Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 163.7 | ||
Character | \(\chi\) | \(=\) | 210.163 |
Dual form | 210.3.v.a.67.7 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0.448288 | − | 1.67303i | 0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 3.99034 | + | 3.01284i | 0.798068 | + | 0.602567i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −5.53495 | + | 4.28537i | −0.790707 | + | 0.612195i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.288675 | − | 0.166667i | ||||
\(10\) | −2.65505 | + | 6.55368i | −0.265505 | + | 0.655368i | ||||
\(11\) | 8.47882 | + | 14.6857i | 0.770802 | + | 1.33507i | 0.937124 | + | 0.348996i | \(0.113477\pi\) |
−0.166322 | + | 0.986071i | \(0.553189\pi\) | |||||||
\(12\) | 0.896575 | + | 3.34607i | 0.0747146 | + | 0.278839i | ||||
\(13\) | 3.05181 | + | 3.05181i | 0.234754 | + | 0.234754i | 0.814674 | − | 0.579920i | \(-0.196916\pi\) |
−0.579920 | + | 0.814674i | \(0.696916\pi\) | |||||||
\(14\) | −7.87985 | − | 5.99233i | −0.562846 | − | 0.428023i | ||||
\(15\) | 6.82939 | − | 5.32535i | 0.455293 | − | 0.355023i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | 10.7449 | + | 2.87910i | 0.632055 | + | 0.169359i | 0.560602 | − | 0.828085i | \(-0.310570\pi\) |
0.0714531 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(18\) | 1.09808 | − | 4.09808i | 0.0610042 | − | 0.227671i | ||||
\(19\) | 5.74405 | + | 3.31633i | 0.302318 | + | 0.174544i | 0.643484 | − | 0.765460i | \(-0.277488\pi\) |
−0.341166 | + | 0.940003i | \(0.610822\pi\) | |||||||
\(20\) | −9.92431 | − | 1.22805i | −0.496215 | − | 0.0614023i | ||||
\(21\) | 4.68831 | + | 11.1812i | 0.223253 | + | 0.532439i | ||||
\(22\) | −16.9576 | + | 16.9576i | −0.770802 | + | 0.770802i | ||||
\(23\) | −16.7817 | + | 4.49666i | −0.729641 | + | 0.195507i | −0.604469 | − | 0.796628i | \(-0.706615\pi\) |
−0.125172 | + | 0.992135i | \(0.539948\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 6.84563 | + | 24.0445i | 0.273825 | + | 0.961779i | ||||
\(26\) | −3.05181 | + | 5.28588i | −0.117377 | + | 0.203303i | ||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 5.30145 | − | 12.9574i | 0.189337 | − | 0.462765i | ||||
\(29\) | − | 35.8861i | − | 1.23745i | −0.785607 | − | 0.618725i | \(-0.787649\pi\) | ||
0.785607 | − | 0.618725i | \(-0.212351\pi\) | |||||||
\(30\) | 9.77430 | + | 7.37991i | 0.325810 | + | 0.245997i | ||||
\(31\) | 22.7901 | + | 39.4736i | 0.735165 | + | 1.27334i | 0.954651 | + | 0.297727i | \(0.0962286\pi\) |
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(32\) | 5.46410 | + | 1.46410i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 28.3707 | − | 7.60190i | 0.859718 | − | 0.230361i | ||||
\(34\) | 15.7317i | 0.462697i | ||||||||
\(35\) | −34.9974 | + | 0.424174i | −0.999927 | + | 0.0121193i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −4.74524 | − | 17.7095i | −0.128250 | − | 0.478635i | 0.871685 | − | 0.490067i | \(-0.163028\pi\) |
−0.999935 | + | 0.0114320i | \(0.996361\pi\) | |||||||
\(38\) | −2.42772 | + | 9.06038i | −0.0638874 | + | 0.238431i | ||||
\(39\) | 6.47386 | − | 3.73768i | 0.165996 | − | 0.0958380i | ||||
\(40\) | −1.95501 | − | 14.0064i | −0.0488752 | − | 0.350159i | ||||
\(41\) | −42.9609 | −1.04783 | −0.523913 | − | 0.851772i | \(-0.675528\pi\) | ||||
−0.523913 | + | 0.851772i | \(0.675528\pi\) | |||||||
\(42\) | −13.5578 | + | 10.4970i | −0.322805 | + | 0.249928i | ||||
\(43\) | −1.98628 | − | 1.98628i | −0.0461926 | − | 0.0461926i | 0.683633 | − | 0.729826i | \(-0.260399\pi\) |
−0.729826 | + | 0.683633i | \(0.760399\pi\) | |||||||
\(44\) | −29.3715 | − | 16.9576i | −0.667534 | − | 0.385401i | ||||
\(45\) | −5.84795 | − | 13.8131i | −0.129955 | − | 0.306958i | ||||
\(46\) | −12.2851 | − | 21.2784i | −0.267067 | − | 0.462574i | ||||
\(47\) | −11.3192 | − | 42.2437i | −0.240833 | − | 0.898801i | −0.975432 | − | 0.220300i | \(-0.929296\pi\) |
0.734599 | − | 0.678501i | \(-0.237370\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | 12.2713 | − | 47.4385i | 0.250434 | − | 0.968134i | ||||
\(50\) | −30.3397 | + | 18.1522i | −0.606794 | + | 0.363044i | ||||
\(51\) | 9.63365 | − | 16.6860i | 0.188895 | − | 0.327176i | ||||
\(52\) | −8.33769 | − | 2.23408i | −0.160340 | − | 0.0429630i | ||||
\(53\) | 22.0156 | − | 82.1632i | 0.415388 | − | 1.55025i | −0.368669 | − | 0.929561i | \(-0.620187\pi\) |
0.784057 | − | 0.620688i | \(-0.213147\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | −10.4124 | + | 84.1464i | −0.189316 | + | 1.52993i | ||||
\(56\) | 19.6406 | + | 2.49916i | 0.350725 | + | 0.0446279i | ||||
\(57\) | 8.12331 | − | 8.12331i | 0.142514 | − | 0.142514i | ||||
\(58\) | 49.0213 | − | 13.1352i | 0.845195 | − | 0.226469i | ||||
\(59\) | −22.0174 | + | 12.7117i | −0.373176 | + | 0.215453i | −0.674845 | − | 0.737960i | \(-0.735789\pi\) |
0.301669 | + | 0.953413i | \(0.402456\pi\) | |||||||
\(60\) | −6.50351 | + | 16.0532i | −0.108392 | + | 0.267553i | ||||
\(61\) | 42.4823 | − | 73.5814i | 0.696431 | − | 1.20625i | −0.273265 | − | 0.961939i | \(-0.588104\pi\) |
0.969696 | − | 0.244314i | \(-0.0785629\pi\) | |||||||
\(62\) | −45.5802 | + | 45.5802i | −0.735165 | + | 0.735165i | ||||
\(63\) | 20.8083 | − | 2.83128i | 0.330290 | − | 0.0449410i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 2.98315 | + | 21.3723i | 0.0458946 | + | 0.328805i | ||||
\(66\) | 20.7688 | + | 35.9726i | 0.314678 | + | 0.545039i | ||||
\(67\) | 60.8022 | + | 16.2919i | 0.907496 | + | 0.243163i | 0.682233 | − | 0.731135i | \(-0.261009\pi\) |
0.225263 | + | 0.974298i | \(0.427676\pi\) | |||||||
\(68\) | −21.4899 | + | 5.75820i | −0.316028 | + | 0.0846794i | ||||
\(69\) | 30.0922i | 0.436119i | ||||||||
\(70\) | −13.3894 | − | 47.6521i | −0.191277 | − | 0.680745i | ||||
\(71\) | 137.965 | 1.94316 | 0.971582 | − | 0.236705i | \(-0.0760674\pi\) | ||||
0.971582 | + | 0.236705i | \(0.0760674\pi\) | |||||||
\(72\) | 2.19615 | + | 8.19615i | 0.0305021 | + | 0.113835i | ||||
\(73\) | 1.87704 | − | 7.00522i | 0.0257129 | − | 0.0959619i | −0.951877 | − | 0.306480i | \(-0.900849\pi\) |
0.977590 | + | 0.210519i | \(0.0675152\pi\) | |||||||
\(74\) | 22.4547 | − | 12.9642i | 0.303442 | − | 0.175193i | ||||
\(75\) | 43.2960 | − | 0.674117i | 0.577280 | − | 0.00898823i | ||||
\(76\) | −13.2653 | −0.174544 | ||||||||
\(77\) | −109.864 | − | 44.9500i | −1.42680 | − | 0.583766i | ||||
\(78\) | 7.47537 | + | 7.47537i | 0.0958380 | + | 0.0958380i | ||||
\(79\) | 35.4965 | + | 20.4939i | 0.449322 | + | 0.259416i | 0.707544 | − | 0.706669i | \(-0.249803\pi\) |
−0.258222 | + | 0.966086i | \(0.583137\pi\) | |||||||
\(80\) | 18.4175 | − | 7.79727i | 0.230218 | − | 0.0974659i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −15.7248 | − | 58.6857i | −0.191766 | − | 0.715679i | ||||
\(83\) | −109.947 | − | 109.947i | −1.32466 | − | 1.32466i | −0.909959 | − | 0.414699i | \(-0.863887\pi\) |
−0.414699 | − | 0.909959i | \(-0.636113\pi\) | |||||||
\(84\) | −19.3016 | − | 14.6781i | −0.229781 | − | 0.174740i | ||||
\(85\) | 34.2017 | + | 43.8613i | 0.402373 | + | 0.516016i | ||||
\(86\) | 1.98628 | − | 3.44034i | 0.0230963 | − | 0.0400040i | ||||
\(87\) | −60.0386 | − | 16.0873i | −0.690098 | − | 0.184911i | ||||
\(88\) | 12.4139 | − | 46.3291i | 0.141066 | − | 0.526467i | ||||
\(89\) | 49.9706 | + | 28.8505i | 0.561467 | + | 0.324163i | 0.753734 | − | 0.657179i | \(-0.228251\pi\) |
−0.192267 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(90\) | 16.7285 | − | 13.0444i | 0.185873 | − | 0.144938i | ||||
\(91\) | −29.9697 | − | 3.81348i | −0.329337 | − | 0.0419064i | ||||
\(92\) | 24.5702 | − | 24.5702i | 0.267067 | − | 0.267067i | ||||
\(93\) | 76.2572 | − | 20.4331i | 0.819970 | − | 0.219710i | ||||
\(94\) | 53.5628 | − | 30.9245i | 0.569817 | − | 0.328984i | ||||
\(95\) | 12.9292 | + | 30.5392i | 0.136096 | + | 0.321465i | ||||
\(96\) | 4.89898 | − | 8.48528i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | −39.7542 | + | 39.7542i | −0.409837 | + | 0.409837i | −0.881682 | − | 0.471845i | \(-0.843588\pi\) |
0.471845 | + | 0.881682i | \(0.343588\pi\) | |||||||
\(98\) | 69.2939 | − | 0.600821i | 0.707080 | − | 0.00613082i | ||||
\(99\) | − | 50.8729i | − | 0.513868i | ||||||
\(100\) | −35.9015 | − | 34.8006i | −0.359015 | − | 0.348006i | ||||
\(101\) | 36.2458 | + | 62.7796i | 0.358869 | + | 0.621580i | 0.987772 | − | 0.155904i | \(-0.0498290\pi\) |
−0.628903 | + | 0.777484i | \(0.716496\pi\) | |||||||
\(102\) | 26.3196 | + | 7.05232i | 0.258036 | + | 0.0691404i | ||||
\(103\) | −152.873 | + | 40.9621i | −1.48420 | + | 0.397690i | −0.907774 | − | 0.419459i | \(-0.862220\pi\) |
−0.576426 | + | 0.817149i | \(0.695553\pi\) | |||||||
\(104\) | − | 12.2072i | − | 0.117377i | ||||||
\(105\) | −14.9793 | + | 58.7420i | −0.142660 | + | 0.559448i | ||||
\(106\) | 120.295 | 1.13486 | ||||||||
\(107\) | −11.6403 | − | 43.4424i | −0.108788 | − | 0.406003i | 0.889959 | − | 0.456040i | \(-0.150733\pi\) |
−0.998747 | + | 0.0500370i | \(0.984066\pi\) | |||||||
\(108\) | 2.68973 | − | 10.0382i | 0.0249049 | − | 0.0929463i | ||||
\(109\) | 83.0179 | − | 47.9304i | 0.761632 | − | 0.439729i | −0.0682492 | − | 0.997668i | \(-0.521741\pi\) |
0.829881 | + | 0.557940i | \(0.188408\pi\) | |||||||
\(110\) | −118.757 | + | 16.5762i | −1.07961 | + | 0.150692i | ||||
\(111\) | −31.7558 | −0.286088 | ||||||||
\(112\) | 3.77505 | + | 27.7444i | 0.0337058 | + | 0.247717i | ||||
\(113\) | −86.6065 | − | 86.6065i | −0.766429 | − | 0.766429i | 0.211047 | − | 0.977476i | \(-0.432313\pi\) |
−0.977476 | + | 0.211047i | \(0.932313\pi\) | |||||||
\(114\) | 14.0700 | + | 8.12331i | 0.123421 | + | 0.0712571i | ||||
\(115\) | −80.5126 | − | 32.6175i | −0.700109 | − | 0.283630i | ||||
\(116\) | 35.8861 | + | 62.1565i | 0.309363 | + | 0.535832i | ||||
\(117\) | −3.35111 | − | 12.5065i | −0.0286420 | − | 0.106893i | ||||
\(118\) | −25.4235 | − | 25.4235i | −0.215453 | − | 0.215453i | ||||
\(119\) | −71.8107 | + | 30.1103i | −0.603451 | + | 0.253028i | ||||
\(120\) | −24.3095 | − | 3.00809i | −0.202579 | − | 0.0250674i | ||||
\(121\) | −83.2807 | + | 144.246i | −0.688270 | + | 1.19212i | ||||
\(122\) | 116.064 | + | 31.0992i | 0.951342 | + | 0.254911i | ||||
\(123\) | −19.2588 | + | 71.8750i | −0.156576 | + | 0.584350i | ||||
\(124\) | −78.9472 | − | 45.5802i | −0.636671 | − | 0.367582i | ||||
\(125\) | −45.1257 | + | 116.570i | −0.361006 | + | 0.932564i | ||||
\(126\) | 11.4840 | + | 27.3883i | 0.0911425 | + | 0.217367i | ||||
\(127\) | 46.1257 | − | 46.1257i | 0.363194 | − | 0.363194i | −0.501793 | − | 0.864988i | \(-0.667326\pi\) |
0.864988 | + | 0.501793i | \(0.167326\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −4.21354 | + | 2.43269i | −0.0326631 | + | 0.0188581i | ||||
\(130\) | −28.1032 | + | 11.8979i | −0.216179 | + | 0.0915221i | ||||
\(131\) | −50.4917 | + | 87.4543i | −0.385433 | + | 0.667590i | −0.991829 | − | 0.127573i | \(-0.959281\pi\) |
0.606396 | + | 0.795163i | \(0.292615\pi\) | |||||||
\(132\) | −41.5376 | + | 41.5376i | −0.314678 | + | 0.314678i | ||||
\(133\) | −46.0047 | + | 6.25965i | −0.345900 | + | 0.0470650i | ||||
\(134\) | 89.0206i | 0.664333i | ||||||||
\(135\) | −25.7313 | + | 3.59158i | −0.190602 | + | 0.0266043i | ||||
\(136\) | −15.7317 | − | 27.2481i | −0.115674 | − | 0.200354i | ||||
\(137\) | −127.593 | − | 34.1884i | −0.931334 | − | 0.249550i | −0.238911 | − | 0.971042i | \(-0.576790\pi\) |
−0.692423 | + | 0.721491i | \(0.743457\pi\) | |||||||
\(138\) | −41.1067 | + | 11.0145i | −0.297875 | + | 0.0798153i | ||||
\(139\) | 49.7454i | 0.357880i | 0.983860 | + | 0.178940i | \(0.0572669\pi\) | ||||
−0.983860 | + | 0.178940i | \(0.942733\pi\) | |||||||
\(140\) | 60.1932 | − | 35.7321i | 0.429951 | − | 0.255229i | ||||
\(141\) | −75.7493 | −0.537229 | ||||||||
\(142\) | 50.4985 | + | 188.463i | 0.355624 | + | 1.32721i | ||||
\(143\) | −18.9423 | + | 70.6937i | −0.132464 | + | 0.494362i | ||||
\(144\) | −10.3923 | + | 6.00000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 108.119 | − | 143.198i | 0.745647 | − | 0.987570i | ||||
\(146\) | 10.2564 | 0.0702490 | ||||||||
\(147\) | −73.8652 | − | 41.7964i | −0.502484 | − | 0.284329i | ||||
\(148\) | 25.9285 | + | 25.9285i | 0.175193 | + | 0.175193i | ||||
\(149\) | 196.729 | + | 113.581i | 1.32033 | + | 0.762291i | 0.983780 | − | 0.179377i | \(-0.0574080\pi\) |
0.336546 | + | 0.941667i | \(0.390741\pi\) | |||||||
\(150\) | 16.7683 | + | 58.8967i | 0.111789 | + | 0.392645i | ||||
\(151\) | 99.4676 | + | 172.283i | 0.658726 | + | 1.14095i | 0.980946 | + | 0.194282i | \(0.0622377\pi\) |
−0.322220 | + | 0.946665i | \(0.604429\pi\) | |||||||
\(152\) | −4.85544 | − | 18.1208i | −0.0319437 | − | 0.119215i | ||||
\(153\) | −23.5975 | − | 23.5975i | −0.154232 | − | 0.154232i | ||||
\(154\) | 21.1900 | − | 166.529i | 0.137597 | − | 1.08136i | ||||
\(155\) | −27.9873 | + | 226.176i | −0.180563 | + | 1.45920i | ||||
\(156\) | −7.47537 | + | 12.9477i | −0.0479190 | + | 0.0829982i | ||||
\(157\) | 268.691 | + | 71.9955i | 1.71141 | + | 0.458570i | 0.975769 | − | 0.218805i | \(-0.0702157\pi\) |
0.735638 | + | 0.677375i | \(0.236882\pi\) | |||||||
\(158\) | −15.0026 | + | 55.9903i | −0.0949530 | + | 0.354369i | ||||
\(159\) | −127.592 | − | 73.6655i | −0.802468 | − | 0.463305i | ||||
\(160\) | 17.3925 | + | 22.3047i | 0.108703 | + | 0.139404i | ||||
\(161\) | 73.6163 | − | 96.8047i | 0.457244 | − | 0.601271i | ||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −202.663 | + | 54.3034i | −1.24333 | + | 0.333150i | −0.819757 | − | 0.572712i | \(-0.805891\pi\) |
−0.423574 | + | 0.905861i | \(0.639225\pi\) | |||||||
\(164\) | 74.4105 | − | 42.9609i | 0.453722 | − | 0.261957i | ||||
\(165\) | 136.112 | + | 55.1420i | 0.824921 | + | 0.334194i | ||||
\(166\) | 109.947 | − | 190.433i | 0.662329 | − | 1.14719i | ||||
\(167\) | 14.8502 | − | 14.8502i | 0.0889236 | − | 0.0889236i | −0.661246 | − | 0.750169i | \(-0.729972\pi\) |
0.750169 | + | 0.661246i | \(0.229972\pi\) | |||||||
\(168\) | 12.9858 | − | 31.7391i | 0.0772966 | − | 0.188923i | ||||
\(169\) | − | 150.373i | − | 0.889781i | ||||||
\(170\) | −47.3970 | + | 62.7748i | −0.278806 | + | 0.369263i | ||||
\(171\) | −9.94898 | − | 17.2321i | −0.0581812 | − | 0.100773i | ||||
\(172\) | 5.42662 | + | 1.45406i | 0.0315501 | + | 0.00845383i | ||||
\(173\) | 123.597 | − | 33.1178i | 0.714435 | − | 0.191432i | 0.116748 | − | 0.993162i | \(-0.462753\pi\) |
0.597687 | + | 0.801729i | \(0.296086\pi\) | |||||||
\(174\) | − | 87.9026i | − | 0.505187i | ||||||
\(175\) | −140.930 | − | 103.749i | −0.805312 | − | 0.592851i | ||||
\(176\) | 67.8305 | 0.385401 | ||||||||
\(177\) | 11.3970 | + | 42.5343i | 0.0643900 | + | 0.240307i | ||||
\(178\) | −21.1200 | + | 78.8211i | −0.118652 | + | 0.442815i | ||||
\(179\) | 128.441 | − | 74.1555i | 0.717548 | − | 0.414277i | −0.0963015 | − | 0.995352i | \(-0.530701\pi\) |
0.813850 | + | 0.581076i | \(0.197368\pi\) | |||||||
\(180\) | 23.9420 | + | 18.0770i | 0.133011 | + | 0.100428i | ||||
\(181\) | −140.949 | −0.778724 | −0.389362 | − | 0.921085i | \(-0.627305\pi\) | ||||
−0.389362 | + | 0.921085i | \(0.627305\pi\) | |||||||
\(182\) | −5.76035 | − | 42.3352i | −0.0316503 | − | 0.232611i | ||||
\(183\) | −104.060 | − | 104.060i | −0.568633 | − | 0.568633i | ||||
\(184\) | 42.5568 | + | 24.5702i | 0.231287 | + | 0.133534i | ||||
\(185\) | 34.4207 | − | 84.9636i | 0.186058 | − | 0.459262i | ||||
\(186\) | 55.8241 | + | 96.6902i | 0.300130 | + | 0.519840i | ||||
\(187\) | 48.8227 | + | 182.209i | 0.261084 | + | 0.974379i | ||||
\(188\) | 61.8490 | + | 61.8490i | 0.328984 | + | 0.328984i | ||||
\(189\) | 4.59126 | − | 36.0821i | 0.0242924 | − | 0.190911i | ||||
\(190\) | −36.9849 | + | 28.8397i | −0.194657 | + | 0.151788i | ||||
\(191\) | 81.4029 | − | 140.994i | 0.426193 | − | 0.738188i | −0.570338 | − | 0.821410i | \(-0.693188\pi\) |
0.996531 | + | 0.0832220i | \(0.0265211\pi\) | |||||||
\(192\) | 13.3843 | + | 3.58630i | 0.0697097 | + | 0.0186787i | ||||
\(193\) | −59.8847 | + | 223.493i | −0.310283 | + | 1.15799i | 0.618018 | + | 0.786164i | \(0.287936\pi\) |
−0.928301 | + | 0.371829i | \(0.878731\pi\) | |||||||
\(194\) | −68.8562 | − | 39.7542i | −0.354929 | − | 0.204918i | ||||
\(195\) | 37.0939 | + | 4.59004i | 0.190225 | + | 0.0235387i | ||||
\(196\) | 26.1840 | + | 94.4373i | 0.133592 | + | 0.481823i | ||||
\(197\) | 175.872 | − | 175.872i | 0.892750 | − | 0.892750i | −0.102031 | − | 0.994781i | \(-0.532534\pi\) |
0.994781 | + | 0.102031i | \(0.0325340\pi\) | |||||||
\(198\) | 69.4937 | − | 18.6208i | 0.350978 | − | 0.0940443i | ||||
\(199\) | −222.868 | + | 128.673i | −1.11994 | + | 0.646598i | −0.941386 | − | 0.337332i | \(-0.890475\pi\) |
−0.178555 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(200\) | 34.3977 | − | 61.7802i | 0.171989 | − | 0.308901i | ||||
\(201\) | 54.5138 | − | 94.4206i | 0.271213 | − | 0.469754i | ||||
\(202\) | −72.4916 | + | 72.4916i | −0.358869 | + | 0.358869i | ||||
\(203\) | 153.785 | + | 198.628i | 0.757561 | + | 0.978461i | ||||
\(204\) | 38.5346i | 0.188895i | ||||||||
\(205\) | −171.429 | − | 129.434i | −0.836237 | − | 0.631386i | ||||
\(206\) | −111.911 | − | 193.835i | −0.543255 | − | 0.940945i | ||||
\(207\) | 50.3452 | + | 13.4900i | 0.243214 | + | 0.0651689i | ||||
\(208\) | 16.6754 | − | 4.46815i | 0.0801701 | − | 0.0214815i | ||||
\(209\) | 112.474i | 0.538154i | ||||||||
\(210\) | −85.7258 | + | 1.03901i | −0.408218 | + | 0.00494767i | ||||
\(211\) | −269.844 | −1.27888 | −0.639441 | − | 0.768840i | \(-0.720834\pi\) | ||||
−0.639441 | + | 0.768840i | \(0.720834\pi\) | |||||||
\(212\) | 44.0311 | + | 164.326i | 0.207694 | + | 0.775125i | ||||
\(213\) | 61.8478 | − | 230.819i | 0.290365 | − | 1.08366i | ||||
\(214\) | 55.0827 | − | 31.8020i | 0.257396 | − | 0.148608i | ||||
\(215\) | −1.94160 | − | 13.9103i | −0.00903069 | − | 0.0646990i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −295.301 | − | 120.821i | −1.36083 | − | 0.556777i | ||||
\(218\) | 95.8608 | + | 95.8608i | 0.439729 | + | 0.439729i | ||||
\(219\) | −10.8785 | − | 6.28071i | −0.0496735 | − | 0.0286790i | ||||
\(220\) | −66.1116 | − | 156.158i | −0.300507 | − | 0.709810i | ||||
\(221\) | 24.0050 | + | 41.5779i | 0.108620 | + | 0.188135i | ||||
\(222\) | −11.6234 | − | 43.3792i | −0.0523578 | − | 0.195402i | ||||
\(223\) | 253.501 | + | 253.501i | 1.13677 | + | 1.13677i | 0.989025 | + | 0.147749i | \(0.0472029\pi\) |
0.147749 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(224\) | −36.5177 | + | 15.3119i | −0.163026 | + | 0.0683569i | ||||
\(225\) | 18.2813 | − | 72.7379i | 0.0812500 | − | 0.323279i | ||||
\(226\) | 86.6065 | − | 150.007i | 0.383215 | − | 0.663747i | ||||
\(227\) | 13.4140 | + | 3.59427i | 0.0590925 | + | 0.0158338i | 0.288244 | − | 0.957557i | \(-0.406929\pi\) |
−0.229152 | + | 0.973391i | \(0.573595\pi\) | |||||||
\(228\) | −5.94668 | + | 22.1933i | −0.0260819 | + | 0.0973390i | ||||
\(229\) | 310.927 | + | 179.514i | 1.35776 | + | 0.783904i | 0.989322 | − | 0.145747i | \(-0.0465586\pi\) |
0.368440 | + | 0.929651i | \(0.379892\pi\) | |||||||
\(230\) | 15.0867 | − | 121.921i | 0.0655941 | − | 0.530091i | ||||
\(231\) | −124.453 | + | 163.655i | −0.538759 | + | 0.708463i | ||||
\(232\) | −71.7721 | + | 71.7721i | −0.309363 | + | 0.309363i | ||||
\(233\) | 205.192 | − | 54.9811i | 0.880653 | − | 0.235970i | 0.209964 | − | 0.977709i | \(-0.432665\pi\) |
0.670689 | + | 0.741739i | \(0.265999\pi\) | |||||||
\(234\) | 15.8576 | − | 9.15542i | 0.0677677 | − | 0.0391257i | ||||
\(235\) | 82.1060 | − | 202.669i | 0.349387 | − | 0.862423i | ||||
\(236\) | 25.4235 | − | 44.0347i | 0.107727 | − | 0.186588i | ||||
\(237\) | 50.1996 | − | 50.1996i | 0.211813 | − | 0.211813i | ||||
\(238\) | −67.4160 | − | 87.0741i | −0.283261 | − | 0.365857i | ||||
\(239\) | − | 145.882i | − | 0.610384i | −0.952291 | − | 0.305192i | \(-0.901279\pi\) | ||
0.952291 | − | 0.305192i | \(-0.0987206\pi\) | |||||||
\(240\) | −4.78877 | − | 34.3084i | −0.0199532 | − | 0.142952i | ||||
\(241\) | −132.371 | − | 229.274i | −0.549258 | − | 0.951343i | −0.998326 | − | 0.0578448i | \(-0.981577\pi\) |
0.449068 | − | 0.893498i | \(-0.351756\pi\) | |||||||
\(242\) | −227.527 | − | 60.9657i | −0.940195 | − | 0.251924i | ||||
\(243\) | 15.0573 | − | 4.03459i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 169.929i | 0.696431i | ||||||||
\(245\) | 191.891 | − | 152.325i | 0.783229 | − | 0.621733i | ||||
\(246\) | −105.232 | −0.427774 | ||||||||
\(247\) | 7.40893 | + | 27.6505i | 0.0299957 | + | 0.111945i | ||||
\(248\) | 33.3670 | − | 124.527i | 0.134544 | − | 0.502127i | ||||
\(249\) | −233.232 | + | 134.657i | −0.936674 | + | 0.540789i | ||||
\(250\) | −175.755 | − | 18.9751i | −0.703021 | − | 0.0759005i | ||||
\(251\) | −301.864 | −1.20265 | −0.601323 | − | 0.799006i | \(-0.705359\pi\) | ||||
−0.601323 | + | 0.799006i | \(0.705359\pi\) | |||||||
\(252\) | −33.2097 | + | 25.7122i | −0.131784 | + | 0.102033i | ||||
\(253\) | −208.326 | − | 208.326i | −0.823423 | − | 0.823423i | ||||
\(254\) | 79.8921 | + | 46.1257i | 0.314536 | + | 0.181597i | ||||
\(255\) | 88.7136 | − | 37.5581i | 0.347897 | − | 0.147287i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 30.6224 | + | 114.284i | 0.119153 | + | 0.444687i | 0.999564 | − | 0.0295256i | \(-0.00939965\pi\) |
−0.880411 | + | 0.474212i | \(0.842733\pi\) | |||||||
\(258\) | −4.86538 | − | 4.86538i | −0.0188581 | − | 0.0188581i | ||||
\(259\) | 102.156 | + | 77.6860i | 0.394426 | + | 0.299946i | ||||
\(260\) | −26.5393 | − | 34.0348i | −0.102074 | − | 0.130903i | ||||
\(261\) | −53.8291 | + | 93.2347i | −0.206242 | + | 0.357221i | ||||
\(262\) | −137.946 | − | 36.9625i | −0.526511 | − | 0.141078i | ||||
\(263\) | 88.0092 | − | 328.455i | 0.334636 | − | 1.24888i | −0.569628 | − | 0.821903i | \(-0.692913\pi\) |
0.904264 | − | 0.426975i | \(-0.140421\pi\) | |||||||
\(264\) | −71.9452 | − | 41.5376i | −0.272520 | − | 0.157339i | ||||
\(265\) | 335.394 | − | 261.530i | 1.26564 | − | 0.986905i | ||||
\(266\) | −25.3897 | − | 60.5524i | −0.0954501 | − | 0.227641i | ||||
\(267\) | 70.6691 | − | 70.6691i | 0.264678 | − | 0.264678i | ||||
\(268\) | −121.604 | + | 32.5838i | −0.453748 | + | 0.121581i | ||||
\(269\) | −319.982 | + | 184.742i | −1.18953 | + | 0.686773i | −0.958199 | − | 0.286103i | \(-0.907640\pi\) |
−0.231327 | + | 0.972876i | \(0.574307\pi\) | |||||||
\(270\) | −14.3245 | − | 33.8350i | −0.0530537 | − | 0.125315i | ||||
\(271\) | 137.014 | − | 237.315i | 0.505586 | − | 0.875700i | −0.494393 | − | 0.869238i | \(-0.664610\pi\) |
0.999979 | − | 0.00646203i | \(-0.00205694\pi\) | |||||||
\(272\) | 31.4634 | − | 31.4634i | 0.115674 | − | 0.115674i | ||||
\(273\) | −19.8151 | + | 48.4307i | −0.0725829 | + | 0.177402i | ||||
\(274\) | − | 186.809i | − | 0.681784i | ||||||
\(275\) | −295.068 | + | 304.402i | −1.07298 | + | 1.10692i | ||||
\(276\) | −30.0922 | − | 52.1212i | −0.109030 | − | 0.188845i | ||||
\(277\) | 54.3485 | + | 14.5626i | 0.196204 | + | 0.0525727i | 0.355583 | − | 0.934645i | \(-0.384282\pi\) |
−0.159379 | + | 0.987218i | \(0.550949\pi\) | |||||||
\(278\) | −67.9534 | + | 18.2081i | −0.244437 | + | 0.0654967i | ||||
\(279\) | − | 136.741i | − | 0.490110i | ||||||
\(280\) | 70.8432 | + | 69.1465i | 0.253011 | + | 0.246952i | ||||
\(281\) | 535.008 | 1.90394 | 0.951971 | − | 0.306187i | \(-0.0990534\pi\) | ||||
0.951971 | + | 0.306187i | \(0.0990534\pi\) | |||||||
\(282\) | −27.7262 | − | 103.475i | −0.0983197 | − | 0.366934i | ||||
\(283\) | −52.4326 | + | 195.681i | −0.185274 | + | 0.691452i | 0.809298 | + | 0.587399i | \(0.199848\pi\) |
−0.994572 | + | 0.104054i | \(0.966819\pi\) | |||||||
\(284\) | −238.962 | + | 137.965i | −0.841414 | + | 0.485791i | ||||
\(285\) | 56.8890 | − | 7.94057i | 0.199610 | − | 0.0278616i | ||||
\(286\) | −103.503 | −0.361898 | ||||||||
\(287\) | 237.786 | − | 184.103i | 0.828524 | − | 0.641474i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | −143.117 | − | 82.6285i | −0.495214 | − | 0.285912i | ||||
\(290\) | 235.186 | + | 95.2791i | 0.810986 | + | 0.328549i | ||||
\(291\) | 48.6887 | + | 84.3313i | 0.167315 | + | 0.289798i | ||||
\(292\) | 3.75408 | + | 14.0104i | 0.0128565 | + | 0.0479809i | ||||
\(293\) | −225.228 | − | 225.228i | −0.768696 | − | 0.768696i | 0.209181 | − | 0.977877i | \(-0.432920\pi\) |
−0.977877 | + | 0.209181i | \(0.932920\pi\) | |||||||
\(294\) | 30.0584 | − | 116.200i | 0.102239 | − | 0.395239i | ||||
\(295\) | −126.155 | − | 15.6106i | −0.427645 | − | 0.0529172i | ||||
\(296\) | −25.9285 | + | 44.9095i | −0.0875963 | + | 0.151721i | ||||
\(297\) | −85.1120 | − | 22.8057i | −0.286573 | − | 0.0767869i | ||||
\(298\) | −83.1473 | + | 310.310i | −0.279018 | + | 1.04131i | ||||
\(299\) | −64.9375 | − | 37.4917i | −0.217182 | − | 0.125390i | ||||
\(300\) | −74.3168 | + | 44.4636i | −0.247723 | + | 0.148212i | ||||
\(301\) | 19.5059 | + | 2.48202i | 0.0648037 | + | 0.00824592i | ||||
\(302\) | −198.935 | + | 198.935i | −0.658726 | + | 0.658726i | ||||
\(303\) | 121.281 | − | 32.4971i | 0.400267 | − | 0.107251i | ||||
\(304\) | 22.9762 | − | 13.2653i | 0.0755796 | − | 0.0436359i | ||||
\(305\) | 391.208 | − | 165.623i | 1.28265 | − | 0.543026i | ||||
\(306\) | 23.5975 | − | 40.8721i | 0.0771161 | − | 0.133569i | ||||
\(307\) | 294.340 | − | 294.340i | 0.958762 | − | 0.958762i | −0.0404208 | − | 0.999183i | \(-0.512870\pi\) |
0.999183 | + | 0.0404208i | \(0.0128699\pi\) | |||||||
\(308\) | 235.239 | − | 32.0079i | 0.763764 | − | 0.103922i | ||||
\(309\) | 274.124i | 0.887132i | ||||||||
\(310\) | −319.206 | + | 44.5548i | −1.02970 | + | 0.143725i | ||||
\(311\) | −116.986 | − | 202.625i | −0.376160 | − | 0.651529i | 0.614340 | − | 0.789042i | \(-0.289422\pi\) |
−0.990500 | + | 0.137513i | \(0.956089\pi\) | |||||||
\(312\) | −20.4231 | − | 5.47235i | −0.0654586 | − | 0.0175396i | ||||
\(313\) | −137.285 | + | 36.7853i | −0.438609 | + | 0.117525i | −0.471365 | − | 0.881938i | \(-0.656238\pi\) |
0.0327556 | + | 0.999463i | \(0.489572\pi\) | |||||||
\(314\) | 393.391i | 1.25284i | ||||||||
\(315\) | 91.5623 | + | 51.3941i | 0.290674 | + | 0.163156i | ||||
\(316\) | −81.9755 | −0.259416 | ||||||||
\(317\) | 18.1584 | + | 67.7680i | 0.0572820 | + | 0.213779i | 0.988634 | − | 0.150340i | \(-0.0480368\pi\) |
−0.931352 | + | 0.364119i | \(0.881370\pi\) | |||||||
\(318\) | 53.9269 | − | 201.258i | 0.169581 | − | 0.632887i | ||||
\(319\) | 527.014 | − | 304.271i | 1.65208 | − | 0.953829i | ||||
\(320\) | −24.1027 | + | 31.9227i | −0.0753209 | + | 0.0997585i | ||||
\(321\) | −77.8987 | −0.242675 | ||||||||
\(322\) | 159.183 | + | 65.1287i | 0.494357 | + | 0.202263i | ||||
\(323\) | 52.1714 | + | 52.1714i | 0.161521 | + | 0.161521i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | −52.4876 | + | 94.2706i | −0.161500 | + | 0.290063i | ||||
\(326\) | −148.360 | − | 256.966i | −0.455091 | − | 0.788240i | ||||
\(327\) | −42.9732 | − | 160.378i | −0.131417 | − | 0.490454i | ||||
\(328\) | 85.9218 | + | 85.9218i | 0.261957 | + | 0.261957i | ||||
\(329\) | 243.680 | + | 185.310i | 0.740670 | + | 0.563252i | ||||
\(330\) | −25.5050 | + | 206.116i | −0.0772879 | + | 0.624593i | ||||
\(331\) | 127.726 | − | 221.227i | 0.385878 | − | 0.668360i | −0.606013 | − | 0.795455i | \(-0.707232\pi\) |
0.991891 | + | 0.127095i | \(0.0405652\pi\) | |||||||
\(332\) | 300.380 | + | 80.4865i | 0.904758 | + | 0.242429i | ||||
\(333\) | −14.2357 | + | 53.1285i | −0.0427499 | + | 0.159545i | ||||
\(334\) | 25.7214 | + | 14.8502i | 0.0770101 | + | 0.0444618i | ||||
\(335\) | 193.537 | + | 248.197i | 0.577721 | + | 0.740888i | ||||
\(336\) | 48.1095 | + | 6.12168i | 0.143183 | + | 0.0182193i | ||||
\(337\) | 2.44497 | − | 2.44497i | 0.00725510 | − | 0.00725510i | −0.703470 | − | 0.710725i | \(-0.748367\pi\) |
0.710725 | + | 0.703470i | \(0.248367\pi\) | |||||||
\(338\) | 205.413 | − | 55.0403i | 0.607732 | − | 0.162841i | ||||
\(339\) | −183.720 | + | 106.071i | −0.541947 | + | 0.312893i | ||||
\(340\) | −103.100 | − | 41.7683i | −0.303237 | − | 0.122848i | ||||
\(341\) | −386.466 | + | 669.379i | −1.13333 | + | 1.96299i | ||||
\(342\) | 19.8980 | − | 19.8980i | 0.0581812 | − | 0.0581812i | ||||
\(343\) | 135.371 | + | 315.157i | 0.394666 | + | 0.918825i | ||||
\(344\) | 7.94513i | 0.0230963i | ||||||||
\(345\) | −90.6629 | + | 120.078i | −0.262791 | + | 0.348053i | ||||
\(346\) | 90.4795 | + | 156.715i | 0.261501 | + | 0.452934i | ||||
\(347\) | −509.917 | − | 136.632i | −1.46950 | − | 0.393752i | −0.566741 | − | 0.823896i | \(-0.691796\pi\) |
−0.902760 | + | 0.430145i | \(0.858463\pi\) | |||||||
\(348\) | 120.077 | − | 32.1746i | 0.345049 | − | 0.0924557i | ||||
\(349\) | − | 74.0257i | − | 0.212108i | −0.994360 | − | 0.106054i | \(-0.966178\pi\) | ||
0.994360 | − | 0.106054i | \(-0.0338216\pi\) | |||||||
\(350\) | 90.1399 | − | 230.488i | 0.257542 | − | 0.658538i | ||||
\(351\) | −22.4261 | −0.0638920 | ||||||||
\(352\) | 24.8277 | + | 92.6583i | 0.0705332 | + | 0.263234i | ||||
\(353\) | −74.2945 | + | 277.271i | −0.210466 | + | 0.785470i | 0.777248 | + | 0.629195i | \(0.216615\pi\) |
−0.987714 | + | 0.156275i | \(0.950051\pi\) | |||||||
\(354\) | −53.9313 | + | 31.1373i | −0.152348 | + | 0.0879584i | ||||
\(355\) | 550.526 | + | 415.665i | 1.55078 | + | 1.17089i | ||||
\(356\) | −115.402 | −0.324163 | ||||||||
\(357\) | 18.1837 | + | 133.640i | 0.0509348 | + | 0.374341i | ||||
\(358\) | 148.311 | + | 148.311i | 0.414277 | + | 0.414277i | ||||
\(359\) | −571.100 | − | 329.725i | −1.59081 | − | 0.918453i | −0.993169 | − | 0.116687i | \(-0.962773\pi\) |
−0.597638 | − | 0.801766i | \(-0.703894\pi\) | |||||||
\(360\) | −15.9303 | + | 39.3221i | −0.0442508 | + | 0.109228i | ||||
\(361\) | −158.504 | − | 274.537i | −0.439069 | − | 0.760490i | ||||
\(362\) | −51.5910 | − | 192.540i | −0.142516 | − | 0.531879i | ||||
\(363\) | 203.995 | + | 203.995i | 0.561970 | + | 0.561970i | ||||
\(364\) | 55.7225 | − | 23.3645i | 0.153084 | − | 0.0641883i | ||||
\(365\) | 28.5956 | − | 22.2980i | 0.0783442 | − | 0.0610904i | ||||
\(366\) | 104.060 | − | 180.237i | 0.284317 | − | 0.492451i | ||||
\(367\) | 377.829 | + | 101.239i | 1.02951 | + | 0.275856i | 0.733759 | − | 0.679410i | \(-0.237764\pi\) |
0.295749 | + | 0.955266i | \(0.404431\pi\) | |||||||
\(368\) | −17.9866 | + | 67.1270i | −0.0488767 | + | 0.182410i | ||||
\(369\) | 111.616 | + | 64.4414i | 0.302482 | + | 0.174638i | ||||
\(370\) | 128.661 | + | 15.9207i | 0.347733 | + | 0.0430289i | ||||
\(371\) | 230.244 | + | 549.114i | 0.620605 | + | 1.48009i | ||||
\(372\) | −111.648 | + | 111.648i | −0.300130 | + | 0.300130i | ||||
\(373\) | −28.3802 | + | 7.60446i | −0.0760864 | + | 0.0203873i | −0.296661 | − | 0.954983i | \(-0.595873\pi\) |
0.220575 | + | 0.975370i | \(0.429207\pi\) | |||||||
\(374\) | −231.032 | + | 133.386i | −0.617731 | + | 0.356647i | ||||
\(375\) | 174.797 | + | 127.754i | 0.466125 | + | 0.340677i | ||||
\(376\) | −61.8490 | + | 107.126i | −0.164492 | + | 0.284909i | ||||
\(377\) | 109.517 | − | 109.517i | 0.290497 | − | 0.290497i | ||||
\(378\) | 50.9696 | − | 6.93520i | 0.134840 | − | 0.0183471i | ||||
\(379\) | 469.896i | 1.23983i | 0.784668 | + | 0.619916i | \(0.212833\pi\) | ||||
−0.784668 | + | 0.619916i | \(0.787167\pi\) | |||||||
\(380\) | −52.9331 | − | 39.9662i | −0.139298 | − | 0.105174i | ||||
\(381\) | −56.4922 | − | 97.8474i | −0.148274 | − | 0.256817i | ||||
\(382\) | 222.397 | + | 59.5911i | 0.582191 | + | 0.155998i | ||||
\(383\) | −524.588 | + | 140.563i | −1.36968 | + | 0.367005i | −0.867362 | − | 0.497678i | \(-0.834186\pi\) |
−0.502318 | + | 0.864683i | \(0.667519\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −302.966 | − | 510.367i | −0.786925 | − | 1.32563i | ||||
\(386\) | −327.216 | −0.847709 | ||||||||
\(387\) | 2.18109 | + | 8.13994i | 0.00563589 | + | 0.0210334i | ||||
\(388\) | 29.1021 | − | 108.610i | 0.0750053 | − | 0.279924i | ||||
\(389\) | −329.553 | + | 190.268i | −0.847180 | + | 0.489120i | −0.859699 | − | 0.510802i | \(-0.829349\pi\) |
0.0125180 | + | 0.999922i | \(0.496015\pi\) | |||||||
\(390\) | 7.30720 | + | 52.3513i | 0.0187364 | + | 0.134234i | ||||
\(391\) | −193.265 | −0.494284 | ||||||||
\(392\) | −119.420 | + | 70.3345i | −0.304642 | + | 0.179425i | ||||
\(393\) | 123.679 | + | 123.679i | 0.314705 | + | 0.314705i | ||||
\(394\) | 304.619 | + | 175.872i | 0.773145 | + | 0.446375i | ||||
\(395\) | 79.8982 | + | 188.723i | 0.202274 | + | 0.477779i | ||||
\(396\) | 50.8729 | + | 88.1145i | 0.128467 | + | 0.222511i | ||||
\(397\) | −88.3122 | − | 329.585i | −0.222449 | − | 0.830190i | −0.983411 | − | 0.181393i | \(-0.941939\pi\) |
0.760962 | − | 0.648797i | \(-0.224727\pi\) | |||||||
\(398\) | −257.346 | − | 257.346i | −0.646598 | − | 0.646598i | ||||
\(399\) | −10.1507 | + | 79.7735i | −0.0254405 | + | 0.199934i | ||||
\(400\) | 96.9838 | + | 24.3750i | 0.242460 | + | 0.0609375i | ||||
\(401\) | −216.181 | + | 374.437i | −0.539105 | + | 0.933757i | 0.459848 | + | 0.887998i | \(0.347904\pi\) |
−0.998952 | + | 0.0457593i | \(0.985429\pi\) | |||||||
\(402\) | 148.934 | + | 39.9068i | 0.370484 | + | 0.0992708i | ||||
\(403\) | −50.9148 | + | 190.017i | −0.126340 | + | 0.471506i | ||||
\(404\) | −125.559 | − | 72.4916i | −0.310790 | − | 0.179435i | ||||
\(405\) | −5.52621 | + | 44.6594i | −0.0136450 | + | 0.110270i | ||||
\(406\) | −215.041 | + | 282.777i | −0.529658 | + | 0.696495i | ||||
\(407\) | 219.843 | − | 219.843i | 0.540155 | − | 0.540155i | ||||
\(408\) | −52.6392 | + | 14.1046i | −0.129018 | + | 0.0345702i | ||||
\(409\) | −219.191 | + | 126.550i | −0.535918 | + | 0.309413i | −0.743423 | − | 0.668821i | \(-0.766799\pi\) |
0.207505 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(410\) | 114.063 | − | 281.552i | 0.278203 | − | 0.686712i | ||||
\(411\) | −114.397 | + | 198.141i | −0.278337 | + | 0.482094i | ||||
\(412\) | 223.821 | − | 223.821i | 0.543255 | − | 0.543255i | ||||
\(413\) | 67.3905 | − | 164.711i | 0.163173 | − | 0.398817i | ||||
\(414\) | 73.7105i | 0.178045i | ||||||||
\(415\) | −107.473 | − | 769.975i | −0.258972 | − | 1.85536i | ||||
\(416\) | 12.2072 | + | 21.1435i | 0.0293443 | + | 0.0508258i | ||||
\(417\) | 83.2256 | + | 22.3002i | 0.199582 | + | 0.0534778i | ||||
\(418\) | −153.643 | + | 41.1684i | −0.367566 | + | 0.0984890i | ||||
\(419\) | − | 456.021i | − | 1.08835i | −0.838970 | − | 0.544177i | \(-0.816842\pi\) | ||
0.838970 | − | 0.544177i | \(-0.183158\pi\) | |||||||
\(420\) | −32.7972 | − | 116.723i | −0.0780885 | − | 0.277913i | ||||
\(421\) | 87.9279 | 0.208855 | 0.104427 | − | 0.994533i | \(-0.466699\pi\) | ||||
0.104427 | + | 0.994533i | \(0.466699\pi\) | |||||||
\(422\) | −98.7698 | − | 368.614i | −0.234052 | − | 0.873493i | ||||
\(423\) | −33.9575 | + | 126.731i | −0.0802777 | + | 0.299600i | ||||
\(424\) | −208.358 | + | 120.295i | −0.491409 | + | 0.283715i | ||||
\(425\) | 4.32947 | + | 278.066i | 0.0101870 | + | 0.654273i | ||||
\(426\) | 337.943 | 0.793293 | ||||||||
\(427\) | 80.1862 | + | 589.321i | 0.187790 | + | 1.38014i | ||||
\(428\) | 63.6040 | + | 63.6040i | 0.148608 | + | 0.148608i | ||||
\(429\) | 109.781 | + | 63.3823i | 0.255900 | + | 0.147744i | ||||
\(430\) | 18.2911 | − | 7.74379i | 0.0425375 | − | 0.0180088i | ||||
\(431\) | −368.932 | − | 639.009i | −0.855991 | − | 1.48262i | −0.875722 | − | 0.482815i | \(-0.839614\pi\) |
0.0197313 | − | 0.999805i | \(-0.493719\pi\) | |||||||
\(432\) | 5.37945 | + | 20.0764i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | 29.1869 | + | 29.1869i | 0.0674062 | + | 0.0674062i | 0.740006 | − | 0.672600i | \(-0.234823\pi\) |
−0.672600 | + | 0.740006i | \(0.734823\pi\) | |||||||
\(434\) | 56.9562 | − | 447.612i | 0.131236 | − | 1.03136i | ||||
\(435\) | −191.106 | − | 245.080i | −0.439324 | − | 0.563403i | ||||
\(436\) | −95.8608 | + | 166.036i | −0.219864 | + | 0.380816i | ||||
\(437\) | −111.308 | − | 29.8248i | −0.254708 | − | 0.0682489i | ||||
\(438\) | 4.59780 | − | 17.1592i | 0.0104973 | − | 0.0391763i | ||||
\(439\) | 353.707 | + | 204.213i | 0.805710 | + | 0.465177i | 0.845464 | − | 0.534033i | \(-0.179324\pi\) |
−0.0397539 | + | 0.999210i | \(0.512657\pi\) | |||||||
\(440\) | 189.118 | − | 147.468i | 0.429813 | − | 0.335155i | ||||
\(441\) | −103.040 | + | 104.842i | −0.233650 | + | 0.237737i | ||||
\(442\) | −48.0100 | + | 48.0100i | −0.108620 | + | 0.108620i | ||||
\(443\) | 572.880 | − | 153.503i | 1.29318 | − | 0.346507i | 0.454314 | − | 0.890841i | \(-0.349884\pi\) |
0.838869 | + | 0.544334i | \(0.183218\pi\) | |||||||
\(444\) | 55.0026 | − | 31.7558i | 0.123880 | − | 0.0715221i | ||||
\(445\) | 112.478 | + | 265.677i | 0.252759 | + | 0.597026i | ||||
\(446\) | −253.501 | + | 439.076i | −0.568387 | + | 0.984475i | ||||
\(447\) | 278.216 | − | 278.216i | 0.622408 | − | 0.622408i | ||||
\(448\) | −34.2829 | − | 44.2796i | −0.0765244 | − | 0.0988383i | ||||
\(449\) | − | 176.194i | − | 0.392415i | −0.980562 | − | 0.196208i | \(-0.937137\pi\) | ||
0.980562 | − | 0.196208i | \(-0.0628627\pi\) | |||||||
\(450\) | 106.053 | − | 1.65124i | 0.235674 | − | 0.00366943i | ||||
\(451\) | −364.258 | − | 630.913i | −0.807667 | − | 1.39892i | ||||
\(452\) | 236.613 | + | 63.4004i | 0.523481 | + | 0.140266i | ||||
\(453\) | 332.825 | − | 89.1802i | 0.734713 | − | 0.196866i | ||||
\(454\) | 19.6394i | 0.0432587i | ||||||||
\(455\) | −108.100 | − | 105.511i | −0.237582 | − | 0.231892i | ||||
\(456\) | −32.4932 | −0.0712571 | ||||||||
\(457\) | −13.4496 | − | 50.1945i | −0.0294302 | − | 0.109835i | 0.949648 | − | 0.313318i | \(-0.101441\pi\) |
−0.979078 | + | 0.203483i | \(0.934774\pi\) | |||||||
\(458\) | −131.413 | + | 490.442i | −0.286929 | + | 1.07083i | ||||
\(459\) | −50.0579 | + | 28.9010i | −0.109059 | + | 0.0629650i | ||||
\(460\) | 172.069 | − | 24.0174i | 0.374064 | − | 0.0522118i | ||||
\(461\) | −420.947 | −0.913117 | −0.456558 | − | 0.889693i | \(-0.650918\pi\) | ||||
−0.456558 | + | 0.889693i | \(0.650918\pi\) | |||||||
\(462\) | −269.110 | − | 110.105i | −0.582489 | − | 0.238322i | ||||
\(463\) | −45.3241 | − | 45.3241i | −0.0978921 | − | 0.0978921i | 0.656465 | − | 0.754357i | \(-0.272051\pi\) |
−0.754357 | + | 0.656465i | \(0.772051\pi\) | |||||||
\(464\) | −124.313 | − | 71.7721i | −0.267916 | − | 0.154681i | ||||
\(465\) | 365.854 | + | 148.216i | 0.786782 | + | 0.318743i | ||||
\(466\) | 150.211 | + | 260.173i | 0.322342 | + | 0.558312i | ||||
\(467\) | 137.330 | + | 512.522i | 0.294068 | + | 1.09748i | 0.941954 | + | 0.335741i | \(0.108987\pi\) |
−0.647886 | + | 0.761737i | \(0.724347\pi\) | |||||||
\(468\) | 18.3108 | + | 18.3108i | 0.0391257 | + | 0.0391257i | ||||
\(469\) | −406.354 | + | 170.385i | −0.866426 | + | 0.363294i | ||||
\(470\) | 306.904 | + | 37.9767i | 0.652988 | + | 0.0808015i | ||||
\(471\) | 240.902 | − | 417.254i | 0.511468 | − | 0.885889i | ||||
\(472\) | 69.4582 | + | 18.6113i | 0.147157 | + | 0.0394306i | ||||
\(473\) | 12.3287 | − | 46.0114i | 0.0260649 | − | 0.0972756i | ||||
\(474\) | 86.9482 | + | 50.1996i | 0.183435 | + | 0.105906i | ||||
\(475\) | −40.4178 | + | 160.815i | −0.0850900 | + | 0.338558i | ||||
\(476\) | 94.2694 | − | 123.963i | 0.198045 | − | 0.260427i | ||||
\(477\) | −180.443 | + | 180.443i | −0.378287 | + | 0.378287i | ||||
\(478\) | 199.278 | − | 53.3964i | 0.416900 | − | 0.111708i | ||||
\(479\) | 287.563 | − | 166.025i | 0.600340 | − | 0.346607i | −0.168835 | − | 0.985644i | \(-0.554001\pi\) |
0.769175 | + | 0.639038i | \(0.220667\pi\) | |||||||
\(480\) | 45.1134 | − | 19.0993i | 0.0939862 | − | 0.0397903i | ||||
\(481\) | 39.5644 | − | 68.5275i | 0.0822544 | − | 0.142469i | ||||
\(482\) | 264.742 | − | 264.742i | 0.549258 | − | 0.549258i | ||||
\(483\) | −128.956 | − | 166.559i | −0.266990 | − | 0.344842i | ||||
\(484\) | − | 333.123i | − | 0.688270i | ||||||
\(485\) | −278.405 | + | 38.8598i | −0.574032 | + | 0.0801234i | ||||
\(486\) | 11.0227 | + | 19.0919i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −718.303 | − | 192.469i | −1.47496 | − | 0.395213i | −0.570328 | − | 0.821417i | \(-0.693184\pi\) |
−0.904627 | + | 0.426204i | \(0.859851\pi\) | |||||||
\(488\) | −232.127 | + | 62.1984i | −0.475671 | + | 0.127456i | ||||
\(489\) | 363.405i | 0.743160i | ||||||||
\(490\) | 278.316 | + | 206.374i | 0.567992 | + | 0.421171i | ||||
\(491\) | 46.6728 | 0.0950567 | 0.0475284 | − | 0.998870i | \(-0.484866\pi\) | ||||
0.0475284 | + | 0.998870i | \(0.484866\pi\) | |||||||
\(492\) | −38.5177 | − | 143.750i | −0.0782880 | − | 0.292175i | ||||
\(493\) | 103.320 | − | 385.594i | 0.209573 | − | 0.782137i | ||||
\(494\) | −35.0594 | + | 20.2416i | −0.0709705 | + | 0.0409748i | ||||
\(495\) | 153.272 | − | 203.000i | 0.309640 | − | 0.410101i | ||||
\(496\) | 182.321 | 0.367582 | ||||||||
\(497\) | −763.627 | + | 591.229i | −1.53647 | + | 1.18959i | ||||
\(498\) | −269.313 | − | 269.313i | −0.540789 | − | 0.540789i | ||||
\(499\) | 216.276 | + | 124.867i | 0.433418 | + | 0.250234i | 0.700802 | − | 0.713356i | \(-0.252826\pi\) |
−0.267384 | + | 0.963590i | \(0.586159\pi\) | |||||||
\(500\) | −38.4104 | − | 247.032i | −0.0768209 | − | 0.494063i | ||||
\(501\) | −18.1878 | − | 31.5021i | −0.0363029 | − | 0.0628785i | ||||
\(502\) | −110.490 | − | 412.354i | −0.220099 | − | 0.821422i | ||||
\(503\) | −77.7709 | − | 77.7709i | −0.154614 | − | 0.154614i | 0.625561 | − | 0.780175i | \(-0.284870\pi\) |
−0.780175 | + | 0.625561i | \(0.784870\pi\) | |||||||
\(504\) | −47.2791 | − | 35.9540i | −0.0938077 | − | 0.0713372i | ||||
\(505\) | −44.5115 | + | 359.715i | −0.0881416 | + | 0.712306i | ||||
\(506\) | 208.326 | − | 360.831i | 0.411712 | − | 0.713106i | ||||
\(507\) | −251.579 | − | 67.4104i | −0.496211 | − | 0.132959i | ||||
\(508\) | −33.7664 | + | 126.018i | −0.0664692 | + | 0.248066i | ||||
\(509\) | −269.664 | − | 155.690i | −0.529791 | − | 0.305875i | 0.211140 | − | 0.977456i | \(-0.432282\pi\) |
−0.740931 | + | 0.671581i | \(0.765616\pi\) | |||||||
\(510\) | 83.7768 | + | 107.438i | 0.164268 | + | 0.210663i | ||||
\(511\) | 19.6306 | + | 46.8173i | 0.0384160 | + | 0.0916190i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −33.2900 | + | 8.92002i | −0.0648927 | + | 0.0173879i | ||||
\(514\) | −144.907 | + | 83.6620i | −0.281920 | + | 0.162767i | ||||
\(515\) | −733.426 | − | 297.128i | −1.42413 | − | 0.576947i | ||||
\(516\) | 4.86538 | − | 8.42708i | 0.00942903 | − | 0.0163316i | ||||
\(517\) | 524.407 | − | 524.407i | 1.01433 | − | 1.01433i | ||||
\(518\) | −68.7293 | + | 167.983i | −0.132682 | + | 0.324292i | ||||
\(519\) | − | 221.629i | − | 0.427030i | ||||||
\(520\) | 36.7784 | − | 48.7110i | 0.0707276 | − | 0.0936749i | ||||
\(521\) | 146.921 | + | 254.474i | 0.281997 | + | 0.488434i | 0.971877 | − | 0.235491i | \(-0.0756698\pi\) |
−0.689879 | + | 0.723924i | \(0.742336\pi\) | |||||||
\(522\) | −147.064 | − | 39.4056i | −0.281732 | − | 0.0754897i | ||||
\(523\) | −27.8292 | + | 7.45680i | −0.0532106 | + | 0.0142577i | −0.285326 | − | 0.958430i | \(-0.592102\pi\) |
0.232116 | + | 0.972688i | \(0.425435\pi\) | |||||||
\(524\) | − | 201.967i | − | 0.385433i | ||||||
\(525\) | −236.752 | + | 189.270i | −0.450957 | + | 0.360515i | ||||
\(526\) | 480.891 | 0.914242 | ||||||||
\(527\) | 131.230 | + | 489.757i | 0.249013 | + | 0.929330i | ||||
\(528\) | 30.4076 | − | 113.483i | 0.0575902 | − | 0.214929i | ||||
\(529\) | −196.720 | + | 113.577i | −0.371872 | + | 0.214700i | ||||
\(530\) | 480.019 | + | 362.430i | 0.905696 | + | 0.683830i | ||||
\(531\) | 76.2704 | 0.143635 | ||||||||
\(532\) | 73.4228 | − | 56.8467i | 0.138013 | − | 0.106855i | ||||
\(533\) | −131.108 | − | 131.108i | −0.245982 | − | 0.245982i | ||||
\(534\) | 122.402 | + | 70.6691i | 0.229218 | + | 0.132339i | ||||
\(535\) | 84.4358 | − | 208.420i | 0.157824 | − | 0.389571i | ||||
\(536\) | −89.0206 | − | 154.188i | −0.166083 | − | 0.287665i | ||||
\(537\) | −66.4860 | − | 248.129i | −0.123810 | − | 0.462066i | ||||
\(538\) | −369.484 | − | 369.484i | −0.686773 | − | 0.686773i | ||||
\(539\) | 800.716 | − | 222.010i | 1.48556 | − | 0.411892i | ||||
\(540\) | 40.9764 | − | 31.9521i | 0.0758822 | − | 0.0591706i | ||||
\(541\) | 429.327 | − | 743.616i | 0.793580 | − | 1.37452i | −0.130157 | − | 0.991493i | \(-0.541548\pi\) |
0.923737 | − | 0.383028i | \(-0.125119\pi\) | |||||||
\(542\) | 374.329 | + | 100.301i | 0.690643 | + | 0.185057i | ||||
\(543\) | −63.1858 | + | 235.812i | −0.116364 | + | 0.434277i | ||||
\(544\) | 54.4962 | + | 31.4634i | 0.100177 | + | 0.0578371i | ||||
\(545\) | 475.676 | + | 58.8607i | 0.872800 | + | 0.108001i | ||||
\(546\) | −73.4104 | − | 9.34108i | −0.134451 | − | 0.0171082i | ||||
\(547\) | −579.972 | + | 579.972i | −1.06028 | + | 1.06028i | −0.0622157 | + | 0.998063i | \(0.519817\pi\) |
−0.998063 | + | 0.0622157i | \(0.980183\pi\) | |||||||
\(548\) | 255.185 | − | 68.3767i | 0.465667 | − | 0.124775i | ||||
\(549\) | −220.744 | + | 127.447i | −0.402084 | + | 0.232144i | ||||
\(550\) | −523.823 | − | 291.652i | −0.952406 | − | 0.530276i | ||||
\(551\) | 119.010 | − | 206.131i | 0.215989 | − | 0.374104i | ||||
\(552\) | 60.1844 | − | 60.1844i | 0.109030 | − | 0.109030i | ||||
\(553\) | −284.295 | + | 38.6827i | −0.514095 | + | 0.0699506i | ||||
\(554\) | 79.5717i | 0.143631i | ||||||||
\(555\) | −126.716 | − | 95.6750i | −0.228318 | − | 0.172387i | ||||
\(556\) | −49.7454 | − | 86.1615i | −0.0894701 | − | 0.154967i | ||||
\(557\) | −877.073 | − | 235.011i | −1.57464 | − | 0.421923i | −0.637377 | − | 0.770552i | \(-0.719981\pi\) |
−0.937261 | + | 0.348629i | \(0.886647\pi\) | |||||||
\(558\) | 186.791 | − | 50.0505i | 0.334751 | − | 0.0896963i | ||||
\(559\) | − | 12.1235i | − | 0.0216878i | ||||||
\(560\) | −68.5255 | + | 122.083i | −0.122367 | + | 0.218005i | ||||
\(561\) | 326.728 | 0.582403 | ||||||||
\(562\) | 195.826 | + | 730.834i | 0.348446 | + | 1.30042i | ||||
\(563\) | 23.9322 | − | 89.3163i | 0.0425084 | − | 0.158644i | −0.941409 | − | 0.337267i | \(-0.890498\pi\) |
0.983918 | + | 0.178623i | \(0.0571643\pi\) | |||||||
\(564\) | 131.202 | − | 75.7493i | 0.232627 | − | 0.134307i | ||||
\(565\) | −84.6582 | − | 606.521i | −0.149837 | − | 1.07349i | ||||
\(566\) | −286.497 | −0.506178 | ||||||||
\(567\) | −58.3084 | − | 23.8565i | −0.102837 | − | 0.0420750i | ||||
\(568\) | −275.929 | − | 275.929i | −0.485791 | − | 0.485791i | ||||
\(569\) | −579.130 | − | 334.361i | −1.01780 | − | 0.587628i | −0.104336 | − | 0.994542i | \(-0.533272\pi\) |
−0.913467 | + | 0.406914i | \(0.866605\pi\) | |||||||
\(570\) | 31.6698 | + | 74.8054i | 0.0555611 | + | 0.131237i | ||||
\(571\) | 47.9078 | + | 82.9787i | 0.0839016 | + | 0.145322i | 0.904923 | − | 0.425576i | \(-0.139929\pi\) |
−0.821021 | + | 0.570898i | \(0.806595\pi\) | |||||||
\(572\) | −37.8847 | − | 141.387i | −0.0662319 | − | 0.247181i | ||||
\(573\) | −199.396 | − | 199.396i | −0.347985 | − | 0.347985i | ||||
\(574\) | 338.525 | + | 257.436i | 0.589766 | + | 0.448494i | ||||
\(575\) | −223.001 | − | 372.726i | −0.387829 | − | 0.648219i | ||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 411.220 | + | 110.186i | 0.712686 | + | 0.190964i | 0.596906 | − | 0.802311i | \(-0.296397\pi\) |
0.115780 | + | 0.993275i | \(0.463063\pi\) | |||||||
\(578\) | 60.4883 | − | 225.745i | 0.104651 | − | 0.390563i | ||||
\(579\) | 347.065 | + | 200.378i | 0.599421 | + | 0.346076i | ||||
\(580\) | −44.0697 | + | 356.144i | −0.0759823 | + | 0.614042i | ||||
\(581\) | 1079.71 | + | 137.387i | 1.85836 | + | 0.236467i | ||||
\(582\) | −97.3774 | + | 97.3774i | −0.167315 | + | 0.167315i | ||||
\(583\) | 1393.29 | − | 373.332i | 2.38987 | − | 0.640364i | ||||
\(584\) | −17.7645 | + | 10.2564i | −0.0304187 | + | 0.0175622i | ||||
\(585\) | 24.3080 | − | 60.0017i | 0.0415522 | − | 0.102567i | ||||
\(586\) | 225.228 | − | 390.106i | 0.384348 | − | 0.665710i | ||||
\(587\) | 139.731 | − | 139.731i | 0.238042 | − | 0.238042i | −0.577997 | − | 0.816039i | \(-0.696165\pi\) |
0.816039 | + | 0.577997i | \(0.196165\pi\) | |||||||
\(588\) | 169.735 | − | 1.47170i | 0.288664 | − | 0.00250290i | ||||
\(589\) | 302.318i | 0.513273i | ||||||||
\(590\) | −24.8515 | − | 178.045i | −0.0421212 | − | 0.301771i | ||||
\(591\) | −215.398 | − | 373.081i | −0.364464 | − | 0.631270i | ||||
\(592\) | −70.8380 | − | 18.9810i | −0.119659 | − | 0.0320625i | ||||
\(593\) | 358.740 | − | 96.1240i | 0.604957 | − | 0.162098i | 0.0566772 | − | 0.998393i | \(-0.481949\pi\) |
0.548280 | + | 0.836295i | \(0.315283\pi\) | |||||||
\(594\) | − | 124.613i | − | 0.209786i | ||||||
\(595\) | −377.267 | − | 96.2033i | −0.634061 | − | 0.161686i | ||||
\(596\) | −454.325 | −0.762291 | ||||||||
\(597\) | 115.365 | + | 430.548i | 0.193241 | + | 0.721186i | ||||
\(598\) | 27.4458 | − | 102.429i | 0.0458960 | − | 0.171286i | ||||
\(599\) | 612.367 | − | 353.550i | 1.02232 | − | 0.590234i | 0.107542 | − | 0.994201i | \(-0.465702\pi\) |
0.914774 | + | 0.403966i | \(0.132369\pi\) | |||||||
\(600\) | −87.9403 | − | 85.2438i | −0.146567 | − | 0.142073i | ||||
\(601\) | −568.154 | −0.945347 | −0.472674 | − | 0.881238i | \(-0.656711\pi\) | ||||
−0.472674 | + | 0.881238i | \(0.656711\pi\) | |||||||
\(602\) | 3.74915 | + | 27.5541i | 0.00622783 | + | 0.0457709i | ||||
\(603\) | −133.531 | − | 133.531i | −0.221444 | − | 0.221444i | ||||
\(604\) | −344.566 | − | 198.935i | −0.570473 | − | 0.329363i | ||||
\(605\) | −766.909 | + | 324.681i | −1.26762 | + | 0.536663i | ||||
\(606\) | 88.7838 | + | 153.778i | 0.146508 | + | 0.253759i | ||||
\(607\) | 68.8578 | + | 256.981i | 0.113439 | + | 0.423362i | 0.999165 | − | 0.0408466i | \(-0.0130055\pi\) |
−0.885726 | + | 0.464209i | \(0.846339\pi\) | |||||||
\(608\) | 26.5306 | + | 26.5306i | 0.0436359 | + | 0.0436359i | ||||
\(609\) | 401.250 | − | 168.245i | 0.658867 | − | 0.276264i | ||||
\(610\) | 369.437 | + | 473.777i | 0.605634 | + | 0.776684i | ||||
\(611\) | 94.3756 | − | 163.463i | 0.154461 | − | 0.267534i | ||||
\(612\) | 64.4696 | + | 17.2746i | 0.105343 | + | 0.0282265i | ||||
\(613\) | −212.919 | + | 794.625i | −0.347340 | + | 1.29629i | 0.542515 | + | 0.840046i | \(0.317472\pi\) |
−0.889855 | + | 0.456243i | \(0.849195\pi\) | |||||||
\(614\) | 509.812 | + | 294.340i | 0.830312 | + | 0.479381i | ||||
\(615\) | −293.397 | + | 228.782i | −0.477068 | + | 0.372003i | ||||
\(616\) | 129.827 | + | 309.627i | 0.210758 | + | 0.502642i | ||||
\(617\) | −49.7691 | + | 49.7691i | −0.0806631 | + | 0.0806631i | −0.746287 | − | 0.665624i | \(-0.768165\pi\) |
0.665624 | + | 0.746287i | \(0.268165\pi\) | |||||||
\(618\) | −374.460 | + | 100.336i | −0.605922 | + | 0.162356i | ||||
\(619\) | 309.731 | − | 178.823i | 0.500373 | − | 0.288891i | −0.228494 | − | 0.973545i | \(-0.573380\pi\) |
0.728868 | + | 0.684655i | \(0.240047\pi\) | |||||||
\(620\) | −177.701 | − | 419.736i | −0.286614 | − | 0.676993i | ||||
\(621\) | 45.1383 | − | 78.1818i | 0.0726865 | − | 0.125897i | ||||
\(622\) | 233.972 | − | 233.972i | 0.376160 | − | 0.376160i | ||||
\(623\) | −400.219 | + | 54.4560i | −0.642407 | + | 0.0874093i | ||||
\(624\) | − | 29.9015i | − | 0.0479190i | ||||||
\(625\) | −531.275 | + | 329.199i | −0.850039 | + | 0.526719i | ||||
\(626\) | −100.499 | − | 174.070i | −0.160542 | − | 0.278067i | ||||
\(627\) | 188.173 | + | 50.4208i | 0.300116 | + | 0.0804159i | ||||
\(628\) | −537.382 | + | 143.991i | −0.855703 | + | 0.229285i | ||||
\(629\) | − | 203.949i | − | 0.324244i | ||||||
\(630\) | −36.6915 | + | 143.888i | −0.0582406 | + | 0.228394i | ||||
\(631\) | −35.2671 | −0.0558908 | −0.0279454 | − | 0.999609i | \(-0.508896\pi\) | ||||
−0.0279454 | + | 0.999609i | \(0.508896\pi\) | |||||||
\(632\) | −30.0051 | − | 111.981i | −0.0474765 | − | 0.177185i | ||||
\(633\) | −120.968 | + | 451.458i | −0.191102 | + | 0.713204i | ||||
\(634\) | −85.9264 | + | 49.6096i | −0.135531 | + | 0.0782486i | ||||
\(635\) | 323.026 | − | 45.0880i | 0.508703 | − | 0.0710048i | ||||
\(636\) | 294.662 | 0.463305 | ||||||||
\(637\) | 182.223 | − | 107.324i | 0.286064 | − | 0.168483i | ||||
\(638\) | 608.543 | + | 608.543i | 0.953829 | + | 0.953829i | ||||
\(639\) | −358.443 | − | 206.947i | −0.560943 | − | 0.323861i | ||||
\(640\) | −52.4294 | − | 21.2404i | −0.0819210 | − | 0.0331881i | ||||
\(641\) | 154.470 | + | 267.550i | 0.240983 | + | 0.417394i | 0.960995 | − | 0.276567i | \(-0.0891969\pi\) |
−0.720012 | + | 0.693962i | \(0.755864\pi\) | |||||||
\(642\) | −28.5129 | − | 106.412i | −0.0444126 | − | 0.165750i | ||||
\(643\) | 356.455 | + | 356.455i | 0.554362 | + | 0.554362i | 0.927697 | − | 0.373335i | \(-0.121786\pi\) |
−0.373335 | + | 0.927697i | \(0.621786\pi\) | |||||||
\(644\) | −30.7025 | + | 241.287i | −0.0476746 | + | 0.374669i | ||||
\(645\) | −24.1428 | − | 2.98745i | −0.0374306 | − | 0.00463171i | ||||
\(646\) | −52.1714 | + | 90.3636i | −0.0807607 | + | 0.139882i | ||||
\(647\) | 297.486 | + | 79.7113i | 0.459794 | + | 0.123201i | 0.481278 | − | 0.876568i | \(-0.340173\pi\) |
−0.0214847 | + | 0.999769i | \(0.506839\pi\) | |||||||
\(648\) | 6.58846 | − | 24.5885i | 0.0101674 | − | 0.0379452i | ||||
\(649\) | −373.362 | − | 215.561i | −0.575289 | − | 0.332143i | ||||
\(650\) | −147.988 | − | 37.1939i | −0.227674 | − | 0.0572214i | ||||
\(651\) | −334.516 | + | 439.886i | −0.513850 | + | 0.675708i | ||||
\(652\) | 296.719 | − | 296.719i | 0.455091 | − | 0.455091i | ||||
\(653\) | 23.9141 | − | 6.40777i | 0.0366219 | − | 0.00981282i | −0.240462 | − | 0.970659i | \(-0.577299\pi\) |
0.277083 | + | 0.960846i | \(0.410632\pi\) | |||||||
\(654\) | 203.352 | − | 117.405i | 0.310935 | − | 0.179518i | ||||
\(655\) | −464.965 | + | 196.849i | −0.709870 | + | 0.300533i | ||||
\(656\) | −85.9218 | + | 148.821i | −0.130978 | + | 0.226861i | ||||
\(657\) | −15.3845 | + | 15.3845i | −0.0234163 | + | 0.0234163i | ||||
\(658\) | −163.945 | + | 400.702i | −0.249156 | + | 0.608969i | ||||
\(659\) | 392.819i | 0.596083i | 0.954553 | + | 0.298042i | \(0.0963334\pi\) | ||||
−0.954553 | + | 0.298042i | \(0.903667\pi\) | |||||||
\(660\) | −290.895 | + | 40.6031i | −0.440750 | + | 0.0615199i | ||||
\(661\) | 630.880 | + | 1092.72i | 0.954433 | + | 1.65313i | 0.735661 | + | 0.677350i | \(0.236872\pi\) |
0.218772 | + | 0.975776i | \(0.429795\pi\) | |||||||
\(662\) | 348.953 | + | 93.5016i | 0.527119 | + | 0.141241i | ||||
\(663\) | 80.3224 | − | 21.5223i | 0.121150 | − | 0.0324620i | ||||
\(664\) | 439.786i | 0.662329i | ||||||||
\(665\) | −202.434 | − | 113.626i | −0.304412 | − | 0.170867i | ||||
\(666\) | −77.7855 | −0.116795 | ||||||||
\(667\) | 161.367 | + | 602.231i | 0.241930 | + | 0.902895i | ||||
\(668\) | −10.8711 | + | 40.5716i | −0.0162741 | + | 0.0607360i | ||||
\(669\) | 537.756 | − | 310.474i | 0.803821 | − | 0.464086i | ||||
\(670\) | −268.205 | + | 355.223i | −0.400305 | + | 0.530183i | ||||
\(671\) | 1440.80 | 2.14724 | ||||||||
\(672\) | 9.24694 | + | 67.9595i | 0.0137603 | + | 0.101130i | ||||
\(673\) | −848.161 | − | 848.161i | −1.26027 | − | 1.26027i | −0.950962 | − | 0.309306i | \(-0.899903\pi\) |
−0.309306 | − | 0.950962i | \(-0.600097\pi\) | |||||||
\(674\) | 4.23481 | + | 2.44497i | 0.00628310 | + | 0.00362755i | ||||
\(675\) | −113.498 | − | 63.1926i | −0.168145 | − | 0.0936187i | ||||
\(676\) | 150.373 | + | 260.454i | 0.222445 | + | 0.385286i | ||||
\(677\) | 196.826 | + | 734.564i | 0.290732 | + | 1.08503i | 0.944548 | + | 0.328374i | \(0.106501\pi\) |
−0.653815 | + | 0.756654i | \(0.726833\pi\) | |||||||
\(678\) | −212.142 | − | 212.142i | −0.312893 | − | 0.312893i | ||||
\(679\) | 49.6761 | − | 390.398i | 0.0731607 | − | 0.574961i | ||||
\(680\) | 19.3192 | − | 156.126i | 0.0284106 | − | 0.229597i | ||||
\(681\) | 12.0267 | − | 20.8308i | 0.0176603 | − | 0.0305885i | ||||
\(682\) | −1055.85 | − | 282.913i | −1.54816 | − | 0.414828i | ||||
\(683\) | −59.8436 | + | 223.339i | −0.0876187 | + | 0.326997i | −0.995797 | − | 0.0915857i | \(-0.970806\pi\) |
0.908179 | + | 0.418583i | \(0.137473\pi\) | |||||||
\(684\) | 34.4643 | + | 19.8980i | 0.0503864 | + | 0.0290906i | ||||
\(685\) | −406.134 | − | 520.839i | −0.592897 | − | 0.760349i | ||||
\(686\) | −380.963 | + | 300.275i | −0.555340 | + | 0.437719i | ||||
\(687\) | 439.718 | − | 439.718i | 0.640055 | − | 0.640055i | ||||
\(688\) | −10.8532 | + | 2.90812i | −0.0157751 | + | 0.00422692i | ||||
\(689\) | 317.933 | − | 183.559i | 0.461442 | − | 0.266413i | ||||
\(690\) | −197.215 | − | 79.8962i | −0.285818 | − | 0.115792i | ||||
\(691\) | −536.360 | + | 929.003i | −0.776209 | + | 1.34443i | 0.157904 | + | 0.987455i | \(0.449526\pi\) |
−0.934112 | + | 0.356979i | \(0.883807\pi\) | |||||||
\(692\) | −180.959 | + | 180.959i | −0.261501 | + | 0.261501i | ||||
\(693\) | 218.009 | + | 281.579i | 0.314587 | + | 0.406319i | ||||
\(694\) | − | 746.570i | − | 1.07575i | ||||||
\(695\) | −149.875 | + | 198.501i | −0.215647 | + | 0.285613i | ||||
\(696\) | 87.9026 | + | 152.252i | 0.126297 | + | 0.218752i | ||||
\(697\) | −461.612 | − | 123.689i | −0.662285 | − | 0.177459i | ||||
\(698\) | 101.121 | − | 27.0953i | 0.144872 | − | 0.0388185i | ||||
\(699\) | − | 367.941i | − | 0.526382i | ||||||
\(700\) | 347.846 | + | 38.7688i | 0.496923 | + | 0.0553840i | ||||
\(701\) | 708.751 | 1.01106 | 0.505528 | − | 0.862810i | \(-0.331298\pi\) | ||||
0.505528 | + | 0.862810i | \(0.331298\pi\) | |||||||
\(702\) | −8.20852 | − | 30.6346i | −0.0116930 | − | 0.0436391i | ||||
\(703\) | 31.4736 | − | 117.461i | 0.0447704 | − | 0.167085i | ||||
\(704\) | −117.486 | + | 67.8305i | −0.166883 | + | 0.0963502i | ||||
\(705\) | −302.265 | − | 228.220i | −0.428745 | − | 0.323717i | ||||
\(706\) | −405.953 | −0.575004 | ||||||||
\(707\) | −469.652 | − | 192.155i | −0.664289 | − | 0.271790i | ||||
\(708\) | −62.2745 | − | 62.2745i | −0.0879584 | − | 0.0879584i | ||||
\(709\) | −328.423 | − | 189.615i | −0.463220 | − | 0.267440i | 0.250177 | − | 0.968200i | \(-0.419511\pi\) |
−0.713397 | + | 0.700760i | \(0.752844\pi\) | |||||||
\(710\) | −366.302 | + | 904.176i | −0.515919 | + | 1.27349i | ||||
\(711\) | −61.4817 | − | 106.489i | −0.0864721 | − | 0.149774i | ||||
\(712\) | −42.2401 | − | 157.642i | −0.0593260 | − | 0.221408i | ||||
\(713\) | −559.957 | − | 559.957i | −0.785354 | − | 0.785354i | ||||
\(714\) | −175.900 | + | 73.7550i | −0.246358 | + | 0.103298i | ||||
\(715\) | −288.575 | + | 225.022i | −0.403601 | + | 0.314716i | ||||
\(716\) | −148.311 | + | 256.882i | −0.207138 | + | 0.358774i | ||||
\(717\) | −244.065 | − | 65.3970i | −0.340397 | − | 0.0912092i | ||||
\(718\) | 241.375 | − | 900.824i | 0.336177 | − | 1.25463i | ||||
\(719\) | −498.664 | − | 287.904i | −0.693552 | − | 0.400422i | 0.111390 | − | 0.993777i | \(-0.464470\pi\) |
−0.804941 | + | 0.593355i | \(0.797803\pi\) | |||||||
\(720\) | −59.5459 | − | 7.36827i | −0.0827026 | − | 0.0102337i | ||||
\(721\) | 670.605 | − | 881.838i | 0.930103 | − | 1.22308i | ||||
\(722\) | 317.008 | − | 317.008i | 0.439069 | − | 0.439069i | ||||
\(723\) | −442.923 | + | 118.681i | −0.612618 | + | 0.164150i | ||||
\(724\) | 244.131 | − | 140.949i | 0.337198 | − | 0.194681i | ||||
\(725\) | 862.862 | − | 245.663i | 1.19015 | − | 0.338845i | ||||
\(726\) | −203.995 | + | 353.330i | −0.280985 | + | 0.486681i | ||||
\(727\) | 841.342 | − | 841.342i | 1.15728 | − | 1.15728i | 0.172220 | − | 0.985058i | \(-0.444906\pi\) |
0.985058 | − | 0.172220i | \(-0.0550941\pi\) | |||||||
\(728\) | 52.3124 | + | 67.5663i | 0.0718577 | + | 0.0928109i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 40.9263 | + | 30.9007i | 0.0560635 | + | 0.0423297i | ||||
\(731\) | −15.6238 | − | 27.0612i | −0.0213732 | − | 0.0370194i | ||||
\(732\) | 284.297 | + | 76.1771i | 0.388384 | + | 0.104067i | ||||
\(733\) | −434.189 | + | 116.341i | −0.592345 | + | 0.158718i | −0.542525 | − | 0.840040i | \(-0.682531\pi\) |
−0.0498201 | + | 0.998758i | \(0.515865\pi\) | |||||||
\(734\) | 553.181i | 0.753652i | ||||||||
\(735\) | −168.821 | − | 389.325i | −0.229689 | − | 0.529694i | ||||
\(736\) | −98.2807 | −0.133534 | ||||||||
\(737\) | 276.272 | + | 1031.06i | 0.374860 | + | 1.39900i | ||||
\(738\) | −47.1743 | + | 176.057i | −0.0639219 | + | 0.238560i | ||||
\(739\) | 725.131 | − | 418.655i | 0.981233 | − | 0.566515i | 0.0785910 | − | 0.996907i | \(-0.474958\pi\) |
0.902642 | + | 0.430392i | \(0.141625\pi\) | |||||||
\(740\) | 25.3452 | + | 181.582i | 0.0342503 | + | 0.245381i | ||||
\(741\) | 49.5815 | 0.0669116 | ||||||||
\(742\) | −665.828 | + | 515.509i | −0.897342 | + | 0.694756i | ||||
\(743\) | 241.494 | + | 241.494i | 0.325025 | + | 0.325025i | 0.850691 | − | 0.525666i | \(-0.176184\pi\) |
−0.525666 | + | 0.850691i | \(0.676184\pi\) | |||||||
\(744\) | −193.380 | − | 111.648i | −0.259920 | − | 0.150065i | ||||
\(745\) | 442.812 | + | 1045.94i | 0.594379 | + | 1.40395i | ||||
\(746\) | −20.7758 | − | 35.9847i | −0.0278495 | − | 0.0482368i | ||||
\(747\) | 120.730 | + | 450.569i | 0.161619 | + | 0.603172i | ||||
\(748\) | −266.772 | − | 266.772i | −0.356647 | − | 0.356647i | ||||
\(749\) | 250.595 | + | 190.568i | 0.334573 | + | 0.254430i | ||||
\(750\) | −110.535 | + | 285.538i | −0.147380 | + | 0.380718i | ||||
\(751\) | 157.587 | − | 272.949i | 0.209836 | − | 0.363447i | −0.741826 | − | 0.670592i | \(-0.766040\pi\) |
0.951663 | + | 0.307145i | \(0.0993735\pi\) | |||||||
\(752\) | −168.975 | − | 45.2766i | −0.224700 | − | 0.0602083i | ||||
\(753\) | −135.322 | + | 505.028i | −0.179710 | + | 0.670688i | ||||
\(754\) | 189.690 | + | 109.517i | 0.251578 | + | 0.145248i | ||||
\(755\) | −122.151 | + | 987.147i | −0.161789 | + | 1.30748i | ||||
\(756\) | 28.1298 | + | 67.0873i | 0.0372088 | + | 0.0887399i | ||||
\(757\) | −650.017 | + | 650.017i | −0.858675 | + | 0.858675i | −0.991182 | − | 0.132507i | \(-0.957697\pi\) |
0.132507 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(758\) | −641.890 | + | 171.994i | −0.846821 | + | 0.226905i | ||||
\(759\) | −441.926 | + | 255.146i | −0.582248 | + | 0.336161i | ||||
\(760\) | 35.2200 | − | 86.9366i | 0.0463421 | − | 0.114390i | ||||
\(761\) | 349.979 | − | 606.182i | 0.459894 | − | 0.796560i | −0.539061 | − | 0.842267i | \(-0.681221\pi\) |
0.998955 | + | 0.0457070i | \(0.0145541\pi\) | |||||||
\(762\) | 112.984 | − | 112.984i | 0.148274 | − | 0.148274i | ||||
\(763\) | −254.100 | + | 621.054i | −0.333028 | + | 0.813964i | ||||
\(764\) | 325.612i | 0.426193i | ||||||||
\(765\) | −23.0667 | − | 165.258i | −0.0301525 | − | 0.216023i | ||||
\(766\) | −384.025 | − | 665.150i | −0.501338 | − | 0.868343i | ||||
\(767\) | −105.986 | − | 28.3990i | −0.138183 | − | 0.0370260i | ||||
\(768\) | −26.7685 | + | 7.17260i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | − | 272.975i | − | 0.354974i | −0.984123 | − | 0.177487i | \(-0.943203\pi\) | ||
0.984123 | − | 0.177487i | \(-0.0567967\pi\) | |||||||
\(770\) | 586.281 | − | 600.667i | 0.761404 | − | 0.780087i | ||||
\(771\) | 204.929 | 0.265797 | ||||||||
\(772\) | −119.769 | − | 446.985i | −0.155142 | − | 0.578996i | ||||
\(773\) | 222.749 | − | 831.312i | 0.288162 | − | 1.07544i | −0.658335 | − | 0.752725i | \(-0.728739\pi\) |
0.946498 | − | 0.322711i | \(-0.104594\pi\) | |||||||
\(774\) | −10.3210 | + | 5.95885i | −0.0133347 | + | 0.00769877i | ||||
\(775\) | −793.110 | + | 818.198i | −1.02337 | + | 1.05574i | ||||
\(776\) | 159.017 | 0.204918 | ||||||||
\(777\) | 175.767 | − | 136.085i | 0.226212 | − | 0.175142i | ||||
\(778\) | −380.535 | − | 380.535i | −0.489120 | − | 0.489120i | ||||
\(779\) | −246.770 | − | 142.472i | −0.316777 | − | 0.182891i | ||||
\(780\) | −68.8386 | + | 29.1437i | −0.0882546 | + | 0.0373638i | ||||
\(781\) | 1169.78 | + | 2026.11i | 1.49779 | + | 2.59425i | ||||
\(782\) | −70.7400 | − | 264.005i | −0.0904603 | − | 0.337602i | ||||
\(783\) | 131.854 | + | 131.854i | 0.168396 | + | 0.168396i | ||||
\(784\) | −139.789 | − | 137.386i | −0.178303 | − | 0.175237i | ||||
\(785\) | 855.257 | + | 1096.81i | 1.08950 | + | 1.39721i | ||||
\(786\) | −123.679 | + | 214.218i | −0.157352 | + | 0.272542i | ||||
\(787\) | 559.283 | + | 149.860i | 0.710652 | + | 0.190419i | 0.595997 | − | 0.802987i | \(-0.296757\pi\) |
0.114655 | + | 0.993405i | \(0.463424\pi\) | |||||||
\(788\) | −128.747 | + | 480.491i | −0.163385 | + | 0.609760i | ||||
\(789\) | −510.062 | − | 294.484i | −0.646466 | − | 0.373238i | ||||
\(790\) | −228.555 | + | 178.220i | −0.289310 | + | 0.225595i | ||||
\(791\) | 850.503 | + | 108.222i | 1.07522 | + | 0.136817i | ||||
\(792\) | −101.746 | + | 101.746i | −0.128467 | + | 0.128467i | ||||
\(793\) | 354.204 | − | 94.9086i | 0.446663 | − | 0.119683i | ||||
\(794\) | 417.898 | − | 241.273i | 0.526319 | − | 0.303871i | ||||
\(795\) | −287.195 | − | 678.366i | −0.361252 | − | 0.853290i | ||||
\(796\) | 257.346 | − | 445.736i | 0.323299 | − | 0.559970i | ||||
\(797\) | −934.809 | + | 934.809i | −1.17291 | + | 1.17291i | −0.191396 | + | 0.981513i | \(0.561302\pi\) |
−0.981513 | + | 0.191396i | \(0.938698\pi\) | |||||||
\(798\) | −112.688 | + | 15.3329i | −0.141213 | + | 0.0192142i | ||||
\(799\) | − | 486.495i | − | 0.608879i | ||||||
\(800\) | 2.20166 | + | 141.404i | 0.00275207 | + | 0.176755i | ||||
\(801\) | −86.5516 | − | 149.912i | −0.108054 | − | 0.187156i | ||||
\(802\) | −590.618 | − | 158.256i | −0.736431 | − | 0.197326i | ||||
\(803\) | 118.792 | − | 31.8302i | 0.147935 | − | 0.0396391i | ||||
\(804\) | 218.055i | 0.271213i | ||||||||
\(805\) | 585.411 | − | 164.490i | 0.727218 | − | 0.204335i | ||||
\(806\) | −278.204 | −0.345166 | ||||||||
\(807\) | 165.635 | + | 618.158i | 0.205248 | + | 0.765996i | ||||
\(808\) | 53.0676 | − | 198.051i | 0.0656777 | − | 0.245112i | ||||
\(809\) | 185.686 | − | 107.206i | 0.229525 | − | 0.132516i | −0.380828 | − | 0.924646i | \(-0.624361\pi\) |
0.610353 | + | 0.792130i | \(0.291028\pi\) | |||||||
\(810\) | −63.0286 | + | 8.79753i | −0.0778131 | + | 0.0108612i | ||||
\(811\) | −527.675 | −0.650647 | −0.325324 | − | 0.945603i | \(-0.605473\pi\) | ||||
−0.325324 | + | 0.945603i | \(0.605473\pi\) | |||||||
\(812\) | −464.991 | − | 190.248i | −0.572649 | − | 0.234296i | ||||
\(813\) | −335.614 | − | 335.614i | −0.412809 | − | 0.412809i | ||||
\(814\) | 380.779 | + | 219.843i | 0.467788 | + | 0.270077i | ||||
\(815\) | −972.301 | − | 393.901i | −1.19301 | − | 0.483315i | ||||
\(816\) | −38.5346 | − | 66.7439i | −0.0472238 | − | 0.0817940i | ||||
\(817\) | −4.82214 | − | 17.9965i | −0.00590225 | − | 0.0220275i | ||||
\(818\) | −253.100 | − | 253.100i | −0.309413 | − | 0.309413i | ||||
\(819\) | 72.1433 | + | 54.8622i | 0.0880870 | + | 0.0669869i | ||||
\(820\) | 426.357 | + | 52.7579i | 0.519948 | + | 0.0643390i | ||||
\(821\) | −6.70379 | + | 11.6113i | −0.00816539 | + | 0.0141429i | −0.870079 | − | 0.492912i | \(-0.835932\pi\) |
0.861914 | + | 0.507055i | \(0.169266\pi\) | |||||||
\(822\) | −312.537 | − | 83.7441i | −0.380215 | − | 0.101878i | ||||
\(823\) | 148.804 | − | 555.346i | 0.180807 | − | 0.674782i | −0.814682 | − | 0.579908i | \(-0.803088\pi\) |
0.995489 | − | 0.0948742i | \(-0.0302449\pi\) | |||||||
\(824\) | 387.670 | + | 223.821i | 0.470473 | + | 0.271628i | ||||
\(825\) | 376.999 | + | 630.119i | 0.456969 | + | 0.763780i | ||||
\(826\) | 249.666 | + | 31.7687i | 0.302260 | + | 0.0384609i | ||||
\(827\) | 485.728 | − | 485.728i | 0.587337 | − | 0.587337i | −0.349572 | − | 0.936909i | \(-0.613673\pi\) |
0.936909 | + | 0.349572i | \(0.113673\pi\) | |||||||
\(828\) | −100.690 | + | 26.9799i | −0.121607 | + | 0.0325845i | ||||
\(829\) | −80.3994 | + | 46.4186i | −0.0969836 | + | 0.0559935i | −0.547707 | − | 0.836670i | \(-0.684499\pi\) |
0.450724 | + | 0.892663i | \(0.351166\pi\) | |||||||
\(830\) | 1012.47 | − | 428.642i | 1.21984 | − | 0.516436i | ||||
\(831\) | 48.7275 | − | 84.3986i | 0.0586372 | − | 0.101563i | ||||
\(832\) | −24.4144 | + | 24.4144i | −0.0293443 | + | 0.0293443i | ||||
\(833\) | 268.434 | − | 474.394i | 0.322250 | − | 0.569501i | ||||
\(834\) | 121.851i | 0.146104i | ||||||||
\(835\) | 103.999 | − | 14.5162i | 0.124550 | − | 0.0173846i | ||||
\(836\) | −112.474 | − | 194.811i | −0.134538 | − | 0.233028i | ||||
\(837\) | −228.772 | − | 61.2992i | −0.273323 | − | 0.0732367i | ||||
\(838\) | 622.936 | − | 166.915i | 0.743360 | − | 0.199183i | ||||
\(839\) | 1256.89i | 1.49808i | 0.662527 | + | 0.749038i | \(0.269484\pi\) | ||||
−0.662527 | + | 0.749038i | \(0.730516\pi\) | |||||||
\(840\) | 147.443 | − | 87.5255i | 0.175527 | − | 0.104197i | ||||
\(841\) | −446.810 | −0.531284 | ||||||||
\(842\) | 32.1839 | + | 120.112i | 0.0382231 | + | 0.142651i | ||||
\(843\) | 239.837 | − | 895.086i | 0.284505 | − | 1.06179i | ||||
\(844\) | 467.384 | − | 269.844i | 0.553772 | − | 0.319720i | ||||
\(845\) | 453.049 | − | 600.039i | 0.536153 | − | 0.710106i | ||||
\(846\) | −185.547 | −0.219323 | ||||||||
\(847\) | −157.194 | − | 1155.28i | −0.185589 | − | 1.36397i | ||||
\(848\) | −240.591 | − | 240.591i | −0.283715 | − | 0.283715i | ||||
\(849\) | 303.876 | + | 175.443i | 0.357922 | + | 0.206646i | ||||
\(850\) | −378.260 | + | 107.693i | −0.445012 | + | 0.126698i | ||||
\(851\) | 159.267 | + | 275.858i | 0.187153 | + | 0.324158i | ||||
\(852\) | 123.696 | + | 461.639i | 0.145183 | + | 0.541829i | ||||
\(853\) | −74.9889 | − | 74.9889i | −0.0879119 | − | 0.0879119i | 0.661783 | − | 0.749695i | \(-0.269800\pi\) |
−0.749695 | + | 0.661783i | \(0.769800\pi\) | |||||||
\(854\) | −775.678 | + | 325.243i | −0.908288 | + | 0.380847i | ||||
\(855\) | 12.2178 | − | 98.7368i | 0.0142898 | − | 0.115482i | ||||
\(856\) | −63.6040 | + | 110.165i | −0.0743038 | + | 0.128698i | ||||
\(857\) | 607.221 | + | 162.704i | 0.708542 | + | 0.189853i | 0.595054 | − | 0.803686i | \(-0.297131\pi\) |
0.113489 | + | 0.993539i | \(0.463797\pi\) | |||||||
\(858\) | −46.3990 | + | 173.164i | −0.0540781 | + | 0.201822i | ||||
\(859\) | −1187.28 | − | 685.475i | −1.38216 | − | 0.797991i | −0.389746 | − | 0.920922i | \(-0.627437\pi\) |
−0.992415 | + | 0.122931i | \(0.960771\pi\) | |||||||
\(860\) | 17.2732 | + | 22.1517i | 0.0200852 | + | 0.0257578i | ||||
\(861\) | −201.414 | − | 480.355i | −0.233930 | − | 0.557904i | ||||
\(862\) | 737.864 | − | 737.864i | 0.855991 | − | 0.855991i | ||||
\(863\) | 751.357 | − | 201.325i | 0.870634 | − | 0.233286i | 0.204272 | − | 0.978914i | \(-0.434517\pi\) |
0.666362 | + | 0.745629i | \(0.267851\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 592.974 | + | 240.227i | 0.685519 | + | 0.277719i | ||||
\(866\) | −29.1869 | + | 50.5532i | −0.0337031 | + | 0.0583755i | ||||
\(867\) | −202.398 | + | 202.398i | −0.233446 | + | 0.233446i | ||||
\(868\) | 632.297 | − | 86.0337i | 0.728452 | − | 0.0991172i | ||||
\(869\) | 695.056i | 0.799834i | ||||||||
\(870\) | 264.836 | − | 350.761i | 0.304409 | − | 0.403174i | ||||
\(871\) | 135.837 | + | 235.276i | 0.155955 | + | 0.270122i | ||||
\(872\) | −261.897 | − | 70.1750i | −0.300340 | − | 0.0804759i | ||||
\(873\) | 162.916 | − | 43.6531i | 0.186616 | − | 0.0500035i | ||||
\(874\) | − | 162.966i | − | 0.186459i | ||||||
\(875\) | −249.779 | − | 838.591i | −0.285461 | − | 0.958390i | ||||
\(876\) | 25.1228 | 0.0286790 | ||||||||
\(877\) | 105.600 | + | 394.106i | 0.120411 | + | 0.449380i | 0.999635 | − | 0.0270295i | \(-0.00860479\pi\) |
−0.879224 | + | 0.476409i | \(0.841938\pi\) | |||||||
\(878\) | −149.494 | + | 557.919i | −0.170267 | + | 0.635443i | ||||
\(879\) | −477.781 | + | 275.847i | −0.543550 | + | 0.313819i | ||||
\(880\) | 270.667 | + | 204.362i | 0.307576 | + | 0.232230i | ||||
\(881\) | 175.519 | 0.199227 | 0.0996134 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996134 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(882\) | −180.932 | − | 102.380i | −0.205138 | − | 0.116077i | ||||
\(883\) | 528.630 | + | 528.630i | 0.598675 | + | 0.598675i | 0.939960 | − | 0.341285i | \(-0.110862\pi\) |
−0.341285 | + | 0.939960i | \(0.610862\pi\) | |||||||
\(884\) | −83.1558 | − | 48.0100i | −0.0940677 | − | 0.0543100i | ||||
\(885\) | −82.6708 | + | 204.064i | −0.0934134 | + | 0.230580i | ||||
\(886\) | 419.377 | + | 726.383i | 0.473338 | + | 0.819845i | ||||
\(887\) | −269.726 | − | 1006.63i | −0.304088 | − | 1.13487i | −0.933727 | − | 0.357985i | \(-0.883464\pi\) |
0.629639 | − | 0.776888i | \(-0.283203\pi\) | |||||||
\(888\) | 63.5116 | + | 63.5116i | 0.0715221 | + | 0.0715221i | ||||
\(889\) | −57.6379 | + | 452.969i | −0.0648345 | + | 0.509526i | ||||
\(890\) | −321.751 | + | 250.892i | −0.361518 | + | 0.281901i | ||||
\(891\) | −76.3094 | + | 132.172i | −0.0856446 | + | 0.148341i | ||||
\(892\) | −692.577 | − | 185.575i | −0.776431 | − | 0.208044i | ||||
\(893\) | 75.0761 | − | 280.188i | 0.0840718 | − | 0.313760i | ||||
\(894\) | 481.885 | + | 278.216i | 0.539021 | + | 0.311204i | ||||
\(895\) | 735.942 | + | 91.0664i | 0.822282 | + | 0.101750i | ||||
\(896\) | 47.9386 | − | 63.0388i | 0.0535029 | − | 0.0703558i | ||||
\(897\) | −91.8355 | + | 91.8355i | −0.102381 | + | 0.102381i | ||||
\(898\) | 240.686 | − | 64.4916i | 0.268025 | − | 0.0718170i | ||||
\(899\) | 1416.55 | − | 817.847i | 1.57570 | − | 0.909730i | ||||
\(900\) | 41.0738 | + | 144.267i | 0.0456375 | + | 0.160297i | ||||
\(901\) | 473.112 | − | 819.454i | 0.525096 | − | 0.909494i | ||||
\(902\) | 728.515 | − | 728.515i | 0.807667 | − | 0.807667i | ||||
\(903\) | 12.8968 | − | 31.5214i | 0.0142821 | − | 0.0349074i | ||||
\(904\) | 346.426i | 0.383215i | ||||||||
\(905\) | −562.435 | − | 424.657i | −0.621475 | − | 0.469234i | ||||
\(906\) | 243.645 | + | 422.005i | 0.268924 | + | 0.465790i | ||||
\(907\) | −873.023 | − | 233.926i | −0.962539 | − | 0.257912i | −0.256864 | − | 0.966448i | \(-0.582689\pi\) |
−0.705675 | + | 0.708536i | \(0.749356\pi\) | |||||||
\(908\) | −26.8280 | + | 7.18854i | −0.0295462 | + | 0.00791689i | ||||
\(909\) | − | 217.475i | − | 0.239246i | ||||||
\(910\) | 104.563 | − | 186.287i | 0.114905 | − | 0.204711i | ||||
\(911\) | −1543.49 | −1.69428 | −0.847140 | − | 0.531370i | \(-0.821678\pi\) | ||||
−0.847140 | + | 0.531370i | \(0.821678\pi\) | |||||||
\(912\) | −11.8934 | − | 44.3866i | −0.0130410 | − | 0.0486695i | ||||
\(913\) | 682.430 | − | 2546.86i | 0.747459 | − | 2.78956i | ||||
\(914\) | 63.6441 | − | 36.7450i | 0.0696325 | − | 0.0402024i | ||||
\(915\) | −101.719 | − | 728.750i | −0.111168 | − | 0.796448i | ||||
\(916\) | −718.056 | −0.783904 | ||||||||
\(917\) | −95.3043 | − | 700.430i | −0.103931 | − | 0.763828i | ||||
\(918\) | −57.8019 | − | 57.8019i | −0.0629650 | − | 0.0629650i | ||||
\(919\) | −1140.39 | − | 658.405i | −1.24090 | − | 0.716436i | −0.271625 | − | 0.962403i | \(-0.587561\pi\) |
−0.969278 | + | 0.245967i | \(0.920894\pi\) | |||||||
\(920\) | 95.7902 | + | 226.260i | 0.104120 | + | 0.245935i | ||||
\(921\) | −360.491 | − | 624.389i | −0.391413 | − | 0.677947i | ||||
\(922\) | −154.077 | − | 575.024i | −0.167112 | − | 0.623670i | ||||
\(923\) | 421.041 | + | 421.041i | 0.456166 | + | 0.456166i | ||||
\(924\) | 51.9046 | − | 407.912i | 0.0561738 | − | 0.441463i | ||||
\(925\) | 393.331 | − | 235.330i | 0.425223 | − | 0.254410i | ||||
\(926\) | 45.3241 | − | 78.5036i | 0.0489461 | − | 0.0847771i | ||||
\(927\) | 458.618 | + | 122.886i | 0.494734 | + | 0.132563i | ||||
\(928\) | 52.5409 | − | 196.085i | 0.0566173 | − | 0.211299i | ||||
\(929\) | −963.700 | − | 556.392i | −1.03735 | − | 0.598915i | −0.118270 | − | 0.992981i | \(-0.537735\pi\) |
−0.919082 | + | 0.394066i | \(0.871068\pi\) | |||||||
\(930\) | −68.5546 | + | 554.016i | −0.0737146 | + | 0.595716i | ||||
\(931\) | 227.809 | − | 231.794i | 0.244692 | − | 0.248973i | ||||
\(932\) | −300.422 | + | 300.422i | −0.322342 | + | 0.322342i | ||||
\(933\) | −391.442 | + | 104.887i | −0.419552 | + | 0.112419i | ||||
\(934\) | −649.852 | + | 375.192i | −0.695773 | + | 0.401705i | ||||
\(935\) | −354.146 | + | 874.170i | −0.378766 | + | 0.934941i | ||||
\(936\) | −18.3108 | + | 31.7153i | −0.0195629 | + | 0.0338839i | ||||
\(937\) | −1008.35 | + | 1008.35i | −1.07614 | + | 1.07614i | −0.0792913 | + | 0.996851i | \(0.525266\pi\) |
−0.996851 | + | 0.0792913i | \(0.974734\pi\) | |||||||
\(938\) | −381.486 | − | 492.724i | −0.406701 | − | 0.525293i | ||||
\(939\) | 246.172i | 0.262164i | ||||||||
\(940\) | 60.4577 | + | 433.140i | 0.0643167 | + | 0.460787i | ||||
\(941\) | −350.515 | − | 607.110i | −0.372492 | − | 0.645176i | 0.617456 | − | 0.786606i | \(-0.288163\pi\) |
−0.989948 | + | 0.141430i | \(0.954830\pi\) | |||||||
\(942\) | 658.156 | + | 176.352i | 0.698679 | + | 0.187210i | ||||
\(943\) | 720.959 | − | 193.180i | 0.764538 | − | 0.204857i | ||||
\(944\) | 101.694i | 0.107727i | ||||||||
\(945\) | 127.030 | − | 130.147i | 0.134424 | − | 0.137722i | ||||
\(946\) | 67.3653 | 0.0712107 | ||||||||
\(947\) | −15.7915 | − | 58.9346i | −0.0166753 | − | 0.0622330i | 0.957087 | − | 0.289801i | \(-0.0935892\pi\) |
−0.973762 | + | 0.227568i | \(0.926923\pi\) | |||||||
\(948\) | −36.7486 | + | 137.148i | −0.0387644 | + | 0.144671i | ||||
\(949\) | 27.1069 | − | 15.6502i | 0.0285637 | − | 0.0164912i | ||||
\(950\) | −234.471 | + | 3.65071i | −0.246812 | + | 0.00384285i | ||||
\(951\) | 121.518 | 0.127779 | ||||||||
\(952\) | 203.842 | + | 83.4007i | 0.214120 | + | 0.0876057i | ||||
\(953\) | 102.107 | + | 102.107i | 0.107142 | + | 0.107142i | 0.758646 | − | 0.651503i | \(-0.225861\pi\) |
−0.651503 | + | 0.758646i | \(0.725861\pi\) | |||||||
\(954\) | −312.536 | − | 180.443i | −0.327606 | − | 0.189144i | ||||
\(955\) | 749.617 | − | 317.360i | 0.784939 | − | 0.332314i | ||||
\(956\) | 145.882 | + | 252.675i | 0.152596 | + | 0.264304i | ||||
\(957\) | −272.802 | − | 1018.11i | −0.285060 | − | 1.06386i | ||||
\(958\) | 332.049 | + | 332.049i | 0.346607 | + | 0.346607i | ||||
\(959\) | 852.729 | − | 357.551i | 0.889185 | − | 0.372837i | ||||
\(960\) | 42.6028 | + | 54.6352i | 0.0443779 | + | 0.0569116i | ||||
\(961\) | −558.278 | + | 966.966i | −0.580934 | + | 1.00621i | ||||
\(962\) | 108.092 | + | 28.9631i | 0.112362 | + | 0.0301072i | ||||
\(963\) | −34.9210 | + | 130.327i | −0.0362628 | + | 0.135334i | ||||
\(964\) | 458.547 | + | 264.742i | 0.475671 | + | 0.274629i | ||||
\(965\) | −912.307 | + | 711.389i | −0.945396 | + | 0.737190i | ||||
\(966\) | 180.322 | − | 237.122i | 0.186669 | − | 0.245468i | ||||
\(967\) | 1.00086 | − | 1.00086i | 0.00103501 | − | 0.00103501i | −0.706589 | − | 0.707624i | \(-0.749767\pi\) |
0.707624 | + | 0.706589i | \(0.249767\pi\) | |||||||
\(968\) | 455.054 | − | 121.931i | 0.470097 | − | 0.125962i | ||||
\(969\) | 110.672 | − | 63.8967i | 0.114213 | − | 0.0659409i | ||||
\(970\) | −154.987 | − | 366.085i | −0.159780 | − | 0.377407i | ||||
\(971\) | −362.599 | + | 628.039i | −0.373428 | + | 0.646796i | −0.990090 | − | 0.140431i | \(-0.955151\pi\) |
0.616662 | + | 0.787228i | \(0.288484\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −213.177 | − | 275.338i | −0.219093 | − | 0.282978i | ||||
\(974\) | − | 1051.67i | − | 1.07974i | ||||||
\(975\) | 134.188 | + | 130.074i | 0.137629 | + | 0.133409i | ||||
\(976\) | −169.929 | − | 294.326i | −0.174108 | − | 0.301563i | ||||
\(977\) | 1031.59 | + | 276.413i | 1.05587 | + | 0.282920i | 0.744677 | − | 0.667425i | \(-0.232604\pi\) |
0.311196 | + | 0.950346i | \(0.399270\pi\) | |||||||
\(978\) | −496.421 | + | 133.016i | −0.507588 | + | 0.136008i | ||||
\(979\) | 978.473i | 0.999462i | ||||||||
\(980\) | −180.041 | + | 455.725i | −0.183715 | + | 0.465026i | ||||
\(981\) | −287.583 | −0.293152 | ||||||||
\(982\) | 17.0834 | + | 63.7563i | 0.0173966 | + | 0.0649249i | ||||
\(983\) | −285.048 | + | 1063.81i | −0.289977 | + | 1.08221i | 0.655147 | + | 0.755501i | \(0.272607\pi\) |
−0.945125 | + | 0.326709i | \(0.894060\pi\) | |||||||
\(984\) | 182.268 | − | 105.232i | 0.185231 | − | 0.106943i | ||||
\(985\) | 1231.66 | − | 171.915i | 1.25042 | − | 0.174533i | ||||
\(986\) | 564.548 | 0.572564 | ||||||||
\(987\) | 419.268 | − | 324.613i | 0.424791 | − | 0.328889i | ||||
\(988\) | −40.4832 | − | 40.4832i | −0.0409748 | − | 0.0409748i | ||||
\(989\) | 42.2649 | + | 24.4017i | 0.0427350 | + | 0.0246731i | ||||
\(990\) | 333.405 | + | 135.070i | 0.336773 | + | 0.136434i | ||||
\(991\) | 245.356 | + | 424.969i | 0.247584 | + | 0.428828i | 0.962855 | − | 0.270019i | \(-0.0870300\pi\) |
−0.715271 | + | 0.698847i | \(0.753697\pi\) | |||||||
\(992\) | 66.7341 | + | 249.055i | 0.0672722 | + | 0.251063i | ||||
\(993\) | −312.863 | − | 312.863i | −0.315068 | − | 0.315068i | ||||
\(994\) | −1087.14 | − | 826.729i | −1.09370 | − | 0.831719i | ||||
\(995\) | −1276.99 | − | 158.016i | −1.28341 | − | 0.158810i | ||||
\(996\) | 269.313 | − | 466.464i | 0.270395 | − | 0.468337i | ||||
\(997\) | −1622.83 | − | 434.835i | −1.62771 | − | 0.436144i | −0.674456 | − | 0.738315i | \(-0.735622\pi\) |
−0.953254 | + | 0.302171i | \(0.902289\pi\) | |||||||
\(998\) | −91.4089 | + | 341.143i | −0.0915921 | + | 0.341826i | ||||
\(999\) | 82.5040 | + | 47.6337i | 0.0825866 | + | 0.0476814i |
(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.v.a.163.7 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.a.37.1 | ✓ | 32 | |
7.4 | even | 3 | inner | 210.3.v.a.193.1 | yes | 32 | |
35.32 | odd | 12 | inner | 210.3.v.a.67.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.a.37.1 | ✓ | 32 | 5.2 | odd | 4 | inner | |
210.3.v.a.67.7 | yes | 32 | 35.32 | odd | 12 | inner | |
210.3.v.a.163.7 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.a.193.1 | yes | 32 | 7.4 | even | 3 | inner |