Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 161.15 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.d.491.6 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.645214 | + | 1.60739i | 0.372515 | + | 0.928026i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | −1.60739 | + | 0.645214i | −0.656214 | + | 0.263408i | ||||
\(7\) | −2.35643 | − | 4.08145i | −0.890645 | − | 1.54264i | −0.839103 | − | 0.543972i | \(-0.816920\pi\) |
−0.0515421 | − | 0.998671i | \(-0.516414\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.16740 | + | 2.07422i | −0.722466 | + | 0.691407i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −3.18522 | + | 5.51697i | −0.960381 | + | 1.66343i | −0.238838 | + | 0.971060i | \(0.576766\pi\) |
−0.721543 | + | 0.692369i | \(0.756567\pi\) | |||||||
\(12\) | −0.645214 | − | 1.60739i | −0.186257 | − | 0.464013i | ||||
\(13\) | −2.96986 | − | 1.71465i | −0.823690 | − | 0.475557i | 0.0279975 | − | 0.999608i | \(-0.491087\pi\) |
−0.851687 | + | 0.524051i | \(0.824420\pi\) | |||||||
\(14\) | 4.08145 | − | 2.35643i | 1.09081 | − | 0.629781i | ||||
\(15\) | −0.244922 | + | 1.71465i | −0.0632387 | + | 0.442720i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.65822 | − | 2.87212i | −0.402177 | − | 0.696592i | 0.591811 | − | 0.806077i | \(-0.298413\pi\) |
−0.993988 | + | 0.109485i | \(0.965080\pi\) | |||||||
\(18\) | −2.07422 | − | 2.16740i | −0.488898 | − | 0.510860i | ||||
\(19\) | −2.56125 | − | 4.43621i | −0.587590 | − | 1.01774i | −0.994547 | − | 0.104289i | \(-0.966743\pi\) |
0.406957 | − | 0.913447i | \(-0.366590\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 5.04008 | − | 6.42110i | 1.09983 | − | 1.40120i | ||||
\(22\) | −5.51697 | − | 3.18522i | −1.17622 | − | 0.679092i | ||||
\(23\) | 4.89435 | 1.02054 | 0.510271 | − | 0.860013i | \(-0.329545\pi\) | ||||
0.510271 | + | 0.860013i | \(0.329545\pi\) | |||||||
\(24\) | 1.60739 | − | 0.645214i | 0.328107 | − | 0.131704i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.71465 | − | 2.96986i | 0.336270 | − | 0.582436i | ||||
\(27\) | −4.73251 | − | 2.14553i | −0.910773 | − | 0.412908i | ||||
\(28\) | 2.35643 | + | 4.08145i | 0.445323 | + | 0.771322i | ||||
\(29\) | −5.57108 | −1.03452 | −0.517262 | − | 0.855827i | \(-0.673049\pi\) | ||||
−0.517262 | + | 0.855827i | \(0.673049\pi\) | |||||||
\(30\) | −1.71465 | − | 0.244922i | −0.313050 | − | 0.0447165i | ||||
\(31\) | 3.67202 | + | 4.18524i | 0.659515 | + | 0.751692i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −10.9231 | − | 1.56027i | −1.90146 | − | 0.271607i | ||||
\(34\) | 2.87212 | − | 1.65822i | 0.492565 | − | 0.284382i | ||||
\(35\) | − | 4.71285i | − | 0.796617i | ||||||
\(36\) | 2.16740 | − | 2.07422i | 0.361233 | − | 0.345703i | ||||
\(37\) | −4.26827 | + | 2.46429i | −0.701699 | + | 0.405126i | −0.807980 | − | 0.589210i | \(-0.799439\pi\) |
0.106281 | + | 0.994336i | \(0.466106\pi\) | |||||||
\(38\) | 4.43621 | − | 2.56125i | 0.719648 | − | 0.415489i | ||||
\(39\) | 0.839911 | − | 5.88003i | 0.134493 | − | 0.941558i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −8.33642 | − | 4.81303i | −1.30193 | − | 0.751670i | −0.321195 | − | 0.947013i | \(-0.604085\pi\) |
−0.980735 | + | 0.195343i | \(0.937418\pi\) | |||||||
\(42\) | 6.42110 | + | 5.04008i | 0.990798 | + | 0.777701i | ||||
\(43\) | −5.26899 | + | 3.04205i | −0.803514 | + | 0.463909i | −0.844698 | − | 0.535243i | \(-0.820220\pi\) |
0.0411847 | + | 0.999152i | \(0.486887\pi\) | |||||||
\(44\) | 3.18522 | − | 5.51697i | 0.480191 | − | 0.831714i | ||||
\(45\) | −2.91413 | + | 0.712629i | −0.434413 | + | 0.106232i | ||||
\(46\) | 4.89435i | 0.721633i | ||||||||
\(47\) | 3.50612i | 0.511421i | 0.966753 | + | 0.255710i | \(0.0823094\pi\) | ||||
−0.966753 | + | 0.255710i | \(0.917691\pi\) | |||||||
\(48\) | 0.645214 | + | 1.60739i | 0.0931287 | + | 0.232007i | ||||
\(49\) | −7.60549 | + | 13.1731i | −1.08650 | + | 1.88187i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 3.54671 | − | 4.51854i | 0.496639 | − | 0.632722i | ||||
\(52\) | 2.96986 | + | 1.71465i | 0.411845 | + | 0.237779i | ||||
\(53\) | −0.645608 | + | 1.11823i | −0.0886810 | + | 0.153600i | −0.906954 | − | 0.421230i | \(-0.861599\pi\) |
0.818273 | + | 0.574830i | \(0.194932\pi\) | |||||||
\(54\) | 2.14553 | − | 4.73251i | 0.291970 | − | 0.644014i | ||||
\(55\) | −5.51697 | + | 3.18522i | −0.743908 | + | 0.429495i | ||||
\(56\) | −4.08145 | + | 2.35643i | −0.545407 | + | 0.314891i | ||||
\(57\) | 5.47816 | − | 6.97923i | 0.725600 | − | 0.924421i | ||||
\(58\) | − | 5.57108i | − | 0.731519i | ||||||
\(59\) | 4.87072 | − | 2.81211i | 0.634114 | − | 0.366106i | −0.148229 | − | 0.988953i | \(-0.547357\pi\) |
0.782344 | + | 0.622847i | \(0.214024\pi\) | |||||||
\(60\) | 0.244922 | − | 1.71465i | 0.0316193 | − | 0.221360i | ||||
\(61\) | − | 1.31888i | − | 0.168866i | −0.996429 | − | 0.0844328i | \(-0.973092\pi\) | ||
0.996429 | − | 0.0844328i | \(-0.0269078\pi\) | |||||||
\(62\) | −4.18524 | + | 3.67202i | −0.531526 | + | 0.466347i | ||||
\(63\) | 13.5731 | + | 3.95837i | 1.71005 | + | 0.498708i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.71465 | − | 2.96986i | −0.212676 | − | 0.368365i | ||||
\(66\) | 1.56027 | − | 10.9231i | 0.192055 | − | 1.34454i | ||||
\(67\) | 7.24848 | − | 12.5547i | 0.885542 | − | 1.53380i | 0.0404514 | − | 0.999182i | \(-0.487120\pi\) |
0.845091 | − | 0.534623i | \(-0.179546\pi\) | |||||||
\(68\) | 1.65822 | + | 2.87212i | 0.201089 | + | 0.348296i | ||||
\(69\) | 3.15791 | + | 7.86713i | 0.380167 | + | 0.947091i | ||||
\(70\) | 4.71285 | 0.563294 | ||||||||
\(71\) | 1.61036 | + | 0.929740i | 0.191114 | + | 0.110340i | 0.592504 | − | 0.805567i | \(-0.298139\pi\) |
−0.401390 | + | 0.915907i | \(0.631473\pi\) | |||||||
\(72\) | 2.07422 | + | 2.16740i | 0.244449 | + | 0.255430i | ||||
\(73\) | 9.05398 | + | 5.22732i | 1.05969 | + | 0.611811i | 0.925346 | − | 0.379124i | \(-0.123774\pi\) |
0.134342 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(74\) | −2.46429 | − | 4.26827i | −0.286467 | − | 0.496176i | ||||
\(75\) | −1.06943 | + | 1.36247i | −0.123487 | + | 0.157324i | ||||
\(76\) | 2.56125 | + | 4.43621i | 0.293795 | + | 0.508868i | ||||
\(77\) | 30.0230 | 3.42144 | ||||||||
\(78\) | 5.88003 | + | 0.839911i | 0.665782 | + | 0.0951012i | ||||
\(79\) | 0.954760 | − | 0.551231i | 0.107419 | − | 0.0620183i | −0.445328 | − | 0.895367i | \(-0.646913\pi\) |
0.552747 | + | 0.833349i | \(0.313580\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | 0.395219 | − | 8.99132i | 0.0439133 | − | 0.999035i | ||||
\(82\) | 4.81303 | − | 8.33642i | 0.531511 | − | 0.920603i | ||||
\(83\) | −3.19991 | + | 5.54241i | −0.351236 | + | 0.608358i | −0.986466 | − | 0.163964i | \(-0.947572\pi\) |
0.635231 | + | 0.772323i | \(0.280905\pi\) | |||||||
\(84\) | −5.04008 | + | 6.42110i | −0.549917 | + | 0.700600i | ||||
\(85\) | − | 3.31644i | − | 0.359718i | ||||||
\(86\) | −3.04205 | − | 5.26899i | −0.328033 | − | 0.568170i | ||||
\(87\) | −3.59454 | − | 8.95489i | −0.385375 | − | 0.960065i | ||||
\(88\) | 5.51697 | + | 3.18522i | 0.588111 | + | 0.339546i | ||||
\(89\) | −6.30402 | −0.668225 | −0.334112 | − | 0.942533i | \(-0.608437\pi\) | ||||
−0.334112 | + | 0.942533i | \(0.608437\pi\) | |||||||
\(90\) | −0.712629 | − | 2.91413i | −0.0751177 | − | 0.307176i | ||||
\(91\) | 16.1618i | 1.69421i | ||||||||
\(92\) | −4.89435 | −0.510271 | ||||||||
\(93\) | −4.35807 | + | 8.60275i | −0.451911 | + | 0.892063i | ||||
\(94\) | −3.50612 | −0.361629 | ||||||||
\(95\) | − | 5.12249i | − | 0.525557i | ||||||
\(96\) | −1.60739 | + | 0.645214i | −0.164053 | + | 0.0658519i | ||||
\(97\) | 0.469167 | 0.0476367 | 0.0238183 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238183 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(98\) | −13.1731 | − | 7.60549i | −1.33068 | − | 0.768270i | ||||
\(99\) | −4.53977 | − | 18.5643i | −0.456264 | − | 1.86578i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 15.8938i | 1.58149i | 0.612143 | + | 0.790747i | \(0.290308\pi\) | ||||
−0.612143 | + | 0.790747i | \(0.709692\pi\) | |||||||
\(102\) | 4.51854 | + | 3.54671i | 0.447402 | + | 0.351176i | ||||
\(103\) | −7.58503 | + | 13.1377i | −0.747375 | + | 1.29449i | 0.201701 | + | 0.979447i | \(0.435353\pi\) |
−0.949077 | + | 0.315045i | \(0.897980\pi\) | |||||||
\(104\) | −1.71465 | + | 2.96986i | −0.168135 | + | 0.291218i | ||||
\(105\) | 7.57539 | − | 3.04080i | 0.739282 | − | 0.296752i | ||||
\(106\) | −1.11823 | − | 0.645608i | −0.108612 | − | 0.0627070i | ||||
\(107\) | 12.6046 | − | 7.27724i | 1.21853 | − | 0.703518i | 0.253925 | − | 0.967224i | \(-0.418278\pi\) |
0.964603 | + | 0.263706i | \(0.0849449\pi\) | |||||||
\(108\) | 4.73251 | + | 2.14553i | 0.455386 | + | 0.206454i | ||||
\(109\) | −13.1729 | −1.26174 | −0.630869 | − | 0.775890i | \(-0.717301\pi\) | ||||
−0.630869 | + | 0.775890i | \(0.717301\pi\) | |||||||
\(110\) | −3.18522 | − | 5.51697i | −0.303699 | − | 0.526022i | ||||
\(111\) | −6.71501 | − | 5.27077i | −0.637361 | − | 0.500280i | ||||
\(112\) | −2.35643 | − | 4.08145i | −0.222661 | − | 0.385661i | ||||
\(113\) | 3.12246 | + | 1.80276i | 0.293737 | + | 0.169589i | 0.639626 | − | 0.768686i | \(-0.279089\pi\) |
−0.345889 | + | 0.938275i | \(0.612423\pi\) | |||||||
\(114\) | 6.97923 | + | 5.47816i | 0.653664 | + | 0.513077i | ||||
\(115\) | 4.23863 | + | 2.44718i | 0.395255 | + | 0.228200i | ||||
\(116\) | 5.57108 | 0.517262 | ||||||||
\(117\) | 9.99341 | − | 2.44381i | 0.923891 | − | 0.225931i | ||||
\(118\) | 2.81211 | + | 4.87072i | 0.258876 | + | 0.448386i | ||||
\(119\) | −7.81495 | + | 13.5359i | −0.716395 | + | 1.24083i | ||||
\(120\) | 1.71465 | + | 0.244922i | 0.156525 | + | 0.0223583i | ||||
\(121\) | −14.7913 | − | 25.6193i | −1.34466 | − | 2.32903i | ||||
\(122\) | 1.31888 | 0.119406 | ||||||||
\(123\) | 2.35764 | − | 16.5053i | 0.212581 | − | 1.48823i | ||||
\(124\) | −3.67202 | − | 4.18524i | −0.329757 | − | 0.375846i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −3.95837 | + | 13.5731i | −0.352640 | + | 1.20919i | ||||
\(127\) | 2.83079 | − | 1.63436i | 0.251192 | − | 0.145026i | −0.369118 | − | 0.929383i | \(-0.620340\pi\) |
0.620310 | + | 0.784357i | \(0.287007\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −8.28939 | − | 6.50654i | −0.729840 | − | 0.572869i | ||||
\(130\) | 2.96986 | − | 1.71465i | 0.260474 | − | 0.150384i | ||||
\(131\) | −8.11286 | + | 4.68396i | −0.708824 | + | 0.409240i | −0.810625 | − | 0.585565i | \(-0.800873\pi\) |
0.101802 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(132\) | 10.9231 | + | 1.56027i | 0.950731 | + | 0.135804i | ||||
\(133\) | −12.0708 | + | 20.9072i | −1.04667 | + | 1.81288i | ||||
\(134\) | 12.5547 | + | 7.24848i | 1.08456 | + | 0.626173i | ||||
\(135\) | −3.02571 | − | 4.22434i | −0.260412 | − | 0.363574i | ||||
\(136\) | −2.87212 | + | 1.65822i | −0.246282 | + | 0.142191i | ||||
\(137\) | −2.06547 | + | 3.57749i | −0.176465 | + | 0.305646i | −0.940667 | − | 0.339331i | \(-0.889799\pi\) |
0.764203 | + | 0.644976i | \(0.223133\pi\) | |||||||
\(138\) | −7.86713 | + | 3.15791i | −0.669694 | + | 0.268819i | ||||
\(139\) | 20.7544i | 1.76037i | 0.474633 | + | 0.880184i | \(0.342581\pi\) | ||||
−0.474633 | + | 0.880184i | \(0.657419\pi\) | |||||||
\(140\) | 4.71285i | 0.398309i | ||||||||
\(141\) | −5.63571 | + | 2.26220i | −0.474612 | + | 0.190512i | ||||
\(142\) | −0.929740 | + | 1.61036i | −0.0780220 | + | 0.135138i | ||||
\(143\) | 18.9193 | − | 10.9231i | 1.58211 | − | 0.913433i | ||||
\(144\) | −2.16740 | + | 2.07422i | −0.180616 | + | 0.172852i | ||||
\(145\) | −4.82470 | − | 2.78554i | −0.400669 | − | 0.231326i | ||||
\(146\) | −5.22732 | + | 9.05398i | −0.432616 | + | 0.749313i | ||||
\(147\) | −26.0814 | − | 3.72551i | −2.15116 | − | 0.307275i | ||||
\(148\) | 4.26827 | − | 2.46429i | 0.350849 | − | 0.202563i | ||||
\(149\) | 0.0549861 | − | 0.0317462i | 0.00450464 | − | 0.00260075i | −0.497746 | − | 0.867323i | \(-0.665839\pi\) |
0.502251 | + | 0.864722i | \(0.332505\pi\) | |||||||
\(150\) | −1.36247 | − | 1.06943i | −0.111245 | − | 0.0873188i | ||||
\(151\) | − | 2.80211i | − | 0.228033i | −0.993479 | − | 0.114016i | \(-0.963628\pi\) | ||
0.993479 | − | 0.114016i | \(-0.0363717\pi\) | |||||||
\(152\) | −4.43621 | + | 2.56125i | −0.359824 | + | 0.207745i | ||||
\(153\) | 9.55144 | + | 2.78551i | 0.772188 | + | 0.225195i | ||||
\(154\) | 30.0230i | 2.41932i | ||||||||
\(155\) | 1.08744 | + | 5.46054i | 0.0873456 | + | 0.438601i | ||||
\(156\) | −0.839911 | + | 5.88003i | −0.0672467 | + | 0.470779i | ||||
\(157\) | 0.873360 | 0.0697017 | 0.0348509 | − | 0.999393i | \(-0.488904\pi\) | ||||
0.0348509 | + | 0.999393i | \(0.488904\pi\) | |||||||
\(158\) | 0.551231 | + | 0.954760i | 0.0438536 | + | 0.0759566i | ||||
\(159\) | −2.21398 | − | 0.316248i | −0.175580 | − | 0.0250801i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −11.5332 | − | 19.9761i | −0.908942 | − | 1.57433i | ||||
\(162\) | 8.99132 | + | 0.395219i | 0.706425 | + | 0.0310514i | ||||
\(163\) | 2.46179 | 0.192822 | 0.0964112 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964112 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(164\) | 8.33642 | + | 4.81303i | 0.650965 | + | 0.375835i | ||||
\(165\) | −8.67952 | − | 6.81276i | −0.675700 | − | 0.530373i | ||||
\(166\) | −5.54241 | − | 3.19991i | −0.430174 | − | 0.248361i | ||||
\(167\) | 6.58051 | + | 11.3978i | 0.509215 | + | 0.881987i | 0.999943 | + | 0.0106739i | \(0.00339766\pi\) |
−0.490728 | + | 0.871313i | \(0.663269\pi\) | |||||||
\(168\) | −6.42110 | − | 5.04008i | −0.495399 | − | 0.388850i | ||||
\(169\) | −0.619974 | − | 1.07383i | −0.0476903 | − | 0.0826020i | ||||
\(170\) | 3.31644 | 0.254359 | ||||||||
\(171\) | 14.7529 | + | 4.30244i | 1.12818 | + | 0.329016i | ||||
\(172\) | 5.26899 | − | 3.04205i | 0.401757 | − | 0.231954i | ||||
\(173\) | −2.37379 | − | 1.37051i | −0.180476 | − | 0.104198i | 0.407040 | − | 0.913410i | \(-0.366561\pi\) |
−0.587516 | + | 0.809212i | \(0.699894\pi\) | |||||||
\(174\) | 8.95489 | − | 3.59454i | 0.678868 | − | 0.272501i | ||||
\(175\) | 2.35643 | − | 4.08145i | 0.178129 | − | 0.308529i | ||||
\(176\) | −3.18522 | + | 5.51697i | −0.240095 | + | 0.415857i | ||||
\(177\) | 7.66282 | + | 6.01473i | 0.575973 | + | 0.452095i | ||||
\(178\) | − | 6.30402i | − | 0.472506i | ||||||
\(179\) | 1.52614 | + | 2.64335i | 0.114069 | + | 0.197573i | 0.917407 | − | 0.397950i | \(-0.130278\pi\) |
−0.803338 | + | 0.595523i | \(0.796945\pi\) | |||||||
\(180\) | 2.91413 | − | 0.712629i | 0.217207 | − | 0.0531162i | ||||
\(181\) | −13.9592 | − | 8.05934i | −1.03758 | − | 0.599046i | −0.118432 | − | 0.992962i | \(-0.537787\pi\) |
−0.919146 | + | 0.393916i | \(0.871120\pi\) | |||||||
\(182\) | −16.1618 | −1.19799 | ||||||||
\(183\) | 2.11996 | − | 0.850962i | 0.156712 | − | 0.0629049i | ||||
\(184\) | − | 4.89435i | − | 0.360816i | ||||||
\(185\) | −4.92857 | −0.362356 | ||||||||
\(186\) | −8.60275 | − | 4.35807i | −0.630784 | − | 0.319549i | ||||
\(187\) | 21.1272 | 1.54497 | ||||||||
\(188\) | − | 3.50612i | − | 0.255710i | ||||||
\(189\) | 2.39494 | + | 24.3713i | 0.174206 | + | 1.77275i | ||||
\(190\) | 5.12249 | 0.371625 | ||||||||
\(191\) | 7.57495 | + | 4.37340i | 0.548104 | + | 0.316448i | 0.748357 | − | 0.663296i | \(-0.230843\pi\) |
−0.200253 | + | 0.979744i | \(0.564176\pi\) | |||||||
\(192\) | −0.645214 | − | 1.60739i | −0.0465643 | − | 0.116003i | ||||
\(193\) | −10.7607 | − | 18.6381i | −0.774574 | − | 1.34160i | −0.935033 | − | 0.354560i | \(-0.884631\pi\) |
0.160459 | − | 0.987043i | \(-0.448703\pi\) | |||||||
\(194\) | 0.469167i | 0.0336842i | ||||||||
\(195\) | 3.66740 | − | 4.67230i | 0.262628 | − | 0.334590i | ||||
\(196\) | 7.60549 | − | 13.1731i | 0.543249 | − | 0.940935i | ||||
\(197\) | −7.08814 | + | 12.2770i | −0.505009 | + | 0.874701i | 0.494974 | + | 0.868908i | \(0.335177\pi\) |
−0.999983 | + | 0.00579339i | \(0.998156\pi\) | |||||||
\(198\) | 18.5643 | − | 4.53977i | 1.31931 | − | 0.322627i | ||||
\(199\) | −6.70999 | − | 3.87401i | −0.475658 | − | 0.274622i | 0.242947 | − | 0.970040i | \(-0.421886\pi\) |
−0.718605 | + | 0.695418i | \(0.755219\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 24.8571 | + | 3.55063i | 1.75329 | + | 0.250442i | ||||
\(202\) | −15.8938 | −1.11828 | ||||||||
\(203\) | 13.1278 | + | 22.7381i | 0.921394 | + | 1.59590i | ||||
\(204\) | −3.54671 | + | 4.51854i | −0.248319 | + | 0.316361i | ||||
\(205\) | −4.81303 | − | 8.33642i | −0.336157 | − | 0.582241i | ||||
\(206\) | −13.1377 | − | 7.58503i | −0.915344 | − | 0.528474i | ||||
\(207\) | −10.6080 | + | 10.1520i | −0.737307 | + | 0.705610i | ||||
\(208\) | −2.96986 | − | 1.71465i | −0.205922 | − | 0.118889i | ||||
\(209\) | 32.6326 | 2.25724 | ||||||||
\(210\) | 3.04080 | + | 7.57539i | 0.209835 | + | 0.522751i | ||||
\(211\) | −7.68821 | − | 13.3164i | −0.529279 | − | 0.916737i | −0.999417 | − | 0.0341446i | \(-0.989129\pi\) |
0.470138 | − | 0.882593i | \(-0.344204\pi\) | |||||||
\(212\) | 0.645608 | − | 1.11823i | 0.0443405 | − | 0.0768000i | ||||
\(213\) | −0.455428 | + | 3.18835i | −0.0312054 | + | 0.218462i | ||||
\(214\) | 7.27724 | + | 12.6046i | 0.497462 | + | 0.861630i | ||||
\(215\) | −6.08411 | −0.414933 | ||||||||
\(216\) | −2.14553 | + | 4.73251i | −0.145985 | + | 0.322007i | ||||
\(217\) | 8.42900 | − | 24.8494i | 0.572198 | − | 1.68689i | ||||
\(218\) | − | 13.1729i | − | 0.892183i | ||||||
\(219\) | −2.56057 | + | 17.9260i | −0.173028 | + | 1.21133i | ||||
\(220\) | 5.51697 | − | 3.18522i | 0.371954 | − | 0.214748i | ||||
\(221\) | 11.3730i | 0.765034i | ||||||||
\(222\) | 5.27077 | − | 6.71501i | 0.353751 | − | 0.450682i | ||||
\(223\) | −9.74718 | + | 5.62754i | −0.652719 | + | 0.376848i | −0.789497 | − | 0.613754i | \(-0.789659\pi\) |
0.136778 | + | 0.990602i | \(0.456325\pi\) | |||||||
\(224\) | 4.08145 | − | 2.35643i | 0.272703 | − | 0.157445i | ||||
\(225\) | −2.88003 | − | 0.839911i | −0.192002 | − | 0.0559940i | ||||
\(226\) | −1.80276 | + | 3.12246i | −0.119918 | + | 0.207703i | ||||
\(227\) | −19.1006 | − | 11.0278i | −1.26775 | − | 0.731938i | −0.293191 | − | 0.956054i | \(-0.594717\pi\) |
−0.974562 | + | 0.224116i | \(0.928050\pi\) | |||||||
\(228\) | −5.47816 | + | 6.97923i | −0.362800 | + | 0.462210i | ||||
\(229\) | −6.32764 | + | 3.65326i | −0.418142 | + | 0.241414i | −0.694282 | − | 0.719703i | \(-0.744278\pi\) |
0.276140 | + | 0.961117i | \(0.410945\pi\) | |||||||
\(230\) | −2.44718 | + | 4.23863i | −0.161362 | + | 0.279487i | ||||
\(231\) | 19.3713 | + | 48.2586i | 1.27453 | + | 3.17518i | ||||
\(232\) | 5.57108i | 0.365759i | ||||||||
\(233\) | 9.29519i | 0.608948i | 0.952521 | + | 0.304474i | \(0.0984806\pi\) | ||||
−0.952521 | + | 0.304474i | \(0.901519\pi\) | |||||||
\(234\) | 2.44381 | + | 9.99341i | 0.159757 | + | 0.653290i | ||||
\(235\) | −1.75306 | + | 3.03639i | −0.114357 | + | 0.198072i | ||||
\(236\) | −4.87072 | + | 2.81211i | −0.317057 | + | 0.183053i | ||||
\(237\) | 1.50207 | + | 1.17901i | 0.0975698 | + | 0.0765848i | ||||
\(238\) | −13.5359 | − | 7.81495i | −0.877401 | − | 0.506568i | ||||
\(239\) | 12.0377 | − | 20.8498i | 0.778651 | − | 1.34866i | −0.154068 | − | 0.988060i | \(-0.549238\pi\) |
0.932719 | − | 0.360603i | \(-0.117429\pi\) | |||||||
\(240\) | −0.244922 | + | 1.71465i | −0.0158097 | + | 0.110680i | ||||
\(241\) | −9.91581 | + | 5.72490i | −0.638733 | + | 0.368773i | −0.784126 | − | 0.620601i | \(-0.786889\pi\) |
0.145393 | + | 0.989374i | \(0.453555\pi\) | |||||||
\(242\) | 25.6193 | − | 14.7913i | 1.64687 | − | 0.950821i | ||||
\(243\) | 14.7075 | − | 5.16606i | 0.943489 | − | 0.331403i | ||||
\(244\) | 1.31888i | 0.0844328i | ||||||||
\(245\) | −13.1731 | + | 7.60549i | −0.841598 | + | 0.485897i | ||||
\(246\) | 16.5053 | + | 2.35764i | 1.05234 | + | 0.150318i | ||||
\(247\) | 17.5665i | 1.11773i | ||||||||
\(248\) | 4.18524 | − | 3.67202i | 0.265763 | − | 0.233174i | ||||
\(249\) | −10.9734 | − | 1.56746i | −0.695413 | − | 0.0993337i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.2082 | + | 19.4132i | 0.707457 | + | 1.22535i | 0.965797 | + | 0.259298i | \(0.0834912\pi\) |
−0.258340 | + | 0.966054i | \(0.583175\pi\) | |||||||
\(252\) | −13.5731 | − | 3.95837i | −0.855027 | − | 0.249354i | ||||
\(253\) | −15.5896 | + | 27.0020i | −0.980110 | + | 1.69760i | ||||
\(254\) | 1.63436 | + | 2.83079i | 0.102549 | + | 0.177620i | ||||
\(255\) | 5.33081 | − | 2.13981i | 0.333828 | − | 0.134000i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.5281 | − | 15.8934i | −1.71716 | − | 0.991401i | −0.924007 | − | 0.382376i | \(-0.875106\pi\) |
−0.793151 | − | 0.609025i | \(-0.791561\pi\) | |||||||
\(258\) | 6.50654 | − | 8.28939i | 0.405080 | − | 0.516075i | ||||
\(259\) | 20.1157 | + | 11.6138i | 1.24993 | + | 0.721647i | ||||
\(260\) | 1.71465 | + | 2.96986i | 0.106338 | + | 0.184183i | ||||
\(261\) | 12.0747 | − | 11.5556i | 0.747408 | − | 0.715277i | ||||
\(262\) | −4.68396 | − | 8.11286i | −0.289376 | − | 0.501214i | ||||
\(263\) | −8.90216 | −0.548931 | −0.274465 | − | 0.961597i | \(-0.588501\pi\) | ||||
−0.274465 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(264\) | −1.56027 | + | 10.9231i | −0.0960277 | + | 0.672268i | ||||
\(265\) | −1.11823 | + | 0.645608i | −0.0686920 | + | 0.0396594i | ||||
\(266\) | −20.9072 | − | 12.0708i | −1.28190 | − | 0.740107i | ||||
\(267\) | −4.06744 | − | 10.1330i | −0.248924 | − | 0.620130i | ||||
\(268\) | −7.24848 | + | 12.5547i | −0.442771 | + | 0.766902i | ||||
\(269\) | −10.2041 | + | 17.6740i | −0.622154 | + | 1.07760i | 0.366929 | + | 0.930249i | \(0.380409\pi\) |
−0.989084 | + | 0.147354i | \(0.952924\pi\) | |||||||
\(270\) | 4.22434 | − | 3.02571i | 0.257085 | − | 0.184139i | ||||
\(271\) | − | 4.77395i | − | 0.289997i | −0.989432 | − | 0.144998i | \(-0.953682\pi\) | ||
0.989432 | − | 0.144998i | \(-0.0463177\pi\) | |||||||
\(272\) | −1.65822 | − | 2.87212i | −0.100544 | − | 0.174148i | ||||
\(273\) | −25.9782 | + | 10.4278i | −1.57227 | + | 0.631119i | ||||
\(274\) | −3.57749 | − | 2.06547i | −0.216124 | − | 0.124779i | ||||
\(275\) | −6.37045 | −0.384152 | ||||||||
\(276\) | −3.15791 | − | 7.86713i | −0.190084 | − | 0.473545i | ||||
\(277\) | 5.06954i | 0.304599i | 0.988334 | + | 0.152300i | \(0.0486679\pi\) | ||||
−0.988334 | + | 0.152300i | \(0.951332\pi\) | |||||||
\(278\) | −20.7544 | −1.24477 | ||||||||
\(279\) | −16.6398 | − | 1.45449i | −0.996201 | − | 0.0870783i | ||||
\(280\) | −4.71285 | −0.281647 | ||||||||
\(281\) | − | 22.2236i | − | 1.32575i | −0.748730 | − | 0.662875i | \(-0.769336\pi\) | ||
0.748730 | − | 0.662875i | \(-0.230664\pi\) | |||||||
\(282\) | −2.26220 | − | 5.63571i | −0.134712 | − | 0.335601i | ||||
\(283\) | 2.14992 | 0.127800 | 0.0638998 | − | 0.997956i | \(-0.479646\pi\) | ||||
0.0638998 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(284\) | −1.61036 | − | 0.929740i | −0.0955571 | − | 0.0551699i | ||||
\(285\) | 8.23384 | − | 3.30511i | 0.487731 | − | 0.195778i | ||||
\(286\) | 10.9231 | + | 18.9193i | 0.645894 | + | 1.11872i | ||||
\(287\) | 45.3662i | 2.67788i | ||||||||
\(288\) | −2.07422 | − | 2.16740i | −0.122225 | − | 0.127715i | ||||
\(289\) | 3.00061 | − | 5.19721i | 0.176507 | − | 0.305718i | ||||
\(290\) | 2.78554 | − | 4.82470i | 0.163573 | − | 0.283316i | ||||
\(291\) | 0.302713 | + | 0.754134i | 0.0177454 | + | 0.0442081i | ||||
\(292\) | −9.05398 | − | 5.22732i | −0.529844 | − | 0.305906i | ||||
\(293\) | 10.4783 | − | 6.04966i | 0.612150 | − | 0.353425i | −0.161656 | − | 0.986847i | \(-0.551684\pi\) |
0.773806 | + | 0.633422i | \(0.218350\pi\) | |||||||
\(294\) | 3.72551 | − | 26.0814i | 0.217276 | − | 1.52110i | ||||
\(295\) | 5.62423 | 0.327455 | ||||||||
\(296\) | 2.46429 | + | 4.26827i | 0.143234 | + | 0.248088i | ||||
\(297\) | 26.9110 | − | 19.2751i | 1.56153 | − | 1.11846i | ||||
\(298\) | 0.0317462 | + | 0.0549861i | 0.00183901 | + | 0.00318526i | ||||
\(299\) | −14.5355 | − | 8.39208i | −0.840611 | − | 0.485327i | ||||
\(300\) | 1.06943 | − | 1.36247i | 0.0617437 | − | 0.0786620i | ||||
\(301\) | 24.8320 | + | 14.3367i | 1.43129 | + | 0.826356i | ||||
\(302\) | 2.80211 | 0.161244 | ||||||||
\(303\) | −25.5475 | + | 10.2549i | −1.46767 | + | 0.589130i | ||||
\(304\) | −2.56125 | − | 4.43621i | −0.146898 | − | 0.254434i | ||||
\(305\) | 0.659441 | − | 1.14219i | 0.0377595 | − | 0.0654014i | ||||
\(306\) | −2.78551 | + | 9.55144i | −0.159237 | + | 0.546019i | ||||
\(307\) | 5.45338 | + | 9.44553i | 0.311241 | + | 0.539085i | 0.978631 | − | 0.205623i | \(-0.0659221\pi\) |
−0.667391 | + | 0.744708i | \(0.732589\pi\) | |||||||
\(308\) | −30.0230 | −1.71072 | ||||||||
\(309\) | −26.0113 | − | 3.71549i | −1.47973 | − | 0.211367i | ||||
\(310\) | −5.46054 | + | 1.08744i | −0.310138 | + | 0.0617627i | ||||
\(311\) | − | 26.9183i | − | 1.52640i | −0.646164 | − | 0.763199i | \(-0.723628\pi\) | ||
0.646164 | − | 0.763199i | \(-0.276372\pi\) | |||||||
\(312\) | −5.88003 | − | 0.839911i | −0.332891 | − | 0.0475506i | ||||
\(313\) | 9.74557 | − | 5.62661i | 0.550852 | − | 0.318035i | −0.198614 | − | 0.980078i | \(-0.563644\pi\) |
0.749466 | + | 0.662043i | \(0.230311\pi\) | |||||||
\(314\) | 0.873360i | 0.0492866i | ||||||||
\(315\) | 9.77549 | + | 10.2146i | 0.550787 | + | 0.575529i | ||||
\(316\) | −0.954760 | + | 0.551231i | −0.0537095 | + | 0.0310092i | ||||
\(317\) | 16.9180 | − | 9.76764i | 0.950212 | − | 0.548605i | 0.0570654 | − | 0.998370i | \(-0.481826\pi\) |
0.893147 | + | 0.449765i | \(0.148492\pi\) | |||||||
\(318\) | 0.316248 | − | 2.21398i | 0.0177343 | − | 0.124154i | ||||
\(319\) | 17.7451 | − | 30.7355i | 0.993537 | − | 1.72086i | ||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 19.8300 | + | 15.5650i | 1.10680 | + | 0.868756i | ||||
\(322\) | 19.9761 | − | 11.5332i | 1.11322 | − | 0.642719i | ||||
\(323\) | −8.49422 | + | 14.7124i | −0.472631 | + | 0.818621i | ||||
\(324\) | −0.395219 | + | 8.99132i | −0.0219566 | + | 0.499518i | ||||
\(325\) | − | 3.42929i | − | 0.190223i | ||||||
\(326\) | 2.46179i | 0.136346i | ||||||||
\(327\) | −8.49936 | − | 21.1740i | −0.470016 | − | 1.17093i | ||||
\(328\) | −4.81303 | + | 8.33642i | −0.265755 | + | 0.460302i | ||||
\(329\) | 14.3101 | − | 8.26192i | 0.788940 | − | 0.455495i | ||||
\(330\) | 6.81276 | − | 8.67952i | 0.375030 | − | 0.477792i | ||||
\(331\) | −11.4095 | − | 6.58730i | −0.627125 | − | 0.362071i | 0.152513 | − | 0.988301i | \(-0.451263\pi\) |
−0.779638 | + | 0.626231i | \(0.784597\pi\) | |||||||
\(332\) | 3.19991 | − | 5.54241i | 0.175618 | − | 0.304179i | ||||
\(333\) | 4.13956 | − | 14.1944i | 0.226846 | − | 0.777849i | ||||
\(334\) | −11.3978 | + | 6.58051i | −0.623659 | + | 0.360070i | ||||
\(335\) | 12.5547 | − | 7.24848i | 0.685938 | − | 0.396027i | ||||
\(336\) | 5.04008 | − | 6.42110i | 0.274959 | − | 0.350300i | ||||
\(337\) | − | 23.5530i | − | 1.28301i | −0.767118 | − | 0.641506i | \(-0.778310\pi\) | ||
0.767118 | − | 0.641506i | \(-0.221690\pi\) | |||||||
\(338\) | 1.07383 | − | 0.619974i | 0.0584085 | − | 0.0337221i | ||||
\(339\) | −0.883070 | + | 6.18218i | −0.0479618 | + | 0.335770i | ||||
\(340\) | 3.31644i | 0.179859i | ||||||||
\(341\) | −34.7861 | + | 6.92751i | −1.88377 | + | 0.375146i | ||||
\(342\) | −4.30244 | + | 14.7529i | −0.232649 | + | 0.797746i | ||||
\(343\) | 38.6971 | 2.08945 | ||||||||
\(344\) | 3.04205 | + | 5.26899i | 0.164017 | + | 0.284085i | ||||
\(345\) | −1.19874 | + | 8.39208i | −0.0645378 | + | 0.451815i | ||||
\(346\) | 1.37051 | − | 2.37379i | 0.0736790 | − | 0.127616i | ||||
\(347\) | 5.57362 | + | 9.65380i | 0.299208 | + | 0.518243i | 0.975955 | − | 0.217972i | \(-0.0699443\pi\) |
−0.676747 | + | 0.736216i | \(0.736611\pi\) | |||||||
\(348\) | 3.59454 | + | 8.95489i | 0.192688 | + | 0.480032i | ||||
\(349\) | 22.1999 | 1.18833 | 0.594165 | − | 0.804343i | \(-0.297482\pi\) | ||||
0.594165 | + | 0.804343i | \(0.297482\pi\) | |||||||
\(350\) | 4.08145 | + | 2.35643i | 0.218163 | + | 0.125956i | ||||
\(351\) | 10.3761 | + | 14.4865i | 0.553833 | + | 0.773233i | ||||
\(352\) | −5.51697 | − | 3.18522i | −0.294055 | − | 0.169773i | ||||
\(353\) | −0.971322 | − | 1.68238i | −0.0516983 | − | 0.0895440i | 0.839018 | − | 0.544103i | \(-0.183130\pi\) |
−0.890716 | + | 0.454559i | \(0.849797\pi\) | |||||||
\(354\) | −6.01473 | + | 7.66282i | −0.319679 | + | 0.407274i | ||||
\(355\) | 0.929740 | + | 1.61036i | 0.0493455 | + | 0.0854688i | ||||
\(356\) | 6.30402 | 0.334112 | ||||||||
\(357\) | −26.7997 | − | 3.82811i | −1.41839 | − | 0.202605i | ||||
\(358\) | −2.64335 | + | 1.52614i | −0.139705 | + | 0.0806590i | ||||
\(359\) | 5.87430 | + | 3.39153i | 0.310034 | + | 0.178998i | 0.646942 | − | 0.762540i | \(-0.276048\pi\) |
−0.336908 | + | 0.941538i | \(0.609381\pi\) | |||||||
\(360\) | 0.712629 | + | 2.91413i | 0.0375588 | + | 0.153588i | ||||
\(361\) | −3.61997 | + | 6.26997i | −0.190525 | + | 0.329999i | ||||
\(362\) | 8.05934 | − | 13.9592i | 0.423590 | − | 0.733679i | ||||
\(363\) | 31.6366 | − | 40.3053i | 1.66049 | − | 2.11548i | ||||
\(364\) | − | 16.1618i | − | 0.847106i | ||||||
\(365\) | 5.22732 | + | 9.05398i | 0.273610 | + | 0.473907i | ||||
\(366\) | 0.850962 | + | 2.11996i | 0.0444805 | + | 0.110812i | ||||
\(367\) | 0.773089 | + | 0.446343i | 0.0403549 | + | 0.0232989i | 0.520042 | − | 0.854141i | \(-0.325916\pi\) |
−0.479687 | + | 0.877440i | \(0.659250\pi\) | |||||||
\(368\) | 4.89435 | 0.255136 | ||||||||
\(369\) | 28.0516 | − | 6.85982i | 1.46031 | − | 0.357108i | ||||
\(370\) | − | 4.92857i | − | 0.256224i | ||||||
\(371\) | 6.08531 | 0.315933 | ||||||||
\(372\) | 4.35807 | − | 8.60275i | 0.225955 | − | 0.446032i | ||||
\(373\) | 25.6902 | 1.33019 | 0.665093 | − | 0.746761i | \(-0.268392\pi\) | ||||
0.665093 | + | 0.746761i | \(0.268392\pi\) | |||||||
\(374\) | 21.1272i | 1.09246i | ||||||||
\(375\) | −1.60739 | + | 0.645214i | −0.0830052 | + | 0.0333187i | ||||
\(376\) | 3.50612 | 0.180815 | ||||||||
\(377\) | 16.5453 | + | 9.55243i | 0.852126 | + | 0.491975i | ||||
\(378\) | −24.3713 | + | 2.39494i | −1.25352 | + | 0.123182i | ||||
\(379\) | 14.5013 | + | 25.1170i | 0.744882 | + | 1.29017i | 0.950250 | + | 0.311489i | \(0.100828\pi\) |
−0.205367 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(380\) | 5.12249i | 0.262778i | ||||||||
\(381\) | 4.45352 | + | 3.49567i | 0.228161 | + | 0.179089i | ||||
\(382\) | −4.37340 | + | 7.57495i | −0.223763 | + | 0.387568i | ||||
\(383\) | −1.37993 | + | 2.39011i | −0.0705113 | + | 0.122129i | −0.899125 | − | 0.437691i | \(-0.855796\pi\) |
0.828614 | + | 0.559820i | \(0.189130\pi\) | |||||||
\(384\) | 1.60739 | − | 0.645214i | 0.0820267 | − | 0.0329260i | ||||
\(385\) | 26.0007 | + | 15.0115i | 1.32512 | + | 0.765056i | ||||
\(386\) | 18.6381 | − | 10.7607i | 0.948656 | − | 0.547707i | ||||
\(387\) | 5.11011 | − | 17.5224i | 0.259761 | − | 0.890713i | ||||
\(388\) | −0.469167 | −0.0238183 | ||||||||
\(389\) | 0.673046 | + | 1.16575i | 0.0341248 | + | 0.0591059i | 0.882583 | − | 0.470156i | \(-0.155802\pi\) |
−0.848459 | + | 0.529262i | \(0.822469\pi\) | |||||||
\(390\) | 4.67230 | + | 3.66740i | 0.236591 | + | 0.185706i | ||||
\(391\) | −8.11591 | − | 14.0572i | −0.410439 | − | 0.710902i | ||||
\(392\) | 13.1731 | + | 7.60549i | 0.665342 | + | 0.384135i | ||||
\(393\) | −12.7635 | − | 10.0184i | −0.643832 | − | 0.505359i | ||||
\(394\) | −12.2770 | − | 7.08814i | −0.618507 | − | 0.357095i | ||||
\(395\) | 1.10246 | 0.0554709 | ||||||||
\(396\) | 4.53977 | + | 18.5643i | 0.228132 | + | 0.932892i | ||||
\(397\) | −1.52687 | − | 2.64462i | −0.0766314 | − | 0.132730i | 0.825163 | − | 0.564894i | \(-0.191083\pi\) |
−0.901795 | + | 0.432165i | \(0.857750\pi\) | |||||||
\(398\) | 3.87401 | − | 6.70999i | 0.194187 | − | 0.336341i | ||||
\(399\) | −41.3942 | − | 5.91281i | −2.07230 | − | 0.296011i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 22.4218 | 1.11969 | 0.559845 | − | 0.828597i | \(-0.310861\pi\) | ||||
0.559845 | + | 0.828597i | \(0.310861\pi\) | |||||||
\(402\) | −3.55063 | + | 24.8571i | −0.177089 | + | 1.23976i | ||||
\(403\) | −3.72917 | − | 18.7258i | −0.185763 | − | 0.932798i | ||||
\(404\) | − | 15.8938i | − | 0.790747i | ||||||
\(405\) | 4.83793 | − | 7.58910i | 0.240399 | − | 0.377105i | ||||
\(406\) | −22.7381 | + | 13.1278i | −1.12847 | + | 0.651524i | ||||
\(407\) | − | 31.3972i | − | 1.55630i | ||||||
\(408\) | −4.51854 | − | 3.54671i | −0.223701 | − | 0.175588i | ||||
\(409\) | −21.5021 | + | 12.4143i | −1.06321 | + | 0.613846i | −0.926319 | − | 0.376740i | \(-0.877045\pi\) |
−0.136893 | + | 0.990586i | \(0.543712\pi\) | |||||||
\(410\) | 8.33642 | − | 4.81303i | 0.411706 | − | 0.237699i | ||||
\(411\) | −7.08309 | − | 1.01176i | −0.349383 | − | 0.0499063i | ||||
\(412\) | 7.58503 | − | 13.1377i | 0.373688 | − | 0.647246i | ||||
\(413\) | −22.9550 | − | 13.2531i | −1.12954 | − | 0.652141i | ||||
\(414\) | −10.1520 | − | 10.6080i | −0.498942 | − | 0.521355i | ||||
\(415\) | −5.54241 | + | 3.19991i | −0.272066 | + | 0.157077i | ||||
\(416\) | 1.71465 | − | 2.96986i | 0.0840675 | − | 0.145609i | ||||
\(417\) | −33.3604 | + | 13.3911i | −1.63367 | + | 0.655763i | ||||
\(418\) | 32.6326i | 1.59611i | ||||||||
\(419\) | 13.9574i | 0.681865i | 0.940088 | + | 0.340933i | \(0.110743\pi\) | ||||
−0.940088 | + | 0.340933i | \(0.889257\pi\) | |||||||
\(420\) | −7.57539 | + | 3.04080i | −0.369641 | + | 0.148376i | ||||
\(421\) | −13.1223 | + | 22.7286i | −0.639544 | + | 1.10772i | 0.345989 | + | 0.938239i | \(0.387544\pi\) |
−0.985533 | + | 0.169484i | \(0.945790\pi\) | |||||||
\(422\) | 13.3164 | − | 7.68821i | 0.648231 | − | 0.374256i | ||||
\(423\) | −7.27248 | − | 7.59916i | −0.353600 | − | 0.369484i | ||||
\(424\) | 1.11823 | + | 0.645608i | 0.0543058 | + | 0.0313535i | ||||
\(425\) | 1.65822 | − | 2.87212i | 0.0804355 | − | 0.139318i | ||||
\(426\) | −3.18835 | − | 0.455428i | −0.154476 | − | 0.0220656i | ||||
\(427\) | −5.38295 | + | 3.10785i | −0.260499 | + | 0.150399i | ||||
\(428\) | −12.6046 | + | 7.27724i | −0.609264 | + | 0.351759i | ||||
\(429\) | 29.7646 | + | 23.3630i | 1.43705 | + | 1.12797i | ||||
\(430\) | − | 6.08411i | − | 0.293402i | ||||||
\(431\) | 0.654160 | − | 0.377680i | 0.0315098 | − | 0.0181922i | −0.484162 | − | 0.874978i | \(-0.660876\pi\) |
0.515672 | + | 0.856786i | \(0.327542\pi\) | |||||||
\(432\) | −4.73251 | − | 2.14553i | −0.227693 | − | 0.103227i | ||||
\(433\) | 5.99857i | 0.288273i | 0.989558 | + | 0.144136i | \(0.0460404\pi\) | ||||
−0.989558 | + | 0.144136i | \(0.953960\pi\) | |||||||
\(434\) | 24.8494 | + | 8.42900i | 1.19281 | + | 0.404605i | ||||
\(435\) | 1.36448 | − | 9.55243i | 0.0654219 | − | 0.458004i | ||||
\(436\) | 13.1729 | 0.630869 | ||||||||
\(437\) | −12.5356 | − | 21.7124i | −0.599661 | − | 1.03864i | ||||
\(438\) | −17.9260 | − | 2.56057i | −0.856538 | − | 0.122349i | ||||
\(439\) | 1.21561 | − | 2.10550i | 0.0580180 | − | 0.100490i | −0.835558 | − | 0.549403i | \(-0.814855\pi\) |
0.893576 | + | 0.448913i | \(0.148189\pi\) | |||||||
\(440\) | 3.18522 | + | 5.51697i | 0.151850 | + | 0.263011i | ||||
\(441\) | −10.8398 | − | 44.3268i | −0.516180 | − | 2.11080i | ||||
\(442\) | −11.3730 | −0.540961 | ||||||||
\(443\) | 18.0112 | + | 10.3987i | 0.855736 | + | 0.494059i | 0.862582 | − | 0.505917i | \(-0.168846\pi\) |
−0.00684619 | + | 0.999977i | \(0.502179\pi\) | |||||||
\(444\) | 6.71501 | + | 5.27077i | 0.318680 | + | 0.250140i | ||||
\(445\) | −5.45944 | − | 3.15201i | −0.258802 | − | 0.149420i | ||||
\(446\) | −5.62754 | − | 9.74718i | −0.266472 | − | 0.461542i | ||||
\(447\) | 0.0865064 | + | 0.0679009i | 0.00409161 | + | 0.00321160i | ||||
\(448\) | 2.35643 | + | 4.08145i | 0.111331 | + | 0.192830i | ||||
\(449\) | −19.2778 | −0.909775 | −0.454888 | − | 0.890549i | \(-0.650321\pi\) | ||||
−0.454888 | + | 0.890549i | \(0.650321\pi\) | |||||||
\(450\) | 0.839911 | − | 2.88003i | 0.0395938 | − | 0.135766i | ||||
\(451\) | 53.1067 | − | 30.6612i | 2.50070 | − | 1.44378i | ||||
\(452\) | −3.12246 | − | 1.80276i | −0.146868 | − | 0.0847945i | ||||
\(453\) | 4.50409 | − | 1.80796i | 0.211621 | − | 0.0849456i | ||||
\(454\) | 11.0278 | − | 19.1006i | 0.517558 | − | 0.896437i | ||||
\(455\) | −8.08088 | + | 13.9965i | −0.378837 | + | 0.656165i | ||||
\(456\) | −6.97923 | − | 5.47816i | −0.326832 | − | 0.256538i | ||||
\(457\) | 9.77722i | 0.457359i | 0.973502 | + | 0.228680i | \(0.0734408\pi\) | ||||
−0.973502 | + | 0.228680i | \(0.926559\pi\) | |||||||
\(458\) | −3.65326 | − | 6.32764i | −0.170706 | − | 0.295671i | ||||
\(459\) | 1.68532 | + | 17.1501i | 0.0786640 | + | 0.800499i | ||||
\(460\) | −4.23863 | − | 2.44718i | −0.197627 | − | 0.114100i | ||||
\(461\) | −15.6965 | −0.731059 | −0.365530 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365530 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(462\) | −48.2586 | + | 19.3713i | −2.24519 | + | 0.901232i | ||||
\(463\) | − | 37.5167i | − | 1.74355i | −0.489908 | − | 0.871774i | \(-0.662970\pi\) | ||
0.489908 | − | 0.871774i | \(-0.337030\pi\) | |||||||
\(464\) | −5.57108 | −0.258631 | ||||||||
\(465\) | −8.07557 | + | 5.27116i | −0.374496 | + | 0.244444i | ||||
\(466\) | −9.29519 | −0.430591 | ||||||||
\(467\) | − | 18.6592i | − | 0.863446i | −0.902006 | − | 0.431723i | \(-0.857906\pi\) | ||
0.902006 | − | 0.431723i | \(-0.142094\pi\) | |||||||
\(468\) | −9.99341 | + | 2.44381i | −0.461946 | + | 0.112965i | ||||
\(469\) | −68.3220 | −3.15482 | ||||||||
\(470\) | −3.03639 | − | 1.75306i | −0.140058 | − | 0.0808627i | ||||
\(471\) | 0.563504 | + | 1.40383i | 0.0259649 | + | 0.0646850i | ||||
\(472\) | −2.81211 | − | 4.87072i | −0.129438 | − | 0.224193i | ||||
\(473\) | − | 38.7585i | − | 1.78212i | ||||||
\(474\) | −1.17901 | + | 1.50207i | −0.0541537 | + | 0.0689922i | ||||
\(475\) | 2.56125 | − | 4.43621i | 0.117518 | − | 0.203547i | ||||
\(476\) | 7.81495 | − | 13.5359i | 0.358198 | − | 0.620416i | ||||
\(477\) | −0.920158 | − | 3.76277i | −0.0421311 | − | 0.172285i | ||||
\(478\) | 20.8498 | + | 12.0377i | 0.953649 | + | 0.550589i | ||||
\(479\) | −0.407841 | + | 0.235467i | −0.0186347 | + | 0.0107588i | −0.509288 | − | 0.860596i | \(-0.670091\pi\) |
0.490654 | + | 0.871355i | \(0.336758\pi\) | |||||||
\(480\) | −1.71465 | − | 0.244922i | −0.0782626 | − | 0.0111791i | ||||
\(481\) | 16.9015 | 0.770643 | ||||||||
\(482\) | −5.72490 | − | 9.91581i | −0.260762 | − | 0.451653i | ||||
\(483\) | 24.6679 | − | 31.4271i | 1.12243 | − | 1.42998i | ||||
\(484\) | 14.7913 | + | 25.6193i | 0.672332 | + | 1.16451i | ||||
\(485\) | 0.406311 | + | 0.234584i | 0.0184496 | + | 0.0106519i | ||||
\(486\) | 5.16606 | + | 14.7075i | 0.234337 | + | 0.667148i | ||||
\(487\) | 16.0925 | + | 9.29103i | 0.729222 | + | 0.421017i | 0.818138 | − | 0.575023i | \(-0.195007\pi\) |
−0.0889154 | + | 0.996039i | \(0.528340\pi\) | |||||||
\(488\) | −1.31888 | −0.0597030 | ||||||||
\(489\) | 1.58838 | + | 3.95706i | 0.0718292 | + | 0.178944i | ||||
\(490\) | −7.60549 | − | 13.1731i | −0.343581 | − | 0.595100i | ||||
\(491\) | 1.07403 | − | 1.86028i | 0.0484704 | − | 0.0839532i | −0.840772 | − | 0.541389i | \(-0.817899\pi\) |
0.889243 | + | 0.457436i | \(0.151232\pi\) | |||||||
\(492\) | −2.35764 | + | 16.5053i | −0.106291 | + | 0.744117i | ||||
\(493\) | 9.23808 | + | 16.0008i | 0.416062 | + | 0.720641i | ||||
\(494\) | −17.5665 | −0.790356 | ||||||||
\(495\) | 5.35061 | − | 18.3471i | 0.240492 | − | 0.824639i | ||||
\(496\) | 3.67202 | + | 4.18524i | 0.164879 | + | 0.187923i | ||||
\(497\) | − | 8.76345i | − | 0.393095i | ||||||
\(498\) | 1.56746 | − | 10.9734i | 0.0702395 | − | 0.491731i | ||||
\(499\) | 13.7161 | − | 7.91901i | 0.614019 | − | 0.354504i | −0.160518 | − | 0.987033i | \(-0.551316\pi\) |
0.774537 | + | 0.632529i | \(0.217983\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | −14.0748 | + | 17.9315i | −0.628817 | + | 0.801118i | ||||
\(502\) | −19.4132 | + | 11.2082i | −0.866455 | + | 0.500248i | ||||
\(503\) | 17.9459 | − | 10.3610i | 0.800166 | − | 0.461976i | −0.0433631 | − | 0.999059i | \(-0.513807\pi\) |
0.843529 | + | 0.537083i | \(0.180474\pi\) | |||||||
\(504\) | 3.95837 | − | 13.5731i | 0.176320 | − | 0.604596i | ||||
\(505\) | −7.94691 | + | 13.7644i | −0.353633 | + | 0.612510i | ||||
\(506\) | −27.0020 | − | 15.5896i | −1.20038 | − | 0.693042i | ||||
\(507\) | 1.32604 | − | 1.68939i | 0.0588915 | − | 0.0750283i | ||||
\(508\) | −2.83079 | + | 1.63436i | −0.125596 | + | 0.0725129i | ||||
\(509\) | 0.867034 | − | 1.50175i | 0.0384306 | − | 0.0665638i | −0.846170 | − | 0.532913i | \(-0.821097\pi\) |
0.884601 | + | 0.466349i | \(0.154431\pi\) | |||||||
\(510\) | 2.13981 | + | 5.33081i | 0.0947526 | + | 0.236052i | ||||
\(511\) | − | 49.2712i | − | 2.17963i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.60310 | + | 26.4897i | 0.114930 | + | 1.16955i | ||||
\(514\) | 15.8934 | − | 27.5281i | 0.701027 | − | 1.21421i | ||||
\(515\) | −13.1377 | + | 7.58503i | −0.578915 | + | 0.334236i | ||||
\(516\) | 8.28939 | + | 6.50654i | 0.364920 | + | 0.286434i | ||||
\(517\) | −19.3432 | − | 11.1678i | −0.850712 | − | 0.491159i | ||||
\(518\) | −11.6138 | + | 20.1157i | −0.510282 | + | 0.883834i | ||||
\(519\) | 0.671337 | − | 4.69988i | 0.0294684 | − | 0.206302i | ||||
\(520\) | −2.96986 | + | 1.71465i | −0.130237 | + | 0.0751922i | ||||
\(521\) | −32.8261 | + | 18.9521i | −1.43814 | + | 0.830308i | −0.997720 | − | 0.0674858i | \(-0.978502\pi\) |
−0.440416 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(522\) | 11.5556 | + | 12.0747i | 0.505777 | + | 0.528497i | ||||
\(523\) | − | 8.57223i | − | 0.374837i | −0.982280 | − | 0.187419i | \(-0.939988\pi\) | ||
0.982280 | − | 0.187419i | \(-0.0600121\pi\) | |||||||
\(524\) | 8.11286 | − | 4.68396i | 0.354412 | − | 0.204620i | ||||
\(525\) | 8.08088 | + | 1.15428i | 0.352678 | + | 0.0503770i | ||||
\(526\) | − | 8.90216i | − | 0.388153i | ||||||
\(527\) | 5.93150 | − | 17.4865i | 0.258380 | − | 0.761726i | ||||
\(528\) | −10.9231 | − | 1.56027i | −0.475365 | − | 0.0679018i | ||||
\(529\) | 0.954681 | 0.0415079 | ||||||||
\(530\) | −0.645608 | − | 1.11823i | −0.0280434 | − | 0.0485726i | ||||
\(531\) | −4.72385 | + | 16.1979i | −0.204998 | + | 0.702930i | ||||
\(532\) | 12.0708 | − | 20.9072i | 0.523335 | − | 0.906442i | ||||
\(533\) | 16.5053 | + | 28.5880i | 0.714924 | + | 1.23828i | ||||
\(534\) | 10.1330 | − | 4.06744i | 0.438498 | − | 0.176016i | ||||
\(535\) | 14.5545 | 0.629245 | ||||||||
\(536\) | −12.5547 | − | 7.24848i | −0.542282 | − | 0.313086i | ||||
\(537\) | −3.26421 | + | 4.15863i | −0.140861 | + | 0.179458i | ||||
\(538\) | −17.6740 | − | 10.2041i | −0.761980 | − | 0.439930i | ||||
\(539\) | −48.4504 | − | 83.9185i | −2.08690 | − | 3.61463i | ||||
\(540\) | 3.02571 | + | 4.22434i | 0.130206 | + | 0.181787i | ||||
\(541\) | 17.5603 | + | 30.4153i | 0.754974 | + | 1.30765i | 0.945387 | + | 0.325950i | \(0.105684\pi\) |
−0.190413 | + | 0.981704i | \(0.560983\pi\) | |||||||
\(542\) | 4.77395 | 0.205059 | ||||||||
\(543\) | 3.94783 | − | 27.6378i | 0.169417 | − | 1.18605i | ||||
\(544\) | 2.87212 | − | 1.65822i | 0.123141 | − | 0.0710956i | ||||
\(545\) | −11.4081 | − | 6.58646i | −0.488669 | − | 0.282133i | ||||
\(546\) | −10.4278 | − | 25.9782i | −0.446268 | − | 1.11177i | ||||
\(547\) | −19.3350 | + | 33.4893i | −0.826706 | + | 1.43190i | 0.0739019 | + | 0.997266i | \(0.476455\pi\) |
−0.900608 | + | 0.434632i | \(0.856878\pi\) | |||||||
\(548\) | 2.06547 | − | 3.57749i | 0.0882323 | − | 0.152823i | ||||
\(549\) | 2.73565 | + | 2.85854i | 0.116755 | + | 0.122000i | ||||
\(550\) | − | 6.37045i | − | 0.271637i | ||||||
\(551\) | 14.2689 | + | 24.7145i | 0.607876 | + | 1.05287i | ||||
\(552\) | 7.86713 | − | 3.15791i | 0.334847 | − | 0.134409i | ||||
\(553\) | −4.49964 | − | 2.59787i | −0.191344 | − | 0.110473i | ||||
\(554\) | −5.06954 | −0.215384 | ||||||||
\(555\) | −3.17998 | − | 7.92213i | −0.134983 | − | 0.336276i | ||||
\(556\) | − | 20.7544i | − | 0.880184i | ||||||
\(557\) | 25.0087 | 1.05965 | 0.529826 | − | 0.848107i | \(-0.322257\pi\) | ||||
0.529826 | + | 0.848107i | \(0.322257\pi\) | |||||||
\(558\) | 1.45449 | − | 16.6398i | 0.0615737 | − | 0.704421i | ||||
\(559\) | 20.8642 | 0.882461 | ||||||||
\(560\) | − | 4.71285i | − | 0.199154i | ||||||
\(561\) | 13.6316 | + | 33.9596i | 0.575526 | + | 1.43378i | ||||
\(562\) | 22.2236 | 0.937447 | ||||||||
\(563\) | −27.9134 | − | 16.1158i | −1.17641 | − | 0.679200i | −0.221228 | − | 0.975222i | \(-0.571006\pi\) |
−0.955181 | + | 0.296022i | \(0.904340\pi\) | |||||||
\(564\) | 5.63571 | − | 2.26220i | 0.237306 | − | 0.0952559i | ||||
\(565\) | 1.80276 | + | 3.12246i | 0.0758425 | + | 0.131363i | ||||
\(566\) | 2.14992i | 0.0903679i | ||||||||
\(567\) | −37.6289 | + | 19.5743i | −1.58027 | + | 0.822044i | ||||
\(568\) | 0.929740 | − | 1.61036i | 0.0390110 | − | 0.0675691i | ||||
\(569\) | 8.43031 | − | 14.6017i | 0.353417 | − | 0.612136i | −0.633429 | − | 0.773801i | \(-0.718353\pi\) |
0.986846 | + | 0.161665i | \(0.0516863\pi\) | |||||||
\(570\) | 3.30511 | + | 8.23384i | 0.138436 | + | 0.344878i | ||||
\(571\) | 11.3902 | + | 6.57613i | 0.476665 | + | 0.275203i | 0.719026 | − | 0.694984i | \(-0.244588\pi\) |
−0.242361 | + | 0.970186i | \(0.577922\pi\) | |||||||
\(572\) | −18.9193 | + | 10.9231i | −0.791056 | + | 0.456716i | ||||
\(573\) | −2.14229 | + | 14.9977i | −0.0894953 | + | 0.626537i | ||||
\(574\) | −45.3662 | −1.89355 | ||||||||
\(575\) | 2.44718 | + | 4.23863i | 0.102054 | + | 0.176763i | ||||
\(576\) | 2.16740 | − | 2.07422i | 0.0903082 | − | 0.0864258i | ||||
\(577\) | 7.01445 | + | 12.1494i | 0.292015 | + | 0.505785i | 0.974286 | − | 0.225314i | \(-0.0723409\pi\) |
−0.682271 | + | 0.731099i | \(0.739008\pi\) | |||||||
\(578\) | 5.19721 | + | 3.00061i | 0.216175 | + | 0.124809i | ||||
\(579\) | 23.0157 | − | 29.3223i | 0.956502 | − | 1.21859i | ||||
\(580\) | 4.82470 | + | 2.78554i | 0.200335 | + | 0.115663i | ||||
\(581\) | 30.1614 | 1.25131 | ||||||||
\(582\) | −0.754134 | + | 0.302713i | −0.0312599 | + | 0.0125479i | ||||
\(583\) | −4.11281 | − | 7.12360i | −0.170335 | − | 0.295029i | ||||
\(584\) | 5.22732 | − | 9.05398i | 0.216308 | − | 0.374656i | ||||
\(585\) | 9.87645 | + | 2.88030i | 0.408341 | + | 0.119086i | ||||
\(586\) | 6.04966 | + | 10.4783i | 0.249909 | + | 0.432855i | ||||
\(587\) | 2.63583 | 0.108792 | 0.0543961 | − | 0.998519i | \(-0.482677\pi\) | ||||
0.0543961 | + | 0.998519i | \(0.482677\pi\) | |||||||
\(588\) | 26.0814 | + | 3.72551i | 1.07558 | + | 0.153637i | ||||
\(589\) | 9.16165 | − | 27.0093i | 0.377499 | − | 1.11290i | ||||
\(590\) | 5.62423i | 0.231546i | ||||||||
\(591\) | −24.3073 | − | 3.47209i | −0.999869 | − | 0.142823i | ||||
\(592\) | −4.26827 | + | 2.46429i | −0.175425 | + | 0.101282i | ||||
\(593\) | 0.710550i | 0.0291788i | 0.999894 | + | 0.0145894i | \(0.00464411\pi\) | ||||
−0.999894 | + | 0.0145894i | \(0.995356\pi\) | |||||||
\(594\) | 19.2751 | + | 26.9110i | 0.790868 | + | 1.10417i | ||||
\(595\) | −13.5359 | + | 7.81495i | −0.554917 | + | 0.320382i | ||||
\(596\) | −0.0549861 | + | 0.0317462i | −0.00225232 | + | 0.00130038i | ||||
\(597\) | 1.89766 | − | 13.2851i | 0.0776663 | − | 0.543724i | ||||
\(598\) | 8.39208 | − | 14.5355i | 0.343178 | − | 0.594401i | ||||
\(599\) | −3.56655 | − | 2.05915i | −0.145725 | − | 0.0841346i | 0.425364 | − | 0.905022i | \(-0.360146\pi\) |
−0.571090 | + | 0.820888i | \(0.693479\pi\) | |||||||
\(600\) | 1.36247 | + | 1.06943i | 0.0556225 | + | 0.0436594i | ||||
\(601\) | −32.9052 | + | 18.9978i | −1.34223 | + | 0.774938i | −0.987135 | − | 0.159891i | \(-0.948886\pi\) |
−0.355098 | + | 0.934829i | \(0.615552\pi\) | |||||||
\(602\) | −14.3367 | + | 24.8320i | −0.584322 | + | 1.01208i | ||||
\(603\) | 10.3309 | + | 42.2460i | 0.420709 | + | 1.72039i | ||||
\(604\) | 2.80211i | 0.114016i | ||||||||
\(605\) | − | 29.5826i | − | 1.20270i | ||||||
\(606\) | −10.2549 | − | 25.5475i | −0.416578 | − | 1.03780i | ||||
\(607\) | 4.63844 | − | 8.03401i | 0.188268 | − | 0.326090i | −0.756405 | − | 0.654104i | \(-0.773046\pi\) |
0.944673 | + | 0.328014i | \(0.106379\pi\) | |||||||
\(608\) | 4.43621 | − | 2.56125i | 0.179912 | − | 0.103872i | ||||
\(609\) | −28.0787 | + | 35.7725i | −1.13780 | + | 1.44957i | ||||
\(610\) | 1.14219 | + | 0.659441i | 0.0462458 | + | 0.0267000i | ||||
\(611\) | 6.01176 | − | 10.4127i | 0.243210 | − | 0.421252i | ||||
\(612\) | −9.55144 | − | 2.78551i | −0.386094 | − | 0.112598i | ||||
\(613\) | 6.90442 | − | 3.98627i | 0.278867 | − | 0.161004i | −0.354044 | − | 0.935229i | \(-0.615194\pi\) |
0.632910 | + | 0.774225i | \(0.281860\pi\) | |||||||
\(614\) | −9.44553 | + | 5.45338i | −0.381190 | + | 0.220080i | ||||
\(615\) | 10.2944 | − | 13.1152i | 0.415111 | − | 0.528856i | ||||
\(616\) | − | 30.0230i | − | 1.20966i | ||||||
\(617\) | −27.4184 | + | 15.8300i | −1.10382 | + | 0.637292i | −0.937222 | − | 0.348733i | \(-0.886612\pi\) |
−0.166599 | + | 0.986025i | \(0.553279\pi\) | |||||||
\(618\) | 3.71549 | − | 26.0113i | 0.149459 | − | 1.04633i | ||||
\(619\) | − | 41.1513i | − | 1.65401i | −0.562193 | − | 0.827006i | \(-0.690042\pi\) | ||
0.562193 | − | 0.827006i | \(-0.309958\pi\) | |||||||
\(620\) | −1.08744 | − | 5.46054i | −0.0436728 | − | 0.219300i | ||||
\(621\) | −23.1626 | − | 10.5010i | −0.929483 | − | 0.421390i | ||||
\(622\) | 26.9183 | 1.07933 | ||||||||
\(623\) | 14.8550 | + | 25.7295i | 0.595151 | + | 1.03083i | ||||
\(624\) | 0.839911 | − | 5.88003i | 0.0336233 | − | 0.235389i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 5.62661 | + | 9.74557i | 0.224884 | + | 0.389511i | ||||
\(627\) | 21.0550 | + | 52.4532i | 0.840856 | + | 2.09478i | ||||
\(628\) | −0.873360 | −0.0348509 | ||||||||
\(629\) | 14.1555 | + | 8.17266i | 0.564415 | + | 0.325865i | ||||
\(630\) | −10.2146 | + | 9.77549i | −0.406960 | + | 0.389465i | ||||
\(631\) | −31.0070 | − | 17.9019i | −1.23437 | − | 0.712663i | −0.266431 | − | 0.963854i | \(-0.585845\pi\) |
−0.967938 | + | 0.251191i | \(0.919178\pi\) | |||||||
\(632\) | −0.551231 | − | 0.954760i | −0.0219268 | − | 0.0379783i | ||||
\(633\) | 16.4441 | − | 20.9499i | 0.653592 | − | 0.832682i | ||||
\(634\) | 9.76764 | + | 16.9180i | 0.387923 | + | 0.671902i | ||||
\(635\) | 3.26872 | 0.129715 | ||||||||
\(636\) | 2.21398 | + | 0.316248i | 0.0877899 | + | 0.0125400i | ||||
\(637\) | 45.1744 | − | 26.0814i | 1.78987 | − | 1.03338i | ||||
\(638\) | 30.7355 | + | 17.7451i | 1.21683 | + | 0.702537i | ||||
\(639\) | −5.41877 | + | 1.32512i | −0.214363 | + | 0.0524209i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 11.0148 | − | 19.0781i | 0.435057 | − | 0.753541i | −0.562243 | − | 0.826972i | \(-0.690061\pi\) |
0.997300 | + | 0.0734307i | \(0.0233948\pi\) | |||||||
\(642\) | −15.5650 | + | 19.8300i | −0.614303 | + | 0.782628i | ||||
\(643\) | − | 0.891118i | − | 0.0351422i | −0.999846 | − | 0.0175711i | \(-0.994407\pi\) | ||
0.999846 | − | 0.0175711i | \(-0.00559335\pi\) | |||||||
\(644\) | 11.5332 | + | 19.9761i | 0.454471 | + | 0.787167i | ||||
\(645\) | −3.92555 | − | 9.77953i | −0.154568 | − | 0.385068i | ||||
\(646\) | −14.7124 | − | 8.49422i | −0.578853 | − | 0.334201i | ||||
\(647\) | 2.41935 | 0.0951144 | 0.0475572 | − | 0.998869i | \(-0.484856\pi\) | ||||
0.0475572 | + | 0.998869i | \(0.484856\pi\) | |||||||
\(648\) | −8.99132 | − | 0.395219i | −0.353212 | − | 0.0155257i | ||||
\(649\) | 35.8288i | 1.40641i | ||||||||
\(650\) | 3.42929 | 0.134508 | ||||||||
\(651\) | 45.3811 | − | 2.48450i | 1.77863 | − | 0.0973752i | ||||
\(652\) | −2.46179 | −0.0964112 | ||||||||
\(653\) | 41.5741i | 1.62692i | 0.581621 | + | 0.813460i | \(0.302419\pi\) | ||||
−0.581621 | + | 0.813460i | \(0.697581\pi\) | |||||||
\(654\) | 21.1740 | − | 8.49936i | 0.827969 | − | 0.332351i | ||||
\(655\) | −9.36792 | −0.366035 | ||||||||
\(656\) | −8.33642 | − | 4.81303i | −0.325482 | − | 0.187917i | ||||
\(657\) | −30.4662 | + | 7.45028i | −1.18860 | + | 0.290663i | ||||
\(658\) | 8.26192 | + | 14.3101i | 0.322083 | + | 0.557865i | ||||
\(659\) | 28.1446i | 1.09636i | 0.836361 | + | 0.548180i | \(0.184679\pi\) | ||||
−0.836361 | + | 0.548180i | \(0.815321\pi\) | |||||||
\(660\) | 8.67952 | + | 6.81276i | 0.337850 | + | 0.265186i | ||||
\(661\) | 8.37062 | − | 14.4983i | 0.325579 | − | 0.563920i | −0.656050 | − | 0.754717i | \(-0.727774\pi\) |
0.981629 | + | 0.190797i | \(0.0611073\pi\) | |||||||
\(662\) | 6.58730 | − | 11.4095i | 0.256023 | − | 0.443444i | ||||
\(663\) | −18.2809 | + | 7.33805i | −0.709972 | + | 0.284986i | ||||
\(664\) | 5.54241 | + | 3.19991i | 0.215087 | + | 0.124181i | ||||
\(665\) | −20.9072 | + | 12.0708i | −0.810746 | + | 0.468085i | ||||
\(666\) | 14.1944 | + | 4.13956i | 0.550022 | + | 0.160405i | ||||
\(667\) | −27.2668 | −1.05578 | ||||||||
\(668\) | −6.58051 | − | 11.3978i | −0.254608 | − | 0.440993i | ||||
\(669\) | −15.3347 | − | 12.0365i | −0.592872 | − | 0.465359i | ||||
\(670\) | 7.24848 | + | 12.5547i | 0.280033 | + | 0.485031i | ||||
\(671\) | 7.27623 | + | 4.20094i | 0.280896 | + | 0.162175i | ||||
\(672\) | 6.42110 | + | 5.04008i | 0.247699 | + | 0.194425i | ||||
\(673\) | −24.4794 | − | 14.1332i | −0.943611 | − | 0.544794i | −0.0525207 | − | 0.998620i | \(-0.516726\pi\) |
−0.891091 | + | 0.453826i | \(0.850059\pi\) | |||||||
\(674\) | 23.5530 | 0.907226 | ||||||||
\(675\) | −0.508171 | − | 5.17124i | −0.0195595 | − | 0.199041i | ||||
\(676\) | 0.619974 | + | 1.07383i | 0.0238452 | + | 0.0413010i | ||||
\(677\) | 16.1530 | − | 27.9779i | 0.620812 | − | 1.07528i | −0.368523 | − | 0.929619i | \(-0.620136\pi\) |
0.989335 | − | 0.145659i | \(-0.0465303\pi\) | |||||||
\(678\) | −6.18218 | − | 0.883070i | −0.237425 | − | 0.0339141i | ||||
\(679\) | −1.10556 | − | 1.91488i | −0.0424274 | − | 0.0734864i | ||||
\(680\) | −3.31644 | −0.127180 | ||||||||
\(681\) | 5.40189 | − | 37.8174i | 0.207001 | − | 1.44917i | ||||
\(682\) | −6.92751 | − | 34.7861i | −0.265268 | − | 1.33203i | ||||
\(683\) | − | 40.5655i | − | 1.55219i | −0.630613 | − | 0.776097i | \(-0.717196\pi\) | ||
0.630613 | − | 0.776097i | \(-0.282804\pi\) | |||||||
\(684\) | −14.7529 | − | 4.30244i | −0.564092 | − | 0.164508i | ||||
\(685\) | −3.57749 | + | 2.06547i | −0.136689 | + | 0.0789174i | ||||
\(686\) | 38.6971i | 1.47746i | ||||||||
\(687\) | −9.95489 | − | 7.81383i | −0.379803 | − | 0.298116i | ||||
\(688\) | −5.26899 | + | 3.04205i | −0.200878 | + | 0.115977i | ||||
\(689\) | 3.83472 | − | 2.21398i | 0.146091 | − | 0.0843459i | ||||
\(690\) | −8.39208 | − | 1.19874i | −0.319481 | − | 0.0456351i | ||||
\(691\) | −6.78386 | + | 11.7500i | −0.258070 | + | 0.446991i | −0.965725 | − | 0.259568i | \(-0.916420\pi\) |
0.707655 | + | 0.706558i | \(0.249753\pi\) | |||||||
\(692\) | 2.37379 | + | 1.37051i | 0.0902380 | + | 0.0520989i | ||||
\(693\) | −65.0717 | + | 62.2743i | −2.47187 | + | 2.36560i | ||||
\(694\) | −9.65380 | + | 5.57362i | −0.366453 | + | 0.211572i | ||||
\(695\) | −10.3772 | + | 17.9739i | −0.393630 | + | 0.681787i | ||||
\(696\) | −8.95489 | + | 3.59454i | −0.339434 | + | 0.136251i | ||||
\(697\) | 31.9243i | 1.20922i | ||||||||
\(698\) | 22.1999i | 0.840277i | ||||||||
\(699\) | −14.9410 | + | 5.99739i | −0.565120 | + | 0.226842i | ||||
\(700\) | −2.35643 | + | 4.08145i | −0.0890645 | + | 0.154264i | ||||
\(701\) | −1.09140 | + | 0.630120i | −0.0412216 | + | 0.0237993i | −0.520469 | − | 0.853880i | \(-0.674243\pi\) |
0.479248 | + | 0.877680i | \(0.340910\pi\) | |||||||
\(702\) | −14.4865 | + | 10.3761i | −0.546758 | + | 0.391619i | ||||
\(703\) | 21.8642 | + | 12.6233i | 0.824623 | + | 0.476096i | ||||
\(704\) | 3.18522 | − | 5.51697i | 0.120048 | − | 0.207929i | ||||
\(705\) | −6.01176 | − | 0.858728i | −0.226416 | − | 0.0323416i | ||||
\(706\) | 1.68238 | − | 0.971322i | 0.0633172 | − | 0.0365562i | ||||
\(707\) | 64.8698 | − | 37.4526i | 2.43968 | − | 1.40855i | ||||
\(708\) | −7.66282 | − | 6.01473i | −0.287986 | − | 0.226047i | ||||
\(709\) | − | 52.1846i | − | 1.95983i | −0.199411 | − | 0.979916i | \(-0.563903\pi\) | ||
0.199411 | − | 0.979916i | \(-0.436097\pi\) | |||||||
\(710\) | −1.61036 | + | 0.929740i | −0.0604356 | + | 0.0348925i | ||||
\(711\) | −0.925970 | + | 3.17512i | −0.0347266 | + | 0.119076i | ||||
\(712\) | 6.30402i | 0.236253i | ||||||||
\(713\) | 17.9722 | + | 20.4840i | 0.673063 | + | 0.767134i | ||||
\(714\) | 3.82811 | − | 26.7997i | 0.143263 | − | 1.00296i | ||||
\(715\) | 21.8461 | 0.816999 | ||||||||
\(716\) | −1.52614 | − | 2.64335i | −0.0570345 | − | 0.0987867i | ||||
\(717\) | 41.2806 | + | 5.89658i | 1.54165 | + | 0.220212i | ||||
\(718\) | −3.39153 | + | 5.87430i | −0.126571 | + | 0.219227i | ||||
\(719\) | 22.9349 | + | 39.7245i | 0.855328 | + | 1.48147i | 0.876340 | + | 0.481693i | \(0.159978\pi\) |
−0.0210118 | + | 0.999779i | \(0.506689\pi\) | |||||||
\(720\) | −2.91413 | + | 0.712629i | −0.108603 | + | 0.0265581i | ||||
\(721\) | 71.4943 | 2.66259 | ||||||||
\(722\) | −6.26997 | − | 3.61997i | −0.233344 | − | 0.134721i | ||||
\(723\) | −15.6000 | − | 12.2448i | −0.580169 | − | 0.455388i | ||||
\(724\) | 13.9592 | + | 8.05934i | 0.518789 | + | 0.299523i | ||||
\(725\) | −2.78554 | − | 4.82470i | −0.103452 | − | 0.179185i | ||||
\(726\) | 40.3053 | + | 31.6366i | 1.49587 | + | 1.17414i | ||||
\(727\) | −20.8556 | − | 36.1230i | −0.773492 | − | 1.33973i | −0.935638 | − | 0.352961i | \(-0.885175\pi\) |
0.162145 | − | 0.986767i | \(-0.448159\pi\) | |||||||
\(728\) | 16.1618 | 0.598994 | ||||||||
\(729\) | 17.7934 | + | 20.3075i | 0.659014 | + | 0.752131i | ||||
\(730\) | −9.05398 | + | 5.22732i | −0.335103 | + | 0.193472i | ||||
\(731\) | 17.4743 | + | 10.0888i | 0.646310 | + | 0.373147i | ||||
\(732\) | −2.11996 | + | 0.850962i | −0.0783559 | + | 0.0314525i | ||||
\(733\) | 11.9558 | − | 20.7081i | 0.441598 | − | 0.764870i | −0.556211 | − | 0.831041i | \(-0.687745\pi\) |
0.997808 | + | 0.0661718i | \(0.0210785\pi\) | |||||||
\(734\) | −0.446343 | + | 0.773089i | −0.0164748 | + | 0.0285352i | ||||
\(735\) | −20.7244 | − | 16.2671i | −0.764433 | − | 0.600021i | ||||
\(736\) | 4.89435i | 0.180408i | ||||||||
\(737\) | 46.1760 | + | 79.9792i | 1.70092 | + | 2.94607i | ||||
\(738\) | 6.85982 | + | 28.0516i | 0.252513 | + | 1.03259i | ||||
\(739\) | 21.4217 | + | 12.3678i | 0.788009 | + | 0.454957i | 0.839261 | − | 0.543729i | \(-0.182988\pi\) |
−0.0512524 | + | 0.998686i | \(0.516321\pi\) | |||||||
\(740\) | 4.92857 | 0.181178 | ||||||||
\(741\) | −28.2362 | + | 11.3342i | −1.03728 | + | 0.416371i | ||||
\(742\) | 6.08531i | 0.223399i | ||||||||
\(743\) | 22.6992 | 0.832752 | 0.416376 | − | 0.909193i | \(-0.363300\pi\) | ||||
0.416376 | + | 0.909193i | \(0.363300\pi\) | |||||||
\(744\) | 8.60275 | + | 4.35807i | 0.315392 | + | 0.159775i | ||||
\(745\) | 0.0634925 | 0.00232618 | ||||||||
\(746\) | 25.6902i | 0.940583i | ||||||||
\(747\) | −4.56070 | − | 18.6499i | −0.166867 | − | 0.682365i | ||||
\(748\) | −21.1272 | −0.772487 | ||||||||
\(749\) | −59.4034 | − | 34.2966i | −2.17055 | − | 1.25317i | ||||
\(750\) | −0.645214 | − | 1.60739i | −0.0235599 | − | 0.0586935i | ||||
\(751\) | −2.09359 | − | 3.62621i | −0.0763963 | − | 0.132322i | 0.825296 | − | 0.564700i | \(-0.191008\pi\) |
−0.901693 | + | 0.432378i | \(0.857675\pi\) | |||||||
\(752\) | 3.50612i | 0.127855i | ||||||||
\(753\) | −23.9729 | + | 30.5417i | −0.873621 | + | 1.11300i | ||||
\(754\) | −9.55243 | + | 16.5453i | −0.347879 | + | 0.602544i | ||||
\(755\) | 1.40106 | − | 2.42670i | 0.0509897 | − | 0.0883168i | ||||
\(756\) | −2.39494 | − | 24.3713i | −0.0871030 | − | 0.886376i | ||||
\(757\) | −8.87601 | − | 5.12457i | −0.322604 | − | 0.186256i | 0.329949 | − | 0.943999i | \(-0.392969\pi\) |
−0.652553 | + | 0.757743i | \(0.726302\pi\) | |||||||
\(758\) | −25.1170 | + | 14.5013i | −0.912291 | + | 0.526711i | ||||
\(759\) | −53.4613 | − | 7.63649i | −1.94052 | − | 0.277187i | ||||
\(760\) | −5.12249 | −0.185812 | ||||||||
\(761\) | 3.16769 | + | 5.48660i | 0.114829 | + | 0.198889i | 0.917711 | − | 0.397248i | \(-0.130035\pi\) |
−0.802883 | + | 0.596137i | \(0.796701\pi\) | |||||||
\(762\) | −3.49567 | + | 4.45352i | −0.126635 | + | 0.161334i | ||||
\(763\) | 31.0410 | + | 53.7646i | 1.12376 | + | 1.94641i | ||||
\(764\) | −7.57495 | − | 4.37340i | −0.274052 | − | 0.158224i | ||||
\(765\) | 6.87903 | + | 7.18804i | 0.248712 | + | 0.259884i | ||||
\(766\) | −2.39011 | − | 1.37993i | −0.0863583 | − | 0.0498590i | ||||
\(767\) | −19.2871 | −0.696418 | ||||||||
\(768\) | 0.645214 | + | 1.60739i | 0.0232822 | + | 0.0580016i | ||||
\(769\) | −2.87363 | − | 4.97727i | −0.103626 | − | 0.179485i | 0.809550 | − | 0.587051i | \(-0.199711\pi\) |
−0.913176 | + | 0.407566i | \(0.866378\pi\) | |||||||
\(770\) | −15.0115 | + | 26.0007i | −0.540976 | + | 0.936999i | ||||
\(771\) | 7.78529 | − | 54.5030i | 0.280380 | − | 1.96288i | ||||
\(772\) | 10.7607 | + | 18.6381i | 0.387287 | + | 0.670801i | ||||
\(773\) | 23.5066 | 0.845474 | 0.422737 | − | 0.906252i | \(-0.361069\pi\) | ||||
0.422737 | + | 0.906252i | \(0.361069\pi\) | |||||||
\(774\) | 17.5224 | + | 5.11011i | 0.629829 | + | 0.183679i | ||||
\(775\) | −1.78851 | + | 5.27269i | −0.0642453 | + | 0.189400i | ||||
\(776\) | − | 0.469167i | − | 0.0168421i | ||||||
\(777\) | −5.68897 | + | 39.8272i | −0.204091 | + | 1.42879i | ||||
\(778\) | −1.16575 | + | 0.673046i | −0.0417942 | + | 0.0241299i | ||||
\(779\) | 49.3095i | 1.76670i | ||||||||
\(780\) | −3.66740 | + | 4.67230i | −0.131314 | + | 0.167295i | ||||
\(781\) | −10.2587 | + | 5.92286i | −0.367085 | + | 0.211936i | ||||
\(782\) | 14.0572 | − | 8.11591i | 0.502684 | − | 0.290224i | ||||
\(783\) | 26.3652 | + | 11.9529i | 0.942216 | + | 0.427163i | ||||
\(784\) | −7.60549 | + | 13.1731i | −0.271625 | + | 0.470468i | ||||
\(785\) | 0.756352 | + | 0.436680i | 0.0269954 | + | 0.0155858i | ||||
\(786\) | 10.0184 | − | 12.7635i | 0.357343 | − | 0.455258i | ||||
\(787\) | 24.2990 | − | 14.0290i | 0.866164 | − | 0.500080i | 9.26051e−5 | − | 1.00000i | \(-0.499971\pi\) |
0.866072 | + | 0.499920i | \(0.166637\pi\) | |||||||
\(788\) | 7.08814 | − | 12.2770i | 0.252504 | − | 0.437350i | ||||
\(789\) | −5.74380 | − | 14.3092i | −0.204485 | − | 0.509422i | ||||
\(790\) | 1.10246i | 0.0392238i | ||||||||
\(791\) | − | 16.9922i | − | 0.604175i | ||||||
\(792\) | −18.5643 | + | 4.53977i | −0.659654 | + | 0.161314i | ||||
\(793\) | −2.26142 | + | 3.91689i | −0.0803053 | + | 0.139093i | ||||
\(794\) | 2.64462 | − | 1.52687i | 0.0938539 | − | 0.0541866i | ||||
\(795\) | −1.75924 | − | 1.38087i | −0.0623937 | − | 0.0489743i | ||||
\(796\) | 6.70999 | + | 3.87401i | 0.237829 | + | 0.137311i | ||||
\(797\) | −11.7819 | + | 20.4069i | −0.417338 | + | 0.722850i | −0.995671 | − | 0.0929505i | \(-0.970370\pi\) |
0.578333 | + | 0.815801i | \(0.303704\pi\) | |||||||
\(798\) | 5.91281 | − | 41.3942i | 0.209311 | − | 1.46534i | ||||
\(799\) | 10.0700 | − | 5.81393i | 0.356252 | − | 0.205682i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 13.6633 | − | 13.0759i | 0.482770 | − | 0.462015i | ||||
\(802\) | 22.4218i | 0.791740i | ||||||||
\(803\) | −57.6779 | + | 33.3004i | −2.03541 | + | 1.17514i | ||||
\(804\) | −24.8571 | − | 3.55063i | −0.876644 | − | 0.125221i | ||||
\(805\) | − | 23.0664i | − | 0.812982i | ||||||
\(806\) | 18.7258 | − | 3.72917i | 0.659588 | − | 0.131354i | ||||
\(807\) | −34.9928 | − | 4.99842i | −1.23181 | − | 0.175953i | ||||
\(808\) | 15.8938 | 0.559142 | ||||||||
\(809\) | −2.84021 | − | 4.91939i | −0.0998566 | − | 0.172957i | 0.811769 | − | 0.583979i | \(-0.198505\pi\) |
−0.911625 | + | 0.411023i | \(0.865172\pi\) | |||||||
\(810\) | 7.58910 | + | 4.83793i | 0.266654 | + | 0.169988i | ||||
\(811\) | −5.10925 | + | 8.84947i | −0.179410 | + | 0.310747i | −0.941679 | − | 0.336514i | \(-0.890752\pi\) |
0.762269 | + | 0.647261i | \(0.224085\pi\) | |||||||
\(812\) | −13.1278 | − | 22.7381i | −0.460697 | − | 0.797950i | ||||
\(813\) | 7.67359 | − | 3.08022i | 0.269124 | − | 0.108028i | ||||
\(814\) | 31.3972 | 1.10047 | ||||||||
\(815\) | 2.13197 | + | 1.23090i | 0.0746798 | + | 0.0431164i | ||||
\(816\) | 3.54671 | − | 4.51854i | 0.124160 | − | 0.158180i | ||||
\(817\) | 26.9904 | + | 15.5829i | 0.944274 | + | 0.545177i | ||||
\(818\) | −12.4143 | − | 21.5021i | −0.434055 | − | 0.751805i | ||||
\(819\) | −33.5230 | − | 35.0289i | −1.17139 | − | 1.22401i | ||||
\(820\) | 4.81303 | + | 8.33642i | 0.168078 | + | 0.291120i | ||||
\(821\) | −27.0881 | −0.945381 | −0.472691 | − | 0.881228i | \(-0.656717\pi\) | ||||
−0.472691 | + | 0.881228i | \(0.656717\pi\) | |||||||
\(822\) | 1.01176 | − | 7.08309i | 0.0352891 | − | 0.247051i | ||||
\(823\) | −17.4328 | + | 10.0649i | −0.607671 | + | 0.350839i | −0.772053 | − | 0.635558i | \(-0.780770\pi\) |
0.164383 | + | 0.986397i | \(0.447437\pi\) | |||||||
\(824\) | 13.1377 | + | 7.58503i | 0.457672 | + | 0.264237i | ||||
\(825\) | −4.11030 | − | 10.2398i | −0.143102 | − | 0.356504i | ||||
\(826\) | 13.2531 | − | 22.9550i | 0.461134 | − | 0.798707i | ||||
\(827\) | −15.6535 | + | 27.1126i | −0.544324 | + | 0.942798i | 0.454325 | + | 0.890836i | \(0.349881\pi\) |
−0.998649 | + | 0.0519614i | \(0.983453\pi\) | |||||||
\(828\) | 10.6080 | − | 10.1520i | 0.368654 | − | 0.352805i | ||||
\(829\) | − | 44.6947i | − | 1.55231i | −0.630541 | − | 0.776156i | \(-0.717167\pi\) | ||
0.630541 | − | 0.776156i | \(-0.282833\pi\) | |||||||
\(830\) | −3.19991 | − | 5.54241i | −0.111070 | − | 0.192380i | ||||
\(831\) | −8.14873 | + | 3.27094i | −0.282676 | + | 0.113468i | ||||
\(832\) | 2.96986 | + | 1.71465i | 0.102961 | + | 0.0594447i | ||||
\(833\) | 50.4463 | 1.74786 | ||||||||
\(834\) | −13.3911 | − | 33.3604i | −0.463694 | − | 1.15518i | ||||
\(835\) | 13.1610i | 0.455456i | ||||||||
\(836\) | −32.6326 | −1.12862 | ||||||||
\(837\) | −8.39833 | − | 27.6852i | −0.290289 | − | 0.956939i | ||||
\(838\) | −13.9574 | −0.482152 | ||||||||
\(839\) | 3.44221i | 0.118838i | 0.998233 | + | 0.0594191i | \(0.0189248\pi\) | ||||
−0.998233 | + | 0.0594191i | \(0.981075\pi\) | |||||||
\(840\) | −3.04080 | − | 7.57539i | −0.104918 | − | 0.261376i | ||||
\(841\) | 2.03692 | 0.0702388 | ||||||||
\(842\) | −22.7286 | − | 13.1223i | −0.783278 | − | 0.452226i | ||||
\(843\) | 35.7220 | − | 14.3390i | 1.23033 | − | 0.493861i | ||||
\(844\) | 7.68821 | + | 13.3164i | 0.264639 | + | 0.458369i | ||||
\(845\) | − | 1.23995i | − | 0.0426555i | ||||||
\(846\) | 7.59916 | − | 7.27248i | 0.261265 | − | 0.250033i | ||||
\(847\) | −69.7092 | + | 120.740i | −2.39524 | + | 4.14867i | ||||
\(848\) | −0.645608 | + | 1.11823i | −0.0221703 | + | 0.0384000i | ||||
\(849\) | 1.38716 | + | 3.45576i | 0.0476072 | + | 0.118601i | ||||
\(850\) | 2.87212 | + | 1.65822i | 0.0985130 | + | 0.0568765i | ||||
\(851\) | −20.8904 | + | 12.0611i | −0.716114 | + | 0.413449i | ||||
\(852\) | 0.455428 | − | 3.18835i | 0.0156027 | − | 0.109231i | ||||
\(853\) | −37.7187 | −1.29146 | −0.645732 | − | 0.763564i | \(-0.723448\pi\) | ||||
−0.645732 | + | 0.763564i | \(0.723448\pi\) | |||||||
\(854\) | −3.10785 | − | 5.38295i | −0.106348 | − | 0.184201i | ||||
\(855\) | 10.6252 | + | 11.1025i | 0.363374 | + | 0.379697i | ||||
\(856\) | −7.27724 | − | 12.6046i | −0.248731 | − | 0.430815i | ||||
\(857\) | −17.6018 | − | 10.1624i | −0.601265 | − | 0.347140i | 0.168274 | − | 0.985740i | \(-0.446181\pi\) |
−0.769539 | + | 0.638600i | \(0.779514\pi\) | |||||||
\(858\) | −23.3630 | + | 29.7646i | −0.797598 | + | 1.01615i | ||||
\(859\) | −19.1802 | − | 11.0737i | −0.654420 | − | 0.377830i | 0.135728 | − | 0.990746i | \(-0.456663\pi\) |
−0.790148 | + | 0.612917i | \(0.789996\pi\) | |||||||
\(860\) | 6.08411 | 0.207466 | ||||||||
\(861\) | −72.9212 | + | 29.2709i | −2.48515 | + | 0.997551i | ||||
\(862\) | 0.377680 | + | 0.654160i | 0.0128638 | + | 0.0222808i | ||||
\(863\) | 9.13662 | − | 15.8251i | 0.311014 | − | 0.538693i | −0.667568 | − | 0.744549i | \(-0.732665\pi\) |
0.978582 | + | 0.205856i | \(0.0659980\pi\) | |||||||
\(864\) | 2.14553 | − | 4.73251i | 0.0729925 | − | 0.161003i | ||||
\(865\) | −1.37051 | − | 2.37379i | −0.0465987 | − | 0.0807113i | ||||
\(866\) | −5.99857 | −0.203840 | ||||||||
\(867\) | 10.2900 | + | 1.46983i | 0.349466 | + | 0.0499182i | ||||
\(868\) | −8.42900 | + | 24.8494i | −0.286099 | + | 0.843443i | ||||
\(869\) | 7.02318i | 0.238245i | ||||||||
\(870\) | 9.55243 | + | 1.36448i | 0.323858 | + | 0.0462603i | ||||
\(871\) | −43.0538 | + | 24.8571i | −1.45882 | + | 0.842252i | ||||
\(872\) | 13.1729i | 0.446092i | ||||||||
\(873\) | −1.01687 | + | 0.973156i | −0.0344159 | + | 0.0329363i | ||||
\(874\) | 21.7124 | − | 12.5356i | 0.734432 | − | 0.424024i | ||||
\(875\) | 4.08145 | − | 2.35643i | 0.137978 | − | 0.0796617i | ||||
\(876\) | 2.56057 | − | 17.9260i | 0.0865138 | − | 0.605664i | ||||
\(877\) | 13.5383 | − | 23.4490i | 0.457155 | − | 0.791816i | −0.541654 | − | 0.840601i | \(-0.682202\pi\) |
0.998809 | + | 0.0487856i | \(0.0155351\pi\) | |||||||
\(878\) | 2.10550 | + | 1.21561i | 0.0710573 | + | 0.0410250i | ||||
\(879\) | 16.4849 | + | 12.9394i | 0.556023 | + | 0.436435i | ||||
\(880\) | −5.51697 | + | 3.18522i | −0.185977 | + | 0.107374i | ||||
\(881\) | −13.6476 | + | 23.6383i | −0.459798 | + | 0.796394i | −0.998950 | − | 0.0458146i | \(-0.985412\pi\) |
0.539152 | + | 0.842209i | \(0.318745\pi\) | |||||||
\(882\) | 44.3268 | − | 10.8398i | 1.49256 | − | 0.364995i | ||||
\(883\) | − | 18.0675i | − | 0.608019i | −0.952669 | − | 0.304010i | \(-0.901674\pi\) | ||
0.952669 | − | 0.304010i | \(-0.0983255\pi\) | |||||||
\(884\) | − | 11.3730i | − | 0.382517i | ||||||
\(885\) | 3.62883 | + | 9.04032i | 0.121982 | + | 0.303887i | ||||
\(886\) | −10.3987 | + | 18.0112i | −0.349353 | + | 0.605097i | ||||
\(887\) | −3.97057 | + | 2.29241i | −0.133319 | + | 0.0769716i | −0.565176 | − | 0.824970i | \(-0.691192\pi\) |
0.431857 | + | 0.901942i | \(0.357858\pi\) | |||||||
\(888\) | −5.27077 | + | 6.71501i | −0.176876 | + | 0.225341i | ||||
\(889\) | −13.3411 | − | 7.70249i | −0.447446 | − | 0.258333i | ||||
\(890\) | 3.15201 | − | 5.45944i | 0.105656 | − | 0.183001i | ||||
\(891\) | 48.3460 | + | 30.8198i | 1.61965 | + | 1.03250i | ||||
\(892\) | 9.74718 | − | 5.62754i | 0.326360 | − | 0.188424i | ||||
\(893\) | 15.5539 | − | 8.98005i | 0.520492 | − | 0.300506i | ||||
\(894\) | −0.0679009 | + | 0.0865064i | −0.00227095 | + | 0.00289321i | ||||
\(895\) | 3.05228i | 0.102026i | ||||||||
\(896\) | −4.08145 | + | 2.35643i | −0.136352 | + | 0.0787227i | ||||
\(897\) | 4.11082 | − | 28.7789i | 0.137256 | − | 0.960900i | ||||
\(898\) | − | 19.2778i | − | 0.643308i | ||||||
\(899\) | −20.4571 | − | 23.3163i | −0.682284 | − | 0.777643i | ||||
\(900\) | 2.88003 | + | 0.839911i | 0.0960009 | + | 0.0279970i | ||||
\(901\) | 4.28224 | 0.142662 | ||||||||
\(902\) | 30.6612 | + | 53.1067i | 1.02091 | + | 1.76826i | ||||
\(903\) | −7.02278 | + | 49.1649i | −0.233704 | + | 1.63611i | ||||
\(904\) | 1.80276 | − | 3.12246i | 0.0599588 | − | 0.103852i | ||||
\(905\) | −8.05934 | − | 13.9592i | −0.267902 | − | 0.464019i | ||||
\(906\) | 1.80796 | + | 4.50409i | 0.0600656 | + | 0.149638i | ||||
\(907\) | −44.5709 | −1.47995 | −0.739977 | − | 0.672633i | \(-0.765163\pi\) | ||||
−0.739977 | + | 0.672633i | \(0.765163\pi\) | |||||||
\(908\) | 19.1006 | + | 11.0278i | 0.633877 | + | 0.365969i | ||||
\(909\) | −32.9673 | − | 34.4482i | −1.09346 | − | 1.14257i | ||||
\(910\) | −13.9965 | − | 8.08088i | −0.463979 | − | 0.267878i | ||||
\(911\) | 4.72481 | + | 8.18361i | 0.156540 | + | 0.271135i | 0.933619 | − | 0.358268i | \(-0.116633\pi\) |
−0.777079 | + | 0.629403i | \(0.783299\pi\) | |||||||
\(912\) | 5.47816 | − | 6.97923i | 0.181400 | − | 0.231105i | ||||
\(913\) | −20.3849 | − | 35.3076i | −0.674640 | − | 1.16851i | ||||
\(914\) | −9.77722 | −0.323402 | ||||||||
\(915\) | 2.26142 | + | 0.323024i | 0.0747602 | + | 0.0106788i | ||||
\(916\) | 6.32764 | − | 3.65326i | 0.209071 | − | 0.120707i | ||||
\(917\) | 38.2347 | + | 22.0748i | 1.26262 | + | 0.728975i | ||||
\(918\) | −17.1501 | + | 1.68532i | −0.566038 | + | 0.0556238i | ||||
\(919\) | −18.8216 | + | 32.6000i | −0.620867 | + | 1.07537i | 0.368457 | + | 0.929645i | \(0.379886\pi\) |
−0.989325 | + | 0.145729i | \(0.953447\pi\) | |||||||
\(920\) | 2.44718 | − | 4.23863i | 0.0806810 | − | 0.139744i | ||||
\(921\) | −11.6640 | + | 14.8601i | −0.384343 | + | 0.489657i | ||||
\(922\) | − | 15.6965i | − | 0.516937i | ||||||
\(923\) | −3.18835 | − | 5.52238i | −0.104946 | − | 0.181771i | ||||
\(924\) | −19.3713 | − | 48.2586i | −0.637267 | − | 1.58759i | ||||
\(925\) | −4.26827 | − | 2.46429i | −0.140340 | − | 0.0810252i | ||||
\(926\) | 37.5167 | 1.23287 | ||||||||
\(927\) | −10.8106 | − | 44.2076i | −0.355068 | − | 1.45197i | ||||
\(928\) | − | 5.57108i | − | 0.182880i | ||||||
\(929\) | 25.0170 | 0.820782 | 0.410391 | − | 0.911910i | \(-0.365392\pi\) | ||||
0.410391 | + | 0.911910i | \(0.365392\pi\) | |||||||
\(930\) | −5.27116 | − | 8.07557i | −0.172848 | − | 0.264808i | ||||
\(931\) | 77.9181 | 2.55366 | ||||||||
\(932\) | − | 9.29519i | − | 0.304474i | ||||||
\(933\) | 43.2682 | − | 17.3681i | 1.41654 | − | 0.568605i | ||||
\(934\) | 18.6592 | 0.610548 | ||||||||
\(935\) | 18.2967 | + | 10.5636i | 0.598366 | + | 0.345467i | ||||
\(936\) | −2.44381 | − | 9.99341i | −0.0798786 | − | 0.326645i | ||||
\(937\) | −14.2317 | − | 24.6500i | −0.464929 | − | 0.805281i | 0.534269 | − | 0.845314i | \(-0.320587\pi\) |
−0.999198 | + | 0.0400334i | \(0.987254\pi\) | |||||||
\(938\) | − | 68.3220i | − | 2.23079i | ||||||
\(939\) | 15.3321 | + | 12.0345i | 0.500345 | + | 0.392733i | ||||
\(940\) | 1.75306 | − | 3.03639i | 0.0571786 | − | 0.0990362i | ||||
\(941\) | −26.5777 | + | 46.0340i | −0.866409 | + | 1.50067i | −0.000768544 | 1.00000i | \(0.500245\pi\) | |
−0.865641 | + | 0.500665i | \(0.833089\pi\) | |||||||
\(942\) | −1.40383 | + | 0.563504i | −0.0457392 | + | 0.0183600i | ||||
\(943\) | −40.8014 | − | 23.5567i | −1.32868 | − | 0.767111i | ||||
\(944\) | 4.87072 | − | 2.81211i | 0.158529 | − | 0.0915265i | ||||
\(945\) | −10.1116 | + | 22.3036i | −0.328930 | + | 0.725537i | ||||
\(946\) | 38.7585 | 1.26015 | ||||||||
\(947\) | 24.9772 | + | 43.2619i | 0.811651 | + | 1.40582i | 0.911708 | + | 0.410840i | \(0.134764\pi\) |
−0.100056 | + | 0.994982i | \(0.531902\pi\) | |||||||
\(948\) | −1.50207 | − | 1.17901i | −0.0487849 | − | 0.0382924i | ||||
\(949\) | −17.9260 | − | 31.0488i | −0.581903 | − | 1.00789i | ||||
\(950\) | 4.43621 | + | 2.56125i | 0.143930 | + | 0.0830978i | ||||
\(951\) | 26.6162 | + | 20.8917i | 0.863088 | + | 0.677458i | ||||
\(952\) | 13.5359 | + | 7.81495i | 0.438701 | + | 0.253284i | ||||
\(953\) | −9.00841 | −0.291811 | −0.145905 | − | 0.989299i | \(-0.546610\pi\) | ||||
−0.145905 | + | 0.989299i | \(0.546610\pi\) | |||||||
\(954\) | 3.76277 | − | 0.920158i | 0.121824 | − | 0.0297912i | ||||
\(955\) | 4.37340 | + | 7.57495i | 0.141520 | + | 0.245120i | ||||
\(956\) | −12.0377 | + | 20.8498i | −0.389326 | + | 0.674332i | ||||
\(957\) | 60.8533 | + | 8.69236i | 1.96711 | + | 0.280984i | ||||
\(958\) | −0.235467 | − | 0.407841i | −0.00760760 | − | 0.0131768i | ||||
\(959\) | 19.4685 | 0.628670 | ||||||||
\(960\) | 0.244922 | − | 1.71465i | 0.00790484 | − | 0.0553400i | ||||
\(961\) | −4.03249 | + | 30.7366i | −0.130080 | + | 0.991503i | ||||
\(962\) | 16.9015i | 0.544927i | ||||||||
\(963\) | −12.2245 | + | 41.9173i | −0.393928 | + | 1.35077i | ||||
\(964\) | 9.91581 | − | 5.72490i | 0.319367 | − | 0.184386i | ||||
\(965\) | − | 21.5215i | − | 0.692800i | ||||||
\(966\) | 31.4271 | + | 24.6679i | 1.01115 | + | 0.793677i | ||||
\(967\) | 19.0116 | − | 10.9764i | 0.611372 | − | 0.352976i | −0.162130 | − | 0.986769i | \(-0.551836\pi\) |
0.773502 | + | 0.633794i | \(0.218503\pi\) | |||||||
\(968\) | −25.6193 | + | 14.7913i | −0.823435 | + | 0.475410i | ||||
\(969\) | −29.1292 | − | 4.16085i | −0.935764 | − | 0.133666i | ||||
\(970\) | −0.234584 | + | 0.406311i | −0.00753202 | + | 0.0130458i | ||||
\(971\) | 2.19230 | + | 1.26572i | 0.0703542 | + | 0.0406190i | 0.534764 | − | 0.845001i | \(-0.320400\pi\) |
−0.464410 | + | 0.885620i | \(0.653734\pi\) | |||||||
\(972\) | −14.7075 | + | 5.16606i | −0.471745 | + | 0.165701i | ||||
\(973\) | 84.7082 | − | 48.9063i | 2.71562 | − | 1.56786i | ||||
\(974\) | −9.29103 | + | 16.0925i | −0.297704 | + | 0.515638i | ||||
\(975\) | 5.51221 | − | 2.21263i | 0.176532 | − | 0.0708608i | ||||
\(976\) | − | 1.31888i | − | 0.0422164i | ||||||
\(977\) | − | 33.8056i | − | 1.08154i | −0.841171 | − | 0.540769i | \(-0.818133\pi\) | ||
0.841171 | − | 0.540769i | \(-0.181867\pi\) | |||||||
\(978\) | −3.95706 | + | 1.58838i | −0.126533 | + | 0.0507909i | ||||
\(979\) | 20.0797 | − | 34.7791i | 0.641750 | − | 1.11154i | ||||
\(980\) | 13.1731 | − | 7.60549i | 0.420799 | − | 0.242948i | ||||
\(981\) | 28.5510 | − | 27.3235i | 0.911562 | − | 0.872374i | ||||
\(982\) | 1.86028 | + | 1.07403i | 0.0593639 | + | 0.0342738i | ||||
\(983\) | −15.2194 | + | 26.3608i | −0.485424 | + | 0.840779i | −0.999860 | − | 0.0167499i | \(-0.994668\pi\) |
0.514436 | + | 0.857529i | \(0.328001\pi\) | |||||||
\(984\) | −16.5053 | − | 2.35764i | −0.526170 | − | 0.0751588i | ||||
\(985\) | −12.2770 | + | 7.08814i | −0.391178 | + | 0.225847i | ||||
\(986\) | −16.0008 | + | 9.23808i | −0.509570 | + | 0.294200i | ||||
\(987\) | 22.5132 | + | 17.6711i | 0.716603 | + | 0.562478i | ||||
\(988\) | − | 17.5665i | − | 0.558866i | ||||||
\(989\) | −25.7883 | + | 14.8889i | −0.820020 | + | 0.473439i | ||||
\(990\) | 18.3471 | + | 5.35061i | 0.583108 | + | 0.170053i | ||||
\(991\) | 24.1624i | 0.767543i | 0.923428 | + | 0.383771i | \(0.125375\pi\) | ||||
−0.923428 | + | 0.383771i | \(0.874625\pi\) | |||||||
\(992\) | −4.18524 | + | 3.67202i | −0.132882 | + | 0.116587i | ||||
\(993\) | 3.22675 | − | 22.5898i | 0.102398 | − | 0.716865i | ||||
\(994\) | 8.76345 | 0.277960 | ||||||||
\(995\) | −3.87401 | − | 6.70999i | −0.122814 | − | 0.212721i | ||||
\(996\) | 10.9734 | + | 1.56746i | 0.347706 | + | 0.0496668i | ||||
\(997\) | −31.2750 | + | 54.1699i | −0.990490 | + | 1.71558i | −0.376091 | + | 0.926583i | \(0.622732\pi\) |
−0.614399 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(998\) | 7.91901 | + | 13.7161i | 0.250672 | + | 0.434177i | ||||
\(999\) | 25.4868 | − | 2.50456i | 0.806368 | − | 0.0792407i |
(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 | 930.2.o.d.161.15 | yes | 36 | |
3.2 | odd | 2 | inner | 930.2.o.d.161.3 | ✓ | 36 | |
31.26 | odd | 6 | inner | 930.2.o.d.491.12 | yes | 36 | |
93.26 | even | 6 | inner | 930.2.o.d.491.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.d.161.3 | ✓ | 36 | 3.2 | odd | 2 | inner | |
930.2.o.d.161.15 | yes | 36 | 1.1 | even | 1 | trivial | |
930.2.o.d.491.6 | yes | 36 | 93.26 | even | 6 | inner | |
930.2.o.d.491.12 | yes | 36 | 31.26 | odd | 6 | inner |