Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(751,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.x (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 841.5 | ||
Root | \(-3.25684i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.841 |
Dual form | 1110.2.x.d.751.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.62842 | − | 2.82051i | −0.615485 | − | 1.06605i | −0.990299 | − | 0.138952i | \(-0.955627\pi\) |
0.374814 | − | 0.927100i | \(-0.377707\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.25915 | −1.58569 | −0.792846 | − | 0.609422i | \(-0.791402\pi\) | ||||
−0.792846 | + | 0.609422i | \(0.791402\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −3.16873 | + | 1.82947i | −0.878848 | + | 0.507403i | −0.870278 | − | 0.492560i | \(-0.836061\pi\) |
−0.00856971 | + | 0.999963i | \(0.502728\pi\) | |||||||
\(14\) | − | 3.25684i | − | 0.870428i | ||||||
\(15\) | −0.866025 | − | 0.500000i | −0.223607 | − | 0.129099i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.95448 | − | 1.12842i | −0.474032 | − | 0.273682i | 0.243894 | − | 0.969802i | \(-0.421575\pi\) |
−0.717926 | + | 0.696119i | \(0.754908\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −3.21087 | + | 1.85380i | −0.736624 | + | 0.425290i | −0.820841 | − | 0.571157i | \(-0.806495\pi\) |
0.0842164 | + | 0.996447i | \(0.473161\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | −1.62842 | + | 2.82051i | −0.355351 | + | 0.615485i | ||||
\(22\) | −4.55456 | − | 2.62957i | −0.971035 | − | 0.560627i | ||||
\(23\) | − | 1.92689i | − | 0.401783i | −0.979613 | − | 0.200892i | \(-0.935616\pi\) | ||
0.979613 | − | 0.200892i | \(-0.0643839\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −3.65894 | −0.717577 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.62842 | − | 2.82051i | 0.307743 | − | 0.533026i | ||||
\(29\) | 3.37764i | 0.627212i | 0.949553 | + | 0.313606i | \(0.101537\pi\) | ||||
−0.949553 | + | 0.313606i | \(0.898463\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | − | 1.35672i | − | 0.243674i | −0.992550 | − | 0.121837i | \(-0.961122\pi\) | ||
0.992550 | − | 0.121837i | \(-0.0388785\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 2.62957 | + | 4.55456i | 0.457750 | + | 0.792846i | ||||
\(34\) | −1.12842 | − | 1.95448i | −0.193523 | − | 0.335191i | ||||
\(35\) | −2.82051 | − | 1.62842i | −0.476753 | − | 0.275253i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −5.27288 | + | 3.03262i | −0.866855 | + | 0.498560i | ||||
\(38\) | −3.70759 | −0.601451 | ||||||||
\(39\) | 3.16873 | + | 1.82947i | 0.507403 | + | 0.292949i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 2.73745 | + | 4.74141i | 0.427518 | + | 0.740484i | 0.996652 | − | 0.0817615i | \(-0.0260546\pi\) |
−0.569133 | + | 0.822245i | \(0.692721\pi\) | |||||||
\(42\) | −2.82051 | + | 1.62842i | −0.435214 | + | 0.251271i | ||||
\(43\) | 3.28360i | 0.500745i | 0.968150 | + | 0.250372i | \(0.0805531\pi\) | ||||
−0.968150 | + | 0.250372i | \(0.919447\pi\) | |||||||
\(44\) | −2.62957 | − | 4.55456i | −0.396423 | − | 0.686625i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0.963443 | − | 1.66873i | 0.142052 | − | 0.246041i | ||||
\(47\) | 3.32765 | 0.485388 | 0.242694 | − | 0.970103i | \(-0.421969\pi\) | ||||
0.242694 | + | 0.970103i | \(0.421969\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.80351 | + | 3.12377i | −0.257645 | + | 0.446254i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 2.25684i | 0.316021i | ||||||||
\(52\) | −3.16873 | − | 1.82947i | −0.439424 | − | 0.253702i | ||||
\(53\) | 5.09487 | − | 8.82457i | 0.699834 | − | 1.21215i | −0.268690 | − | 0.963227i | \(-0.586591\pi\) |
0.968524 | − | 0.248921i | \(-0.0800759\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | −4.55456 | + | 2.62957i | −0.614136 | + | 0.354572i | ||||
\(56\) | 2.82051 | − | 1.62842i | 0.376906 | − | 0.217607i | ||||
\(57\) | 3.21087 | + | 1.85380i | 0.425290 | + | 0.245541i | ||||
\(58\) | −1.68882 | + | 2.92512i | −0.221753 | + | 0.384087i | ||||
\(59\) | −9.55745 | − | 5.51800i | −1.24427 | − | 0.718382i | −0.274313 | − | 0.961640i | \(-0.588450\pi\) |
−0.969962 | + | 0.243258i | \(0.921784\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | −1.07094 | + | 0.618309i | −0.137120 | + | 0.0791663i | −0.566991 | − | 0.823724i | \(-0.691892\pi\) |
0.429871 | + | 0.902890i | \(0.358559\pi\) | |||||||
\(62\) | 0.678359 | − | 1.17495i | 0.0861517 | − | 0.149219i | ||||
\(63\) | 3.25684 | 0.410324 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.82947 | + | 3.16873i | −0.226918 | + | 0.393033i | ||||
\(66\) | 5.25915i | 0.647356i | ||||||||
\(67\) | −6.93555 | − | 12.0127i | −0.847312 | − | 1.46759i | −0.883598 | − | 0.468246i | \(-0.844886\pi\) |
0.0362858 | − | 0.999341i | \(-0.488447\pi\) | |||||||
\(68\) | − | 2.25684i | − | 0.273682i | ||||||
\(69\) | −1.66873 | + | 0.963443i | −0.200892 | + | 0.115985i | ||||
\(70\) | −1.62842 | − | 2.82051i | −0.194634 | − | 0.337115i | ||||
\(71\) | −0.215263 | − | 0.372847i | −0.0255471 | − | 0.0442488i | 0.852969 | − | 0.521961i | \(-0.174799\pi\) |
−0.878516 | + | 0.477712i | \(0.841466\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 4.23689 | 0.495891 | 0.247945 | − | 0.968774i | \(-0.420245\pi\) | ||||
0.247945 | + | 0.968774i | \(0.420245\pi\) | |||||||
\(74\) | −6.08275 | − | 0.0101124i | −0.707106 | − | 0.00117555i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −3.21087 | − | 1.85380i | −0.368312 | − | 0.212645i | ||||
\(77\) | 8.56411 | + | 14.8335i | 0.975971 | + | 1.69043i | ||||
\(78\) | 1.82947 | + | 3.16873i | 0.207147 | + | 0.358788i | ||||
\(79\) | 6.26143 | − | 3.61504i | 0.704466 | − | 0.406724i | −0.104542 | − | 0.994520i | \(-0.533338\pi\) |
0.809009 | + | 0.587797i | \(0.200004\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 5.47491i | 0.604602i | ||||||||
\(83\) | 6.83148 | − | 11.8325i | 0.749853 | − | 1.29878i | −0.198040 | − | 0.980194i | \(-0.563458\pi\) |
0.947893 | − | 0.318589i | \(-0.103209\pi\) | |||||||
\(84\) | −3.25684 | −0.355351 | ||||||||
\(85\) | −2.25684 | −0.244789 | ||||||||
\(86\) | −1.64180 | + | 2.84368i | −0.177040 | + | 0.306642i | ||||
\(87\) | 2.92512 | − | 1.68882i | 0.313606 | − | 0.181060i | ||||
\(88\) | − | 5.25915i | − | 0.560627i | ||||||
\(89\) | −9.75521 | − | 5.63218i | −1.03405 | − | 0.597009i | −0.115908 | − | 0.993260i | \(-0.536978\pi\) |
−0.918142 | + | 0.396251i | \(0.870311\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 10.3201 | + | 5.95829i | 1.08184 | + | 0.624599i | ||||
\(92\) | 1.66873 | − | 0.963443i | 0.173977 | − | 0.100446i | ||||
\(93\) | −1.17495 | + | 0.678359i | −0.121837 | + | 0.0703426i | ||||
\(94\) | 2.88183 | + | 1.66383i | 0.297238 | + | 0.171611i | ||||
\(95\) | −1.85380 | + | 3.21087i | −0.190196 | + | 0.329428i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 4.69418i | 0.476622i | 0.971189 | + | 0.238311i | \(0.0765938\pi\) | ||||
−0.971189 | + | 0.238311i | \(0.923406\pi\) | |||||||
\(98\) | −3.12377 | + | 1.80351i | −0.315549 | + | 0.182182i | ||||
\(99\) | 2.62957 | − | 4.55456i | 0.264282 | − | 0.457750i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.91358 | −0.986438 | −0.493219 | − | 0.869905i | \(-0.664180\pi\) | ||||
−0.493219 | + | 0.869905i | \(0.664180\pi\) | |||||||
\(102\) | −1.12842 | + | 1.95448i | −0.111730 | + | 0.193523i | ||||
\(103\) | − | 11.0762i | − | 1.09137i | −0.837991 | − | 0.545684i | \(-0.816270\pi\) | ||
0.837991 | − | 0.545684i | \(-0.183730\pi\) | |||||||
\(104\) | −1.82947 | − | 3.16873i | −0.179394 | − | 0.310720i | ||||
\(105\) | 3.25684i | 0.317835i | ||||||||
\(106\) | 8.82457 | − | 5.09487i | 0.857118 | − | 0.494857i | ||||
\(107\) | −6.80147 | − | 11.7805i | −0.657523 | − | 1.13886i | −0.981255 | − | 0.192714i | \(-0.938271\pi\) |
0.323732 | − | 0.946149i | \(-0.395062\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −6.42341 | − | 3.70856i | −0.615251 | − | 0.355215i | 0.159767 | − | 0.987155i | \(-0.448926\pi\) |
−0.775018 | + | 0.631939i | \(0.782259\pi\) | |||||||
\(110\) | −5.25915 | −0.501440 | ||||||||
\(111\) | 5.26276 | + | 3.05013i | 0.499519 | + | 0.289506i | ||||
\(112\) | 3.25684 | 0.307743 | ||||||||
\(113\) | 0.273291 | + | 0.157785i | 0.0257090 | + | 0.0148431i | 0.512799 | − | 0.858508i | \(-0.328608\pi\) |
−0.487090 | + | 0.873352i | \(0.661942\pi\) | |||||||
\(114\) | 1.85380 | + | 3.21087i | 0.173624 | + | 0.300726i | ||||
\(115\) | −0.963443 | − | 1.66873i | −0.0898415 | − | 0.155610i | ||||
\(116\) | −2.92512 | + | 1.68882i | −0.271591 | + | 0.156803i | ||||
\(117\) | − | 3.65894i | − | 0.338269i | ||||||
\(118\) | −5.51800 | − | 9.55745i | −0.507973 | − | 0.879835i | ||||
\(119\) | 7.35018i | 0.673790i | ||||||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 16.6586 | 1.51442 | ||||||||
\(122\) | −1.23662 | −0.111958 | ||||||||
\(123\) | 2.73745 | − | 4.74141i | 0.246828 | − | 0.427518i | ||||
\(124\) | 1.17495 | − | 0.678359i | 0.105514 | − | 0.0609185i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 2.82051 | + | 1.62842i | 0.251271 | + | 0.145071i | ||||
\(127\) | −7.33602 | + | 12.7064i | −0.650966 | + | 1.12751i | 0.331923 | + | 0.943307i | \(0.392303\pi\) |
−0.982889 | + | 0.184200i | \(0.941031\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.84368 | − | 1.64180i | 0.250372 | − | 0.144553i | ||||
\(130\) | −3.16873 | + | 1.82947i | −0.277916 | + | 0.160455i | ||||
\(131\) | −7.34599 | − | 4.24121i | −0.641822 | − | 0.370556i | 0.143494 | − | 0.989651i | \(-0.454166\pi\) |
−0.785316 | + | 0.619095i | \(0.787500\pi\) | |||||||
\(132\) | −2.62957 | + | 4.55456i | −0.228875 | + | 0.396423i | ||||
\(133\) | 10.4573 | + | 6.03753i | 0.906763 | + | 0.523520i | ||||
\(134\) | − | 13.8711i | − | 1.19828i | ||||||
\(135\) | 0.866025 | − | 0.500000i | 0.0745356 | − | 0.0430331i | ||||
\(136\) | 1.12842 | − | 1.95448i | 0.0967613 | − | 0.167596i | ||||
\(137\) | 14.1845 | 1.21186 | 0.605931 | − | 0.795517i | \(-0.292801\pi\) | ||||
0.605931 | + | 0.795517i | \(0.292801\pi\) | |||||||
\(138\) | −1.92689 | −0.164027 | ||||||||
\(139\) | −10.6538 | + | 18.4528i | −0.903640 | + | 1.56515i | −0.0809066 | + | 0.996722i | \(0.525782\pi\) |
−0.822733 | + | 0.568428i | \(0.807552\pi\) | |||||||
\(140\) | − | 3.25684i | − | 0.275253i | ||||||
\(141\) | −1.66383 | − | 2.88183i | −0.140119 | − | 0.242694i | ||||
\(142\) | − | 0.430527i | − | 0.0361290i | ||||||
\(143\) | 16.6648 | − | 9.62144i | 1.39358 | − | 0.804586i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.68882 | + | 2.92512i | 0.140249 | + | 0.242918i | ||||
\(146\) | 3.66926 | + | 2.11845i | 0.303670 | + | 0.175324i | ||||
\(147\) | 3.60702 | 0.297502 | ||||||||
\(148\) | −5.26276 | − | 3.05013i | −0.432596 | − | 0.250720i | ||||
\(149\) | 8.36723 | 0.685470 | 0.342735 | − | 0.939432i | \(-0.388647\pi\) | ||||
0.342735 | + | 0.939432i | \(0.388647\pi\) | |||||||
\(150\) | −0.866025 | − | 0.500000i | −0.0707107 | − | 0.0408248i | ||||
\(151\) | 6.96505 | + | 12.0638i | 0.566808 | + | 0.981740i | 0.996879 | + | 0.0789449i | \(0.0251551\pi\) |
−0.430071 | + | 0.902795i | \(0.641512\pi\) | |||||||
\(152\) | −1.85380 | − | 3.21087i | −0.150363 | − | 0.260436i | ||||
\(153\) | 1.95448 | − | 1.12842i | 0.158011 | − | 0.0912275i | ||||
\(154\) | 17.1282i | 1.38023i | ||||||||
\(155\) | −0.678359 | − | 1.17495i | −0.0544871 | − | 0.0943745i | ||||
\(156\) | 3.65894i | 0.292949i | ||||||||
\(157\) | −4.49155 | + | 7.77960i | −0.358465 | + | 0.620880i | −0.987705 | − | 0.156332i | \(-0.950033\pi\) |
0.629240 | + | 0.777211i | \(0.283366\pi\) | |||||||
\(158\) | 7.23008 | 0.575194 | ||||||||
\(159\) | −10.1897 | −0.808098 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −5.43480 | + | 3.13778i | −0.428322 | + | 0.247292i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 17.2881 | + | 9.98128i | 1.35411 | + | 0.781794i | 0.988822 | − | 0.149101i | \(-0.0476380\pi\) |
0.365286 | + | 0.930895i | \(0.380971\pi\) | |||||||
\(164\) | −2.73745 | + | 4.74141i | −0.213759 | + | 0.370242i | ||||
\(165\) | 4.55456 | + | 2.62957i | 0.354572 | + | 0.204712i | ||||
\(166\) | 11.8325 | − | 6.83148i | 0.918378 | − | 0.530226i | ||||
\(167\) | −7.09782 | + | 4.09793i | −0.549246 | + | 0.317107i | −0.748818 | − | 0.662776i | \(-0.769378\pi\) |
0.199572 | + | 0.979883i | \(0.436045\pi\) | |||||||
\(168\) | −2.82051 | − | 1.62842i | −0.217607 | − | 0.125635i | ||||
\(169\) | 0.193909 | − | 0.335860i | 0.0149161 | − | 0.0258354i | ||||
\(170\) | −1.95448 | − | 1.12842i | −0.149902 | − | 0.0865460i | ||||
\(171\) | − | 3.70759i | − | 0.283527i | ||||||
\(172\) | −2.84368 | + | 1.64180i | −0.216829 | + | 0.125186i | ||||
\(173\) | 7.96169 | − | 13.7901i | 0.605316 | − | 1.04844i | −0.386685 | − | 0.922212i | \(-0.626380\pi\) |
0.992001 | − | 0.126227i | \(-0.0402868\pi\) | |||||||
\(174\) | 3.37764 | 0.256058 | ||||||||
\(175\) | −3.25684 | −0.246194 | ||||||||
\(176\) | 2.62957 | − | 4.55456i | 0.198212 | − | 0.343313i | ||||
\(177\) | 11.0360i | 0.829516i | ||||||||
\(178\) | −5.63218 | − | 9.75521i | −0.422149 | − | 0.731184i | ||||
\(179\) | 0.900657i | 0.0673182i | 0.999433 | + | 0.0336591i | \(0.0107161\pi\) | ||||
−0.999433 | + | 0.0336591i | \(0.989284\pi\) | |||||||
\(180\) | −0.866025 | + | 0.500000i | −0.0645497 | + | 0.0372678i | ||||
\(181\) | 1.45760 | + | 2.52464i | 0.108343 | + | 0.187655i | 0.915099 | − | 0.403229i | \(-0.132112\pi\) |
−0.806756 | + | 0.590884i | \(0.798779\pi\) | |||||||
\(182\) | 5.95829 | + | 10.3201i | 0.441658 | + | 0.764974i | ||||
\(183\) | 1.07094 | + | 0.618309i | 0.0791663 | + | 0.0457067i | ||||
\(184\) | 1.92689 | 0.142052 | ||||||||
\(185\) | −3.05013 | + | 5.26276i | −0.224250 | + | 0.386926i | ||||
\(186\) | −1.35672 | −0.0994794 | ||||||||
\(187\) | 10.2789 | + | 5.93453i | 0.751669 | + | 0.433976i | ||||
\(188\) | 1.66383 | + | 2.88183i | 0.121347 | + | 0.210179i | ||||
\(189\) | −1.62842 | − | 2.82051i | −0.118450 | − | 0.205162i | ||||
\(190\) | −3.21087 | + | 1.85380i | −0.232941 | + | 0.134489i | ||||
\(191\) | − | 27.0970i | − | 1.96067i | −0.197342 | − | 0.980335i | \(-0.563231\pi\) | ||
0.197342 | − | 0.980335i | \(-0.436769\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 16.6359i | 1.19748i | 0.800943 | + | 0.598740i | \(0.204332\pi\) | ||||
−0.800943 | + | 0.598740i | \(0.795668\pi\) | |||||||
\(194\) | −2.34709 | + | 4.06528i | −0.168511 | + | 0.291870i | ||||
\(195\) | 3.65894 | 0.262022 | ||||||||
\(196\) | −3.60702 | −0.257645 | ||||||||
\(197\) | −8.59600 | + | 14.8887i | −0.612439 | + | 1.06078i | 0.378389 | + | 0.925647i | \(0.376478\pi\) |
−0.990828 | + | 0.135129i | \(0.956855\pi\) | |||||||
\(198\) | 4.55456 | − | 2.62957i | 0.323678 | − | 0.186876i | ||||
\(199\) | 2.73511i | 0.193887i | 0.995290 | + | 0.0969433i | \(0.0309066\pi\) | ||||
−0.995290 | + | 0.0969433i | \(0.969093\pi\) | |||||||
\(200\) | 0.866025 | + | 0.500000i | 0.0612372 | + | 0.0353553i | ||||
\(201\) | −6.93555 | + | 12.0127i | −0.489196 | + | 0.847312i | ||||
\(202\) | −8.58541 | − | 4.95679i | −0.604067 | − | 0.348758i | ||||
\(203\) | 9.52666 | − | 5.50022i | 0.668640 | − | 0.386040i | ||||
\(204\) | −1.95448 | + | 1.12842i | −0.136841 | + | 0.0790053i | ||||
\(205\) | 4.74141 | + | 2.73745i | 0.331154 | + | 0.191192i | ||||
\(206\) | 5.53809 | − | 9.59224i | 0.385857 | − | 0.668323i | ||||
\(207\) | 1.66873 | + | 0.963443i | 0.115985 | + | 0.0669639i | ||||
\(208\) | − | 3.65894i | − | 0.253702i | ||||||
\(209\) | 16.8864 | − | 9.74939i | 1.16806 | − | 0.674380i | ||||
\(210\) | −1.62842 | + | 2.82051i | −0.112372 | + | 0.194634i | ||||
\(211\) | −18.8199 | −1.29561 | −0.647807 | − | 0.761804i | \(-0.724314\pi\) | ||||
−0.647807 | + | 0.761804i | \(0.724314\pi\) | |||||||
\(212\) | 10.1897 | 0.699834 | ||||||||
\(213\) | −0.215263 | + | 0.372847i | −0.0147496 | + | 0.0255471i | ||||
\(214\) | − | 13.6029i | − | 0.929877i | ||||||
\(215\) | 1.64180 | + | 2.84368i | 0.111970 | + | 0.193938i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −3.82664 | + | 2.20931i | −0.259769 | + | 0.149978i | ||||
\(218\) | −3.70856 | − | 6.42341i | −0.251175 | − | 0.435048i | ||||
\(219\) | −2.11845 | − | 3.66926i | −0.143151 | − | 0.247945i | ||||
\(220\) | −4.55456 | − | 2.62957i | −0.307068 | − | 0.177286i | ||||
\(221\) | 8.25764 | 0.555469 | ||||||||
\(222\) | 3.03262 | + | 5.27288i | 0.203536 | + | 0.353892i | ||||
\(223\) | 25.6392 | 1.71693 | 0.858466 | − | 0.512871i | \(-0.171418\pi\) | ||||
0.858466 | + | 0.512871i | \(0.171418\pi\) | |||||||
\(224\) | 2.82051 | + | 1.62842i | 0.188453 | + | 0.108803i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | 0.157785 | + | 0.273291i | 0.0104957 | + | 0.0181790i | ||||
\(227\) | 14.0727 | − | 8.12488i | 0.934039 | − | 0.539268i | 0.0459521 | − | 0.998944i | \(-0.485368\pi\) |
0.888087 | + | 0.459676i | \(0.152034\pi\) | |||||||
\(228\) | 3.70759i | 0.245541i | ||||||||
\(229\) | −5.87416 | − | 10.1743i | −0.388176 | − | 0.672340i | 0.604029 | − | 0.796963i | \(-0.293561\pi\) |
−0.992204 | + | 0.124623i | \(0.960228\pi\) | |||||||
\(230\) | − | 1.92689i | − | 0.127055i | ||||||
\(231\) | 8.56411 | − | 14.8335i | 0.563477 | − | 0.975971i | ||||
\(232\) | −3.37764 | −0.221753 | ||||||||
\(233\) | 10.3859 | 0.680403 | 0.340202 | − | 0.940353i | \(-0.389505\pi\) | ||||
0.340202 | + | 0.940353i | \(0.389505\pi\) | |||||||
\(234\) | 1.82947 | − | 3.16873i | 0.119596 | − | 0.207147i | ||||
\(235\) | 2.88183 | − | 1.66383i | 0.187990 | − | 0.108536i | ||||
\(236\) | − | 11.0360i | − | 0.718382i | ||||||
\(237\) | −6.26143 | − | 3.61504i | −0.406724 | − | 0.234822i | ||||
\(238\) | −3.67509 | + | 6.36544i | −0.238221 | + | 0.412610i | ||||
\(239\) | 3.68278 | + | 2.12625i | 0.238219 | + | 0.137536i | 0.614358 | − | 0.789027i | \(-0.289415\pi\) |
−0.376139 | + | 0.926563i | \(0.622748\pi\) | |||||||
\(240\) | 0.866025 | − | 0.500000i | 0.0559017 | − | 0.0322749i | ||||
\(241\) | 5.12924 | − | 2.96137i | 0.330403 | − | 0.190758i | −0.325617 | − | 0.945502i | \(-0.605572\pi\) |
0.656020 | + | 0.754743i | \(0.272239\pi\) | |||||||
\(242\) | 14.4268 | + | 8.32932i | 0.927390 | + | 0.535429i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.07094 | − | 0.618309i | −0.0685601 | − | 0.0395832i | ||||
\(245\) | 3.60702i | 0.230444i | ||||||||
\(246\) | 4.74141 | − | 2.73745i | 0.302301 | − | 0.174534i | ||||
\(247\) | 6.78293 | − | 11.7484i | 0.431587 | − | 0.747531i | ||||
\(248\) | 1.35672 | 0.0861517 | ||||||||
\(249\) | −13.6630 | −0.865856 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | − | 11.4250i | − | 0.721137i | −0.932733 | − | 0.360568i | \(-0.882583\pi\) | ||
0.932733 | − | 0.360568i | \(-0.117417\pi\) | |||||||
\(252\) | 1.62842 | + | 2.82051i | 0.102581 | + | 0.177675i | ||||
\(253\) | 10.1338i | 0.637105i | ||||||||
\(254\) | −12.7064 | + | 7.33602i | −0.797267 | + | 0.460303i | ||||
\(255\) | 1.12842 | + | 1.95448i | 0.0706645 | + | 0.122394i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −20.3226 | − | 11.7333i | −1.26769 | − | 0.731901i | −0.293139 | − | 0.956070i | \(-0.594700\pi\) |
−0.974550 | + | 0.224169i | \(0.928033\pi\) | |||||||
\(258\) | 3.28360 | 0.204428 | ||||||||
\(259\) | 17.1400 | + | 9.93381i | 1.06503 | + | 0.617257i | ||||
\(260\) | −3.65894 | −0.226918 | ||||||||
\(261\) | −2.92512 | − | 1.68882i | −0.181060 | − | 0.104535i | ||||
\(262\) | −4.24121 | − | 7.34599i | −0.262023 | − | 0.453837i | ||||
\(263\) | 10.3985 | + | 18.0108i | 0.641200 | + | 1.11059i | 0.985165 | + | 0.171609i | \(0.0548965\pi\) |
−0.343965 | + | 0.938982i | \(0.611770\pi\) | |||||||
\(264\) | −4.55456 | + | 2.62957i | −0.280314 | + | 0.161839i | ||||
\(265\) | − | 10.1897i | − | 0.625950i | ||||||
\(266\) | 6.03753 | + | 10.4573i | 0.370184 | + | 0.641178i | ||||
\(267\) | 11.2644i | 0.689367i | ||||||||
\(268\) | 6.93555 | − | 12.0127i | 0.423656 | − | 0.733794i | ||||
\(269\) | 20.4144 | 1.24469 | 0.622345 | − | 0.782743i | \(-0.286180\pi\) | ||||
0.622345 | + | 0.782743i | \(0.286180\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −9.87486 | + | 17.1038i | −0.599855 | + | 1.03898i | 0.392987 | + | 0.919544i | \(0.371442\pi\) |
−0.992842 | + | 0.119435i | \(0.961892\pi\) | |||||||
\(272\) | 1.95448 | − | 1.12842i | 0.118508 | − | 0.0684206i | ||||
\(273\) | − | 11.9166i | − | 0.721224i | ||||||
\(274\) | 12.2841 | + | 7.09224i | 0.742111 | + | 0.428458i | ||||
\(275\) | −2.62957 | + | 4.55456i | −0.158569 | + | 0.274650i | ||||
\(276\) | −1.66873 | − | 0.963443i | −0.100446 | − | 0.0579925i | ||||
\(277\) | 0.559700 | − | 0.323143i | 0.0336291 | − | 0.0194158i | −0.483091 | − | 0.875570i | \(-0.660486\pi\) |
0.516720 | + | 0.856154i | \(0.327153\pi\) | |||||||
\(278\) | −18.4528 | + | 10.6538i | −1.10673 | + | 0.638970i | ||||
\(279\) | 1.17495 | + | 0.678359i | 0.0703426 | + | 0.0406123i | ||||
\(280\) | 1.62842 | − | 2.82051i | 0.0973168 | − | 0.168558i | ||||
\(281\) | −1.71343 | − | 0.989249i | −0.102215 | − | 0.0590136i | 0.448021 | − | 0.894023i | \(-0.352129\pi\) |
−0.550236 | + | 0.835009i | \(0.685462\pi\) | |||||||
\(282\) | − | 3.32765i | − | 0.198159i | ||||||
\(283\) | −6.32516 | + | 3.65183i | −0.375992 | + | 0.217079i | −0.676073 | − | 0.736835i | \(-0.736320\pi\) |
0.300081 | + | 0.953914i | \(0.402986\pi\) | |||||||
\(284\) | 0.215263 | − | 0.372847i | 0.0127735 | − | 0.0221244i | ||||
\(285\) | 3.70759 | 0.219619 | ||||||||
\(286\) | 19.2429 | 1.13786 | ||||||||
\(287\) | 8.91546 | − | 15.4420i | 0.526263 | − | 0.911514i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −5.95333 | − | 10.3115i | −0.350196 | − | 0.606557i | ||||
\(290\) | 3.37764i | 0.198342i | ||||||||
\(291\) | 4.06528 | − | 2.34709i | 0.238311 | − | 0.137589i | ||||
\(292\) | 2.11845 | + | 3.66926i | 0.123973 | + | 0.214727i | ||||
\(293\) | −5.66939 | − | 9.81967i | −0.331209 | − | 0.573671i | 0.651540 | − | 0.758614i | \(-0.274123\pi\) |
−0.982749 | + | 0.184943i | \(0.940790\pi\) | |||||||
\(294\) | 3.12377 | + | 1.80351i | 0.182182 | + | 0.105183i | ||||
\(295\) | −11.0360 | −0.642541 | ||||||||
\(296\) | −3.03262 | − | 5.27288i | −0.176267 | − | 0.306480i | ||||
\(297\) | −5.25915 | −0.305167 | ||||||||
\(298\) | 7.24623 | + | 4.18361i | 0.419763 | + | 0.242350i | ||||
\(299\) | 3.52518 | + | 6.10579i | 0.203866 | + | 0.353107i | ||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | 9.26143 | − | 5.34709i | 0.533820 | − | 0.308201i | ||||
\(302\) | 13.9301i | 0.801587i | ||||||||
\(303\) | 4.95679 | + | 8.58541i | 0.284760 | + | 0.493219i | ||||
\(304\) | − | 3.70759i | − | 0.212645i | ||||||
\(305\) | −0.618309 | + | 1.07094i | −0.0354043 | + | 0.0613220i | ||||
\(306\) | 2.25684 | 0.129015 | ||||||||
\(307\) | −9.54245 | −0.544616 | −0.272308 | − | 0.962210i | \(-0.587787\pi\) | ||||
−0.272308 | + | 0.962210i | \(0.587787\pi\) | |||||||
\(308\) | −8.56411 | + | 14.8335i | −0.487985 | + | 0.845215i | ||||
\(309\) | −9.59224 | + | 5.53809i | −0.545684 | + | 0.315051i | ||||
\(310\) | − | 1.35672i | − | 0.0770564i | ||||||
\(311\) | −11.7442 | − | 6.78050i | −0.665951 | − | 0.384487i | 0.128590 | − | 0.991698i | \(-0.458955\pi\) |
−0.794541 | + | 0.607211i | \(0.792288\pi\) | |||||||
\(312\) | −1.82947 | + | 3.16873i | −0.103573 | + | 0.179394i | ||||
\(313\) | 2.94389 | + | 1.69966i | 0.166399 | + | 0.0960703i | 0.580887 | − | 0.813985i | \(-0.302706\pi\) |
−0.414488 | + | 0.910055i | \(0.636039\pi\) | |||||||
\(314\) | −7.77960 | + | 4.49155i | −0.439028 | + | 0.253473i | ||||
\(315\) | 2.82051 | − | 1.62842i | 0.158918 | − | 0.0917511i | ||||
\(316\) | 6.26143 | + | 3.61504i | 0.352233 | + | 0.203362i | ||||
\(317\) | −9.98619 | + | 17.2966i | −0.560880 | + | 0.971473i | 0.436540 | + | 0.899685i | \(0.356204\pi\) |
−0.997420 | + | 0.0717881i | \(0.977129\pi\) | |||||||
\(318\) | −8.82457 | − | 5.09487i | −0.494857 | − | 0.285706i | ||||
\(319\) | − | 17.7635i | − | 0.994565i | ||||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −6.80147 | + | 11.7805i | −0.379621 | + | 0.657523i | ||||
\(322\) | −6.27556 | −0.349724 | ||||||||
\(323\) | 8.36746 | 0.465578 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 3.65894i | 0.202961i | ||||||||
\(326\) | 9.98128 | + | 17.2881i | 0.552812 | + | 0.957499i | ||||
\(327\) | 7.41712i | 0.410167i | ||||||||
\(328\) | −4.74141 | + | 2.73745i | −0.261801 | + | 0.151151i | ||||
\(329\) | −5.41882 | − | 9.38567i | −0.298749 | − | 0.517449i | ||||
\(330\) | 2.62957 | + | 4.55456i | 0.144753 | + | 0.250720i | ||||
\(331\) | 8.55298 | + | 4.93807i | 0.470114 | + | 0.271421i | 0.716288 | − | 0.697805i | \(-0.245840\pi\) |
−0.246173 | + | 0.969226i | \(0.579173\pi\) | |||||||
\(332\) | 13.6630 | 0.749853 | ||||||||
\(333\) | 0.0101124 | − | 6.08275i | 0.000554158 | − | 0.333333i | ||||
\(334\) | −8.19586 | −0.448457 | ||||||||
\(335\) | −12.0127 | − | 6.93555i | −0.656325 | − | 0.378930i | ||||
\(336\) | −1.62842 | − | 2.82051i | −0.0888377 | − | 0.153871i | ||||
\(337\) | −1.52567 | − | 2.64253i | −0.0831084 | − | 0.143948i | 0.821475 | − | 0.570244i | \(-0.193151\pi\) |
−0.904584 | + | 0.426296i | \(0.859818\pi\) | |||||||
\(338\) | 0.335860 | − | 0.193909i | 0.0182684 | − | 0.0105473i | ||||
\(339\) | − | 0.315569i | − | 0.0171394i | ||||||
\(340\) | −1.12842 | − | 1.95448i | −0.0611972 | − | 0.105997i | ||||
\(341\) | 7.13518i | 0.386392i | ||||||||
\(342\) | 1.85380 | − | 3.21087i | 0.100242 | − | 0.173624i | ||||
\(343\) | −11.0504 | −0.596665 | ||||||||
\(344\) | −3.28360 | −0.177040 | ||||||||
\(345\) | −0.963443 | + | 1.66873i | −0.0518700 | + | 0.0898415i | ||||
\(346\) | 13.7901 | − | 7.96169i | 0.741358 | − | 0.428023i | ||||
\(347\) | − | 26.8643i | − | 1.44215i | −0.692855 | − | 0.721077i | \(-0.743647\pi\) | ||
0.692855 | − | 0.721077i | \(-0.256353\pi\) | |||||||
\(348\) | 2.92512 | + | 1.68882i | 0.156803 | + | 0.0905302i | ||||
\(349\) | −8.06293 | + | 13.9654i | −0.431599 | + | 0.747551i | −0.997011 | − | 0.0772571i | \(-0.975384\pi\) |
0.565412 | + | 0.824808i | \(0.308717\pi\) | |||||||
\(350\) | −2.82051 | − | 1.62842i | −0.150763 | − | 0.0870428i | ||||
\(351\) | −3.16873 | + | 1.82947i | −0.169134 | + | 0.0976498i | ||||
\(352\) | 4.55456 | − | 2.62957i | 0.242759 | − | 0.140157i | ||||
\(353\) | −15.0990 | − | 8.71739i | −0.803636 | − | 0.463980i | 0.0411047 | − | 0.999155i | \(-0.486912\pi\) |
−0.844741 | + | 0.535175i | \(0.820246\pi\) | |||||||
\(354\) | −5.51800 | + | 9.55745i | −0.293278 | + | 0.507973i | ||||
\(355\) | −0.372847 | − | 0.215263i | −0.0197887 | − | 0.0114250i | ||||
\(356\) | − | 11.2644i | − | 0.597009i | ||||||
\(357\) | 6.36544 | − | 3.67509i | 0.336895 | − | 0.194506i | ||||
\(358\) | −0.450328 | + | 0.779992i | −0.0238006 | + | 0.0412238i | ||||
\(359\) | −5.13196 | −0.270854 | −0.135427 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135427 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −2.62687 | + | 4.54988i | −0.138256 | + | 0.239467i | ||||
\(362\) | 2.91520i | 0.153220i | ||||||||
\(363\) | −8.32932 | − | 14.4268i | −0.437176 | − | 0.757211i | ||||
\(364\) | 11.9166i | 0.624599i | ||||||||
\(365\) | 3.66926 | − | 2.11845i | 0.192058 | − | 0.110885i | ||||
\(366\) | 0.618309 | + | 1.07094i | 0.0323195 | + | 0.0559791i | ||||
\(367\) | −2.33684 | − | 4.04753i | −0.121982 | − | 0.211279i | 0.798567 | − | 0.601906i | \(-0.205592\pi\) |
−0.920549 | + | 0.390626i | \(0.872258\pi\) | |||||||
\(368\) | 1.66873 | + | 0.963443i | 0.0869887 | + | 0.0502229i | ||||
\(369\) | −5.47491 | −0.285012 | ||||||||
\(370\) | −5.27288 | + | 3.03262i | −0.274124 | + | 0.157658i | ||||
\(371\) | −33.1864 | −1.72295 | ||||||||
\(372\) | −1.17495 | − | 0.678359i | −0.0609185 | − | 0.0351713i | ||||
\(373\) | 13.4218 | + | 23.2473i | 0.694956 | + | 1.20370i | 0.970196 | + | 0.242323i | \(0.0779093\pi\) |
−0.275240 | + | 0.961376i | \(0.588757\pi\) | |||||||
\(374\) | 5.93453 | + | 10.2789i | 0.306867 | + | 0.531510i | ||||
\(375\) | −0.866025 | + | 0.500000i | −0.0447214 | + | 0.0258199i | ||||
\(376\) | 3.32765i | 0.171611i | ||||||||
\(377\) | −6.17928 | − | 10.7028i | −0.318249 | − | 0.551224i | ||||
\(378\) | − | 3.25684i | − | 0.167514i | ||||||
\(379\) | −14.0580 | + | 24.3491i | −0.722109 | + | 1.25073i | 0.238043 | + | 0.971255i | \(0.423494\pi\) |
−0.960153 | + | 0.279476i | \(0.909839\pi\) | |||||||
\(380\) | −3.70759 | −0.190196 | ||||||||
\(381\) | 14.6720 | 0.751671 | ||||||||
\(382\) | 13.5485 | − | 23.4667i | 0.693201 | − | 1.20066i | ||||
\(383\) | −22.9304 | + | 13.2389i | −1.17169 | + | 0.676474i | −0.954077 | − | 0.299561i | \(-0.903160\pi\) |
−0.217611 | + | 0.976036i | \(0.569826\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 14.8335 | + | 8.56411i | 0.755984 | + | 0.436467i | ||||
\(386\) | −8.31797 | + | 14.4071i | −0.423373 | + | 0.733304i | ||||
\(387\) | −2.84368 | − | 1.64180i | −0.144553 | − | 0.0834575i | ||||
\(388\) | −4.06528 | + | 2.34709i | −0.206383 | + | 0.119156i | ||||
\(389\) | −24.6665 | + | 14.2412i | −1.25064 | + | 0.722057i | −0.971236 | − | 0.238117i | \(-0.923470\pi\) |
−0.279403 | + | 0.960174i | \(0.590136\pi\) | |||||||
\(390\) | 3.16873 | + | 1.82947i | 0.160455 | + | 0.0926387i | ||||
\(391\) | −2.17434 | + | 3.76607i | −0.109961 | + | 0.190458i | ||||
\(392\) | −3.12377 | − | 1.80351i | −0.157774 | − | 0.0910911i | ||||
\(393\) | 8.48241i | 0.427881i | ||||||||
\(394\) | −14.8887 | + | 8.59600i | −0.750082 | + | 0.433060i | ||||
\(395\) | 3.61504 | − | 6.26143i | 0.181892 | − | 0.315047i | ||||
\(396\) | 5.25915 | 0.264282 | ||||||||
\(397\) | −21.6765 | −1.08791 | −0.543956 | − | 0.839114i | \(-0.683074\pi\) | ||||
−0.543956 | + | 0.839114i | \(0.683074\pi\) | |||||||
\(398\) | −1.36755 | + | 2.36867i | −0.0685493 | + | 0.118731i | ||||
\(399\) | − | 12.0751i | − | 0.604509i | ||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | − | 8.46569i | − | 0.422756i | −0.977404 | − | 0.211378i | \(-0.932205\pi\) | ||
0.977404 | − | 0.211378i | \(-0.0677951\pi\) | |||||||
\(402\) | −12.0127 | + | 6.93555i | −0.599140 | + | 0.345914i | ||||
\(403\) | 2.48207 | + | 4.29908i | 0.123641 | + | 0.214152i | ||||
\(404\) | −4.95679 | − | 8.58541i | −0.246609 | − | 0.427140i | ||||
\(405\) | −0.866025 | − | 0.500000i | −0.0430331 | − | 0.0248452i | ||||
\(406\) | 11.0004 | 0.545942 | ||||||||
\(407\) | 27.7308 | − | 15.9490i | 1.37457 | − | 0.790562i | ||||
\(408\) | −2.25684 | −0.111730 | ||||||||
\(409\) | −1.34173 | − | 0.774650i | −0.0663445 | − | 0.0383040i | 0.466461 | − | 0.884542i | \(-0.345529\pi\) |
−0.532805 | + | 0.846238i | \(0.678862\pi\) | |||||||
\(410\) | 2.73745 | + | 4.74141i | 0.135193 | + | 0.234161i | ||||
\(411\) | −7.09224 | − | 12.2841i | −0.349834 | − | 0.605931i | ||||
\(412\) | 9.59224 | − | 5.53809i | 0.472576 | − | 0.272842i | ||||
\(413\) | 35.9425i | 1.76862i | ||||||||
\(414\) | 0.963443 | + | 1.66873i | 0.0473506 | + | 0.0820137i | ||||
\(415\) | − | 13.6630i | − | 0.670689i | ||||||
\(416\) | 1.82947 | − | 3.16873i | 0.0896971 | − | 0.155360i | ||||
\(417\) | 21.3075 | 1.04343 | ||||||||
\(418\) | 19.4988 | 0.953717 | ||||||||
\(419\) | −16.3095 | + | 28.2489i | −0.796772 | + | 1.38005i | 0.124936 | + | 0.992165i | \(0.460127\pi\) |
−0.921708 | + | 0.387884i | \(0.873206\pi\) | |||||||
\(420\) | −2.82051 | + | 1.62842i | −0.137627 | + | 0.0794588i | ||||
\(421\) | 2.38884i | 0.116425i | 0.998304 | + | 0.0582124i | \(0.0185401\pi\) | ||||
−0.998304 | + | 0.0582124i | \(0.981460\pi\) | |||||||
\(422\) | −16.2985 | − | 9.40994i | −0.793398 | − | 0.458069i | ||||
\(423\) | −1.66383 | + | 2.88183i | −0.0808980 | + | 0.140119i | ||||
\(424\) | 8.82457 | + | 5.09487i | 0.428559 | + | 0.247429i | ||||
\(425\) | −1.95448 | + | 1.12842i | −0.0948064 | + | 0.0547365i | ||||
\(426\) | −0.372847 | + | 0.215263i | −0.0180645 | + | 0.0104295i | ||||
\(427\) | 3.48789 | + | 2.01373i | 0.168791 | + | 0.0974515i | ||||
\(428\) | 6.80147 | − | 11.7805i | 0.328761 | − | 0.569431i | ||||
\(429\) | −16.6648 | − | 9.62144i | −0.804586 | − | 0.464528i | ||||
\(430\) | 3.28360i | 0.158349i | ||||||||
\(431\) | 13.1116 | − | 7.56997i | 0.631562 | − | 0.364633i | −0.149795 | − | 0.988717i | \(-0.547861\pi\) |
0.781357 | + | 0.624084i | \(0.214528\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 33.0099 | 1.58635 | 0.793177 | − | 0.608991i | \(-0.208425\pi\) | ||||
0.793177 | + | 0.608991i | \(0.208425\pi\) | |||||||
\(434\) | −4.41862 | −0.212100 | ||||||||
\(435\) | 1.68882 | − | 2.92512i | 0.0809727 | − | 0.140249i | ||||
\(436\) | − | 7.41712i | − | 0.355215i | ||||||
\(437\) | 3.57206 | + | 6.18698i | 0.170875 | + | 0.295963i | ||||
\(438\) | − | 4.23689i | − | 0.202447i | ||||||
\(439\) | 12.4278 | − | 7.17520i | 0.593147 | − | 0.342454i | −0.173194 | − | 0.984888i | \(-0.555409\pi\) |
0.766341 | + | 0.642434i | \(0.222075\pi\) | |||||||
\(440\) | −2.62957 | − | 4.55456i | −0.125360 | − | 0.217130i | ||||
\(441\) | −1.80351 | − | 3.12377i | −0.0858815 | − | 0.148751i | ||||
\(442\) | 7.15133 | + | 4.12882i | 0.340154 | + | 0.196388i | ||||
\(443\) | 2.18743 | 0.103928 | 0.0519639 | − | 0.998649i | \(-0.483452\pi\) | ||||
0.0519639 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(444\) | −0.0101124 | + | 6.08275i | −0.000479915 | + | 0.288675i | ||||
\(445\) | −11.2644 | −0.533981 | ||||||||
\(446\) | 22.2042 | + | 12.8196i | 1.05140 | + | 0.607027i | ||||
\(447\) | −4.18361 | − | 7.24623i | −0.197878 | − | 0.342735i | ||||
\(448\) | 1.62842 | + | 2.82051i | 0.0769357 | + | 0.133257i | ||||
\(449\) | −32.0199 | + | 18.4867i | −1.51111 | + | 0.872441i | −0.511196 | + | 0.859464i | \(0.670797\pi\) |
−0.999916 | + | 0.0129764i | \(0.995869\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −14.3967 | − | 24.9358i | −0.677913 | − | 1.17418i | ||||
\(452\) | 0.315569i | 0.0148431i | ||||||||
\(453\) | 6.96505 | − | 12.0638i | 0.327247 | − | 0.566808i | ||||
\(454\) | 16.2498 | 0.762639 | ||||||||
\(455\) | 11.9166 | 0.558658 | ||||||||
\(456\) | −1.85380 | + | 3.21087i | −0.0868120 | + | 0.150363i | ||||
\(457\) | 13.9843 | − | 8.07387i | 0.654160 | − | 0.377679i | −0.135888 | − | 0.990724i | \(-0.543389\pi\) |
0.790048 | + | 0.613045i | \(0.210055\pi\) | |||||||
\(458\) | − | 11.7483i | − | 0.548963i | ||||||
\(459\) | −1.95448 | − | 1.12842i | −0.0912275 | − | 0.0526702i | ||||
\(460\) | 0.963443 | − | 1.66873i | 0.0449208 | − | 0.0778050i | ||||
\(461\) | −18.0603 | − | 10.4271i | −0.841152 | − | 0.485639i | 0.0165035 | − | 0.999864i | \(-0.494747\pi\) |
−0.857656 | + | 0.514224i | \(0.828080\pi\) | |||||||
\(462\) | 14.8335 | − | 8.56411i | 0.690116 | − | 0.398438i | ||||
\(463\) | −32.8561 | + | 18.9695i | −1.52695 | + | 0.881585i | −0.527463 | + | 0.849578i | \(0.676857\pi\) |
−0.999488 | + | 0.0320070i | \(0.989810\pi\) | |||||||
\(464\) | −2.92512 | − | 1.68882i | −0.135795 | − | 0.0784014i | ||||
\(465\) | −0.678359 | + | 1.17495i | −0.0314582 | + | 0.0544871i | ||||
\(466\) | 8.99446 | + | 5.19295i | 0.416660 | + | 0.240559i | ||||
\(467\) | 11.6625i | 0.539676i | 0.962906 | + | 0.269838i | \(0.0869702\pi\) | ||||
−0.962906 | + | 0.269838i | \(0.913030\pi\) | |||||||
\(468\) | 3.16873 | − | 1.82947i | 0.146475 | − | 0.0845672i | ||||
\(469\) | −22.5880 | + | 39.1236i | −1.04302 | + | 1.80656i | ||||
\(470\) | 3.32765 | 0.153493 | ||||||||
\(471\) | 8.98311 | 0.413920 | ||||||||
\(472\) | 5.51800 | − | 9.55745i | 0.253986 | − | 0.439917i | ||||
\(473\) | − | 17.2690i | − | 0.794028i | ||||||
\(474\) | −3.61504 | − | 6.26143i | −0.166044 | − | 0.287597i | ||||
\(475\) | 3.70759i | 0.170116i | ||||||||
\(476\) | −6.36544 | + | 3.67509i | −0.291760 | + | 0.168448i | ||||
\(477\) | 5.09487 | + | 8.82457i | 0.233278 | + | 0.404049i | ||||
\(478\) | 2.12625 | + | 3.68278i | 0.0972526 | + | 0.168446i | ||||
\(479\) | −32.7632 | − | 18.9158i | −1.49699 | − | 0.864286i | −0.496993 | − | 0.867755i | \(-0.665563\pi\) |
−0.999994 | + | 0.00346864i | \(0.998896\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 11.1602 | − | 19.2561i | 0.508864 | − | 0.878003i | ||||
\(482\) | 5.92273 | 0.269773 | ||||||||
\(483\) | 5.43480 | + | 3.13778i | 0.247292 | + | 0.142774i | ||||
\(484\) | 8.32932 | + | 14.4268i | 0.378605 | + | 0.655764i | ||||
\(485\) | 2.34709 | + | 4.06528i | 0.106576 | + | 0.184595i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | − | 34.0667i | − | 1.54371i | −0.635799 | − | 0.771855i | \(-0.719329\pi\) | ||
0.635799 | − | 0.771855i | \(-0.280671\pi\) | |||||||
\(488\) | −0.618309 | − | 1.07094i | −0.0279895 | − | 0.0484793i | ||||
\(489\) | − | 19.9626i | − | 0.902738i | ||||||
\(490\) | −1.80351 | + | 3.12377i | −0.0814744 | + | 0.141118i | ||||
\(491\) | 33.6933 | 1.52056 | 0.760278 | − | 0.649598i | \(-0.225063\pi\) | ||||
0.760278 | + | 0.649598i | \(0.225063\pi\) | |||||||
\(492\) | 5.47491 | 0.246828 | ||||||||
\(493\) | 3.81140 | − | 6.60154i | 0.171657 | − | 0.297318i | ||||
\(494\) | 11.7484 | − | 6.78293i | 0.528584 | − | 0.305178i | ||||
\(495\) | − | 5.25915i | − | 0.236381i | ||||||
\(496\) | 1.17495 | + | 0.678359i | 0.0527569 | + | 0.0304592i | ||||
\(497\) | −0.701079 | + | 1.21430i | −0.0314477 | + | 0.0544690i | ||||
\(498\) | −11.8325 | − | 6.83148i | −0.530226 | − | 0.306126i | ||||
\(499\) | −0.744312 | + | 0.429729i | −0.0333200 | + | 0.0192373i | −0.516567 | − | 0.856246i | \(-0.672790\pi\) |
0.483247 | + | 0.875484i | \(0.339457\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | 7.09782 | + | 4.09793i | 0.317107 | + | 0.183082i | ||||
\(502\) | 5.71248 | − | 9.89430i | 0.254960 | − | 0.441604i | ||||
\(503\) | 32.4710 | + | 18.7472i | 1.44781 | + | 0.835895i | 0.998351 | − | 0.0574051i | \(-0.0182827\pi\) |
0.449461 | + | 0.893300i | \(0.351616\pi\) | |||||||
\(504\) | 3.25684i | 0.145071i | ||||||||
\(505\) | −8.58541 | + | 4.95679i | −0.382046 | + | 0.220574i | ||||
\(506\) | −5.06689 | + | 8.77611i | −0.225251 | + | 0.390146i | ||||
\(507\) | −0.387818 | −0.0172236 | ||||||||
\(508\) | −14.6720 | −0.650966 | ||||||||
\(509\) | 13.1662 | − | 22.8045i | 0.583580 | − | 1.01079i | −0.411471 | − | 0.911423i | \(-0.634985\pi\) |
0.995051 | − | 0.0993671i | \(-0.0316818\pi\) | |||||||
\(510\) | 2.25684i | 0.0999347i | ||||||||
\(511\) | −6.89945 | − | 11.9502i | −0.305214 | − | 0.528646i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.21087 | + | 1.85380i | −0.141763 | + | 0.0818471i | ||||
\(514\) | −11.7333 | − | 20.3226i | −0.517532 | − | 0.896392i | ||||
\(515\) | −5.53809 | − | 9.59224i | −0.244037 | − | 0.422685i | ||||
\(516\) | 2.84368 | + | 1.64180i | 0.125186 | + | 0.0722763i | ||||
\(517\) | −17.5006 | −0.769676 | ||||||||
\(518\) | 9.87676 | + | 17.1729i | 0.433960 | + | 0.754535i | ||||
\(519\) | −15.9234 | −0.698959 | ||||||||
\(520\) | −3.16873 | − | 1.82947i | −0.138958 | − | 0.0802275i | ||||
\(521\) | 0.172543 | + | 0.298854i | 0.00755926 | + | 0.0130930i | 0.869780 | − | 0.493439i | \(-0.164260\pi\) |
−0.862221 | + | 0.506532i | \(0.830927\pi\) | |||||||
\(522\) | −1.68882 | − | 2.92512i | −0.0739176 | − | 0.128029i | ||||
\(523\) | 33.3875 | − | 19.2763i | 1.45993 | − | 0.842893i | 0.460926 | − | 0.887439i | \(-0.347517\pi\) |
0.999007 | + | 0.0445455i | \(0.0141840\pi\) | |||||||
\(524\) | − | 8.48241i | − | 0.370556i | ||||||
\(525\) | 1.62842 | + | 2.82051i | 0.0710701 | + | 0.123097i | ||||
\(526\) | 20.7970i | 0.906794i | ||||||||
\(527\) | −1.53095 | + | 2.65168i | −0.0666892 | + | 0.115509i | ||||
\(528\) | −5.25915 | −0.228875 | ||||||||
\(529\) | 19.2871 | 0.838570 | ||||||||
\(530\) | 5.09487 | − | 8.82457i | 0.221307 | − | 0.383315i | ||||
\(531\) | 9.55745 | − | 5.51800i | 0.414758 | − | 0.239461i | ||||
\(532\) | 12.0751i | 0.523520i | ||||||||
\(533\) | −17.3485 | − | 10.0162i | −0.751448 | − | 0.433848i | ||||
\(534\) | −5.63218 | + | 9.75521i | −0.243728 | + | 0.422149i | ||||
\(535\) | −11.7805 | − | 6.80147i | −0.509315 | − | 0.294053i | ||||
\(536\) | 12.0127 | − | 6.93555i | 0.518871 | − | 0.299570i | ||||
\(537\) | 0.779992 | − | 0.450328i | 0.0336591 | − | 0.0194331i | ||||
\(538\) | 17.6794 | + | 10.2072i | 0.762214 | + | 0.440064i | ||||
\(539\) | 9.48494 | − | 16.4284i | 0.408545 | − | 0.707621i | ||||
\(540\) | 0.866025 | + | 0.500000i | 0.0372678 | + | 0.0215166i | ||||
\(541\) | − | 0.789062i | − | 0.0339244i | −0.999856 | − | 0.0169622i | \(-0.994601\pi\) | ||
0.999856 | − | 0.0169622i | \(-0.00539950\pi\) | |||||||
\(542\) | −17.1038 | + | 9.87486i | −0.734669 | + | 0.424162i | ||||
\(543\) | 1.45760 | − | 2.52464i | 0.0625517 | − | 0.108343i | ||||
\(544\) | 2.25684 | 0.0967613 | ||||||||
\(545\) | −7.41712 | −0.317714 | ||||||||
\(546\) | 5.95829 | − | 10.3201i | 0.254991 | − | 0.441658i | ||||
\(547\) | − | 27.8104i | − | 1.18909i | −0.804063 | − | 0.594544i | \(-0.797332\pi\) | ||
0.804063 | − | 0.594544i | \(-0.202668\pi\) | |||||||
\(548\) | 7.09224 | + | 12.2841i | 0.302965 | + | 0.524752i | ||||
\(549\) | − | 1.23662i | − | 0.0527776i | ||||||
\(550\) | −4.55456 | + | 2.62957i | −0.194207 | + | 0.112125i | ||||
\(551\) | −6.26145 | − | 10.8452i | −0.266747 | − | 0.462019i | ||||
\(552\) | −0.963443 | − | 1.66873i | −0.0410069 | − | 0.0710260i | ||||
\(553\) | −20.3925 | − | 11.7736i | −0.867178 | − | 0.500665i | ||||
\(554\) | 0.646286 | 0.0274581 | ||||||||
\(555\) | 6.08275 | + | 0.0101124i | 0.258199 | + | 0.000429249i | ||||
\(556\) | −21.3075 | −0.903640 | ||||||||
\(557\) | 8.64914 | + | 4.99358i | 0.366476 | + | 0.211585i | 0.671918 | − | 0.740626i | \(-0.265471\pi\) |
−0.305442 | + | 0.952211i | \(0.598804\pi\) | |||||||
\(558\) | 0.678359 | + | 1.17495i | 0.0287172 | + | 0.0497397i | ||||
\(559\) | −6.00725 | − | 10.4049i | −0.254080 | − | 0.440079i | ||||
\(560\) | 2.82051 | − | 1.62842i | 0.119188 | − | 0.0688134i | ||||
\(561\) | − | 11.8691i | − | 0.501113i | ||||||
\(562\) | −0.989249 | − | 1.71343i | −0.0417289 | − | 0.0722766i | ||||
\(563\) | − | 35.7694i | − | 1.50750i | −0.657161 | − | 0.753751i | \(-0.728243\pi\) | ||
0.657161 | − | 0.753751i | \(-0.271757\pi\) | |||||||
\(564\) | 1.66383 | − | 2.88183i | 0.0700597 | − | 0.121347i | ||||
\(565\) | 0.315569 | 0.0132761 | ||||||||
\(566\) | −7.30367 | −0.306996 | ||||||||
\(567\) | −1.62842 | + | 2.82051i | −0.0683873 | + | 0.118450i | ||||
\(568\) | 0.372847 | − | 0.215263i | 0.0156443 | − | 0.00903225i | ||||
\(569\) | − | 1.94164i | − | 0.0813977i | −0.999171 | − | 0.0406989i | \(-0.987042\pi\) | ||
0.999171 | − | 0.0406989i | \(-0.0129584\pi\) | |||||||
\(570\) | 3.21087 | + | 1.85380i | 0.134489 | + | 0.0776470i | ||||
\(571\) | −12.2709 | + | 21.2539i | −0.513523 | + | 0.889448i | 0.486354 | + | 0.873762i | \(0.338327\pi\) |
−0.999877 | + | 0.0156863i | \(0.995007\pi\) | |||||||
\(572\) | 16.6648 | + | 9.62144i | 0.696792 | + | 0.402293i | ||||
\(573\) | −23.4667 | + | 13.5485i | −0.980335 | + | 0.565996i | ||||
\(574\) | 15.4420 | − | 8.91546i | 0.644538 | − | 0.372124i | ||||
\(575\) | −1.66873 | − | 0.963443i | −0.0695909 | − | 0.0401783i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 16.6742 | + | 9.62685i | 0.694156 | + | 0.400771i | 0.805167 | − | 0.593048i | \(-0.202076\pi\) |
−0.111011 | + | 0.993819i | \(0.535409\pi\) | |||||||
\(578\) | − | 11.9067i | − | 0.495252i | ||||||
\(579\) | 14.4071 | − | 8.31797i | 0.598740 | − | 0.345683i | ||||
\(580\) | −1.68882 | + | 2.92512i | −0.0701244 | + | 0.121459i | ||||
\(581\) | −44.4981 | −1.84609 | ||||||||
\(582\) | 4.69418 | 0.194580 | ||||||||
\(583\) | −26.7947 | + | 46.4097i | −1.10972 | + | 1.92209i | ||||
\(584\) | 4.23689i | 0.175324i | ||||||||
\(585\) | −1.82947 | − | 3.16873i | −0.0756392 | − | 0.131011i | ||||
\(586\) | − | 11.3388i | − | 0.468400i | ||||||
\(587\) | −0.346155 | + | 0.199853i | −0.0142873 | + | 0.00824880i | −0.507127 | − | 0.861872i | \(-0.669292\pi\) |
0.492839 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(588\) | 1.80351 | + | 3.12377i | 0.0743756 | + | 0.128822i | ||||
\(589\) | 2.51508 | + | 4.35625i | 0.103632 | + | 0.179496i | ||||
\(590\) | −9.55745 | − | 5.51800i | −0.393474 | − | 0.227172i | ||||
\(591\) | 17.1920 | 0.707184 | ||||||||
\(592\) | 0.0101124 | − | 6.08275i | 0.000415618 | − | 0.250000i | ||||
\(593\) | −14.6432 | −0.601325 | −0.300663 | − | 0.953731i | \(-0.597208\pi\) | ||||
−0.300663 | + | 0.953731i | \(0.597208\pi\) | |||||||
\(594\) | −4.55456 | − | 2.62957i | −0.186876 | − | 0.107893i | ||||
\(595\) | 3.67509 | + | 6.36544i | 0.150664 | + | 0.260958i | ||||
\(596\) | 4.18361 | + | 7.24623i | 0.171367 | + | 0.296817i | ||||
\(597\) | 2.36867 | − | 1.36755i | 0.0969433 | − | 0.0559702i | ||||
\(598\) | 7.05035i | 0.288310i | ||||||||
\(599\) | 6.43257 | + | 11.1415i | 0.262828 | + | 0.455231i | 0.966992 | − | 0.254806i | \(-0.0820116\pi\) |
−0.704165 | + | 0.710037i | \(0.748678\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | 8.59490 | − | 14.8868i | 0.350593 | − | 0.607246i | −0.635760 | − | 0.771887i | \(-0.719313\pi\) |
0.986354 | + | 0.164641i | \(0.0526466\pi\) | |||||||
\(602\) | 10.6942 | 0.435862 | ||||||||
\(603\) | 13.8711 | 0.564875 | ||||||||
\(604\) | −6.96505 | + | 12.0638i | −0.283404 | + | 0.490870i | ||||
\(605\) | 14.4268 | − | 8.32932i | 0.586533 | − | 0.338635i | ||||
\(606\) | 9.91358i | 0.402712i | ||||||||
\(607\) | −42.1054 | − | 24.3095i | −1.70900 | − | 0.986694i | −0.935796 | − | 0.352542i | \(-0.885317\pi\) |
−0.773208 | − | 0.634152i | \(-0.781349\pi\) | |||||||
\(608\) | 1.85380 | − | 3.21087i | 0.0751814 | − | 0.130218i | ||||
\(609\) | −9.52666 | − | 5.50022i | −0.386040 | − | 0.222880i | ||||
\(610\) | −1.07094 | + | 0.618309i | −0.0433612 | + | 0.0250346i | ||||
\(611\) | −10.5444 | + | 6.08783i | −0.426582 | + | 0.246287i | ||||
\(612\) | 1.95448 | + | 1.12842i | 0.0790053 | + | 0.0456137i | ||||
\(613\) | 14.6936 | − | 25.4501i | 0.593471 | − | 1.02792i | −0.400290 | − | 0.916389i | \(-0.631091\pi\) |
0.993761 | − | 0.111533i | \(-0.0355761\pi\) | |||||||
\(614\) | −8.26401 | − | 4.77123i | −0.333508 | − | 0.192551i | ||||
\(615\) | − | 5.47491i | − | 0.220770i | ||||||
\(616\) | −14.8335 | + | 8.56411i | −0.597658 | + | 0.345058i | ||||
\(617\) | −7.39870 | + | 12.8149i | −0.297860 | + | 0.515909i | −0.975646 | − | 0.219350i | \(-0.929606\pi\) |
0.677786 | + | 0.735259i | \(0.262940\pi\) | |||||||
\(618\) | −11.0762 | −0.445549 | ||||||||
\(619\) | −38.0010 | −1.52739 | −0.763694 | − | 0.645579i | \(-0.776616\pi\) | ||||
−0.763694 | + | 0.645579i | \(0.776616\pi\) | |||||||
\(620\) | 0.678359 | − | 1.17495i | 0.0272436 | − | 0.0471872i | ||||
\(621\) | − | 1.92689i | − | 0.0773233i | ||||||
\(622\) | −6.78050 | − | 11.7442i | −0.271873 | − | 0.470899i | ||||
\(623\) | 36.6862i | 1.46980i | ||||||||
\(624\) | −3.16873 | + | 1.82947i | −0.126851 | + | 0.0732373i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 1.69966 | + | 2.94389i | 0.0679320 | + | 0.117662i | ||||
\(627\) | −16.8864 | − | 9.74939i | −0.674380 | − | 0.389353i | ||||
\(628\) | −8.98311 | −0.358465 | ||||||||
\(629\) | 13.7278 | + | 0.0228222i | 0.547364 | + | 0.000909979i | ||||
\(630\) | 3.25684 | 0.129756 | ||||||||
\(631\) | −42.9542 | − | 24.7996i | −1.70998 | − | 0.987258i | −0.934555 | − | 0.355818i | \(-0.884202\pi\) |
−0.775425 | − | 0.631440i | \(-0.782464\pi\) | |||||||
\(632\) | 3.61504 | + | 6.26143i | 0.143799 | + | 0.249066i | ||||
\(633\) | 9.40994 | + | 16.2985i | 0.374012 | + | 0.647807i | ||||
\(634\) | −17.2966 | + | 9.98619i | −0.686935 | + | 0.396602i | ||||
\(635\) | 14.6720i | 0.582242i | ||||||||
\(636\) | −5.09487 | − | 8.82457i | −0.202025 | − | 0.349917i | ||||
\(637\) | − | 13.1979i | − | 0.522919i | ||||||
\(638\) | 8.88175 | − | 15.3836i | 0.351632 | − | 0.609044i | ||||
\(639\) | 0.430527 | 0.0170314 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −16.7195 | + | 28.9590i | −0.660379 | + | 1.14381i | 0.320137 | + | 0.947371i | \(0.396271\pi\) |
−0.980516 | + | 0.196439i | \(0.937062\pi\) | |||||||
\(642\) | −11.7805 | + | 6.80147i | −0.464939 | + | 0.268432i | ||||
\(643\) | − | 33.3367i | − | 1.31467i | −0.753598 | − | 0.657336i | \(-0.771683\pi\) | ||
0.753598 | − | 0.657336i | \(-0.228317\pi\) | |||||||
\(644\) | −5.43480 | − | 3.13778i | −0.214161 | − | 0.123646i | ||||
\(645\) | 1.64180 | − | 2.84368i | 0.0646459 | − | 0.111970i | ||||
\(646\) | 7.24643 | + | 4.18373i | 0.285107 | + | 0.164607i | ||||
\(647\) | 14.3341 | − | 8.27578i | 0.563530 | − | 0.325354i | −0.191031 | − | 0.981584i | \(-0.561183\pi\) |
0.754561 | + | 0.656230i | \(0.227850\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 50.2641 | + | 29.0200i | 1.97304 | + | 1.13913i | ||||
\(650\) | −1.82947 | + | 3.16873i | −0.0717577 | + | 0.124288i | ||||
\(651\) | 3.82664 | + | 2.20931i | 0.149978 | + | 0.0865897i | ||||
\(652\) | 19.9626i | 0.781794i | ||||||||
\(653\) | 4.84180 | − | 2.79541i | 0.189474 | − | 0.109393i | −0.402262 | − | 0.915525i | \(-0.631776\pi\) |
0.591736 | + | 0.806132i | \(0.298443\pi\) | |||||||
\(654\) | −3.70856 | + | 6.42341i | −0.145016 | + | 0.251175i | ||||
\(655\) | −8.48241 | −0.331435 | ||||||||
\(656\) | −5.47491 | −0.213759 | ||||||||
\(657\) | −2.11845 | + | 3.66926i | −0.0826485 | + | 0.143151i | ||||
\(658\) | − | 10.8376i | − | 0.422495i | ||||||
\(659\) | 9.79210 | + | 16.9604i | 0.381446 | + | 0.660684i | 0.991269 | − | 0.131853i | \(-0.0420928\pi\) |
−0.609823 | + | 0.792538i | \(0.708759\pi\) | |||||||
\(660\) | 5.25915i | 0.204712i | ||||||||
\(661\) | −9.20675 | + | 5.31552i | −0.358101 | + | 0.206750i | −0.668248 | − | 0.743939i | \(-0.732955\pi\) |
0.310146 | + | 0.950689i | \(0.399622\pi\) | |||||||
\(662\) | 4.93807 | + | 8.55298i | 0.191923 | + | 0.332421i | ||||
\(663\) | −4.12882 | − | 7.15133i | −0.160350 | − | 0.277735i | ||||
\(664\) | 11.8325 | + | 6.83148i | 0.459189 | + | 0.265113i | ||||
\(665\) | 12.0751 | 0.468250 | ||||||||
\(666\) | 3.05013 | − | 5.26276i | 0.118190 | − | 0.203928i | ||||
\(667\) | 6.50832 | 0.252003 | ||||||||
\(668\) | −7.09782 | − | 4.09793i | −0.274623 | − | 0.158554i | ||||
\(669\) | −12.8196 | − | 22.2042i | −0.495635 | − | 0.858466i | ||||
\(670\) | −6.93555 | − | 12.0127i | −0.267944 | − | 0.464092i | ||||
\(671\) | 5.63224 | − | 3.25178i | 0.217430 | − | 0.125533i | ||||
\(672\) | − | 3.25684i | − | 0.125635i | ||||||
\(673\) | −11.6444 | − | 20.1688i | −0.448860 | − | 0.777449i | 0.549452 | − | 0.835525i | \(-0.314837\pi\) |
−0.998312 | + | 0.0580767i | \(0.981503\pi\) | |||||||
\(674\) | − | 3.05134i | − | 0.117533i | ||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 0.387818 | 0.0149161 | ||||||||
\(677\) | −19.3235 | −0.742661 | −0.371331 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371331 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(678\) | 0.157785 | − | 0.273291i | 0.00605968 | − | 0.0104957i | ||||
\(679\) | 13.2400 | − | 7.64411i | 0.508104 | − | 0.293354i | ||||
\(680\) | − | 2.25684i | − | 0.0865460i | ||||||
\(681\) | −14.0727 | − | 8.12488i | −0.539268 | − | 0.311346i | ||||
\(682\) | −3.56759 | + | 6.17925i | −0.136610 | + | 0.236616i | ||||
\(683\) | 9.23123 | + | 5.32965i | 0.353223 | + | 0.203933i | 0.666104 | − | 0.745859i | \(-0.267961\pi\) |
−0.312881 | + | 0.949792i | \(0.601294\pi\) | |||||||
\(684\) | 3.21087 | − | 1.85380i | 0.122771 | − | 0.0708817i | ||||
\(685\) | 12.2841 | − | 7.09224i | 0.469352 | − | 0.270981i | ||||
\(686\) | −9.56992 | − | 5.52519i | −0.365381 | − | 0.210953i | ||||
\(687\) | −5.87416 | + | 10.1743i | −0.224113 | + | 0.388176i | ||||
\(688\) | −2.84368 | − | 1.64180i | −0.108414 | − | 0.0625931i | ||||
\(689\) | 37.2836i | 1.42039i | ||||||||
\(690\) | −1.66873 | + | 0.963443i | −0.0635275 | + | 0.0366776i | ||||
\(691\) | −15.6445 | + | 27.0971i | −0.595146 | + | 1.03082i | 0.398380 | + | 0.917220i | \(0.369572\pi\) |
−0.993526 | + | 0.113603i | \(0.963761\pi\) | |||||||
\(692\) | 15.9234 | 0.605316 | ||||||||
\(693\) | −17.1282 | −0.650647 | ||||||||
\(694\) | 13.4322 | − | 23.2652i | 0.509878 | − | 0.883135i | ||||
\(695\) | 21.3075i | 0.808240i | ||||||||
\(696\) | 1.68882 | + | 2.92512i | 0.0640145 | + | 0.110876i | ||||
\(697\) | − | 12.3560i | − | 0.468017i | ||||||
\(698\) | −13.9654 | + | 8.06293i | −0.528599 | + | 0.305187i | ||||
\(699\) | −5.19295 | − | 8.99446i | −0.196415 | − | 0.340202i | ||||
\(700\) | −1.62842 | − | 2.82051i | −0.0615485 | − | 0.106605i | ||||
\(701\) | 30.0642 | + | 17.3576i | 1.13551 | + | 0.655586i | 0.945315 | − | 0.326160i | \(-0.105755\pi\) |
0.190194 | + | 0.981746i | \(0.439088\pi\) | |||||||
\(702\) | −3.65894 | −0.138098 | ||||||||
\(703\) | 11.3087 | − | 19.5122i | 0.426514 | − | 0.735916i | ||||
\(704\) | 5.25915 | 0.198212 | ||||||||
\(705\) | −2.88183 | − | 1.66383i | −0.108536 | − | 0.0626633i | ||||
\(706\) | −8.71739 | − | 15.0990i | −0.328083 | − | 0.568257i | ||||
\(707\) | 16.1435 | + | 27.9613i | 0.607138 | + | 1.05159i | ||||
\(708\) | −9.55745 | + | 5.51800i | −0.359191 | + | 0.207379i | ||||
\(709\) | − | 14.9127i | − | 0.560056i | −0.959992 | − | 0.280028i | \(-0.909656\pi\) | ||
0.959992 | − | 0.280028i | \(-0.0903438\pi\) | |||||||
\(710\) | −0.215263 | − | 0.372847i | −0.00807869 | − | 0.0139927i | ||||
\(711\) | 7.23008i | 0.271149i | ||||||||
\(712\) | 5.63218 | − | 9.75521i | 0.211075 | − | 0.365592i | ||||
\(713\) | −2.61424 | −0.0979041 | ||||||||
\(714\) | 7.35018 | 0.275074 | ||||||||
\(715\) | 9.62144 | − | 16.6648i | 0.359822 | − | 0.623229i | ||||
\(716\) | −0.779992 | + | 0.450328i | −0.0291497 | + | 0.0168296i | ||||
\(717\) | − | 4.25251i | − | 0.158813i | ||||||
\(718\) | −4.44441 | − | 2.56598i | −0.165864 | − | 0.0957615i | ||||
\(719\) | 24.6771 | − | 42.7419i | 0.920300 | − | 1.59401i | 0.121348 | − | 0.992610i | \(-0.461278\pi\) |
0.798951 | − | 0.601396i | \(-0.205388\pi\) | |||||||
\(720\) | −0.866025 | − | 0.500000i | −0.0322749 | − | 0.0186339i | ||||
\(721\) | −31.2404 | + | 18.0367i | −1.16345 | + | 0.671721i | ||||
\(722\) | −4.54988 | + | 2.62687i | −0.169329 | + | 0.0977621i | ||||
\(723\) | −5.12924 | − | 2.96137i | −0.190758 | − | 0.110134i | ||||
\(724\) | −1.45760 | + | 2.52464i | −0.0541713 | + | 0.0938275i | ||||
\(725\) | 2.92512 | + | 1.68882i | 0.108636 | + | 0.0627212i | ||||
\(726\) | − | 16.6586i | − | 0.618260i | ||||||
\(727\) | −16.9389 | + | 9.77968i | −0.628229 | + | 0.362708i | −0.780066 | − | 0.625697i | \(-0.784815\pi\) |
0.151837 | + | 0.988406i | \(0.451481\pi\) | |||||||
\(728\) | −5.95829 | + | 10.3201i | −0.220829 | + | 0.382487i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.23689 | 0.156814 | ||||||||
\(731\) | 3.70529 | − | 6.41775i | 0.137045 | − | 0.237369i | ||||
\(732\) | 1.23662i | 0.0457067i | ||||||||
\(733\) | −3.88876 | − | 6.73552i | −0.143635 | − | 0.248782i | 0.785228 | − | 0.619207i | \(-0.212546\pi\) |
−0.928863 | + | 0.370424i | \(0.879212\pi\) | |||||||
\(734\) | − | 4.67369i | − | 0.172509i | ||||||
\(735\) | 3.12377 | − | 1.80351i | 0.115222 | − | 0.0665235i | ||||
\(736\) | 0.963443 | + | 1.66873i | 0.0355130 | + | 0.0615103i | ||||
\(737\) | 36.4751 | + | 63.1767i | 1.34358 | + | 2.32714i | ||||
\(738\) | −4.74141 | − | 2.73745i | −0.174534 | − | 0.100767i | ||||
\(739\) | 9.29956 | 0.342090 | 0.171045 | − | 0.985263i | \(-0.445286\pi\) | ||||
0.171045 | + | 0.985263i | \(0.445286\pi\) | |||||||
\(740\) | −6.08275 | − | 0.0101124i | −0.223606 | − | 0.000371740i | ||||
\(741\) | −13.5659 | −0.498354 | ||||||||
\(742\) | −28.7402 | − | 16.5932i | −1.05509 | − | 0.609155i | ||||
\(743\) | 6.76607 | + | 11.7192i | 0.248223 | + | 0.429935i | 0.963033 | − | 0.269384i | \(-0.0868201\pi\) |
−0.714810 | + | 0.699319i | \(0.753487\pi\) | |||||||
\(744\) | −0.678359 | − | 1.17495i | −0.0248699 | − | 0.0430759i | ||||
\(745\) | 7.24623 | − | 4.18361i | 0.265481 | − | 0.153276i | ||||
\(746\) | 26.8436i | 0.982816i | ||||||||
\(747\) | 6.83148 | + | 11.8325i | 0.249951 | + | 0.432928i | ||||
\(748\) | 11.8691i | 0.433976i | ||||||||
\(749\) | −22.1513 | + | 38.3672i | −0.809391 | + | 1.40191i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −2.87915 | −0.105062 | −0.0525309 | − | 0.998619i | \(-0.516729\pi\) | ||||
−0.0525309 | + | 0.998619i | \(0.516729\pi\) | |||||||
\(752\) | −1.66383 | + | 2.88183i | −0.0606735 | + | 0.105090i | ||||
\(753\) | −9.89430 | + | 5.71248i | −0.360568 | + | 0.208174i | ||||
\(754\) | − | 12.3586i | − | 0.450072i | ||||||
\(755\) | 12.0638 | + | 6.96505i | 0.439047 | + | 0.253484i | ||||
\(756\) | 1.62842 | − | 2.82051i | 0.0592251 | − | 0.102581i | ||||
\(757\) | −26.6459 | − | 15.3840i | −0.968463 | − | 0.559143i | −0.0696959 | − | 0.997568i | \(-0.522203\pi\) |
−0.898767 | + | 0.438426i | \(0.855536\pi\) | |||||||
\(758\) | −24.3491 | + | 14.0580i | −0.884400 | + | 0.510608i | ||||
\(759\) | 8.77611 | − | 5.06689i | 0.318553 | − | 0.183916i | ||||
\(760\) | −3.21087 | − | 1.85380i | −0.116471 | − | 0.0672443i | ||||
\(761\) | 5.21225 | − | 9.02789i | 0.188944 | − | 0.327261i | −0.755954 | − | 0.654624i | \(-0.772827\pi\) |
0.944898 | + | 0.327364i | \(0.106160\pi\) | |||||||
\(762\) | 12.7064 | + | 7.33602i | 0.460303 | + | 0.265756i | ||||
\(763\) | 24.1564i | 0.874520i | ||||||||
\(764\) | 23.4667 | − | 13.5485i | 0.848995 | − | 0.490167i | ||||
\(765\) | 1.12842 | − | 1.95448i | 0.0407982 | − | 0.0706645i | ||||
\(766\) | −26.4777 | −0.956679 | ||||||||
\(767\) | 40.3800 | 1.45804 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 10.2078i | 0.368104i | 0.982917 | + | 0.184052i | \(0.0589214\pi\) | ||||
−0.982917 | + | 0.184052i | \(0.941079\pi\) | |||||||
\(770\) | 8.56411 | + | 14.8335i | 0.308629 | + | 0.534561i | ||||
\(771\) | 23.4665i | 0.845126i | ||||||||
\(772\) | −14.4071 | + | 8.31797i | −0.518524 | + | 0.299370i | ||||
\(773\) | −15.3580 | − | 26.6008i | −0.552389 | − | 0.956765i | −0.998102 | − | 0.0615892i | \(-0.980383\pi\) |
0.445713 | − | 0.895176i | \(-0.352950\pi\) | |||||||
\(774\) | −1.64180 | − | 2.84368i | −0.0590134 | − | 0.102214i | ||||
\(775\) | −1.17495 | − | 0.678359i | −0.0422055 | − | 0.0243674i | ||||
\(776\) | −4.69418 | −0.168511 | ||||||||
\(777\) | 0.0329346 | − | 19.8106i | 0.00118152 | − | 0.710700i | ||||
\(778\) | −28.4824 | −1.02114 | ||||||||
\(779\) | −17.5792 | − | 10.1494i | −0.629841 | − | 0.363639i | ||||
\(780\) | 1.82947 | + | 3.16873i | 0.0655055 | + | 0.113459i | ||||
\(781\) | 1.13210 | + | 1.96086i | 0.0405098 | + | 0.0701650i | ||||
\(782\) | −3.76607 | + | 2.17434i | −0.134674 | + | 0.0777542i | ||||
\(783\) | 3.37764i | 0.120707i | ||||||||
\(784\) | −1.80351 | − | 3.12377i | −0.0644111 | − | 0.111563i | ||||
\(785\) | 8.98311i | 0.320621i | ||||||||
\(786\) | −4.24121 | + | 7.34599i | −0.151279 | + | 0.262023i | ||||
\(787\) | 20.5669 | 0.733129 | 0.366565 | − | 0.930393i | \(-0.380534\pi\) | ||||
0.366565 | + | 0.930393i | \(0.380534\pi\) | |||||||
\(788\) | −17.1920 | −0.612439 | ||||||||
\(789\) | 10.3985 | − | 18.0108i | 0.370197 | − | 0.641200i | ||||
\(790\) | 6.26143 | − | 3.61504i | 0.222772 | − | 0.128617i | ||||
\(791\) | − | 1.02776i | − | 0.0365429i | ||||||
\(792\) | 4.55456 | + | 2.62957i | 0.161839 | + | 0.0934378i | ||||
\(793\) | 2.26235 | − | 3.91851i | 0.0803385 | − | 0.139150i | ||||
\(794\) | −18.7724 | − | 10.8382i | −0.666207 | − | 0.384635i | ||||
\(795\) | −8.82457 | + | 5.09487i | −0.312975 | + | 0.180696i | ||||
\(796\) | −2.36867 | + | 1.36755i | −0.0839554 | + | 0.0484717i | ||||
\(797\) | −13.8819 | − | 8.01472i | −0.491722 | − | 0.283896i | 0.233567 | − | 0.972341i | \(-0.424960\pi\) |
−0.725289 | + | 0.688445i | \(0.758294\pi\) | |||||||
\(798\) | 6.03753 | − | 10.4573i | 0.213726 | − | 0.370184i | ||||
\(799\) | −6.50384 | − | 3.75499i | −0.230089 | − | 0.132842i | ||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 9.75521 | − | 5.63218i | 0.344684 | − | 0.199003i | ||||
\(802\) | 4.23284 | − | 7.33150i | 0.149467 | − | 0.258884i | ||||
\(803\) | −22.2825 | −0.786331 | ||||||||
\(804\) | −13.8711 | −0.489196 | ||||||||
\(805\) | −3.13778 | + | 5.43480i | −0.110592 | + | 0.191551i | ||||
\(806\) | 4.96415i | 0.174855i | ||||||||
\(807\) | −10.2072 | − | 17.6794i | −0.359311 | − | 0.622345i | ||||
\(808\) | − | 9.91358i | − | 0.348758i | ||||||
\(809\) | 27.9429 | − | 16.1329i | 0.982421 | − | 0.567201i | 0.0794206 | − | 0.996841i | \(-0.474693\pi\) |
0.903000 | + | 0.429640i | \(0.141360\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | −8.33138 | − | 14.4304i | −0.292554 | − | 0.506719i | 0.681859 | − | 0.731484i | \(-0.261172\pi\) |
−0.974413 | + | 0.224765i | \(0.927839\pi\) | |||||||
\(812\) | 9.52666 | + | 5.50022i | 0.334320 | + | 0.193020i | ||||
\(813\) | 19.7497 | 0.692653 | ||||||||
\(814\) | 31.9901 | + | 0.0531828i | 1.12125 | + | 0.00186405i | ||||
\(815\) | 19.9626 | 0.699258 | ||||||||
\(816\) | −1.95448 | − | 1.12842i | −0.0684206 | − | 0.0395026i | ||||
\(817\) | −6.08714 | − | 10.5432i | −0.212962 | − | 0.368861i | ||||
\(818\) | −0.774650 | − | 1.34173i | −0.0270850 | − | 0.0469126i | ||||
\(819\) | −10.3201 | + | 5.95829i | −0.360612 | + | 0.208200i | ||||
\(820\) | 5.47491i | 0.191192i | ||||||||
\(821\) | 13.8817 | + | 24.0439i | 0.484476 | + | 0.839137i | 0.999841 | − | 0.0178335i | \(-0.00567689\pi\) |
−0.515365 | + | 0.856971i | \(0.672344\pi\) | |||||||
\(822\) | − | 14.1845i | − | 0.494741i | ||||||
\(823\) | 16.7352 | − | 28.9863i | 0.583353 | − | 1.01040i | −0.411725 | − | 0.911308i | \(-0.635074\pi\) |
0.995079 | − | 0.0990896i | \(-0.0315930\pi\) | |||||||
\(824\) | 11.0762 | 0.385857 | ||||||||
\(825\) | 5.25915 | 0.183100 | ||||||||
\(826\) | −17.9713 | + | 31.1271i | −0.625300 | + | 1.08305i | ||||
\(827\) | −9.46985 | + | 5.46742i | −0.329299 | + | 0.190121i | −0.655530 | − | 0.755169i | \(-0.727555\pi\) |
0.326231 | + | 0.945290i | \(0.394221\pi\) | |||||||
\(828\) | 1.92689i | 0.0669639i | ||||||||
\(829\) | 19.8859 | + | 11.4811i | 0.690665 | + | 0.398756i | 0.803861 | − | 0.594817i | \(-0.202776\pi\) |
−0.113196 | + | 0.993573i | \(0.536109\pi\) | |||||||
\(830\) | 6.83148 | − | 11.8325i | 0.237124 | − | 0.410711i | ||||
\(831\) | −0.559700 | − | 0.323143i | −0.0194158 | − | 0.0112097i | ||||
\(832\) | 3.16873 | − | 1.82947i | 0.109856 | − | 0.0634254i | ||||
\(833\) | 7.04987 | − | 4.07024i | 0.244263 | − | 0.141026i | ||||
\(834\) | 18.4528 | + | 10.6538i | 0.638970 | + | 0.368909i | ||||
\(835\) | −4.09793 | + | 7.09782i | −0.141815 | + | 0.245630i | ||||
\(836\) | 16.8864 | + | 9.74939i | 0.584030 | + | 0.337190i | ||||
\(837\) | − | 1.35672i | − | 0.0468950i | ||||||
\(838\) | −28.2489 | + | 16.3095i | −0.975842 | + | 0.563403i | ||||
\(839\) | −19.2123 | + | 33.2767i | −0.663282 | + | 1.14884i | 0.316466 | + | 0.948604i | \(0.397504\pi\) |
−0.979748 | + | 0.200235i | \(0.935830\pi\) | |||||||
\(840\) | −3.25684 | −0.112372 | ||||||||
\(841\) | 17.5916 | 0.606606 | ||||||||
\(842\) | −1.19442 | + | 2.06879i | −0.0411624 | + | 0.0712954i | ||||
\(843\) | 1.97850i | 0.0681431i | ||||||||
\(844\) | −9.40994 | − | 16.2985i | −0.323904 | − | 0.561017i | ||||
\(845\) | − | 0.387818i | − | 0.0133413i | ||||||
\(846\) | −2.88183 | + | 1.66383i | −0.0990794 | + | 0.0572035i | ||||
\(847\) | −27.1273 | − | 46.9858i | −0.932104 | − | 1.61445i | ||||
\(848\) | 5.09487 | + | 8.82457i | 0.174958 | + | 0.303037i | ||||
\(849\) | 6.32516 | + | 3.65183i | 0.217079 | + | 0.125331i | ||||
\(850\) | −2.25684 | −0.0774091 | ||||||||
\(851\) | 5.84351 | + | 10.1602i | 0.200313 | + | 0.348288i | ||||
\(852\) | −0.430527 | −0.0147496 | ||||||||
\(853\) | −4.33922 | − | 2.50525i | −0.148572 | − | 0.0857781i | 0.423871 | − | 0.905723i | \(-0.360671\pi\) |
−0.572443 | + | 0.819944i | \(0.694004\pi\) | |||||||
\(854\) | 2.01373 | + | 3.48789i | 0.0689086 | + | 0.119353i | ||||
\(855\) | −1.85380 | − | 3.21087i | −0.0633985 | − | 0.109809i | ||||
\(856\) | 11.7805 | − | 6.80147i | 0.402649 | − | 0.232469i | ||||
\(857\) | − | 6.93762i | − | 0.236985i | −0.992955 | − | 0.118492i | \(-0.962194\pi\) | ||
0.992955 | − | 0.118492i | \(-0.0378061\pi\) | |||||||
\(858\) | −9.62144 | − | 16.6648i | −0.328471 | − | 0.568928i | ||||
\(859\) | 14.9800i | 0.511110i | 0.966795 | + | 0.255555i | \(0.0822581\pi\) | ||||
−0.966795 | + | 0.255555i | \(0.917742\pi\) | |||||||
\(860\) | −1.64180 | + | 2.84368i | −0.0559850 | + | 0.0969688i | ||||
\(861\) | −17.8309 | −0.607676 | ||||||||
\(862\) | 15.1399 | 0.515668 | ||||||||
\(863\) | 4.92892 | − | 8.53713i | 0.167782 | − | 0.290607i | −0.769858 | − | 0.638216i | \(-0.779673\pi\) |
0.937640 | + | 0.347608i | \(0.113006\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | − | 15.9234i | − | 0.541411i | ||||||
\(866\) | 28.5874 | + | 16.5049i | 0.971440 | + | 0.560861i | ||||
\(867\) | −5.95333 | + | 10.3115i | −0.202186 | + | 0.350196i | ||||
\(868\) | −3.82664 | − | 2.20931i | −0.129884 | − | 0.0749888i | ||||
\(869\) | −32.9298 | + | 19.0120i | −1.11707 | + | 0.644939i | ||||
\(870\) | 2.92512 | − | 1.68882i | 0.0991709 | − | 0.0572563i | ||||
\(871\) | 43.9538 | + | 25.3767i | 1.48932 | + | 0.859858i | ||||
\(872\) | 3.70856 | − | 6.42341i | 0.125588 | − | 0.217524i | ||||
\(873\) | −4.06528 | − | 2.34709i | −0.137589 | − | 0.0794370i | ||||
\(874\) | 7.14411i | 0.241653i | ||||||||
\(875\) | −2.82051 | + | 1.62842i | −0.0953506 | + | 0.0550507i | ||||
\(876\) | 2.11845 | − | 3.66926i | 0.0715757 | − | 0.123973i | ||||
\(877\) | −51.9937 | −1.75570 | −0.877851 | − | 0.478933i | \(-0.841024\pi\) | ||||
−0.877851 | + | 0.478933i | \(0.841024\pi\) | |||||||
\(878\) | 14.3504 | 0.484302 | ||||||||
\(879\) | −5.66939 | + | 9.81967i | −0.191224 | + | 0.331209i | ||||
\(880\) | − | 5.25915i | − | 0.177286i | ||||||
\(881\) | −4.43573 | − | 7.68291i | −0.149444 | − | 0.258844i | 0.781578 | − | 0.623807i | \(-0.214415\pi\) |
−0.931022 | + | 0.364963i | \(0.881082\pi\) | |||||||
\(882\) | − | 3.60702i | − | 0.121455i | ||||||
\(883\) | 22.0975 | − | 12.7580i | 0.743639 | − | 0.429340i | −0.0797521 | − | 0.996815i | \(-0.525413\pi\) |
0.823391 | + | 0.567475i | \(0.192080\pi\) | |||||||
\(884\) | 4.12882 | + | 7.15133i | 0.138867 | + | 0.240525i | ||||
\(885\) | 5.51800 | + | 9.55745i | 0.185485 | + | 0.321270i | ||||
\(886\) | 1.89437 | + | 1.09371i | 0.0636425 | + | 0.0367440i | ||||
\(887\) | −6.43597 | −0.216099 | −0.108049 | − | 0.994146i | \(-0.534460\pi\) | ||||
−0.108049 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(888\) | −3.05013 | + | 5.26276i | −0.102356 | + | 0.176607i | ||||
\(889\) | 47.7845 | 1.60264 | ||||||||
\(890\) | −9.75521 | − | 5.63218i | −0.326995 | − | 0.188791i | ||||
\(891\) | 2.62957 | + | 4.55456i | 0.0880940 | + | 0.152583i | ||||
\(892\) | 12.8196 | + | 22.2042i | 0.429233 | + | 0.743453i | ||||
\(893\) | −10.6847 | + | 6.16879i | −0.357549 | + | 0.206431i | ||||
\(894\) | − | 8.36723i | − | 0.279842i | ||||||
\(895\) | 0.450328 | + | 0.779992i | 0.0150528 | + | 0.0260722i | ||||
\(896\) | 3.25684i | 0.108803i | ||||||||
\(897\) | 3.52518 | − | 6.10579i | 0.117702 | − | 0.203866i | ||||
\(898\) | −36.9734 | −1.23382 | ||||||||
\(899\) | 4.58250 | 0.152835 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −19.9157 | + | 11.4983i | −0.663487 | + | 0.383064i | ||||
\(902\) | − | 28.7933i | − | 0.958714i | ||||||
\(903\) | −9.26143 | − | 5.34709i | −0.308201 | − | 0.177940i | ||||
\(904\) | −0.157785 | + | 0.273291i | −0.00524783 | + | 0.00908952i | ||||
\(905\) | 2.52464 | + | 1.45760i | 0.0839218 | + | 0.0484523i | ||||
\(906\) | 12.0638 | − | 6.96505i | 0.400794 | − | 0.231398i | ||||
\(907\) | −46.2924 | + | 26.7269i | −1.53711 | + | 0.887453i | −0.538108 | + | 0.842876i | \(0.680861\pi\) |
−0.999006 | + | 0.0445775i | \(0.985806\pi\) | |||||||
\(908\) | 14.0727 | + | 8.12488i | 0.467019 | + | 0.269634i | ||||
\(909\) | 4.95679 | − | 8.58541i | 0.164406 | − | 0.284760i | ||||
\(910\) | 10.3201 | + | 5.95829i | 0.342107 | + | 0.197515i | ||||
\(911\) | 2.44321i | 0.0809472i | 0.999181 | + | 0.0404736i | \(0.0128867\pi\) | ||||
−0.999181 | + | 0.0404736i | \(0.987113\pi\) | |||||||
\(912\) | −3.21087 | + | 1.85380i | −0.106323 | + | 0.0613854i | ||||
\(913\) | −35.9278 | + | 62.2288i | −1.18904 | + | 2.05947i | ||||
\(914\) | 16.1477 | 0.534119 | ||||||||
\(915\) | 1.23662 | 0.0408813 | ||||||||
\(916\) | 5.87416 | − | 10.1743i | 0.194088 | − | 0.336170i | ||||
\(917\) | 27.6259i | 0.912287i | ||||||||
\(918\) | −1.12842 | − | 1.95448i | −0.0372435 | − | 0.0645076i | ||||
\(919\) | 10.2898i | 0.339428i | 0.985493 | + | 0.169714i | \(0.0542843\pi\) | ||||
−0.985493 | + | 0.169714i | \(0.945716\pi\) | |||||||
\(920\) | 1.66873 | − | 0.963443i | 0.0550165 | − | 0.0317638i | ||||
\(921\) | 4.77123 | + | 8.26401i | 0.157217 | + | 0.272308i | ||||
\(922\) | −10.4271 | − | 18.0603i | −0.343399 | − | 0.594784i | ||||
\(923\) | 1.36422 | + | 0.787635i | 0.0449040 | + | 0.0259253i | ||||
\(924\) | 17.1282 | 0.563477 | ||||||||
\(925\) | −0.0101124 | + | 6.08275i | −0.000332495 | + | 0.200000i | ||||
\(926\) | −37.9389 | −1.24675 | ||||||||
\(927\) | 9.59224 | + | 5.53809i | 0.315051 | + | 0.181895i | ||||
\(928\) | −1.68882 | − | 2.92512i | −0.0554382 | − | 0.0960218i | ||||
\(929\) | −27.0673 | − | 46.8819i | −0.888048 | − | 1.53814i | −0.842180 | − | 0.539196i | \(-0.818728\pi\) |
−0.0458675 | − | 0.998948i | \(-0.514605\pi\) | |||||||
\(930\) | −1.17495 | + | 0.678359i | −0.0385282 | + | 0.0222443i | ||||
\(931\) | − | 13.3734i | − | 0.438295i | ||||||
\(932\) | 5.19295 | + | 8.99446i | 0.170101 | + | 0.294623i | ||||
\(933\) | 13.5610i | 0.443967i | ||||||||
\(934\) | −5.83125 | + | 10.1000i | −0.190804 | + | 0.330483i | ||||
\(935\) | 11.8691 | 0.388160 | ||||||||
\(936\) | 3.65894 | 0.119596 | ||||||||
\(937\) | 5.26556 | − | 9.12022i | 0.172018 | − | 0.297945i | −0.767107 | − | 0.641519i | \(-0.778304\pi\) |
0.939125 | + | 0.343575i | \(0.111638\pi\) | |||||||
\(938\) | −39.1236 | + | 22.5880i | −1.27743 | + | 0.737524i | ||||
\(939\) | − | 3.39931i | − | 0.110932i | ||||||
\(940\) | 2.88183 | + | 1.66383i | 0.0939950 | + | 0.0542680i | ||||
\(941\) | 8.95327 | − | 15.5075i | 0.291868 | − | 0.505531i | −0.682383 | − | 0.730995i | \(-0.739056\pi\) |
0.974252 | + | 0.225464i | \(0.0723897\pi\) | |||||||
\(942\) | 7.77960 | + | 4.49155i | 0.253473 | + | 0.146343i | ||||
\(943\) | 9.13615 | − | 5.27476i | 0.297514 | − | 0.171770i | ||||
\(944\) | 9.55745 | − | 5.51800i | 0.311069 | − | 0.179596i | ||||
\(945\) | −2.82051 | − | 1.62842i | −0.0917511 | − | 0.0529726i | ||||
\(946\) | 8.63448 | − | 14.9554i | 0.280731 | − | 0.486241i | ||||
\(947\) | 31.6666 | + | 18.2827i | 1.02903 | + | 0.594109i | 0.916706 | − | 0.399563i | \(-0.130838\pi\) |
0.112321 | + | 0.993672i | \(0.464171\pi\) | |||||||
\(948\) | − | 7.23008i | − | 0.234822i | ||||||
\(949\) | −13.4256 | + | 7.75126i | −0.435813 | + | 0.251617i | ||||
\(950\) | −1.85380 | + | 3.21087i | −0.0601451 | + | 0.104174i | ||||
\(951\) | 19.9724 | 0.647649 | ||||||||
\(952\) | −7.35018 | −0.238221 | ||||||||
\(953\) | −8.28478 | + | 14.3497i | −0.268370 | + | 0.464831i | −0.968441 | − | 0.249242i | \(-0.919818\pi\) |
0.700071 | + | 0.714073i | \(0.253152\pi\) | |||||||
\(954\) | 10.1897i | 0.329905i | ||||||||
\(955\) | −13.5485 | − | 23.4667i | −0.438419 | − | 0.759364i | ||||
\(956\) | 4.25251i | 0.137536i | ||||||||
\(957\) | −15.3836 | + | 8.88175i | −0.497282 | + | 0.287106i | ||||
\(958\) | −18.9158 | − | 32.7632i | −0.611142 | − | 1.05853i | ||||
\(959\) | −23.0983 | − | 40.0074i | −0.745883 | − | 1.29191i | ||||
\(960\) | 0.866025 | + | 0.500000i | 0.0279508 | + | 0.0161374i | ||||
\(961\) | 29.1593 | 0.940623 | ||||||||
\(962\) | 19.2931 | − | 11.0962i | 0.622035 | − | 0.357755i | ||||
\(963\) | 13.6029 | 0.438348 | ||||||||
\(964\) | 5.12924 | + | 2.96137i | 0.165202 | + | 0.0953792i | ||||
\(965\) | 8.31797 | + | 14.4071i | 0.267765 | + | 0.463782i | ||||
\(966\) | 3.13778 | + | 5.43480i | 0.100956 | + | 0.174862i | ||||
\(967\) | −15.2004 | + | 8.77593i | −0.488810 | + | 0.282215i | −0.724081 | − | 0.689715i | \(-0.757736\pi\) |
0.235270 | + | 0.971930i | \(0.424402\pi\) | |||||||
\(968\) | 16.6586i | 0.535429i | ||||||||
\(969\) | −4.18373 | − | 7.24643i | −0.134401 | − | 0.232789i | ||||
\(970\) | 4.69418i | 0.150721i | ||||||||
\(971\) | −2.09429 | + | 3.62741i | −0.0672088 | + | 0.116409i | −0.897672 | − | 0.440665i | \(-0.854743\pi\) |
0.830463 | + | 0.557074i | \(0.188076\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 69.3952 | 2.22471 | ||||||||
\(974\) | 17.0334 | − | 29.5026i | 0.545784 | − | 0.945325i | ||||
\(975\) | 3.16873 | − | 1.82947i | 0.101481 | − | 0.0585899i | ||||
\(976\) | − | 1.23662i | − | 0.0395832i | ||||||
\(977\) | 13.6731 | + | 7.89414i | 0.437440 | + | 0.252556i | 0.702511 | − | 0.711673i | \(-0.252062\pi\) |
−0.265071 | + | 0.964229i | \(0.585395\pi\) | |||||||
\(978\) | 9.98128 | − | 17.2881i | 0.319166 | − | 0.552812i | ||||
\(979\) | 51.3041 | + | 29.6204i | 1.63969 | + | 0.946673i | ||||
\(980\) | −3.12377 | + | 1.80351i | −0.0997853 | + | 0.0576111i | ||||
\(981\) | 6.42341 | − | 3.70856i | 0.205084 | − | 0.118405i | ||||
\(982\) | 29.1792 | + | 16.8466i | 0.931146 | + | 0.537597i | ||||
\(983\) | −15.4215 | + | 26.7108i | −0.491869 | + | 0.851941i | −0.999956 | − | 0.00936410i | \(-0.997019\pi\) |
0.508088 | + | 0.861305i | \(0.330353\pi\) | |||||||
\(984\) | 4.74141 | + | 2.73745i | 0.151151 | + | 0.0872668i | ||||
\(985\) | 17.1920i | 0.547782i | ||||||||
\(986\) | 6.60154 | − | 3.81140i | 0.210236 | − | 0.121380i | ||||
\(987\) | −5.41882 | + | 9.38567i | −0.172483 | + | 0.298749i | ||||
\(988\) | 13.5659 | 0.431587 | ||||||||
\(989\) | 6.32713 | 0.201191 | ||||||||
\(990\) | 2.62957 | − | 4.55456i | 0.0835733 | − | 0.144753i | ||||
\(991\) | 43.2922i | 1.37522i | 0.726079 | + | 0.687612i | \(0.241341\pi\) | ||||
−0.726079 | + | 0.687612i | \(0.758659\pi\) | |||||||
\(992\) | 0.678359 | + | 1.17495i | 0.0215379 | + | 0.0373048i | ||||
\(993\) | − | 9.87613i | − | 0.313410i | ||||||
\(994\) | −1.21430 | + | 0.701079i | −0.0385154 | + | 0.0222369i | ||||
\(995\) | 1.36755 | + | 2.36867i | 0.0433544 | + | 0.0750920i | ||||
\(996\) | −6.83148 | − | 11.8325i | −0.216464 | − | 0.374926i | ||||
\(997\) | 9.17242 | + | 5.29570i | 0.290493 | + | 0.167716i | 0.638164 | − | 0.769900i | \(-0.279694\pi\) |
−0.347671 | + | 0.937617i | \(0.613027\pi\) | |||||||
\(998\) | −0.859458 | −0.0272057 | ||||||||
\(999\) | −5.27288 | + | 3.03262i | −0.166826 | + | 0.0959478i |
(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 | 1110.2.x.d.841.5 | yes | 16 | |
37.11 | even | 6 | inner | 1110.2.x.d.751.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.x.d.751.5 | ✓ | 16 | 37.11 | even | 6 | inner | |
1110.2.x.d.841.5 | yes | 16 | 1.1 | even | 1 | trivial |