | ||||
\(143\) | 11.2375 | − | 16.4509i | 0.939723 | − | 1.37570i | ||||
\(144\) | − | 7.77113i | − | 0.647594i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.961808 | + | 1.66590i | −0.0795998 | + | 0.137871i | ||||
\(147\) | −21.6893 | − | 5.81164i | −1.78891 | − | 0.479336i | ||||
\(148\) | − | 3.20615i | − | 0.263544i | ||||||
\(149\) | −3.13976 | + | 11.7177i | −0.257219 | + | 0.959955i | 0.709623 | + | 0.704581i | \(0.248865\pi\) |
−0.966842 | + | 0.255374i | \(0.917801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6336 | − | 11.6336i | −0.946728 | − | 0.946728i | 0.0519227 | − | 0.998651i | \(-0.483465\pi\) |
−0.998651 | + | 0.0519227i | \(0.983465\pi\) | |||||||
\(152\) | 0.507152 | − | 1.89272i | 0.0411354 | − | 0.153520i | ||||
\(153\) | −16.3600 | + | 4.38365i | −1.32263 | + | 0.354397i | ||||
\(154\) | −0.568779 | − | 2.12271i | −0.0458335 | − | 0.171053i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.894772 | + | 11.7993i | −0.0716391 | + | 0.944702i | ||||
\(157\) | 11.8065 | + | 11.8065i | 0.942259 | + | 0.942259i | 0.998422 | − | 0.0561623i | \(-0.0178864\pi\) |
−0.0561623 | + | 0.998422i | \(0.517886\pi\) | |||||||
\(158\) | −8.08158 | − | 4.66590i | −0.642936 | − | 0.371199i | ||||
\(159\) | 23.5705 | + | 13.6084i | 1.86926 | + | 1.07922i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.67456 | + | 1.67456i | −0.131974 | + | 0.131974i | ||||
\(162\) | −14.0385 | − | 24.3154i | −1.10297 | − | 1.91040i | ||||
\(163\) | 4.90281 | + | 8.49192i | 0.384018 | + | 0.665138i | 0.991632 | − | 0.129094i | \(-0.0412068\pi\) |
−0.607615 | + | 0.794232i | \(0.707873\pi\) | |||||||
\(164\) | 6.24953 | − | 6.24953i | 0.488007 | − | 0.488007i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.97854 | + | 3.45171i | 0.464025 | + | 0.267905i | ||||
\(167\) | 1.49354 | + | 0.862295i | 0.115574 | + | 0.0667264i | 0.556672 | − | 0.830732i | \(-0.312078\pi\) |
−0.441099 | + | 0.897459i | \(0.645411\pi\) | |||||||
\(168\) | 0.922968 | + | 0.922968i | 0.0712085 | + | 0.0712085i | ||||
\(169\) | 1.96037 | − | 12.8513i | 0.150798 | − | 0.988565i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.94114 | − | 14.7085i | −0.301387 | − | 1.12479i | ||||
\(172\) | −6.92885 | + | 1.85658i | −0.528320 | + | 0.141563i | ||||
\(173\) | −1.59092 | + | 5.93741i | −0.120956 | + | 0.451413i | −0.999663 | − | 0.0259475i | \(-0.991740\pi\) |
0.878708 | + | 0.477360i | \(0.158406\pi\) | |||||||
\(174\) | 10.6171 | + | 10.6171i | 0.804878 | + | 0.804878i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.43012 | − | 5.33728i | 0.107799 | − | 0.402313i | ||||
\(177\) | − | 21.6963i | − | 1.63080i | ||||||
\(178\) | −7.03702 | − | 1.88556i | −0.527447 | − | 0.141329i | ||||
\(179\) | −4.29272 | + | 7.43522i | −0.320853 | + | 0.555734i | −0.980664 | − | 0.195697i | \(-0.937303\pi\) |
0.659811 | + | 0.751432i | \(0.270636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.60797i | 0.193849i | 0.995292 | + | 0.0969246i | \(0.0309006\pi\) | ||||
−0.995292 | + | 0.0969246i | \(0.969099\pi\) | |||||||
\(182\) | −0.934401 | − | 1.08775i | −0.0692624 | − | 0.0806290i | ||||
\(183\) | −17.2886 | + | 17.2886i | −1.27801 | + | 1.27801i | ||||
\(184\) | −5.75159 | + | 1.54113i | −0.424013 | + | 0.113614i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0406 | − | 5.79693i | 0.736211 | − | 0.425052i | ||||
\(187\) | −12.0429 | −0.880665 | ||||||||
\(188\) | 10.2279 | − | 5.90510i | 0.745949 | − | 0.430674i | ||||
\(189\) | 6.01543 | + | 1.61183i | 0.437558 | + | 0.117243i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.396828 | − | 0.687326i | −0.0287135 | − | 0.0497332i | 0.851312 | − | 0.524660i | \(-0.175808\pi\) |
−0.880025 | + | 0.474927i | \(0.842474\pi\) | |||||||
\(192\) | 0.849429 | + | 3.17011i | 0.0613022 | + | 0.228783i | ||||
\(193\) | 7.27684 | − | 12.6039i | 0.523799 | − | 0.907246i | −0.475818 | − | 0.879544i | \(-0.657848\pi\) |
0.999616 | − | 0.0277019i | \(-0.00881891\pi\) | |||||||
\(194\) | 4.14407 | 0.297527 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.84182 | 0.488702 | ||||||||
\(197\) | −7.03549 | + | 12.1858i | −0.501258 | + | 0.868204i | 0.498741 | + | 0.866751i | \(0.333796\pi\) |
−0.999999 | + | 0.00145289i | \(0.999538\pi\) | |||||||
\(198\) | −11.1136 | − | 41.4767i | −0.789812 | − | 2.94762i | ||||
\(199\) | −8.96205 | − | 15.5227i | −0.635303 | − | 1.10038i | −0.986451 | − | 0.164056i | \(-0.947542\pi\) |
0.351148 | − | 0.936320i | \(-0.385791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.94251 | + | 1.05639i | 0.278083 | + | 0.0745121i | ||||
\(202\) | 8.21761 | − | 4.74444i | 0.578189 | − | 0.333817i | ||||
\(203\) | −1.81953 | −0.127706 | ||||||||
\(204\) | 6.19465 | − | 3.57648i | 0.433712 | − | 0.250404i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.42885 | + | 1.45466i | −0.378246 | + | 0.101351i | ||||
\(207\) | −32.7200 | + | 32.7200i | −2.27420 | + | 2.27420i | ||||
\(208\) | −0.667168 | − | 3.54329i | −0.0462598 | − | 0.245683i | ||||
\(209\) | − | 10.8272i | − | 0.748936i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.78407 | − | 10.0183i | 0.398192 | − | 0.689688i | −0.595311 | − | 0.803495i | \(-0.702971\pi\) |
0.993503 | + | 0.113807i | \(0.0363046\pi\) | |||||||
\(212\) | −8.01033 | − | 2.14636i | −0.550152 | − | 0.147413i | ||||
\(213\) | − | 33.8482i | − | 2.31924i | ||||||
\(214\) | 2.73013 | − | 10.1890i | 0.186628 | − | 0.696506i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.0723 | + | 11.0723i | 0.753373 | + | 0.753373i | ||||
\(217\) | −0.363634 | + | 1.35710i | −0.0246851 | + | 0.0921261i | ||||
\(218\) | −6.22999 | + | 1.66932i | −0.421948 | + | 0.113061i | ||||
\(219\) | −1.63397 | − | 6.09808i | −0.110414 | − | 0.412070i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.08308 | + | 3.40329i | −0.476460 | + | 0.228930i | ||||
\(222\) | 7.44045 | + | 7.44045i | 0.499370 | + | 0.499370i | ||||
\(223\) | 7.20043 | + | 4.15717i | 0.482177 | + | 0.278385i | 0.721323 | − | 0.692599i | \(-0.243534\pi\) |
−0.239146 | + | 0.970984i | \(0.576868\pi\) | |||||||
\(224\) | −0.344430 | − | 0.198857i | −0.0230132 | − | 0.0132867i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.4066 | − | 12.4066i | 0.825275 | − | 0.825275i | ||||
\(227\) | −1.56478 | − | 2.71029i | −0.103858 | − | 0.179888i | 0.809413 | − | 0.587240i | \(-0.199786\pi\) |
−0.913271 | + | 0.407352i | \(0.866452\pi\) | |||||||
\(228\) | 3.21545 | + | 5.56933i | 0.212949 | + | 0.368838i | ||||
\(229\) | −8.68998 | + | 8.68998i | −0.574250 | + | 0.574250i | −0.933313 | − | 0.359063i | \(-0.883096\pi\) |
0.359063 | + | 0.933313i | \(0.383096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.24609 | + | 3.60618i | 0.410963 | + | 0.237269i | ||||
\(232\) | −3.96205 | − | 2.28749i | −0.260121 | − | 0.150181i | ||||
\(233\) | −10.1868 | − | 10.1868i | −0.667360 | − | 0.667360i | 0.289744 | − | 0.957104i | \(-0.406430\pi\) |
−0.957104 | + | 0.289744i | \(0.906430\pi\) | |||||||
\(234\) | −18.2577 | − | 21.2540i | −1.19354 | − | 1.38942i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.71101 | + | 6.38556i | 0.111377 | + | 0.415665i | ||||
\(237\) | 29.5828 | − | 7.92670i | 1.92161 | − | 0.514894i | ||||
\(238\) | −0.224348 | + | 0.837279i | −0.0145423 | + | 0.0542727i | ||||
\(239\) | 14.4047 | + | 14.4047i | 0.931764 | + | 0.931764i | 0.997816 | − | 0.0660522i | \(-0.0210404\pi\) |
−0.0660522 | + | 0.997816i | \(0.521040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.44774 | − | 27.7954i | 0.479751 | − | 1.79046i | −0.122863 | − | 0.992424i | \(-0.539208\pi\) |
0.602615 | − | 0.798032i | \(-0.294126\pi\) | |||||||
\(242\) | − | 19.5318i | − | 1.25555i | ||||||
\(243\) | 43.6323 | + | 11.6913i | 2.79902 | + | 0.749994i | ||||
\(244\) | 3.72490 | − | 6.45171i | 0.238462 | − | 0.413029i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 29.0064i | 1.84938i | ||||||||
\(247\) | −3.05974 | − | 6.36808i | −0.194687 | − | 0.405191i | ||||
\(248\) | −2.49794 | + | 2.49794i | −0.158620 | + | 0.158620i | ||||
\(249\) | −21.8846 | + | 5.86397i | −1.38688 | + | 0.371614i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7318 | + | 11.3922i | −1.24546 | + | 0.719067i | −0.970201 | − | 0.242303i | \(-0.922097\pi\) |
−0.275260 | + | 0.961370i | \(0.588764\pi\) | |||||||
\(252\) | −3.09069 | −0.194695 | ||||||||
\(253\) | −28.4938 | + | 16.4509i | −1.79139 | + | 1.03426i | ||||
\(254\) | 1.20689 | + | 0.323386i | 0.0757273 | + | 0.0202911i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.05226 | + | 3.92708i | 0.0656380 | + | 0.244965i | 0.990948 | − | 0.134248i | \(-0.0428617\pi\) |
−0.925310 | + | 0.379212i | \(0.876195\pi\) | |||||||
\(258\) | 11.7711 | − | 20.3882i | 0.732838 | − | 1.26931i | ||||
\(259\) | −1.27513 | −0.0792327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −35.5527 | −2.20066 | ||||||||
\(262\) | 5.14636 | − | 8.91376i | 0.317943 | − | 0.550694i | ||||
\(263\) | 2.38612 | + | 8.90510i | 0.147134 | + | 0.549112i | 0.999651 | + | 0.0264126i | \(0.00840838\pi\) |
−0.852517 | + | 0.522700i | \(0.824925\pi\) | |||||||
\(264\) | 9.06727 | + | 15.7050i | 0.558052 | + | 0.966575i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.752760 | − | 0.201701i | −0.0461547 | − | 0.0123671i | ||||
\(267\) | 20.7065 | − | 11.9549i | 1.26722 | − | 0.731628i | ||||
\(268\) | −1.24365 | −0.0759680 | ||||||||
\(269\) | −5.07512 | + | 2.93012i | −0.309435 | + | 0.178653i | −0.646674 | − | 0.762767i | \(-0.723840\pi\) |
0.337238 | + | 0.941419i | \(0.390507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4457 | − | 3.33481i | 0.756022 | − | 0.202575i | 0.139834 | − | 0.990175i | \(-0.455343\pi\) |
0.616187 | + | 0.787600i | \(0.288676\pi\) | |||||||
\(272\) | −1.54113 | + | 1.54113i | −0.0934450 | + | 0.0934450i | ||||
\(273\) | 4.69276 | + | 0.355863i | 0.284019 | + | 0.0215378i | ||||
\(274\) | − | 6.18185i | − | 0.373459i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.77113 | − | 16.9241i | 0.588153 | − | 1.01871i | ||||
\(277\) | −25.4675 | − | 6.82400i | −1.53019 | − | 0.410014i | −0.607112 | − | 0.794616i | \(-0.707672\pi\) |
−0.923083 | + | 0.384602i | \(0.874339\pi\) | |||||||
\(278\) | 20.2927i | 1.21708i | ||||||||
\(279\) | −7.10523 | + | 26.5171i | −0.425379 | + | 1.58754i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.139761 | − | 0.139761i | −0.00833744 | − | 0.00833744i | 0.702926 | − | 0.711263i | \(-0.251877\pi\) |
−0.711263 | + | 0.702926i | \(0.751877\pi\) | |||||||
\(282\) | −10.0319 | + | 37.4397i | −0.597393 | + | 2.22950i | ||||
\(283\) | 5.94251 | − | 1.59229i | 0.353245 | − | 0.0946518i | −0.0778327 | − | 0.996966i | \(-0.524800\pi\) |
0.431078 | + | 0.902315i | \(0.358133\pi\) | |||||||
\(284\) | 2.66932 | + | 9.96205i | 0.158395 | + | 0.591139i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.62819 | − | 17.9574i | −0.510195 | − | 1.06184i | ||||
\(287\) | −2.48553 | − | 2.48553i | −0.146716 | − | 0.146716i | ||||
\(288\) | −6.72999 | − | 3.88556i | −0.396569 | − | 0.228959i | ||||
\(289\) | −10.6086 | − | 6.12491i | −0.624038 | − | 0.360289i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.61706 | + | 9.61706i | −0.563762 | + | 0.563762i | ||||
\(292\) | 0.961808 | + | 1.66590i | 0.0562856 | + | 0.0974895i | ||||
\(293\) | 2.50715 | + | 4.34251i | 0.146469 | + | 0.253692i | 0.929920 | − | 0.367761i | \(-0.119876\pi\) |
−0.783451 | + | 0.621454i | \(0.786542\pi\) | |||||||
\(294\) | −15.8777 | + | 15.8777i | −0.926006 | + | 0.926006i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.77661 | − | 1.60307i | −0.161387 | − | 0.0931768i | ||||
\(297\) | 74.9305 | + | 43.2611i | 4.34791 | + | 2.51027i | ||||
\(298\) | 8.57799 | + | 8.57799i | 0.496909 | + | 0.496909i | ||||
\(299\) | −12.1098 | + | 17.7279i | −0.700326 | + | 1.02523i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.738388 | + | 2.75570i | 0.0425600 | + | 0.158836i | ||||
\(302\) | −15.8918 | + | 4.25819i | −0.914469 | + | 0.245031i | ||||
\(303\) | −8.06012 | + | 30.0808i | −0.463042 | + | 1.72810i | ||||
\(304\) | −1.38556 | − | 1.38556i | −0.0794676 | − | 0.0794676i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.38365 | + | 16.3600i | −0.250596 | + | 0.935239i | ||||
\(307\) | − | 3.05180i | − | 0.174176i | −0.996201 | − | 0.0870878i | \(-0.972244\pi\) | ||
0.996201 | − | 0.0870878i | \(-0.0277561\pi\) | |||||||
\(308\) | −2.12271 | − | 0.568779i | −0.120953 | − | 0.0324092i | ||||
\(309\) | 9.22284 | − | 15.9744i | 0.524669 | − | 0.908754i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0132i | 0.737911i | 0.929447 | + | 0.368955i | \(0.120285\pi\) | ||||
−0.929447 | + | 0.368955i | \(0.879715\pi\) | |||||||
\(312\) | 9.77113 | + | 6.67456i | 0.553181 | + | 0.377872i | ||||
\(313\) | −11.3443 | + | 11.3443i | −0.641220 | + | 0.641220i | −0.950855 | − | 0.309636i | \(-0.899793\pi\) |
0.309636 | + | 0.950855i | \(0.399793\pi\) | |||||||
\(314\) | 16.1279 | − | 4.32147i | 0.910153 | − | 0.243875i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.08158 | + | 4.66590i | −0.454624 | + | 0.262477i | ||||
\(317\) | 23.0586 | 1.29510 | 0.647551 | − | 0.762022i | \(-0.275793\pi\) | ||||
0.647551 | + | 0.762022i | \(0.275793\pi\) | |||||||
\(318\) | 23.5705 | − | 13.6084i | 1.32177 | − | 0.763122i | ||||
\(319\) | −24.4179 | − | 6.54276i | −1.36714 | − | 0.366324i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3097 | + | 29.9812i | 0.966131 | + | 1.67339i | ||||
\(322\) | 0.612931 | + | 2.28749i | 0.0341573 | + | 0.127477i | ||||
\(323\) | −2.13534 | + | 3.69852i | −0.118813 | + | 0.205791i | ||||
\(324\) | −28.0771 | −1.55984 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.80562 | 0.543083 | ||||||||
\(327\) | 10.5839 | − | 18.3318i | 0.585289 | − | 1.01375i | ||||
\(328\) | −2.28749 | − | 8.53702i | −0.126305 | − | 0.471378i | ||||
\(329\) | −2.34854 | − | 4.06780i | −0.129479 | − | 0.224265i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.1917 | + | 5.67829i | 1.16480 | + | 0.312107i | 0.788881 | − | 0.614546i | \(-0.210661\pi\) |
0.375918 | + | 0.926653i | \(0.377327\pi\) | |||||||
\(332\) | 5.97854 | − | 3.45171i | 0.328115 | − | 0.189437i | ||||
\(333\) | −24.9154 | −1.36536 | ||||||||
\(334\) | 1.49354 | − | 0.862295i | 0.0817228 | − | 0.0471827i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.26080 | − | 0.337830i | 0.0687821 | − | 0.0184301i | ||||
\(337\) | 11.6622 | − | 11.6622i | 0.635281 | − | 0.635281i | −0.314107 | − | 0.949388i | \(-0.601705\pi\) |
0.949388 | + | 0.314107i | \(0.101705\pi\) | |||||||
\(338\) | −10.1494 | − | 8.12340i | −0.552055 | − | 0.441855i | ||||
\(339\) | 57.5836i | 3.12751i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.75986 | + | 16.9046i | −0.528526 | + | 0.915434i | ||||
\(342\) | −14.7085 | − | 3.94114i | −0.795347 | − | 0.213113i | ||||
\(343\) | − | 5.50509i | − | 0.297247i | ||||||
\(344\) | −1.85658 | + | 6.92885i | −0.100100 | + | 0.373579i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.34649 | + | 4.34649i | 0.233669 | + | 0.233669i | ||||
\(347\) | 1.25395 | − | 4.67982i | 0.0673158 | − | 0.251226i | −0.924065 | − | 0.382234i | \(-0.875155\pi\) |
0.991381 | + | 0.131008i | \(0.0418214\pi\) | |||||||
\(348\) | 14.5032 | − | 3.88612i | 0.777452 | − | 0.208318i | ||||
\(349\) | −2.97604 | − | 11.1067i | −0.159304 | − | 0.594530i | −0.998698 | − | 0.0510072i | \(-0.983757\pi\) |
0.839395 | − | 0.543523i | \(-0.182910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 56.2961 | + | 4.26907i | 3.00486 | + | 0.227866i | ||||
\(352\) | −3.90716 | − | 3.90716i | −0.208252 | − | 0.208252i | ||||
\(353\) | 2.22407 | + | 1.28407i | 0.118375 | + | 0.0683440i | 0.558019 | − | 0.829828i | \(-0.311562\pi\) |
−0.439643 | + | 0.898172i | \(0.644895\pi\) | |||||||
\(354\) | −18.7896 | − | 10.8482i | −0.998654 | − | 0.576573i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.15146 | + | 5.15146i | −0.273027 | + | 0.273027i | ||||
\(357\) | −1.42242 | − | 2.46370i | −0.0752823 | − | 0.130393i | ||||
\(358\) | 4.29272 | + | 7.43522i | 0.226877 | + | 0.392963i | ||||
\(359\) | 9.62118 | − | 9.62118i | 0.507786 | − | 0.507786i | −0.406060 | − | 0.913846i | \(-0.633098\pi\) |
0.913846 | + | 0.406060i | \(0.133098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1293 | + | 7.58021i | 0.691016 | + | 0.398959i | ||||
\(362\) | 2.25857 | + | 1.30399i | 0.118708 | + | 0.0685361i | ||||
\(363\) | 45.3271 | + | 45.3271i | 2.37905 | + | 2.37905i | ||||
\(364\) | −1.40922 | + | 0.265342i | −0.0738629 | + | 0.0139077i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.32807 | + | 23.6167i | 0.330774 | + | 1.23446i | ||||
\(367\) | 16.2901 | − | 4.36492i | 0.850337 | − | 0.227847i | 0.192771 | − | 0.981244i | \(-0.438253\pi\) |
0.657566 | + | 0.753397i | \(0.271586\pi\) | |||||||
\(368\) | −1.54113 | + | 5.75159i | −0.0803372 | + | 0.299822i | ||||
\(369\) | −48.5659 | − | 48.5659i | −2.52824 | − | 2.52824i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.853638 | + | 3.18582i | −0.0443187 | + | 0.165400i | ||||
\(372\) | − | 11.5939i | − | 0.601114i | ||||||
\(373\) | −2.52552 | − | 0.676711i | −0.130766 | − | 0.0350388i | 0.192842 | − | 0.981230i | \(-0.438229\pi\) |
−0.323609 | + | 0.946191i | \(0.604896\pi\) | |||||||
\(374\) | −6.02146 | + | 10.4295i | −0.311362 | + | 0.539295i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 11.8102i | − | 0.609065i | ||||||
\(377\) | −16.2105 | + | 3.05228i | −0.834881 | + | 0.157200i | ||||
\(378\) | 4.40360 | − | 4.40360i | 0.226497 | − | 0.226497i | ||||
\(379\) | 1.46920 | − | 0.393670i | 0.0754676 | − | 0.0202215i | −0.220888 | − | 0.975299i | \(-0.570895\pi\) |
0.296355 | + | 0.955078i | \(0.404229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.55130 | + | 2.05034i | −0.181938 | + | 0.105042i | ||||
\(382\) | −0.793656 | −0.0406070 | ||||||||
\(383\) | −3.25326 | + | 1.87827i | −0.166234 | + | 0.0959753i | −0.580809 | − | 0.814040i | \(-0.697264\pi\) |
0.414575 | + | 0.910015i | \(0.363930\pi\) | |||||||
\(384\) | 3.17011 | + | 0.849429i | 0.161774 | + | 0.0433472i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.27684 | − | 12.6039i | −0.370382 | − | 0.641520i | ||||
\(387\) | 14.4277 | + | 53.8450i | 0.733402 | + | 2.73710i | ||||
\(388\) | 2.07203 | − | 3.58887i | 0.105192 | − | 0.182197i | ||||
\(389\) | 14.0639 | 0.713066 | 0.356533 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356533 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9778 | 0.656313 | ||||||||
\(392\) | 3.42091 | − | 5.92519i | 0.172782 | − | 0.299267i | ||||
\(393\) | 8.74293 | + | 32.6291i | 0.441023 | + | 1.64592i | ||||
\(394\) | 7.03549 | + | 12.1858i | 0.354443 | + | 0.613913i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −41.4767 | − | 11.1136i | −2.08428 | − | 0.558482i | ||||
\(397\) | −14.8529 | + | 8.57531i | −0.745444 | + | 0.430383i | −0.824046 | − | 0.566524i | \(-0.808288\pi\) |
0.0786011 | + | 0.996906i | \(0.474955\pi\) | |||||||
\(398\) | −17.9241 | −0.898454 | ||||||||
\(399\) | 2.21500 | − | 1.27883i | 0.110889 | − | 0.0640216i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.20232 | + | 0.590110i | −0.109979 | + | 0.0294687i | −0.313389 | − | 0.949625i | \(-0.601464\pi\) |
0.203410 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(402\) | 2.88612 | − | 2.88612i | 0.143946 | − | 0.143946i | ||||
\(403\) | −0.963118 | + | 12.7006i | −0.0479763 | + | 0.632662i | ||||
\(404\) | − | 9.48888i | − | 0.472089i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.909766 | + | 1.57576i | −0.0451509 | + | 0.0782037i | ||||
\(407\) | −17.1121 | − | 4.58518i | −0.848216 | − | 0.227279i | ||||
\(408\) | − | 7.15296i | − | 0.354124i | ||||||
\(409\) | 4.81911 | − | 17.9851i | 0.238289 | − | 0.889308i | −0.738349 | − | 0.674419i | \(-0.764394\pi\) |
0.976638 | − | 0.214889i | \(-0.0689391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3461 | + | 14.3461i | 0.707641 | + | 0.707641i | ||||
\(412\) | −1.45466 | + | 5.42885i | −0.0716658 | + | 0.267460i | ||||
\(413\) | 2.53963 | − | 0.680491i | 0.124967 | − | 0.0334848i | ||||
\(414\) | 11.9763 | + | 44.6963i | 0.588605 | + | 2.19671i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.40216 | − | 1.19386i | −0.166805 | − | 0.0585338i | ||||
\(417\) | −47.0930 | − | 47.0930i | −2.30615 | − | 2.30615i | ||||
\(418\) | −9.37667 | − | 5.41362i | −0.458628 | − | 0.264789i | ||||
\(419\) | −8.19164 | − | 4.72944i | −0.400188 | − | 0.231048i | 0.286377 | − | 0.958117i | \(-0.407549\pi\) |
−0.686565 | + | 0.727068i | \(0.740882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3656 | + | 23.3656i | −1.13877 | + | 1.13877i | −0.150101 | + | 0.988671i | \(0.547960\pi\) |
−0.988671 | + | 0.150101i | \(0.952040\pi\) | |||||||
\(422\) | −5.78407 | − | 10.0183i | −0.281564 | − | 0.487683i | ||||
\(423\) | −45.8893 | − | 79.4826i | −2.23121 | − | 3.86458i | ||||
\(424\) | −5.86397 | + | 5.86397i | −0.284780 | + | 0.284780i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −29.3134 | − | 16.9241i | −1.42024 | − | 0.819975i | ||||
\(427\) | −2.56594 | − | 1.48144i | −0.124174 | − | 0.0716921i | ||||
\(428\) | −7.45887 | − | 7.45887i | −0.360538 | − | 0.360538i | ||||
\(429\) | 61.6967 | + | 21.6501i | 2.97874 | + | 1.04528i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.65683 | − | 28.5757i | −0.368817 | − | 1.37644i | −0.862172 | − | 0.506615i | \(-0.830897\pi\) |
0.493356 | − | 0.869828i | \(-0.335770\pi\) | |||||||
\(432\) | 15.1250 | − | 4.05273i | 0.727702 | − | 0.194987i | ||||
\(433\) | 6.41568 | − | 23.9436i | 0.308318 | − | 1.15066i | −0.621734 | − | 0.783229i | \(-0.713571\pi\) |
0.930052 | − | 0.367429i | \(-0.119762\pi\) | |||||||
\(434\) | 0.993467 | + | 0.993467i | 0.0476880 | + | 0.0476880i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.66932 | + | 6.22999i | −0.0799460 | + | 0.298363i | ||||
\(437\) | 11.6677i | 0.558142i | ||||||||
\(438\) | −6.09808 | − | 1.63397i | −0.291377 | − | 0.0780743i | ||||
\(439\) | 3.29091 | − | 5.70002i | 0.157067 | − | 0.272047i | −0.776743 | − | 0.629818i | \(-0.783130\pi\) |
0.933810 | + | 0.357770i | \(0.116463\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 53.1687i | − | 2.53184i | ||||||
\(442\) | −0.594206 | + | 7.83577i | −0.0282635 | + | 0.372710i | ||||
\(443\) | 20.1315 | − | 20.1315i | 0.956478 | − | 0.956478i | −0.0426135 | − | 0.999092i | \(-0.513568\pi\) |
0.999092 | + | 0.0426135i | \(0.0135684\pi\) | |||||||
\(444\) | 10.1638 | − | 2.72339i | 0.482355 | − | 0.129247i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.20043 | − | 4.15717i | 0.340950 | − | 0.196848i | ||||
\(447\) | −39.8136 | −1.88312 | ||||||||
\(448\) | −0.344430 | + | 0.198857i | −0.0162728 | + | 0.00939511i | ||||
\(449\) | −5.40716 | − | 1.44884i | −0.255180 | − | 0.0683752i | 0.128961 | − | 0.991650i | \(-0.458836\pi\) |
−0.384141 | + | 0.923274i | \(0.625502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.4179 | − | 42.2931i | −1.14980 | − | 1.99150i | ||||
\(452\) | −4.54113 | − | 16.9477i | −0.213597 | − | 0.797155i | ||||
\(453\) | 26.9979 | − | 46.7617i | 1.26847 | − | 2.19706i | ||||
\(454\) | −3.12957 | −0.146878 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.43091 | 0.301155 | ||||||||
\(457\) | 10.3741 | − | 17.9685i | 0.485280 | − | 0.840530i | −0.514577 | − | 0.857444i | \(-0.672051\pi\) |
0.999857 | + | 0.0169144i | \(0.00538428\pi\) | |||||||
\(458\) | 3.18076 | + | 11.8707i | 0.148627 | + | 0.554683i | ||||
\(459\) | −17.0639 | − | 29.5555i | −0.796472 | − | 1.37953i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3277 | + | 6.51858i | 1.13305 | + | 0.303600i | 0.776154 | − | 0.630543i | \(-0.217168\pi\) |
0.356898 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(462\) | 6.24609 | − | 3.60618i | 0.290594 | − | 0.167775i | ||||
\(463\) | −32.2152 | −1.49717 | −0.748585 | − | 0.663039i | \(-0.769266\pi\) | ||||
−0.748585 | + | 0.663039i | \(0.769266\pi\) | |||||||
\(464\) | −3.96205 | + | 2.28749i | −0.183933 | + | 0.106194i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.9154 | + | 3.72863i | −0.644620 | + | 0.172725i | ||||
\(467\) | −20.5381 | + | 20.5381i | −0.950392 | + | 0.950392i | −0.998826 | − | 0.0484344i | \(-0.984577\pi\) |
0.0484344 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(468\) | −27.5353 | + | 5.18465i | −1.27282 | + | 0.239661i | ||||
\(469\) | 0.494617i | 0.0228393i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.3991 | + | 47.4566i | −1.26248 | + | 2.18668i | ||||
\(472\) | 6.38556 | + | 1.71101i | 0.293919 | + | 0.0787555i | ||||
\(473\) | 39.6363i | 1.82248i | ||||||||
\(474\) | 7.92670 | − | 29.5828i | 0.364085 | − | 1.35878i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.612931 | + | 0.612931i | 0.0280936 | + | 0.0280936i | ||||
\(477\) | −16.6797 | + | 62.2493i | −0.763709 | + | 2.85020i | ||||
\(478\) | 19.6772 | − | 5.27249i | 0.900015 | − | 0.241158i | ||||
\(479\) | 7.18639 | + | 26.8200i | 0.328355 | + | 1.22544i | 0.910896 | + | 0.412636i | \(0.135392\pi\) |
−0.582542 | + | 0.812801i | \(0.697942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3603 | + | 2.13904i | −0.517985 | + | 0.0975319i | ||||
\(482\) | −20.3476 | − | 20.3476i | −0.926808 | − | 0.926808i | ||||
\(483\) | −6.73095 | − | 3.88612i | −0.306269 | − | 0.176824i | ||||
\(484\) | −16.9150 | − | 9.76589i | −0.768865 | − | 0.443904i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 31.9411 | − | 31.9411i | 1.44888 | − | 1.44888i | ||||
\(487\) | −20.0068 | − | 34.6529i | −0.906596 | − | 1.57027i | −0.818760 | − | 0.574136i | \(-0.805338\pi\) |
−0.0878365 | − | 0.996135i | \(-0.527995\pi\) | |||||||
\(488\) | −3.72490 | − | 6.45171i | −0.168618 | − | 0.292055i | ||||
\(489\) | −22.7557 | + | 22.7557i | −1.02905 | + | 1.02905i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8394 | + | 9.14486i | 0.714820 | + | 0.412702i | 0.812843 | − | 0.582483i | \(-0.197919\pi\) |
−0.0980231 | + | 0.995184i | \(0.531252\pi\) | |||||||
\(492\) | 25.1202 | + | 14.5032i | 1.13251 | + | 0.653854i | ||||
\(493\) | 7.05065 | + | 7.05065i | 0.317545 | + | 0.317545i | ||||
\(494\) | −7.04479 | − | 0.534224i | −0.316960 | − | 0.0240359i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.914311 | + | 3.41225i | 0.0410538 | + | 0.153215i | ||||
\(497\) | 3.96205 | − | 1.06163i | 0.177722 | − | 0.0476205i | ||||
\(498\) | −5.86397 | + | 21.8846i | −0.262771 | + | 0.980674i | ||||
\(499\) | 17.4889 | + | 17.4889i | 0.782910 | + | 0.782910i | 0.980321 | − | 0.197411i | \(-0.0632534\pi\) |
−0.197411 | + | 0.980321i | \(0.563253\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.46492 | + | 5.46714i | −0.0654476 | + | 0.244254i | ||||
\(502\) | 22.7843i | 1.01691i | ||||||||
\(503\) | −11.5921 | − | 3.10609i | −0.516865 | − | 0.138494i | −0.00904899 | − | 0.999959i | \(-0.502880\pi\) |
−0.507816 | + | 0.861465i | \(0.669547\pi\) | |||||||
\(504\) | −1.54534 | + | 2.67661i | −0.0688351 | + | 0.119226i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 32.9018i | 1.46267i | ||||||||
\(507\) | 42.4054 | − | 4.70170i | 1.88329 | − | 0.208810i | ||||
\(508\) | 0.883508 | − | 0.883508i | 0.0391993 | − | 0.0391993i | ||||
\(509\) | 17.3871 | − | 4.65885i | 0.770668 | − | 0.206500i | 0.148002 | − | 0.988987i | \(-0.452716\pi\) |
0.622667 | + | 0.782487i | \(0.286049\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.662552 | − | 0.382525i | 0.0293096 | − | 0.0169219i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 26.5720 | − | 15.3413i | 1.17318 | − | 0.677337i | ||||
\(514\) | 3.92708 | + | 1.05226i | 0.173216 | + | 0.0464131i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.7711 | − | 20.3882i | −0.518195 | − | 0.897540i | ||||
\(517\) | −16.8900 | − | 63.0344i | −0.742822 | − | 2.77225i | ||||
\(518\) | −0.637565 | + | 1.10430i | −0.0280130 | + | 0.0485199i | ||||
\(519\) | −20.1736 | −0.885524 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.4787 | 0.940998 | 0.470499 | − | 0.882400i | \(-0.344074\pi\) | ||||
0.470499 | + | 0.882400i | \(0.344074\pi\) | |||||||
\(522\) | −17.7764 | + | 30.7896i | −0.778050 | + | 1.34762i | ||||
\(523\) | −2.93344 | − | 10.9477i | −0.128270 | − | 0.478711i | 0.871665 | − | 0.490103i | \(-0.163041\pi\) |
−0.999935 | + | 0.0113912i | \(0.996374\pi\) | |||||||
\(524\) | −5.14636 | − | 8.91376i | −0.224820 | − | 0.389399i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.90510 | + | 2.38612i | 0.388281 | + | 0.104040i | ||||
\(527\) | 6.66782 | − | 3.84967i | 0.290455 | − | 0.167694i | ||||
\(528\) | 18.1345 | 0.789205 | ||||||||
\(529\) | 10.7871 | − | 6.22794i | 0.469005 | − | 0.270780i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.6230 | − | 13.2965i | 2.15346 | − | 0.577017i | ||||
\(532\) | −0.551058 | + | 0.551058i | −0.0238914 | + | 0.0238914i | ||||
\(533\) | −26.3134 | − | 17.9744i | −1.13976 | − | 0.778558i | ||||
\(534\) | − | 23.9098i | − | 1.03468i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.621825 | + | 1.07703i | −0.0268587 | + | 0.0465207i | ||||
\(537\) | −27.2168 | − | 7.29272i | −1.17449 | − | 0.314704i | ||||
\(538\) | 5.86024i | 0.252653i | ||||||||
\(539\) | 9.78463 | − | 36.5167i | 0.421454 | − | 1.57289i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.33292 | + | 8.33292i | 0.358260 | + | 0.358260i | 0.863171 | − | 0.504911i | \(-0.168475\pi\) |
−0.504911 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(542\) | 3.33481 | − | 12.4457i | 0.143242 | − | 0.534588i | ||||
\(543\) | −8.26757 | + | 2.21529i | −0.354795 | + | 0.0950671i | ||||
\(544\) | 0.564094 | + | 2.10523i | 0.0241853 | + | 0.0902609i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.65457 | − | 3.88612i | 0.113605 | − | 0.166310i | ||||
\(547\) | −0.364520 | − | 0.364520i | −0.0155858 | − | 0.0155858i | 0.699271 | − | 0.714857i | \(-0.253508\pi\) |
−0.714857 | + | 0.699271i | \(0.753508\pi\) | |||||||
\(548\) | −5.35364 | − | 3.09092i | −0.228696 | − | 0.132038i | ||||
\(549\) | −50.1371 | − | 28.9467i | −2.13980 | − | 1.23541i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.33892 | + | 6.33892i | −0.270047 | + | 0.270047i | ||||
\(552\) | −9.77113 | − | 16.9241i | −0.415887 | − | 0.720337i | ||||
\(553\) | 1.85569 | + | 3.21416i | 0.0789121 | + | 0.136680i | ||||
\(554\) | −18.6435 | + | 18.6435i | −0.792087 | + | 0.792087i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.5740 | + | 10.1464i | 0.745304 | + | 0.430302i | ||||
\(557\) | 3.33950 | + | 1.92806i | 0.141499 | + | 0.0816947i | 0.569078 | − | 0.822283i | \(-0.307300\pi\) |
−0.427579 | + | 0.903978i | \(0.640633\pi\) | |||||||
\(558\) | 19.4118 | + | 19.4118i | 0.821769 | + | 0.821769i | ||||
\(559\) | 11.2011 | + | 23.3123i | 0.473756 | + | 0.986004i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.2296 | − | 38.1774i | −0.431894 | − | 1.61185i | ||||
\(562\) | −0.190917 | + | 0.0511561i | −0.00805335 | + | 0.00215789i | ||||
\(563\) | 5.64567 | − | 21.0699i | 0.237937 | − | 0.887992i | −0.738866 | − | 0.673852i | \(-0.764639\pi\) |
0.976803 | − | 0.214140i | \(-0.0686948\pi\) | |||||||
\(564\) | 27.4077 | + | 27.4077i | 1.15407 | + | 1.15407i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.59229 | − | 5.94251i | 0.0669289 | − | 0.249782i | ||||
\(567\) | 11.1666i | 0.468955i | ||||||||
\(568\) | 9.96205 | + | 2.66932i | 0.417998 | + | 0.112002i | ||||
\(569\) | 18.5740 | − | 32.1712i | 0.778664 | − | 1.34869i | −0.154047 | − | 0.988063i | \(-0.549231\pi\) |
0.932712 | − | 0.360623i | \(-0.117436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6031i | 0.527423i | 0.964602 | + | 0.263712i | \(0.0849467\pi\) | ||||
−0.964602 | + | 0.263712i | \(0.915053\pi\) | |||||||
\(572\) | −19.8656 | − | 1.50646i | −0.830624 | − | 0.0629883i | ||||
\(573\) | 1.84182 | − | 1.84182i | 0.0769433 | − | 0.0769433i | ||||
\(574\) | −3.39529 | + | 0.909766i | −0.141717 | + | 0.0379729i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.72999 | + | 3.88556i | −0.280416 | + | 0.161899i | ||||
\(577\) | 2.81590 | 0.117227 | 0.0586136 | − | 0.998281i | \(-0.481332\pi\) | ||||
0.0586136 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(578\) | −10.6086 | + | 6.12491i | −0.441262 | + | 0.254763i | ||||
\(579\) | 46.1368 | + | 12.3623i | 1.91738 | + | 0.513760i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.37280 | − | 2.37775i | −0.0569531 | − | 0.0986457i | ||||
\(582\) | 3.52009 | + | 13.1372i | 0.145912 | + | 0.544553i | ||||
\(583\) | −22.9115 | + | 39.6838i | −0.948896 | + | 1.64354i | ||||
\(584\) | 1.92362 | 0.0795998 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.01430 | 0.207139 | ||||||||
\(587\) | −10.2105 | + | 17.6850i | −0.421431 | + | 0.729939i | −0.996080 | − | 0.0884607i | \(-0.971805\pi\) |
0.574649 | + | 0.818400i | \(0.305139\pi\) | |||||||
\(588\) | 5.81164 | + | 21.6893i | 0.239668 | + | 0.894453i | ||||
\(589\) | 3.46106 | + | 5.99474i | 0.142611 | + | 0.247009i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.6065 | − | 11.9523i | −1.83487 | − | 0.491651i | ||||
\(592\) | −2.77661 | + | 1.60307i | −0.114118 | + | 0.0658859i | ||||
\(593\) | −24.9304 | −1.02377 | −0.511885 | − | 0.859054i | \(-0.671053\pi\) | ||||
−0.511885 | + | 0.859054i | \(0.671053\pi\) | |||||||
\(594\) | 74.9305 | − | 43.2611i | 3.07443 | − | 1.77503i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.7177 | − | 3.13976i | 0.479978 | − | 0.128610i | ||||
\(597\) | 41.5961 | − | 41.5961i | 1.70242 | − | 1.70242i | ||||
\(598\) | 9.29796 | + | 19.3513i | 0.380222 | + | 0.791335i | ||||
\(599\) | 25.0801i | 1.02474i | 0.858764 | + | 0.512372i | \(0.171233\pi\) | ||||
−0.858764 | + | 0.512372i | \(0.828767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.69465 | + | 13.3275i | −0.313871 | + | 0.543641i | −0.979197 | − | 0.202912i | \(-0.934959\pi\) |
0.665326 | + | 0.746553i | \(0.268293\pi\) | |||||||
\(602\) | 2.75570 | + | 0.738388i | 0.112314 | + | 0.0300945i | ||||
\(603\) | 9.66456i | 0.393571i | ||||||||
\(604\) | −4.25819 | + | 15.8918i | −0.173263 | + | 0.646627i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.0207 | + | 22.0207i | 0.894528 | + | 0.894528i | ||||
\(607\) | −4.72767 | + | 17.6439i | −0.191890 | + | 0.716144i | 0.801160 | + | 0.598450i | \(0.204217\pi\) |
−0.993050 | + | 0.117693i | \(0.962450\pi\) | |||||||
\(608\) | −1.89272 | + | 0.507152i | −0.0767598 | + | 0.0205677i | ||||
\(609\) | −1.54556 | − | 5.76812i | −0.0626294 | − | 0.233736i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.7472 | − | 32.3008i | −1.12253 | − | 1.30675i | ||||
\(612\) | 11.9763 | + | 11.9763i | 0.484115 | + | 0.484115i | ||||
\(613\) | 33.5187 | + | 19.3521i | 1.35381 | + | 0.781622i | 0.988781 | − | 0.149374i | \(-0.0477259\pi\) |
0.365029 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(614\) | −2.64294 | − | 1.52590i | −0.106660 | − | 0.0615804i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.55393 | + | 1.55393i | −0.0626097 | + | 0.0626097i | ||||
\(617\) | 14.3799 | + | 24.9068i | 0.578915 | + | 1.00271i | 0.995604 | + | 0.0936610i | \(0.0298570\pi\) |
−0.416689 | + | 0.909049i | \(0.636810\pi\) | |||||||
\(618\) | −9.22284 | − | 15.9744i | −0.370997 | − | 0.642586i | ||||
\(619\) | −21.8733 | + | 21.8733i | −0.879164 | + | 0.879164i | −0.993448 | − | 0.114284i | \(-0.963542\pi\) |
0.114284 | + | 0.993448i | \(0.463542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −80.7470 | − | 46.6193i | −3.24027 | − | 1.87077i | ||||
\(622\) | 11.2698 | + | 6.50660i | 0.451876 | + | 0.260891i | ||||
\(623\) | 2.04881 | + | 2.04881i | 0.0820837 | + | 0.0820837i | ||||
\(624\) | 10.6659 | − | 5.12477i | 0.426978 | − | 0.205155i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.15231 | + | 15.4966i | 0.165960 | + | 0.619371i | ||||
\(627\) | 34.3235 | − | 9.19697i | 1.37075 | − | 0.367291i | ||||
\(628\) | 4.32147 | − | 16.1279i | 0.172445 | − | 0.643575i | ||||
\(629\) | 4.94110 | + | 4.94110i | 0.197015 | + | 0.197015i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.51748 | − | 24.3236i | 0.259457 | − | 0.968306i | −0.706100 | − | 0.708113i | \(-0.749547\pi\) |
0.965556 | − | 0.260194i | \(-0.0837864\pi\) | |||||||
\(632\) | 9.33180i | 0.371199i | ||||||||
\(633\) | 36.6723 | + | 9.82630i | 1.45759 | + | 0.390560i | ||||
\(634\) | 11.5293 | − | 19.9694i | 0.457888 | − | 0.793085i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 27.2168i | − | 1.07922i | ||||||
\(637\) | −4.56465 | − | 24.2425i | −0.180858 | − | 0.960525i | ||||
\(638\) | −17.8752 | + | 17.8752i | −0.707684 | + | 0.707684i | ||||
\(639\) | 77.4163 | − | 20.7436i | 3.06254 | − | 0.820606i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.3685 | + | 9.45035i | −0.646516 | + | 0.373266i | −0.787120 | − | 0.616800i | \(-0.788429\pi\) |
0.140604 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(642\) | 34.6193 | 1.36632 | ||||||||
\(643\) | −0.0203318 | + | 0.0117386i | −0.000801809 | + | 0.000462925i | −0.500401 | − | 0.865794i | \(-0.666814\pi\) |
0.499599 | + | 0.866257i | \(0.333481\pi\) | |||||||
\(644\) | 2.28749 | + | 0.612931i | 0.0901397 | + | 0.0241528i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.13534 | + | 3.69852i | 0.0840138 | + | 0.145516i | ||||
\(647\) | 3.83864 | + | 14.3260i | 0.150913 | + | 0.563214i | 0.999421 | + | 0.0340314i | \(0.0108346\pi\) |
−0.848508 | + | 0.529182i | \(0.822499\pi\) | |||||||
\(648\) | −14.0385 | + | 24.3154i | −0.551485 | + | 0.955201i | ||||
\(649\) | 36.5285 | 1.43387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.61104 | −0.180721 | ||||||||
\(652\) | 4.90281 | − | 8.49192i | 0.192009 | − | 0.332569i | ||||
\(653\) | −0.538667 | − | 2.01033i | −0.0210797 | − | 0.0786703i | 0.954585 | − | 0.297940i | \(-0.0962994\pi\) |
−0.975664 | + | 0.219269i | \(0.929633\pi\) | |||||||
\(654\) | −10.5839 | − | 18.3318i | −0.413862 | − | 0.716830i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.53702 | − | 2.28749i | −0.333315 | − | 0.0893114i | ||||
\(657\) | 12.9459 | − | 7.47434i | 0.505069 | − | 0.291602i | ||||
\(658\) | −4.69709 | −0.183111 | ||||||||
\(659\) | −1.41305 | + | 0.815824i | −0.0550445 | + | 0.0317800i | −0.527270 | − | 0.849698i | \(-0.676784\pi\) |
0.472225 | + | 0.881478i | \(0.343451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.86055 | − | 2.64213i | 0.383531 | − | 0.102767i | −0.0619018 | − | 0.998082i | \(-0.519717\pi\) |
0.445433 | + | 0.895315i | \(0.353050\pi\) | |||||||
\(662\) | 15.5134 | − | 15.5134i | 0.602944 | − | 0.602944i | ||||
\(663\) | −16.8054 | − | 19.5633i | −0.652667 | − | 0.759776i | ||||
\(664\) | − | 6.90343i | − | 0.267905i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.4577 | + | 21.5774i | −0.482726 | + | 0.836106i | ||||
\(667\) | 26.3134 | + | 7.05065i | 1.01886 | + | 0.273002i | ||||
\(668\) | − | 1.72459i | − | 0.0667264i | ||||||
\(669\) | −7.06244 | + | 26.3574i | −0.273050 | + | 1.01904i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.1075 | − | 29.1075i | −1.12368 | − | 1.12368i | ||||
\(672\) | 0.337830 | − | 1.26080i | 0.0130321 | − | 0.0486363i | ||||
\(673\) | 21.5553 | − | 5.77572i | 0.830894 | − | 0.222637i | 0.181791 | − | 0.983337i | \(-0.441811\pi\) |
0.649104 | + | 0.760700i | \(0.275144\pi\) | |||||||
\(674\) | −4.26866 | − | 15.9309i | −0.164423 | − | 0.613634i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1098 | + | 4.72794i | −0.465760 | + | 0.181844i | ||||
\(677\) | 23.5555 | + | 23.5555i | 0.905310 | + | 0.905310i | 0.995889 | − | 0.0905794i | \(-0.0288719\pi\) |
−0.0905794 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(678\) | 49.8688 | + | 28.7918i | 1.91520 | + | 1.10574i | ||||
\(679\) | −1.42734 | − | 0.824077i | −0.0547764 | − | 0.0316252i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.26274 | − | 7.26274i | 0.278309 | − | 0.278309i | ||||
\(682\) | 9.75986 | + | 16.9046i | 0.373725 | + | 0.647310i | ||||
\(683\) | 8.97635 | + | 15.5475i | 0.343470 | + | 0.594908i | 0.985075 | − | 0.172128i | \(-0.0550641\pi\) |
−0.641604 | + | 0.767036i | \(0.721731\pi\) | |||||||
\(684\) | −10.7674 | + | 10.7674i | −0.411702 | + | 0.411702i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.76755 | − | 2.75254i | −0.182026 | − | 0.105093i | ||||
\(687\) | −34.9297 | − | 20.1667i | −1.33265 | − | 0.769407i | ||||
\(688\) | 5.07227 | + | 5.07227i | 0.193379 | + | 0.193379i | ||||
\(689\) | −2.26094 | + | 29.8149i | −0.0861348 | + | 1.13586i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.72708 | − | 10.1776i | −0.103743 | − | 0.387174i | 0.894457 | − | 0.447155i | \(-0.147563\pi\) |
−0.998200 | + | 0.0599808i | \(0.980896\pi\) | |||||||
\(692\) | 5.93741 | − | 1.59092i | 0.225706 | − | 0.0604779i | ||||
\(693\) | −4.42005 | + | 16.4959i | −0.167904 | + | 0.626626i | ||||
\(694\) | −3.42587 | − | 3.42587i | −0.130044 | − | 0.130044i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.88612 | − | 14.5032i | 0.147303 | − | 0.549742i | ||||
\(697\) | 19.2627i | 0.729628i | ||||||||
\(698\) | −11.1067 | − | 2.97604i | −0.420396 | − | 0.112645i | ||||
\(699\) | 23.6403 | − | 40.9463i | 0.894160 | − | 1.54873i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.5789i | 1.38156i | 0.723063 | + | 0.690782i | \(0.242734\pi\) | ||||
−0.723063 | + | 0.690782i | \(0.757266\pi\) | |||||||
\(702\) | 31.8452 | − | 46.6193i | 1.20192 | − | 1.75953i | ||||
\(703\) | −4.44232 | + | 4.44232i | −0.167545 | + | 0.167545i | ||||
\(704\) | −5.33728 | + | 1.43012i | −0.201156 | + | 0.0538997i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.22407 | − | 1.28407i | 0.0837039 | − | 0.0483265i | ||||
\(707\) | −3.77386 | −0.141931 | ||||||||
\(708\) | −18.7896 | + | 10.8482i | −0.706155 | + | 0.407699i | ||||
\(709\) | 0.801931 | + | 0.214877i | 0.0301172 | + | 0.00806987i | 0.273846 | − | 0.961774i | \(-0.411704\pi\) |
−0.243729 | + | 0.969843i | \(0.578371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.2593 | + | 62.8030i | 1.35983 | + | 2.35530i | ||||
\(712\) | 1.88556 | + | 7.03702i | 0.0706645 | + | 0.263724i | ||||
\(713\) | 10.5175 | − | 18.2168i | 0.393883 | − | 0.682225i | ||||
\(714\) | −2.84483 | −0.106465 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.58545 | 0.320853 | ||||||||
\(717\) | −33.4288 | + | 57.9003i | −1.24842 | + | 2.16233i | ||||
\(718\) | −3.52159 | − | 13.1428i | −0.131425 | − | 0.490484i | ||||
\(719\) | −20.6441 | − | 35.7566i | −0.769894 | − | 1.33349i | −0.937620 | − | 0.347661i | \(-0.886976\pi\) |
0.167726 | − | 0.985834i | \(-0.446357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.15913 | + | 0.578537i | 0.0804102 | + | 0.0215459i | ||||
\(722\) | 13.1293 | − | 7.58021i | 0.488622 | − | 0.282106i | ||||
\(723\) | 94.4407 | 3.51229 | ||||||||
\(724\) | 2.25857 | − | 1.30399i | 0.0839392 | − | 0.0484623i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 61.9179 | − | 16.5909i | 2.29799 | − | 0.615744i | ||||
\(727\) | −33.1540 | + | 33.1540i | −1.22961 | + | 1.22961i | −0.265503 | + | 0.964110i | \(0.585538\pi\) |
−0.964110 | + | 0.265503i | \(0.914462\pi\) | |||||||
\(728\) | −0.474815 | + | 1.35309i | −0.0175978 | + | 0.0501488i | ||||
\(729\) | 64.0191i | 2.37108i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.81705 | − | 13.5395i | 0.289124 | − | 0.500777i | ||||
\(732\) | 23.6167 | + | 6.32807i | 0.872898 | + | 0.233892i | ||||
\(733\) | − | 24.3075i | − | 0.897818i | −0.893577 | − | 0.448909i | \(-0.851813\pi\) | ||
0.893577 | − | 0.448909i | \(-0.148187\pi\) | |||||||
\(734\) | 4.36492 | − | 16.2901i | 0.161112 | − | 0.601279i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.21046 | + | 4.21046i | 0.155199 | + | 0.155199i | ||||
\(737\) | −1.77857 | + | 6.63770i | −0.0655144 | + | 0.244503i | ||||
\(738\) | −66.3423 | + | 17.7764i | −2.44209 | + | 0.654357i | ||||
\(739\) | −4.44320 | − | 16.5822i | −0.163446 | − | 0.609987i | −0.998233 | − | 0.0594155i | \(-0.981076\pi\) |
0.834788 | − | 0.550572i | \(-0.185590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.5885 | − | 15.1090i | 0.646129 | − | 0.555041i | ||||
\(742\) | 2.33218 | + | 2.33218i | 0.0856171 | + | 0.0856171i | ||||
\(743\) | −11.3927 | − | 6.57760i | −0.417959 | − | 0.241309i | 0.276245 | − | 0.961087i | \(-0.410910\pi\) |
−0.694204 | + | 0.719778i | \(0.744243\pi\) | |||||||
\(744\) | −10.0406 | − | 5.79693i | −0.368106 | − | 0.212526i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.84881 | + | 1.84881i | −0.0676897 | + | 0.0676897i | ||||
\(747\) | −26.8237 | − | 46.4600i | −0.981428 | − | 1.69988i | ||||
\(748\) | 6.02146 | + | 10.4295i | 0.220166 | + | 0.381339i | ||||
\(749\) | −2.96650 | + | 2.96650i | −0.108393 | + | 0.108393i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8322 | − | 20.6878i | −1.30754 | − | 0.754907i | −0.325853 | − | 0.945421i | \(-0.605651\pi\) |
−0.981685 | + | 0.190513i | \(0.938985\pi\) | |||||||
\(752\) | −10.2279 | − | 5.90510i | −0.372975 | − | 0.215337i | ||||
\(753\) | −52.8752 | − | 52.8752i | −1.92688 | − | 1.92688i | ||||
\(754\) | −5.46188 | + | 15.5648i | −0.198910 | + | 0.566837i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.61183 | − | 6.01543i | −0.0586216 | − | 0.218779i | ||||
\(757\) | −45.7542 | + | 12.2598i | −1.66296 | + | 0.445590i | −0.963200 | − | 0.268785i | \(-0.913378\pi\) |
−0.699763 | + | 0.714375i | \(0.746711\pi\) | |||||||
\(758\) | 0.393670 | − | 1.46920i | 0.0142987 | − | 0.0533636i | ||||
\(759\) | −76.3547 | − | 76.3547i | −2.77150 | − | 2.77150i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.40042 | − | 5.22643i | 0.0507651 | − | 0.189458i | −0.935887 | − | 0.352300i | \(-0.885400\pi\) |
0.986652 | + | 0.162842i | \(0.0520662\pi\) | |||||||
\(762\) | 4.10068i | 0.148552i | ||||||||
\(763\) | 2.47776 | + | 0.663913i | 0.0897008 | + | 0.0240353i | ||||
\(764\) | −0.396828 | + | 0.687326i | −0.0143567 | + | 0.0248666i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.75655i | 0.135730i | ||||||||
\(767\) | 21.4844 | − | 10.3228i | 0.775755 | − | 0.372736i | ||||
\(768\) | 2.32068 | − | 2.32068i | 0.0837404 | − | 0.0837404i | ||||
\(769\) | 36.2611 | − | 9.71614i | 1.30761 | − | 0.350373i | 0.463287 | − | 0.886208i | \(-0.346670\pi\) |
0.844323 | + | 0.535835i | \(0.180003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5555 | + | 6.67155i | −0.416160 | + | 0.240270i | ||||
\(772\) | −14.5537 | −0.523799 | ||||||||
\(773\) | −12.5863 | + | 7.26671i | −0.452698 | + | 0.261365i | −0.708969 | − | 0.705240i | \(-0.750839\pi\) |
0.256271 | + | 0.966605i | \(0.417506\pi\) | |||||||
\(774\) | 53.8450 | + | 14.4277i | 1.93542 | + | 0.518594i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.07203 | − | 3.58887i | −0.0743817 | − | 0.128833i | ||||
\(777\) | −1.08313 | − | 4.04230i | −0.0388571 | − | 0.145017i | ||||
\(778\) | 7.03193 | − | 12.1797i | 0.252107 | − | 0.436662i | ||||
\(779\) | −17.3183 | −0.620491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.9877 | 2.03918 | ||||||||
\(782\) | 6.48888 | − | 11.2391i | 0.232042 | − | 0.401908i | ||||
\(783\) | −18.5412 | − | 69.1965i | −0.662607 | − | 2.47288i | ||||
\(784\) | −3.42091 | − | 5.92519i | −0.122175 | − | 0.211614i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.6291 | + | 8.74293i | 1.16384 | + | 0.311850i | ||||
\(787\) | 38.5792 | − | 22.2737i | 1.37520 | − | 0.793971i | 0.383622 | − | 0.923490i | \(-0.374677\pi\) |
0.991577 | + | 0.129519i | \(0.0413434\pi\) | |||||||
\(788\) | 14.0710 | 0.501258 | ||||||||
\(789\) | −26.2033 | + | 15.1285i | −0.932863 | + | 0.538589i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.74036 | + | 1.80607i | −0.239659 | + | 0.0642166i | ||||
\(792\) | −30.3630 | + | 30.3630i | −1.07890 | + | 1.07890i | ||||
\(793\) | −25.3454 | − | 8.89401i | −0.900042 | − | 0.315836i | ||||
\(794\) | 17.1506i | 0.608653i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.96205 | + | 15.5227i | −0.317651 | + | 0.550188i | ||||
\(797\) | 18.7076 | + | 5.01270i | 0.662658 | + | 0.177559i | 0.574445 | − | 0.818543i | \(-0.305218\pi\) |
0.0882130 | + | 0.996102i | \(0.471884\pi\) | |||||||
\(798\) | − | 2.55766i | − | 0.0905403i | ||||||
\(799\) | −6.66207 | + | 24.8632i | −0.235687 | + | 0.879596i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.0326 | + | 40.0326i | 1.41448 | + | 1.41448i | ||||
\(802\) | −0.590110 | + | 2.20232i | −0.0208375 | + | 0.0777666i | ||||
\(803\) | 10.2669 | − | 2.75100i | 0.362310 | − | 0.0970807i | ||||
\(804\) | −1.05639 | − | 3.94251i | −0.0372561 | − | 0.139041i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.5175 | + | 7.18438i | 0.370463 | + | 0.253059i | ||||
\(807\) | −13.5998 | − | 13.5998i | −0.478734 | − | 0.478734i | ||||
\(808\) | −8.21761 | − | 4.74444i | −0.289094 | − | 0.166909i | ||||
\(809\) | 16.2434 | + | 9.37810i | 0.571086 | + | 0.329717i | 0.757583 | − | 0.652739i | \(-0.226380\pi\) |
−0.186497 | + | 0.982456i | \(0.559713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.8918 | + | 20.8918i | −0.733609 | + | 0.733609i | −0.971333 | − | 0.237724i | \(-0.923599\pi\) |
0.237724 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(812\) | 0.909766 | + | 1.57576i | 0.0319265 | + | 0.0552984i | ||||
\(813\) | 21.1434 | + | 36.6215i | 0.741533 | + | 1.28437i | ||||
\(814\) | −12.5269 | + | 12.5269i | −0.439069 | + | 0.439069i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.19465 | − | 3.57648i | −0.216856 | − | 0.125202i | ||||
\(817\) | 12.1728 | + | 7.02796i | 0.425872 | + | 0.245877i | ||||
\(818\) | −13.1660 | − | 13.1660i | −0.460340 | − | 0.460340i | ||||
\(819\) | 2.06201 | + | 10.9512i | 0.0720524 | + | 0.382666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.52604 | + | 13.1594i | 0.123060 | + | 0.459265i | 0.999763 | − | 0.0217666i | \(-0.00692907\pi\) |
−0.876704 | + | 0.481031i | \(0.840262\pi\) | |||||||
\(822\) | 19.5971 | − | 5.25104i | 0.683529 | − | 0.183151i | ||||
\(823\) | 5.05496 | − | 18.8654i | 0.176205 | − | 0.657606i | −0.820138 | − | 0.572165i | \(-0.806104\pi\) |
0.996343 | − | 0.0854405i | \(-0.0272297\pi\) | |||||||
\(824\) | 3.97420 | + | 3.97420i | 0.138448 | + | 0.138448i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.680491 | − | 2.53963i | 0.0236773 | − | 0.0883650i | ||||
\(827\) | 6.90343i | 0.240056i | 0.992771 | + | 0.120028i | \(0.0382984\pi\) | ||||
−0.992771 | + | 0.120028i | \(0.961702\pi\) | |||||||
\(828\) | 44.6963 | + | 11.9763i | 1.55331 | + | 0.416207i | ||||
\(829\) | −9.06163 | + | 15.6952i | −0.314723 | + | 0.545117i | −0.979379 | − | 0.202033i | \(-0.935245\pi\) |
0.664655 | + | 0.747150i | \(0.268578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 86.5313i | − | 3.00174i | ||||||
\(832\) | −2.73499 | + | 2.34943i | −0.0948188 | + | 0.0814518i | ||||
\(833\) | −10.5442 | + | 10.5442i | −0.365334 | + | 0.365334i | ||||
\(834\) | −64.3302 | + | 17.2372i | −2.22757 | + | 0.596876i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.37667 | + | 5.41362i | −0.324299 | + | 0.187234i | ||||
\(837\) | −55.3158 | −1.91199 | ||||||||
\(838\) | −8.19164 | + | 4.72944i | −0.282975 | + | 0.163376i | ||||
\(839\) | −13.8579 | − | 3.71322i | −0.478429 | − | 0.128195i | 0.0115419 | − | 0.999933i | \(-0.496326\pi\) |
−0.489971 | + | 0.871739i | \(0.662993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.03480 | − | 6.98847i | −0.139131 | − | 0.240982i | ||||
\(842\) | 8.55242 | + | 31.9181i | 0.294736 | + | 1.09997i | ||||
\(843\) | 0.324341 | − | 0.561775i | 0.0111709 | − | 0.0193485i | ||||
\(844\) | −11.5681 | −0.398192 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −91.7786 | −3.15541 | ||||||||
\(847\) | −3.88403 | + | 6.72734i | −0.133457 | + | 0.231154i | ||||
\(848\) | 2.14636 | + | 8.01033i | 0.0737064 | + | 0.275076i | ||||
\(849\) | 10.0955 | + | 17.4859i | 0.346476 | + | 0.600113i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4405 | + | 4.94110i | 0.632131 | + | 0.169379i | ||||
\(852\) | −29.3134 | + | 16.9241i | −1.00426 | + | 0.579810i | ||||
\(853\) | 21.5765 | 0.738764 | 0.369382 | − | 0.929278i | \(-0.379569\pi\) | ||||
0.369382 | + | 0.929278i | \(0.379569\pi\) | |||||||
\(854\) | −2.56594 | + | 1.48144i | −0.0878046 | + | 0.0506940i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.1890 | + | 2.73013i | −0.348253 | + | 0.0933141i | ||||
\(857\) | −5.36230 | + | 5.36230i | −0.183173 | + | 0.183173i | −0.792737 | − | 0.609564i | \(-0.791344\pi\) |
0.609564 | + | 0.792737i | \(0.291344\pi\) | |||||||
\(858\) | 49.5979 | − | 42.6058i | 1.69324 | − | 1.45454i | ||||
\(859\) | − | 28.8595i | − | 0.984673i | −0.870405 | − | 0.492336i | \(-0.836143\pi\) | ||
0.870405 | − | 0.492336i | \(-0.163857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.76812 | − | 9.99067i | 0.196577 | − | 0.340481i | ||||
\(862\) | −28.5757 | − | 7.65683i | −0.973292 | − | 0.260793i | ||||
\(863\) | − | 56.4179i | − | 1.92049i | −0.279160 | − | 0.960245i | \(-0.590056\pi\) | ||
0.279160 | − | 0.960245i | \(-0.409944\pi\) | |||||||
\(864\) | 4.05273 | − | 15.1250i | 0.137877 | − | 0.514563i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.5280 | − | 17.5280i | −0.595624 | − | 0.595624i | ||||
\(867\) | 10.4053 | − | 38.8333i | 0.353384 | − | 1.31885i | ||||
\(868\) | 1.35710 | − | 0.363634i | 0.0460630 | − | 0.0123426i | ||||
\(869\) | 13.3456 | + | 49.8064i | 0.452718 | + | 1.68957i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.829724 | + | 4.40661i | 0.0281141 | + | 0.149312i | ||||
\(872\) | 4.56067 | + | 4.56067i | 0.154444 | + | 0.154444i | ||||
\(873\) | −27.8896 | − | 16.1020i | −0.943919 | − | 0.544972i | ||||
\(874\) | 10.1045 | + | 5.83386i | 0.341791 | + | 0.197333i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.46410 | + | 4.46410i | −0.150828 | + | 0.150828i | ||||
\(877\) | 7.06228 | + | 12.2322i | 0.238476 | + | 0.413053i | 0.960277 | − | 0.279048i | \(-0.0900188\pi\) |
−0.721801 | + | 0.692101i | \(0.756685\pi\) | |||||||
\(878\) | −3.29091 | − | 5.70002i | −0.111063 | − | 0.192366i | ||||
\(879\) | −11.6366 | + | 11.6366i | −0.392493 | + | 0.392493i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6470 | − | 7.87910i | −0.459779 | − | 0.265454i | 0.252172 | − | 0.967682i | \(-0.418855\pi\) |
−0.711951 | + | 0.702229i | \(0.752188\pi\) | |||||||
\(882\) | −46.0454 | − | 26.5843i | −1.55043 | − | 0.895141i | ||||
\(883\) | −5.11749 | − | 5.11749i | −0.172217 | − | 0.172217i | 0.615736 | − | 0.787953i | \(-0.288859\pi\) |
−0.787953 | + | 0.615736i | \(0.788859\pi\) | |||||||
\(884\) | 6.48888 | + | 4.43248i | 0.218245 | + | 0.149081i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.36865 | − | 27.5002i | −0.247555 | − | 0.923887i | ||||
\(887\) | 21.1993 | − | 5.68034i | 0.711804 | − | 0.190727i | 0.115292 | − | 0.993332i | \(-0.463220\pi\) |
0.596512 | + | 0.802604i | \(0.296553\pi\) | |||||||
\(888\) | 2.72339 | − | 10.1638i | 0.0913911 | − | 0.341076i | ||||
\(889\) | −0.351384 | − | 0.351384i | −0.0117850 | − | 0.0117850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.1535 | + | 149.855i | −1.34519 | + | 5.02033i | ||||
\(892\) | − | 8.31434i | − | 0.278385i | ||||||
\(893\) | −22.3534 | − | 5.98957i | −0.748027 | − | 0.200433i | ||||
\(894\) | −19.9068 | + | 34.4795i | −0.665782 | + | 1.15317i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.397714i | 0.0132867i | ||||||||
\(897\) | −66.4859 | − | 23.3307i | −2.21990 | − | 0.778989i | ||||
\(898\) | −3.95832 | + | 3.95832i | −0.132091 | + | 0.132091i | ||||
\(899\) | 15.6110 | − | 4.18295i | 0.520655 | − | 0.139509i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.6528 | − | 9.03716i | 0.521471 | − | 0.301072i | ||||
\(902\) | −48.8358 | −1.62606 | ||||||||
\(903\) | −8.10867 | + | 4.68154i | −0.269840 | + | 0.155792i | ||||
\(904\) | −16.9477 | − | 4.54113i | −0.563674 | − | 0.151036i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26.9979 | − | 46.7617i | −0.896944 | − | 1.55355i | ||||
\(907\) | −5.06878 | − | 18.9169i | −0.168306 | − | 0.628127i | −0.997595 | − | 0.0693072i | \(-0.977921\pi\) |
0.829289 | − | 0.558819i | \(-0.188746\pi\) | |||||||
\(908\) | −1.56478 | + | 2.71029i | −0.0519292 | + | 0.0899440i | ||||
\(909\) | −73.7393 | −2.44578 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2386 | 1.69761 | 0.848806 | − | 0.528705i | \(-0.177322\pi\) | ||||
0.848806 | + | 0.528705i | \(0.177322\pi\) | |||||||
\(912\) | 3.21545 | − | 5.56933i | 0.106474 | − | 0.184419i | ||||
\(913\) | −9.87273 | − | 36.8455i | −0.326740 | − | 1.21941i | ||||
\(914\) | −10.3741 | − | 17.9685i | −0.343145 | − | 0.594344i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.8707 | + | 3.18076i | 0.392220 | + | 0.105095i | ||||
\(917\) | −3.54513 | + | 2.04678i | −0.117070 | + | 0.0675906i | ||||
\(918\) | −34.1277 | −1.12638 | ||||||||
\(919\) | 0.175850 | − | 0.101527i | 0.00580076 | − | 0.00334907i | −0.497097 | − | 0.867695i | \(-0.665601\pi\) |
0.502898 | + | 0.864346i | \(0.332267\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.67456 | − | 2.59229i | 0.318788 | − | 0.0854189i | ||||
\(922\) | 17.8091 | − | 17.8091i | 0.586511 | − | 0.586511i | ||||
\(923\) | 33.5175 | − | 16.1045i | 1.10324 | − | 0.530087i | ||||
\(924\) | − | 7.21236i | − | 0.237269i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.1076 | + | 27.8992i | −0.529329 | + | 0.916825i | ||||
\(927\) | 42.1883 | + | 11.3043i | 1.38565 | + | 0.371283i | ||||
\(928\) | 4.57498i | 0.150181i | ||||||||
\(929\) | 9.43399 | − | 35.2081i | 0.309519 | − | 1.15514i | −0.619466 | − | 0.785024i | \(-0.712651\pi\) |
0.928985 | − | 0.370118i | \(-0.120683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.47979 | − | 9.47979i | −0.310687 | − | 0.310687i | ||||
\(932\) | −3.72863 | + | 13.9154i | −0.122135 | + | 0.455815i | ||||
\(933\) | −41.2533 | + | 11.0538i | −1.35057 | + | 0.361885i | ||||
\(934\) | 7.51748 | + | 28.0556i | 0.245980 | + | 0.918008i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.27763 | + | 26.4386i | −0.303249 | + | 0.864174i | ||||
\(937\) | 25.1436 | + | 25.1436i | 0.821405 | + | 0.821405i | 0.986310 | − | 0.164904i | \(-0.0527316\pi\) |
−0.164904 | + | 0.986310i | \(0.552732\pi\) | |||||||
\(938\) | 0.428351 | + | 0.247308i | 0.0139862 | + | 0.00807491i | ||||
\(939\) | −45.5990 | − | 26.3266i | −1.48807 | − | 0.859136i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.5125 | − | 32.5125i | 1.05988 | − | 1.05988i | 0.0617896 | − | 0.998089i | \(-0.480319\pi\) |
0.998089 | − | 0.0617896i | \(-0.0196808\pi\) | |||||||
\(942\) | 27.3991 | + | 47.4566i | 0.892710 | + | 1.54622i | ||||
\(943\) | 26.3134 | + | 45.5761i | 0.856882 | + | 1.48416i | ||||
\(944\) | 4.67456 | − | 4.67456i | 0.152144 | − | 0.152144i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.3261 | + | 19.8182i | 1.11604 | + | 0.644344i | ||||
\(947\) | −29.8823 | − | 17.2526i | −0.971045 | − | 0.560633i | −0.0714906 | − | 0.997441i | \(-0.522776\pi\) |
−0.899555 | + | 0.436808i | \(0.856109\pi\) | |||||||
\(948\) | −21.6561 | − | 21.6561i | −0.703359 | − | 0.703359i | ||||
\(949\) | 5.26108 | − | 4.51940i | 0.170782 | − | 0.146706i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5867 | + | 73.0984i | 0.635141 | + | 2.37038i | ||||
\(952\) | 0.837279 | − | 0.224348i | 0.0271364 | − | 0.00727117i | ||||
\(953\) | −12.5168 | + | 46.7133i | −0.405459 | + | 1.51319i | 0.397750 | + | 0.917494i | \(0.369791\pi\) |
−0.803208 | + | 0.595698i | \(0.796875\pi\) | |||||||
\(954\) | 45.5697 | + | 45.5697i | 1.47537 | + | 1.47537i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.27249 | − | 19.6772i | 0.170525 | − | 0.636407i | ||||
\(957\) | − | 82.9651i | − | 2.68188i | ||||||
\(958\) | 26.8200 | + | 7.18639i | 0.866514 | + | 0.232182i | ||||
\(959\) | −1.22930 | + | 2.12922i | −0.0396963 | + | 0.0687560i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5206i | 0.597437i | ||||||||
\(962\) | −3.82769 | + | 10.9078i | −0.123410 | + | 0.351683i | ||||
\(963\) | −57.9638 | + | 57.9638i | −1.86786 | + | 1.86786i | ||||
\(964\) | −27.7954 | + | 7.44774i | −0.895228 | + | 0.239876i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.73095 | + | 3.88612i | −0.216565 | + | 0.125034i | ||||
\(967\) | 59.9161 | 1.92677 | 0.963385 | − | 0.268121i | \(-0.0864026\pi\) | ||||
0.963385 | + | 0.268121i | \(0.0864026\pi\) | |||||||
\(968\) | −16.9150 | + | 9.76589i | −0.543669 | + | 0.313888i | ||||
\(969\) | −13.5385 | − | 3.62764i | −0.434920 | − | 0.116537i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8825 | − | 39.6337i | −0.734336 | − | 1.27191i | −0.955014 | − | 0.296560i | \(-0.904160\pi\) |
0.220678 | − | 0.975347i | \(-0.429173\pi\) | |||||||
\(972\) | −11.6913 | − | 43.6323i | −0.374997 | − | 1.39951i | ||||
\(973\) | 4.03535 | − | 6.98943i | 0.129367 | − | 0.224071i | ||||
\(974\) | −40.0137 | −1.28212 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.44980 | −0.238462 | ||||||||
\(977\) | −26.1173 | + | 45.2364i | −0.835565 | + | 1.44724i | 0.0580046 | + | 0.998316i | \(0.481526\pi\) |
−0.893570 | + | 0.448925i | \(0.851807\pi\) | |||||||
\(978\) | 8.32917 | + | 31.0849i | 0.266338 | + | 0.993985i | ||||
\(979\) | 20.1276 | + | 34.8620i | 0.643280 | + | 1.11419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.4141 | + | 12.9725i | 1.54574 | + | 0.414181i | ||||
\(982\) | 15.8394 | − | 9.14486i | 0.505454 | − | 0.291824i | ||||
\(983\) | 52.3414 | 1.66943 | 0.834716 | − | 0.550680i | \(-0.185632\pi\) | ||||
0.834716 | + | 0.550680i | \(0.185632\pi\) | |||||||
\(984\) | 25.1202 | − | 14.5032i | 0.800804 | − | 0.462344i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.63137 | − | 2.58072i | 0.306725 | − | 0.0821868i | ||||
\(987\) | 10.9004 | − | 10.9004i | 0.346965 | − | 0.346965i | ||||
\(988\) | −3.98505 | + | 5.83386i | −0.126781 | + | 0.185600i | ||||
\(989\) | − | 42.7132i | − | 1.35820i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.4130 | + | 37.0883i | −0.680205 | + | 1.17815i | 0.294713 | + | 0.955586i | \(0.404776\pi\) |
−0.974918 | + | 0.222564i | \(0.928557\pi\) | |||||||
\(992\) | 3.41225 | + | 0.914311i | 0.108339 | + | 0.0290294i | ||||
\(993\) | 72.0032i | 2.28495i | ||||||||
\(994\) | 1.06163 | − | 3.96205i | 0.0336728 | − | 0.125668i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.0207 | + | 16.0207i | 0.507634 | + | 0.507634i | ||||
\(997\) | 5.50169 | − | 20.5326i | 0.174240 | − | 0.650274i | −0.822440 | − | 0.568853i | \(-0.807388\pi\) |
0.996680 | − | 0.0814210i | \(-0.0259458\pi\) | |||||||
\(998\) | 23.8902 | − | 6.40137i | 0.756233 | − | 0.202632i | ||||
\(999\) | −12.9937 | − | 48.4930i | −0.411101 | − | 1.53425i |
(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 | 650.2.w.d.357.2 | yes | 8 | |
5.2 | odd | 4 | 650.2.t.d.643.2 | yes | 8 | ||
5.3 | odd | 4 | 650.2.t.c.643.1 | yes | 8 | ||
5.4 | even | 2 | 650.2.w.c.357.1 | yes | 8 | ||
13.11 | odd | 12 | 650.2.t.c.557.1 | ✓ | 8 | ||
65.24 | odd | 12 | 650.2.t.d.557.2 | yes | 8 | ||
65.37 | even | 12 | 650.2.w.c.193.1 | yes | 8 | ||
65.63 | even | 12 | inner | 650.2.w.d.193.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
650.2.t.c.557.1 | ✓ | 8 | 13.11 | odd | 12 | ||
650.2.t.c.643.1 | yes | 8 | 5.3 | odd | 4 | ||
650.2.t.d.557.2 | yes | 8 | 65.24 | odd | 12 | ||
650.2.t.d.643.2 | yes | 8 | 5.2 | odd | 4 | ||
650.2.w.c.193.1 | yes | 8 | 65.37 | even | 12 | ||
650.2.w.c.357.1 | yes | 8 | 5.4 | even | 2 | ||
650.2.w.d.193.2 | yes | 8 | 65.63 | even | 12 | inner | |
650.2.w.d.357.2 | yes | 8 | 1.1 | even | 1 | trivial |