Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(331,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.331");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.q (of order \(3\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 9x^{10} + 61x^{8} - 2x^{7} + 164x^{6} - 36x^{5} + 328x^{4} - 40x^{3} + 164x^{2} + 16x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(-1.16512 - 2.01805i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.991 |
Dual form | 1155.2.q.h.331.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16512 | − | 2.01805i | −0.823867 | − | 1.42698i | −0.902782 | − | 0.430098i | \(-0.858479\pi\) |
0.0789150 | − | 0.996881i | \(-0.474854\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.71503 | + | 2.97052i | −0.857514 | + | 1.48526i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 2.33025 | 0.951320 | ||||||||
\(7\) | −1.60347 | + | 2.10449i | −0.606055 | + | 0.795422i | ||||
\(8\) | 3.33238 | 1.17818 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.16512 | − | 2.01805i | 0.368445 | − | 0.638165i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −1.71503 | − | 2.97052i | −0.495086 | − | 0.857514i | ||||
\(13\) | −6.56567 | −1.82099 | −0.910494 | − | 0.413522i | \(-0.864299\pi\) | ||||
−0.910494 | + | 0.413522i | \(0.864299\pi\) | |||||||
\(14\) | 6.11522 | + | 0.783901i | 1.63436 | + | 0.209506i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.452585 | − | 0.783901i | −0.113146 | − | 0.195975i | ||||
\(17\) | 1.27775 | − | 2.21312i | 0.309899 | − | 0.536762i | −0.668441 | − | 0.743765i | \(-0.733038\pi\) |
0.978340 | + | 0.207004i | \(0.0663713\pi\) | |||||||
\(18\) | −1.16512 | + | 2.01805i | −0.274622 | + | 0.475660i | ||||
\(19\) | 1.19422 | + | 2.06845i | 0.273973 | + | 0.474536i | 0.969876 | − | 0.243601i | \(-0.0783287\pi\) |
−0.695902 | + | 0.718136i | \(0.744995\pi\) | |||||||
\(20\) | −3.43006 | −0.766984 | ||||||||
\(21\) | −1.02081 | − | 2.44089i | −0.222758 | − | 0.532646i | ||||
\(22\) | 2.33025 | 0.496811 | ||||||||
\(23\) | 1.85935 | + | 3.22048i | 0.387700 | + | 0.671517i | 0.992140 | − | 0.125134i | \(-0.0399362\pi\) |
−0.604439 | + | 0.796651i | \(0.706603\pi\) | |||||||
\(24\) | −1.66619 | + | 2.88593i | −0.340110 | + | 0.589088i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 7.64982 | + | 13.2499i | 1.50025 | + | 2.59851i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.50142 | − | 8.37240i | −0.661706 | − | 1.58223i | ||||
\(29\) | −4.34552 | −0.806943 | −0.403472 | − | 0.914992i | \(-0.632197\pi\) | ||||
−0.403472 | + | 0.914992i | \(0.632197\pi\) | |||||||
\(30\) | 1.16512 | + | 2.01805i | 0.212722 | + | 0.368445i | ||||
\(31\) | 4.63958 | − | 8.03599i | 0.833294 | − | 1.44331i | −0.0621183 | − | 0.998069i | \(-0.519786\pi\) |
0.895412 | − | 0.445238i | \(-0.146881\pi\) | |||||||
\(32\) | 2.27775 | − | 3.94518i | 0.402653 | − | 0.697415i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | −5.95494 | −1.02126 | ||||||||
\(35\) | −2.62428 | − | 0.336402i | −0.443584 | − | 0.0568624i | ||||
\(36\) | 3.43006 | 0.571676 | ||||||||
\(37\) | −3.49343 | − | 6.05080i | −0.574316 | − | 0.994745i | −0.996116 | − | 0.0880557i | \(-0.971935\pi\) |
0.421799 | − | 0.906689i | \(-0.361399\pi\) | |||||||
\(38\) | 2.78283 | − | 4.82001i | 0.451435 | − | 0.781909i | ||||
\(39\) | 3.28283 | − | 5.68603i | 0.525674 | − | 0.910494i | ||||
\(40\) | 1.66619 | + | 2.88593i | 0.263448 | + | 0.456306i | ||||
\(41\) | 5.85125 | 0.913811 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(42\) | −3.73649 | + | 4.90398i | −0.576552 | + | 0.756701i | ||||
\(43\) | −0.577059 | −0.0880007 | −0.0440004 | − | 0.999032i | \(-0.514010\pi\) | ||||
−0.0440004 | + | 0.999032i | \(0.514010\pi\) | |||||||
\(44\) | −1.71503 | − | 2.97052i | −0.258550 | − | 0.447822i | ||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 4.33274 | − | 7.50452i | 0.638827 | − | 1.10648i | ||||
\(47\) | −0.610040 | − | 1.05662i | −0.0889835 | − | 0.154124i | 0.818098 | − | 0.575079i | \(-0.195029\pi\) |
−0.907082 | + | 0.420955i | \(0.861695\pi\) | |||||||
\(48\) | 0.905171 | 0.130650 | ||||||||
\(49\) | −1.85776 | − | 6.74898i | −0.265394 | − | 0.964140i | ||||
\(50\) | 2.33025 | 0.329547 | ||||||||
\(51\) | 1.27775 | + | 2.21312i | 0.178921 | + | 0.309899i | ||||
\(52\) | 11.2603 | − | 19.5034i | 1.56152 | − | 2.70464i | ||||
\(53\) | −0.857818 | + | 1.48578i | −0.117830 | + | 0.204088i | −0.918908 | − | 0.394473i | \(-0.870927\pi\) |
0.801077 | + | 0.598561i | \(0.204261\pi\) | |||||||
\(54\) | −1.16512 | − | 2.01805i | −0.158553 | − | 0.274622i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −5.34338 | + | 7.01297i | −0.714040 | + | 0.937147i | ||||
\(57\) | −2.38844 | −0.316357 | ||||||||
\(58\) | 5.06307 | + | 8.76950i | 0.664814 | + | 1.15149i | ||||
\(59\) | 5.88478 | − | 10.1927i | 0.766133 | − | 1.32698i | −0.173513 | − | 0.984832i | \(-0.555512\pi\) |
0.939646 | − | 0.342149i | \(-0.111155\pi\) | |||||||
\(60\) | 1.71503 | − | 2.97052i | 0.221409 | − | 0.383492i | ||||
\(61\) | −5.05392 | − | 8.75364i | −0.647088 | − | 1.12079i | −0.983815 | − | 0.179187i | \(-0.942653\pi\) |
0.336727 | − | 0.941602i | \(-0.390680\pi\) | |||||||
\(62\) | −21.6228 | −2.74609 | ||||||||
\(63\) | 2.62428 | + | 0.336402i | 0.330628 | + | 0.0423827i | ||||
\(64\) | −12.4258 | −1.55322 | ||||||||
\(65\) | −3.28283 | − | 5.68603i | −0.407185 | − | 0.705266i | ||||
\(66\) | −1.16512 | + | 2.01805i | −0.143417 | + | 0.248405i | ||||
\(67\) | 6.05184 | − | 10.4821i | 0.739350 | − | 1.28059i | −0.213438 | − | 0.976957i | \(-0.568466\pi\) |
0.952788 | − | 0.303636i | \(-0.0982006\pi\) | |||||||
\(68\) | 4.38275 | + | 7.59114i | 0.531486 | + | 0.920561i | ||||
\(69\) | −3.71869 | −0.447678 | ||||||||
\(70\) | 2.37873 | + | 5.68788i | 0.284313 | + | 0.679832i | ||||
\(71\) | 1.12615 | 0.133649 | 0.0668245 | − | 0.997765i | \(-0.478713\pi\) | ||||
0.0668245 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(72\) | −1.66619 | − | 2.88593i | −0.196363 | − | 0.340110i | ||||
\(73\) | −3.83339 | + | 6.63963i | −0.448664 | + | 0.777110i | −0.998299 | − | 0.0582954i | \(-0.981433\pi\) |
0.549635 | + | 0.835405i | \(0.314767\pi\) | |||||||
\(74\) | −8.14056 | + | 14.0999i | −0.946321 | + | 1.63908i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −8.19250 | −0.939744 | ||||||||
\(77\) | −1.02081 | − | 2.44089i | −0.116332 | − | 0.278165i | ||||
\(78\) | −15.2996 | −1.73234 | ||||||||
\(79\) | −0.372163 | − | 0.644604i | −0.0418716 | − | 0.0725237i | 0.844330 | − | 0.535823i | \(-0.179999\pi\) |
−0.886202 | + | 0.463300i | \(0.846665\pi\) | |||||||
\(80\) | 0.452585 | − | 0.783901i | 0.0506006 | − | 0.0876428i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.81743 | − | 11.8081i | −0.752859 | − | 1.30399i | ||||
\(83\) | −12.9061 | −1.41663 | −0.708313 | − | 0.705898i | \(-0.750544\pi\) | ||||
−0.708313 | + | 0.705898i | \(0.750544\pi\) | |||||||
\(84\) | 9.00142 | + | 1.15388i | 0.982135 | + | 0.125898i | ||||
\(85\) | 2.55550 | 0.277183 | ||||||||
\(86\) | 0.672346 | + | 1.16454i | 0.0725009 | + | 0.125575i | ||||
\(87\) | 2.17276 | − | 3.76333i | 0.232944 | − | 0.403472i | ||||
\(88\) | −1.66619 | + | 2.88593i | −0.177617 | + | 0.307641i | ||||
\(89\) | 8.03826 | + | 13.9227i | 0.852054 | + | 1.47580i | 0.879352 | + | 0.476173i | \(0.157976\pi\) |
−0.0272977 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(90\) | −2.33025 | −0.245630 | ||||||||
\(91\) | 10.5279 | − | 13.8174i | 1.10362 | − | 1.44845i | ||||
\(92\) | −12.7553 | −1.32983 | ||||||||
\(93\) | 4.63958 | + | 8.03599i | 0.481102 | + | 0.833294i | ||||
\(94\) | −1.42154 | + | 2.46219i | −0.146621 | + | 0.253955i | ||||
\(95\) | −1.19422 | + | 2.06845i | −0.122525 | + | 0.212219i | ||||
\(96\) | 2.27775 | + | 3.94518i | 0.232472 | + | 0.402653i | ||||
\(97\) | −4.43219 | −0.450021 | −0.225010 | − | 0.974356i | \(-0.572242\pi\) | ||||
−0.225010 | + | 0.974356i | \(0.572242\pi\) | |||||||
\(98\) | −11.4553 | + | 11.6125i | −1.15716 | + | 1.17303i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.71503 | − | 2.97052i | −0.171503 | − | 0.297052i | ||||
\(101\) | −5.27118 | + | 9.12995i | −0.524502 | + | 0.908464i | 0.475091 | + | 0.879937i | \(0.342415\pi\) |
−0.999593 | + | 0.0285272i | \(0.990918\pi\) | |||||||
\(102\) | 2.97747 | − | 5.15713i | 0.294813 | − | 0.510632i | ||||
\(103\) | −2.96541 | − | 5.13625i | −0.292191 | − | 0.506089i | 0.682137 | − | 0.731225i | \(-0.261051\pi\) |
−0.974328 | + | 0.225135i | \(0.927718\pi\) | |||||||
\(104\) | −21.8793 | −2.14544 | ||||||||
\(105\) | 1.60347 | − | 2.10449i | 0.156483 | − | 0.205377i | ||||
\(106\) | 3.99786 | 0.388306 | ||||||||
\(107\) | −8.39232 | − | 14.5359i | −0.811317 | − | 1.40524i | −0.911943 | − | 0.410317i | \(-0.865418\pi\) |
0.100626 | − | 0.994924i | \(-0.467915\pi\) | |||||||
\(108\) | −1.71503 | + | 2.97052i | −0.165029 | + | 0.285838i | ||||
\(109\) | 8.28442 | − | 14.3490i | 0.793504 | − | 1.37439i | −0.130281 | − | 0.991477i | \(-0.541588\pi\) |
0.923785 | − | 0.382912i | \(-0.125079\pi\) | |||||||
\(110\) | 1.16512 | + | 2.01805i | 0.111090 | + | 0.192414i | ||||
\(111\) | 6.98686 | 0.663163 | ||||||||
\(112\) | 2.37542 | + | 0.304502i | 0.224456 | + | 0.0287727i | ||||
\(113\) | 17.2975 | 1.62721 | 0.813606 | − | 0.581417i | \(-0.197502\pi\) | ||||
0.813606 | + | 0.581417i | \(0.197502\pi\) | |||||||
\(114\) | 2.78283 | + | 4.82001i | 0.260636 | + | 0.451435i | ||||
\(115\) | −1.85935 | + | 3.22048i | −0.173385 | + | 0.300311i | ||||
\(116\) | 7.45269 | − | 12.9084i | 0.691965 | − | 1.19852i | ||||
\(117\) | 3.28283 | + | 5.68603i | 0.303498 | + | 0.525674i | ||||
\(118\) | −27.4260 | −2.52477 | ||||||||
\(119\) | 2.60867 | + | 6.23769i | 0.239136 | + | 0.571808i | ||||
\(120\) | −3.33238 | −0.304204 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −11.7769 | + | 20.3982i | −1.06623 | + | 1.84676i | ||||
\(123\) | −2.92562 | + | 5.06733i | −0.263795 | + | 0.456906i | ||||
\(124\) | 15.9140 | + | 27.5639i | 1.42912 | + | 2.47531i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.37873 | − | 5.68788i | −0.211914 | − | 0.506717i | ||||
\(127\) | −6.96467 | −0.618015 | −0.309007 | − | 0.951060i | \(-0.599997\pi\) | ||||
−0.309007 | + | 0.951060i | \(0.599997\pi\) | |||||||
\(128\) | 9.92208 | + | 17.1855i | 0.876996 | + | 1.51900i | ||||
\(129\) | 0.288530 | − | 0.499748i | 0.0254036 | − | 0.0440004i | ||||
\(130\) | −7.64982 | + | 13.2499i | −0.670933 | + | 1.16209i | ||||
\(131\) | 7.80481 | + | 13.5183i | 0.681910 | + | 1.18110i | 0.974397 | + | 0.224833i | \(0.0721837\pi\) |
−0.292488 | + | 0.956269i | \(0.594483\pi\) | |||||||
\(132\) | 3.43006 | 0.298548 | ||||||||
\(133\) | −6.26794 | − | 0.803478i | −0.543499 | − | 0.0696704i | ||||
\(134\) | −28.2046 | −2.43651 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 4.25795 | − | 7.37498i | 0.365116 | − | 0.632400i | ||||
\(137\) | −1.11869 | + | 1.93762i | −0.0955757 | + | 0.165542i | −0.909849 | − | 0.414940i | \(-0.863803\pi\) |
0.814273 | + | 0.580482i | \(0.197136\pi\) | |||||||
\(138\) | 4.33274 | + | 7.50452i | 0.368827 | + | 0.638827i | ||||
\(139\) | −12.3721 | −1.04939 | −0.524693 | − | 0.851292i | \(-0.675820\pi\) | ||||
−0.524693 | + | 0.851292i | \(0.675820\pi\) | |||||||
\(140\) | 5.50000 | − | 7.21852i | 0.464835 | − | 0.610076i | ||||
\(141\) | 1.22008 | 0.102749 | ||||||||
\(142\) | −1.31210 | − | 2.27262i | −0.110109 | − | 0.190714i | ||||
\(143\) | 3.28283 | − | 5.68603i | 0.274524 | − | 0.475490i | ||||
\(144\) | −0.452585 | + | 0.783901i | −0.0377154 | + | 0.0653251i | ||||
\(145\) | −2.17276 | − | 3.76333i | −0.180438 | − | 0.312528i | ||||
\(146\) | 17.8655 | 1.47856 | ||||||||
\(147\) | 6.77367 | + | 1.76563i | 0.558683 | + | 0.145626i | ||||
\(148\) | 23.9653 | 1.96994 | ||||||||
\(149\) | −1.69522 | − | 2.93620i | −0.138878 | − | 0.240543i | 0.788194 | − | 0.615426i | \(-0.211016\pi\) |
−0.927072 | + | 0.374883i | \(0.877683\pi\) | |||||||
\(150\) | −1.16512 | + | 2.01805i | −0.0951320 | + | 0.164773i | ||||
\(151\) | 0.460315 | − | 0.797288i | 0.0374599 | − | 0.0648824i | −0.846688 | − | 0.532090i | \(-0.821407\pi\) |
0.884148 | + | 0.467208i | \(0.154740\pi\) | |||||||
\(152\) | 3.97961 | + | 6.89288i | 0.322789 | + | 0.559086i | ||||
\(153\) | −2.55550 | −0.206600 | ||||||||
\(154\) | −3.73649 | + | 4.90398i | −0.301095 | + | 0.395174i | ||||
\(155\) | 9.27917 | 0.745321 | ||||||||
\(156\) | 11.2603 | + | 19.5034i | 0.901546 | + | 1.56152i | ||||
\(157\) | −9.81237 | + | 16.9955i | −0.783113 | + | 1.35639i | 0.147007 | + | 0.989135i | \(0.453036\pi\) |
−0.930120 | + | 0.367256i | \(0.880297\pi\) | |||||||
\(158\) | −0.867231 | + | 1.50209i | −0.0689932 | + | 0.119500i | ||||
\(159\) | −0.857818 | − | 1.48578i | −0.0680294 | − | 0.117830i | ||||
\(160\) | 4.55550 | 0.360144 | ||||||||
\(161\) | −9.75888 | − | 1.25098i | −0.769108 | − | 0.0985908i | ||||
\(162\) | 2.33025 | 0.183082 | ||||||||
\(163\) | −5.09803 | − | 8.83005i | −0.399309 | − | 0.691623i | 0.594332 | − | 0.804220i | \(-0.297416\pi\) |
−0.993641 | + | 0.112597i | \(0.964083\pi\) | |||||||
\(164\) | −10.0351 | + | 17.3812i | −0.783606 | + | 1.35725i | ||||
\(165\) | 0.500000 | − | 0.866025i | 0.0389249 | − | 0.0674200i | ||||
\(166\) | 15.0372 | + | 26.0452i | 1.16711 | + | 2.02150i | ||||
\(167\) | 0.708129 | 0.0547967 | 0.0273983 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273983 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(168\) | −3.40172 | − | 8.13399i | −0.262448 | − | 0.627551i | ||||
\(169\) | 30.1080 | 2.31600 | ||||||||
\(170\) | −2.97747 | − | 5.15713i | −0.228362 | − | 0.395534i | ||||
\(171\) | 1.19422 | − | 2.06845i | 0.0913244 | − | 0.158179i | ||||
\(172\) | 0.989673 | − | 1.71416i | 0.0754618 | − | 0.130704i | ||||
\(173\) | −6.76671 | − | 11.7203i | −0.514464 | − | 0.891077i | −0.999859 | − | 0.0167825i | \(-0.994658\pi\) |
0.485395 | − | 0.874295i | \(-0.338676\pi\) | |||||||
\(174\) | −10.1261 | −0.767661 | ||||||||
\(175\) | −1.02081 | − | 2.44089i | −0.0771657 | − | 0.184514i | ||||
\(176\) | 0.905171 | 0.0682298 | ||||||||
\(177\) | 5.88478 | + | 10.1927i | 0.442327 | + | 0.766133i | ||||
\(178\) | 18.7311 | − | 32.4433i | 1.40396 | − | 2.43173i | ||||
\(179\) | 6.98764 | − | 12.1029i | 0.522281 | − | 0.904617i | −0.477383 | − | 0.878695i | \(-0.658415\pi\) |
0.999664 | − | 0.0259216i | \(-0.00825204\pi\) | |||||||
\(180\) | 1.71503 | + | 2.97052i | 0.127831 | + | 0.221409i | ||||
\(181\) | −9.94639 | −0.739309 | −0.369655 | − | 0.929169i | \(-0.620524\pi\) | ||||
−0.369655 | + | 0.929169i | \(0.620524\pi\) | |||||||
\(182\) | −40.1505 | − | 5.14683i | −2.97615 | − | 0.381509i | ||||
\(183\) | 10.1078 | 0.747193 | ||||||||
\(184\) | 6.19606 | + | 10.7319i | 0.456779 | + | 0.791165i | ||||
\(185\) | 3.49343 | − | 6.05080i | 0.256842 | − | 0.444863i | ||||
\(186\) | 10.8114 | − | 18.7259i | 0.792729 | − | 1.37305i | ||||
\(187\) | 1.27775 | + | 2.21312i | 0.0934382 | + | 0.161840i | ||||
\(188\) | 4.18494 | 0.305218 | ||||||||
\(189\) | −1.60347 | + | 2.10449i | −0.116635 | + | 0.153079i | ||||
\(190\) | 5.56567 | 0.403776 | ||||||||
\(191\) | −6.24144 | − | 10.8105i | −0.451615 | − | 0.782220i | 0.546872 | − | 0.837216i | \(-0.315819\pi\) |
−0.998487 | + | 0.0549966i | \(0.982485\pi\) | |||||||
\(192\) | 6.21289 | − | 10.7610i | 0.448377 | − | 0.776611i | ||||
\(193\) | −0.859332 | + | 1.48841i | −0.0618561 | + | 0.107138i | −0.895295 | − | 0.445474i | \(-0.853035\pi\) |
0.833439 | + | 0.552611i | \(0.186369\pi\) | |||||||
\(194\) | 5.16405 | + | 8.94440i | 0.370757 | + | 0.642171i | ||||
\(195\) | 6.56567 | 0.470177 | ||||||||
\(196\) | 23.2341 | + | 6.05620i | 1.65958 | + | 0.432585i | ||||
\(197\) | 0.0590259 | 0.00420542 | 0.00210271 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210271 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(198\) | −1.16512 | − | 2.01805i | −0.0828018 | − | 0.143417i | ||||
\(199\) | −10.6909 | + | 18.5171i | −0.757856 | + | 1.31265i | 0.186085 | + | 0.982534i | \(0.440420\pi\) |
−0.943942 | + | 0.330112i | \(0.892913\pi\) | |||||||
\(200\) | −1.66619 | + | 2.88593i | −0.117818 | + | 0.204066i | ||||
\(201\) | 6.05184 | + | 10.4821i | 0.426864 | + | 0.739350i | ||||
\(202\) | 24.5663 | 1.72848 | ||||||||
\(203\) | 6.96792 | − | 9.14511i | 0.489052 | − | 0.641861i | ||||
\(204\) | −8.76550 | −0.613707 | ||||||||
\(205\) | 2.92562 | + | 5.06733i | 0.204334 | + | 0.353918i | ||||
\(206\) | −6.91015 | + | 11.9687i | −0.481453 | + | 0.833901i | ||||
\(207\) | 1.85935 | − | 3.22048i | 0.129233 | − | 0.223839i | ||||
\(208\) | 2.97152 | + | 5.14683i | 0.206038 | + | 0.356869i | ||||
\(209\) | −2.38844 | −0.165212 | ||||||||
\(210\) | −6.11522 | − | 0.783901i | −0.421990 | − | 0.0540943i | ||||
\(211\) | 16.1643 | 1.11280 | 0.556398 | − | 0.830916i | \(-0.312183\pi\) | ||||
0.556398 | + | 0.830916i | \(0.312183\pi\) | |||||||
\(212\) | −2.94236 | − | 5.09633i | −0.202082 | − | 0.350017i | ||||
\(213\) | −0.563073 | + | 0.975271i | −0.0385811 | + | 0.0668245i | ||||
\(214\) | −19.5562 | + | 33.8723i | −1.33683 | + | 2.31546i | ||||
\(215\) | −0.288530 | − | 0.499748i | −0.0196776 | − | 0.0340825i | ||||
\(216\) | 3.33238 | 0.226740 | ||||||||
\(217\) | 9.47223 | + | 22.6494i | 0.643017 | + | 1.53754i | ||||
\(218\) | −38.6095 | −2.61497 | ||||||||
\(219\) | −3.83339 | − | 6.63963i | −0.259037 | − | 0.448664i | ||||
\(220\) | 1.71503 | − | 2.97052i | 0.115627 | − | 0.200272i | ||||
\(221\) | −8.38927 | + | 14.5306i | −0.564323 | + | 0.977437i | ||||
\(222\) | −8.14056 | − | 14.0999i | −0.546358 | − | 0.946321i | ||||
\(223\) | −9.06835 | −0.607262 | −0.303631 | − | 0.952790i | \(-0.598199\pi\) | ||||
−0.303631 | + | 0.952790i | \(0.598199\pi\) | |||||||
\(224\) | 4.65028 | + | 11.1195i | 0.310710 | + | 0.742951i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −20.1537 | − | 34.9073i | −1.34061 | − | 2.32200i | ||||
\(227\) | 6.65868 | − | 11.5332i | 0.441952 | − | 0.765483i | −0.555882 | − | 0.831261i | \(-0.687619\pi\) |
0.997834 | + | 0.0657776i | \(0.0209528\pi\) | |||||||
\(228\) | 4.09625 | − | 7.09491i | 0.271281 | − | 0.469872i | ||||
\(229\) | −8.97166 | − | 15.5394i | −0.592864 | − | 1.02687i | −0.993845 | − | 0.110784i | \(-0.964664\pi\) |
0.400981 | − | 0.916087i | \(-0.368669\pi\) | |||||||
\(230\) | 8.66547 | 0.571384 | ||||||||
\(231\) | 2.62428 | + | 0.336402i | 0.172665 | + | 0.0221336i | ||||
\(232\) | −14.4809 | −0.950721 | ||||||||
\(233\) | −4.33046 | − | 7.50057i | −0.283698 | − | 0.491379i | 0.688595 | − | 0.725146i | \(-0.258228\pi\) |
−0.972293 | + | 0.233768i | \(0.924895\pi\) | |||||||
\(234\) | 7.64982 | − | 13.2499i | 0.500084 | − | 0.866171i | ||||
\(235\) | 0.610040 | − | 1.05662i | 0.0397946 | − | 0.0689263i | ||||
\(236\) | 20.1851 | + | 34.9616i | 1.31394 | + | 2.27581i | ||||
\(237\) | 0.744325 | 0.0483491 | ||||||||
\(238\) | 9.54858 | − | 12.5321i | 0.618942 | − | 0.812336i | ||||
\(239\) | −5.89784 | −0.381499 | −0.190750 | − | 0.981639i | \(-0.561092\pi\) | ||||
−0.190750 | + | 0.981639i | \(0.561092\pi\) | |||||||
\(240\) | 0.452585 | + | 0.783901i | 0.0292143 | + | 0.0506006i | ||||
\(241\) | −12.8722 | + | 22.2953i | −0.829170 | + | 1.43616i | 0.0695205 | + | 0.997581i | \(0.477853\pi\) |
−0.898690 | + | 0.438584i | \(0.855480\pi\) | |||||||
\(242\) | −1.16512 | + | 2.01805i | −0.0748970 | + | 0.129725i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 34.6704 | 2.21955 | ||||||||
\(245\) | 4.91591 | − | 4.98335i | 0.314066 | − | 0.318375i | ||||
\(246\) | 13.6349 | 0.869327 | ||||||||
\(247\) | −7.84086 | − | 13.5808i | −0.498902 | − | 0.864124i | ||||
\(248\) | 15.4609 | − | 26.7790i | 0.981767 | − | 1.70047i | ||||
\(249\) | 6.45304 | − | 11.1770i | 0.408945 | − | 0.708313i | ||||
\(250\) | 1.16512 | + | 2.01805i | 0.0736889 | + | 0.127633i | ||||
\(251\) | −20.9817 | −1.32435 | −0.662176 | − | 0.749348i | \(-0.730367\pi\) | ||||
−0.662176 | + | 0.749348i | \(0.730367\pi\) | |||||||
\(252\) | −5.50000 | + | 7.21852i | −0.346467 | + | 0.454724i | ||||
\(253\) | −3.71869 | −0.233792 | ||||||||
\(254\) | 8.11471 | + | 14.0551i | 0.509162 | + | 0.881895i | ||||
\(255\) | −1.27775 | + | 2.21312i | −0.0800157 | + | 0.138591i | ||||
\(256\) | 10.6951 | − | 18.5245i | 0.668445 | − | 1.15778i | ||||
\(257\) | 6.87262 | + | 11.9037i | 0.428702 | + | 0.742534i | 0.996758 | − | 0.0804559i | \(-0.0256376\pi\) |
−0.568056 | + | 0.822990i | \(0.692304\pi\) | |||||||
\(258\) | −1.34469 | −0.0837168 | ||||||||
\(259\) | 18.3355 | + | 2.35040i | 1.13931 | + | 0.146046i | ||||
\(260\) | 22.5206 | 1.39667 | ||||||||
\(261\) | 2.17276 | + | 3.76333i | 0.134491 | + | 0.232944i | ||||
\(262\) | 18.1872 | − | 31.5011i | 1.12361 | − | 1.94614i | ||||
\(263\) | 13.2124 | − | 22.8846i | 0.814713 | − | 1.41112i | −0.0948205 | − | 0.995494i | \(-0.530228\pi\) |
0.909534 | − | 0.415630i | \(-0.136439\pi\) | |||||||
\(264\) | −1.66619 | − | 2.88593i | −0.102547 | − | 0.177617i | ||||
\(265\) | −1.71564 | −0.105391 | ||||||||
\(266\) | 5.68147 | + | 13.5852i | 0.348353 | + | 0.832962i | ||||
\(267\) | −16.0765 | −0.983867 | ||||||||
\(268\) | 20.7582 | + | 35.9542i | 1.26801 | + | 2.19625i | ||||
\(269\) | 10.7518 | − | 18.6226i | 0.655546 | − | 1.13544i | −0.326210 | − | 0.945297i | \(-0.605772\pi\) |
0.981757 | − | 0.190142i | \(-0.0608950\pi\) | |||||||
\(270\) | 1.16512 | − | 2.01805i | 0.0709072 | − | 0.122815i | ||||
\(271\) | −6.49818 | − | 11.2552i | −0.394736 | − | 0.683704i | 0.598331 | − | 0.801249i | \(-0.295831\pi\) |
−0.993068 | + | 0.117545i | \(0.962497\pi\) | |||||||
\(272\) | −2.31316 | −0.140256 | ||||||||
\(273\) | 6.70227 | + | 16.0261i | 0.405640 | + | 0.969943i | ||||
\(274\) | 5.21363 | 0.314967 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 6.37766 | − | 11.0464i | 0.383890 | − | 0.664917i | ||||
\(277\) | 7.59172 | − | 13.1492i | 0.456142 | − | 0.790062i | −0.542611 | − | 0.839984i | \(-0.682564\pi\) |
0.998753 | + | 0.0499226i | \(0.0158975\pi\) | |||||||
\(278\) | 14.4150 | + | 24.9675i | 0.864554 | + | 1.49745i | ||||
\(279\) | −9.27917 | −0.555529 | ||||||||
\(280\) | −8.74510 | − | 1.12102i | −0.522620 | − | 0.0669939i | ||||
\(281\) | 9.45336 | 0.563940 | 0.281970 | − | 0.959423i | \(-0.409012\pi\) | ||||
0.281970 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(282\) | −1.42154 | − | 2.46219i | −0.0846518 | − | 0.146621i | ||||
\(283\) | 9.09011 | − | 15.7445i | 0.540351 | − | 0.935915i | −0.458533 | − | 0.888677i | \(-0.651625\pi\) |
0.998884 | − | 0.0472377i | \(-0.0150418\pi\) | |||||||
\(284\) | −1.93137 | + | 3.34524i | −0.114606 | + | 0.198503i | ||||
\(285\) | −1.19422 | − | 2.06845i | −0.0707396 | − | 0.122525i | ||||
\(286\) | −15.2996 | −0.904686 | ||||||||
\(287\) | −9.38231 | + | 12.3139i | −0.553820 | + | 0.726866i | ||||
\(288\) | −4.55550 | −0.268435 | ||||||||
\(289\) | 5.23472 | + | 9.06680i | 0.307925 | + | 0.533341i | ||||
\(290\) | −5.06307 | + | 8.76950i | −0.297314 | + | 0.514963i | ||||
\(291\) | 2.21610 | − | 3.83839i | 0.129910 | − | 0.225010i | ||||
\(292\) | −13.1487 | − | 22.7743i | −0.769472 | − | 1.33276i | ||||
\(293\) | 28.7950 | 1.68222 | 0.841112 | − | 0.540862i | \(-0.181902\pi\) | ||||
0.841112 | + | 0.540862i | \(0.181902\pi\) | |||||||
\(294\) | −4.32903 | − | 15.7268i | −0.252474 | − | 0.917206i | ||||
\(295\) | 11.7696 | 0.685250 | ||||||||
\(296\) | −11.6414 | − | 20.1636i | −0.676646 | − | 1.17198i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | −3.95027 | + | 6.84208i | −0.228833 | + | 0.396351i | ||||
\(299\) | −12.2078 | − | 21.1446i | −0.705998 | − | 1.22282i | ||||
\(300\) | 3.43006 | 0.198034 | ||||||||
\(301\) | 0.925298 | − | 1.21442i | 0.0533333 | − | 0.0699977i | ||||
\(302\) | −2.14529 | −0.123448 | ||||||||
\(303\) | −5.27118 | − | 9.12995i | −0.302821 | − | 0.524502i | ||||
\(304\) | 1.08097 | − | 1.87230i | 0.0619982 | − | 0.107384i | ||||
\(305\) | 5.05392 | − | 8.75364i | 0.289387 | − | 0.501232i | ||||
\(306\) | 2.97747 | + | 5.15713i | 0.170211 | + | 0.294813i | ||||
\(307\) | −25.7537 | −1.46984 | −0.734920 | − | 0.678154i | \(-0.762780\pi\) | ||||
−0.734920 | + | 0.678154i | \(0.762780\pi\) | |||||||
\(308\) | 9.00142 | + | 1.15388i | 0.512903 | + | 0.0657483i | ||||
\(309\) | 5.93083 | 0.337393 | ||||||||
\(310\) | −10.8114 | − | 18.7259i | −0.614045 | − | 1.06356i | ||||
\(311\) | 3.47750 | − | 6.02320i | 0.197191 | − | 0.341544i | −0.750426 | − | 0.660955i | \(-0.770152\pi\) |
0.947616 | + | 0.319410i | \(0.103485\pi\) | |||||||
\(312\) | 10.9397 | − | 18.9481i | 0.619336 | − | 1.07272i | ||||
\(313\) | 7.97224 | + | 13.8083i | 0.450618 | + | 0.780493i | 0.998424 | − | 0.0561122i | \(-0.0178705\pi\) |
−0.547807 | + | 0.836605i | \(0.684537\pi\) | |||||||
\(314\) | 45.7305 | 2.58072 | ||||||||
\(315\) | 1.02081 | + | 2.44089i | 0.0575159 | + | 0.137529i | ||||
\(316\) | 2.55308 | 0.143622 | ||||||||
\(317\) | −3.05779 | − | 5.29625i | −0.171743 | − | 0.297467i | 0.767287 | − | 0.641304i | \(-0.221606\pi\) |
−0.939029 | + | 0.343837i | \(0.888273\pi\) | |||||||
\(318\) | −1.99893 | + | 3.46225i | −0.112094 | + | 0.194153i | ||||
\(319\) | 2.17276 | − | 3.76333i | 0.121651 | − | 0.210706i | ||||
\(320\) | −6.21289 | − | 10.7610i | −0.347311 | − | 0.601560i | ||||
\(321\) | 16.7846 | 0.936828 | ||||||||
\(322\) | 8.84577 | + | 21.1515i | 0.492955 | + | 1.17873i | ||||
\(323\) | 6.10366 | 0.339617 | ||||||||
\(324\) | −1.71503 | − | 2.97052i | −0.0952793 | − | 0.165029i | ||||
\(325\) | 3.28283 | − | 5.68603i | 0.182099 | − | 0.315404i | ||||
\(326\) | −11.8797 | + | 20.5762i | −0.657955 | + | 1.13961i | ||||
\(327\) | 8.28442 | + | 14.3490i | 0.458130 | + | 0.793504i | ||||
\(328\) | 19.4986 | 1.07663 | ||||||||
\(329\) | 3.20183 | + | 0.410438i | 0.176523 | + | 0.0226282i | ||||
\(330\) | −2.33025 | −0.128276 | ||||||||
\(331\) | −1.10750 | − | 1.91825i | −0.0608737 | − | 0.105436i | 0.833982 | − | 0.551791i | \(-0.186055\pi\) |
−0.894856 | + | 0.446355i | \(0.852722\pi\) | |||||||
\(332\) | 22.1343 | − | 38.3377i | 1.21478 | − | 2.10406i | ||||
\(333\) | −3.49343 | + | 6.05080i | −0.191439 | + | 0.331582i | ||||
\(334\) | −0.825059 | − | 1.42904i | −0.0451452 | − | 0.0781938i | ||||
\(335\) | 12.1037 | 0.661295 | ||||||||
\(336\) | −1.45142 | + | 1.90492i | −0.0791812 | + | 0.103922i | ||||
\(337\) | −12.9876 | −0.707480 | −0.353740 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353740 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(338\) | −35.0795 | − | 60.7595i | −1.90807 | − | 3.30488i | ||||
\(339\) | −8.64875 | + | 14.9801i | −0.469735 | + | 0.813606i | ||||
\(340\) | −4.38275 | + | 7.59114i | −0.237688 | + | 0.411687i | ||||
\(341\) | 4.63958 | + | 8.03599i | 0.251248 | + | 0.435173i | ||||
\(342\) | −5.56567 | −0.300957 | ||||||||
\(343\) | 17.1820 | + | 6.91217i | 0.927742 | + | 0.373222i | ||||
\(344\) | −1.92298 | −0.103680 | ||||||||
\(345\) | −1.85935 | − | 3.22048i | −0.100104 | − | 0.173385i | ||||
\(346\) | −15.7681 | + | 27.3112i | −0.847699 | + | 1.46826i | ||||
\(347\) | 2.93144 | − | 5.07741i | 0.157368 | − | 0.272570i | −0.776551 | − | 0.630055i | \(-0.783032\pi\) |
0.933919 | + | 0.357485i | \(0.116366\pi\) | |||||||
\(348\) | 7.45269 | + | 12.9084i | 0.399506 | + | 0.691965i | ||||
\(349\) | 9.96125 | 0.533213 | 0.266607 | − | 0.963805i | \(-0.414098\pi\) | ||||
0.266607 | + | 0.963805i | \(0.414098\pi\) | |||||||
\(350\) | −3.73649 | + | 4.90398i | −0.199724 | + | 0.262129i | ||||
\(351\) | −6.56567 | −0.350449 | ||||||||
\(352\) | 2.27775 | + | 3.94518i | 0.121404 | + | 0.210279i | ||||
\(353\) | −3.45653 | + | 5.98689i | −0.183973 | + | 0.318650i | −0.943230 | − | 0.332141i | \(-0.892229\pi\) |
0.759257 | + | 0.650791i | \(0.225562\pi\) | |||||||
\(354\) | 13.7130 | − | 23.7516i | 0.728837 | − | 1.26238i | ||||
\(355\) | 0.563073 | + | 0.975271i | 0.0298848 | + | 0.0517620i | ||||
\(356\) | −55.1434 | −2.92259 | ||||||||
\(357\) | −6.70633 | − | 0.859675i | −0.354937 | − | 0.0454988i | ||||
\(358\) | −32.5659 | −1.72116 | ||||||||
\(359\) | −2.54804 | − | 4.41333i | −0.134480 | − | 0.232926i | 0.790919 | − | 0.611921i | \(-0.209603\pi\) |
−0.925399 | + | 0.378995i | \(0.876270\pi\) | |||||||
\(360\) | 1.66619 | − | 2.88593i | 0.0878160 | − | 0.152102i | ||||
\(361\) | 6.64767 | − | 11.5141i | 0.349877 | − | 0.606005i | ||||
\(362\) | 11.5888 | + | 20.0724i | 0.609093 | + | 1.05498i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 22.9892 | + | 54.9704i | 1.20496 | + | 2.88123i | ||||
\(365\) | −7.66678 | −0.401298 | ||||||||
\(366\) | −11.7769 | − | 20.3982i | −0.615588 | − | 1.06623i | ||||
\(367\) | 7.83395 | − | 13.5688i | 0.408929 | − | 0.708286i | −0.585841 | − | 0.810426i | \(-0.699236\pi\) |
0.994770 | + | 0.102140i | \(0.0325691\pi\) | |||||||
\(368\) | 1.68303 | − | 2.91509i | 0.0877338 | − | 0.151959i | ||||
\(369\) | −2.92562 | − | 5.06733i | −0.152302 | − | 0.263795i | ||||
\(370\) | −16.2811 | −0.846415 | ||||||||
\(371\) | −1.75133 | − | 4.18768i | −0.0909246 | − | 0.217414i | ||||
\(372\) | −31.8281 | −1.65021 | ||||||||
\(373\) | 11.0271 | + | 19.0995i | 0.570962 | + | 0.988936i | 0.996467 | + | 0.0839797i | \(0.0267631\pi\) |
−0.425505 | + | 0.904956i | \(0.639904\pi\) | |||||||
\(374\) | 2.97747 | − | 5.15713i | 0.153961 | − | 0.266669i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −2.03289 | − | 3.52107i | −0.104838 | − | 0.181585i | ||||
\(377\) | 28.5312 | 1.46943 | ||||||||
\(378\) | 6.11522 | + | 0.783901i | 0.314533 | + | 0.0403195i | ||||
\(379\) | 7.40055 | 0.380141 | 0.190070 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190070 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(380\) | −4.09625 | − | 7.09491i | −0.210133 | − | 0.363961i | ||||
\(381\) | 3.48234 | − | 6.03158i | 0.178406 | − | 0.309007i | ||||
\(382\) | −14.5441 | + | 25.1911i | −0.744141 | + | 1.28889i | ||||
\(383\) | 8.40005 | + | 14.5493i | 0.429223 | + | 0.743435i | 0.996804 | − | 0.0798816i | \(-0.0254542\pi\) |
−0.567582 | + | 0.823317i | \(0.692121\pi\) | |||||||
\(384\) | −19.8442 | −1.01267 | ||||||||
\(385\) | 1.60347 | − | 2.10449i | 0.0817205 | − | 0.107255i | ||||
\(386\) | 4.00491 | 0.203845 | ||||||||
\(387\) | 0.288530 | + | 0.499748i | 0.0146668 | + | 0.0254036i | ||||
\(388\) | 7.60133 | − | 13.1659i | 0.385899 | − | 0.668397i | ||||
\(389\) | 8.98127 | − | 15.5560i | 0.455369 | − | 0.788722i | −0.543341 | − | 0.839512i | \(-0.682841\pi\) |
0.998709 | + | 0.0507906i | \(0.0161741\pi\) | |||||||
\(390\) | −7.64982 | − | 13.2499i | −0.387363 | − | 0.670933i | ||||
\(391\) | 9.50310 | 0.480593 | ||||||||
\(392\) | −6.19076 | − | 22.4902i | −0.312680 | − | 1.13593i | ||||
\(393\) | −15.6096 | −0.787402 | ||||||||
\(394\) | −0.0687725 | − | 0.119117i | −0.00346471 | − | 0.00600105i | ||||
\(395\) | 0.372163 | − | 0.644604i | 0.0187255 | − | 0.0324336i | ||||
\(396\) | −1.71503 | + | 2.97052i | −0.0861834 | + | 0.149274i | ||||
\(397\) | 0.221618 | + | 0.383854i | 0.0111227 | + | 0.0192651i | 0.871533 | − | 0.490337i | \(-0.163126\pi\) |
−0.860410 | + | 0.509602i | \(0.829793\pi\) | |||||||
\(398\) | 49.8248 | 2.49749 | ||||||||
\(399\) | 3.82980 | − | 5.02646i | 0.191730 | − | 0.251638i | ||||
\(400\) | 0.905171 | 0.0452585 | ||||||||
\(401\) | −14.8143 | − | 25.6592i | −0.739793 | − | 1.28136i | −0.952588 | − | 0.304262i | \(-0.901590\pi\) |
0.212795 | − | 0.977097i | \(-0.431743\pi\) | |||||||
\(402\) | 14.1023 | − | 24.4259i | 0.703359 | − | 1.21825i | ||||
\(403\) | −30.4620 | + | 52.7617i | −1.51742 | + | 2.62825i | ||||
\(404\) | −18.0804 | − | 31.3162i | −0.899535 | − | 1.55804i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −26.5738 | − | 3.40646i | −1.31884 | − | 0.169060i | ||||
\(407\) | 6.98686 | 0.346326 | ||||||||
\(408\) | 4.25795 | + | 7.37498i | 0.210800 | + | 0.365116i | ||||
\(409\) | −4.49593 | + | 7.78718i | −0.222310 | + | 0.385051i | −0.955509 | − | 0.294962i | \(-0.904693\pi\) |
0.733199 | + | 0.680014i | \(0.238026\pi\) | |||||||
\(410\) | 6.81743 | − | 11.8081i | 0.336689 | − | 0.583162i | ||||
\(411\) | −1.11869 | − | 1.93762i | −0.0551807 | − | 0.0955757i | ||||
\(412\) | 20.3431 | 1.00223 | ||||||||
\(413\) | 12.0144 | + | 28.7282i | 0.591192 | + | 1.41362i | ||||
\(414\) | −8.66547 | −0.425885 | ||||||||
\(415\) | −6.45304 | − | 11.1770i | −0.316767 | − | 0.548657i | ||||
\(416\) | −14.9549 | + | 25.9027i | −0.733226 | + | 1.26998i | ||||
\(417\) | 6.18604 | − | 10.7145i | 0.302932 | − | 0.524693i | ||||
\(418\) | 2.78283 | + | 4.82001i | 0.136113 | + | 0.235754i | ||||
\(419\) | 16.4514 | 0.803704 | 0.401852 | − | 0.915705i | \(-0.368367\pi\) | ||||
0.401852 | + | 0.915705i | \(0.368367\pi\) | |||||||
\(420\) | 3.50142 | + | 8.37240i | 0.170852 | + | 0.408531i | ||||
\(421\) | −28.4904 | −1.38854 | −0.694268 | − | 0.719717i | \(-0.744272\pi\) | ||||
−0.694268 | + | 0.719717i | \(0.744272\pi\) | |||||||
\(422\) | −18.8334 | − | 32.6204i | −0.916797 | − | 1.58794i | ||||
\(423\) | −0.610040 | + | 1.05662i | −0.0296612 | + | 0.0513746i | ||||
\(424\) | −2.85858 | + | 4.95121i | −0.138825 | + | 0.240452i | ||||
\(425\) | 1.27775 | + | 2.21312i | 0.0619799 | + | 0.107352i | ||||
\(426\) | 2.62420 | 0.127143 | ||||||||
\(427\) | 26.5258 | + | 3.40030i | 1.28367 | + | 0.164552i | ||||
\(428\) | 57.5723 | 2.78286 | ||||||||
\(429\) | 3.28283 | + | 5.68603i | 0.158497 | + | 0.274524i | ||||
\(430\) | −0.672346 | + | 1.16454i | −0.0324234 | + | 0.0561589i | ||||
\(431\) | −13.8344 | + | 23.9619i | −0.666379 | + | 1.15420i | 0.312531 | + | 0.949908i | \(0.398823\pi\) |
−0.978910 | + | 0.204294i | \(0.934510\pi\) | |||||||
\(432\) | −0.452585 | − | 0.783901i | −0.0217750 | − | 0.0377154i | ||||
\(433\) | −31.9507 | −1.53545 | −0.767727 | − | 0.640777i | \(-0.778612\pi\) | ||||
−0.767727 | + | 0.640777i | \(0.778612\pi\) | |||||||
\(434\) | 34.6715 | − | 45.5049i | 1.66428 | − | 2.18430i | ||||
\(435\) | 4.34552 | 0.208352 | ||||||||
\(436\) | 28.4160 | + | 49.2180i | 1.36088 | + | 2.35711i | ||||
\(437\) | −4.44094 | + | 7.69194i | −0.212439 | + | 0.367955i | ||||
\(438\) | −8.93275 | + | 15.4720i | −0.426823 | + | 0.739280i | ||||
\(439\) | −17.0448 | − | 29.5224i | −0.813503 | − | 1.40903i | −0.910398 | − | 0.413733i | \(-0.864225\pi\) |
0.0968954 | − | 0.995295i | \(-0.469109\pi\) | |||||||
\(440\) | −3.33238 | −0.158865 | ||||||||
\(441\) | −4.91591 | + | 4.98335i | −0.234091 | + | 0.237303i | ||||
\(442\) | 39.0982 | 1.85971 | ||||||||
\(443\) | 20.5709 | + | 35.6298i | 0.977353 | + | 1.69283i | 0.671941 | + | 0.740605i | \(0.265461\pi\) |
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(444\) | −11.9827 | + | 20.7546i | −0.568672 | + | 0.984968i | ||||
\(445\) | −8.03826 | + | 13.9227i | −0.381050 | + | 0.659998i | ||||
\(446\) | 10.5658 | + | 18.3004i | 0.500303 | + | 0.866550i | ||||
\(447\) | 3.39043 | 0.160362 | ||||||||
\(448\) | 19.9244 | − | 26.1499i | 0.941339 | − | 1.23547i | ||||
\(449\) | −32.0369 | −1.51191 | −0.755957 | − | 0.654621i | \(-0.772828\pi\) | ||||
−0.755957 | + | 0.654621i | \(0.772828\pi\) | |||||||
\(450\) | −1.16512 | − | 2.01805i | −0.0549245 | − | 0.0951320i | ||||
\(451\) | −2.92562 | + | 5.06733i | −0.137762 | + | 0.238611i | ||||
\(452\) | −29.6657 | + | 51.3825i | −1.39536 | + | 2.41683i | ||||
\(453\) | 0.460315 | + | 0.797288i | 0.0216275 | + | 0.0374599i | ||||
\(454\) | −31.0327 | −1.45644 | ||||||||
\(455\) | 17.2301 | + | 2.20871i | 0.807761 | + | 0.103546i | ||||
\(456\) | −7.95921 | −0.372724 | ||||||||
\(457\) | 10.7819 | + | 18.6748i | 0.504357 | + | 0.873571i | 0.999987 | + | 0.00503788i | \(0.00160361\pi\) |
−0.495631 | + | 0.868533i | \(0.665063\pi\) | |||||||
\(458\) | −20.9062 | + | 36.2106i | −0.976882 | + | 1.69201i | ||||
\(459\) | 1.27775 | − | 2.21312i | 0.0596402 | − | 0.103300i | ||||
\(460\) | −6.37766 | − | 11.0464i | −0.297360 | − | 0.515043i | ||||
\(461\) | −23.9259 | −1.11434 | −0.557171 | − | 0.830398i | \(-0.688113\pi\) | ||||
−0.557171 | + | 0.830398i | \(0.688113\pi\) | |||||||
\(462\) | −2.37873 | − | 5.68788i | −0.110669 | − | 0.264624i | ||||
\(463\) | −15.7595 | −0.732407 | −0.366203 | − | 0.930535i | \(-0.619343\pi\) | ||||
−0.366203 | + | 0.930535i | \(0.619343\pi\) | |||||||
\(464\) | 1.96672 | + | 3.40646i | 0.0913027 | + | 0.158141i | ||||
\(465\) | −4.63958 | + | 8.03599i | −0.215156 | + | 0.372660i | ||||
\(466\) | −10.0910 | + | 17.4782i | −0.467458 | + | 0.809661i | ||||
\(467\) | −0.209846 | − | 0.363463i | −0.00971050 | − | 0.0168191i | 0.861129 | − | 0.508386i | \(-0.169758\pi\) |
−0.870840 | + | 0.491567i | \(0.836424\pi\) | |||||||
\(468\) | −22.5206 | −1.04102 | ||||||||
\(469\) | 12.3555 | + | 29.5438i | 0.570525 | + | 1.36421i | ||||
\(470\) | −2.84309 | −0.131142 | ||||||||
\(471\) | −9.81237 | − | 16.9955i | −0.452130 | − | 0.783113i | ||||
\(472\) | 19.6103 | − | 33.9661i | 0.902639 | − | 1.56342i | ||||
\(473\) | 0.288530 | − | 0.499748i | 0.0132666 | − | 0.0229784i | ||||
\(474\) | −0.867231 | − | 1.50209i | −0.0398332 | − | 0.0689932i | ||||
\(475\) | −2.38844 | −0.109589 | ||||||||
\(476\) | −23.0031 | − | 2.94873i | −1.05435 | − | 0.135155i | ||||
\(477\) | 1.71564 | 0.0785536 | ||||||||
\(478\) | 6.87171 | + | 11.9022i | 0.314305 | + | 0.544392i | ||||
\(479\) | −15.9645 | + | 27.6514i | −0.729439 | + | 1.26342i | 0.227682 | + | 0.973736i | \(0.426885\pi\) |
−0.957121 | + | 0.289689i | \(0.906448\pi\) | |||||||
\(480\) | −2.27775 | + | 3.94518i | −0.103965 | + | 0.180072i | ||||
\(481\) | 22.9367 | + | 39.7275i | 1.04582 | + | 1.81142i | ||||
\(482\) | 59.9907 | 2.73250 | ||||||||
\(483\) | 5.96282 | − | 7.82595i | 0.271318 | − | 0.356093i | ||||
\(484\) | 3.43006 | 0.155912 | ||||||||
\(485\) | −2.21610 | − | 3.83839i | −0.100628 | − | 0.174292i | ||||
\(486\) | −1.16512 | + | 2.01805i | −0.0528511 | + | 0.0915408i | ||||
\(487\) | −4.50884 | + | 7.80954i | −0.204315 | + | 0.353884i | −0.949914 | − | 0.312511i | \(-0.898830\pi\) |
0.745599 | + | 0.666395i | \(0.232163\pi\) | |||||||
\(488\) | −16.8416 | − | 29.1705i | −0.762383 | − | 1.32049i | ||||
\(489\) | 10.1961 | 0.461082 | ||||||||
\(490\) | −15.7843 | − | 4.11435i | −0.713063 | − | 0.185867i | ||||
\(491\) | 26.8024 | 1.20957 | 0.604787 | − | 0.796388i | \(-0.293258\pi\) | ||||
0.604787 | + | 0.796388i | \(0.293258\pi\) | |||||||
\(492\) | −10.0351 | − | 17.3812i | −0.452415 | − | 0.783606i | ||||
\(493\) | −5.55248 | + | 9.61718i | −0.250071 | + | 0.433136i | ||||
\(494\) | −18.2712 | + | 31.6466i | −0.822058 | + | 1.42385i | ||||
\(495\) | 0.500000 | + | 0.866025i | 0.0224733 | + | 0.0389249i | ||||
\(496\) | −8.39923 | −0.377137 | ||||||||
\(497\) | −1.80574 | + | 2.36996i | −0.0809987 | + | 0.106307i | ||||
\(498\) | −30.0744 | −1.34767 | ||||||||
\(499\) | 6.74371 | + | 11.6805i | 0.301890 | + | 0.522889i | 0.976564 | − | 0.215227i | \(-0.0690491\pi\) |
−0.674674 | + | 0.738116i | \(0.735716\pi\) | |||||||
\(500\) | 1.71503 | − | 2.97052i | 0.0766984 | − | 0.132845i | ||||
\(501\) | −0.354065 | + | 0.613258i | −0.0158184 | + | 0.0273983i | ||||
\(502\) | 24.4463 | + | 42.3422i | 1.09109 | + | 1.88982i | ||||
\(503\) | 0.989318 | 0.0441115 | 0.0220557 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220557 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(504\) | 8.74510 | + | 1.12102i | 0.389538 | + | 0.0499343i | ||||
\(505\) | −10.5424 | −0.469129 | ||||||||
\(506\) | 4.33274 | + | 7.50452i | 0.192614 | + | 0.333617i | ||||
\(507\) | −15.0540 | + | 26.0743i | −0.668571 | + | 1.15800i | ||||
\(508\) | 11.9446 | − | 20.6887i | 0.529956 | − | 0.917911i | ||||
\(509\) | 6.82082 | + | 11.8140i | 0.302328 | + | 0.523647i | 0.976663 | − | 0.214779i | \(-0.0689030\pi\) |
−0.674335 | + | 0.738425i | \(0.735570\pi\) | |||||||
\(510\) | 5.95494 | 0.263689 | ||||||||
\(511\) | −7.82630 | − | 18.7138i | −0.346215 | − | 0.827849i | ||||
\(512\) | −10.1563 | −0.448847 | ||||||||
\(513\) | 1.19422 | + | 2.06845i | 0.0527262 | + | 0.0913244i | ||||
\(514\) | 16.0149 | − | 27.7386i | 0.706387 | − | 1.22350i | ||||
\(515\) | 2.96541 | − | 5.13625i | 0.130672 | − | 0.226330i | ||||
\(516\) | 0.989673 | + | 1.71416i | 0.0435679 | + | 0.0754618i | ||||
\(517\) | 1.22008 | 0.0536591 | ||||||||
\(518\) | −16.6199 | − | 39.7404i | −0.730235 | − | 1.74609i | ||||
\(519\) | 13.5334 | 0.594051 | ||||||||
\(520\) | −10.9397 | − | 18.9481i | −0.479736 | − | 0.830927i | ||||
\(521\) | −15.1607 | + | 26.2592i | −0.664204 | + | 1.15043i | 0.315297 | + | 0.948993i | \(0.397896\pi\) |
−0.979501 | + | 0.201441i | \(0.935437\pi\) | |||||||
\(522\) | 5.06307 | − | 8.76950i | 0.221605 | − | 0.383830i | ||||
\(523\) | 4.78322 | + | 8.28479i | 0.209156 | + | 0.362268i | 0.951449 | − | 0.307807i | \(-0.0995951\pi\) |
−0.742293 | + | 0.670075i | \(0.766262\pi\) | |||||||
\(524\) | −53.5419 | −2.33899 | ||||||||
\(525\) | 2.62428 | + | 0.336402i | 0.114533 | + | 0.0146818i | ||||
\(526\) | −61.5765 | −2.68486 | ||||||||
\(527\) | −11.8564 | − | 20.5360i | −0.516475 | − | 0.894560i | ||||
\(528\) | −0.452585 | + | 0.783901i | −0.0196963 | + | 0.0341149i | ||||
\(529\) | 4.58567 | − | 7.94260i | 0.199377 | − | 0.345331i | ||||
\(530\) | 1.99893 | + | 3.46225i | 0.0868279 | + | 0.150390i | ||||
\(531\) | −11.7696 | −0.510755 | ||||||||
\(532\) | 13.1364 | − | 17.2410i | 0.569537 | − | 0.747493i | ||||
\(533\) | −38.4173 | −1.66404 | ||||||||
\(534\) | 18.7311 | + | 32.4433i | 0.810576 | + | 1.40396i | ||||
\(535\) | 8.39232 | − | 14.5359i | 0.362832 | − | 0.628443i | ||||
\(536\) | 20.1671 | − | 34.9304i | 0.871085 | − | 1.50876i | ||||
\(537\) | 6.98764 | + | 12.1029i | 0.301539 | + | 0.522281i | ||||
\(538\) | −50.1085 | −2.16033 | ||||||||
\(539\) | 6.77367 | + | 1.76563i | 0.291762 | + | 0.0760509i | ||||
\(540\) | −3.43006 | −0.147606 | ||||||||
\(541\) | −11.3900 | − | 19.7281i | −0.489695 | − | 0.848176i | 0.510235 | − | 0.860035i | \(-0.329558\pi\) |
−0.999930 | + | 0.0118589i | \(0.996225\pi\) | |||||||
\(542\) | −15.1424 | + | 26.2274i | −0.650421 | + | 1.12656i | ||||
\(543\) | 4.97320 | − | 8.61383i | 0.213420 | − | 0.369655i | ||||
\(544\) | −5.82078 | − | 10.0819i | −0.249564 | − | 0.432257i | ||||
\(545\) | 16.5688 | 0.709731 | ||||||||
\(546\) | 24.5325 | − | 32.1979i | 1.04990 | − | 1.37794i | ||||
\(547\) | −41.7796 | −1.78637 | −0.893184 | − | 0.449691i | \(-0.851534\pi\) | ||||
−0.893184 | + | 0.449691i | \(0.851534\pi\) | |||||||
\(548\) | −3.83715 | − | 6.64614i | −0.163915 | − | 0.283909i | ||||
\(549\) | −5.05392 | + | 8.75364i | −0.215696 | + | 0.373596i | ||||
\(550\) | −1.16512 | + | 2.01805i | −0.0496811 | + | 0.0860501i | ||||
\(551\) | −5.18952 | − | 8.98851i | −0.221081 | − | 0.382923i | ||||
\(552\) | −12.3921 | −0.527443 | ||||||||
\(553\) | 1.95332 | + | 0.250393i | 0.0830634 | + | 0.0106478i | ||||
\(554\) | −35.3812 | −1.50320 | ||||||||
\(555\) | 3.49343 | + | 6.05080i | 0.148288 | + | 0.256842i | ||||
\(556\) | 21.2184 | − | 36.7514i | 0.899863 | − | 1.55861i | ||||
\(557\) | 7.32912 | − | 12.6944i | 0.310545 | − | 0.537879i | −0.667936 | − | 0.744219i | \(-0.732822\pi\) |
0.978480 | + | 0.206340i | \(0.0661552\pi\) | |||||||
\(558\) | 10.8114 | + | 18.7259i | 0.457682 | + | 0.792729i | ||||
\(559\) | 3.78878 | 0.160248 | ||||||||
\(560\) | 0.924004 | + | 2.20942i | 0.0390463 | + | 0.0933652i | ||||
\(561\) | −2.55550 | −0.107893 | ||||||||
\(562\) | −11.0143 | − | 19.0774i | −0.464612 | − | 0.804731i | ||||
\(563\) | −5.25892 | + | 9.10871i | −0.221637 | + | 0.383886i | −0.955305 | − | 0.295621i | \(-0.904473\pi\) |
0.733668 | + | 0.679508i | \(0.237807\pi\) | |||||||
\(564\) | −2.09247 | + | 3.62427i | −0.0881090 | + | 0.152609i | ||||
\(565\) | 8.64875 | + | 14.9801i | 0.363855 | + | 0.630216i | ||||
\(566\) | −42.3644 | −1.78071 | ||||||||
\(567\) | −1.02081 | − | 2.44089i | −0.0428698 | − | 0.102508i | ||||
\(568\) | 3.75275 | 0.157462 | ||||||||
\(569\) | 2.50344 | + | 4.33609i | 0.104950 | + | 0.181779i | 0.913718 | − | 0.406350i | \(-0.133198\pi\) |
−0.808768 | + | 0.588128i | \(0.799865\pi\) | |||||||
\(570\) | −2.78283 | + | 4.82001i | −0.116560 | + | 0.201888i | ||||
\(571\) | 4.26835 | − | 7.39299i | 0.178625 | − | 0.309387i | −0.762785 | − | 0.646652i | \(-0.776169\pi\) |
0.941410 | + | 0.337265i | \(0.109502\pi\) | |||||||
\(572\) | 11.2603 | + | 19.5034i | 0.470817 | + | 0.815479i | ||||
\(573\) | 12.4829 | 0.521480 | ||||||||
\(574\) | 35.7817 | + | 4.58680i | 1.49350 | + | 0.191449i | ||||
\(575\) | −3.71869 | −0.155080 | ||||||||
\(576\) | 6.21289 | + | 10.7610i | 0.258870 | + | 0.448377i | ||||
\(577\) | −3.57975 | + | 6.20030i | −0.149027 | + | 0.258122i | −0.930868 | − | 0.365356i | \(-0.880947\pi\) |
0.781841 | + | 0.623478i | \(0.214281\pi\) | |||||||
\(578\) | 12.1982 | − | 21.1279i | 0.507378 | − | 0.878804i | ||||
\(579\) | −0.859332 | − | 1.48841i | −0.0357126 | − | 0.0618561i | ||||
\(580\) | 14.9054 | 0.618912 | ||||||||
\(581\) | 20.6945 | − | 27.1607i | 0.858554 | − | 1.12682i | ||||
\(582\) | −10.3281 | −0.428114 | ||||||||
\(583\) | −0.857818 | − | 1.48578i | −0.0355272 | − | 0.0615349i | ||||
\(584\) | −12.7743 | + | 22.1258i | −0.528606 | + | 0.915572i | ||||
\(585\) | −3.28283 | + | 5.68603i | −0.135728 | + | 0.235089i | ||||
\(586\) | −33.5498 | − | 58.1099i | −1.38593 | − | 2.40050i | ||||
\(587\) | 29.4112 | 1.21393 | 0.606964 | − | 0.794729i | \(-0.292387\pi\) | ||||
0.606964 | + | 0.794729i | \(0.292387\pi\) | |||||||
\(588\) | −16.8618 | + | 17.0932i | −0.695371 | + | 0.704911i | ||||
\(589\) | 22.1628 | 0.913201 | ||||||||
\(590\) | −13.7130 | − | 23.7516i | −0.564555 | − | 0.977838i | ||||
\(591\) | −0.0295129 | + | 0.0511179i | −0.00121400 | + | 0.00210271i | ||||
\(592\) | −3.16215 | + | 5.47700i | −0.129964 | + | 0.225104i | ||||
\(593\) | −0.772727 | − | 1.33840i | −0.0317321 | − | 0.0549616i | 0.849723 | − | 0.527229i | \(-0.176769\pi\) |
−0.881455 | + | 0.472267i | \(0.843436\pi\) | |||||||
\(594\) | 2.33025 | 0.0956112 | ||||||||
\(595\) | −4.09767 | + | 5.37802i | −0.167988 | + | 0.220477i | ||||
\(596\) | 11.6294 | 0.476358 | ||||||||
\(597\) | −10.6909 | − | 18.5171i | −0.437549 | − | 0.757856i | ||||
\(598\) | −28.4473 | + | 49.2722i | −1.16330 | + | 2.01489i | ||||
\(599\) | −5.26067 | + | 9.11175i | −0.214945 | + | 0.372296i | −0.953256 | − | 0.302165i | \(-0.902291\pi\) |
0.738310 | + | 0.674461i | \(0.235624\pi\) | |||||||
\(600\) | −1.66619 | − | 2.88593i | −0.0680220 | − | 0.117818i | ||||
\(601\) | −35.8037 | −1.46046 | −0.730232 | − | 0.683199i | \(-0.760588\pi\) | ||||
−0.730232 | + | 0.683199i | \(0.760588\pi\) | |||||||
\(602\) | −3.52884 | − | 0.452357i | −0.143825 | − | 0.0184367i | ||||
\(603\) | −12.1037 | −0.492900 | ||||||||
\(604\) | 1.57890 | + | 2.73474i | 0.0642447 | + | 0.111275i | ||||
\(605\) | 0.500000 | − | 0.866025i | 0.0203279 | − | 0.0352089i | ||||
\(606\) | −12.2832 | + | 21.2750i | −0.498969 | + | 0.864240i | ||||
\(607\) | −0.282003 | − | 0.488444i | −0.0114462 | − | 0.0198253i | 0.860246 | − | 0.509880i | \(-0.170310\pi\) |
−0.871692 | + | 0.490055i | \(0.836977\pi\) | |||||||
\(608\) | 10.8805 | 0.441264 | ||||||||
\(609\) | 4.43593 | + | 10.6069i | 0.179753 | + | 0.429815i | ||||
\(610\) | −23.5538 | −0.953664 | ||||||||
\(611\) | 4.00532 | + | 6.93742i | 0.162038 | + | 0.280658i | ||||
\(612\) | 4.38275 | − | 7.59114i | 0.177162 | − | 0.306854i | ||||
\(613\) | 6.82819 | − | 11.8268i | 0.275788 | − | 0.477679i | −0.694546 | − | 0.719449i | \(-0.744395\pi\) |
0.970334 | + | 0.241770i | \(0.0777279\pi\) | |||||||
\(614\) | 30.0062 | + | 51.9723i | 1.21095 | + | 2.09743i | ||||
\(615\) | −5.85125 | −0.235945 | ||||||||
\(616\) | −3.40172 | − | 8.13399i | −0.137059 | − | 0.327728i | ||||
\(617\) | −26.4948 | −1.06664 | −0.533320 | − | 0.845913i | \(-0.679056\pi\) | ||||
−0.533320 | + | 0.845913i | \(0.679056\pi\) | |||||||
\(618\) | −6.91015 | − | 11.9687i | −0.277967 | − | 0.481453i | ||||
\(619\) | −6.10828 | + | 10.5799i | −0.245513 | + | 0.425240i | −0.962276 | − | 0.272076i | \(-0.912290\pi\) |
0.716763 | + | 0.697317i | \(0.245623\pi\) | |||||||
\(620\) | −15.9140 | + | 27.5639i | −0.639123 | + | 1.10699i | ||||
\(621\) | 1.85935 | + | 3.22048i | 0.0746130 | + | 0.129233i | ||||
\(622\) | −16.2069 | −0.649836 | ||||||||
\(623\) | −42.1893 | − | 5.40818i | −1.69028 | − | 0.216674i | ||||
\(624\) | −5.94305 | −0.237912 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 18.5773 | − | 32.1768i | 0.742498 | − | 1.28604i | ||||
\(627\) | 1.19422 | − | 2.06845i | 0.0476926 | − | 0.0826061i | ||||
\(628\) | −33.6570 | − | 58.2956i | −1.34306 | − | 2.32625i | ||||
\(629\) | −17.8549 | −0.711921 | ||||||||
\(630\) | 3.73649 | − | 4.90398i | 0.148865 | − | 0.195379i | ||||
\(631\) | −15.4089 | −0.613417 | −0.306709 | − | 0.951803i | \(-0.599228\pi\) | ||||
−0.306709 | + | 0.951803i | \(0.599228\pi\) | |||||||
\(632\) | −1.24019 | − | 2.14807i | −0.0493321 | − | 0.0854456i | ||||
\(633\) | −8.08215 | + | 13.9987i | −0.321237 | + | 0.556398i | ||||
\(634\) | −7.12541 | + | 12.3416i | −0.282986 | + | 0.490147i | ||||
\(635\) | −3.48234 | − | 6.03158i | −0.138192 | − | 0.239356i | ||||
\(636\) | 5.88473 | 0.233345 | ||||||||
\(637\) | 12.1974 | + | 44.3116i | 0.483279 | + | 1.75569i | ||||
\(638\) | −10.1261 | −0.400898 | ||||||||
\(639\) | −0.563073 | − | 0.975271i | −0.0222748 | − | 0.0385811i | ||||
\(640\) | −9.92208 | + | 17.1855i | −0.392204 | + | 0.679318i | ||||
\(641\) | 6.95746 | − | 12.0507i | 0.274803 | − | 0.475973i | −0.695282 | − | 0.718737i | \(-0.744721\pi\) |
0.970085 | + | 0.242764i | \(0.0780539\pi\) | |||||||
\(642\) | −19.5562 | − | 33.8723i | −0.771822 | − | 1.33683i | ||||
\(643\) | −16.1658 | −0.637519 | −0.318759 | − | 0.947836i | \(-0.603266\pi\) | ||||
−0.318759 | + | 0.947836i | \(0.603266\pi\) | |||||||
\(644\) | 20.4528 | − | 26.8434i | 0.805953 | − | 1.05778i | ||||
\(645\) | 0.577059 | 0.0227217 | ||||||||
\(646\) | −7.11152 | − | 12.3175i | −0.279799 | − | 0.484626i | ||||
\(647\) | 14.8425 | − | 25.7080i | 0.583519 | − | 1.01068i | −0.411540 | − | 0.911392i | \(-0.635009\pi\) |
0.995058 | − | 0.0992922i | \(-0.0316579\pi\) | |||||||
\(648\) | −1.66619 | + | 2.88593i | −0.0654542 | + | 0.113370i | ||||
\(649\) | 5.88478 | + | 10.1927i | 0.230998 | + | 0.400100i | ||||
\(650\) | −15.2996 | −0.600101 | ||||||||
\(651\) | −24.3511 | − | 3.12153i | −0.954395 | − | 0.122343i | ||||
\(652\) | 34.9731 | 1.36965 | ||||||||
\(653\) | 0.155150 | + | 0.268728i | 0.00607149 | + | 0.0105161i | 0.869045 | − | 0.494733i | \(-0.164734\pi\) |
−0.862974 | + | 0.505249i | \(0.831401\pi\) | |||||||
\(654\) | 19.3048 | − | 33.4368i | 0.754876 | − | 1.30748i | ||||
\(655\) | −7.80481 | + | 13.5183i | −0.304959 | + | 0.528205i | ||||
\(656\) | −2.64819 | − | 4.58680i | −0.103394 | − | 0.179084i | ||||
\(657\) | 7.66678 | 0.299110 | ||||||||
\(658\) | −2.90224 | − | 6.93968i | −0.113141 | − | 0.270537i | ||||
\(659\) | 22.0773 | 0.860008 | 0.430004 | − | 0.902827i | \(-0.358512\pi\) | ||||
0.430004 | + | 0.902827i | \(0.358512\pi\) | |||||||
\(660\) | 1.71503 | + | 2.97052i | 0.0667574 | + | 0.115627i | ||||
\(661\) | −22.2299 | + | 38.5032i | −0.864641 | + | 1.49760i | 0.00276183 | + | 0.999996i | \(0.499121\pi\) |
−0.867403 | + | 0.497606i | \(0.834212\pi\) | |||||||
\(662\) | −2.58075 | + | 4.46999i | −0.100304 | + | 0.173731i | ||||
\(663\) | −8.38927 | − | 14.5306i | −0.325812 | − | 0.564323i | ||||
\(664\) | −43.0080 | −1.66904 | ||||||||
\(665\) | −2.43814 | − | 5.82993i | −0.0945469 | − | 0.226075i | ||||
\(666\) | 16.2811 | 0.630880 | ||||||||
\(667\) | −8.07983 | − | 13.9947i | −0.312852 | − | 0.541876i | ||||
\(668\) | −1.21446 | + | 2.10351i | −0.0469889 | + | 0.0813872i | ||||
\(669\) | 4.53417 | − | 7.85342i | 0.175301 | − | 0.303631i | ||||
\(670\) | −14.1023 | − | 24.4259i | −0.544819 | − | 0.943655i | ||||
\(671\) | 10.1078 | 0.390209 | ||||||||
\(672\) | −11.9549 | − | 1.53248i | −0.461170 | − | 0.0591167i | ||||
\(673\) | −5.27727 | −0.203424 | −0.101712 | − | 0.994814i | \(-0.532432\pi\) | ||||
−0.101712 | + | 0.994814i | \(0.532432\pi\) | |||||||
\(674\) | 15.1322 | + | 26.2097i | 0.582869 | + | 1.00956i | ||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −51.6360 | + | 89.4362i | −1.98600 | + | 3.43985i | ||||
\(677\) | −23.5956 | − | 40.8688i | −0.906853 | − | 1.57072i | −0.818410 | − | 0.574634i | \(-0.805144\pi\) |
−0.0884428 | − | 0.996081i | \(-0.528189\pi\) | |||||||
\(678\) | 40.3074 | 1.54800 | ||||||||
\(679\) | 7.10690 | − | 9.32750i | 0.272738 | − | 0.357957i | ||||
\(680\) | 8.51590 | 0.326570 | ||||||||
\(681\) | 6.65868 | + | 11.5332i | 0.255161 | + | 0.441952i | ||||
\(682\) | 10.8114 | − | 18.7259i | 0.413989 | − | 0.717050i | ||||
\(683\) | 8.49512 | − | 14.7140i | 0.325057 | − | 0.563015i | −0.656467 | − | 0.754355i | \(-0.727950\pi\) |
0.981524 | + | 0.191340i | \(0.0612833\pi\) | |||||||
\(684\) | 4.09625 | + | 7.09491i | 0.156624 | + | 0.271281i | ||||
\(685\) | −2.23737 | −0.0854855 | ||||||||
\(686\) | −6.07005 | − | 42.7278i | −0.231756 | − | 1.63135i | ||||
\(687\) | 17.9433 | 0.684580 | ||||||||
\(688\) | 0.261169 | + | 0.452357i | 0.00995696 | + | 0.0172460i | ||||
\(689\) | 5.63215 | − | 9.75517i | 0.214568 | − | 0.371642i | ||||
\(690\) | −4.33274 | + | 7.50452i | −0.164944 | + | 0.285692i | ||||
\(691\) | −5.81784 | − | 10.0768i | −0.221321 | − | 0.383340i | 0.733888 | − | 0.679270i | \(-0.237704\pi\) |
−0.955209 | + | 0.295931i | \(0.904370\pi\) | |||||||
\(692\) | 46.4204 | 1.76464 | ||||||||
\(693\) | −1.60347 | + | 2.10449i | −0.0609109 | + | 0.0799430i | ||||
\(694\) | −13.6620 | −0.518602 | ||||||||
\(695\) | −6.18604 | − | 10.7145i | −0.234650 | − | 0.406425i | ||||
\(696\) | 7.24047 | − | 12.5409i | 0.274449 | − | 0.475360i | ||||
\(697\) | 7.47642 | − | 12.9495i | 0.283190 | − | 0.490499i | ||||
\(698\) | −11.6061 | − | 20.1023i | −0.439297 | − | 0.760885i | ||||
\(699\) | 8.66091 | 0.327586 | ||||||||
\(700\) | 9.00142 | + | 1.15388i | 0.340222 | + | 0.0436125i | ||||
\(701\) | 6.31631 | 0.238564 | 0.119282 | − | 0.992860i | \(-0.461941\pi\) | ||||
0.119282 | + | 0.992860i | \(0.461941\pi\) | |||||||
\(702\) | 7.64982 | + | 13.2499i | 0.288724 | + | 0.500084i | ||||
\(703\) | 8.34386 | − | 14.4520i | 0.314695 | − | 0.545067i | ||||
\(704\) | 6.21289 | − | 10.7610i | 0.234157 | − | 0.405572i | ||||
\(705\) | 0.610040 | + | 1.05662i | 0.0229754 | + | 0.0397946i | ||||
\(706\) | 16.1091 | 0.606276 | ||||||||
\(707\) | −10.7617 | − | 25.7328i | −0.404735 | − | 0.967780i | ||||
\(708\) | −40.3702 | −1.51721 | ||||||||
\(709\) | −8.48268 | − | 14.6924i | −0.318574 | − | 0.551786i | 0.661617 | − | 0.749842i | \(-0.269870\pi\) |
−0.980191 | + | 0.198056i | \(0.936537\pi\) | |||||||
\(710\) | 1.31210 | − | 2.27262i | 0.0492422 | − | 0.0852901i | ||||
\(711\) | −0.372163 | + | 0.644604i | −0.0139572 | + | 0.0241746i | ||||
\(712\) | 26.7866 | + | 46.3957i | 1.00387 | + | 1.73875i | ||||
\(713\) | 34.5064 | 1.29227 | ||||||||
\(714\) | 6.07884 | + | 14.5354i | 0.227495 | + | 0.543973i | ||||
\(715\) | 6.56567 | 0.245542 | ||||||||
\(716\) | 23.9680 | + | 41.5138i | 0.895726 | + | 1.55144i | ||||
\(717\) | 2.94892 | − | 5.10768i | 0.110129 | − | 0.190750i | ||||
\(718\) | −5.93755 | + | 10.2841i | −0.221588 | + | 0.383801i | ||||
\(719\) | 4.76647 | + | 8.25577i | 0.177759 | + | 0.307888i | 0.941113 | − | 0.338093i | \(-0.109782\pi\) |
−0.763353 | + | 0.645981i | \(0.776448\pi\) | |||||||
\(720\) | −0.905171 | −0.0337337 | ||||||||
\(721\) | 15.5641 | + | 1.99514i | 0.579639 | + | 0.0743031i | ||||
\(722\) | −30.9814 | −1.15301 | ||||||||
\(723\) | −12.8722 | − | 22.2953i | −0.478721 | − | 0.829170i | ||||
\(724\) | 17.0583 | − | 29.5459i | 0.633968 | − | 1.09806i | ||||
\(725\) | 2.17276 | − | 3.76333i | 0.0806943 | − | 0.139767i | ||||
\(726\) | −1.16512 | − | 2.01805i | −0.0432418 | − | 0.0748970i | ||||
\(727\) | 45.7753 | 1.69771 | 0.848855 | − | 0.528625i | \(-0.177292\pi\) | ||||
0.848855 | + | 0.528625i | \(0.177292\pi\) | |||||||
\(728\) | 35.0829 | − | 46.0448i | 1.30026 | − | 1.70653i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.93275 | + | 15.4720i | 0.330616 | + | 0.572644i | ||||
\(731\) | −0.737336 | + | 1.27710i | −0.0272714 | + | 0.0472354i | ||||
\(732\) | −17.3352 | + | 30.0255i | −0.640728 | + | 1.10977i | ||||
\(733\) | −3.27485 | − | 5.67221i | −0.120959 | − | 0.209508i | 0.799187 | − | 0.601083i | \(-0.205264\pi\) |
−0.920146 | + | 0.391575i | \(0.871930\pi\) | |||||||
\(734\) | −36.5101 | −1.34761 | ||||||||
\(735\) | 1.85776 | + | 6.74898i | 0.0685244 | + | 0.248940i | ||||
\(736\) | 16.9405 | 0.624435 | ||||||||
\(737\) | 6.05184 | + | 10.4821i | 0.222923 | + | 0.386113i | ||||
\(738\) | −6.81743 | + | 11.8081i | −0.250953 | + | 0.434663i | ||||
\(739\) | 10.3270 | − | 17.8868i | 0.379884 | − | 0.657978i | −0.611161 | − | 0.791506i | \(-0.709297\pi\) |
0.991045 | + | 0.133528i | \(0.0426306\pi\) | |||||||
\(740\) | 11.9827 | + | 20.7546i | 0.440491 | + | 0.762953i | ||||
\(741\) | 15.6817 | 0.576083 | ||||||||
\(742\) | −6.41045 | + | 8.41345i | −0.235335 | + | 0.308868i | ||||
\(743\) | 39.7387 | 1.45787 | 0.728936 | − | 0.684582i | \(-0.240015\pi\) | ||||
0.728936 | + | 0.684582i | \(0.240015\pi\) | |||||||
\(744\) | 15.4609 | + | 26.7790i | 0.566823 | + | 0.981767i | ||||
\(745\) | 1.69522 | − | 2.93620i | 0.0621079 | − | 0.107574i | ||||
\(746\) | 25.6959 | − | 44.5066i | 0.940794 | − | 1.62950i | ||||
\(747\) | 6.45304 | + | 11.1770i | 0.236104 | + | 0.408945i | ||||
\(748\) | −8.76550 | −0.320498 | ||||||||
\(749\) | 44.0476 | + | 5.64640i | 1.60946 | + | 0.206315i | ||||
\(750\) | −2.33025 | −0.0850886 | ||||||||
\(751\) | −21.2623 | − | 36.8274i | −0.775873 | − | 1.34385i | −0.934302 | − | 0.356481i | \(-0.883976\pi\) |
0.158429 | − | 0.987370i | \(-0.449357\pi\) | |||||||
\(752\) | −0.552191 | + | 0.956422i | −0.0201363 | + | 0.0348771i | ||||
\(753\) | 10.4908 | − | 18.1707i | 0.382308 | − | 0.662176i | ||||
\(754\) | −33.2424 | − | 57.5776i | −1.21062 | − | 2.09685i | ||||
\(755\) | 0.920629 | 0.0335051 | ||||||||
\(756\) | −3.50142 | − | 8.37240i | −0.127345 | − | 0.304501i | ||||
\(757\) | −37.5157 | −1.36353 | −0.681767 | − | 0.731570i | \(-0.738788\pi\) | ||||
−0.681767 | + | 0.731570i | \(0.738788\pi\) | |||||||
\(758\) | −8.62256 | − | 14.9347i | −0.313185 | − | 0.542453i | ||||
\(759\) | 1.85935 | − | 3.22048i | 0.0674900 | − | 0.116896i | ||||
\(760\) | −3.97961 | + | 6.89288i | −0.144356 | + | 0.250031i | ||||
\(761\) | −22.4966 | − | 38.9653i | −0.815501 | − | 1.41249i | −0.908967 | − | 0.416867i | \(-0.863128\pi\) |
0.0934663 | − | 0.995622i | \(-0.470205\pi\) | |||||||
\(762\) | −16.2294 | −0.587930 | ||||||||
\(763\) | 16.9136 | + | 40.4428i | 0.612312 | + | 1.46413i | ||||
\(764\) | 42.8170 | 1.54906 | ||||||||
\(765\) | −1.27775 | − | 2.21312i | −0.0461971 | − | 0.0800157i | ||||
\(766\) | 19.5742 | − | 33.9035i | 0.707245 | − | 1.22498i | ||||
\(767\) | −38.6375 | + | 66.9221i | −1.39512 | + | 2.41642i | ||||
\(768\) | 10.6951 | + | 18.5245i | 0.385927 | + | 0.668445i | ||||
\(769\) | 0.330307 | 0.0119112 | 0.00595559 | − | 0.999982i | \(-0.498104\pi\) | ||||
0.00595559 | + | 0.999982i | \(0.498104\pi\) | |||||||
\(770\) | −6.11522 | − | 0.783901i | −0.220377 | − | 0.0282498i | ||||
\(771\) | −13.7452 | −0.495023 | ||||||||
\(772\) | −2.94756 | − | 5.10532i | −0.106085 | − | 0.183744i | ||||
\(773\) | −3.84785 | + | 6.66467i | −0.138398 | + | 0.239712i | −0.926890 | − | 0.375333i | \(-0.877528\pi\) |
0.788493 | + | 0.615044i | \(0.210862\pi\) | |||||||
\(774\) | 0.672346 | − | 1.16454i | 0.0241670 | − | 0.0418584i | ||||
\(775\) | 4.63958 | + | 8.03599i | 0.166659 | + | 0.288661i | ||||
\(776\) | −14.7698 | −0.530204 | ||||||||
\(777\) | −11.2032 | + | 14.7038i | −0.401914 | + | 0.527495i | ||||
\(778\) | −41.8572 | −1.50065 | ||||||||
\(779\) | 6.98769 | + | 12.1030i | 0.250360 | + | 0.433636i | ||||
\(780\) | −11.2603 | + | 19.5034i | −0.403183 | + | 0.698334i | ||||
\(781\) | −0.563073 | + | 0.975271i | −0.0201483 | + | 0.0348980i | ||||
\(782\) | −11.0723 | − | 19.1778i | −0.395944 | − | 0.685796i | ||||
\(783\) | −4.34552 | −0.155296 | ||||||||
\(784\) | −4.44974 | + | 4.51079i | −0.158919 | + | 0.161100i | ||||
\(785\) | −19.6247 | −0.700437 | ||||||||
\(786\) | 18.1872 | + | 31.5011i | 0.648714 | + | 1.12361i | ||||
\(787\) | 13.5195 | − | 23.4165i | 0.481919 | − | 0.834709i | −0.517865 | − | 0.855462i | \(-0.673273\pi\) |
0.999785 | + | 0.0207535i | \(0.00660652\pi\) | |||||||
\(788\) | −0.101231 | + | 0.175337i | −0.00360621 | + | 0.00624613i | ||||
\(789\) | 13.2124 | + | 22.8846i | 0.470375 | + | 0.814713i | ||||
\(790\) | −1.73446 | −0.0617094 | ||||||||
\(791\) | −27.7360 | + | 36.4024i | −0.986180 | + | 1.29432i | ||||
\(792\) | 3.33238 | 0.118411 | ||||||||
\(793\) | 33.1823 | + | 57.4735i | 1.17834 | + | 2.04094i | ||||
\(794\) | 0.516425 | − | 0.894474i | 0.0183272 | − | 0.0317437i | ||||
\(795\) | 0.857818 | − | 1.48578i | 0.0304237 | − | 0.0526954i | ||||
\(796\) | −36.6703 | − | 63.5148i | −1.29974 | − | 2.25122i | ||||
\(797\) | −13.7899 | −0.488465 | −0.244232 | − | 0.969717i | \(-0.578536\pi\) | ||||
−0.244232 | + | 0.969717i | \(0.578536\pi\) | |||||||
\(798\) | −14.6059 | − | 1.87230i | −0.517042 | − | 0.0662788i | ||||
\(799\) | −3.11791 | −0.110304 | ||||||||
\(800\) | 2.27775 | + | 3.94518i | 0.0805306 | + | 0.139483i | ||||
\(801\) | 8.03826 | − | 13.9227i | 0.284018 | − | 0.491934i | ||||
\(802\) | −34.5211 | + | 59.7923i | −1.21898 | + | 2.11134i | ||||
\(803\) | −3.83339 | − | 6.63963i | −0.135277 | − | 0.234307i | ||||
\(804\) | −41.5163 | −1.46417 | ||||||||
\(805\) | −3.79606 | − | 9.07693i | −0.133794 | − | 0.319920i | ||||
\(806\) | 141.968 | 5.00060 | ||||||||
\(807\) | 10.7518 | + | 18.6226i | 0.378480 | + | 0.655546i | ||||
\(808\) | −17.5656 | + | 30.4245i | −0.617955 | + | 1.07033i | ||||
\(809\) | −12.1582 | + | 21.0586i | −0.427460 | + | 0.740382i | −0.996647 | − | 0.0818264i | \(-0.973925\pi\) |
0.569187 | + | 0.822208i | \(0.307258\pi\) | |||||||
\(810\) | 1.16512 | + | 2.01805i | 0.0409383 | + | 0.0709072i | ||||
\(811\) | 25.5442 | 0.896978 | 0.448489 | − | 0.893788i | \(-0.351962\pi\) | ||||
0.448489 | + | 0.893788i | \(0.351962\pi\) | |||||||
\(812\) | 15.2155 | + | 36.3824i | 0.533959 | + | 1.27677i | ||||
\(813\) | 12.9964 | 0.455802 | ||||||||
\(814\) | −8.14056 | − | 14.0999i | −0.285326 | − | 0.494200i | ||||
\(815\) | 5.09803 | − | 8.83005i | 0.178576 | − | 0.309303i | ||||
\(816\) | 1.15658 | − | 2.00326i | 0.0404884 | − | 0.0701280i | ||||
\(817\) | −0.689137 | − | 1.19362i | −0.0241098 | − | 0.0417595i | ||||
\(818\) | 20.9533 | 0.732614 | ||||||||
\(819\) | −17.2301 | − | 2.20871i | −0.602070 | − | 0.0771784i | ||||
\(820\) | −20.0701 | −0.700878 | ||||||||
\(821\) | −16.2600 | − | 28.1632i | −0.567478 | − | 0.982901i | −0.996814 | − | 0.0797562i | \(-0.974586\pi\) |
0.429336 | − | 0.903145i | \(-0.358747\pi\) | |||||||
\(822\) | −2.60681 | + | 4.51513i | −0.0909231 | + | 0.157483i | ||||
\(823\) | 23.4197 | − | 40.5641i | 0.816359 | − | 1.41398i | −0.0919884 | − | 0.995760i | \(-0.529322\pi\) |
0.908348 | − | 0.418216i | \(-0.137344\pi\) | |||||||
\(824\) | −9.88190 | − | 17.1160i | −0.344252 | − | 0.596262i | ||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 43.9768 | − | 57.7177i | 1.53015 | − | 2.00826i | ||||
\(827\) | 36.2843 | 1.26173 | 0.630864 | − | 0.775893i | \(-0.282701\pi\) | ||||
0.630864 | + | 0.775893i | \(0.282701\pi\) | |||||||
\(828\) | 6.37766 | + | 11.0464i | 0.221639 | + | 0.383890i | ||||
\(829\) | 19.2797 | − | 33.3934i | 0.669612 | − | 1.15980i | −0.308401 | − | 0.951256i | \(-0.599794\pi\) |
0.978013 | − | 0.208545i | \(-0.0668727\pi\) | |||||||
\(830\) | −15.0372 | + | 26.0452i | −0.521948 | + | 0.904041i | ||||
\(831\) | 7.59172 | + | 13.1492i | 0.263354 | + | 0.456142i | ||||
\(832\) | 81.5835 | 2.82840 | ||||||||
\(833\) | −17.3101 | − | 4.51205i | −0.599759 | − | 0.156333i | ||||
\(834\) | −28.8300 | −0.998301 | ||||||||
\(835\) | 0.354065 | + | 0.613258i | 0.0122529 | + | 0.0212227i | ||||
\(836\) | 4.09625 | − | 7.09491i | 0.141672 | − | 0.245383i | ||||
\(837\) | 4.63958 | − | 8.03599i | 0.160367 | − | 0.277765i | ||||
\(838\) | −19.1679 | − | 33.1998i | −0.662145 | − | 1.14687i | ||||
\(839\) | −40.9551 | −1.41393 | −0.706964 | − | 0.707249i | \(-0.749936\pi\) | ||||
−0.706964 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(840\) | 5.34338 | − | 7.01297i | 0.184364 | − | 0.241970i | ||||
\(841\) | −10.1164 | −0.348843 | ||||||||
\(842\) | 33.1948 | + | 57.4951i | 1.14397 | + | 1.98141i | ||||
\(843\) | −4.72668 | + | 8.18685i | −0.162796 | + | 0.281970i | ||||
\(844\) | −27.7222 | + | 48.0163i | −0.954239 | + | 1.65279i | ||||
\(845\) | 15.0540 | + | 26.0743i | 0.517873 | + | 0.896982i | ||||
\(846\) | 2.84309 | 0.0977474 | ||||||||
\(847\) | 2.62428 | + | 0.336402i | 0.0901712 | + | 0.0115589i | ||||
\(848\) | 1.55294 | 0.0533283 | ||||||||
\(849\) | 9.09011 | + | 15.7445i | 0.311972 | + | 0.540351i | ||||
\(850\) | 2.97747 | − | 5.15713i | 0.102126 | − | 0.176888i | ||||
\(851\) | 12.9910 | − | 22.5011i | 0.445325 | − | 0.771326i | ||||
\(852\) | −1.93137 | − | 3.34524i | −0.0661677 | − | 0.114606i | ||||
\(853\) | 55.8708 | 1.91298 | 0.956489 | − | 0.291768i | \(-0.0942436\pi\) | ||||
0.956489 | + | 0.291768i | \(0.0942436\pi\) | |||||||
\(854\) | −24.0438 | − | 57.4922i | −0.822763 | − | 1.96734i | ||||
\(855\) | 2.38844 | 0.0816831 | ||||||||
\(856\) | −27.9665 | − | 48.4393i | −0.955874 | − | 1.65562i | ||||
\(857\) | −3.04891 | + | 5.28087i | −0.104149 | + | 0.180391i | −0.913390 | − | 0.407085i | \(-0.866545\pi\) |
0.809241 | + | 0.587476i | \(0.199878\pi\) | |||||||
\(858\) | 7.64982 | − | 13.2499i | 0.261160 | − | 0.452343i | ||||
\(859\) | −13.9519 | − | 24.1653i | −0.476031 | − | 0.824510i | 0.523592 | − | 0.851969i | \(-0.324592\pi\) |
−0.999623 | + | 0.0274593i | \(0.991258\pi\) | |||||||
\(860\) | 1.97935 | 0.0674951 | ||||||||
\(861\) | −5.97299 | − | 14.2823i | −0.203559 | − | 0.486738i | ||||
\(862\) | 64.4751 | 2.19603 | ||||||||
\(863\) | 15.2615 | + | 26.4337i | 0.519507 | + | 0.899813i | 0.999743 | + | 0.0226736i | \(0.00721785\pi\) |
−0.480236 | + | 0.877140i | \(0.659449\pi\) | |||||||
\(864\) | 2.27775 | − | 3.94518i | 0.0774906 | − | 0.134218i | ||||
\(865\) | 6.76671 | − | 11.7203i | 0.230075 | − | 0.398502i | ||||
\(866\) | 37.2266 | + | 64.4783i | 1.26501 | + | 2.19106i | ||||
\(867\) | −10.4694 | −0.355561 | ||||||||
\(868\) | −83.5257 | − | 10.7070i | −2.83505 | − | 0.363420i | ||||
\(869\) | 0.744325 | 0.0252495 | ||||||||
\(870\) | −5.06307 | − | 8.76950i | −0.171654 | − | 0.297314i | ||||
\(871\) | −39.7344 | + | 68.8220i | −1.34635 | + | 2.33194i | ||||
\(872\) | 27.6069 | − | 47.8165i | 0.934887 | − | 1.61927i | ||||
\(873\) | 2.21610 | + | 3.83839i | 0.0750035 | + | 0.129910i | ||||
\(874\) | 20.6970 | 0.700086 | ||||||||
\(875\) | 1.60347 | − | 2.10449i | 0.0542072 | − | 0.0711447i | ||||
\(876\) | 26.2975 | 0.888510 | ||||||||
\(877\) | 18.0631 | + | 31.2862i | 0.609947 | + | 1.05646i | 0.991249 | + | 0.132008i | \(0.0421426\pi\) |
−0.381302 | + | 0.924451i | \(0.624524\pi\) | |||||||
\(878\) | −39.7186 | + | 68.7945i | −1.34044 | + | 2.32170i | ||||
\(879\) | −14.3975 | + | 24.9372i | −0.485616 | + | 0.841112i | ||||
\(880\) | 0.452585 | + | 0.783901i | 0.0152567 | + | 0.0264253i | ||||
\(881\) | −42.0321 | −1.41610 | −0.708048 | − | 0.706164i | \(-0.750424\pi\) | ||||
−0.708048 | + | 0.706164i | \(0.750424\pi\) | |||||||
\(882\) | 15.7843 | + | 4.11435i | 0.531486 | + | 0.138537i | ||||
\(883\) | −37.1106 | −1.24887 | −0.624436 | − | 0.781076i | \(-0.714671\pi\) | ||||
−0.624436 | + | 0.781076i | \(0.714671\pi\) | |||||||
\(884\) | −28.7757 | − | 49.8409i | −0.967830 | − | 1.67633i | ||||
\(885\) | −5.88478 | + | 10.1927i | −0.197815 | + | 0.342625i | ||||
\(886\) | 47.9353 | − | 83.0264i | 1.61042 | − | 2.78933i | ||||
\(887\) | −13.9045 | − | 24.0834i | −0.466869 | − | 0.808641i | 0.532415 | − | 0.846484i | \(-0.321285\pi\) |
−0.999284 | + | 0.0378427i | \(0.987951\pi\) | |||||||
\(888\) | 23.2829 | 0.781323 | ||||||||
\(889\) | 11.1677 | − | 14.6571i | 0.374551 | − | 0.491583i | ||||
\(890\) | 37.4623 | 1.25574 | ||||||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | 15.5525 | − | 26.9377i | 0.520735 | − | 0.901940i | ||||
\(893\) | 1.45705 | − | 2.52368i | 0.0487582 | − | 0.0844517i | ||||
\(894\) | −3.95027 | − | 6.84208i | −0.132117 | − | 0.228833i | ||||
\(895\) | 13.9753 | 0.467142 | ||||||||
\(896\) | −52.0766 | − | 6.67562i | −1.73976 | − | 0.223017i | ||||
\(897\) | 24.4157 | 0.815216 | ||||||||
\(898\) | 37.3269 | + | 64.6522i | 1.24562 | + | 2.15747i | ||||
\(899\) | −20.1614 | + | 34.9206i | −0.672421 | + | 1.16467i | ||||
\(900\) | −1.71503 | + | 2.97052i | −0.0571676 | + | 0.0990172i | ||||
\(901\) | 2.19215 | + | 3.79692i | 0.0730312 | + | 0.126494i | ||||
\(902\) | 13.6349 | 0.453991 | ||||||||
\(903\) | 0.589065 | + | 1.40854i | 0.0196029 | + | 0.0468733i | ||||
\(904\) | 57.6419 | 1.91714 | ||||||||
\(905\) | −4.97320 | − | 8.61383i | −0.165315 | − | 0.286333i | ||||
\(906\) | 1.07265 | − | 1.85788i | 0.0356363 | − | 0.0617239i | ||||
\(907\) | −7.49181 | + | 12.9762i | −0.248761 | + | 0.430867i | −0.963182 | − | 0.268849i | \(-0.913357\pi\) |
0.714421 | + | 0.699716i | \(0.246690\pi\) | |||||||
\(908\) | 22.8396 | + | 39.5594i | 0.757960 | + | 1.31283i | ||||
\(909\) | 10.5424 | 0.349668 | ||||||||
\(910\) | −15.6180 | − | 37.3448i | −0.517730 | − | 1.23797i | ||||
\(911\) | −24.1417 | −0.799851 | −0.399925 | − | 0.916548i | \(-0.630964\pi\) | ||||
−0.399925 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(912\) | 1.08097 | + | 1.87230i | 0.0357947 | + | 0.0619982i | ||||
\(913\) | 6.45304 | − | 11.1770i | 0.213565 | − | 0.369905i | ||||
\(914\) | 25.1245 | − | 43.5170i | 0.831046 | − | 1.43941i | ||||
\(915\) | 5.05392 | + | 8.75364i | 0.167077 | + | 0.289387i | ||||
\(916\) | 61.5466 | 2.03356 | ||||||||
\(917\) | −40.9640 | − | 5.25112i | −1.35275 | − | 0.173407i | ||||
\(918\) | −5.95494 | −0.196542 | ||||||||
\(919\) | 13.6668 | + | 23.6715i | 0.450825 | + | 0.780851i | 0.998437 | − | 0.0558807i | \(-0.0177967\pi\) |
−0.547613 | + | 0.836732i | \(0.684463\pi\) | |||||||
\(920\) | −6.19606 | + | 10.7319i | −0.204278 | + | 0.353820i | ||||
\(921\) | 12.8768 | − | 22.3033i | 0.424306 | − | 0.734920i | ||||
\(922\) | 27.8767 | + | 48.2838i | 0.918070 | + | 1.59014i | ||||
\(923\) | −7.39390 | −0.243373 | ||||||||
\(924\) | −5.50000 | + | 7.21852i | −0.180937 | + | 0.237472i | ||||
\(925\) | 6.98686 | 0.229727 | ||||||||
\(926\) | 18.3618 | + | 31.8036i | 0.603406 | + | 1.04513i | ||||
\(927\) | −2.96541 | + | 5.13625i | −0.0973970 | + | 0.168696i | ||||
\(928\) | −9.89800 | + | 17.1438i | −0.324918 | + | 0.562774i | ||||
\(929\) | 4.76244 | + | 8.24879i | 0.156251 | + | 0.270634i | 0.933514 | − | 0.358542i | \(-0.116726\pi\) |
−0.777263 | + | 0.629176i | \(0.783393\pi\) | |||||||
\(930\) | 21.6228 | 0.709038 | ||||||||
\(931\) | 11.7414 | − | 11.9025i | 0.384808 | − | 0.390087i | ||||
\(932\) | 29.7074 | 0.973099 | ||||||||
\(933\) | 3.47750 | + | 6.02320i | 0.113848 | + | 0.197191i | ||||
\(934\) | −0.488992 | + | 0.846959i | −0.0160003 | + | 0.0277134i | ||||
\(935\) | −1.27775 | + | 2.21312i | −0.0417868 | + | 0.0723769i | ||||
\(936\) | 10.9397 | + | 18.9481i | 0.357574 | + | 0.619336i | ||||
\(937\) | 9.95761 | 0.325301 | 0.162650 | − | 0.986684i | \(-0.447996\pi\) | ||||
0.162650 | + | 0.986684i | \(0.447996\pi\) | |||||||
\(938\) | 45.2253 | − | 59.3563i | 1.47666 | − | 1.93805i | ||||
\(939\) | −15.9445 | −0.520328 | ||||||||
\(940\) | 2.09247 | + | 3.62427i | 0.0682489 | + | 0.118211i | ||||
\(941\) | −10.6309 | + | 18.4132i | −0.346556 | + | 0.600253i | −0.985635 | − | 0.168888i | \(-0.945982\pi\) |
0.639079 | + | 0.769141i | \(0.279316\pi\) | |||||||
\(942\) | −22.8653 | + | 39.6038i | −0.744991 | + | 1.29036i | ||||
\(943\) | 10.8795 | + | 18.8438i | 0.354285 | + | 0.613640i | ||||
\(944\) | −10.6535 | −0.346741 | ||||||||
\(945\) | −2.62428 | − | 0.336402i | −0.0853678 | − | 0.0109432i | ||||
\(946\) | −1.34469 | −0.0437197 | ||||||||
\(947\) | 4.80819 | + | 8.32803i | 0.156245 | + | 0.270625i | 0.933512 | − | 0.358547i | \(-0.116728\pi\) |
−0.777267 | + | 0.629172i | \(0.783394\pi\) | |||||||
\(948\) | −1.27654 | + | 2.21103i | −0.0414600 | + | 0.0718109i | ||||
\(949\) | 25.1688 | − | 43.5936i | 0.817013 | − | 1.41511i | ||||
\(950\) | 2.78283 | + | 4.82001i | 0.0902870 | + | 0.156382i | ||||
\(951\) | 6.11558 | 0.198311 | ||||||||
\(952\) | 8.69308 | + | 20.7864i | 0.281744 | + | 0.673691i | ||||
\(953\) | −16.6598 | −0.539665 | −0.269833 | − | 0.962907i | \(-0.586968\pi\) | ||||
−0.269833 | + | 0.962907i | \(0.586968\pi\) | |||||||
\(954\) | −1.99893 | − | 3.46225i | −0.0647177 | − | 0.112094i | ||||
\(955\) | 6.24144 | − | 10.8105i | 0.201968 | − | 0.349819i | ||||
\(956\) | 10.1150 | − | 17.5196i | 0.327141 | − | 0.566625i | ||||
\(957\) | 2.17276 | + | 3.76333i | 0.0702354 | + | 0.121651i | ||||
\(958\) | 74.4027 | 2.40384 | ||||||||
\(959\) | −2.28392 | − | 5.46118i | −0.0737516 | − | 0.176351i | ||||
\(960\) | 12.4258 | 0.401040 | ||||||||
\(961\) | −27.5515 | − | 47.7205i | −0.888757 | − | 1.53937i | ||||
\(962\) | 53.4482 | − | 92.5750i | 1.72324 | − | 2.98474i | ||||
\(963\) | −8.39232 | + | 14.5359i | −0.270439 | + | 0.468414i | ||||
\(964\) | −44.1523 | − | 76.4740i | −1.42205 | − | 2.46306i | ||||
\(965\) | −1.71866 | −0.0553257 | ||||||||
\(966\) | −22.7406 | − | 2.91509i | −0.731667 | − | 0.0937914i | ||||
\(967\) | 8.39085 | 0.269831 | 0.134916 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134916 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(968\) | −1.66619 | − | 2.88593i | −0.0535534 | − | 0.0927573i | ||||
\(969\) | −3.05183 | + | 5.28592i | −0.0980389 | + | 0.169808i | ||||
\(970\) | −5.16405 | + | 8.94440i | −0.165808 | + | 0.287187i | ||||
\(971\) | −23.9270 | − | 41.4428i | −0.767855 | − | 1.32996i | −0.938724 | − | 0.344670i | \(-0.887991\pi\) |
0.170869 | − | 0.985294i | \(-0.445343\pi\) | |||||||
\(972\) | 3.43006 | 0.110019 | ||||||||
\(973\) | 19.8383 | − | 26.0369i | 0.635986 | − | 0.834705i | ||||
\(974\) | 21.0134 | 0.673314 | ||||||||
\(975\) | 3.28283 | + | 5.68603i | 0.105135 | + | 0.182099i | ||||
\(976\) | −4.57466 | + | 7.92354i | −0.146431 | + | 0.253626i | ||||
\(977\) | −13.7822 | + | 23.8714i | −0.440931 | + | 0.763715i | −0.997759 | − | 0.0669132i | \(-0.978685\pi\) |
0.556828 | + | 0.830628i | \(0.312018\pi\) | |||||||
\(978\) | −11.8797 | − | 20.5762i | −0.379870 | − | 0.657955i | ||||
\(979\) | −16.0765 | −0.513808 | ||||||||
\(980\) | 6.37221 | + | 23.1494i | 0.203553 | + | 0.739480i | ||||
\(981\) | −16.5688 | −0.529002 | ||||||||
\(982\) | −31.2281 | − | 54.0886i | −0.996528 | − | 1.72604i | ||||
\(983\) | −7.32652 | + | 12.6899i | −0.233680 | + | 0.404745i | −0.958888 | − | 0.283784i | \(-0.908410\pi\) |
0.725209 | + | 0.688529i | \(0.241743\pi\) | |||||||
\(984\) | −9.74930 | + | 16.8863i | −0.310796 | + | 0.538315i | ||||
\(985\) | 0.0295129 | + | 0.0511179i | 0.000940360 | + | 0.00162875i | ||||
\(986\) | 25.8773 | 0.824102 | ||||||||
\(987\) | −1.95636 | + | 2.56765i | −0.0622718 | + | 0.0817291i | ||||
\(988\) | 53.7892 | 1.71126 | ||||||||
\(989\) | −1.07295 | − | 1.85841i | −0.0341179 | − | 0.0590940i | ||||
\(990\) | 1.16512 | − | 2.01805i | 0.0370301 | − | 0.0641380i | ||||
\(991\) | −23.5251 | + | 40.7467i | −0.747301 | + | 1.29436i | 0.201811 | + | 0.979424i | \(0.435317\pi\) |
−0.949112 | + | 0.314939i | \(0.898016\pi\) | |||||||
\(992\) | −21.1356 | − | 36.6079i | −0.671056 | − | 1.16230i | ||||
\(993\) | 2.21500 | 0.0702909 | ||||||||
\(994\) | 6.88663 | + | 0.882787i | 0.218431 | + | 0.0280003i | ||||
\(995\) | −21.3818 | −0.677847 | ||||||||
\(996\) | 22.1343 | + | 38.3377i | 0.701352 | + | 1.21478i | ||||
\(997\) | −4.93494 | + | 8.54756i | −0.156291 | + | 0.270704i | −0.933528 | − | 0.358504i | \(-0.883287\pi\) |
0.777237 | + | 0.629208i | \(0.216620\pi\) | |||||||
\(998\) | 15.7145 | − | 27.2184i | 0.497435 | − | 0.861582i | ||||
\(999\) | −3.49343 | − | 6.05080i | −0.110527 | − | 0.191439i |
(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 | 1155.2.q.h.991.1 | yes | 12 | |
7.2 | even | 3 | inner | 1155.2.q.h.331.1 | ✓ | 12 | |
7.3 | odd | 6 | 8085.2.a.bx.1.6 | 6 | |||
7.4 | even | 3 | 8085.2.a.bz.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.q.h.331.1 | ✓ | 12 | 7.2 | even | 3 | inner | |
1155.2.q.h.991.1 | yes | 12 | 1.1 | even | 1 | trivial | |
8085.2.a.bx.1.6 | 6 | 7.3 | odd | 6 | |||
8085.2.a.bz.1.6 | 6 | 7.4 | even | 3 |