Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(31,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(1.01575 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.61 |
Dual form | 210.3.o.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.387298 | − | 0.223607i | ||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −5.10237 | + | 4.79227i | −0.728910 | + | 0.684610i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.73861 | − | 1.58114i | 0.273861 | − | 0.158114i | ||||
\(11\) | 9.03504 | + | 15.6491i | 0.821367 | + | 1.42265i | 0.904664 | + | 0.426125i | \(0.140122\pi\) |
−0.0832974 | + | 0.996525i | \(0.526545\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.250000 | − | 0.144338i | ||||
\(13\) | 18.6604i | 1.43542i | 0.696344 | + | 0.717708i | \(0.254809\pi\) | ||||
−0.696344 | + | 0.717708i | \(0.745191\pi\) | |||||||
\(14\) | −2.26139 | − | 9.63774i | −0.161528 | − | 0.688410i | ||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.33462 | − | 0.770543i | 0.0785070 | − | 0.0453261i | −0.460233 | − | 0.887798i | \(-0.652234\pi\) |
0.538740 | + | 0.842472i | \(0.318901\pi\) | |||||||
\(18\) | 2.12132 | + | 3.67423i | 0.117851 | + | 0.204124i | ||||
\(19\) | 29.4836 | + | 17.0224i | 1.55177 | + | 0.895914i | 0.997998 | + | 0.0632454i | \(0.0201451\pi\) |
0.553771 | + | 0.832669i | \(0.313188\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | −3.50333 | + | 11.6072i | −0.166825 | + | 0.552723i | ||||
\(22\) | −25.5549 | −1.16159 | ||||||||
\(23\) | 13.4938 | − | 23.3720i | 0.586687 | − | 1.01617i | −0.407975 | − | 0.912993i | \(-0.633765\pi\) |
0.994663 | − | 0.103179i | \(-0.0329015\pi\) | |||||||
\(24\) | 4.24264 | − | 2.44949i | 0.176777 | − | 0.102062i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | −22.8542 | − | 13.1949i | −0.879009 | − | 0.507496i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 13.4028 | + | 4.04529i | 0.478672 | + | 0.144475i | ||||
\(29\) | −16.4662 | −0.567802 | −0.283901 | − | 0.958854i | \(-0.591629\pi\) | ||||
−0.283901 | + | 0.958854i | \(0.591629\pi\) | |||||||
\(30\) | 2.73861 | − | 4.74342i | 0.0912871 | − | 0.158114i | ||||
\(31\) | −24.1988 | + | 13.9712i | −0.780605 | + | 0.450683i | −0.836645 | − | 0.547746i | \(-0.815486\pi\) |
0.0560395 | + | 0.998429i | \(0.482153\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 27.1051 | + | 15.6491i | 0.821367 | + | 0.474216i | ||||
\(34\) | 2.17942i | 0.0641007i | ||||||||
\(35\) | 15.2386 | − | 3.57557i | 0.435389 | − | 0.102159i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −25.8353 | + | 44.7480i | −0.698251 | + | 1.20941i | 0.270821 | + | 0.962630i | \(0.412705\pi\) |
−0.969072 | + | 0.246777i | \(0.920629\pi\) | |||||||
\(38\) | −41.6961 | + | 24.0733i | −1.09727 | + | 0.633507i | ||||
\(39\) | 16.1604 | + | 27.9906i | 0.414369 | + | 0.717708i | ||||
\(40\) | −5.47723 | − | 3.16228i | −0.136931 | − | 0.0790569i | ||||
\(41\) | − | 37.4818i | − | 0.914191i | −0.889418 | − | 0.457095i | \(-0.848890\pi\) | ||
0.889418 | − | 0.457095i | \(-0.151110\pi\) | |||||||
\(42\) | −11.7386 | − | 12.4982i | −0.279491 | − | 0.297576i | ||||
\(43\) | −63.6947 | −1.48127 | −0.740636 | − | 0.671907i | \(-0.765476\pi\) | ||||
−0.740636 | + | 0.671907i | \(0.765476\pi\) | |||||||
\(44\) | 18.0701 | − | 31.2983i | 0.410684 | − | 0.711325i | ||||
\(45\) | −5.80948 | + | 3.35410i | −0.129099 | + | 0.0745356i | ||||
\(46\) | 19.0831 | + | 33.0529i | 0.414851 | + | 0.718542i | ||||
\(47\) | −24.4572 | − | 14.1204i | −0.520367 | − | 0.300434i | 0.216718 | − | 0.976234i | \(-0.430465\pi\) |
−0.737085 | + | 0.675800i | \(0.763798\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 3.06832 | − | 48.9038i | 0.0626188 | − | 0.998038i | ||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 1.33462 | − | 2.31163i | 0.0261690 | − | 0.0453261i | ||||
\(52\) | 32.3208 | − | 18.6604i | 0.621553 | − | 0.358854i | ||||
\(53\) | −0.221841 | − | 0.384239i | −0.00418567 | − | 0.00724980i | 0.863925 | − | 0.503621i | \(-0.167999\pi\) |
−0.868111 | + | 0.496371i | \(0.834666\pi\) | |||||||
\(54\) | 6.36396 | + | 3.67423i | 0.117851 | + | 0.0680414i | ||||
\(55\) | − | 40.4059i | − | 0.734653i | ||||||
\(56\) | −14.4317 | + | 13.5546i | −0.257709 | + | 0.242046i | ||||
\(57\) | 58.9672 | 1.03451 | ||||||||
\(58\) | 11.6434 | − | 20.1669i | 0.200748 | − | 0.347706i | ||||
\(59\) | 64.2260 | − | 37.0809i | 1.08858 | − | 0.628490i | 0.155379 | − | 0.987855i | \(-0.450340\pi\) |
0.933197 | + | 0.359365i | \(0.117007\pi\) | |||||||
\(60\) | 3.87298 | + | 6.70820i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 91.0443 | + | 52.5645i | 1.49253 | + | 0.861712i | 0.999963 | − | 0.00856246i | \(-0.00272555\pi\) |
0.492566 | + | 0.870275i | \(0.336059\pi\) | |||||||
\(62\) | − | 39.5164i | − | 0.637361i | ||||||
\(63\) | 4.79713 | + | 20.4447i | 0.0761449 | + | 0.324520i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 20.8630 | − | 36.1357i | 0.320969 | − | 0.555934i | ||||
\(66\) | −38.3324 | + | 22.1312i | −0.580794 | + | 0.335322i | ||||
\(67\) | 6.35442 | + | 11.0062i | 0.0948420 | + | 0.164271i | 0.909543 | − | 0.415611i | \(-0.136432\pi\) |
−0.814701 | + | 0.579882i | \(0.803099\pi\) | |||||||
\(68\) | −2.66924 | − | 1.54109i | −0.0392535 | − | 0.0226630i | ||||
\(69\) | − | 46.7439i | − | 0.677448i | ||||||
\(70\) | −6.39617 | + | 21.1917i | −0.0913738 | + | 0.302739i | ||||
\(71\) | −45.7647 | −0.644573 | −0.322286 | − | 0.946642i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946642i | \(0.604451\pi\) | |||||||
\(72\) | 4.24264 | − | 7.34847i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 31.5463 | − | 18.2133i | 0.432141 | − | 0.249497i | −0.268117 | − | 0.963386i | \(-0.586401\pi\) |
0.700258 | + | 0.713889i | \(0.253068\pi\) | |||||||
\(74\) | −36.5366 | − | 63.2833i | −0.493738 | − | 0.855179i | ||||
\(75\) | 7.50000 | + | 4.33013i | 0.100000 | + | 0.0577350i | ||||
\(76\) | − | 68.0895i | − | 0.895914i | ||||||
\(77\) | −121.095 | − | 36.5494i | −1.57266 | − | 0.474667i | ||||
\(78\) | −45.7085 | −0.586006 | ||||||||
\(79\) | 66.5990 | − | 115.353i | 0.843025 | − | 1.46016i | −0.0442994 | − | 0.999018i | \(-0.514106\pi\) |
0.887325 | − | 0.461145i | \(-0.152561\pi\) | |||||||
\(80\) | 7.74597 | − | 4.47214i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 45.9057 | + | 26.5037i | 0.559825 | + | 0.323215i | ||||
\(83\) | 49.9265i | 0.601524i | 0.953699 | + | 0.300762i | \(0.0972409\pi\) | ||||
−0.953699 | + | 0.300762i | \(0.902759\pi\) | |||||||
\(84\) | 23.6076 | − | 5.53924i | 0.281042 | − | 0.0659434i | ||||
\(85\) | −3.44597 | −0.0405409 | ||||||||
\(86\) | 45.0389 | − | 78.0097i | 0.523709 | − | 0.907090i | ||||
\(87\) | −24.6994 | + | 14.2602i | −0.283901 | + | 0.163910i | ||||
\(88\) | 25.5549 | + | 44.2625i | 0.290397 | + | 0.502983i | ||||
\(89\) | 85.9133 | + | 49.6020i | 0.965318 | + | 0.557326i | 0.897806 | − | 0.440392i | \(-0.145161\pi\) |
0.0675121 | + | 0.997718i | \(0.478494\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | −89.4257 | − | 95.2123i | −0.982700 | − | 1.04629i | ||||
\(92\) | −53.9752 | −0.586687 | ||||||||
\(93\) | −24.1988 | + | 41.9135i | −0.260202 | + | 0.450683i | ||||
\(94\) | 34.5878 | − | 19.9693i | 0.367955 | − | 0.212439i | ||||
\(95\) | −38.0632 | − | 65.9274i | −0.400665 | − | 0.693972i | ||||
\(96\) | −8.48528 | − | 4.89898i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 150.376i | 1.55027i | 0.631796 | + | 0.775134i | \(0.282318\pi\) | ||||
−0.631796 | + | 0.775134i | \(0.717682\pi\) | |||||||
\(98\) | 57.7251 | + | 38.3381i | 0.589032 | + | 0.391206i | ||||
\(99\) | 54.2102 | 0.547578 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 40.7726 | − | 23.5401i | 0.403689 | − | 0.233070i | −0.284386 | − | 0.958710i | \(-0.591790\pi\) |
0.688074 | + | 0.725640i | \(0.258456\pi\) | |||||||
\(102\) | 1.88744 | + | 3.26914i | 0.0185043 | + | 0.0320504i | ||||
\(103\) | −65.7708 | − | 37.9728i | −0.638552 | − | 0.368668i | 0.145505 | − | 0.989358i | \(-0.453519\pi\) |
−0.784056 | + | 0.620690i | \(0.786853\pi\) | |||||||
\(104\) | 52.7796i | 0.507496i | ||||||||
\(105\) | 19.7614 | − | 18.5604i | 0.188204 | − | 0.176765i | ||||
\(106\) | 0.627460 | 0.00591944 | ||||||||
\(107\) | 53.6125 | − | 92.8597i | 0.501052 | − | 0.867847i | −0.498947 | − | 0.866632i | \(-0.666280\pi\) |
0.999999 | − | 0.00121497i | \(-0.000386738\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −40.4452 | − | 70.0532i | −0.371057 | − | 0.642690i | 0.618671 | − | 0.785650i | \(-0.287671\pi\) |
−0.989728 | + | 0.142960i | \(0.954338\pi\) | |||||||
\(110\) | 49.4869 | + | 28.5713i | 0.449881 | + | 0.259739i | ||||
\(111\) | 89.4961i | 0.806271i | ||||||||
\(112\) | −6.39617 | − | 27.2597i | −0.0571087 | − | 0.243390i | ||||
\(113\) | −79.9061 | −0.707134 | −0.353567 | − | 0.935409i | \(-0.615031\pi\) | ||||
−0.353567 | + | 0.935409i | \(0.615031\pi\) | |||||||
\(114\) | −41.6961 | + | 72.2198i | −0.365755 | + | 0.633507i | ||||
\(115\) | −52.2613 | + | 30.1731i | −0.454446 | + | 0.262375i | ||||
\(116\) | 16.4662 | + | 28.5204i | 0.141950 | + | 0.245865i | ||||
\(117\) | 48.4812 | + | 27.9906i | 0.414369 | + | 0.239236i | ||||
\(118\) | 104.881i | 0.888819i | ||||||||
\(119\) | −3.11707 | + | 10.3275i | −0.0261939 | + | 0.0867853i | ||||
\(120\) | −10.9545 | −0.0912871 | ||||||||
\(121\) | −102.764 | + | 177.992i | −0.849288 | + | 1.47101i | ||||
\(122\) | −128.756 | + | 74.3374i | −1.05538 | + | 0.609323i | ||||
\(123\) | −32.4602 | − | 56.2227i | −0.263904 | − | 0.457095i | ||||
\(124\) | 48.3975 | + | 27.9423i | 0.390303 | + | 0.225341i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −28.4317 | − | 8.58136i | −0.225648 | − | 0.0681060i | ||||
\(127\) | 99.1937 | 0.781053 | 0.390526 | − | 0.920592i | \(-0.372293\pi\) | ||||
0.390526 | + | 0.920592i | \(0.372293\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −95.5420 | + | 55.1612i | −0.740636 | + | 0.427606i | ||||
\(130\) | 29.5047 | + | 51.1036i | 0.226959 | + | 0.393105i | ||||
\(131\) | 144.309 | + | 83.3170i | 1.10160 | + | 0.636008i | 0.936640 | − | 0.350293i | \(-0.113918\pi\) |
0.164958 | + | 0.986301i | \(0.447251\pi\) | |||||||
\(132\) | − | 62.5966i | − | 0.474216i | ||||||
\(133\) | −232.012 | + | 54.4390i | −1.74445 | + | 0.409316i | ||||
\(134\) | −17.9730 | −0.134127 | ||||||||
\(135\) | −5.80948 | + | 10.0623i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 3.77487 | − | 2.17942i | 0.0277564 | − | 0.0160252i | ||||
\(137\) | 75.7587 | + | 131.218i | 0.552983 | + | 0.957795i | 0.998057 | + | 0.0623012i | \(0.0198439\pi\) |
−0.445074 | + | 0.895494i | \(0.646823\pi\) | |||||||
\(138\) | 57.2494 | + | 33.0529i | 0.414851 | + | 0.239514i | ||||
\(139\) | − | 151.816i | − | 1.09220i | −0.837719 | − | 0.546101i | \(-0.816111\pi\) | ||
0.837719 | − | 0.546101i | \(-0.183889\pi\) | |||||||
\(140\) | −21.4317 | − | 22.8185i | −0.153083 | − | 0.162989i | ||||
\(141\) | −48.9145 | −0.346911 | ||||||||
\(142\) | 32.3605 | − | 56.0500i | 0.227891 | − | 0.394719i | ||||
\(143\) | −292.019 | + | 168.597i | −2.04209 | + | 1.17900i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 31.8867 | + | 18.4098i | 0.219909 | + | 0.126964i | ||||
\(146\) | 51.5149i | 0.352842i | ||||||||
\(147\) | −37.7495 | − | 76.0130i | −0.256799 | − | 0.517095i | ||||
\(148\) | 103.341 | 0.698251 | ||||||||
\(149\) | −16.5970 | + | 28.7468i | −0.111389 | + | 0.192931i | −0.916331 | − | 0.400423i | \(-0.868863\pi\) |
0.804941 | + | 0.593354i | \(0.202197\pi\) | |||||||
\(150\) | −10.6066 | + | 6.12372i | −0.0707107 | + | 0.0408248i | ||||
\(151\) | 4.65158 | + | 8.05678i | 0.0308052 | + | 0.0533562i | 0.881017 | − | 0.473085i | \(-0.156860\pi\) |
−0.850212 | + | 0.526441i | \(0.823526\pi\) | |||||||
\(152\) | 83.3923 | + | 48.1465i | 0.548633 | + | 0.316754i | ||||
\(153\) | − | 4.62326i | − | 0.0302174i | ||||||
\(154\) | 130.391 | − | 122.466i | 0.846693 | − | 0.795235i | ||||
\(155\) | 62.4809 | 0.403103 | ||||||||
\(156\) | 32.3208 | − | 55.9812i | 0.207184 | − | 0.358854i | ||||
\(157\) | −20.7746 | + | 11.9942i | −0.132322 | + | 0.0763963i | −0.564700 | − | 0.825296i | \(-0.691008\pi\) |
0.432378 | + | 0.901693i | \(0.357675\pi\) | |||||||
\(158\) | 94.1852 | + | 163.134i | 0.596109 | + | 1.03249i | ||||
\(159\) | −0.665522 | − | 0.384239i | −0.00418567 | − | 0.00241660i | ||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 43.1543 | + | 183.918i | 0.268039 | + | 1.14235i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 126.564 | − | 219.215i | 0.776464 | − | 1.34488i | −0.157504 | − | 0.987518i | \(-0.550345\pi\) |
0.933968 | − | 0.357357i | \(-0.116322\pi\) | |||||||
\(164\) | −64.9204 | + | 37.4818i | −0.395856 | + | 0.228548i | ||||
\(165\) | −34.9926 | − | 60.6089i | −0.212076 | − | 0.367327i | ||||
\(166\) | −61.1472 | − | 35.3033i | −0.368357 | − | 0.212671i | ||||
\(167\) | 85.7259i | 0.513329i | 0.966501 | + | 0.256664i | \(0.0826235\pi\) | ||||
−0.966501 | + | 0.256664i | \(0.917376\pi\) | |||||||
\(168\) | −9.90890 | + | 32.8301i | −0.0589816 | + | 0.195417i | ||||
\(169\) | −179.211 | −1.06042 | ||||||||
\(170\) | 2.43667 | − | 4.22044i | 0.0143334 | − | 0.0248261i | ||||
\(171\) | 88.4508 | − | 51.0671i | 0.517256 | − | 0.298638i | ||||
\(172\) | 63.6947 | + | 110.322i | 0.370318 | + | 0.641409i | ||||
\(173\) | −16.8672 | − | 9.73826i | −0.0974980 | − | 0.0562905i | 0.450458 | − | 0.892798i | \(-0.351261\pi\) |
−0.547956 | + | 0.836507i | \(0.684594\pi\) | |||||||
\(174\) | − | 40.3339i | − | 0.231804i | ||||||
\(175\) | −33.5071 | − | 10.1132i | −0.191469 | − | 0.0577899i | ||||
\(176\) | −72.2803 | −0.410684 | ||||||||
\(177\) | 64.2260 | − | 111.243i | 0.362859 | − | 0.628490i | ||||
\(178\) | −121.500 | + | 70.1479i | −0.682583 | + | 0.394089i | ||||
\(179\) | −126.417 | − | 218.961i | −0.706241 | − | 1.22324i | −0.966242 | − | 0.257637i | \(-0.917056\pi\) |
0.260001 | − | 0.965608i | \(-0.416277\pi\) | |||||||
\(180\) | 11.6190 | + | 6.70820i | 0.0645497 | + | 0.0372678i | ||||
\(181\) | 144.224i | 0.796820i | 0.917207 | + | 0.398410i | \(0.130438\pi\) | ||||
−0.917207 | + | 0.398410i | \(0.869562\pi\) | |||||||
\(182\) | 179.844 | − | 42.1984i | 0.988155 | − | 0.231859i | ||||
\(183\) | 182.089 | 0.995020 | ||||||||
\(184\) | 38.1663 | − | 66.1059i | 0.207425 | − | 0.359271i | ||||
\(185\) | 100.060 | − | 57.7695i | 0.540863 | − | 0.312267i | ||||
\(186\) | −34.2222 | − | 59.2746i | −0.183990 | − | 0.318681i | ||||
\(187\) | 24.1167 | + | 13.9238i | 0.128966 | + | 0.0744587i | ||||
\(188\) | 56.4816i | 0.300434i | ||||||||
\(189\) | 24.9014 | + | 26.5127i | 0.131753 | + | 0.140279i | ||||
\(190\) | 107.659 | 0.566626 | ||||||||
\(191\) | 157.049 | − | 272.017i | 0.822246 | − | 1.42417i | −0.0817601 | − | 0.996652i | \(-0.526054\pi\) |
0.904006 | − | 0.427520i | \(-0.140613\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −26.4142 | − | 45.7507i | −0.136861 | − | 0.237050i | 0.789446 | − | 0.613820i | \(-0.210368\pi\) |
−0.926307 | + | 0.376770i | \(0.877035\pi\) | |||||||
\(194\) | −184.172 | − | 106.332i | −0.949342 | − | 0.548103i | ||||
\(195\) | − | 72.2714i | − | 0.370623i | ||||||
\(196\) | −87.7723 | + | 43.5893i | −0.447818 | + | 0.222395i | ||||
\(197\) | 54.2005 | 0.275129 | 0.137565 | − | 0.990493i | \(-0.456073\pi\) | ||||
0.137565 | + | 0.990493i | \(0.456073\pi\) | |||||||
\(198\) | −38.3324 | + | 66.3937i | −0.193598 | + | 0.335322i | ||||
\(199\) | 19.8934 | − | 11.4855i | 0.0999670 | − | 0.0577160i | −0.449183 | − | 0.893440i | \(-0.648285\pi\) |
0.549150 | + | 0.835724i | \(0.314952\pi\) | |||||||
\(200\) | 7.07107 | + | 12.2474i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 19.0632 | + | 11.0062i | 0.0948420 | + | 0.0547571i | ||||
\(202\) | 66.5813i | 0.329611i | ||||||||
\(203\) | 84.0168 | − | 78.9107i | 0.413876 | − | 0.388722i | ||||
\(204\) | −5.33848 | −0.0261690 | ||||||||
\(205\) | −41.9060 | + | 72.5832i | −0.204419 | + | 0.354065i | ||||
\(206\) | 93.0140 | − | 53.7017i | 0.451524 | − | 0.260688i | ||||
\(207\) | −40.4814 | − | 70.1159i | −0.195562 | − | 0.338724i | ||||
\(208\) | −64.6415 | − | 37.3208i | −0.310777 | − | 0.179427i | ||||
\(209\) | 615.191i | 2.94350i | ||||||||
\(210\) | 8.75832 | + | 37.3268i | 0.0417063 | + | 0.177747i | ||||
\(211\) | −292.203 | −1.38485 | −0.692425 | − | 0.721490i | \(-0.743457\pi\) | ||||
−0.692425 | + | 0.721490i | \(0.743457\pi\) | |||||||
\(212\) | −0.443681 | + | 0.768479i | −0.00209284 | + | 0.00362490i | ||||
\(213\) | −68.6470 | + | 39.6334i | −0.322286 | + | 0.186072i | ||||
\(214\) | 75.8196 | + | 131.323i | 0.354297 | + | 0.613661i | ||||
\(215\) | 123.344 | + | 71.2128i | 0.573694 | + | 0.331222i | ||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 56.5174 | − | 187.253i | 0.260449 | − | 0.862917i | ||||
\(218\) | 114.396 | 0.524754 | ||||||||
\(219\) | 31.5463 | − | 54.6398i | 0.144047 | − | 0.249497i | ||||
\(220\) | −69.9851 | + | 40.4059i | −0.318114 | + | 0.183663i | ||||
\(221\) | 14.3786 | + | 24.9045i | 0.0650617 | + | 0.112690i | ||||
\(222\) | −109.610 | − | 63.2833i | −0.493738 | − | 0.285060i | ||||
\(223\) | − | 271.305i | − | 1.21661i | −0.793702 | − | 0.608306i | \(-0.791849\pi\) | ||
0.793702 | − | 0.608306i | \(-0.208151\pi\) | |||||||
\(224\) | 37.9089 | + | 11.4418i | 0.169236 | + | 0.0510795i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 56.5021 | − | 97.8646i | 0.250009 | − | 0.433029i | ||||
\(227\) | 128.699 | − | 74.3044i | 0.566956 | − | 0.327332i | −0.188977 | − | 0.981982i | \(-0.560517\pi\) |
0.755933 | + | 0.654649i | \(0.227184\pi\) | |||||||
\(228\) | −58.9672 | − | 102.134i | −0.258628 | − | 0.447957i | ||||
\(229\) | 21.9394 | + | 12.6667i | 0.0958053 | + | 0.0553132i | 0.547137 | − | 0.837043i | \(-0.315718\pi\) |
−0.451332 | + | 0.892356i | \(0.649051\pi\) | |||||||
\(230\) | − | 85.3423i | − | 0.371054i | ||||||
\(231\) | −213.295 | + | 50.0473i | −0.923356 | + | 0.216655i | ||||
\(232\) | −46.5736 | −0.200748 | ||||||||
\(233\) | 204.443 | − | 354.106i | 0.877438 | − | 1.51977i | 0.0232943 | − | 0.999729i | \(-0.492585\pi\) |
0.854143 | − | 0.520038i | \(-0.174082\pi\) | |||||||
\(234\) | −68.5627 | + | 39.5847i | −0.293003 | + | 0.169165i | ||||
\(235\) | 31.5742 | + | 54.6881i | 0.134358 | + | 0.232715i | ||||
\(236\) | −128.452 | − | 74.1618i | −0.544288 | − | 0.314245i | ||||
\(237\) | − | 230.706i | − | 0.973442i | ||||||
\(238\) | −10.4444 | − | 11.1202i | −0.0438840 | − | 0.0467236i | ||||
\(239\) | 67.0352 | 0.280482 | 0.140241 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(240\) | 7.74597 | − | 13.4164i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 205.143 | − | 118.440i | 0.851217 | − | 0.491451i | −0.00984406 | − | 0.999952i | \(-0.503134\pi\) |
0.861061 | + | 0.508501i | \(0.169800\pi\) | |||||||
\(242\) | −145.330 | − | 251.719i | −0.600537 | − | 1.04016i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 210.258i | − | 0.861712i | ||||||
\(245\) | −60.6179 | + | 91.2714i | −0.247420 | + | 0.372536i | ||||
\(246\) | 91.8113 | 0.373217 | ||||||||
\(247\) | −317.644 | + | 550.176i | −1.28601 | + | 2.22743i | ||||
\(248\) | −68.4444 | + | 39.5164i | −0.275986 | + | 0.159340i | ||||
\(249\) | 43.2376 | + | 74.8897i | 0.173645 | + | 0.300762i | ||||
\(250\) | 13.6931 | + | 7.90569i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | 483.382i | 1.92582i | 0.269815 | + | 0.962912i | \(0.413037\pi\) | ||||
−0.269815 | + | 0.962912i | \(0.586963\pi\) | |||||||
\(252\) | 30.6142 | − | 28.7536i | 0.121485 | − | 0.114102i | ||||
\(253\) | 487.668 | 1.92754 | ||||||||
\(254\) | −70.1406 | + | 121.487i | −0.276144 | + | 0.478295i | ||||
\(255\) | −5.16896 | + | 2.98430i | −0.0202704 | + | 0.0117031i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −281.097 | − | 162.291i | −1.09376 | − | 0.631484i | −0.159187 | − | 0.987248i | \(-0.550887\pi\) |
−0.934576 | + | 0.355764i | \(0.884221\pi\) | |||||||
\(258\) | − | 156.019i | − | 0.604727i | ||||||
\(259\) | −82.6234 | − | 352.131i | −0.319009 | − | 1.35958i | ||||
\(260\) | −83.4519 | −0.320969 | ||||||||
\(261\) | −24.6994 | + | 42.7806i | −0.0946336 | + | 0.163910i | ||||
\(262\) | −204.084 | + | 117.828i | −0.778948 | + | 0.449726i | ||||
\(263\) | −153.686 | − | 266.192i | −0.584358 | − | 1.01214i | −0.994955 | − | 0.100320i | \(-0.968013\pi\) |
0.410598 | − | 0.911817i | \(-0.365320\pi\) | |||||||
\(264\) | 76.6648 | + | 44.2625i | 0.290397 | + | 0.167661i | ||||
\(265\) | 0.992102i | 0.00374378i | ||||||||
\(266\) | 97.3834 | − | 322.650i | 0.366103 | − | 1.21297i | ||||
\(267\) | 171.827 | 0.643545 | ||||||||
\(268\) | 12.7088 | − | 22.0123i | 0.0474210 | − | 0.0821356i | ||||
\(269\) | −65.6866 | + | 37.9242i | −0.244188 | + | 0.140982i | −0.617100 | − | 0.786885i | \(-0.711693\pi\) |
0.372912 | + | 0.927867i | \(0.378359\pi\) | |||||||
\(270\) | −8.21584 | − | 14.2302i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −18.8151 | − | 10.8629i | −0.0694283 | − | 0.0400844i | 0.464884 | − | 0.885372i | \(-0.346096\pi\) |
−0.534312 | + | 0.845287i | \(0.679429\pi\) | |||||||
\(272\) | 6.16434i | 0.0226630i | ||||||||
\(273\) | −216.595 | − | 65.3735i | −0.793387 | − | 0.239463i | ||||
\(274\) | −214.278 | −0.782036 | ||||||||
\(275\) | −45.1752 | + | 78.2457i | −0.164273 | + | 0.284530i | ||||
\(276\) | −80.9628 | + | 46.7439i | −0.293344 | + | 0.169362i | ||||
\(277\) | 55.8659 | + | 96.7627i | 0.201682 | + | 0.349324i | 0.949071 | − | 0.315064i | \(-0.102026\pi\) |
−0.747388 | + | 0.664387i | \(0.768693\pi\) | |||||||
\(278\) | 185.936 | + | 107.350i | 0.668835 | + | 0.386152i | ||||
\(279\) | 83.8270i | 0.300455i | ||||||||
\(280\) | 43.1013 | − | 10.1132i | 0.153933 | − | 0.0361187i | ||||
\(281\) | −188.298 | −0.670101 | −0.335051 | − | 0.942200i | \(-0.608753\pi\) | ||||
−0.335051 | + | 0.942200i | \(0.608753\pi\) | |||||||
\(282\) | 34.5878 | − | 59.9078i | 0.122652 | − | 0.212439i | ||||
\(283\) | 187.769 | − | 108.408i | 0.663495 | − | 0.383069i | −0.130113 | − | 0.991499i | \(-0.541534\pi\) |
0.793607 | + | 0.608430i | \(0.208201\pi\) | |||||||
\(284\) | 45.7647 | + | 79.2667i | 0.161143 | + | 0.279108i | ||||
\(285\) | −114.190 | − | 65.9274i | −0.400665 | − | 0.231324i | ||||
\(286\) | − | 476.866i | − | 1.66736i | ||||||
\(287\) | 179.623 | + | 191.246i | 0.625864 | + | 0.666363i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −143.313 | + | 248.225i | −0.495891 | + | 0.858909i | ||||
\(290\) | −45.0947 | + | 26.0354i | −0.155499 | + | 0.0897773i | ||||
\(291\) | 130.230 | + | 225.564i | 0.447524 | + | 0.775134i | ||||
\(292\) | −63.0926 | − | 36.4265i | −0.216071 | − | 0.124748i | ||||
\(293\) | 57.3776i | 0.195828i | 0.995195 | + | 0.0979140i | \(0.0312170\pi\) | ||||
−0.995195 | + | 0.0979140i | \(0.968783\pi\) | |||||||
\(294\) | 119.789 | + | 7.51583i | 0.407447 | + | 0.0255640i | ||||
\(295\) | −165.831 | −0.562138 | ||||||||
\(296\) | −73.0732 | + | 126.567i | −0.246869 | + | 0.427590i | ||||
\(297\) | 81.3153 | − | 46.9474i | 0.273789 | − | 0.158072i | ||||
\(298\) | −23.4717 | − | 40.6541i | −0.0787640 | − | 0.136423i | ||||
\(299\) | 436.130 | + | 251.800i | 1.45863 | + | 0.842140i | ||||
\(300\) | − | 17.3205i | − | 0.0577350i | ||||||
\(301\) | 324.994 | − | 305.242i | 1.07971 | − | 1.01409i | ||||
\(302\) | −13.1567 | −0.0435651 | ||||||||
\(303\) | 40.7726 | − | 70.6202i | 0.134563 | − | 0.233070i | ||||
\(304\) | −117.934 | + | 68.0895i | −0.387942 | + | 0.223979i | ||||
\(305\) | −117.538 | − | 203.581i | −0.385370 | − | 0.667480i | ||||
\(306\) | 5.66231 | + | 3.26914i | 0.0185043 | + | 0.0106835i | ||||
\(307\) | 291.273i | 0.948773i | 0.880317 | + | 0.474386i | \(0.157330\pi\) | ||||
−0.880317 | + | 0.474386i | \(0.842670\pi\) | |||||||
\(308\) | 57.7896 | + | 246.292i | 0.187629 | + | 0.799650i | ||||
\(309\) | −131.542 | −0.425701 | ||||||||
\(310\) | −44.1807 | + | 76.5232i | −0.142518 | + | 0.246849i | ||||
\(311\) | 216.368 | − | 124.920i | 0.695717 | − | 0.401673i | −0.110033 | − | 0.993928i | \(-0.535096\pi\) |
0.805750 | + | 0.592255i | \(0.201762\pi\) | |||||||
\(312\) | 45.7085 | + | 79.1694i | 0.146502 | + | 0.253748i | ||||
\(313\) | −3.27832 | − | 1.89274i | −0.0104739 | − | 0.00604709i | 0.494754 | − | 0.869033i | \(-0.335258\pi\) |
−0.505228 | + | 0.862986i | \(0.668592\pi\) | |||||||
\(314\) | − | 33.9248i | − | 0.108041i | ||||||
\(315\) | 13.5683 | − | 44.9544i | 0.0430740 | − | 0.142712i | ||||
\(316\) | −266.396 | −0.843025 | ||||||||
\(317\) | 35.6805 | − | 61.8004i | 0.112557 | − | 0.194954i | −0.804244 | − | 0.594300i | \(-0.797429\pi\) |
0.916800 | + | 0.399346i | \(0.130763\pi\) | |||||||
\(318\) | 0.941190 | − | 0.543397i | 0.00295972 | − | 0.00170879i | ||||
\(319\) | −148.773 | − | 257.683i | −0.466373 | − | 0.807783i | ||||
\(320\) | −15.4919 | − | 8.94427i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | − | 185.719i | − | 0.578565i | ||||||
\(322\) | −255.768 | − | 77.1968i | −0.794310 | − | 0.239742i | ||||
\(323\) | 52.4659 | 0.162433 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −80.8019 | + | 46.6510i | −0.248621 | + | 0.143542i | ||||
\(326\) | 178.988 | + | 310.016i | 0.549043 | + | 0.950970i | ||||
\(327\) | −121.336 | − | 70.0532i | −0.371057 | − | 0.214230i | ||||
\(328\) | − | 106.015i | − | 0.323215i | ||||||
\(329\) | 192.459 | − | 45.1582i | 0.584981 | − | 0.137259i | ||||
\(330\) | 98.9739 | 0.299921 | ||||||||
\(331\) | 170.983 | − | 296.152i | 0.516566 | − | 0.894718i | −0.483249 | − | 0.875483i | \(-0.660544\pi\) |
0.999815 | − | 0.0192351i | \(-0.00612311\pi\) | |||||||
\(332\) | 86.4752 | − | 49.9265i | 0.260467 | − | 0.150381i | ||||
\(333\) | 77.5059 | + | 134.244i | 0.232750 | + | 0.403135i | ||||
\(334\) | −104.992 | − | 60.6174i | −0.314349 | − | 0.181489i | ||||
\(335\) | − | 28.4178i | − | 0.0848293i | ||||||
\(336\) | −33.2018 | − | 35.3502i | −0.0988149 | − | 0.105209i | ||||
\(337\) | 246.396 | 0.731145 | 0.365573 | − | 0.930783i | \(-0.380873\pi\) | ||||
0.365573 | + | 0.930783i | \(0.380873\pi\) | |||||||
\(338\) | 126.721 | − | 219.487i | 0.374915 | − | 0.649371i | ||||
\(339\) | −119.859 | + | 69.2007i | −0.353567 | + | 0.204132i | ||||
\(340\) | 3.44597 | + | 5.96860i | 0.0101352 | + | 0.0175547i | ||||
\(341\) | −437.273 | − | 252.460i | −1.28233 | − | 0.740352i | ||||
\(342\) | 144.440i | 0.422338i | ||||||||
\(343\) | 218.705 | + | 264.230i | 0.637623 | + | 0.770349i | ||||
\(344\) | −180.156 | −0.523709 | ||||||||
\(345\) | −52.2613 | + | 90.5192i | −0.151482 | + | 0.262375i | ||||
\(346\) | 23.8538 | − | 13.7720i | 0.0689415 | − | 0.0398034i | ||||
\(347\) | −69.1758 | − | 119.816i | −0.199354 | − | 0.345291i | 0.748965 | − | 0.662609i | \(-0.230551\pi\) |
−0.948319 | + | 0.317318i | \(0.897218\pi\) | |||||||
\(348\) | 49.3987 | + | 28.5204i | 0.141950 | + | 0.0819551i | ||||
\(349\) | 115.858i | 0.331971i | 0.986128 | + | 0.165986i | \(0.0530805\pi\) | ||||
−0.986128 | + | 0.165986i | \(0.946919\pi\) | |||||||
\(350\) | 36.0792 | − | 33.8865i | 0.103083 | − | 0.0968184i | ||||
\(351\) | 96.9623 | 0.276246 | ||||||||
\(352\) | 51.1099 | − | 88.5249i | 0.145199 | − | 0.251491i | ||||
\(353\) | 162.136 | − | 93.6093i | 0.459309 | − | 0.265182i | −0.252445 | − | 0.967611i | \(-0.581235\pi\) |
0.711754 | + | 0.702429i | \(0.247901\pi\) | |||||||
\(354\) | 90.8293 | + | 157.321i | 0.256580 | + | 0.444409i | ||||
\(355\) | 88.6229 | + | 51.1664i | 0.249642 | + | 0.144131i | ||||
\(356\) | − | 198.408i | − | 0.557326i | ||||||
\(357\) | 4.26823 | + | 18.1906i | 0.0119558 | + | 0.0509542i | ||||
\(358\) | 357.562 | 0.998775 | ||||||||
\(359\) | −318.748 | + | 552.087i | −0.887876 | + | 1.53785i | −0.0454957 | + | 0.998965i | \(0.514487\pi\) |
−0.842381 | + | 0.538883i | \(0.818847\pi\) | |||||||
\(360\) | −16.4317 | + | 9.48683i | −0.0456435 | + | 0.0263523i | ||||
\(361\) | 399.022 | + | 691.127i | 1.10532 | + | 1.91448i | ||||
\(362\) | −176.638 | − | 101.982i | −0.487951 | − | 0.281718i | ||||
\(363\) | 355.984i | 0.980673i | ||||||||
\(364\) | −75.4868 | + | 250.102i | −0.207381 | + | 0.687094i | ||||
\(365\) | −81.4522 | −0.223157 | ||||||||
\(366\) | −128.756 | + | 223.012i | −0.351793 | + | 0.609323i | ||||
\(367\) | 47.6750 | − | 27.5252i | 0.129905 | − | 0.0750005i | −0.433639 | − | 0.901087i | \(-0.642771\pi\) |
0.563544 | + | 0.826086i | \(0.309437\pi\) | |||||||
\(368\) | 53.9752 | + | 93.4878i | 0.146672 | + | 0.254043i | ||||
\(369\) | −97.3806 | − | 56.2227i | −0.263904 | − | 0.152365i | ||||
\(370\) | 163.397i | 0.441613i | ||||||||
\(371\) | 2.97329 | + | 0.897411i | 0.00801426 | + | 0.00241890i | ||||
\(372\) | 96.7950 | 0.260202 | ||||||||
\(373\) | −134.578 | + | 233.097i | −0.360800 | + | 0.624924i | −0.988093 | − | 0.153859i | \(-0.950830\pi\) |
0.627293 | + | 0.778784i | \(0.284163\pi\) | |||||||
\(374\) | −34.1061 | + | 19.6912i | −0.0911929 | + | 0.0526502i | ||||
\(375\) | −9.68246 | − | 16.7705i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −69.1755 | − | 39.9385i | −0.183978 | − | 0.106219i | ||||
\(377\) | − | 307.267i | − | 0.815031i | ||||||
\(378\) | −50.0792 | + | 11.7505i | −0.132485 | + | 0.0310860i | ||||
\(379\) | 469.785 | 1.23954 | 0.619769 | − | 0.784784i | \(-0.287226\pi\) | ||||
0.619769 | + | 0.784784i | \(0.287226\pi\) | |||||||
\(380\) | −76.1264 | + | 131.855i | −0.200333 | + | 0.346986i | ||||
\(381\) | 148.791 | − | 85.9043i | 0.390526 | − | 0.225471i | ||||
\(382\) | 222.101 | + | 384.690i | 0.581416 | + | 1.00704i | ||||
\(383\) | −348.324 | − | 201.105i | −0.909462 | − | 0.525078i | −0.0292039 | − | 0.999573i | \(-0.509297\pi\) |
−0.880258 | + | 0.474495i | \(0.842631\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 193.636 | + | 206.166i | 0.502951 | + | 0.535496i | ||||
\(386\) | 74.7107 | 0.193551 | ||||||||
\(387\) | −95.5420 | + | 165.484i | −0.246879 | + | 0.427606i | ||||
\(388\) | 260.459 | − | 150.376i | 0.671286 | − | 0.387567i | ||||
\(389\) | 55.3803 | + | 95.9215i | 0.142366 | + | 0.246585i | 0.928387 | − | 0.371615i | \(-0.121196\pi\) |
−0.786021 | + | 0.618200i | \(0.787862\pi\) | |||||||
\(390\) | 88.5141 | + | 51.1036i | 0.226959 | + | 0.131035i | ||||
\(391\) | − | 41.5902i | − | 0.106369i | ||||||
\(392\) | 8.67853 | − | 138.321i | 0.0221391 | − | 0.352860i | ||||
\(393\) | 288.619 | 0.734399 | ||||||||
\(394\) | −38.3255 | + | 66.3817i | −0.0972729 | + | 0.168482i | ||||
\(395\) | −257.937 | + | 148.920i | −0.653005 | + | 0.377012i | ||||
\(396\) | −54.2102 | − | 93.8949i | −0.136895 | − | 0.237108i | ||||
\(397\) | 363.569 | + | 209.907i | 0.915792 | + | 0.528733i | 0.882290 | − | 0.470706i | \(-0.156001\pi\) |
0.0335018 | + | 0.999439i | \(0.489334\pi\) | |||||||
\(398\) | 32.4858i | 0.0816227i | ||||||||
\(399\) | −300.873 | + | 282.587i | −0.754066 | + | 0.708238i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | −157.034 | + | 271.990i | −0.391605 | + | 0.678280i | −0.992661 | − | 0.120927i | \(-0.961413\pi\) |
0.601056 | + | 0.799207i | \(0.294747\pi\) | |||||||
\(402\) | −26.9595 | + | 15.5651i | −0.0670634 | + | 0.0387191i | ||||
\(403\) | −260.708 | − | 451.559i | −0.646917 | − | 1.12049i | ||||
\(404\) | −81.5451 | − | 47.0801i | −0.201844 | − | 0.116535i | ||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 37.2366 | + | 158.697i | 0.0917156 | + | 0.390880i | ||||
\(407\) | −933.691 | −2.29408 | ||||||||
\(408\) | 3.77487 | − | 6.53827i | 0.00925214 | − | 0.0160252i | ||||
\(409\) | 105.506 | − | 60.9140i | 0.257961 | − | 0.148934i | −0.365443 | − | 0.930834i | \(-0.619082\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(410\) | −59.2640 | − | 102.648i | −0.144546 | − | 0.250361i | ||||
\(411\) | 227.276 | + | 131.218i | 0.552983 | + | 0.319265i | ||||
\(412\) | 151.891i | 0.368668i | ||||||||
\(413\) | −150.003 | + | 496.989i | −0.363203 | + | 1.20336i | ||||
\(414\) | 114.499 | 0.276567 | ||||||||
\(415\) | 55.8195 | − | 96.6822i | 0.134505 | − | 0.232969i | ||||
\(416\) | 91.4169 | − | 52.7796i | 0.219752 | − | 0.126874i | ||||
\(417\) | −131.477 | − | 227.724i | −0.315292 | − | 0.546101i | ||||
\(418\) | −753.452 | − | 435.006i | −1.80252 | − | 1.04068i | ||||
\(419\) | 43.0872i | 0.102833i | 0.998677 | + | 0.0514167i | \(0.0163737\pi\) | ||||
−0.998677 | + | 0.0514167i | \(0.983626\pi\) | |||||||
\(420\) | −51.9089 | − | 15.6674i | −0.123593 | − | 0.0373032i | ||||
\(421\) | 135.571 | 0.322022 | 0.161011 | − | 0.986953i | \(-0.448525\pi\) | ||||
0.161011 | + | 0.986953i | \(0.448525\pi\) | |||||||
\(422\) | 206.619 | − | 357.874i | 0.489618 | − | 0.848043i | ||||
\(423\) | −73.3717 | + | 42.3612i | −0.173456 | + | 0.100145i | ||||
\(424\) | −0.627460 | − | 1.08679i | −0.00147986 | − | 0.00256319i | ||||
\(425\) | 6.67310 | + | 3.85272i | 0.0157014 | + | 0.00906521i | ||||
\(426\) | − | 112.100i | − | 0.263146i | ||||||
\(427\) | −716.445 | + | 168.106i | −1.67786 | + | 0.393690i | ||||
\(428\) | −214.450 | −0.501052 | ||||||||
\(429\) | −292.019 | + | 505.792i | −0.680698 | + | 1.17900i | ||||
\(430\) | −174.435 | + | 100.710i | −0.405663 | + | 0.234210i | ||||
\(431\) | −95.6132 | − | 165.607i | −0.221840 | − | 0.384239i | 0.733527 | − | 0.679661i | \(-0.237873\pi\) |
−0.955367 | + | 0.295422i | \(0.904540\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 339.825i | − | 0.784815i | −0.919791 | − | 0.392408i | \(-0.871642\pi\) | ||
0.919791 | − | 0.392408i | \(-0.128358\pi\) | |||||||
\(434\) | 189.373 | + | 201.627i | 0.436344 | + | 0.464579i | ||||
\(435\) | 63.7735 | 0.146606 | ||||||||
\(436\) | −80.8905 | + | 140.106i | −0.185529 | + | 0.321345i | ||||
\(437\) | 795.692 | − | 459.393i | 1.82081 | − | 1.05124i | ||||
\(438\) | 44.6132 | + | 77.2723i | 0.101857 | + | 0.176421i | ||||
\(439\) | 286.015 | + | 165.131i | 0.651515 | + | 0.376153i | 0.789037 | − | 0.614346i | \(-0.210580\pi\) |
−0.137521 | + | 0.990499i | \(0.543914\pi\) | |||||||
\(440\) | − | 114.285i | − | 0.259739i | ||||||
\(441\) | −122.453 | − | 81.3275i | −0.277672 | − | 0.184416i | ||||
\(442\) | −40.6690 | −0.0920112 | ||||||||
\(443\) | 280.831 | − | 486.414i | 0.633931 | − | 1.09800i | −0.352810 | − | 0.935695i | \(-0.614774\pi\) |
0.986741 | − | 0.162305i | \(-0.0518928\pi\) | |||||||
\(444\) | 155.012 | − | 89.4961i | 0.349125 | − | 0.201568i | ||||
\(445\) | −110.914 | − | 192.108i | −0.249244 | − | 0.431703i | ||||
\(446\) | 332.279 | + | 191.841i | 0.745020 | + | 0.430138i | ||||
\(447\) | 57.4936i | 0.128621i | ||||||||
\(448\) | −40.8189 | + | 38.3381i | −0.0911137 | + | 0.0855762i | ||||
\(449\) | −386.250 | −0.860244 | −0.430122 | − | 0.902771i | \(-0.641529\pi\) | ||||
−0.430122 | + | 0.902771i | \(0.641529\pi\) | |||||||
\(450\) | −10.6066 | + | 18.3712i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | 586.558 | − | 338.650i | 1.30057 | − | 0.750886i | ||||
\(452\) | 79.9061 | + | 138.401i | 0.176783 | + | 0.306198i | ||||
\(453\) | 13.9548 | + | 8.05678i | 0.0308052 | + | 0.0177854i | ||||
\(454\) | 210.165i | 0.462918i | ||||||||
\(455\) | 66.7215 | + | 284.359i | 0.146641 | + | 0.624964i | ||||
\(456\) | 166.785 | 0.365755 | ||||||||
\(457\) | −249.533 | + | 432.203i | −0.546024 | + | 0.945741i | 0.452518 | + | 0.891755i | \(0.350526\pi\) |
−0.998542 | + | 0.0539854i | \(0.982808\pi\) | |||||||
\(458\) | −31.0270 | + | 17.9135i | −0.0677446 | + | 0.0391124i | ||||
\(459\) | −4.00386 | − | 6.93489i | −0.00872300 | − | 0.0151087i | ||||
\(460\) | 104.523 | + | 60.3461i | 0.227223 | + | 0.131187i | ||||
\(461\) | − | 618.290i | − | 1.34119i | −0.741823 | − | 0.670596i | \(-0.766038\pi\) | ||
0.741823 | − | 0.670596i | \(-0.233962\pi\) | |||||||
\(462\) | 89.5273 | − | 296.621i | 0.193782 | − | 0.642037i | ||||
\(463\) | −194.433 | −0.419941 | −0.209971 | − | 0.977708i | \(-0.567337\pi\) | ||||
−0.209971 | + | 0.977708i | \(0.567337\pi\) | |||||||
\(464\) | 32.9325 | − | 57.0407i | 0.0709752 | − | 0.122933i | ||||
\(465\) | 93.7214 | − | 54.1101i | 0.201551 | − | 0.116366i | ||||
\(466\) | 289.126 | + | 500.781i | 0.620442 | + | 1.07464i | ||||
\(467\) | 131.449 | + | 75.8923i | 0.281476 | + | 0.162510i | 0.634091 | − | 0.773258i | \(-0.281374\pi\) |
−0.352615 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(468\) | − | 111.962i | − | 0.239236i | ||||||
\(469\) | −85.1671 | − | 25.7055i | −0.181593 | − | 0.0548091i | ||||
\(470\) | −89.3052 | −0.190011 | ||||||||
\(471\) | −20.7746 | + | 35.9827i | −0.0441074 | + | 0.0763963i | ||||
\(472\) | 181.659 | − | 104.881i | 0.384870 | − | 0.222205i | ||||
\(473\) | −575.484 | − | 996.767i | −1.21667 | − | 2.10733i | ||||
\(474\) | 282.556 | + | 163.134i | 0.596109 | + | 0.344164i | ||||
\(475\) | 170.224i | 0.358366i | ||||||||
\(476\) | 21.0047 | − | 4.92852i | 0.0441276 | − | 0.0103540i | ||||
\(477\) | −1.33104 | −0.00279045 | ||||||||
\(478\) | −47.4010 | + | 82.1010i | −0.0991653 | + | 0.171759i | ||||
\(479\) | 194.656 | − | 112.385i | 0.406381 | − | 0.234624i | −0.282853 | − | 0.959163i | \(-0.591281\pi\) |
0.689233 | + | 0.724539i | \(0.257947\pi\) | |||||||
\(480\) | 10.9545 | + | 18.9737i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | −835.016 | − | 482.097i | −1.73600 | − | 1.00228i | ||||
\(482\) | 334.998i | 0.695016i | ||||||||
\(483\) | 224.009 | + | 238.505i | 0.463788 | + | 0.493799i | ||||
\(484\) | 411.055 | 0.849288 | ||||||||
\(485\) | 168.126 | − | 291.202i | 0.346651 | − | 0.600417i | ||||
\(486\) | 19.0919 | − | 11.0227i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −34.7814 | − | 60.2432i | −0.0714198 | − | 0.123703i | 0.828104 | − | 0.560575i | \(-0.189420\pi\) |
−0.899524 | + | 0.436872i | \(0.856086\pi\) | |||||||
\(488\) | 257.512 | + | 148.675i | 0.527689 | + | 0.304661i | ||||
\(489\) | − | 438.429i | − | 0.896584i | ||||||
\(490\) | −68.9208 | − | 138.780i | −0.140655 | − | 0.283225i | ||||
\(491\) | −750.454 | −1.52842 | −0.764210 | − | 0.644967i | \(-0.776871\pi\) | ||||
−0.764210 | + | 0.644967i | \(0.776871\pi\) | |||||||
\(492\) | −64.9204 | + | 112.445i | −0.131952 | + | 0.228548i | ||||
\(493\) | −21.9762 | + | 12.6880i | −0.0445764 | + | 0.0257362i | ||||
\(494\) | −449.217 | − | 778.067i | −0.909346 | − | 1.57503i | ||||
\(495\) | −104.978 | − | 60.6089i | −0.212076 | − | 0.122442i | ||||
\(496\) | − | 111.769i | − | 0.225341i | ||||||
\(497\) | 233.508 | − | 219.317i | 0.469835 | − | 0.441281i | ||||
\(498\) | −122.294 | −0.245571 | ||||||||
\(499\) | −80.0848 | + | 138.711i | −0.160491 | + | 0.277978i | −0.935045 | − | 0.354530i | \(-0.884641\pi\) |
0.774554 | + | 0.632508i | \(0.217974\pi\) | |||||||
\(500\) | −19.3649 | + | 11.1803i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | 74.2408 | + | 128.589i | 0.148185 | + | 0.256664i | ||||
\(502\) | −592.019 | − | 341.803i | −1.17932 | − | 0.680882i | ||||
\(503\) | 724.412i | 1.44018i | 0.693879 | + | 0.720092i | \(0.255900\pi\) | ||||
−0.693879 | + | 0.720092i | \(0.744100\pi\) | |||||||
\(504\) | 13.5683 | + | 57.8265i | 0.0269213 | + | 0.114735i | ||||
\(505\) | −105.274 | −0.208464 | ||||||||
\(506\) | −344.834 | + | 597.269i | −0.681489 | + | 1.18037i | ||||
\(507\) | −268.816 | + | 155.201i | −0.530209 | + | 0.306117i | ||||
\(508\) | −99.1937 | − | 171.809i | −0.195263 | − | 0.338206i | ||||
\(509\) | −711.944 | − | 411.041i | −1.39871 | − | 0.807547i | −0.404454 | − | 0.914558i | \(-0.632538\pi\) |
−0.994258 | + | 0.107012i | \(0.965872\pi\) | |||||||
\(510\) | − | 8.44088i | − | 0.0165507i | ||||||
\(511\) | −73.6780 | + | 244.109i | −0.144184 | + | 0.477709i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 88.4508 | − | 153.201i | 0.172419 | − | 0.298638i | ||||
\(514\) | 397.531 | − | 229.515i | 0.773407 | − | 0.446527i | ||||
\(515\) | 84.9098 | + | 147.068i | 0.164873 | + | 0.285569i | ||||
\(516\) | 191.084 | + | 110.322i | 0.370318 | + | 0.213803i | ||||
\(517\) | − | 510.313i | − | 0.987066i | ||||||
\(518\) | 489.694 | + | 147.801i | 0.945355 | + | 0.285331i | ||||
\(519\) | −33.7343 | −0.0649987 | ||||||||
\(520\) | 59.0094 | − | 102.207i | 0.113480 | − | 0.196552i | ||||
\(521\) | 392.147 | − | 226.406i | 0.752681 | − | 0.434561i | −0.0739805 | − | 0.997260i | \(-0.523570\pi\) |
0.826662 | + | 0.562699i | \(0.190237\pi\) | |||||||
\(522\) | −34.9302 | − | 60.5008i | −0.0669161 | − | 0.115902i | ||||
\(523\) | 843.597 | + | 487.051i | 1.61300 | + | 0.931264i | 0.988671 | + | 0.150100i | \(0.0479597\pi\) |
0.624326 | + | 0.781164i | \(0.285374\pi\) | |||||||
\(524\) | − | 333.268i | − | 0.636008i | ||||||
\(525\) | −59.0189 | + | 13.8481i | −0.112417 | + | 0.0263774i | ||||
\(526\) | 434.690 | 0.826406 | ||||||||
\(527\) | −21.5308 | + | 37.2924i | −0.0408553 | + | 0.0707635i | ||||
\(528\) | −108.420 | + | 62.5966i | −0.205342 | + | 0.118554i | ||||
\(529\) | −99.6657 | − | 172.626i | −0.188404 | − | 0.326325i | ||||
\(530\) | −1.21507 | − | 0.701522i | −0.00229259 | − | 0.00132363i | ||||
\(531\) | − | 222.485i | − | 0.418993i | ||||||
\(532\) | 326.303 | + | 347.418i | 0.613352 | + | 0.653041i | ||||
\(533\) | 699.426 | 1.31224 | ||||||||
\(534\) | −121.500 | + | 210.444i | −0.227528 | + | 0.394089i | ||||
\(535\) | −207.640 | + | 119.881i | −0.388113 | + | 0.224077i | ||||
\(536\) | 17.9730 | + | 31.1302i | 0.0335317 | + | 0.0580786i | ||||
\(537\) | −379.251 | − | 218.961i | −0.706241 | − | 0.407748i | ||||
\(538\) | − | 107.266i | − | 0.199379i | ||||||
\(539\) | 793.026 | − | 393.831i | 1.47129 | − | 0.730670i | ||||
\(540\) | 23.2379 | 0.0430331 | ||||||||
\(541\) | −138.078 | + | 239.158i | −0.255228 | + | 0.442067i | −0.964957 | − | 0.262407i | \(-0.915484\pi\) |
0.709730 | + | 0.704474i | \(0.248817\pi\) | |||||||
\(542\) | 26.6085 | − | 15.3624i | 0.0490932 | − | 0.0283440i | ||||
\(543\) | 124.902 | + | 216.337i | 0.230022 | + | 0.398410i | ||||
\(544\) | −7.54975 | − | 4.35885i | −0.0138782 | − | 0.00801259i | ||||
\(545\) | 180.877i | 0.331884i | ||||||||
\(546\) | 233.221 | − | 219.047i | 0.427146 | − | 0.401186i | ||||
\(547\) | 426.436 | 0.779591 | 0.389795 | − | 0.920901i | \(-0.372546\pi\) | ||||
0.389795 | + | 0.920901i | \(0.372546\pi\) | |||||||
\(548\) | 151.517 | − | 262.436i | 0.276492 | − | 0.478897i | ||||
\(549\) | 273.133 | − | 157.693i | 0.497510 | − | 0.287237i | ||||
\(550\) | −63.8874 | − | 110.656i | −0.116159 | − | 0.201193i | ||||
\(551\) | −485.484 | − | 280.295i | −0.881097 | − | 0.508702i | ||||
\(552\) | − | 132.212i | − | 0.239514i | ||||||
\(553\) | 212.989 | + | 907.733i | 0.385152 | + | 1.64147i | ||||
\(554\) | −158.013 | −0.285222 | ||||||||
\(555\) | 100.060 | − | 173.308i | 0.180288 | − | 0.312267i | ||||
\(556\) | −262.953 | + | 151.816i | −0.472938 | + | 0.273051i | ||||
\(557\) | 60.9782 | + | 105.617i | 0.109476 | + | 0.189618i | 0.915558 | − | 0.402186i | \(-0.131749\pi\) |
−0.806082 | + | 0.591804i | \(0.798416\pi\) | |||||||
\(558\) | −102.667 | − | 59.2746i | −0.183990 | − | 0.106227i | ||||
\(559\) | − | 1188.57i | − | 2.12624i | ||||||
\(560\) | −18.0911 | + | 59.9392i | −0.0323055 | + | 0.107034i | ||||
\(561\) | 48.2334 | 0.0859775 | ||||||||
\(562\) | 133.147 | − | 230.618i | 0.236917 | − | 0.410351i | ||||
\(563\) | −376.532 | + | 217.391i | −0.668796 | + | 0.386130i | −0.795620 | − | 0.605796i | \(-0.792855\pi\) |
0.126824 | + | 0.991925i | \(0.459522\pi\) | |||||||
\(564\) | 48.9145 | + | 84.7224i | 0.0867278 | + | 0.150217i | ||||
\(565\) | 154.737 | + | 89.3377i | 0.273872 | + | 0.158120i | ||||
\(566\) | 306.625i | 0.541741i | ||||||||
\(567\) | 60.3127 | + | 18.2038i | 0.106372 | + | 0.0321055i | ||||
\(568\) | −129.442 | −0.227891 | ||||||||
\(569\) | 148.138 | − | 256.583i | 0.260349 | − | 0.450937i | −0.705986 | − | 0.708226i | \(-0.749496\pi\) |
0.966335 | + | 0.257289i | \(0.0828291\pi\) | |||||||
\(570\) | 161.488 | − | 93.2354i | 0.283313 | − | 0.163571i | ||||
\(571\) | −29.9578 | − | 51.8885i | −0.0524655 | − | 0.0908730i | 0.838600 | − | 0.544748i | \(-0.183375\pi\) |
−0.891065 | + | 0.453875i | \(0.850041\pi\) | |||||||
\(572\) | 584.039 | + | 337.195i | 1.02105 | + | 0.589502i | ||||
\(573\) | − | 544.034i | − | 0.949448i | ||||||
\(574\) | −361.240 | + | 84.7609i | −0.629338 | + | 0.147667i | ||||
\(575\) | 134.938 | 0.234675 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 288.128 | − | 166.351i | 0.499355 | − | 0.288303i | −0.229092 | − | 0.973405i | \(-0.573576\pi\) |
0.728447 | + | 0.685102i | \(0.240242\pi\) | |||||||
\(578\) | −202.675 | − | 351.043i | −0.350648 | − | 0.607340i | ||||
\(579\) | −79.2426 | − | 45.7507i | −0.136861 | − | 0.0790168i | ||||
\(580\) | − | 73.6393i | − | 0.126964i | ||||||
\(581\) | −239.261 | − | 254.743i | −0.411809 | − | 0.438456i | ||||
\(582\) | −368.345 | −0.632895 | ||||||||
\(583\) | 4.00868 | − | 6.94323i | 0.00687595 | − | 0.0119095i | ||||
\(584\) | 89.2264 | − | 51.5149i | 0.152785 | − | 0.0882104i | ||||
\(585\) | −62.5889 | − | 108.407i | −0.106990 | − | 0.185311i | ||||
\(586\) | −70.2729 | − | 40.5721i | −0.119920 | − | 0.0692356i | ||||
\(587\) | − | 656.221i | − | 1.11792i | −0.829194 | − | 0.558961i | \(-0.811200\pi\) | ||
0.829194 | − | 0.558961i | \(-0.188800\pi\) | |||||||
\(588\) | −93.9089 | + | 141.397i | −0.159709 | + | 0.240471i | ||||
\(589\) | −951.289 | −1.61509 | ||||||||
\(590\) | 117.260 | − | 203.100i | 0.198746 | − | 0.344238i | ||||
\(591\) | 81.3007 | − | 46.9390i | 0.137565 | − | 0.0794230i | ||||
\(592\) | −103.341 | − | 178.992i | −0.174563 | − | 0.302352i | ||||
\(593\) | −353.808 | − | 204.271i | −0.596640 | − | 0.344471i | 0.171078 | − | 0.985257i | \(-0.445275\pi\) |
−0.767719 | + | 0.640787i | \(0.778608\pi\) | |||||||
\(594\) | 132.787i | 0.223548i | ||||||||
\(595\) | 17.5826 | − | 16.5140i | 0.0295506 | − | 0.0277547i | ||||
\(596\) | 66.3879 | 0.111389 | ||||||||
\(597\) | 19.8934 | − | 34.4564i | 0.0333223 | − | 0.0577160i | ||||
\(598\) | −616.781 | + | 356.099i | −1.03141 | + | 0.595483i | ||||
\(599\) | 588.643 | + | 1019.56i | 0.982709 | + | 1.70210i | 0.651705 | + | 0.758472i | \(0.274054\pi\) |
0.331003 | + | 0.943630i | \(0.392613\pi\) | |||||||
\(600\) | 21.2132 | + | 12.2474i | 0.0353553 | + | 0.0204124i | ||||
\(601\) | 162.592i | 0.270536i | 0.990809 | + | 0.135268i | \(0.0431896\pi\) | ||||
−0.990809 | + | 0.135268i | \(0.956810\pi\) | |||||||
\(602\) | 144.038 | + | 613.873i | 0.239266 | + | 1.01972i | ||||
\(603\) | 38.1265 | 0.0632280 | ||||||||
\(604\) | 9.30317 | − | 16.1136i | 0.0154026 | − | 0.0266781i | ||||
\(605\) | 398.003 | − | 229.787i | 0.657855 | − | 0.379813i | ||||
\(606\) | 57.6611 | + | 99.8720i | 0.0951504 | + | 0.164805i | ||||
\(607\) | −318.116 | − | 183.664i | −0.524079 | − | 0.302577i | 0.214523 | − | 0.976719i | \(-0.431180\pi\) |
−0.738602 | + | 0.674142i | \(0.764514\pi\) | |||||||
\(608\) | − | 192.586i | − | 0.316754i | ||||||
\(609\) | 57.6866 | − | 191.127i | 0.0947235 | − | 0.313837i | ||||
\(610\) | 332.447 | 0.544995 | ||||||||
\(611\) | 263.492 | − | 456.382i | 0.431248 | − | 0.746943i | ||||
\(612\) | −8.00772 | + | 4.62326i | −0.0130845 | + | 0.00755434i | ||||
\(613\) | −182.636 | − | 316.335i | −0.297938 | − | 0.516044i | 0.677726 | − | 0.735315i | \(-0.262966\pi\) |
−0.975664 | + | 0.219270i | \(0.929632\pi\) | |||||||
\(614\) | −356.735 | − | 205.961i | −0.581002 | − | 0.335442i | ||||
\(615\) | 145.166i | 0.236043i | ||||||||
\(616\) | −342.508 | − | 103.377i | −0.556020 | − | 0.167820i | ||||
\(617\) | −64.2245 | −0.104092 | −0.0520458 | − | 0.998645i | \(-0.516574\pi\) | ||||
−0.0520458 | + | 0.998645i | \(0.516574\pi\) | |||||||
\(618\) | 93.0140 | − | 161.105i | 0.150508 | − | 0.260688i | ||||
\(619\) | −990.646 | + | 571.949i | −1.60040 | + | 0.923989i | −0.608989 | + | 0.793178i | \(0.708425\pi\) |
−0.991407 | + | 0.130811i | \(0.958242\pi\) | |||||||
\(620\) | −62.4809 | − | 108.220i | −0.100776 | − | 0.174549i | ||||
\(621\) | −121.444 | − | 70.1159i | −0.195562 | − | 0.112908i | ||||
\(622\) | 353.328i | 0.568051i | ||||||||
\(623\) | −676.067 | + | 158.632i | −1.08518 | + | 0.254625i | ||||
\(624\) | −129.283 | −0.207184 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 4.63624 | − | 2.67674i | 0.00740614 | − | 0.00427594i | ||||
\(627\) | 532.771 | + | 922.787i | 0.849715 | + | 1.47175i | ||||
\(628\) | 41.5492 | + | 23.9884i | 0.0661611 | + | 0.0381982i | ||||
\(629\) | 79.6288i | 0.126596i | ||||||||
\(630\) | 45.4635 | + | 48.4053i | 0.0721642 | + | 0.0768338i | ||||
\(631\) | 257.367 | 0.407872 | 0.203936 | − | 0.978984i | \(-0.434627\pi\) | ||||
0.203936 | + | 0.978984i | \(0.434627\pi\) | |||||||
\(632\) | 188.370 | − | 326.267i | 0.298055 | − | 0.516246i | ||||
\(633\) | −438.305 | + | 253.055i | −0.692425 | + | 0.399771i | ||||
\(634\) | 50.4598 | + | 87.3990i | 0.0795897 | + | 0.137853i | ||||
\(635\) | −192.088 | − | 110.902i | −0.302501 | − | 0.174649i | ||||
\(636\) | 1.53696i | 0.00241660i | ||||||||
\(637\) | 912.565 | + | 57.2562i | 1.43260 | + | 0.0898841i | ||||
\(638\) | 420.794 | 0.659552 | ||||||||
\(639\) | −68.6470 | + | 118.900i | −0.107429 | + | 0.186072i | ||||
\(640\) | 21.9089 | − | 12.6491i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | −99.4860 | − | 172.315i | −0.155204 | − | 0.268822i | 0.777929 | − | 0.628352i | \(-0.216270\pi\) |
−0.933133 | + | 0.359530i | \(0.882937\pi\) | |||||||
\(642\) | 227.459 | + | 131.323i | 0.354297 | + | 0.204554i | ||||
\(643\) | − | 708.223i | − | 1.10144i | −0.834692 | − | 0.550718i | \(-0.814354\pi\) | ||
0.834692 | − | 0.550718i | \(-0.185646\pi\) | |||||||
\(644\) | 275.401 | − | 258.664i | 0.427642 | − | 0.401652i | ||||
\(645\) | 246.688 | 0.382463 | ||||||||
\(646\) | −37.0990 | + | 64.2573i | −0.0574288 | + | 0.0994695i | ||||
\(647\) | −140.794 | + | 81.2876i | −0.217611 | + | 0.125638i | −0.604844 | − | 0.796344i | \(-0.706764\pi\) |
0.387233 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(648\) | −12.7279 | − | 22.0454i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 1160.57 | + | 670.054i | 1.78824 | + | 1.03244i | ||||
\(650\) | − | 131.949i | − | 0.202998i | ||||||
\(651\) | −77.3897 | − | 329.825i | −0.118878 | − | 0.506644i | ||||
\(652\) | −506.255 | −0.776464 | ||||||||
\(653\) | −497.880 | + | 862.354i | −0.762450 | + | 1.32060i | 0.179134 | + | 0.983825i | \(0.442671\pi\) |
−0.941584 | + | 0.336778i | \(0.890663\pi\) | |||||||
\(654\) | 171.595 | − | 99.0702i | 0.262377 | − | 0.151483i | ||||
\(655\) | −186.303 | − | 322.686i | −0.284431 | − | 0.492650i | ||||
\(656\) | 129.841 | + | 74.9636i | 0.197928 | + | 0.114274i | ||||
\(657\) | − | 109.280i | − | 0.166331i | ||||||
\(658\) | −80.7815 | + | 267.644i | −0.122768 | + | 0.406754i | ||||
\(659\) | 897.542 | 1.36198 | 0.680988 | − | 0.732295i | \(-0.261551\pi\) | ||||
0.680988 | + | 0.732295i | \(0.261551\pi\) | |||||||
\(660\) | −69.9851 | + | 121.218i | −0.106038 | + | 0.183663i | ||||
\(661\) | −74.7048 | + | 43.1308i | −0.113018 | + | 0.0652508i | −0.555443 | − | 0.831554i | \(-0.687451\pi\) |
0.442426 | + | 0.896805i | \(0.354118\pi\) | |||||||
\(662\) | 241.807 | + | 418.822i | 0.365267 | + | 0.632661i | ||||
\(663\) | 43.1359 | + | 24.9045i | 0.0650617 | + | 0.0375634i | ||||
\(664\) | 141.213i | 0.212671i | ||||||||
\(665\) | 510.154 | + | 153.977i | 0.767149 | + | 0.231544i | ||||
\(666\) | −219.220 | −0.329159 | ||||||||
\(667\) | −222.192 | + | 384.848i | −0.333122 | + | 0.576984i | ||||
\(668\) | 148.482 | − | 85.7259i | 0.222278 | − | 0.128332i | ||||
\(669\) | −234.957 | − | 406.957i | −0.351206 | − | 0.608306i | ||||
\(670\) | 34.8046 | + | 20.0944i | 0.0519471 | + | 0.0299917i | ||||
\(671\) | 1899.69i | 2.83113i | ||||||||
\(672\) | 66.7723 | − | 15.6674i | 0.0993635 | − | 0.0233145i | ||||
\(673\) | 486.598 | 0.723028 | 0.361514 | − | 0.932367i | \(-0.382260\pi\) | ||||
0.361514 | + | 0.932367i | \(0.382260\pi\) | |||||||
\(674\) | −174.228 | + | 301.772i | −0.258499 | + | 0.447733i | ||||
\(675\) | 22.5000 | − | 12.9904i | 0.0333333 | − | 0.0192450i | ||||
\(676\) | 179.211 | + | 310.402i | 0.265105 | + | 0.459175i | ||||
\(677\) | 47.5668 | + | 27.4627i | 0.0702612 | + | 0.0405653i | 0.534719 | − | 0.845030i | \(-0.320417\pi\) |
−0.464458 | + | 0.885595i | \(0.653751\pi\) | |||||||
\(678\) | − | 195.729i | − | 0.288686i | ||||||
\(679\) | −720.643 | − | 767.274i | −1.06133 | − | 1.13001i | ||||
\(680\) | −9.74668 | −0.0143334 | ||||||||
\(681\) | 128.699 | − | 222.913i | 0.188985 | − | 0.327332i | ||||
\(682\) | 618.398 | − | 357.032i | 0.906742 | − | 0.523508i | ||||
\(683\) | 477.185 | + | 826.509i | 0.698661 | + | 1.21012i | 0.968931 | + | 0.247331i | \(0.0795535\pi\) |
−0.270270 | + | 0.962784i | \(0.587113\pi\) | |||||||
\(684\) | −176.902 | − | 102.134i | −0.258628 | − | 0.149319i | ||||
\(685\) | − | 338.803i | − | 0.494603i | ||||||
\(686\) | −478.261 | + | 81.0188i | −0.697174 | + | 0.118103i | ||||
\(687\) | 43.8788 | 0.0638702 | ||||||||
\(688\) | 127.389 | − | 220.645i | 0.185159 | − | 0.320705i | ||||
\(689\) | 7.17006 | − | 4.13964i | 0.0104065 | − | 0.00600818i | ||||
\(690\) | −73.9086 | − | 128.013i | −0.107114 | − | 0.185527i | ||||
\(691\) | −22.3860 | − | 12.9246i | −0.0323966 | − | 0.0187042i | 0.483714 | − | 0.875226i | \(-0.339287\pi\) |
−0.516111 | + | 0.856522i | \(0.672621\pi\) | |||||||
\(692\) | 38.9530i | 0.0562905i | ||||||||
\(693\) | −276.601 | + | 259.790i | −0.399135 | + | 0.374877i | ||||
\(694\) | 195.659 | 0.281929 | ||||||||
\(695\) | −169.736 | + | 293.991i | −0.244224 | + | 0.423008i | ||||
\(696\) | −69.8604 | + | 40.3339i | −0.100374 | + | 0.0579510i | ||||
\(697\) | −28.8814 | − | 50.0240i | −0.0414367 | − | 0.0717704i | ||||
\(698\) | −141.896 | − | 81.9239i | −0.203290 | − | 0.117370i | ||||
\(699\) | − | 708.211i | − | 1.01318i | ||||||
\(700\) | 15.9904 | + | 68.1491i | 0.0228435 | + | 0.0973559i | ||||
\(701\) | −942.060 | −1.34388 | −0.671940 | − | 0.740606i | \(-0.734539\pi\) | ||||
−0.671940 | + | 0.740606i | \(0.734539\pi\) | |||||||
\(702\) | −68.5627 | + | 118.754i | −0.0976677 | + | 0.169165i | ||||
\(703\) | −1523.44 | + | 879.556i | −2.16705 | + | 1.25115i | ||||
\(704\) | 72.2803 | + | 125.193i | 0.102671 | + | 0.177831i | ||||
\(705\) | 94.7225 | + | 54.6881i | 0.134358 | + | 0.0775717i | ||||
\(706\) | 264.767i | 0.375024i | ||||||||
\(707\) | −95.2264 | + | 315.503i | −0.134691 | + | 0.446256i | ||||
\(708\) | −256.904 | −0.362859 | ||||||||
\(709\) | 168.282 | − | 291.473i | 0.237351 | − | 0.411105i | −0.722602 | − | 0.691264i | \(-0.757054\pi\) |
0.959953 | + | 0.280160i | \(0.0903874\pi\) | |||||||
\(710\) | −125.332 | + | 72.3603i | −0.176524 | + | 0.101916i | ||||
\(711\) | −199.797 | − | 346.059i | −0.281008 | − | 0.486721i | ||||
\(712\) | 242.999 | + | 140.296i | 0.341291 | + | 0.197045i | ||||
\(713\) | 754.097i | 1.05764i | ||||||||
\(714\) | −25.2970 | − | 7.63524i | −0.0354300 | − | 0.0106936i | ||||
\(715\) | 753.991 | 1.05453 | ||||||||
\(716\) | −252.834 | + | 437.922i | −0.353120 | + | 0.611622i | ||||
\(717\) | 100.553 | − | 58.0542i | 0.140241 | − | 0.0809681i | ||||
\(718\) | −450.777 | − | 780.769i | −0.627823 | − | 1.08742i | ||||
\(719\) | −111.447 | − | 64.3438i | −0.155002 | − | 0.0894907i | 0.420493 | − | 0.907296i | \(-0.361857\pi\) |
−0.575495 | + | 0.817805i | \(0.695191\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | 517.563 | − | 121.440i | 0.717840 | − | 0.168433i | ||||
\(722\) | −1128.61 | −1.56317 | ||||||||
\(723\) | 205.143 | − | 355.319i | 0.283739 | − | 0.491451i | ||||
\(724\) | 249.804 | − | 144.224i | 0.345033 | − | 0.199205i | ||||
\(725\) | −41.1656 | − | 71.3009i | −0.0567802 | − | 0.0983461i | ||||
\(726\) | −435.990 | − | 251.719i | −0.600537 | − | 0.346720i | ||||
\(727\) | 684.683i | 0.941792i | 0.882189 | + | 0.470896i | \(0.156069\pi\) | ||||
−0.882189 | + | 0.470896i | \(0.843931\pi\) | |||||||
\(728\) | −252.934 | − | 269.301i | −0.347437 | − | 0.369919i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 57.5954 | − | 99.7582i | 0.0788978 | − | 0.136655i | ||||
\(731\) | −85.0082 | + | 49.0795i | −0.116290 | + | 0.0671402i | ||||
\(732\) | −182.089 | − | 315.387i | −0.248755 | − | 0.430856i | ||||
\(733\) | 512.533 | + | 295.911i | 0.699227 | + | 0.403699i | 0.807059 | − | 0.590470i | \(-0.201058\pi\) |
−0.107832 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(734\) | 77.8530i | 0.106067i | ||||||||
\(735\) | −11.8836 | + | 189.404i | −0.0161681 | + | 0.257692i | ||||
\(736\) | −152.665 | −0.207425 | ||||||||
\(737\) | −114.825 | + | 198.882i | −0.155800 | + | 0.269854i | ||||
\(738\) | 137.717 | − | 79.5110i | 0.186608 | − | 0.107738i | ||||
\(739\) | −252.105 | − | 436.659i | −0.341144 | − | 0.590878i | 0.643502 | − | 0.765445i | \(-0.277481\pi\) |
−0.984645 | + | 0.174567i | \(0.944148\pi\) | |||||||
\(740\) | −200.119 | − | 115.539i | −0.270431 | − | 0.156134i | ||||
\(741\) | 1100.35i | 1.48496i | ||||||||
\(742\) | −3.20153 | + | 3.00696i | −0.00431473 | + | 0.00405250i | ||||
\(743\) | 983.540 | 1.32374 | 0.661871 | − | 0.749618i | \(-0.269763\pi\) | ||||
0.661871 | + | 0.749618i | \(0.269763\pi\) | |||||||
\(744\) | −68.4444 | + | 118.549i | −0.0919952 | + | 0.159340i | ||||
\(745\) | 64.2798 | − | 37.1120i | 0.0862816 | − | 0.0498147i | ||||
\(746\) | −190.323 | − | 329.649i | −0.255124 | − | 0.441888i | ||||
\(747\) | 129.713 | + | 74.8897i | 0.173645 | + | 0.100254i | ||||
\(748\) | − | 55.6951i | − | 0.0744587i | ||||||
\(749\) | 171.457 | + | 730.730i | 0.228915 | + | 0.975607i | ||||
\(750\) | 27.3861 | 0.0365148 | ||||||||
\(751\) | −458.462 | + | 794.080i | −0.610469 | + | 1.05736i | 0.380692 | + | 0.924702i | \(0.375686\pi\) |
−0.991161 | + | 0.132662i | \(0.957648\pi\) | |||||||
\(752\) | 97.8290 | − | 56.4816i | 0.130092 | − | 0.0751085i | ||||
\(753\) | 418.621 | + | 725.073i | 0.555938 | + | 0.962912i | ||||
\(754\) | 376.323 | + | 217.270i | 0.499103 | + | 0.288157i | ||||
\(755\) | − | 20.8025i | − | 0.0275530i | ||||||
\(756\) | 21.0200 | − | 69.6431i | 0.0278042 | − | 0.0921205i | ||||
\(757\) | 82.2419 | 0.108642 | 0.0543209 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543209 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(758\) | −332.188 | + | 575.367i | −0.438243 | + | 0.759059i | ||||
\(759\) | 731.502 | − | 422.333i | 0.963771 | − | 0.556434i | ||||
\(760\) | −107.659 | − | 186.471i | −0.141656 | − | 0.245356i | ||||
\(761\) | 303.297 | + | 175.108i | 0.398550 | + | 0.230103i | 0.685858 | − | 0.727735i | \(-0.259427\pi\) |
−0.287308 | + | 0.957838i | \(0.592760\pi\) | |||||||
\(762\) | 242.974i | 0.318864i | ||||||||
\(763\) | 542.080 | + | 163.613i | 0.710459 | + | 0.214434i | ||||
\(764\) | −628.196 | −0.822246 | ||||||||
\(765\) | −5.16896 | + | 8.95290i | −0.00675681 | + | 0.0117031i | ||||
\(766\) | 492.604 | − | 284.405i | 0.643087 | − | 0.371286i | ||||
\(767\) | 691.944 | + | 1198.48i | 0.902144 | + | 1.56256i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 319.560i | 0.415553i | 0.978176 | + | 0.207777i | \(0.0666227\pi\) | ||||
−0.978176 | + | 0.207777i | \(0.933377\pi\) | |||||||
\(770\) | −389.422 | + | 91.3734i | −0.505743 | + | 0.118667i | ||||
\(771\) | −562.194 | −0.729175 | ||||||||
\(772\) | −52.8284 | + | 91.5015i | −0.0684306 | + | 0.118525i | ||||
\(773\) | −866.904 | + | 500.507i | −1.12148 | + | 0.647487i | −0.941778 | − | 0.336235i | \(-0.890847\pi\) |
−0.179702 | + | 0.983721i | \(0.557513\pi\) | |||||||
\(774\) | −135.117 | − | 234.029i | −0.174570 | − | 0.302363i | ||||
\(775\) | −120.994 | − | 69.8558i | −0.156121 | − | 0.0901365i | ||||
\(776\) | 425.328i | 0.548103i | ||||||||
\(777\) | −428.889 | − | 456.642i | −0.551981 | − | 0.587699i | ||||
\(778\) | −156.639 | −0.201336 | ||||||||
\(779\) | 638.030 | − | 1105.10i | 0.819037 | − | 1.41861i | ||||
\(780\) | −125.178 | + | 72.2714i | −0.160484 | + | 0.0926557i | ||||
\(781\) | −413.485 | − | 716.178i | −0.529431 | − | 0.917001i | ||||
\(782\) | 50.9374 | + | 29.4087i | 0.0651374 | + | 0.0376071i | ||||
\(783\) | 85.5611i | 0.109273i | ||||||||
\(784\) | 163.271 | + | 108.437i | 0.208254 | + | 0.138312i | ||||
\(785\) | 53.6398 | 0.0683309 | ||||||||
\(786\) | −204.084 | + | 353.484i | −0.259649 | + | 0.449726i | ||||
\(787\) | 112.324 | − | 64.8506i | 0.142725 | − | 0.0824022i | −0.426937 | − | 0.904281i | \(-0.640407\pi\) |
0.569662 | + | 0.821879i | \(0.307074\pi\) | |||||||
\(788\) | −54.2005 | − | 93.8780i | −0.0687823 | − | 0.119134i | ||||
\(789\) | −461.058 | − | 266.192i | −0.584358 | − | 0.337379i | ||||
\(790\) | − | 421.209i | − | 0.533176i | ||||||
\(791\) | 407.710 | − | 382.931i | 0.515437 | − | 0.484111i | ||||
\(792\) | 153.330 | 0.193598 | ||||||||
\(793\) | −980.874 | + | 1698.92i | −1.23692 | + | 2.14240i | ||||
\(794\) | −514.165 | + | 296.853i | −0.647563 | + | 0.373870i | ||||
\(795\) | 0.859185 | + | 1.48815i | 0.00108074 | + | 0.00187189i | ||||
\(796\) | −39.7869 | − | 22.9710i | −0.0499835 | − | 0.0288580i | ||||
\(797\) | − | 420.926i | − | 0.528138i | −0.964504 | − | 0.264069i | \(-0.914935\pi\) | ||
0.964504 | − | 0.264069i | \(-0.0850647\pi\) | |||||||
\(798\) | −133.348 | − | 568.311i | −0.167102 | − | 0.712169i | ||||
\(799\) | −43.5215 | −0.0544700 | ||||||||
\(800\) | 14.1421 | − | 24.4949i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 257.740 | − | 148.806i | 0.321773 | − | 0.185775i | ||||
\(802\) | −222.079 | − | 384.652i | −0.276907 | − | 0.479616i | ||||
\(803\) | 570.044 | + | 329.115i | 0.709893 | + | 0.409857i | ||||
\(804\) | − | 44.0247i | − | 0.0547571i | ||||||
\(805\) | 122.059 | − | 404.404i | 0.151626 | − | 0.502366i | ||||
\(806\) | 737.392 | 0.914879 | ||||||||
\(807\) | −65.6866 | + | 113.773i | −0.0813961 | + | 0.140982i | ||||
\(808\) | 115.322 | − | 66.5813i | 0.142726 | − | 0.0824026i | ||||
\(809\) | 582.166 | + | 1008.34i | 0.719612 | + | 1.24640i | 0.961154 | + | 0.276014i | \(0.0890135\pi\) |
−0.241542 | + | 0.970390i | \(0.577653\pi\) | |||||||
\(810\) | −24.6475 | − | 14.2302i | −0.0304290 | − | 0.0175682i | ||||
\(811\) | − | 753.691i | − | 0.929335i | −0.885485 | − | 0.464668i | \(-0.846174\pi\) | ||
0.885485 | − | 0.464668i | \(-0.153826\pi\) | |||||||
\(812\) | −220.694 | − | 66.6108i | −0.271791 | − | 0.0820330i | ||||
\(813\) | −37.6301 | −0.0462855 | ||||||||
\(814\) | 660.219 | − | 1143.53i | 0.811080 | − | 1.40483i | ||||
\(815\) | −490.179 | + | 283.005i | −0.601447 | + | 0.347245i | ||||
\(816\) | 5.33848 | + | 9.24652i | 0.00654225 | + | 0.0113315i | ||||
\(817\) | −1877.95 | − | 1084.23i | −2.29859 | − | 1.32709i | ||||
\(818\) | 172.291i | 0.210625i | ||||||||
\(819\) | −381.507 | + | 89.5163i | −0.465821 | + | 0.109300i | ||||
\(820\) | 167.624 | 0.204419 | ||||||||
\(821\) | 184.398 | − | 319.387i | 0.224602 | − | 0.389022i | −0.731598 | − | 0.681736i | \(-0.761225\pi\) |
0.956200 | + | 0.292714i | \(0.0945584\pi\) | |||||||
\(822\) | −321.417 | + | 185.570i | −0.391018 | + | 0.225754i | ||||
\(823\) | 258.123 | + | 447.082i | 0.313636 | + | 0.543234i | 0.979147 | − | 0.203155i | \(-0.0651194\pi\) |
−0.665510 | + | 0.746389i | \(0.731786\pi\) | |||||||
\(824\) | −186.028 | − | 107.403i | −0.225762 | − | 0.130344i | ||||
\(825\) | 156.491i | 0.189687i | ||||||||
\(826\) | −502.616 | − | 535.139i | −0.608494 | − | 0.647869i | ||||
\(827\) | −534.206 | −0.645957 | −0.322978 | − | 0.946406i | \(-0.604684\pi\) | ||||
−0.322978 | + | 0.946406i | \(0.604684\pi\) | |||||||
\(828\) | −80.9628 | + | 140.232i | −0.0977812 | + | 0.169362i | ||||
\(829\) | 692.720 | − | 399.942i | 0.835610 | − | 0.482439i | −0.0201599 | − | 0.999797i | \(-0.506418\pi\) |
0.855769 | + | 0.517357i | \(0.173084\pi\) | |||||||
\(830\) | 78.9407 | + | 136.729i | 0.0951092 | + | 0.164734i | ||||
\(831\) | 167.598 | + | 96.7627i | 0.201682 | + | 0.116441i | ||||
\(832\) | 149.283i | 0.179427i | ||||||||
\(833\) | −33.5875 | − | 67.6323i | −0.0403211 | − | 0.0811912i | ||||
\(834\) | 371.872 | 0.445890 | ||||||||
\(835\) | 95.8445 | − | 166.008i | 0.114784 | − | 0.198811i | ||||
\(836\) | 1065.54 | − | 615.191i | 1.27457 | − | 0.735874i | ||||
\(837\) | 72.5963 | + | 125.740i | 0.0867339 | + | 0.150228i | ||||
\(838\) | −52.7708 | − | 30.4673i | −0.0629724 | − | 0.0363571i | ||||
\(839\) | − | 1250.09i | − | 1.48998i | −0.667078 | − | 0.744988i | \(-0.732455\pi\) | ||
0.667078 | − | 0.744988i | \(-0.267545\pi\) | |||||||
\(840\) | 55.8936 | − | 52.4967i | 0.0665401 | − | 0.0624960i | ||||
\(841\) | −569.863 | −0.677601 | ||||||||
\(842\) | −95.8634 | + | 166.040i | −0.113852 | + | 0.197198i | ||||
\(843\) | −282.448 | + | 163.071i | −0.335051 | + | 0.193442i | ||||
\(844\) | 292.203 | + | 506.111i | 0.346212 | + | 0.599657i | ||||
\(845\) | 347.040 | + | 200.364i | 0.410698 | + | 0.237117i | ||||
\(846\) | − | 119.816i | − | 0.141626i | ||||||
\(847\) | −328.647 | − | 1400.65i | −0.388013 | − | 1.65366i | ||||
\(848\) | 1.77473 | 0.00209284 | ||||||||
\(849\) | 187.769 | − | 325.225i | 0.221165 | − | 0.383069i | ||||
\(850\) | −9.43719 | + | 5.44856i | −0.0111026 | + | 0.00641007i | ||||
\(851\) | 697.233 | + | 1207.64i | 0.819310 | + | 1.41909i | ||||
\(852\) | 137.294 | + | 79.2667i | 0.161143 | + | 0.0930361i | ||||
\(853\) | − | 427.261i | − | 0.500893i | −0.968130 | − | 0.250446i | \(-0.919423\pi\) | ||
0.968130 | − | 0.250446i | \(-0.0805774\pi\) | |||||||
\(854\) | 300.716 | − | 996.330i | 0.352127 | − | 1.16666i | ||||
\(855\) | −228.379 | −0.267110 | ||||||||
\(856\) | 151.639 | − | 262.647i | 0.177149 | − | 0.306830i | ||||
\(857\) | 364.774 | − | 210.603i | 0.425641 | − | 0.245744i | −0.271847 | − | 0.962341i | \(-0.587634\pi\) |
0.697488 | + | 0.716597i | \(0.254301\pi\) | |||||||
\(858\) | −412.978 | − | 715.298i | −0.481326 | − | 0.833681i | ||||
\(859\) | 666.524 | + | 384.818i | 0.775930 | + | 0.447983i | 0.834986 | − | 0.550271i | \(-0.185476\pi\) |
−0.0590558 | + | 0.998255i | \(0.518809\pi\) | |||||||
\(860\) | − | 284.851i | − | 0.331222i | ||||||
\(861\) | 435.058 | + | 131.311i | 0.505294 | + | 0.152510i | ||||
\(862\) | 270.435 | 0.313730 | ||||||||
\(863\) | 759.204 | − | 1314.98i | 0.879726 | − | 1.52373i | 0.0280846 | − | 0.999606i | \(-0.491059\pi\) |
0.851641 | − | 0.524125i | \(-0.175607\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 21.7754 | + | 37.7161i | 0.0251739 | + | 0.0436024i | ||||
\(866\) | 416.199 | + | 240.293i | 0.480599 | + | 0.277474i | ||||
\(867\) | 496.449i | 0.572606i | ||||||||
\(868\) | −380.849 | + | 89.3619i | −0.438766 | + | 0.102952i | ||||
\(869\) | 2406.90 | 2.76973 | ||||||||
\(870\) | −45.0947 | + | 78.1063i | −0.0518330 | + | 0.0897773i | ||||
\(871\) | −205.380 | + | 118.576i | −0.235798 | + | 0.136138i | ||||
\(872\) | −114.396 | − | 198.140i | −0.131189 | − | 0.227225i | ||||
\(873\) | 390.689 | + | 225.564i | 0.447524 | + | 0.258378i | ||||
\(874\) | 1299.36i | 1.48668i | ||||||||
\(875\) | 53.5792 | + | 57.0462i | 0.0612334 | + | 0.0651957i | ||||
\(876\) | −126.185 | −0.144047 | ||||||||
\(877\) | 802.916 | − | 1390.69i | 0.915525 | − | 1.58574i | 0.109395 | − | 0.993998i | \(-0.465109\pi\) |
0.806131 | − | 0.591738i | \(-0.201558\pi\) | |||||||
\(878\) | −404.487 | + | 233.530i | −0.460691 | + | 0.265980i | ||||
\(879\) | 49.6905 | + | 86.0664i | 0.0565307 | + | 0.0979140i | ||||
\(880\) | 139.970 | + | 80.8118i | 0.159057 | + | 0.0918316i | ||||
\(881\) | 538.120i | 0.610806i | 0.952223 | + | 0.305403i | \(0.0987912\pi\) | ||||
−0.952223 | + | 0.305403i | \(0.901209\pi\) | |||||||
\(882\) | 186.193 | − | 92.4670i | 0.211103 | − | 0.104838i | ||||
\(883\) | 880.262 | 0.996899 | 0.498450 | − | 0.866919i | \(-0.333903\pi\) | ||||
0.498450 | + | 0.866919i | \(0.333903\pi\) | |||||||
\(884\) | 28.7573 | − | 49.8091i | 0.0325309 | − | 0.0563451i | ||||
\(885\) | −248.746 | + | 143.614i | −0.281069 | + | 0.162275i | ||||
\(886\) | 397.155 | + | 687.893i | 0.448257 | + | 0.776403i | ||||
\(887\) | 696.988 | + | 402.406i | 0.785781 | + | 0.453671i | 0.838475 | − | 0.544940i | \(-0.183448\pi\) |
−0.0526943 | + | 0.998611i | \(0.516781\pi\) | |||||||
\(888\) | 253.133i | 0.285060i | ||||||||
\(889\) | −506.123 | + | 475.363i | −0.569317 | + | 0.534717i | ||||
\(890\) | 313.711 | 0.352484 | ||||||||
\(891\) | 81.3153 | − | 140.842i | 0.0912630 | − | 0.158072i | ||||
\(892\) | −469.913 | + | 271.305i | −0.526809 | + | 0.304153i | ||||
\(893\) | −480.725 | − | 832.641i | −0.538326 | − | 0.932408i | ||||
\(894\) | −70.4150 | − | 40.6541i | −0.0787640 | − | 0.0454744i | ||||
\(895\) | 565.354i | 0.631681i | ||||||||
\(896\) | −18.0911 | − | 77.1020i | −0.0201910 | − | 0.0860513i | ||||
\(897\) | 872.261 | 0.972420 | ||||||||
\(898\) | 273.120 | − | 473.057i | 0.304142 | − | 0.526790i | ||||
\(899\) | 398.463 | − | 230.053i | 0.443229 | − | 0.255898i | ||||
\(900\) | −15.0000 | − | 25.9808i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −0.592146 | − | 0.341876i | −0.000657210 | − | 0.000379440i | ||||
\(902\) | 957.846i | 1.06191i | ||||||||
\(903\) | 223.143 | − | 739.316i | 0.247113 | − | 0.818733i | ||||
\(904\) | −226.009 | −0.250009 | ||||||||
\(905\) | 161.248 | − | 279.289i | 0.178174 | − | 0.308607i | ||||
\(906\) | −19.7350 | + | 11.3940i | −0.0217826 | + | 0.0125762i | ||||
\(907\) | −533.167 | − | 923.473i | −0.587836 | − | 1.01816i | −0.994515 | − | 0.104591i | \(-0.966647\pi\) |
0.406679 | − | 0.913571i | \(-0.366687\pi\) | |||||||
\(908\) | −257.398 | − | 148.609i | −0.283478 | − | 0.163666i | ||||
\(909\) | − | 141.240i | − | 0.155380i | ||||||
\(910\) | −395.446 | − | 119.355i | −0.434556 | − | 0.131159i | ||||
\(911\) | −1052.95 | −1.15582 | −0.577911 | − | 0.816100i | \(-0.696132\pi\) | ||||
−0.577911 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(912\) | −117.934 | + | 204.268i | −0.129314 | + | 0.223979i | ||||
\(913\) | −781.306 | + | 451.087i | −0.855757 | + | 0.494072i | ||||
\(914\) | −352.893 | − | 611.228i | −0.386097 | − | 0.668740i | ||||
\(915\) | −352.613 | − | 203.581i | −0.385370 | − | 0.222493i | ||||
\(916\) | − | 50.6669i | − | 0.0553132i | ||||||
\(917\) | −1135.60 | + | 266.455i | −1.23838 | + | 0.290572i | ||||
\(918\) | 11.3246 | 0.0123362 | ||||||||
\(919\) | 714.350 | − | 1237.29i | 0.777312 | − | 1.34634i | −0.156174 | − | 0.987730i | \(-0.549916\pi\) |
0.933486 | − | 0.358614i | \(-0.116751\pi\) | |||||||
\(920\) | −147.817 | + | 85.3423i | −0.160671 | + | 0.0927634i | ||||
\(921\) | 252.250 | + | 436.910i | 0.273887 | + | 0.474386i | ||||
\(922\) | 757.247 | + | 437.197i | 0.821309 | + | 0.474183i | ||||
\(923\) | − | 853.987i | − | 0.925230i | ||||||
\(924\) | 299.980 | + | 319.391i | 0.324653 | + | 0.345661i | ||||
\(925\) | −258.353 | −0.279300 | ||||||||
\(926\) | 137.485 | − | 238.131i | 0.148472 | − | 0.257160i | ||||
\(927\) | −197.313 | + | 113.918i | −0.212851 | + | 0.122889i | ||||
\(928\) | 46.5736 | + | 80.6678i | 0.0501870 | + | 0.0869265i | ||||
\(929\) | −1523.62 | − | 879.664i | −1.64007 | − | 0.946893i | −0.980808 | − | 0.194978i | \(-0.937537\pi\) |
−0.659260 | − | 0.751915i | \(-0.729130\pi\) | |||||||
\(930\) | 153.046i | 0.164566i | ||||||||
\(931\) | 922.925 | − | 1389.63i | 0.991326 | − | 1.49262i | ||||
\(932\) | −817.772 | −0.877438 | ||||||||
\(933\) | 216.368 | − | 374.761i | 0.231906 | − | 0.401673i | ||||
\(934\) | −185.897 | + | 107.328i | −0.199034 | + | 0.114912i | ||||
\(935\) | −31.1345 | − | 53.9265i | −0.0332989 | − | 0.0576754i | ||||
\(936\) | 137.125 | + | 79.1694i | 0.146502 | + | 0.0845827i | ||||
\(937\) | − | 1264.00i | − | 1.34898i | −0.738284 | − | 0.674490i | \(-0.764363\pi\) | ||
0.738284 | − | 0.674490i | \(-0.235637\pi\) | |||||||
\(938\) | 91.7049 | − | 86.1315i | 0.0977664 | − | 0.0918246i | ||||
\(939\) | −6.55664 | −0.00698258 | ||||||||
\(940\) | 63.1483 | − | 109.376i | 0.0671791 | − | 0.116358i | ||||
\(941\) | 228.636 | − | 132.003i | 0.242971 | − | 0.140280i | −0.373570 | − | 0.927602i | \(-0.621867\pi\) |
0.616542 | + | 0.787322i | \(0.288533\pi\) | |||||||
\(942\) | −29.3797 | − | 50.8872i | −0.0311887 | − | 0.0540203i | ||||
\(943\) | −876.024 | − | 505.773i | −0.928975 | − | 0.536344i | ||||
\(944\) | 296.647i | 0.314245i | ||||||||
\(945\) | −18.5792 | − | 79.1822i | −0.0196605 | − | 0.0837906i | ||||
\(946\) | 1627.71 | 1.72063 | ||||||||
\(947\) | 34.9924 | − | 60.6086i | 0.0369508 | − | 0.0640006i | −0.846959 | − | 0.531659i | \(-0.821569\pi\) |
0.883909 | + | 0.467658i | \(0.154902\pi\) | |||||||
\(948\) | −399.594 | + | 230.706i | −0.421513 | + | 0.243360i | ||||
\(949\) | 339.867 | + | 588.667i | 0.358132 | + | 0.620302i | ||||
\(950\) | −208.481 | − | 120.366i | −0.219453 | − | 0.126701i | ||||
\(951\) | − | 123.601i | − | 0.129969i | ||||||
\(952\) | −8.81641 | + | 29.2104i | −0.00926094 | + | 0.0306832i | ||||
\(953\) | −1410.53 | −1.48009 | −0.740047 | − | 0.672555i | \(-0.765197\pi\) | ||||
−0.740047 | + | 0.672555i | \(0.765197\pi\) | |||||||
\(954\) | 0.941190 | − | 1.63019i | 0.000986573 | − | 0.00170879i | ||||
\(955\) | −608.248 | + | 351.172i | −0.636909 | + | 0.367720i | ||||
\(956\) | −67.0352 | − | 116.108i | −0.0701205 | − | 0.121452i | ||||
\(957\) | −446.319 | − | 257.683i | −0.466373 | − | 0.269261i | ||||
\(958\) | 317.872i | 0.331808i | ||||||||
\(959\) | −1015.38 | − | 306.466i | −1.05879 | − | 0.319568i | ||||
\(960\) | −30.9839 | −0.0322749 | ||||||||
\(961\) | −90.1133 | + | 156.081i | −0.0937704 | + | 0.162415i | ||||
\(962\) | 1180.89 | − | 681.788i | 1.22754 | − | 0.708719i | ||||
\(963\) | −160.838 | − | 278.579i | −0.167017 | − | 0.289282i | ||||
\(964\) | −410.287 | − | 236.879i | −0.425609 | − | 0.245725i | ||||
\(965\) | 118.128i | 0.122412i | ||||||||
\(966\) | −450.506 | + | 105.706i | −0.466362 | + | 0.109427i | ||||
\(967\) | −1581.56 | −1.63554 | −0.817768 | − | 0.575548i | \(-0.804789\pi\) | ||||
−0.817768 | + | 0.575548i | \(0.804789\pi\) | |||||||
\(968\) | −290.660 | + | 503.438i | −0.300269 | + | 0.520080i | ||||
\(969\) | 78.6988 | − | 45.4368i | 0.0812165 | − | 0.0468904i | ||||
\(970\) | 237.765 | + | 411.822i | 0.245119 | + | 0.424559i | ||||
\(971\) | −518.308 | − | 299.245i | −0.533788 | − | 0.308182i | 0.208770 | − | 0.977965i | \(-0.433054\pi\) |
−0.742557 | + | 0.669782i | \(0.766387\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 727.544 | + | 774.622i | 0.747732 | + | 0.796117i | ||||
\(974\) | 98.3767 | 0.101003 | ||||||||
\(975\) | −80.8019 | + | 139.953i | −0.0828738 | + | 0.143542i | ||||
\(976\) | −364.177 | + | 210.258i | −0.373132 | + | 0.215428i | ||||
\(977\) | 86.3897 | + | 149.631i | 0.0884235 | + | 0.153154i | 0.906845 | − | 0.421465i | \(-0.138484\pi\) |
−0.818421 | + | 0.574618i | \(0.805150\pi\) | |||||||
\(978\) | 536.964 | + | 310.016i | 0.549043 | + | 0.316990i | ||||
\(979\) | 1792.63i | 1.83108i | ||||||||
\(980\) | 218.705 | + | 13.7220i | 0.223168 | + | 0.0140020i | ||||
\(981\) | −242.671 | −0.247371 | ||||||||
\(982\) | 530.651 | − | 919.115i | 0.540378 | − | 0.935962i | ||||
\(983\) | −187.419 | + | 108.206i | −0.190660 | + | 0.110078i | −0.592292 | − | 0.805724i | \(-0.701777\pi\) |
0.401631 | + | 0.915801i | \(0.368443\pi\) | |||||||
\(984\) | −91.8113 | − | 159.022i | −0.0933042 | − | 0.161608i | ||||
\(985\) | −104.959 | − | 60.5980i | −0.106557 | − | 0.0615208i | ||||
\(986\) | − | 35.8869i | − | 0.0363965i | ||||||
\(987\) | 249.580 | − | 234.411i | 0.252867 | − | 0.237499i | ||||
\(988\) | 1270.58 | 1.28601 | ||||||||
\(989\) | −859.484 | + | 1488.67i | −0.869043 | + | 1.50523i | ||||
\(990\) | 148.461 | − | 85.7139i | 0.149960 | − | 0.0865797i | ||||
\(991\) | 160.993 | + | 278.849i | 0.162455 | + | 0.281381i | 0.935749 | − | 0.352667i | \(-0.114725\pi\) |
−0.773293 | + | 0.634048i | \(0.781392\pi\) | |||||||
\(992\) | 136.889 | + | 79.0328i | 0.137993 | + | 0.0796702i | ||||
\(993\) | − | 592.303i | − | 0.596479i | ||||||
\(994\) | 103.492 | + | 441.068i | 0.104116 | + | 0.443731i | ||||
\(995\) | −51.3646 | −0.0516227 | ||||||||
\(996\) | 86.4752 | − | 149.779i | 0.0868225 | − | 0.150381i | ||||
\(997\) | −40.5409 | + | 23.4063i | −0.0406629 | + | 0.0234767i | −0.520194 | − | 0.854048i | \(-0.674140\pi\) |
0.479531 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(998\) | −113.257 | − | 196.167i | −0.113484 | − | 0.196560i | ||||
\(999\) | 232.518 | + | 134.244i | 0.232750 | + | 0.134378i |
(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 | 210.3.o.a.61.1 | yes | 8 | |
3.2 | odd | 2 | 630.3.v.b.271.4 | 8 | |||
5.2 | odd | 4 | 1050.3.q.c.649.1 | 16 | |||
5.3 | odd | 4 | 1050.3.q.c.649.8 | 16 | |||
5.4 | even | 2 | 1050.3.p.b.901.4 | 8 | |||
7.2 | even | 3 | 1470.3.f.a.391.8 | 8 | |||
7.3 | odd | 6 | inner | 210.3.o.a.31.1 | ✓ | 8 | |
7.5 | odd | 6 | 1470.3.f.a.391.5 | 8 | |||
21.17 | even | 6 | 630.3.v.b.451.4 | 8 | |||
35.3 | even | 12 | 1050.3.q.c.199.1 | 16 | |||
35.17 | even | 12 | 1050.3.q.c.199.8 | 16 | |||
35.24 | odd | 6 | 1050.3.p.b.451.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.a.31.1 | ✓ | 8 | 7.3 | odd | 6 | inner | |
210.3.o.a.61.1 | yes | 8 | 1.1 | even | 1 | trivial | |
630.3.v.b.271.4 | 8 | 3.2 | odd | 2 | |||
630.3.v.b.451.4 | 8 | 21.17 | even | 6 | |||
1050.3.p.b.451.4 | 8 | 35.24 | odd | 6 | |||
1050.3.p.b.901.4 | 8 | 5.4 | even | 2 | |||
1050.3.q.c.199.1 | 16 | 35.3 | even | 12 | |||
1050.3.q.c.199.8 | 16 | 35.17 | even | 12 | |||
1050.3.q.c.649.1 | 16 | 5.2 | odd | 4 | |||
1050.3.q.c.649.8 | 16 | 5.3 | odd | 4 | |||
1470.3.f.a.391.5 | 8 | 7.5 | odd | 6 | |||
1470.3.f.a.391.8 | 8 | 7.2 | even | 3 |