Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,3,Mod(13,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.l (of order \(4\), 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: | \(3.05177896084\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 69.25 | ||
Character | \(\chi\) | \(=\) | 112.69 |
Dual form | 112.3.l.b.13.25 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89147 | − | 0.649887i | 0.945733 | − | 0.324944i | ||||
\(3\) | −1.75534 | − | 1.75534i | −0.585114 | − | 0.585114i | 0.351190 | − | 0.936304i | \(-0.385777\pi\) |
−0.936304 | + | 0.351190i | \(0.885777\pi\) | |||||||
\(4\) | 3.15529 | − | 2.45848i | 0.788823 | − | 0.614620i | ||||
\(5\) | 3.25602 | − | 3.25602i | 0.651203 | − | 0.651203i | −0.302079 | − | 0.953283i | \(-0.597681\pi\) |
0.953283 | + | 0.302079i | \(0.0976808\pi\) | |||||||
\(6\) | −4.46095 | − | 2.17940i | −0.743491 | − | 0.363233i | ||||
\(7\) | −4.90539 | + | 4.99371i | −0.700770 | + | 0.713388i | ||||
\(8\) | 4.37040 | − | 6.70072i | 0.546300 | − | 0.837590i | ||||
\(9\) | − | 2.83754i | − | 0.315283i | ||||||
\(10\) | 4.04260 | − | 8.27469i | 0.404260 | − | 0.827469i | ||||
\(11\) | −2.01178 | − | 2.01178i | −0.182889 | − | 0.182889i | 0.609725 | − | 0.792613i | \(-0.291280\pi\) |
−0.792613 | + | 0.609725i | \(0.791280\pi\) | |||||||
\(12\) | −9.85410 | − | 1.22314i | −0.821175 | − | 0.101929i | ||||
\(13\) | 6.07310 | + | 6.07310i | 0.467162 | + | 0.467162i | 0.900994 | − | 0.433832i | \(-0.142839\pi\) |
−0.433832 | + | 0.900994i | \(0.642839\pi\) | |||||||
\(14\) | −6.03303 | + | 12.6334i | −0.430930 | + | 0.902385i | ||||
\(15\) | −11.4309 | −0.762057 | ||||||||
\(16\) | 3.91175 | − | 15.5145i | 0.244484 | − | 0.969653i | ||||
\(17\) | − | 9.55815i | − | 0.562244i | −0.959672 | − | 0.281122i | \(-0.909293\pi\) | ||
0.959672 | − | 0.281122i | \(-0.0907065\pi\) | |||||||
\(18\) | −1.84408 | − | 5.36712i | −0.102449 | − | 0.298173i | ||||
\(19\) | 25.2086 | + | 25.2086i | 1.32677 | + | 1.32677i | 0.908173 | + | 0.418595i | \(0.137477\pi\) |
0.418595 | + | 0.908173i | \(0.362523\pi\) | |||||||
\(20\) | 2.26883 | − | 18.2785i | 0.113442 | − | 0.913927i | ||||
\(21\) | 17.3763 | − | 0.155043i | 0.827444 | − | 0.00738300i | ||||
\(22\) | −5.11264 | − | 2.49778i | −0.232393 | − | 0.113535i | ||||
\(23\) | 14.0394i | 0.610408i | 0.952287 | + | 0.305204i | \(0.0987247\pi\) | ||||
−0.952287 | + | 0.305204i | \(0.901275\pi\) | |||||||
\(24\) | −19.4336 | + | 4.09052i | −0.809733 | + | 0.170438i | ||||
\(25\) | 3.79671i | 0.151869i | ||||||||
\(26\) | 15.4339 | + | 7.54024i | 0.593612 | + | 0.290009i | ||||
\(27\) | −20.7789 | + | 20.7789i | −0.769591 | + | 0.769591i | ||||
\(28\) | −3.20099 | + | 27.8164i | −0.114321 | + | 0.993444i | ||||
\(29\) | −11.2161 | + | 11.2161i | −0.386764 | + | 0.386764i | −0.873531 | − | 0.486768i | \(-0.838176\pi\) |
0.486768 | + | 0.873531i | \(0.338176\pi\) | |||||||
\(30\) | −21.6211 | + | 7.42876i | −0.720702 | + | 0.247625i | ||||
\(31\) | 16.5180i | 0.532837i | 0.963857 | + | 0.266419i | \(0.0858404\pi\) | ||||
−0.963857 | + | 0.266419i | \(0.914160\pi\) | |||||||
\(32\) | −2.68371 | − | 31.8873i | −0.0838659 | − | 0.996477i | ||||
\(33\) | 7.06271i | 0.214022i | ||||||||
\(34\) | −6.21172 | − | 18.0789i | −0.182698 | − | 0.531733i | ||||
\(35\) | 0.287592 | + | 32.2316i | 0.00821691 | + | 0.920904i | ||||
\(36\) | −6.97605 | − | 8.95328i | −0.193779 | − | 0.248702i | ||||
\(37\) | 27.6654 | + | 27.6654i | 0.747714 | + | 0.747714i | 0.974049 | − | 0.226335i | \(-0.0726746\pi\) |
−0.226335 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(38\) | 64.0639 | + | 31.2985i | 1.68589 | + | 0.823644i | ||||
\(39\) | − | 21.3208i | − | 0.546686i | ||||||
\(40\) | −7.58757 | − | 36.0477i | −0.189689 | − | 0.901193i | ||||
\(41\) | 12.9650 | 0.316219 | 0.158110 | − | 0.987422i | \(-0.449460\pi\) | ||||
0.158110 | + | 0.987422i | \(0.449460\pi\) | |||||||
\(42\) | 32.7660 | − | 11.5859i | 0.780142 | − | 0.275855i | ||||
\(43\) | −50.9760 | − | 50.9760i | −1.18549 | − | 1.18549i | −0.978301 | − | 0.207187i | \(-0.933569\pi\) |
−0.207187 | − | 0.978301i | \(-0.566431\pi\) | |||||||
\(44\) | −11.2937 | − | 1.40183i | −0.256674 | − | 0.0318598i | ||||
\(45\) | −9.23909 | − | 9.23909i | −0.205313 | − | 0.205313i | ||||
\(46\) | 9.12403 | + | 26.5550i | 0.198348 | + | 0.577284i | ||||
\(47\) | − | 66.5020i | − | 1.41494i | −0.706745 | − | 0.707468i | \(-0.749837\pi\) | ||
0.706745 | − | 0.707468i | \(-0.250163\pi\) | |||||||
\(48\) | −34.0996 | + | 20.3667i | −0.710409 | + | 0.424307i | ||||
\(49\) | −0.874351 | − | 48.9922i | −0.0178439 | − | 0.999841i | ||||
\(50\) | 2.46744 | + | 7.18136i | 0.0493487 | + | 0.143627i | ||||
\(51\) | −16.7778 | + | 16.7778i | −0.328977 | + | 0.328977i | ||||
\(52\) | 34.0930 | + | 4.23181i | 0.655635 | + | 0.0813810i | ||||
\(53\) | 39.3660 | + | 39.3660i | 0.742755 | + | 0.742755i | 0.973107 | − | 0.230353i | \(-0.0739880\pi\) |
−0.230353 | + | 0.973107i | \(0.573988\pi\) | |||||||
\(54\) | −25.7987 | + | 52.8067i | −0.477754 | + | 0.977901i | ||||
\(55\) | −13.1008 | −0.238196 | ||||||||
\(56\) | 12.0230 | + | 54.6941i | 0.214696 | + | 0.976681i | ||||
\(57\) | − | 88.4994i | − | 1.55262i | ||||||
\(58\) | −13.9257 | + | 28.5042i | −0.240099 | + | 0.491452i | ||||
\(59\) | −30.4313 | + | 30.4313i | −0.515785 | + | 0.515785i | −0.916293 | − | 0.400508i | \(-0.868834\pi\) |
0.400508 | + | 0.916293i | \(0.368834\pi\) | |||||||
\(60\) | −36.0677 | + | 28.1025i | −0.601128 | + | 0.468375i | ||||
\(61\) | 11.9950 | + | 11.9950i | 0.196639 | + | 0.196639i | 0.798558 | − | 0.601918i | \(-0.205597\pi\) |
−0.601918 | + | 0.798558i | \(0.705597\pi\) | |||||||
\(62\) | 10.7348 | + | 31.2432i | 0.173142 | + | 0.503922i | ||||
\(63\) | 14.1699 | + | 13.9192i | 0.224919 | + | 0.220940i | ||||
\(64\) | −25.7993 | − | 58.5696i | −0.403114 | − | 0.915150i | ||||
\(65\) | 39.5482 | 0.608434 | ||||||||
\(66\) | 4.58997 | + | 13.3589i | 0.0695450 | + | 0.202407i | ||||
\(67\) | −19.5294 | + | 19.5294i | −0.291483 | + | 0.291483i | −0.837666 | − | 0.546183i | \(-0.816080\pi\) |
0.546183 | + | 0.837666i | \(0.316080\pi\) | |||||||
\(68\) | −23.4985 | − | 30.1587i | −0.345566 | − | 0.443511i | ||||
\(69\) | 24.6440 | − | 24.6440i | 0.357159 | − | 0.357159i | ||||
\(70\) | 21.4909 | + | 60.7782i | 0.307013 | + | 0.868260i | ||||
\(71\) | − | 69.7628i | − | 0.982574i | −0.870998 | − | 0.491287i | \(-0.836527\pi\) | ||
0.870998 | − | 0.491287i | \(-0.163473\pi\) | |||||||
\(72\) | −19.0136 | − | 12.4012i | −0.264078 | − | 0.172239i | ||||
\(73\) | −143.326 | −1.96337 | −0.981686 | − | 0.190507i | \(-0.938987\pi\) | ||||
−0.981686 | + | 0.190507i | \(0.938987\pi\) | |||||||
\(74\) | 70.3076 | + | 34.3488i | 0.950103 | + | 0.464173i | ||||
\(75\) | 6.66453 | − | 6.66453i | 0.0888604 | − | 0.0888604i | ||||
\(76\) | 141.515 | + | 17.5657i | 1.86204 | + | 0.231127i | ||||
\(77\) | 19.9148 | − | 0.177693i | 0.258633 | − | 0.00230770i | ||||
\(78\) | −13.8561 | − | 40.3275i | −0.177642 | − | 0.517019i | ||||
\(79\) | 66.7548 | 0.844998 | 0.422499 | − | 0.906363i | \(-0.361153\pi\) | ||||
0.422499 | + | 0.906363i | \(0.361153\pi\) | |||||||
\(80\) | −37.7786 | − | 63.2520i | −0.472233 | − | 0.790650i | ||||
\(81\) | 47.4105 | 0.585314 | ||||||||
\(82\) | 24.5229 | − | 8.42578i | 0.299059 | − | 0.102753i | ||||
\(83\) | −60.7490 | − | 60.7490i | −0.731916 | − | 0.731916i | 0.239083 | − | 0.970999i | \(-0.423153\pi\) |
−0.970999 | + | 0.239083i | \(0.923153\pi\) | |||||||
\(84\) | 54.4462 | − | 43.2085i | 0.648169 | − | 0.514387i | ||||
\(85\) | −31.1215 | − | 31.1215i | −0.366135 | − | 0.366135i | ||||
\(86\) | −129.548 | − | 63.2908i | −1.50637 | − | 0.735939i | ||||
\(87\) | 39.3763 | 0.452602 | ||||||||
\(88\) | −22.2726 | + | 4.68809i | −0.253098 | + | 0.0532737i | ||||
\(89\) | −78.9394 | −0.886960 | −0.443480 | − | 0.896284i | \(-0.646256\pi\) | ||||
−0.443480 | + | 0.896284i | \(0.646256\pi\) | |||||||
\(90\) | −23.4798 | − | 11.4711i | −0.260887 | − | 0.127456i | ||||
\(91\) | −60.1182 | + | 0.536415i | −0.660640 | + | 0.00589467i | ||||
\(92\) | 34.5156 | + | 44.2984i | 0.375169 | + | 0.481504i | ||||
\(93\) | 28.9947 | − | 28.9947i | 0.311771 | − | 0.311771i | ||||
\(94\) | −43.2188 | − | 125.786i | −0.459775 | − | 1.33815i | ||||
\(95\) | 164.159 | 1.72799 | ||||||||
\(96\) | −51.2623 | + | 60.6839i | −0.533982 | + | 0.632124i | ||||
\(97\) | 35.4878i | 0.365854i | 0.983126 | + | 0.182927i | \(0.0585572\pi\) | ||||
−0.983126 | + | 0.182927i | \(0.941443\pi\) | |||||||
\(98\) | −33.4932 | − | 92.0989i | −0.341768 | − | 0.939785i | ||||
\(99\) | −5.70850 | + | 5.70850i | −0.0576616 | + | 0.0576616i | ||||
\(100\) | 9.33414 | + | 11.9797i | 0.0933414 | + | 0.119797i | ||||
\(101\) | 135.312 | − | 135.312i | 1.33972 | − | 1.33972i | 0.443400 | − | 0.896324i | \(-0.353772\pi\) |
0.896324 | − | 0.443400i | \(-0.146228\pi\) | |||||||
\(102\) | −20.8310 | + | 42.6384i | −0.204225 | + | 0.418023i | ||||
\(103\) | −76.3602 | −0.741361 | −0.370680 | − | 0.928760i | \(-0.620875\pi\) | ||||
−0.370680 | + | 0.928760i | \(0.620875\pi\) | |||||||
\(104\) | 67.2360 | − | 14.1523i | 0.646500 | − | 0.136080i | ||||
\(105\) | 56.0727 | − | 57.0824i | 0.534026 | − | 0.543642i | ||||
\(106\) | 100.043 | + | 48.8760i | 0.943801 | + | 0.461094i | ||||
\(107\) | 61.8636 | + | 61.8636i | 0.578164 | + | 0.578164i | 0.934397 | − | 0.356233i | \(-0.115939\pi\) |
−0.356233 | + | 0.934397i | \(0.615939\pi\) | |||||||
\(108\) | −14.4790 | + | 116.648i | −0.134065 | + | 1.08008i | ||||
\(109\) | −95.4954 | + | 95.4954i | −0.876105 | + | 0.876105i | −0.993129 | − | 0.117024i | \(-0.962664\pi\) |
0.117024 | + | 0.993129i | \(0.462664\pi\) | |||||||
\(110\) | −24.7796 | + | 8.51401i | −0.225269 | + | 0.0774001i | ||||
\(111\) | − | 97.1246i | − | 0.874996i | ||||||
\(112\) | 58.2861 | + | 95.6385i | 0.520412 | + | 0.853916i | ||||
\(113\) | −141.353 | −1.25091 | −0.625456 | − | 0.780260i | \(-0.715087\pi\) | ||||
−0.625456 | + | 0.780260i | \(0.715087\pi\) | |||||||
\(114\) | −57.5147 | − | 167.394i | −0.504515 | − | 1.46837i | ||||
\(115\) | 45.7125 | + | 45.7125i | 0.397500 | + | 0.397500i | ||||
\(116\) | −7.81555 | + | 62.9649i | −0.0673754 | + | 0.542801i | ||||
\(117\) | 17.2327 | − | 17.2327i | 0.147288 | − | 0.147288i | ||||
\(118\) | −37.7829 | + | 77.3367i | −0.320194 | + | 0.655396i | ||||
\(119\) | 47.7306 | + | 46.8864i | 0.401098 | + | 0.394003i | ||||
\(120\) | −49.9573 | + | 76.5949i | −0.416311 | + | 0.638291i | ||||
\(121\) | − | 112.906i | − | 0.933103i | ||||||
\(122\) | 30.4835 | + | 14.8927i | 0.249865 | + | 0.122072i | ||||
\(123\) | −22.7580 | − | 22.7580i | −0.185024 | − | 0.185024i | ||||
\(124\) | 40.6091 | + | 52.1190i | 0.327493 | + | 0.420315i | ||||
\(125\) | 93.7626 | + | 93.7626i | 0.750101 | + | 0.750101i | ||||
\(126\) | 35.8478 | + | 17.1190i | 0.284506 | + | 0.135865i | ||||
\(127\) | −80.1444 | −0.631058 | −0.315529 | − | 0.948916i | \(-0.602182\pi\) | ||||
−0.315529 | + | 0.948916i | \(0.602182\pi\) | |||||||
\(128\) | −86.8621 | − | 94.0158i | −0.678610 | − | 0.734499i | ||||
\(129\) | 178.961i | 1.38729i | ||||||||
\(130\) | 74.8042 | − | 25.7019i | 0.575417 | − | 0.197707i | ||||
\(131\) | 90.0359 | + | 90.0359i | 0.687297 | + | 0.687297i | 0.961634 | − | 0.274337i | \(-0.0884582\pi\) |
−0.274337 | + | 0.961634i | \(0.588458\pi\) | |||||||
\(132\) | 17.3635 | + | 22.2849i | 0.131542 | + | 0.168825i | ||||
\(133\) | −249.542 | + | 2.22658i | −1.87626 | + | 0.0167412i | ||||
\(134\) | −24.2472 | + | 49.6310i | −0.180950 | + | 0.370381i | ||||
\(135\) | 135.313i | 1.00232i | ||||||||
\(136\) | −64.0465 | − | 41.7729i | −0.470930 | − | 0.307154i | ||||
\(137\) | 253.079i | 1.84729i | 0.383247 | + | 0.923646i | \(0.374806\pi\) | ||||
−0.383247 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(138\) | 30.5974 | − | 62.6290i | 0.221720 | − | 0.453833i | ||||
\(139\) | 49.2592 | − | 49.2592i | 0.354382 | − | 0.354382i | −0.507355 | − | 0.861737i | \(-0.669377\pi\) |
0.861737 | + | 0.507355i | \(0.169377\pi\) | |||||||
\(140\) | 80.1483 | + | 100.993i | 0.572488 | + | 0.721380i | ||||
\(141\) | −116.734 | + | 116.734i | −0.827899 | + | 0.827899i | ||||
\(142\) | −45.3379 | − | 131.954i | −0.319281 | − | 0.929253i | ||||
\(143\) | − | 24.4354i | − | 0.170877i | ||||||
\(144\) | −44.0229 | − | 11.0997i | −0.305715 | − | 0.0770816i | ||||
\(145\) | 73.0399i | 0.503723i | ||||||||
\(146\) | −271.097 | + | 93.1458i | −1.85683 | + | 0.637985i | ||||
\(147\) | −84.4633 | + | 87.5329i | −0.574580 | + | 0.595462i | ||||
\(148\) | 155.307 | + | 19.2776i | 1.04937 | + | 0.130254i | ||||
\(149\) | 40.4528 | + | 40.4528i | 0.271495 | + | 0.271495i | 0.829702 | − | 0.558207i | \(-0.188510\pi\) |
−0.558207 | + | 0.829702i | \(0.688510\pi\) | |||||||
\(150\) | 8.27455 | − | 16.9369i | 0.0551636 | − | 0.112913i | ||||
\(151\) | − | 34.5523i | − | 0.228823i | −0.993433 | − | 0.114412i | \(-0.963502\pi\) | ||
0.993433 | − | 0.114412i | \(-0.0364983\pi\) | |||||||
\(152\) | 279.087 | − | 58.7442i | 1.83610 | − | 0.386475i | ||||
\(153\) | −27.1217 | −0.177266 | ||||||||
\(154\) | 37.5527 | − | 13.2785i | 0.243848 | − | 0.0862238i | ||||
\(155\) | 53.7828 | + | 53.7828i | 0.346986 | + | 0.346986i | ||||
\(156\) | −52.4167 | − | 67.2732i | −0.336004 | − | 0.431239i | ||||
\(157\) | 17.2009 | + | 17.2009i | 0.109560 | + | 0.109560i | 0.759762 | − | 0.650202i | \(-0.225316\pi\) |
−0.650202 | + | 0.759762i | \(0.725316\pi\) | |||||||
\(158\) | 126.265 | − | 43.3831i | 0.799143 | − | 0.274577i | ||||
\(159\) | − | 138.202i | − | 0.869193i | ||||||
\(160\) | −112.564 | − | 95.0873i | −0.703523 | − | 0.594295i | ||||
\(161\) | −70.1087 | − | 68.8687i | −0.435458 | − | 0.427756i | ||||
\(162\) | 89.6753 | − | 30.8115i | 0.553551 | − | 0.190194i | ||||
\(163\) | −38.9774 | + | 38.9774i | −0.239125 | + | 0.239125i | −0.816488 | − | 0.577363i | \(-0.804082\pi\) |
0.577363 | + | 0.816488i | \(0.304082\pi\) | |||||||
\(164\) | 40.9083 | − | 31.8742i | 0.249441 | − | 0.194355i | ||||
\(165\) | 22.9963 | + | 22.9963i | 0.139372 | + | 0.139372i | ||||
\(166\) | −154.385 | − | 75.4248i | −0.930029 | − | 0.454366i | ||||
\(167\) | 137.053 | 0.820679 | 0.410339 | − | 0.911933i | \(-0.365410\pi\) | ||||
0.410339 | + | 0.911933i | \(0.365410\pi\) | |||||||
\(168\) | 74.9025 | − | 117.111i | 0.445848 | − | 0.697092i | ||||
\(169\) | − | 95.2349i | − | 0.563520i | ||||||
\(170\) | −79.0907 | − | 38.6398i | −0.465239 | − | 0.227293i | ||||
\(171\) | 71.5305 | − | 71.5305i | 0.418307 | − | 0.418307i | ||||
\(172\) | −286.168 | − | 35.5207i | −1.66377 | − | 0.206516i | ||||
\(173\) | 59.0992 | + | 59.0992i | 0.341614 | + | 0.341614i | 0.856974 | − | 0.515360i | \(-0.172342\pi\) |
−0.515360 | + | 0.856974i | \(0.672342\pi\) | |||||||
\(174\) | 74.4791 | − | 25.5902i | 0.428041 | − | 0.147070i | ||||
\(175\) | −18.9597 | − | 18.6243i | −0.108341 | − | 0.106425i | ||||
\(176\) | −39.0812 | + | 23.3420i | −0.222052 | + | 0.132625i | ||||
\(177\) | 106.835 | 0.603586 | ||||||||
\(178\) | −149.311 | + | 51.3017i | −0.838827 | + | 0.288212i | ||||
\(179\) | 150.604 | − | 150.604i | 0.841364 | − | 0.841364i | −0.147673 | − | 0.989036i | \(-0.547178\pi\) |
0.989036 | + | 0.147673i | \(0.0471782\pi\) | |||||||
\(180\) | −51.8661 | − | 6.43791i | −0.288145 | − | 0.0357662i | ||||
\(181\) | −195.403 | + | 195.403i | −1.07958 | + | 1.07958i | −0.0830294 | + | 0.996547i | \(0.526460\pi\) |
−0.996547 | + | 0.0830294i | \(0.973540\pi\) | |||||||
\(182\) | −113.363 | + | 40.0847i | −0.622874 | + | 0.220246i | ||||
\(183\) | − | 42.1106i | − | 0.230113i | ||||||
\(184\) | 94.0740 | + | 61.3577i | 0.511272 | + | 0.333466i | ||||
\(185\) | 180.158 | 0.973828 | ||||||||
\(186\) | 35.9992 | − | 73.6858i | 0.193544 | − | 0.396160i | ||||
\(187\) | −19.2288 | + | 19.2288i | −0.102828 | + | 0.102828i | ||||
\(188\) | −163.494 | − | 209.833i | −0.869648 | − | 1.11613i | ||||
\(189\) | −1.83533 | − | 205.693i | −0.00971073 | − | 1.08832i | ||||
\(190\) | 310.502 | − | 106.685i | 1.63422 | − | 0.561500i | ||||
\(191\) | 59.1682 | 0.309781 | 0.154891 | − | 0.987932i | \(-0.450497\pi\) | ||||
0.154891 | + | 0.987932i | \(0.450497\pi\) | |||||||
\(192\) | −57.5231 | + | 148.096i | −0.299600 | + | 0.771335i | ||||
\(193\) | −190.929 | −0.989269 | −0.494634 | − | 0.869101i | \(-0.664698\pi\) | ||||
−0.494634 | + | 0.869101i | \(0.664698\pi\) | |||||||
\(194\) | 23.0631 | + | 67.1241i | 0.118882 | + | 0.346000i | ||||
\(195\) | −69.4207 | − | 69.4207i | −0.356004 | − | 0.356004i | ||||
\(196\) | −123.205 | − | 152.435i | −0.628598 | − | 0.777730i | ||||
\(197\) | 142.902 | + | 142.902i | 0.725390 | + | 0.725390i | 0.969698 | − | 0.244308i | \(-0.0785608\pi\) |
−0.244308 | + | 0.969698i | \(0.578561\pi\) | |||||||
\(198\) | −7.08756 | + | 14.5073i | −0.0357958 | + | 0.0732693i | ||||
\(199\) | 138.990 | 0.698440 | 0.349220 | − | 0.937041i | \(-0.386447\pi\) | ||||
0.349220 | + | 0.937041i | \(0.386447\pi\) | |||||||
\(200\) | 25.4407 | + | 16.5931i | 0.127204 | + | 0.0829657i | ||||
\(201\) | 68.5614 | 0.341102 | ||||||||
\(202\) | 168.001 | − | 343.876i | 0.831687 | − | 1.70236i | ||||
\(203\) | −0.990681 | − | 111.030i | −0.00488020 | − | 0.546944i | ||||
\(204\) | −11.6910 | + | 94.1869i | −0.0573088 | + | 0.461700i | ||||
\(205\) | 42.2142 | − | 42.2142i | 0.205923 | − | 0.205923i | ||||
\(206\) | −144.433 | + | 49.6255i | −0.701130 | + | 0.240901i | ||||
\(207\) | 39.8374 | 0.192451 | ||||||||
\(208\) | 117.977 | − | 70.4644i | 0.567198 | − | 0.338771i | ||||
\(209\) | − | 101.428i | − | 0.485302i | ||||||
\(210\) | 68.9626 | − | 144.410i | 0.328393 | − | 0.687669i | ||||
\(211\) | 212.666 | − | 212.666i | 1.00789 | − | 1.00789i | 0.00792508 | − | 0.999969i | \(-0.497477\pi\) |
0.999969 | − | 0.00792508i | \(-0.00252266\pi\) | |||||||
\(212\) | 220.992 | + | 27.4307i | 1.04241 | + | 0.129390i | ||||
\(213\) | −122.458 | + | 122.458i | −0.574918 | + | 0.574918i | ||||
\(214\) | 157.217 | + | 76.8085i | 0.734660 | + | 0.358918i | ||||
\(215\) | −331.957 | −1.54399 | ||||||||
\(216\) | 48.4217 | + | 230.046i | 0.224174 | + | 1.06503i | ||||
\(217\) | −82.4860 | − | 81.0270i | −0.380120 | − | 0.373396i | ||||
\(218\) | −118.565 | + | 242.688i | −0.543877 | + | 1.11325i | ||||
\(219\) | 251.586 | + | 251.586i | 1.14880 | + | 1.14880i | ||||
\(220\) | −41.3367 | + | 32.2079i | −0.187894 | + | 0.146400i | ||||
\(221\) | 58.0476 | − | 58.0476i | 0.262659 | − | 0.262659i | ||||
\(222\) | −63.1200 | − | 183.708i | −0.284324 | − | 0.827513i | ||||
\(223\) | 346.003i | 1.55158i | 0.630988 | + | 0.775792i | \(0.282650\pi\) | ||||
−0.630988 | + | 0.775792i | \(0.717350\pi\) | |||||||
\(224\) | 172.401 | + | 143.018i | 0.769645 | + | 0.638472i | ||||
\(225\) | 10.7733 | 0.0478815 | ||||||||
\(226\) | −267.364 | + | 91.8635i | −1.18303 | + | 0.406476i | ||||
\(227\) | −189.005 | − | 189.005i | −0.832622 | − | 0.832622i | 0.155252 | − | 0.987875i | \(-0.450381\pi\) |
−0.987875 | + | 0.155252i | \(0.950381\pi\) | |||||||
\(228\) | −217.574 | − | 279.242i | −0.954272 | − | 1.22474i | ||||
\(229\) | 151.137 | − | 151.137i | 0.659987 | − | 0.659987i | −0.295390 | − | 0.955377i | \(-0.595450\pi\) |
0.955377 | + | 0.295390i | \(0.0954496\pi\) | |||||||
\(230\) | 116.172 | + | 56.7557i | 0.505094 | + | 0.246764i | ||||
\(231\) | −35.2692 | − | 34.6453i | −0.152680 | − | 0.149980i | ||||
\(232\) | 26.1372 | + | 124.175i | 0.112661 | + | 0.535238i | ||||
\(233\) | 10.5086i | 0.0451015i | 0.999746 | + | 0.0225507i | \(0.00717873\pi\) | ||||
−0.999746 | + | 0.0225507i | \(0.992821\pi\) | |||||||
\(234\) | 21.3958 | − | 43.7944i | 0.0914348 | − | 0.187155i | ||||
\(235\) | −216.532 | − | 216.532i | −0.921411 | − | 0.921411i | ||||
\(236\) | −21.2049 | + | 170.834i | −0.0898513 | + | 0.723875i | ||||
\(237\) | −117.178 | − | 117.178i | −0.494420 | − | 0.494420i | ||||
\(238\) | 120.752 | + | 57.6645i | 0.507361 | + | 0.242288i | ||||
\(239\) | −362.334 | −1.51604 | −0.758021 | − | 0.652230i | \(-0.773834\pi\) | ||||
−0.758021 | + | 0.652230i | \(0.773834\pi\) | |||||||
\(240\) | −44.7146 | + | 177.343i | −0.186311 | + | 0.738931i | ||||
\(241\) | − | 363.356i | − | 1.50770i | −0.657046 | − | 0.753851i | \(-0.728194\pi\) | ||
0.657046 | − | 0.753851i | \(-0.271806\pi\) | |||||||
\(242\) | −73.3759 | − | 213.557i | −0.303206 | − | 0.882467i | ||||
\(243\) | 103.789 | + | 103.789i | 0.427115 | + | 0.427115i | ||||
\(244\) | 67.3371 | + | 8.35825i | 0.275972 | + | 0.0342551i | ||||
\(245\) | −162.366 | − | 156.673i | −0.662720 | − | 0.639480i | ||||
\(246\) | −57.8362 | − | 28.2559i | −0.235106 | − | 0.114861i | ||||
\(247\) | 306.189i | 1.23963i | ||||||||
\(248\) | 110.682 | + | 72.1900i | 0.446299 | + | 0.291089i | ||||
\(249\) | 213.271i | 0.856509i | ||||||||
\(250\) | 238.284 | + | 116.414i | 0.953136 | + | 0.465655i | ||||
\(251\) | 54.1542 | − | 54.1542i | 0.215754 | − | 0.215754i | −0.590952 | − | 0.806706i | \(-0.701248\pi\) |
0.806706 | + | 0.590952i | \(0.201248\pi\) | |||||||
\(252\) | 78.9303 | + | 9.08294i | 0.313216 | + | 0.0360434i | ||||
\(253\) | 28.2441 | − | 28.2441i | 0.111637 | − | 0.111637i | ||||
\(254\) | −151.590 | + | 52.0848i | −0.596813 | + | 0.205058i | ||||
\(255\) | 109.258i | 0.428462i | ||||||||
\(256\) | −225.396 | − | 121.377i | −0.880455 | − | 0.474130i | ||||
\(257\) | 45.3701i | 0.176537i | 0.996097 | + | 0.0882687i | \(0.0281334\pi\) | ||||
−0.996097 | + | 0.0882687i | \(0.971867\pi\) | |||||||
\(258\) | 116.304 | + | 338.498i | 0.450792 | + | 1.31201i | ||||
\(259\) | −273.863 | + | 2.44358i | −1.05739 | + | 0.00943469i | ||||
\(260\) | 124.786 | − | 97.2286i | 0.479947 | − | 0.373956i | ||||
\(261\) | 31.8263 | + | 31.8263i | 0.121940 | + | 0.121940i | ||||
\(262\) | 228.813 | + | 111.787i | 0.873333 | + | 0.426667i | ||||
\(263\) | − | 502.464i | − | 1.91051i | −0.295787 | − | 0.955254i | \(-0.595582\pi\) | ||
0.295787 | − | 0.955254i | \(-0.404418\pi\) | |||||||
\(264\) | 47.3253 | + | 30.8669i | 0.179262 | + | 0.116920i | ||||
\(265\) | 256.353 | 0.967368 | ||||||||
\(266\) | −470.554 | + | 166.386i | −1.76900 | + | 0.625511i | ||||
\(267\) | 138.566 | + | 138.566i | 0.518973 | + | 0.518973i | ||||
\(268\) | −13.6083 | + | 109.633i | −0.0507772 | + | 0.409080i | ||||
\(269\) | −81.3588 | − | 81.3588i | −0.302449 | − | 0.302449i | 0.539522 | − | 0.841971i | \(-0.318605\pi\) |
−0.841971 | + | 0.539522i | \(0.818605\pi\) | |||||||
\(270\) | 87.9383 | + | 255.940i | 0.325698 | + | 0.947927i | ||||
\(271\) | 192.959i | 0.712026i | 0.934481 | + | 0.356013i | \(0.115864\pi\) | ||||
−0.934481 | + | 0.356013i | \(0.884136\pi\) | |||||||
\(272\) | −148.289 | − | 37.3890i | −0.545182 | − | 0.137460i | ||||
\(273\) | 106.470 | + | 104.587i | 0.389999 | + | 0.383101i | ||||
\(274\) | 164.473 | + | 478.691i | 0.600266 | + | 1.74705i | ||||
\(275\) | 7.63814 | − | 7.63814i | 0.0277750 | − | 0.0277750i | ||||
\(276\) | 17.1722 | − | 138.346i | 0.0622181 | − | 0.501252i | ||||
\(277\) | −211.837 | − | 211.837i | −0.764756 | − | 0.764756i | 0.212422 | − | 0.977178i | \(-0.431865\pi\) |
−0.977178 | + | 0.212422i | \(0.931865\pi\) | |||||||
\(278\) | 61.1591 | − | 125.185i | 0.219997 | − | 0.450306i | ||||
\(279\) | 46.8704 | 0.167994 | ||||||||
\(280\) | 217.232 | + | 138.938i | 0.775829 | + | 0.496207i | ||||
\(281\) | 85.3556i | 0.303756i | 0.988399 | + | 0.151878i | \(0.0485322\pi\) | ||||
−0.988399 | + | 0.151878i | \(0.951468\pi\) | |||||||
\(282\) | −144.934 | + | 296.662i | −0.513951 | + | 1.05199i | ||||
\(283\) | −87.4756 | + | 87.4756i | −0.309101 | + | 0.309101i | −0.844561 | − | 0.535460i | \(-0.820138\pi\) |
0.535460 | + | 0.844561i | \(0.320138\pi\) | |||||||
\(284\) | −171.510 | − | 220.122i | −0.603910 | − | 0.775077i | ||||
\(285\) | −288.156 | − | 288.156i | −1.01107 | − | 1.01107i | ||||
\(286\) | −15.8803 | − | 46.2188i | −0.0555255 | − | 0.161604i | ||||
\(287\) | −63.5983 | + | 64.7435i | −0.221597 | + | 0.225587i | ||||
\(288\) | −90.4815 | + | 7.61514i | −0.314172 | + | 0.0264415i | ||||
\(289\) | 197.642 | 0.683882 | ||||||||
\(290\) | 47.4677 | + | 138.153i | 0.163682 | + | 0.476388i | ||||
\(291\) | 62.2933 | − | 62.2933i | 0.214066 | − | 0.214066i | ||||
\(292\) | −452.236 | + | 352.365i | −1.54875 | + | 1.20673i | ||||
\(293\) | 30.7055 | − | 30.7055i | 0.104797 | − | 0.104797i | −0.652764 | − | 0.757561i | \(-0.726391\pi\) |
0.757561 | + | 0.652764i | \(0.226391\pi\) | |||||||
\(294\) | −102.873 | + | 220.457i | −0.349908 | + | 0.749854i | ||||
\(295\) | 198.170i | 0.671762i | ||||||||
\(296\) | 306.287 | − | 64.4694i | 1.03475 | − | 0.217802i | ||||
\(297\) | 83.6052 | 0.281499 | ||||||||
\(298\) | 102.805 | + | 50.2253i | 0.344983 | + | 0.168541i | ||||
\(299\) | −85.2627 | + | 85.2627i | −0.285159 | + | 0.285159i | ||||
\(300\) | 4.64393 | − | 37.4132i | 0.0154798 | − | 0.124711i | ||||
\(301\) | 504.617 | − | 4.50252i | 1.67647 | − | 0.0149585i | ||||
\(302\) | −22.4551 | − | 65.3546i | −0.0743547 | − | 0.216406i | ||||
\(303\) | −475.038 | −1.56778 | ||||||||
\(304\) | 489.707 | − | 292.488i | 1.61088 | − | 0.962131i | ||||
\(305\) | 78.1117 | 0.256104 | ||||||||
\(306\) | −51.2997 | + | 17.6260i | −0.167646 | + | 0.0576014i | ||||
\(307\) | 31.6433 | + | 31.6433i | 0.103073 | + | 0.103073i | 0.756763 | − | 0.653690i | \(-0.226780\pi\) |
−0.653690 | + | 0.756763i | \(0.726780\pi\) | |||||||
\(308\) | 62.4001 | − | 49.5208i | 0.202598 | − | 0.160782i | ||||
\(309\) | 134.038 | + | 134.038i | 0.433781 | + | 0.433781i | ||||
\(310\) | 136.681 | + | 66.7756i | 0.440907 | + | 0.215405i | ||||
\(311\) | −499.800 | −1.60708 | −0.803538 | − | 0.595254i | \(-0.797052\pi\) | ||||
−0.803538 | + | 0.595254i | \(0.797052\pi\) | |||||||
\(312\) | −142.864 | − | 93.1801i | −0.457899 | − | 0.298654i | ||||
\(313\) | −52.7521 | −0.168537 | −0.0842685 | − | 0.996443i | \(-0.526855\pi\) | ||||
−0.0842685 | + | 0.996443i | \(0.526855\pi\) | |||||||
\(314\) | 43.7136 | + | 21.3563i | 0.139215 | + | 0.0680137i | ||||
\(315\) | 91.4587 | − | 0.816055i | 0.290345 | − | 0.00259065i | ||||
\(316\) | 210.631 | − | 164.115i | 0.666554 | − | 0.519353i | ||||
\(317\) | 218.091 | − | 218.091i | 0.687983 | − | 0.687983i | −0.273803 | − | 0.961786i | \(-0.588282\pi\) |
0.961786 | + | 0.273803i | \(0.0882816\pi\) | |||||||
\(318\) | −89.8155 | − | 261.404i | −0.282439 | − | 0.822024i | ||||
\(319\) | 45.1287 | 0.141469 | ||||||||
\(320\) | −274.706 | − | 106.701i | −0.858458 | − | 0.333440i | ||||
\(321\) | − | 217.184i | − | 0.676584i | ||||||
\(322\) | −177.365 | − | 84.7000i | −0.550824 | − | 0.263044i | ||||
\(323\) | 240.947 | − | 240.947i | 0.745967 | − | 0.745967i | ||||
\(324\) | 149.594 | − | 116.558i | 0.461709 | − | 0.359746i | ||||
\(325\) | −23.0578 | + | 23.0578i | −0.0709471 | + | 0.0709471i | ||||
\(326\) | −48.3935 | + | 99.0553i | −0.148446 | + | 0.303851i | ||||
\(327\) | 335.254 | 1.02524 | ||||||||
\(328\) | 56.6622 | − | 86.8748i | 0.172750 | − | 0.264862i | ||||
\(329\) | 332.092 | + | 326.218i | 1.00940 | + | 0.991544i | ||||
\(330\) | 58.4418 | + | 28.5517i | 0.177096 | + | 0.0865204i | ||||
\(331\) | −20.4515 | − | 20.4515i | −0.0617871 | − | 0.0617871i | 0.675538 | − | 0.737325i | \(-0.263911\pi\) |
−0.737325 | + | 0.675538i | \(0.763911\pi\) | |||||||
\(332\) | −341.031 | − | 42.3307i | −1.02720 | − | 0.127502i | ||||
\(333\) | 78.5018 | − | 78.5018i | 0.235741 | − | 0.235741i | ||||
\(334\) | 259.232 | − | 89.0692i | 0.776143 | − | 0.266674i | ||||
\(335\) | 127.176i | 0.379629i | ||||||||
\(336\) | 65.5663 | − | 270.191i | 0.195138 | − | 0.804138i | ||||
\(337\) | 451.093 | 1.33855 | 0.669277 | − | 0.743013i | \(-0.266604\pi\) | ||||
0.669277 | + | 0.743013i | \(0.266604\pi\) | |||||||
\(338\) | −61.8919 | − | 180.134i | −0.183112 | − | 0.532940i | ||||
\(339\) | 248.123 | + | 248.123i | 0.731926 | + | 0.731926i | ||||
\(340\) | −174.709 | − | 21.6858i | −0.513850 | − | 0.0637818i | ||||
\(341\) | 33.2304 | − | 33.2304i | 0.0974500 | − | 0.0974500i | ||||
\(342\) | 88.8107 | − | 181.784i | 0.259681 | − | 0.531533i | ||||
\(343\) | 248.942 | + | 235.959i | 0.725779 | + | 0.687928i | ||||
\(344\) | −564.361 | + | 118.791i | −1.64058 | + | 0.345321i | ||||
\(345\) | − | 160.482i | − | 0.465166i | ||||||
\(346\) | 150.192 | + | 73.3763i | 0.434081 | + | 0.212070i | ||||
\(347\) | −313.926 | − | 313.926i | −0.904687 | − | 0.904687i | 0.0911505 | − | 0.995837i | \(-0.470946\pi\) |
−0.995837 | + | 0.0911505i | \(0.970946\pi\) | |||||||
\(348\) | 124.244 | − | 96.8060i | 0.357023 | − | 0.278178i | ||||
\(349\) | −400.540 | − | 400.540i | −1.14768 | − | 1.14768i | −0.987008 | − | 0.160670i | \(-0.948634\pi\) |
−0.160670 | − | 0.987008i | \(-0.551366\pi\) | |||||||
\(350\) | −47.9654 | − | 22.9057i | −0.137044 | − | 0.0654448i | ||||
\(351\) | −252.385 | −0.719046 | ||||||||
\(352\) | −58.7510 | + | 69.5491i | −0.166906 | + | 0.197583i | ||||
\(353\) | 464.090i | 1.31470i | 0.753584 | + | 0.657352i | \(0.228323\pi\) | ||||
−0.753584 | + | 0.657352i | \(0.771677\pi\) | |||||||
\(354\) | 202.074 | − | 69.4306i | 0.570832 | − | 0.196132i | ||||
\(355\) | −227.149 | − | 227.149i | −0.639855 | − | 0.639855i | ||||
\(356\) | −249.077 | + | 194.071i | −0.699654 | + | 0.545143i | ||||
\(357\) | −1.48192 | − | 166.085i | −0.00415105 | − | 0.465225i | ||||
\(358\) | 186.987 | − | 382.738i | 0.522310 | − | 1.06910i | ||||
\(359\) | − | 126.355i | − | 0.351963i | −0.984393 | − | 0.175982i | \(-0.943690\pi\) | ||
0.984393 | − | 0.175982i | \(-0.0563099\pi\) | |||||||
\(360\) | −102.287 | + | 21.5301i | −0.284131 | + | 0.0598057i | ||||
\(361\) | 909.946i | 2.52063i | ||||||||
\(362\) | −242.609 | + | 496.589i | −0.670190 | + | 1.37179i | ||||
\(363\) | −198.188 | + | 198.188i | −0.545972 | + | 0.545972i | ||||
\(364\) | −188.372 | + | 149.492i | −0.517505 | + | 0.410693i | ||||
\(365\) | −466.672 | + | 466.672i | −1.27855 | + | 1.27855i | ||||
\(366\) | −27.3672 | − | 79.6508i | −0.0747737 | − | 0.217625i | ||||
\(367\) | − | 90.0661i | − | 0.245412i | −0.992443 | − | 0.122706i | \(-0.960843\pi\) | ||
0.992443 | − | 0.122706i | \(-0.0391572\pi\) | |||||||
\(368\) | 217.814 | + | 54.9186i | 0.591885 | + | 0.149235i | ||||
\(369\) | − | 36.7887i | − | 0.0996985i | ||||||
\(370\) | 340.763 | − | 117.082i | 0.920981 | − | 0.316439i | ||||
\(371\) | −389.688 | + | 3.47705i | −1.05037 | + | 0.00937211i | ||||
\(372\) | 20.2039 | − | 162.770i | 0.0543114 | − | 0.437553i | ||||
\(373\) | −363.710 | − | 363.710i | −0.975094 | − | 0.975094i | 0.0246037 | − | 0.999697i | \(-0.492168\pi\) |
−0.999697 | + | 0.0246037i | \(0.992168\pi\) | |||||||
\(374\) | −23.8741 | + | 48.8673i | −0.0638346 | + | 0.130661i | ||||
\(375\) | − | 329.171i | − | 0.877789i | ||||||
\(376\) | −445.611 | − | 290.640i | −1.18514 | − | 0.772979i | ||||
\(377\) | −136.234 | −0.361362 | ||||||||
\(378\) | −137.149 | − | 387.868i | −0.362827 | − | 1.02611i | ||||
\(379\) | 290.869 | + | 290.869i | 0.767465 | + | 0.767465i | 0.977660 | − | 0.210194i | \(-0.0674096\pi\) |
−0.210194 | + | 0.977660i | \(0.567410\pi\) | |||||||
\(380\) | 517.970 | − | 403.582i | 1.36308 | − | 1.06206i | ||||
\(381\) | 140.681 | + | 140.681i | 0.369241 | + | 0.369241i | ||||
\(382\) | 111.915 | − | 38.4527i | 0.292970 | − | 0.100661i | ||||
\(383\) | 234.051i | 0.611099i | 0.952176 | + | 0.305550i | \(0.0988402\pi\) | ||||
−0.952176 | + | 0.305550i | \(0.901160\pi\) | |||||||
\(384\) | −12.5572 | + | 317.503i | −0.0327011 | + | 0.826830i | ||||
\(385\) | 64.2643 | − | 65.4214i | 0.166920 | − | 0.169926i | ||||
\(386\) | −361.136 | + | 124.082i | −0.935584 | + | 0.321457i | ||||
\(387\) | −144.647 | + | 144.647i | −0.373764 | + | 0.373764i | ||||
\(388\) | 87.2462 | + | 111.975i | 0.224861 | + | 0.288594i | ||||
\(389\) | 83.4977 | + | 83.4977i | 0.214647 | + | 0.214647i | 0.806238 | − | 0.591591i | \(-0.201500\pi\) |
−0.591591 | + | 0.806238i | \(0.701500\pi\) | |||||||
\(390\) | −176.423 | − | 86.1913i | −0.452366 | − | 0.221003i | ||||
\(391\) | 134.191 | 0.343198 | ||||||||
\(392\) | −332.104 | − | 208.257i | −0.847205 | − | 0.531267i | ||||
\(393\) | − | 316.088i | − | 0.804295i | ||||||
\(394\) | 363.164 | + | 177.424i | 0.921736 | + | 0.450314i | ||||
\(395\) | 217.355 | − | 217.355i | 0.550265 | − | 0.550265i | ||||
\(396\) | −3.97775 | + | 32.0462i | −0.0100448 | + | 0.0809248i | ||||
\(397\) | 174.436 | + | 174.436i | 0.439386 | + | 0.439386i | 0.891805 | − | 0.452419i | \(-0.149439\pi\) |
−0.452419 | + | 0.891805i | \(0.649439\pi\) | |||||||
\(398\) | 262.894 | − | 90.3275i | 0.660538 | − | 0.226954i | ||||
\(399\) | 441.941 | + | 434.124i | 1.10762 | + | 1.08803i | ||||
\(400\) | 58.9039 | + | 14.8518i | 0.147260 | + | 0.0371294i | ||||
\(401\) | −187.735 | −0.468168 | −0.234084 | − | 0.972216i | \(-0.575209\pi\) | ||||
−0.234084 | + | 0.972216i | \(0.575209\pi\) | |||||||
\(402\) | 129.682 | − | 44.5572i | 0.322591 | − | 0.110839i | ||||
\(403\) | −100.315 | + | 100.315i | −0.248921 | + | 0.248921i | ||||
\(404\) | 94.2871 | − | 759.612i | 0.233384 | − | 1.88023i | ||||
\(405\) | 154.369 | − | 154.369i | 0.381159 | − | 0.381159i | ||||
\(406\) | −74.0307 | − | 209.365i | −0.182342 | − | 0.515678i | ||||
\(407\) | − | 111.313i | − | 0.273497i | ||||||
\(408\) | 39.0977 | + | 185.749i | 0.0958278 | + | 0.455268i | ||||
\(409\) | −144.940 | −0.354377 | −0.177188 | − | 0.984177i | \(-0.556700\pi\) | ||||
−0.177188 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(410\) | 52.4123 | − | 107.281i | 0.127835 | − | 0.261662i | ||||
\(411\) | 444.240 | − | 444.240i | 1.08088 | − | 1.08088i | ||||
\(412\) | −240.939 | + | 187.730i | −0.584803 | + | 0.455655i | ||||
\(413\) | −2.68789 | − | 301.243i | −0.00650820 | − | 0.729401i | ||||
\(414\) | 75.3511 | − | 25.8898i | 0.182008 | − | 0.0625358i | ||||
\(415\) | −395.600 | −0.953253 | ||||||||
\(416\) | 177.356 | − | 209.953i | 0.426337 | − | 0.504695i | ||||
\(417\) | −172.933 | −0.414708 | ||||||||
\(418\) | −65.9168 | − | 191.848i | −0.157696 | − | 0.458966i | ||||
\(419\) | 177.168 | + | 177.168i | 0.422835 | + | 0.422835i | 0.886179 | − | 0.463344i | \(-0.153350\pi\) |
−0.463344 | + | 0.886179i | \(0.653350\pi\) | |||||||
\(420\) | 36.5900 | − | 317.965i | 0.0871190 | − | 0.757061i | ||||
\(421\) | 468.234 | + | 468.234i | 1.11220 | + | 1.11220i | 0.992853 | + | 0.119342i | \(0.0380784\pi\) |
0.119342 | + | 0.992853i | \(0.461922\pi\) | |||||||
\(422\) | 264.041 | − | 540.459i | 0.625690 | − | 1.28071i | ||||
\(423\) | −188.702 | −0.446105 | ||||||||
\(424\) | 435.825 | − | 91.7355i | 1.02789 | − | 0.216357i | ||||
\(425\) | 36.2895 | 0.0853871 | ||||||||
\(426\) | −152.041 | + | 311.208i | −0.356903 | + | 0.730535i | ||||
\(427\) | −118.740 | + | 1.05947i | −0.278079 | + | 0.00248120i | ||||
\(428\) | 347.288 | + | 43.1073i | 0.811421 | + | 0.100718i | ||||
\(429\) | −42.8926 | + | 42.8926i | −0.0999827 | + | 0.0999827i | ||||
\(430\) | −627.886 | + | 215.735i | −1.46020 | + | 0.501709i | ||||
\(431\) | 497.233 | 1.15367 | 0.576836 | − | 0.816860i | \(-0.304287\pi\) | ||||
0.576836 | + | 0.816860i | \(0.304287\pi\) | |||||||
\(432\) | 241.092 | + | 403.656i | 0.558083 | + | 0.934389i | ||||
\(433\) | − | 210.739i | − | 0.486696i | −0.969939 | − | 0.243348i | \(-0.921754\pi\) | ||
0.969939 | − | 0.243348i | \(-0.0782457\pi\) | |||||||
\(434\) | −208.678 | − | 99.6533i | −0.480825 | − | 0.229616i | ||||
\(435\) | 128.210 | − | 128.210i | 0.294736 | − | 0.294736i | ||||
\(436\) | −66.5424 | + | 536.090i | −0.152620 | + | 1.22956i | ||||
\(437\) | −353.913 | + | 353.913i | −0.809870 | + | 0.809870i | ||||
\(438\) | 639.370 | + | 312.365i | 1.45975 | + | 0.713161i | ||||
\(439\) | 762.892 | 1.73779 | 0.868897 | − | 0.494993i | \(-0.164829\pi\) | ||||
0.868897 | + | 0.494993i | \(0.164829\pi\) | |||||||
\(440\) | −57.2555 | + | 87.7845i | −0.130126 | + | 0.199510i | ||||
\(441\) | −139.017 | + | 2.48101i | −0.315232 | + | 0.00562587i | ||||
\(442\) | 72.0707 | − | 147.519i | 0.163056 | − | 0.333754i | ||||
\(443\) | −140.252 | − | 140.252i | −0.316596 | − | 0.316596i | 0.530862 | − | 0.847458i | \(-0.321868\pi\) |
−0.847458 | + | 0.530862i | \(0.821868\pi\) | |||||||
\(444\) | −238.779 | − | 306.456i | −0.537790 | − | 0.690217i | ||||
\(445\) | −257.028 | + | 257.028i | −0.577591 | + | 0.577591i | ||||
\(446\) | 224.863 | + | 654.454i | 0.504178 | + | 1.46739i | ||||
\(447\) | − | 142.017i | − | 0.317711i | ||||||
\(448\) | 419.035 | + | 158.472i | 0.935346 | + | 0.353733i | ||||
\(449\) | −599.904 | −1.33609 | −0.668044 | − | 0.744122i | \(-0.732868\pi\) | ||||
−0.668044 | + | 0.744122i | \(0.732868\pi\) | |||||||
\(450\) | 20.3774 | − | 7.00146i | 0.0452831 | − | 0.0155588i | ||||
\(451\) | −26.0827 | − | 26.0827i | −0.0578330 | − | 0.0578330i | ||||
\(452\) | −446.010 | + | 347.514i | −0.986748 | + | 0.768835i | ||||
\(453\) | −60.6512 | + | 60.6512i | −0.133888 | + | 0.133888i | ||||
\(454\) | −480.329 | − | 234.665i | −1.05799 | − | 0.516883i | ||||
\(455\) | −193.999 | + | 197.493i | −0.426372 | + | 0.434050i | ||||
\(456\) | −593.010 | − | 386.778i | −1.30046 | − | 0.848196i | ||||
\(457\) | − | 557.580i | − | 1.22009i | −0.792368 | − | 0.610044i | \(-0.791152\pi\) | ||
0.792368 | − | 0.610044i | \(-0.208848\pi\) | |||||||
\(458\) | 187.648 | − | 384.092i | 0.409713 | − | 0.838630i | ||||
\(459\) | 198.608 | + | 198.608i | 0.432698 | + | 0.432698i | ||||
\(460\) | 256.620 | + | 31.8530i | 0.557869 | + | 0.0692457i | ||||
\(461\) | 482.593 | + | 482.593i | 1.04684 | + | 1.04684i | 0.998848 | + | 0.0479917i | \(0.0152821\pi\) |
0.0479917 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(462\) | −89.2260 | − | 42.6095i | −0.193130 | − | 0.0922284i | ||||
\(463\) | −326.635 | −0.705475 | −0.352737 | − | 0.935722i | \(-0.614749\pi\) | ||||
−0.352737 | + | 0.935722i | \(0.614749\pi\) | |||||||
\(464\) | 130.138 | + | 217.887i | 0.280469 | + | 0.469584i | ||||
\(465\) | − | 188.814i | − | 0.406052i | ||||||
\(466\) | 6.82944 | + | 19.8768i | 0.0146554 | + | 0.0426540i | ||||
\(467\) | −213.948 | − | 213.948i | −0.458132 | − | 0.458132i | 0.439910 | − | 0.898042i | \(-0.355010\pi\) |
−0.898042 | + | 0.439910i | \(0.855010\pi\) | |||||||
\(468\) | 12.0079 | − | 96.7404i | 0.0256580 | − | 0.206710i | ||||
\(469\) | −1.72496 | − | 193.323i | −0.00367794 | − | 0.412203i | ||||
\(470\) | −550.284 | − | 268.841i | −1.17082 | − | 0.572003i | ||||
\(471\) | − | 60.3870i | − | 0.128210i | ||||||
\(472\) | 70.9148 | + | 336.909i | 0.150243 | + | 0.713789i | ||||
\(473\) | 205.105i | 0.433625i | ||||||||
\(474\) | −297.790 | − | 145.485i | −0.628249 | − | 0.306931i | ||||
\(475\) | −95.7098 | + | 95.7098i | −0.201494 | + | 0.201494i | ||||
\(476\) | 265.873 | + | 30.5955i | 0.558558 | + | 0.0642762i | ||||
\(477\) | 111.703 | − | 111.703i | 0.234178 | − | 0.234178i | ||||
\(478\) | −685.343 | + | 235.476i | −1.43377 | + | 0.492629i | ||||
\(479\) | − | 437.605i | − | 0.913581i | −0.889574 | − | 0.456790i | \(-0.848999\pi\) | ||
0.889574 | − | 0.456790i | \(-0.151001\pi\) | |||||||
\(480\) | 30.6771 | + | 364.499i | 0.0639106 | + | 0.759372i | ||||
\(481\) | 336.030i | 0.698607i | ||||||||
\(482\) | −236.140 | − | 687.276i | −0.489918 | − | 1.42588i | ||||
\(483\) | 2.17671 | + | 243.953i | 0.00450665 | + | 0.505079i | ||||
\(484\) | −277.576 | − | 356.250i | −0.573504 | − | 0.736054i | ||||
\(485\) | 115.549 | + | 115.549i | 0.238245 | + | 0.238245i | ||||
\(486\) | 263.764 | + | 128.862i | 0.542725 | + | 0.265149i | ||||
\(487\) | 681.542i | 1.39947i | 0.714402 | + | 0.699735i | \(0.246699\pi\) | ||||
−0.714402 | + | 0.699735i | \(0.753301\pi\) | |||||||
\(488\) | 132.798 | − | 27.9522i | 0.272127 | − | 0.0572791i | ||||
\(489\) | 136.837 | 0.279831 | ||||||||
\(490\) | −408.930 | − | 190.821i | −0.834551 | − | 0.389431i | ||||
\(491\) | 324.611 | + | 324.611i | 0.661122 | + | 0.661122i | 0.955644 | − | 0.294523i | \(-0.0951607\pi\) |
−0.294523 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(492\) | −127.758 | − | 15.8581i | −0.259671 | − | 0.0322318i | ||||
\(493\) | 107.206 | + | 107.206i | 0.217455 | + | 0.217455i | ||||
\(494\) | 198.988 | + | 579.146i | 0.402810 | + | 1.17236i | ||||
\(495\) | 37.1740i | 0.0750989i | ||||||||
\(496\) | 256.267 | + | 64.6141i | 0.516668 | + | 0.130270i | ||||
\(497\) | 348.375 | + | 342.213i | 0.700956 | + | 0.688558i | ||||
\(498\) | 138.602 | + | 403.395i | 0.278317 | + | 0.810029i | ||||
\(499\) | 23.3782 | − | 23.3782i | 0.0468501 | − | 0.0468501i | −0.683294 | − | 0.730144i | \(-0.739453\pi\) |
0.730144 | + | 0.683294i | \(0.239453\pi\) | |||||||
\(500\) | 526.362 | + | 65.3349i | 1.05272 | + | 0.130670i | ||||
\(501\) | −240.576 | − | 240.576i | −0.480191 | − | 0.480191i | ||||
\(502\) | 67.2368 | − | 137.625i | 0.133938 | − | 0.274154i | ||||
\(503\) | −693.554 | −1.37884 | −0.689418 | − | 0.724364i | \(-0.742133\pi\) | ||||
−0.689418 | + | 0.724364i | \(0.742133\pi\) | |||||||
\(504\) | 155.197 | − | 34.1157i | 0.307930 | − | 0.0676900i | ||||
\(505\) | − | 881.157i | − | 1.74487i | ||||||
\(506\) | 35.0673 | − | 71.7783i | 0.0693030 | − | 0.141854i | ||||
\(507\) | −167.170 | + | 167.170i | −0.329724 | + | 0.329724i | ||||
\(508\) | −252.879 | + | 197.033i | −0.497793 | + | 0.387861i | ||||
\(509\) | 175.357 | + | 175.357i | 0.344512 | + | 0.344512i | 0.858061 | − | 0.513548i | \(-0.171669\pi\) |
−0.513548 | + | 0.858061i | \(0.671669\pi\) | |||||||
\(510\) | 71.0052 | + | 206.657i | 0.139226 | + | 0.405211i | ||||
\(511\) | 703.070 | − | 715.730i | 1.37587 | − | 1.40065i | ||||
\(512\) | −505.211 | − | 83.0986i | −0.986741 | − | 0.162302i | ||||
\(513\) | −1047.62 | −2.04214 | ||||||||
\(514\) | 29.4855 | + | 85.8160i | 0.0573647 | + | 0.166957i | ||||
\(515\) | −248.630 | + | 248.630i | −0.482777 | + | 0.482777i | ||||
\(516\) | 439.971 | + | 564.673i | 0.852658 | + | 1.09433i | ||||
\(517\) | −133.787 | + | 133.787i | −0.258776 | + | 0.258776i | ||||
\(518\) | −516.414 | + | 182.602i | −0.996939 | + | 0.352513i | ||||
\(519\) | − | 207.479i | − | 0.399766i | ||||||
\(520\) | 172.841 | − | 265.002i | 0.332387 | − | 0.509619i | ||||
\(521\) | 602.394 | 1.15623 | 0.578113 | − | 0.815957i | \(-0.303789\pi\) | ||||
0.578113 | + | 0.815957i | \(0.303789\pi\) | |||||||
\(522\) | 80.8819 | + | 39.5149i | 0.154946 | + | 0.0756990i | ||||
\(523\) | −296.480 | + | 296.480i | −0.566883 | + | 0.566883i | −0.931254 | − | 0.364371i | \(-0.881284\pi\) |
0.364371 | + | 0.931254i | \(0.381284\pi\) | |||||||
\(524\) | 505.441 | + | 62.7381i | 0.964583 | + | 0.119729i | ||||
\(525\) | 0.588654 | + | 65.9729i | 0.00112125 | + | 0.125663i | ||||
\(526\) | −326.545 | − | 950.393i | −0.620808 | − | 1.80683i | ||||
\(527\) | 157.881 | 0.299585 | ||||||||
\(528\) | 109.574 | + | 27.6275i | 0.207527 | + | 0.0523249i | ||||
\(529\) | 331.895 | 0.627401 | ||||||||
\(530\) | 484.883 | − | 166.600i | 0.914873 | − | 0.314340i | ||||
\(531\) | 86.3502 | + | 86.3502i | 0.162618 | + | 0.162618i | ||||
\(532\) | −781.905 | + | 620.521i | −1.46975 | + | 1.16639i | ||||
\(533\) | 78.7377 | + | 78.7377i | 0.147726 | + | 0.147726i | ||||
\(534\) | 352.145 | + | 172.040i | 0.659447 | + | 0.322173i | ||||
\(535\) | 402.858 | 0.753005 | ||||||||
\(536\) | 45.5097 | + | 216.212i | 0.0849062 | + | 0.403380i | ||||
\(537\) | −528.724 | −0.984588 | ||||||||
\(538\) | −206.762 | − | 101.013i | −0.384315 | − | 0.187757i | ||||
\(539\) | −96.8023 | + | 100.320i | −0.179596 | + | 0.186123i | ||||
\(540\) | 332.665 | + | 426.953i | 0.616046 | + | 0.790653i | ||||
\(541\) | −221.579 | + | 221.579i | −0.409573 | + | 0.409573i | −0.881590 | − | 0.472017i | \(-0.843526\pi\) |
0.472017 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(542\) | 125.402 | + | 364.976i | 0.231368 | + | 0.673387i | ||||
\(543\) | 686.000 | 1.26335 | ||||||||
\(544\) | −304.783 | + | 25.6513i | −0.560263 | + | 0.0471531i | ||||
\(545\) | 621.869i | 1.14104i | ||||||||
\(546\) | 269.353 | + | 128.629i | 0.493321 | + | 0.235584i | ||||
\(547\) | 545.973 | − | 545.973i | 0.998123 | − | 0.998123i | −0.00187545 | − | 0.999998i | \(-0.500597\pi\) |
0.999998 | + | 0.00187545i | \(0.000596974\pi\) | |||||||
\(548\) | 622.190 | + | 798.538i | 1.13538 | + | 1.45719i | ||||
\(549\) | 34.0363 | − | 34.0363i | 0.0619969 | − | 0.0619969i | ||||
\(550\) | 9.48335 | − | 19.4112i | 0.0172425 | − | 0.0352931i | ||||
\(551\) | −565.486 | −1.02629 | ||||||||
\(552\) | −57.4284 | − | 272.836i | −0.104037 | − | 0.494268i | ||||
\(553\) | −327.458 | + | 333.355i | −0.592149 | + | 0.602811i | ||||
\(554\) | −538.354 | − | 263.013i | −0.971758 | − | 0.474753i | ||||
\(555\) | −316.239 | − | 316.239i | −0.569800 | − | 0.569800i | ||||
\(556\) | 34.3244 | − | 276.530i | 0.0617345 | − | 0.497356i | ||||
\(557\) | 87.7052 | − | 87.7052i | 0.157460 | − | 0.157460i | −0.623980 | − | 0.781440i | \(-0.714485\pi\) |
0.781440 | + | 0.623980i | \(0.214485\pi\) | |||||||
\(558\) | 88.6539 | − | 30.4605i | 0.158878 | − | 0.0545887i | ||||
\(559\) | − | 619.165i | − | 1.10763i | ||||||
\(560\) | 501.181 | + | 121.620i | 0.894966 | + | 0.217179i | ||||
\(561\) | 67.5064 | 0.120332 | ||||||||
\(562\) | 55.4715 | + | 161.447i | 0.0987037 | + | 0.287273i | ||||
\(563\) | 125.548 | + | 125.548i | 0.222997 | + | 0.222997i | 0.809759 | − | 0.586762i | \(-0.199598\pi\) |
−0.586762 | + | 0.809759i | \(0.699598\pi\) | |||||||
\(564\) | −81.3415 | + | 655.317i | −0.144223 | + | 1.16191i | ||||
\(565\) | −460.248 | + | 460.248i | −0.814598 | + | 0.814598i | ||||
\(566\) | −108.608 | + | 222.307i | −0.191887 | + | 0.392768i | ||||
\(567\) | −232.567 | + | 236.754i | −0.410170 | + | 0.417556i | ||||
\(568\) | −467.461 | − | 304.891i | −0.822994 | − | 0.536780i | ||||
\(569\) | − | 963.505i | − | 1.69333i | −0.532126 | − | 0.846665i | \(-0.678607\pi\) | ||
0.532126 | − | 0.846665i | \(-0.321393\pi\) | |||||||
\(570\) | −732.305 | − | 357.768i | −1.28475 | − | 0.627663i | ||||
\(571\) | −254.297 | − | 254.297i | −0.445355 | − | 0.445355i | 0.448452 | − | 0.893807i | \(-0.351975\pi\) |
−0.893807 | + | 0.448452i | \(0.851975\pi\) | |||||||
\(572\) | −60.0741 | − | 77.1010i | −0.105025 | − | 0.134792i | ||||
\(573\) | −103.860 | − | 103.860i | −0.181257 | − | 0.181257i | ||||
\(574\) | −78.2181 | + | 163.792i | −0.136269 | + | 0.285352i | ||||
\(575\) | −53.3036 | −0.0927018 | ||||||||
\(576\) | −166.194 | + | 73.2066i | −0.288531 | + | 0.127095i | ||||
\(577\) | − | 792.088i | − | 1.37277i | −0.727239 | − | 0.686384i | \(-0.759197\pi\) | ||
0.727239 | − | 0.686384i | \(-0.240803\pi\) | |||||||
\(578\) | 373.833 | − | 128.445i | 0.646770 | − | 0.222223i | ||||
\(579\) | 335.146 | + | 335.146i | 0.578835 | + | 0.578835i | ||||
\(580\) | 179.567 | + | 230.462i | 0.309599 | + | 0.397349i | ||||
\(581\) | 601.361 | − | 5.36574i | 1.03504 | − | 0.00923535i | ||||
\(582\) | 77.3421 | − | 158.309i | 0.132890 | − | 0.272009i | ||||
\(583\) | − | 158.391i | − | 0.271683i | ||||||
\(584\) | −626.392 | + | 960.388i | −1.07259 | + | 1.64450i | ||||
\(585\) | − | 112.220i | − | 0.191829i | ||||||
\(586\) | 38.1233 | − | 78.0336i | 0.0650569 | − | 0.133163i | ||||
\(587\) | 436.848 | − | 436.848i | 0.744204 | − | 0.744204i | −0.229180 | − | 0.973384i | \(-0.573604\pi\) |
0.973384 | + | 0.229180i | \(0.0736044\pi\) | |||||||
\(588\) | −51.3086 | + | 483.843i | −0.0872595 | + | 0.822863i | ||||
\(589\) | −416.394 | + | 416.394i | −0.706952 | + | 0.706952i | ||||
\(590\) | 128.788 | + | 374.831i | 0.218285 | + | 0.635307i | ||||
\(591\) | − | 501.683i | − | 0.848872i | ||||||
\(592\) | 537.434 | − | 320.994i | 0.907828 | − | 0.542219i | ||||
\(593\) | − | 668.916i | − | 1.12802i | −0.825768 | − | 0.564010i | \(-0.809258\pi\) | ||
0.825768 | − | 0.564010i | \(-0.190742\pi\) | |||||||
\(594\) | 158.136 | − | 54.3339i | 0.266223 | − | 0.0914713i | ||||
\(595\) | 308.075 | − | 2.74885i | 0.517773 | − | 0.00461991i | ||||
\(596\) | 227.093 | + | 28.1880i | 0.381028 | + | 0.0472953i | ||||
\(597\) | −243.974 | − | 243.974i | −0.408667 | − | 0.408667i | ||||
\(598\) | −105.860 | + | 216.683i | −0.177024 | + | 0.362346i | ||||
\(599\) | − | 411.756i | − | 0.687405i | −0.939079 | − | 0.343703i | \(-0.888319\pi\) | ||
0.939079 | − | 0.343703i | \(-0.111681\pi\) | |||||||
\(600\) | −15.5305 | − | 73.7838i | −0.0258842 | − | 0.122973i | ||||
\(601\) | −688.982 | −1.14639 | −0.573196 | − | 0.819418i | \(-0.694297\pi\) | ||||
−0.573196 | + | 0.819418i | \(0.694297\pi\) | |||||||
\(602\) | 951.539 | − | 336.460i | 1.58063 | − | 0.558904i | ||||
\(603\) | 55.4154 | + | 55.4154i | 0.0918995 | + | 0.0918995i | ||||
\(604\) | −84.9463 | − | 109.023i | −0.140639 | − | 0.180501i | ||||
\(605\) | −367.622 | − | 367.622i | −0.607640 | − | 0.607640i | ||||
\(606\) | −898.519 | + | 308.721i | −1.48270 | + | 0.509441i | ||||
\(607\) | − | 768.094i | − | 1.26539i | −0.774400 | − | 0.632697i | \(-0.781948\pi\) | ||
0.774400 | − | 0.632697i | \(-0.218052\pi\) | |||||||
\(608\) | 736.180 | − | 871.485i | 1.21082 | − | 1.43336i | ||||
\(609\) | −193.156 | + | 196.634i | −0.317170 | + | 0.322880i | ||||
\(610\) | 147.746 | − | 50.7638i | 0.242206 | − | 0.0832194i | ||||
\(611\) | 403.873 | − | 403.873i | 0.661004 | − | 0.661004i | ||||
\(612\) | −85.5768 | + | 66.6781i | −0.139831 | + | 0.108951i | ||||
\(613\) | −163.362 | − | 163.362i | −0.266495 | − | 0.266495i | 0.561191 | − | 0.827686i | \(-0.310343\pi\) |
−0.827686 | + | 0.561191i | \(0.810343\pi\) | |||||||
\(614\) | 80.4168 | + | 39.2877i | 0.130972 | + | 0.0639864i | ||||
\(615\) | −148.201 | −0.240977 | ||||||||
\(616\) | 85.8448 | − | 134.220i | 0.139358 | − | 0.217889i | ||||
\(617\) | − | 652.431i | − | 1.05742i | −0.848801 | − | 0.528712i | \(-0.822675\pi\) | ||
0.848801 | − | 0.528712i | \(-0.177325\pi\) | |||||||
\(618\) | 340.639 | + | 166.419i | 0.551195 | + | 0.269287i | ||||
\(619\) | 78.1751 | − | 78.1751i | 0.126293 | − | 0.126293i | −0.641135 | − | 0.767428i | \(-0.721536\pi\) |
0.767428 | + | 0.641135i | \(0.221536\pi\) | |||||||
\(620\) | 301.924 | + | 37.4765i | 0.486975 | + | 0.0604459i | ||||
\(621\) | −291.724 | − | 291.724i | −0.469765 | − | 0.469765i | ||||
\(622\) | −945.356 | + | 324.814i | −1.51986 | + | 0.522209i | ||||
\(623\) | 387.228 | − | 394.201i | 0.621554 | − | 0.632746i | ||||
\(624\) | −330.780 | − | 83.4014i | −0.530096 | − | 0.133656i | ||||
\(625\) | 515.667 | 0.825067 | ||||||||
\(626\) | −99.7788 | + | 34.2829i | −0.159391 | + | 0.0547650i | ||||
\(627\) | −178.041 | + | 178.041i | −0.283957 | + | 0.283957i | ||||
\(628\) | 96.5620 | + | 11.9858i | 0.153761 | + | 0.0190857i | ||||
\(629\) | 264.430 | − | 264.430i | 0.420398 | − | 0.420398i | ||||
\(630\) | 172.461 | − | 60.9814i | 0.273747 | − | 0.0967958i | ||||
\(631\) | 219.948i | 0.348570i | 0.984695 | + | 0.174285i | \(0.0557614\pi\) | ||||
−0.984695 | + | 0.174285i | \(0.944239\pi\) | |||||||
\(632\) | 291.745 | − | 447.305i | 0.461622 | − | 0.707762i | ||||
\(633\) | −746.602 | −1.17947 | ||||||||
\(634\) | 270.777 | − | 554.245i | 0.427093 | − | 0.874204i | ||||
\(635\) | −260.951 | + | 260.951i | −0.410947 | + | 0.410947i | ||||
\(636\) | −339.766 | − | 436.067i | −0.534223 | − | 0.685639i | ||||
\(637\) | 292.225 | − | 302.845i | 0.458751 | − | 0.475423i | ||||
\(638\) | 85.3595 | − | 29.3286i | 0.133792 | − | 0.0459696i | ||||
\(639\) | −197.955 | −0.309789 | ||||||||
\(640\) | −588.942 | − | 23.2926i | −0.920221 | − | 0.0363947i | ||||
\(641\) | −186.577 | −0.291072 | −0.145536 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145536 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(642\) | −141.145 | − | 410.795i | −0.219852 | − | 0.639868i | ||||
\(643\) | 215.904 | + | 215.904i | 0.335776 | + | 0.335776i | 0.854775 | − | 0.518999i | \(-0.173695\pi\) |
−0.518999 | + | 0.854775i | \(0.673695\pi\) | |||||||
\(644\) | −390.526 | − | 44.9399i | −0.606407 | − | 0.0697825i | ||||
\(645\) | 582.699 | + | 582.699i | 0.903409 | + | 0.903409i | ||||
\(646\) | 299.155 | − | 612.333i | 0.463089 | − | 0.947883i | ||||
\(647\) | 663.677 | 1.02578 | 0.512888 | − | 0.858456i | \(-0.328576\pi\) | ||||
0.512888 | + | 0.858456i | \(0.328576\pi\) | |||||||
\(648\) | 207.202 | − | 317.684i | 0.319757 | − | 0.490253i | ||||
\(649\) | 122.442 | 0.188663 | ||||||||
\(650\) | −28.6281 | + | 58.5981i | −0.0440433 | + | 0.0901509i | ||||
\(651\) | 2.56099 | + | 287.021i | 0.00393394 | + | 0.440893i | ||||
\(652\) | −27.1599 | + | 218.810i | −0.0416563 | + | 0.335598i | ||||
\(653\) | −411.703 | + | 411.703i | −0.630479 | + | 0.630479i | −0.948188 | − | 0.317709i | \(-0.897086\pi\) |
0.317709 | + | 0.948188i | \(0.397086\pi\) | |||||||
\(654\) | 634.123 | − | 217.878i | 0.969606 | − | 0.333146i | ||||
\(655\) | 586.317 | 0.895140 | ||||||||
\(656\) | 50.7158 | − | 201.145i | 0.0773106 | − | 0.306623i | ||||
\(657\) | 406.694i | 0.619017i | ||||||||
\(658\) | 840.146 | + | 401.208i | 1.27682 | + | 0.609739i | ||||
\(659\) | −149.906 | + | 149.906i | −0.227475 | + | 0.227475i | −0.811637 | − | 0.584162i | \(-0.801423\pi\) |
0.584162 | + | 0.811637i | \(0.301423\pi\) | |||||||
\(660\) | 129.096 | + | 16.0241i | 0.195600 | + | 0.0242790i | ||||
\(661\) | 166.233 | − | 166.233i | 0.251487 | − | 0.251487i | −0.570093 | − | 0.821580i | \(-0.693093\pi\) |
0.821580 | + | 0.570093i | \(0.193093\pi\) | |||||||
\(662\) | −51.9746 | − | 25.3922i | −0.0785115 | − | 0.0383568i | ||||
\(663\) | −203.787 | −0.307371 | ||||||||
\(664\) | −672.560 | + | 141.565i | −1.01289 | + | 0.213200i | ||||
\(665\) | −805.264 | + | 819.764i | −1.21092 | + | 1.23273i | ||||
\(666\) | 97.4662 | − | 199.501i | 0.146346 | − | 0.299551i | ||||
\(667\) | −157.468 | − | 157.468i | −0.236084 | − | 0.236084i | ||||
\(668\) | 432.443 | − | 336.943i | 0.647370 | − | 0.504406i | ||||
\(669\) | 607.355 | − | 607.355i | 0.907854 | − | 0.907854i | ||||
\(670\) | 82.6499 | + | 240.549i | 0.123358 | + | 0.359028i | ||||
\(671\) | − | 48.2625i | − | 0.0719262i | ||||||
\(672\) | −51.5769 | − | 553.667i | −0.0767513 | − | 0.823909i | ||||
\(673\) | 315.076 | 0.468167 | 0.234083 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234083 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(674\) | 853.227 | − | 293.160i | 1.26592 | − | 0.434955i | ||||
\(675\) | −78.8917 | − | 78.8917i | −0.116877 | − | 0.116877i | ||||
\(676\) | −234.133 | − | 300.494i | −0.346351 | − | 0.444518i | ||||
\(677\) | 496.264 | − | 496.264i | 0.733034 | − | 0.733034i | −0.238186 | − | 0.971220i | \(-0.576553\pi\) |
0.971220 | + | 0.238186i | \(0.0765528\pi\) | |||||||
\(678\) | 630.568 | + | 308.064i | 0.930042 | + | 0.454372i | ||||
\(679\) | −177.216 | − | 174.082i | −0.260996 | − | 0.256379i | ||||
\(680\) | −344.549 | + | 72.5231i | −0.506690 | + | 0.106652i | ||||
\(681\) | 663.538i | 0.974359i | ||||||||
\(682\) | 41.2582 | − | 84.4503i | 0.0604959 | − | 0.123827i | ||||
\(683\) | −387.884 | − | 387.884i | −0.567913 | − | 0.567913i | 0.363631 | − | 0.931543i | \(-0.381537\pi\) |
−0.931543 | + | 0.363631i | \(0.881537\pi\) | |||||||
\(684\) | 49.8433 | − | 401.556i | 0.0728703 | − | 0.587070i | ||||
\(685\) | 824.029 | + | 824.029i | 1.20296 | + | 1.20296i | ||||
\(686\) | 624.213 | + | 284.525i | 0.909931 | + | 0.414760i | ||||
\(687\) | −530.594 | −0.772335 | ||||||||
\(688\) | −990.270 | + | 591.460i | −1.43935 | + | 0.859680i | ||||
\(689\) | 478.147i | 0.693973i | ||||||||
\(690\) | −104.295 | − | 303.547i | −0.151153 | − | 0.439923i | ||||
\(691\) | −776.671 | − | 776.671i | −1.12398 | − | 1.12398i | −0.991137 | − | 0.132844i | \(-0.957589\pi\) |
−0.132844 | − | 0.991137i | \(-0.542411\pi\) | |||||||
\(692\) | 331.769 | + | 41.1810i | 0.479436 | + | 0.0595102i | ||||
\(693\) | −0.504211 | − | 56.5090i | −0.000727577 | − | 0.0815426i | ||||
\(694\) | −797.798 | − | 389.764i | −1.14956 | − | 0.561620i | ||||
\(695\) | − | 320.777i | − | 0.461550i | ||||||
\(696\) | 172.090 | − | 263.850i | 0.247256 | − | 0.379095i | ||||
\(697\) | − | 123.921i | − | 0.177792i | ||||||
\(698\) | −1017.91 | − | 497.302i | −1.45833 | − | 0.712467i | ||||
\(699\) | 18.4463 | − | 18.4463i | 0.0263895 | − | 0.0263895i | ||||
\(700\) | −105.611 | − | 12.1532i | −0.150873 | − | 0.0173617i | ||||
\(701\) | −504.506 | + | 504.506i | −0.719695 | + | 0.719695i | −0.968543 | − | 0.248848i | \(-0.919948\pi\) |
0.248848 | + | 0.968543i | \(0.419948\pi\) | |||||||
\(702\) | −477.378 | + | 164.022i | −0.680026 | + | 0.233650i | ||||
\(703\) | 1394.81i | 1.98409i | ||||||||
\(704\) | −65.9265 | + | 169.731i | −0.0936457 | + | 0.241096i | ||||
\(705\) | 760.174i | 1.07826i | ||||||||
\(706\) | 301.606 | + | 877.812i | 0.427205 | + | 1.24336i | ||||
\(707\) | 11.9516 | + | 1339.47i | 0.0169047 | + | 1.89458i | ||||
\(708\) | 337.095 | − | 262.651i | 0.476123 | − | 0.370976i | ||||
\(709\) | 329.265 | + | 329.265i | 0.464408 | + | 0.464408i | 0.900097 | − | 0.435689i | \(-0.143495\pi\) |
−0.435689 | + | 0.900097i | \(0.643495\pi\) | |||||||
\(710\) | −577.265 | − | 282.023i | −0.813050 | − | 0.397216i | ||||
\(711\) | − | 189.420i | − | 0.266413i | ||||||
\(712\) | −344.997 | + | 528.951i | −0.484546 | + | 0.742909i | ||||
\(713\) | −231.902 | −0.325249 | ||||||||
\(714\) | −110.740 | − | 313.182i | −0.155098 | − | 0.438630i | ||||
\(715\) | −79.5622 | − | 79.5622i | −0.111276 | − | 0.111276i | ||||
\(716\) | 104.943 | − | 845.457i | 0.146568 | − | 1.18081i | ||||
\(717\) | 636.021 | + | 636.021i | 0.887058 | + | 0.887058i | ||||
\(718\) | −82.1164 | − | 238.996i | −0.114368 | − | 0.332863i | ||||
\(719\) | 612.721i | 0.852185i | 0.904680 | + | 0.426093i | \(0.140110\pi\) | ||||
−0.904680 | + | 0.426093i | \(0.859890\pi\) | |||||||
\(720\) | −179.480 | + | 107.198i | −0.249278 | + | 0.148887i | ||||
\(721\) | 374.576 | − | 381.321i | 0.519523 | − | 0.528878i | ||||
\(722\) | 591.362 | + | 1721.13i | 0.819061 | + | 2.38384i | ||||
\(723\) | −637.814 | + | 637.814i | −0.882177 | + | 0.882177i | ||||
\(724\) | −136.159 | + | 1096.95i | −0.188066 | + | 1.51512i | ||||
\(725\) | −42.5845 | − | 42.5845i | −0.0587372 | − | 0.0587372i | ||||
\(726\) | −246.066 | + | 503.666i | −0.338934 | + | 0.693754i | ||||
\(727\) | 884.961 | 1.21728 | 0.608639 | − | 0.793447i | \(-0.291716\pi\) | ||||
0.608639 | + | 0.793447i | \(0.291716\pi\) | |||||||
\(728\) | −259.146 | + | 405.180i | −0.355970 | + | 0.556566i | ||||
\(729\) | − | 791.064i | − | 1.08514i | ||||||
\(730\) | −579.411 | + | 1185.98i | −0.793713 | + | 1.62463i | ||||
\(731\) | −487.236 | + | 487.236i | −0.666534 | + | 0.666534i | ||||
\(732\) | −103.528 | − | 132.871i | −0.141432 | − | 0.181518i | ||||
\(733\) | 630.619 | + | 630.619i | 0.860327 | + | 0.860327i | 0.991376 | − | 0.131049i | \(-0.0418346\pi\) |
−0.131049 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(734\) | −58.5328 | − | 170.357i | −0.0797450 | − | 0.232094i | ||||
\(735\) | 9.99458 | + | 560.022i | 0.0135981 | + | 0.761935i | ||||
\(736\) | 447.678 | − | 37.6776i | 0.608258 | − | 0.0511925i | ||||
\(737\) | 78.5774 | 0.106618 | ||||||||
\(738\) | −23.9085 | − | 69.5847i | −0.0323964 | − | 0.0942882i | ||||
\(739\) | −885.422 | + | 885.422i | −1.19813 | + | 1.19813i | −0.223410 | + | 0.974725i | \(0.571719\pi\) |
−0.974725 | + | 0.223410i | \(0.928281\pi\) | |||||||
\(740\) | 568.452 | − | 442.915i | 0.768178 | − | 0.598534i | ||||
\(741\) | 537.466 | − | 537.466i | 0.725325 | − | 0.725325i | ||||
\(742\) | −734.822 | + | 259.830i | −0.990326 | + | 0.350175i | ||||
\(743\) | 454.580i | 0.611817i | 0.952061 | + | 0.305909i | \(0.0989602\pi\) | ||||
−0.952061 | + | 0.305909i | \(0.901040\pi\) | |||||||
\(744\) | −67.5670 | − | 321.003i | −0.0908158 | − | 0.431456i | ||||
\(745\) | 263.430 | 0.353597 | ||||||||
\(746\) | −924.316 | − | 451.575i | −1.23903 | − | 0.605328i | ||||
\(747\) | −172.378 | + | 172.378i | −0.230760 | + | 0.230760i | ||||
\(748\) | −13.3989 | + | 107.946i | −0.0179130 | + | 0.144313i | ||||
\(749\) | −612.394 | + | 5.46418i | −0.817615 | + | 0.00729530i | ||||
\(750\) | −213.924 | − | 622.616i | −0.285232 | − | 0.830154i | ||||
\(751\) | 220.761 | 0.293956 | 0.146978 | − | 0.989140i | \(-0.453045\pi\) | ||||
0.146978 | + | 0.989140i | \(0.453045\pi\) | |||||||
\(752\) | −1031.74 | − | 260.139i | −1.37200 | − | 0.345929i | ||||
\(753\) | −190.119 | −0.252481 | ||||||||
\(754\) | −257.681 | + | 88.5365i | −0.341752 | + | 0.117422i | ||||
\(755\) | −112.503 | − | 112.503i | −0.149011 | − | 0.149011i | ||||
\(756\) | −511.483 | − | 644.509i | −0.676565 | − | 0.852525i | ||||
\(757\) | 195.831 | + | 195.831i | 0.258693 | + | 0.258693i | 0.824522 | − | 0.565829i | \(-0.191444\pi\) |
−0.565829 | + | 0.824522i | \(0.691444\pi\) | |||||||
\(758\) | 739.202 | + | 361.137i | 0.975201 | + | 0.476435i | ||||
\(759\) | −99.1562 | −0.130641 | ||||||||
\(760\) | 717.441 | − | 1099.98i | 0.944001 | − | 1.44735i | ||||
\(761\) | 1450.33 | 1.90583 | 0.952913 | − | 0.303244i | \(-0.0980698\pi\) | ||||
0.952913 | + | 0.303244i | \(0.0980698\pi\) | |||||||
\(762\) | 357.520 | + | 174.666i | 0.469186 | + | 0.229221i | ||||
\(763\) | −8.43476 | − | 945.319i | −0.0110547 | − | 1.23895i | ||||
\(764\) | 186.693 | − | 145.464i | 0.244363 | − | 0.190398i | ||||
\(765\) | −88.3086 | + | 88.3086i | −0.115436 | + | 0.115436i | ||||
\(766\) | 152.107 | + | 442.700i | 0.198573 | + | 0.577937i | ||||
\(767\) | −369.625 | −0.481910 | ||||||||
\(768\) | 182.589 | + | 608.707i | 0.237747 | + | 0.792587i | ||||
\(769\) | 95.3790i | 0.124030i | 0.998075 | + | 0.0620150i | \(0.0197527\pi\) | ||||
−0.998075 | + | 0.0620150i | \(0.980247\pi\) | |||||||
\(770\) | 79.0372 | − | 165.507i | 0.102646 | − | 0.214944i | ||||
\(771\) | 79.6401 | − | 79.6401i | 0.103295 | − | 0.103295i | ||||
\(772\) | −602.436 | + | 469.395i | −0.780358 | + | 0.608024i | ||||
\(773\) | 811.244 | − | 811.244i | 1.04948 | − | 1.04948i | 0.0507646 | − | 0.998711i | \(-0.483834\pi\) |
0.998711 | − | 0.0507646i | \(-0.0161658\pi\) | |||||||
\(774\) | −179.590 | + | 367.598i | −0.232029 | + | 0.474933i | ||||
\(775\) | −62.7140 | −0.0809212 | ||||||||
\(776\) | 237.794 | + | 155.096i | 0.306436 | + | 0.199866i | ||||
\(777\) | 485.012 | + | 476.434i | 0.624211 | + | 0.613171i | ||||
\(778\) | 212.197 | + | 103.669i | 0.272747 | + | 0.133251i | ||||
\(779\) | 326.829 | + | 326.829i | 0.419550 | + | 0.419550i | ||||
\(780\) | −389.712 | − | 48.3732i | −0.499631 | − | 0.0620169i | ||||
\(781\) | −140.347 | + | 140.347i | −0.179702 | + | 0.179702i | ||||
\(782\) | 253.817 | − | 87.2088i | 0.324574 | − | 0.111520i | ||||
\(783\) | − | 466.119i | − | 0.595299i | ||||||
\(784\) | −763.507 | − | 178.080i | −0.973861 | − | 0.227143i | ||||
\(785\) | 112.013 | 0.142692 | ||||||||
\(786\) | −205.422 | − | 597.870i | −0.261351 | − | 0.760648i | ||||
\(787\) | 96.6979 | + | 96.6979i | 0.122869 | + | 0.122869i | 0.765867 | − | 0.642998i | \(-0.222310\pi\) |
−0.642998 | + | 0.765867i | \(0.722310\pi\) | |||||||
\(788\) | 802.218 | + | 99.5757i | 1.01804 | + | 0.126365i | ||||
\(789\) | −881.996 | + | 881.996i | −1.11787 | + | 1.11787i | ||||
\(790\) | 269.863 | − | 552.376i | 0.341599 | − | 0.699210i | ||||
\(791\) | 693.391 | − | 705.876i | 0.876601 | − | 0.892385i | ||||
\(792\) | 13.3027 | + | 63.1995i | 0.0167963 | + | 0.0797973i | ||||
\(793\) | 145.694i | 0.183725i | ||||||||
\(794\) | 443.304 | + | 216.576i | 0.558318 | + | 0.272766i | ||||
\(795\) | −449.987 | − | 449.987i | −0.566021 | − | 0.566021i | ||||
\(796\) | 438.553 | − | 341.703i | 0.550946 | − | 0.429275i | ||||
\(797\) | −581.633 | − | 581.633i | −0.729778 | − | 0.729778i | 0.240798 | − | 0.970575i | \(-0.422591\pi\) |
−0.970575 | + | 0.240798i | \(0.922591\pi\) | |||||||
\(798\) | 1118.05 | + | 533.919i | 1.40106 | + | 0.669072i | ||||
\(799\) | −635.636 | −0.795539 | ||||||||
\(800\) | 121.067 | − | 10.1893i | 0.151333 | − | 0.0127366i | ||||
\(801\) | 223.994i | 0.279643i | ||||||||
\(802\) | −355.095 | + | 122.007i | −0.442762 | + | 0.152128i | ||||
\(803\) | 288.340 | + | 288.340i | 0.359079 | + | 0.359079i | ||||
\(804\) | 216.331 | − | 168.557i | 0.269069 | − | 0.209648i | ||||
\(805\) | −452.513 | + | 4.03762i | −0.562128 | + | 0.00501567i | ||||
\(806\) | −124.549 | + | 254.937i | −0.154528 | + | 0.316299i | ||||
\(807\) | 285.625i | 0.353935i | ||||||||
\(808\) | −315.321 | − | 1498.06i | −0.390249 | − | 1.85403i | ||||
\(809\) | − | 296.533i | − | 0.366543i | −0.983062 | − | 0.183272i | \(-0.941331\pi\) | ||
0.983062 | − | 0.183272i | \(-0.0586688\pi\) | |||||||
\(810\) | 191.662 | − | 392.307i | 0.236619 | − | 0.484329i | ||||
\(811\) | −605.219 | + | 605.219i | −0.746262 | + | 0.746262i | −0.973775 | − | 0.227513i | \(-0.926941\pi\) |
0.227513 | + | 0.973775i | \(0.426941\pi\) | |||||||
\(812\) | −276.090 | − | 347.896i | −0.340013 | − | 0.428443i | ||||
\(813\) | 338.709 | − | 338.709i | 0.416617 | − | 0.416617i | ||||
\(814\) | −72.3411 | − | 210.545i | −0.0888711 | − | 0.258655i | ||||
\(815\) | 253.822i | 0.311438i | ||||||||
\(816\) | 194.668 | + | 325.929i | 0.238564 | + | 0.399423i | ||||
\(817\) | − | 2570.07i | − | 3.14574i | ||||||
\(818\) | −274.149 | + | 94.1947i | −0.335146 | + | 0.115152i | ||||
\(819\) | 1.52210 | + | 170.588i | 0.00185849 | + | 0.208288i | ||||
\(820\) | 29.4154 | − | 236.981i | 0.0358724 | − | 0.289001i | ||||
\(821\) | 460.505 | + | 460.505i | 0.560907 | + | 0.560907i | 0.929565 | − | 0.368658i | \(-0.120183\pi\) |
−0.368658 | + | 0.929565i | \(0.620183\pi\) | |||||||
\(822\) | 551.560 | − | 1128.97i | 0.670997 | − | 1.37345i | ||||
\(823\) | 1126.18i | 1.36839i | 0.729300 | + | 0.684194i | \(0.239846\pi\) | ||||
−0.729300 | + | 0.684194i | \(0.760154\pi\) | |||||||
\(824\) | −333.724 | + | 511.668i | −0.405005 | + | 0.620956i | ||||
\(825\) | −26.8151 | −0.0325031 | ||||||||
\(826\) | −200.858 | − | 568.044i | −0.243169 | − | 0.687704i | ||||
\(827\) | 686.896 | + | 686.896i | 0.830587 | + | 0.830587i | 0.987597 | − | 0.157010i | \(-0.0501855\pi\) |
−0.157010 | + | 0.987597i | \(0.550185\pi\) | |||||||
\(828\) | 125.699 | − | 97.9395i | 0.151810 | − | 0.118284i | ||||
\(829\) | −732.088 | − | 732.088i | −0.883098 | − | 0.883098i | 0.110750 | − | 0.993848i | \(-0.464675\pi\) |
−0.993848 | + | 0.110750i | \(0.964675\pi\) | |||||||
\(830\) | −748.264 | + | 257.095i | −0.901523 | + | 0.309753i | ||||
\(831\) | 743.694i | 0.894939i | ||||||||
\(832\) | 199.017 | − | 512.381i | 0.239204 | − | 0.615842i | ||||
\(833\) | −468.275 | + | 8.35718i | −0.562154 | + | 0.0100326i | ||||
\(834\) | −327.098 | + | 112.387i | −0.392204 | + | 0.134757i | ||||
\(835\) | 446.248 | − | 446.248i | 0.534429 | − | 0.534429i | ||||
\(836\) | −249.359 | − | 320.035i | −0.298276 | − | 0.382817i | ||||
\(837\) | −343.226 | − | 343.226i | −0.410067 | − | 0.410067i | ||||
\(838\) | 450.247 | + | 219.968i | 0.537287 | + | 0.262492i | ||||
\(839\) | −903.003 | −1.07628 | −0.538142 | − | 0.842854i | \(-0.680874\pi\) | ||||
−0.538142 | + | 0.842854i | \(0.680874\pi\) | |||||||
\(840\) | −137.433 | − | 625.200i | −0.163611 | − | 0.744286i | ||||
\(841\) | 589.396i | 0.700828i | ||||||||
\(842\) | 1189.95 | + | 581.350i | 1.41324 | + | 0.690439i | ||||
\(843\) | 149.828 | − | 149.828i | 0.177732 | − | 0.177732i | ||||
\(844\) | 148.188 | − | 1193.86i | 0.175578 | − | 1.41452i | ||||
\(845\) | −310.086 | − | 310.086i | −0.366966 | − | 0.366966i | ||||
\(846\) | −356.924 | + | 122.635i | −0.421896 | + | 0.144959i | ||||
\(847\) | 563.818 | + | 553.845i | 0.665664 | + | 0.653891i | ||||
\(848\) | 764.732 | − | 456.752i | 0.901806 | − | 0.538623i | ||||
\(849\) | 307.099 | 0.361719 | ||||||||
\(850\) | 68.6404 | − | 23.5841i | 0.0807535 | − | 0.0277460i | ||||
\(851\) | −388.406 | + | 388.406i | −0.456411 | + | 0.456411i | ||||
\(852\) | −85.3299 | + | 687.449i | −0.100152 | + | 0.806865i | ||||
\(853\) | 38.7225 | − | 38.7225i | 0.0453957 | − | 0.0453957i | −0.684045 | − | 0.729440i | \(-0.739781\pi\) |
0.729440 | + | 0.684045i | \(0.239781\pi\) | |||||||
\(854\) | −223.903 | + | 79.1713i | −0.262182 | + | 0.0927064i | ||||
\(855\) | − | 465.809i | − | 0.544806i | ||||||
\(856\) | 684.899 | − | 144.162i | 0.800115 | − | 0.168414i | ||||
\(857\) | −653.919 | −0.763032 | −0.381516 | − | 0.924362i | \(-0.624598\pi\) | ||||
−0.381516 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(858\) | −53.2545 | + | 109.005i | −0.0620682 | + | 0.127046i | ||||
\(859\) | −340.187 | + | 340.187i | −0.396026 | + | 0.396026i | −0.876829 | − | 0.480802i | \(-0.840345\pi\) |
0.480802 | + | 0.876829i | \(0.340345\pi\) | |||||||
\(860\) | −1047.42 | + | 816.111i | −1.21793 | + | 0.948966i | ||||
\(861\) | 225.284 | − | 2.01013i | 0.261654 | − | 0.00233465i | ||||
\(862\) | 940.499 | − | 323.145i | 1.09107 | − | 0.374879i | ||||
\(863\) | −106.239 | −0.123104 | −0.0615519 | − | 0.998104i | \(-0.519605\pi\) | ||||
−0.0615519 | + | 0.998104i | \(0.519605\pi\) | |||||||
\(864\) | 718.348 | + | 606.819i | 0.831422 | + | 0.702337i | ||||
\(865\) | 384.856 | 0.444920 | ||||||||
\(866\) | −136.957 | − | 398.606i | −0.158149 | − | 0.460284i | ||||
\(867\) | −346.929 | − | 346.929i | −0.400149 | − | 0.400149i | ||||
\(868\) | −459.471 | − | 52.8738i | −0.529344 | − | 0.0609145i | ||||
\(869\) | −134.296 | − | 134.296i | −0.154541 | − | 0.154541i | ||||
\(870\) | 159.183 | − | 325.827i | 0.182969 | − | 0.374514i | ||||
\(871\) | −237.207 | −0.272339 | ||||||||
\(872\) | 222.535 | + | 1057.24i | 0.255201 | + | 1.21243i | ||||
\(873\) | 100.698 | 0.115347 | ||||||||
\(874\) | −439.411 | + | 899.419i | −0.502759 | + | 1.02908i | ||||
\(875\) | −928.165 | + | 8.28170i | −1.06076 | + | 0.00946480i | ||||
\(876\) | 1412.35 | + | 175.309i | 1.61227 | + | 0.200124i | ||||
\(877\) | −535.021 | + | 535.021i | −0.610059 | + | 0.610059i | −0.942961 | − | 0.332903i | \(-0.891972\pi\) |
0.332903 | + | 0.942961i | \(0.391972\pi\) | |||||||
\(878\) | 1442.98 | − | 495.794i | 1.64349 | − | 0.564685i | ||||
\(879\) | −107.797 | −0.122636 | ||||||||
\(880\) | −51.2468 | + | 203.251i | −0.0582350 | + | 0.230967i | ||||
\(881\) | 370.517i | 0.420564i | 0.977641 | + | 0.210282i | \(0.0674382\pi\) | ||||
−0.977641 | + | 0.210282i | \(0.932562\pi\) | |||||||
\(882\) | −261.335 | + | 95.0385i | −0.296298 | + | 0.107753i | ||||
\(883\) | 109.056 | − | 109.056i | 0.123507 | − | 0.123507i | −0.642652 | − | 0.766158i | \(-0.722166\pi\) |
0.766158 | + | 0.642652i | \(0.222166\pi\) | |||||||
\(884\) | 40.4483 | − | 325.866i | 0.0457560 | − | 0.368627i | ||||
\(885\) | 347.856 | − | 347.856i | 0.393057 | − | 0.393057i | ||||
\(886\) | −356.430 | − | 174.134i | −0.402291 | − | 0.196539i | ||||
\(887\) | 1435.92 | 1.61884 | 0.809422 | − | 0.587227i | \(-0.199780\pi\) | ||||
0.809422 | + | 0.587227i | \(0.199780\pi\) | |||||||
\(888\) | −650.805 | − | 424.473i | −0.732888 | − | 0.478010i | ||||
\(889\) | 393.139 | − | 400.218i | 0.442226 | − | 0.450189i | ||||
\(890\) | −319.121 | + | 653.199i | −0.358563 | + | 0.733932i | ||||
\(891\) | −95.3792 | − | 95.3792i | −0.107047 | − | 0.107047i | ||||
\(892\) | 850.643 | + | 1091.74i | 0.953635 | + | 1.22393i | ||||
\(893\) | 1676.42 | − | 1676.42i | 1.87729 | − | 1.87729i | ||||
\(894\) | −92.2950 | − | 268.620i | −0.103238 | − | 0.300470i | ||||
\(895\) | − | 980.739i | − | 1.09580i | ||||||
\(896\) | 895.580 | + | 27.4195i | 0.999532 | + | 0.0306021i | ||||
\(897\) | 299.330 | 0.333702 | ||||||||
\(898\) | −1134.70 | + | 389.870i | −1.26358 | + | 0.434153i | ||||
\(899\) | −185.268 | − | 185.268i | −0.206082 | − | 0.206082i | ||||
\(900\) | 33.9930 | − | 26.4860i | 0.0377700 | − | 0.0294289i | ||||
\(901\) | 376.266 | − | 376.266i | 0.417609 | − | 0.417609i | ||||
\(902\) | −66.2853 | − | 32.3837i | −0.0734870 | − | 0.0359021i | ||||
\(903\) | −893.679 | − | 877.872i | −0.989677 | − | 0.972172i | ||||
\(904\) | −617.768 | + | 947.167i | −0.683372 | + | 1.04775i | ||||
\(905\) | 1272.47i | 1.40605i | ||||||||
\(906\) | −75.3033 | + | 154.136i | −0.0831162 | + | 0.170128i | ||||
\(907\) | 726.879 | + | 726.879i | 0.801410 | + | 0.801410i | 0.983316 | − | 0.181906i | \(-0.0582265\pi\) |
−0.181906 | + | 0.983316i | \(0.558227\pi\) | |||||||
\(908\) | −1061.03 | − | 131.701i | −1.16854 | − | 0.145045i | ||||
\(909\) | −383.954 | − | 383.954i | −0.422392 | − | 0.422392i | ||||
\(910\) | −238.596 | + | 499.628i | −0.262193 | + | 0.549042i | ||||
\(911\) | −474.695 | −0.521070 | −0.260535 | − | 0.965464i | \(-0.583899\pi\) | ||||
−0.260535 | + | 0.965464i | \(0.583899\pi\) | |||||||
\(912\) | −1373.02 | − | 346.187i | −1.50550 | − | 0.379591i | ||||
\(913\) | 244.427i | 0.267718i | ||||||||
\(914\) | −362.364 | − | 1054.64i | −0.396460 | − | 1.15388i | ||||
\(915\) | −137.113 | − | 137.113i | −0.149850 | − | 0.149850i | ||||
\(916\) | 105.314 | − | 848.448i | 0.114972 | − | 0.926254i | ||||
\(917\) | −891.275 | + | 7.95254i | −0.971946 | + | 0.00867235i | ||||
\(918\) | 504.734 | + | 246.588i | 0.549819 | + | 0.268614i | ||||
\(919\) | − | 947.682i | − | 1.03121i | −0.856827 | − | 0.515605i | \(-0.827567\pi\) | ||
0.856827 | − | 0.515605i | \(-0.172433\pi\) | |||||||
\(920\) | 506.088 | − | 106.525i | 0.550096 | − | 0.115788i | ||||
\(921\) | − | 111.090i | − | 0.120619i | ||||||
\(922\) | 1226.44 | + | 599.178i | 1.33019 | + | 0.649867i | ||||
\(923\) | 423.676 | − | 423.676i | 0.459021 | − | 0.459021i | ||||
\(924\) | −196.459 | − | 22.6076i | −0.212618 | − | 0.0244671i | ||||
\(925\) | −105.038 | + | 105.038i | −0.113554 | + | 0.113554i | ||||
\(926\) | −617.819 | + | 212.276i | −0.667191 | + | 0.229240i | ||||
\(927\) | 216.675i | 0.233738i | ||||||||
\(928\) | 387.753 | + | 327.551i | 0.417837 | + | 0.352965i | ||||
\(929\) | 448.957i | 0.483269i | 0.970367 | + | 0.241634i | \(0.0776834\pi\) | ||||
−0.970367 | + | 0.241634i | \(0.922317\pi\) | |||||||
\(930\) | −122.708 | − | 357.136i | −0.131944 | − | 0.384017i | ||||
\(931\) | 1212.98 | − | 1257.07i | 1.30288 | − | 1.35023i | ||||
\(932\) | 25.8353 | + | 33.1579i | 0.0277203 | + | 0.0355771i | ||||
\(933\) | 877.321 | + | 877.321i | 0.940323 | + | 0.940323i | ||||
\(934\) | −543.716 | − | 265.633i | −0.582138 | − | 0.284404i | ||||
\(935\) | 125.219i | 0.133924i | ||||||||
\(936\) | −40.1577 | − | 190.785i | −0.0429036 | − | 0.203830i | ||||
\(937\) | 857.680 | 0.915347 | 0.457674 | − | 0.889120i | \(-0.348683\pi\) | ||||
0.457674 | + | 0.889120i | \(0.348683\pi\) | |||||||
\(938\) | −128.901 | − | 364.543i | −0.137421 | − | 0.388639i | ||||
\(939\) | 92.5980 | + | 92.5980i | 0.0986134 | + | 0.0986134i | ||||
\(940\) | −1215.56 | − | 150.882i | −1.29315 | − | 0.160513i | ||||
\(941\) | −151.657 | − | 151.657i | −0.161166 | − | 0.161166i | 0.621917 | − | 0.783083i | \(-0.286354\pi\) |
−0.783083 | + | 0.621917i | \(0.786354\pi\) | |||||||
\(942\) | −39.2447 | − | 114.220i | −0.0416611 | − | 0.121253i | ||||
\(943\) | 182.021i | 0.193023i | ||||||||
\(944\) | 353.086 | + | 591.165i | 0.374031 | + | 0.626234i | ||||
\(945\) | −675.715 | − | 663.764i | −0.715043 | − | 0.702395i | ||||
\(946\) | 133.295 | + | 387.949i | 0.140904 | + | 0.410094i | ||||
\(947\) | 908.719 | − | 908.719i | 0.959577 | − | 0.959577i | −0.0396372 | − | 0.999214i | \(-0.512620\pi\) |
0.999214 | + | 0.0396372i | \(0.0126202\pi\) | |||||||
\(948\) | −657.809 | − | 81.6508i | −0.693891 | − | 0.0861295i | ||||
\(949\) | −870.434 | − | 870.434i | −0.917212 | − | 0.917212i | ||||
\(950\) | −118.831 | + | 243.232i | −0.125086 | + | 0.256034i | ||||
\(951\) | −765.648 | −0.805097 | ||||||||
\(952\) | 522.774 | − | 114.917i | 0.549133 | − | 0.120712i | ||||
\(953\) | − | 844.182i | − | 0.885815i | −0.896567 | − | 0.442908i | \(-0.853947\pi\) | ||
0.896567 | − | 0.442908i | \(-0.146053\pi\) | |||||||
\(954\) | 138.688 | − | 283.876i | 0.145375 | − | 0.297564i | ||||
\(955\) | 192.653 | − | 192.653i | 0.201731 | − | 0.201731i | ||||
\(956\) | −1143.27 | + | 890.792i | −1.19589 | + | 0.931790i | ||||
\(957\) | −79.2164 | − | 79.2164i | −0.0827758 | − | 0.0827758i | ||||
\(958\) | −284.394 | − | 827.716i | −0.296862 | − | 0.864004i | ||||
\(959\) | −1263.80 | − | 1241.45i | −1.31784 | − | 1.29453i | ||||
\(960\) | 294.908 | + | 669.500i | 0.307195 | + | 0.697396i | ||||
\(961\) | 688.157 | 0.716084 | ||||||||
\(962\) | 218.382 | + | 635.589i | 0.227008 | + | 0.660696i | ||||
\(963\) | 175.541 | − | 175.541i | 0.182285 | − | 0.182285i | ||||
\(964\) | −893.304 | − | 1146.49i | −0.926663 | − | 1.18931i | ||||
\(965\) | −621.668 | + | 621.668i | −0.644215 | + | 0.644215i | ||||
\(966\) | 162.659 | + | 460.014i | 0.168384 | + | 0.476205i | ||||
\(967\) | 1481.66i | 1.53223i | 0.642705 | + | 0.766114i | \(0.277812\pi\) | ||||
−0.642705 | + | 0.766114i | \(0.722188\pi\) | |||||||
\(968\) | −756.548 | − | 493.442i | −0.781558 | − | 0.509754i | ||||
\(969\) | −845.890 | −0.872952 | ||||||||
\(970\) | 293.651 | + | 143.463i | 0.302733 | + | 0.147900i | ||||
\(971\) | 736.360 | − | 736.360i | 0.758352 | − | 0.758352i | −0.217671 | − | 0.976022i | \(-0.569846\pi\) |
0.976022 | + | 0.217671i | \(0.0698458\pi\) | |||||||
\(972\) | 582.647 | + | 72.3214i | 0.599432 | + | 0.0744047i | ||||
\(973\) | 4.35088 | + | 487.621i | 0.00447161 | + | 0.501152i | ||||
\(974\) | 442.926 | + | 1289.11i | 0.454749 | + | 1.32353i | ||||
\(975\) | 80.9488 | 0.0830244 | ||||||||
\(976\) | 233.017 | − | 139.174i | 0.238747 | − | 0.142597i | ||||
\(977\) | 736.267 | 0.753600 | 0.376800 | − | 0.926295i | \(-0.377024\pi\) | ||||
0.376800 | + | 0.926295i | \(0.377024\pi\) | |||||||
\(978\) | 258.823 | − | 88.9288i | 0.264645 | − | 0.0909293i | ||||
\(979\) | 158.808 | + | 158.808i | 0.162215 | + | 0.162215i | ||||
\(980\) | −897.490 | − | 95.1732i | −0.915806 | − | 0.0971155i | ||||
\(981\) | 270.972 | + | 270.972i | 0.276221 | + | 0.276221i | ||||
\(982\) | 824.951 | + | 403.030i | 0.840072 | + | 0.410417i | ||||
\(983\) | −564.432 | −0.574194 | −0.287097 | − | 0.957902i | \(-0.592690\pi\) | ||||
−0.287097 | + | 0.957902i | \(0.592690\pi\) | |||||||
\(984\) | −251.957 | + | 53.0335i | −0.256053 | + | 0.0538958i | ||||
\(985\) | 930.581 | 0.944752 | ||||||||
\(986\) | 272.447 | + | 133.104i | 0.276316 | + | 0.134994i | ||||
\(987\) | −10.3107 | − | 1155.56i | −0.0104465 | − | 1.17078i | ||||
\(988\) | 752.759 | + | 966.115i | 0.761902 | + | 0.977849i | ||||
\(989\) | 715.672 | − | 715.672i | 0.723632 | − | 0.723632i | ||||
\(990\) | 24.1589 | + | 70.3133i | 0.0244029 | + | 0.0710235i | ||||
\(991\) | −715.833 | −0.722334 | −0.361167 | − | 0.932501i | \(-0.617622\pi\) | ||||
−0.361167 | + | 0.932501i | \(0.617622\pi\) | |||||||
\(992\) | 526.713 | − | 44.3294i | 0.530960 | − | 0.0446869i | ||||
\(993\) | 71.7989i | 0.0723051i | ||||||||
\(994\) | 881.340 | + | 420.880i | 0.886660 | + | 0.423421i | ||||
\(995\) | 452.552 | − | 452.552i | 0.454826 | − | 0.454826i | ||||
\(996\) | 524.322 | + | 672.932i | 0.526428 | + | 0.675634i | ||||
\(997\) | −892.876 | + | 892.876i | −0.895562 | + | 0.895562i | −0.995040 | − | 0.0994775i | \(-0.968283\pi\) |
0.0994775 | + | 0.995040i | \(0.468283\pi\) | |||||||
\(998\) | 29.0259 | − | 59.4123i | 0.0290841 | − | 0.0595314i | ||||
\(999\) | −1149.72 | −1.15087 |
(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 | 112.3.l.b.69.25 | yes | 56 | |
4.3 | odd | 2 | 448.3.l.b.433.19 | 56 | |||
7.6 | odd | 2 | inner | 112.3.l.b.69.26 | yes | 56 | |
16.3 | odd | 4 | 448.3.l.b.209.10 | 56 | |||
16.13 | even | 4 | inner | 112.3.l.b.13.26 | yes | 56 | |
28.27 | even | 2 | 448.3.l.b.433.10 | 56 | |||
112.13 | odd | 4 | inner | 112.3.l.b.13.25 | ✓ | 56 | |
112.83 | even | 4 | 448.3.l.b.209.19 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.l.b.13.25 | ✓ | 56 | 112.13 | odd | 4 | inner | |
112.3.l.b.13.26 | yes | 56 | 16.13 | even | 4 | inner | |
112.3.l.b.69.25 | yes | 56 | 1.1 | even | 1 | trivial | |
112.3.l.b.69.26 | yes | 56 | 7.6 | odd | 2 | inner | |
448.3.l.b.209.10 | 56 | 16.3 | odd | 4 | |||
448.3.l.b.209.19 | 56 | 112.83 | even | 4 | |||
448.3.l.b.433.10 | 56 | 28.27 | even | 2 | |||
448.3.l.b.433.19 | 56 | 4.3 | odd | 2 |