Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
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: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44897 | −1.02458 | −0.512290 | − | 0.858813i | \(-0.671203\pi\) | ||||
−0.512290 | + | 0.858813i | \(0.671203\pi\) | |||||||
\(3\) | −0.334420 | −0.193078 | −0.0965388 | − | 0.995329i | \(-0.530777\pi\) | ||||
−0.0965388 | + | 0.995329i | \(0.530777\pi\) | |||||||
\(4\) | 0.0995284 | 0.0497642 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.484566 | 0.197823 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.75374 | 0.973593 | ||||||||
\(9\) | −2.88816 | −0.962721 | ||||||||
\(10\) | 1.44897 | 0.458206 | ||||||||
\(11\) | 1.28070 | 0.386146 | 0.193073 | − | 0.981184i | \(-0.438155\pi\) | ||||
0.193073 | + | 0.981184i | \(0.438155\pi\) | |||||||
\(12\) | −0.0332843 | −0.00960835 | ||||||||
\(13\) | −2.76676 | −0.767361 | −0.383680 | − | 0.923466i | \(-0.625344\pi\) | ||||
−0.383680 | + | 0.923466i | \(0.625344\pi\) | |||||||
\(14\) | 1.44897 | 0.387255 | ||||||||
\(15\) | 0.334420 | 0.0863469 | ||||||||
\(16\) | −4.18915 | −1.04729 | ||||||||
\(17\) | −5.48093 | −1.32932 | −0.664660 | − | 0.747146i | \(-0.731424\pi\) | ||||
−0.664660 | + | 0.747146i | \(0.731424\pi\) | |||||||
\(18\) | 4.18488 | 0.986385 | ||||||||
\(19\) | 2.60890 | 0.598523 | 0.299262 | − | 0.954171i | \(-0.403260\pi\) | ||||
0.299262 | + | 0.954171i | \(0.403260\pi\) | |||||||
\(20\) | −0.0995284 | −0.0222552 | ||||||||
\(21\) | 0.334420 | 0.0729765 | ||||||||
\(22\) | −1.85570 | −0.395637 | ||||||||
\(23\) | −6.54731 | −1.36521 | −0.682604 | − | 0.730789i | \(-0.739153\pi\) | ||||
−0.682604 | + | 0.730789i | \(0.739153\pi\) | |||||||
\(24\) | −0.920905 | −0.187979 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.00896 | 0.786222 | ||||||||
\(27\) | 1.96912 | 0.378957 | ||||||||
\(28\) | −0.0995284 | −0.0188091 | ||||||||
\(29\) | −7.08572 | −1.31579 | −0.657893 | − | 0.753112i | \(-0.728552\pi\) | ||||
−0.657893 | + | 0.753112i | \(0.728552\pi\) | |||||||
\(30\) | −0.484566 | −0.0884693 | ||||||||
\(31\) | −9.08612 | −1.63192 | −0.815958 | − | 0.578112i | \(-0.803790\pi\) | ||||
−0.815958 | + | 0.578112i | \(0.803790\pi\) | |||||||
\(32\) | 0.562503 | 0.0994374 | ||||||||
\(33\) | −0.428292 | −0.0745561 | ||||||||
\(34\) | 7.94173 | 1.36200 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.287454 | −0.0479090 | ||||||||
\(37\) | −5.27324 | −0.866915 | −0.433458 | − | 0.901174i | \(-0.642707\pi\) | ||||
−0.433458 | + | 0.901174i | \(0.642707\pi\) | |||||||
\(38\) | −3.78024 | −0.613235 | ||||||||
\(39\) | 0.925260 | 0.148160 | ||||||||
\(40\) | −2.75374 | −0.435404 | ||||||||
\(41\) | −3.98210 | −0.621899 | −0.310950 | − | 0.950426i | \(-0.600647\pi\) | ||||
−0.310950 | + | 0.950426i | \(0.600647\pi\) | |||||||
\(42\) | −0.484566 | −0.0747702 | ||||||||
\(43\) | 4.75514 | 0.725152 | 0.362576 | − | 0.931954i | \(-0.381897\pi\) | ||||
0.362576 | + | 0.931954i | \(0.381897\pi\) | |||||||
\(44\) | 0.127466 | 0.0192162 | ||||||||
\(45\) | 2.88816 | 0.430542 | ||||||||
\(46\) | 9.48688 | 1.39876 | ||||||||
\(47\) | 10.9570 | 1.59825 | 0.799123 | − | 0.601168i | \(-0.205298\pi\) | ||||
0.799123 | + | 0.601168i | \(0.205298\pi\) | |||||||
\(48\) | 1.40094 | 0.202208 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.44897 | −0.204916 | ||||||||
\(51\) | 1.83293 | 0.256662 | ||||||||
\(52\) | −0.275371 | −0.0381871 | ||||||||
\(53\) | −11.4309 | −1.57016 | −0.785078 | − | 0.619396i | \(-0.787377\pi\) | ||||
−0.785078 | + | 0.619396i | \(0.787377\pi\) | |||||||
\(54\) | −2.85321 | −0.388272 | ||||||||
\(55\) | −1.28070 | −0.172690 | ||||||||
\(56\) | −2.75374 | −0.367983 | ||||||||
\(57\) | −0.872470 | −0.115561 | ||||||||
\(58\) | 10.2670 | 1.34813 | ||||||||
\(59\) | −8.15041 | −1.06109 | −0.530547 | − | 0.847656i | \(-0.678013\pi\) | ||||
−0.530547 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(60\) | 0.0332843 | 0.00429698 | ||||||||
\(61\) | −14.6321 | −1.87345 | −0.936726 | − | 0.350063i | \(-0.886160\pi\) | ||||
−0.936726 | + | 0.350063i | \(0.886160\pi\) | |||||||
\(62\) | 13.1656 | 1.67203 | ||||||||
\(63\) | 2.88816 | 0.363874 | ||||||||
\(64\) | 7.56325 | 0.945406 | ||||||||
\(65\) | 2.76676 | 0.343174 | ||||||||
\(66\) | 0.620585 | 0.0763887 | ||||||||
\(67\) | 1.19958 | 0.146551 | 0.0732757 | − | 0.997312i | \(-0.476655\pi\) | ||||
0.0732757 | + | 0.997312i | \(0.476655\pi\) | |||||||
\(68\) | −0.545508 | −0.0661526 | ||||||||
\(69\) | 2.18955 | 0.263591 | ||||||||
\(70\) | −1.44897 | −0.173186 | ||||||||
\(71\) | 8.09731 | 0.960974 | 0.480487 | − | 0.877002i | \(-0.340460\pi\) | ||||
0.480487 | + | 0.877002i | \(0.340460\pi\) | |||||||
\(72\) | −7.95324 | −0.937298 | ||||||||
\(73\) | 14.8891 | 1.74264 | 0.871320 | − | 0.490715i | \(-0.163264\pi\) | ||||
0.871320 | + | 0.490715i | \(0.163264\pi\) | |||||||
\(74\) | 7.64079 | 0.888224 | ||||||||
\(75\) | −0.334420 | −0.0386155 | ||||||||
\(76\) | 0.259660 | 0.0297850 | ||||||||
\(77\) | −1.28070 | −0.145949 | ||||||||
\(78\) | −1.34068 | −0.151802 | ||||||||
\(79\) | −11.2918 | −1.27043 | −0.635216 | − | 0.772334i | \(-0.719089\pi\) | ||||
−0.635216 | + | 0.772334i | \(0.719089\pi\) | |||||||
\(80\) | 4.18915 | 0.468361 | ||||||||
\(81\) | 8.00598 | 0.889553 | ||||||||
\(82\) | 5.76996 | 0.637185 | ||||||||
\(83\) | −14.2236 | −1.56125 | −0.780623 | − | 0.625002i | \(-0.785098\pi\) | ||||
−0.780623 | + | 0.625002i | \(0.785098\pi\) | |||||||
\(84\) | 0.0332843 | 0.00363161 | ||||||||
\(85\) | 5.48093 | 0.594490 | ||||||||
\(86\) | −6.89008 | −0.742977 | ||||||||
\(87\) | 2.36961 | 0.254049 | ||||||||
\(88\) | 3.52671 | 0.375949 | ||||||||
\(89\) | 7.10603 | 0.753237 | 0.376619 | − | 0.926368i | \(-0.377087\pi\) | ||||
0.376619 | + | 0.926368i | \(0.377087\pi\) | |||||||
\(90\) | −4.18488 | −0.441125 | ||||||||
\(91\) | 2.76676 | 0.290035 | ||||||||
\(92\) | −0.651643 | −0.0679385 | ||||||||
\(93\) | 3.03858 | 0.315086 | ||||||||
\(94\) | −15.8764 | −1.63753 | ||||||||
\(95\) | −2.60890 | −0.267668 | ||||||||
\(96\) | −0.188112 | −0.0191991 | ||||||||
\(97\) | −9.93147 | −1.00839 | −0.504194 | − | 0.863590i | \(-0.668210\pi\) | ||||
−0.504194 | + | 0.863590i | \(0.668210\pi\) | |||||||
\(98\) | −1.44897 | −0.146369 | ||||||||
\(99\) | −3.69887 | −0.371751 | ||||||||
\(100\) | 0.0995284 | 0.00995284 | ||||||||
\(101\) | −7.35364 | −0.731714 | −0.365857 | − | 0.930671i | \(-0.619224\pi\) | ||||
−0.365857 | + | 0.930671i | \(0.619224\pi\) | |||||||
\(102\) | −2.65587 | −0.262971 | ||||||||
\(103\) | 3.52525 | 0.347353 | 0.173676 | − | 0.984803i | \(-0.444435\pi\) | ||||
0.173676 | + | 0.984803i | \(0.444435\pi\) | |||||||
\(104\) | −7.61892 | −0.747097 | ||||||||
\(105\) | −0.334420 | −0.0326361 | ||||||||
\(106\) | 16.5631 | 1.60875 | ||||||||
\(107\) | −17.2285 | −1.66554 | −0.832770 | − | 0.553619i | \(-0.813246\pi\) | ||||
−0.832770 | + | 0.553619i | \(0.813246\pi\) | |||||||
\(108\) | 0.195983 | 0.0188585 | ||||||||
\(109\) | −4.63683 | −0.444128 | −0.222064 | − | 0.975032i | \(-0.571279\pi\) | ||||
−0.222064 | + | 0.975032i | \(0.571279\pi\) | |||||||
\(110\) | 1.85570 | 0.176934 | ||||||||
\(111\) | 1.76348 | 0.167382 | ||||||||
\(112\) | 4.18915 | 0.395838 | ||||||||
\(113\) | 13.9686 | 1.31406 | 0.657029 | − | 0.753865i | \(-0.271813\pi\) | ||||
0.657029 | + | 0.753865i | \(0.271813\pi\) | |||||||
\(114\) | 1.26419 | 0.118402 | ||||||||
\(115\) | 6.54731 | 0.610540 | ||||||||
\(116\) | −0.705230 | −0.0654790 | ||||||||
\(117\) | 7.99085 | 0.738754 | ||||||||
\(118\) | 11.8097 | 1.08717 | ||||||||
\(119\) | 5.48093 | 0.502436 | ||||||||
\(120\) | 0.920905 | 0.0840667 | ||||||||
\(121\) | −9.35980 | −0.850891 | ||||||||
\(122\) | 21.2016 | 1.91950 | ||||||||
\(123\) | 1.33169 | 0.120075 | ||||||||
\(124\) | −0.904327 | −0.0812109 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.18488 | −0.372818 | ||||||||
\(127\) | −3.23631 | −0.287176 | −0.143588 | − | 0.989638i | \(-0.545864\pi\) | ||||
−0.143588 | + | 0.989638i | \(0.545864\pi\) | |||||||
\(128\) | −12.0840 | −1.06808 | ||||||||
\(129\) | −1.59022 | −0.140011 | ||||||||
\(130\) | −4.00896 | −0.351609 | ||||||||
\(131\) | −0.438322 | −0.0382964 | −0.0191482 | − | 0.999817i | \(-0.506095\pi\) | ||||
−0.0191482 | + | 0.999817i | \(0.506095\pi\) | |||||||
\(132\) | −0.0426272 | −0.00371023 | ||||||||
\(133\) | −2.60890 | −0.226221 | ||||||||
\(134\) | −1.73815 | −0.150154 | ||||||||
\(135\) | −1.96912 | −0.169475 | ||||||||
\(136\) | −15.0930 | −1.29422 | ||||||||
\(137\) | −19.0566 | −1.62812 | −0.814059 | − | 0.580782i | \(-0.802747\pi\) | ||||
−0.814059 | + | 0.580782i | \(0.802747\pi\) | |||||||
\(138\) | −3.17261 | −0.270070 | ||||||||
\(139\) | 7.63665 | 0.647732 | 0.323866 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323866 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(140\) | 0.0995284 | 0.00841168 | ||||||||
\(141\) | −3.66425 | −0.308585 | ||||||||
\(142\) | −11.7328 | −0.984595 | ||||||||
\(143\) | −3.54339 | −0.296313 | ||||||||
\(144\) | 12.0990 | 1.00825 | ||||||||
\(145\) | 7.08572 | 0.588437 | ||||||||
\(146\) | −21.5740 | −1.78547 | ||||||||
\(147\) | −0.334420 | −0.0275825 | ||||||||
\(148\) | −0.524837 | −0.0431413 | ||||||||
\(149\) | −3.89493 | −0.319085 | −0.159542 | − | 0.987191i | \(-0.551002\pi\) | ||||
−0.159542 | + | 0.987191i | \(0.551002\pi\) | |||||||
\(150\) | 0.484566 | 0.0395647 | ||||||||
\(151\) | −16.0726 | −1.30797 | −0.653985 | − | 0.756507i | \(-0.726904\pi\) | ||||
−0.653985 | + | 0.756507i | \(0.726904\pi\) | |||||||
\(152\) | 7.18423 | 0.582718 | ||||||||
\(153\) | 15.8298 | 1.27977 | ||||||||
\(154\) | 1.85570 | 0.149537 | ||||||||
\(155\) | 9.08612 | 0.729815 | ||||||||
\(156\) | 0.0920896 | 0.00737307 | ||||||||
\(157\) | −15.0373 | −1.20011 | −0.600053 | − | 0.799960i | \(-0.704854\pi\) | ||||
−0.600053 | + | 0.799960i | \(0.704854\pi\) | |||||||
\(158\) | 16.3616 | 1.30166 | ||||||||
\(159\) | 3.82273 | 0.303162 | ||||||||
\(160\) | −0.562503 | −0.0444698 | ||||||||
\(161\) | 6.54731 | 0.516000 | ||||||||
\(162\) | −11.6005 | −0.911418 | ||||||||
\(163\) | 23.2829 | 1.82366 | 0.911830 | − | 0.410568i | \(-0.134670\pi\) | ||||
0.911830 | + | 0.410568i | \(0.134670\pi\) | |||||||
\(164\) | −0.396332 | −0.0309483 | ||||||||
\(165\) | 0.428292 | 0.0333425 | ||||||||
\(166\) | 20.6097 | 1.59962 | ||||||||
\(167\) | 0.502309 | 0.0388698 | 0.0194349 | − | 0.999811i | \(-0.493813\pi\) | ||||
0.0194349 | + | 0.999811i | \(0.493813\pi\) | |||||||
\(168\) | 0.920905 | 0.0710493 | ||||||||
\(169\) | −5.34505 | −0.411157 | ||||||||
\(170\) | −7.94173 | −0.609103 | ||||||||
\(171\) | −7.53494 | −0.576211 | ||||||||
\(172\) | 0.473272 | 0.0360866 | ||||||||
\(173\) | −25.0670 | −1.90581 | −0.952905 | − | 0.303269i | \(-0.901922\pi\) | ||||
−0.952905 | + | 0.303269i | \(0.901922\pi\) | |||||||
\(174\) | −3.43350 | −0.260293 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −5.36505 | −0.404406 | ||||||||
\(177\) | 2.72566 | 0.204873 | ||||||||
\(178\) | −10.2965 | −0.771752 | ||||||||
\(179\) | 22.5898 | 1.68844 | 0.844222 | − | 0.535993i | \(-0.180063\pi\) | ||||
0.844222 | + | 0.535993i | \(0.180063\pi\) | |||||||
\(180\) | 0.287454 | 0.0214256 | ||||||||
\(181\) | −15.7216 | −1.16858 | −0.584289 | − | 0.811546i | \(-0.698627\pi\) | ||||
−0.584289 | + | 0.811546i | \(0.698627\pi\) | |||||||
\(182\) | −4.00896 | −0.297164 | ||||||||
\(183\) | 4.89328 | 0.361722 | ||||||||
\(184\) | −18.0296 | −1.32916 | ||||||||
\(185\) | 5.27324 | 0.387696 | ||||||||
\(186\) | −4.40283 | −0.322831 | ||||||||
\(187\) | −7.01943 | −0.513312 | ||||||||
\(188\) | 1.09053 | 0.0795354 | ||||||||
\(189\) | −1.96912 | −0.143232 | ||||||||
\(190\) | 3.78024 | 0.274247 | ||||||||
\(191\) | 10.9594 | 0.792991 | 0.396496 | − | 0.918037i | \(-0.370226\pi\) | ||||
0.396496 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(192\) | −2.52930 | −0.182537 | ||||||||
\(193\) | −13.0071 | −0.936272 | −0.468136 | − | 0.883656i | \(-0.655074\pi\) | ||||
−0.468136 | + | 0.883656i | \(0.655074\pi\) | |||||||
\(194\) | 14.3905 | 1.03317 | ||||||||
\(195\) | −0.925260 | −0.0662592 | ||||||||
\(196\) | 0.0995284 | 0.00710917 | ||||||||
\(197\) | 8.24681 | 0.587561 | 0.293780 | − | 0.955873i | \(-0.405087\pi\) | ||||
0.293780 | + | 0.955873i | \(0.405087\pi\) | |||||||
\(198\) | 5.35958 | 0.380888 | ||||||||
\(199\) | 0.954882 | 0.0676898 | 0.0338449 | − | 0.999427i | \(-0.489225\pi\) | ||||
0.0338449 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(200\) | 2.75374 | 0.194719 | ||||||||
\(201\) | −0.401162 | −0.0282958 | ||||||||
\(202\) | 10.6552 | 0.749700 | ||||||||
\(203\) | 7.08572 | 0.497320 | ||||||||
\(204\) | 0.182429 | 0.0127726 | ||||||||
\(205\) | 3.98210 | 0.278122 | ||||||||
\(206\) | −5.10799 | −0.355891 | ||||||||
\(207\) | 18.9097 | 1.31431 | ||||||||
\(208\) | 11.5904 | 0.803647 | ||||||||
\(209\) | 3.34123 | 0.231117 | ||||||||
\(210\) | 0.484566 | 0.0334383 | ||||||||
\(211\) | −10.5900 | −0.729045 | −0.364522 | − | 0.931195i | \(-0.618768\pi\) | ||||
−0.364522 | + | 0.931195i | \(0.618768\pi\) | |||||||
\(212\) | −1.13770 | −0.0781376 | ||||||||
\(213\) | −2.70790 | −0.185543 | ||||||||
\(214\) | 24.9636 | 1.70648 | ||||||||
\(215\) | −4.75514 | −0.324298 | ||||||||
\(216\) | 5.42244 | 0.368950 | ||||||||
\(217\) | 9.08612 | 0.616806 | ||||||||
\(218\) | 6.71865 | 0.455045 | ||||||||
\(219\) | −4.97922 | −0.336465 | ||||||||
\(220\) | −0.127466 | −0.00859376 | ||||||||
\(221\) | 15.1644 | 1.02007 | ||||||||
\(222\) | −2.55523 | −0.171496 | ||||||||
\(223\) | 21.5634 | 1.44399 | 0.721997 | − | 0.691897i | \(-0.243225\pi\) | ||||
0.721997 | + | 0.691897i | \(0.243225\pi\) | |||||||
\(224\) | −0.562503 | −0.0375838 | ||||||||
\(225\) | −2.88816 | −0.192544 | ||||||||
\(226\) | −20.2402 | −1.34636 | ||||||||
\(227\) | 2.83245 | 0.187996 | 0.0939982 | − | 0.995572i | \(-0.470035\pi\) | ||||
0.0939982 | + | 0.995572i | \(0.470035\pi\) | |||||||
\(228\) | −0.0868355 | −0.00575082 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −9.48688 | −0.625547 | ||||||||
\(231\) | 0.428292 | 0.0281796 | ||||||||
\(232\) | −19.5122 | −1.28104 | ||||||||
\(233\) | 4.36674 | 0.286075 | 0.143037 | − | 0.989717i | \(-0.454313\pi\) | ||||
0.143037 | + | 0.989717i | \(0.454313\pi\) | |||||||
\(234\) | −11.5785 | −0.756913 | ||||||||
\(235\) | −10.9570 | −0.714757 | ||||||||
\(236\) | −0.811197 | −0.0528044 | ||||||||
\(237\) | 3.77622 | 0.245292 | ||||||||
\(238\) | −7.94173 | −0.514786 | ||||||||
\(239\) | −7.43132 | −0.480692 | −0.240346 | − | 0.970687i | \(-0.577261\pi\) | ||||
−0.240346 | + | 0.970687i | \(0.577261\pi\) | |||||||
\(240\) | −1.40094 | −0.0904301 | ||||||||
\(241\) | −30.3116 | −1.95254 | −0.976270 | − | 0.216556i | \(-0.930518\pi\) | ||||
−0.976270 | + | 0.216556i | \(0.930518\pi\) | |||||||
\(242\) | 13.5621 | 0.871806 | ||||||||
\(243\) | −8.58472 | −0.550710 | ||||||||
\(244\) | −1.45631 | −0.0932308 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −1.92959 | −0.123026 | ||||||||
\(247\) | −7.21821 | −0.459283 | ||||||||
\(248\) | −25.0208 | −1.58882 | ||||||||
\(249\) | 4.75667 | 0.301442 | ||||||||
\(250\) | 1.44897 | 0.0916412 | ||||||||
\(251\) | 7.54658 | 0.476336 | 0.238168 | − | 0.971224i | \(-0.423453\pi\) | ||||
0.238168 | + | 0.971224i | \(0.423453\pi\) | |||||||
\(252\) | 0.287454 | 0.0181079 | ||||||||
\(253\) | −8.38514 | −0.527170 | ||||||||
\(254\) | 4.68933 | 0.294234 | ||||||||
\(255\) | −1.83293 | −0.114783 | ||||||||
\(256\) | 2.38286 | 0.148929 | ||||||||
\(257\) | −25.5149 | −1.59158 | −0.795788 | − | 0.605576i | \(-0.792943\pi\) | ||||
−0.795788 | + | 0.605576i | \(0.792943\pi\) | |||||||
\(258\) | 2.30418 | 0.143452 | ||||||||
\(259\) | 5.27324 | 0.327663 | ||||||||
\(260\) | 0.275371 | 0.0170778 | ||||||||
\(261\) | 20.4647 | 1.26673 | ||||||||
\(262\) | 0.635118 | 0.0392377 | ||||||||
\(263\) | 0.118886 | 0.00733085 | 0.00366542 | − | 0.999993i | \(-0.498833\pi\) | ||||
0.00366542 | + | 0.999993i | \(0.498833\pi\) | |||||||
\(264\) | −1.17940 | −0.0725873 | ||||||||
\(265\) | 11.4309 | 0.702196 | ||||||||
\(266\) | 3.78024 | 0.231781 | ||||||||
\(267\) | −2.37640 | −0.145433 | ||||||||
\(268\) | 0.119392 | 0.00729301 | ||||||||
\(269\) | −17.7563 | −1.08262 | −0.541311 | − | 0.840822i | \(-0.682072\pi\) | ||||
−0.541311 | + | 0.840822i | \(0.682072\pi\) | |||||||
\(270\) | 2.85321 | 0.173641 | ||||||||
\(271\) | −28.5012 | −1.73133 | −0.865663 | − | 0.500627i | \(-0.833103\pi\) | ||||
−0.865663 | + | 0.500627i | \(0.833103\pi\) | |||||||
\(272\) | 22.9604 | 1.39218 | ||||||||
\(273\) | −0.925260 | −0.0559993 | ||||||||
\(274\) | 27.6126 | 1.66814 | ||||||||
\(275\) | 1.28070 | 0.0772292 | ||||||||
\(276\) | 0.217923 | 0.0131174 | ||||||||
\(277\) | −6.13518 | −0.368627 | −0.184313 | − | 0.982868i | \(-0.559006\pi\) | ||||
−0.184313 | + | 0.982868i | \(0.559006\pi\) | |||||||
\(278\) | −11.0653 | −0.663654 | ||||||||
\(279\) | 26.2422 | 1.57108 | ||||||||
\(280\) | 2.75374 | 0.164567 | ||||||||
\(281\) | −2.81507 | −0.167933 | −0.0839664 | − | 0.996469i | \(-0.526759\pi\) | ||||
−0.0839664 | + | 0.996469i | \(0.526759\pi\) | |||||||
\(282\) | 5.30940 | 0.316170 | ||||||||
\(283\) | 21.6921 | 1.28946 | 0.644732 | − | 0.764409i | \(-0.276969\pi\) | ||||
0.644732 | + | 0.764409i | \(0.276969\pi\) | |||||||
\(284\) | 0.805912 | 0.0478221 | ||||||||
\(285\) | 0.872470 | 0.0516807 | ||||||||
\(286\) | 5.13428 | 0.303597 | ||||||||
\(287\) | 3.98210 | 0.235056 | ||||||||
\(288\) | −1.62460 | −0.0957305 | ||||||||
\(289\) | 13.0406 | 0.767094 | ||||||||
\(290\) | −10.2670 | −0.602901 | ||||||||
\(291\) | 3.32129 | 0.194697 | ||||||||
\(292\) | 1.48189 | 0.0867211 | ||||||||
\(293\) | 7.53736 | 0.440337 | 0.220169 | − | 0.975462i | \(-0.429339\pi\) | ||||
0.220169 | + | 0.975462i | \(0.429339\pi\) | |||||||
\(294\) | 0.484566 | 0.0282605 | ||||||||
\(295\) | 8.15041 | 0.474535 | ||||||||
\(296\) | −14.5211 | −0.844022 | ||||||||
\(297\) | 2.52186 | 0.146333 | ||||||||
\(298\) | 5.64365 | 0.326928 | ||||||||
\(299\) | 18.1148 | 1.04761 | ||||||||
\(300\) | −0.0332843 | −0.00192167 | ||||||||
\(301\) | −4.75514 | −0.274082 | ||||||||
\(302\) | 23.2888 | 1.34012 | ||||||||
\(303\) | 2.45920 | 0.141278 | ||||||||
\(304\) | −10.9291 | −0.626826 | ||||||||
\(305\) | 14.6321 | 0.837833 | ||||||||
\(306\) | −22.9370 | −1.31122 | ||||||||
\(307\) | 22.5849 | 1.28899 | 0.644495 | − | 0.764608i | \(-0.277067\pi\) | ||||
0.644495 | + | 0.764608i | \(0.277067\pi\) | |||||||
\(308\) | −0.127466 | −0.00726306 | ||||||||
\(309\) | −1.17891 | −0.0670660 | ||||||||
\(310\) | −13.1656 | −0.747753 | ||||||||
\(311\) | 20.1645 | 1.14342 | 0.571712 | − | 0.820454i | \(-0.306279\pi\) | ||||
0.571712 | + | 0.820454i | \(0.306279\pi\) | |||||||
\(312\) | 2.54792 | 0.144248 | ||||||||
\(313\) | 24.1799 | 1.36673 | 0.683364 | − | 0.730078i | \(-0.260516\pi\) | ||||
0.683364 | + | 0.730078i | \(0.260516\pi\) | |||||||
\(314\) | 21.7887 | 1.22961 | ||||||||
\(315\) | −2.88816 | −0.162730 | ||||||||
\(316\) | −1.12386 | −0.0632220 | ||||||||
\(317\) | −32.1807 | −1.80745 | −0.903725 | − | 0.428113i | \(-0.859178\pi\) | ||||
−0.903725 | + | 0.428113i | \(0.859178\pi\) | |||||||
\(318\) | −5.53904 | −0.310614 | ||||||||
\(319\) | −9.07469 | −0.508085 | ||||||||
\(320\) | −7.56325 | −0.422798 | ||||||||
\(321\) | 5.76155 | 0.321578 | ||||||||
\(322\) | −9.48688 | −0.528683 | ||||||||
\(323\) | −14.2992 | −0.795630 | ||||||||
\(324\) | 0.796822 | 0.0442679 | ||||||||
\(325\) | −2.76676 | −0.153472 | ||||||||
\(326\) | −33.7364 | −1.86849 | ||||||||
\(327\) | 1.55065 | 0.0857512 | ||||||||
\(328\) | −10.9656 | −0.605476 | ||||||||
\(329\) | −10.9570 | −0.604080 | ||||||||
\(330\) | −0.620585 | −0.0341621 | ||||||||
\(331\) | 17.1037 | 0.940106 | 0.470053 | − | 0.882638i | \(-0.344235\pi\) | ||||
0.470053 | + | 0.882638i | \(0.344235\pi\) | |||||||
\(332\) | −1.41566 | −0.0776942 | ||||||||
\(333\) | 15.2300 | 0.834597 | ||||||||
\(334\) | −0.727833 | −0.0398253 | ||||||||
\(335\) | −1.19958 | −0.0655398 | ||||||||
\(336\) | −1.40094 | −0.0764274 | ||||||||
\(337\) | 12.9189 | 0.703739 | 0.351869 | − | 0.936049i | \(-0.385546\pi\) | ||||
0.351869 | + | 0.936049i | \(0.385546\pi\) | |||||||
\(338\) | 7.74484 | 0.421264 | ||||||||
\(339\) | −4.67139 | −0.253715 | ||||||||
\(340\) | 0.545508 | 0.0295843 | ||||||||
\(341\) | −11.6366 | −0.630157 | ||||||||
\(342\) | 10.9179 | 0.590374 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.0944 | 0.706003 | ||||||||
\(345\) | −2.18955 | −0.117881 | ||||||||
\(346\) | 36.3215 | 1.95265 | ||||||||
\(347\) | −16.4850 | −0.884959 | −0.442480 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442480 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(348\) | 0.235843 | 0.0126425 | ||||||||
\(349\) | 18.1603 | 0.972098 | 0.486049 | − | 0.873931i | \(-0.338438\pi\) | ||||
0.486049 | + | 0.873931i | \(0.338438\pi\) | |||||||
\(350\) | 1.44897 | 0.0774510 | ||||||||
\(351\) | −5.44808 | −0.290797 | ||||||||
\(352\) | 0.720398 | 0.0383974 | ||||||||
\(353\) | 8.01974 | 0.426847 | 0.213424 | − | 0.976960i | \(-0.431539\pi\) | ||||
0.213424 | + | 0.976960i | \(0.431539\pi\) | |||||||
\(354\) | −3.94942 | −0.209909 | ||||||||
\(355\) | −8.09731 | −0.429761 | ||||||||
\(356\) | 0.707251 | 0.0374842 | ||||||||
\(357\) | −1.83293 | −0.0970091 | ||||||||
\(358\) | −32.7321 | −1.72995 | ||||||||
\(359\) | −18.2538 | −0.963399 | −0.481700 | − | 0.876336i | \(-0.659980\pi\) | ||||
−0.481700 | + | 0.876336i | \(0.659980\pi\) | |||||||
\(360\) | 7.95324 | 0.419172 | ||||||||
\(361\) | −12.1936 | −0.641770 | ||||||||
\(362\) | 22.7802 | 1.19730 | ||||||||
\(363\) | 3.13011 | 0.164288 | ||||||||
\(364\) | 0.275371 | 0.0144334 | ||||||||
\(365\) | −14.8891 | −0.779333 | ||||||||
\(366\) | −7.09024 | −0.370613 | ||||||||
\(367\) | −3.17942 | −0.165964 | −0.0829822 | − | 0.996551i | \(-0.526444\pi\) | ||||
−0.0829822 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(368\) | 27.4277 | 1.42977 | ||||||||
\(369\) | 11.5009 | 0.598715 | ||||||||
\(370\) | −7.64079 | −0.397226 | ||||||||
\(371\) | 11.4309 | 0.593464 | ||||||||
\(372\) | 0.302425 | 0.0156800 | ||||||||
\(373\) | 13.1734 | 0.682094 | 0.341047 | − | 0.940046i | \(-0.389218\pi\) | ||||
0.341047 | + | 0.940046i | \(0.389218\pi\) | |||||||
\(374\) | 10.1710 | 0.525929 | ||||||||
\(375\) | 0.334420 | 0.0172694 | ||||||||
\(376\) | 30.1727 | 1.55604 | ||||||||
\(377\) | 19.6045 | 1.00968 | ||||||||
\(378\) | 2.85321 | 0.146753 | ||||||||
\(379\) | 22.2542 | 1.14312 | 0.571560 | − | 0.820560i | \(-0.306338\pi\) | ||||
0.571560 | + | 0.820560i | \(0.306338\pi\) | |||||||
\(380\) | −0.259660 | −0.0133203 | ||||||||
\(381\) | 1.08229 | 0.0554472 | ||||||||
\(382\) | −15.8798 | −0.812483 | ||||||||
\(383\) | −4.89810 | −0.250281 | −0.125141 | − | 0.992139i | \(-0.539938\pi\) | ||||
−0.125141 | + | 0.992139i | \(0.539938\pi\) | |||||||
\(384\) | 4.04112 | 0.206223 | ||||||||
\(385\) | 1.28070 | 0.0652706 | ||||||||
\(386\) | 18.8470 | 0.959285 | ||||||||
\(387\) | −13.7336 | −0.698119 | ||||||||
\(388\) | −0.988464 | −0.0501816 | ||||||||
\(389\) | −31.6877 | −1.60663 | −0.803315 | − | 0.595554i | \(-0.796932\pi\) | ||||
−0.803315 | + | 0.595554i | \(0.796932\pi\) | |||||||
\(390\) | 1.34068 | 0.0678879 | ||||||||
\(391\) | 35.8853 | 1.81480 | ||||||||
\(392\) | 2.75374 | 0.139085 | ||||||||
\(393\) | 0.146584 | 0.00739417 | ||||||||
\(394\) | −11.9494 | −0.602003 | ||||||||
\(395\) | 11.2918 | 0.568155 | ||||||||
\(396\) | −0.368143 | −0.0184999 | ||||||||
\(397\) | −9.98880 | −0.501324 | −0.250662 | − | 0.968075i | \(-0.580648\pi\) | ||||
−0.250662 | + | 0.968075i | \(0.580648\pi\) | |||||||
\(398\) | −1.38360 | −0.0693536 | ||||||||
\(399\) | 0.872470 | 0.0436781 | ||||||||
\(400\) | −4.18915 | −0.209458 | ||||||||
\(401\) | −20.9647 | −1.04693 | −0.523464 | − | 0.852048i | \(-0.675360\pi\) | ||||
−0.523464 | + | 0.852048i | \(0.675360\pi\) | |||||||
\(402\) | 0.581274 | 0.0289913 | ||||||||
\(403\) | 25.1391 | 1.25227 | ||||||||
\(404\) | −0.731896 | −0.0364132 | ||||||||
\(405\) | −8.00598 | −0.397820 | ||||||||
\(406\) | −10.2670 | −0.509544 | ||||||||
\(407\) | −6.75344 | −0.334756 | ||||||||
\(408\) | 5.04741 | 0.249884 | ||||||||
\(409\) | −4.47431 | −0.221240 | −0.110620 | − | 0.993863i | \(-0.535284\pi\) | ||||
−0.110620 | + | 0.993863i | \(0.535284\pi\) | |||||||
\(410\) | −5.76996 | −0.284958 | ||||||||
\(411\) | 6.37292 | 0.314353 | ||||||||
\(412\) | 0.350862 | 0.0172857 | ||||||||
\(413\) | 8.15041 | 0.401055 | ||||||||
\(414\) | −27.3997 | −1.34662 | ||||||||
\(415\) | 14.2236 | 0.698211 | ||||||||
\(416\) | −1.55631 | −0.0763044 | ||||||||
\(417\) | −2.55385 | −0.125063 | ||||||||
\(418\) | −4.84135 | −0.236798 | ||||||||
\(419\) | 15.1396 | 0.739620 | 0.369810 | − | 0.929107i | \(-0.379423\pi\) | ||||
0.369810 | + | 0.929107i | \(0.379423\pi\) | |||||||
\(420\) | −0.0332843 | −0.00162411 | ||||||||
\(421\) | −26.8311 | −1.30767 | −0.653833 | − | 0.756639i | \(-0.726840\pi\) | ||||
−0.653833 | + | 0.756639i | \(0.726840\pi\) | |||||||
\(422\) | 15.3446 | 0.746965 | ||||||||
\(423\) | −31.6457 | −1.53866 | ||||||||
\(424\) | −31.4777 | −1.52869 | ||||||||
\(425\) | −5.48093 | −0.265864 | ||||||||
\(426\) | 3.92368 | 0.190103 | ||||||||
\(427\) | 14.6321 | 0.708098 | ||||||||
\(428\) | −1.71472 | −0.0828842 | ||||||||
\(429\) | 1.18498 | 0.0572114 | ||||||||
\(430\) | 6.89008 | 0.332269 | ||||||||
\(431\) | 16.9811 | 0.817953 | 0.408976 | − | 0.912545i | \(-0.365886\pi\) | ||||
0.408976 | + | 0.912545i | \(0.365886\pi\) | |||||||
\(432\) | −8.24894 | −0.396877 | ||||||||
\(433\) | −7.70046 | −0.370060 | −0.185030 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185030 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(434\) | −13.1656 | −0.631967 | ||||||||
\(435\) | −2.36961 | −0.113614 | ||||||||
\(436\) | −0.461496 | −0.0221017 | ||||||||
\(437\) | −17.0813 | −0.817109 | ||||||||
\(438\) | 7.21477 | 0.344735 | ||||||||
\(439\) | 11.5626 | 0.551852 | 0.275926 | − | 0.961179i | \(-0.411015\pi\) | ||||
0.275926 | + | 0.961179i | \(0.411015\pi\) | |||||||
\(440\) | −3.52671 | −0.168129 | ||||||||
\(441\) | −2.88816 | −0.137532 | ||||||||
\(442\) | −21.9728 | −1.04514 | ||||||||
\(443\) | 4.60378 | 0.218732 | 0.109366 | − | 0.994002i | \(-0.465118\pi\) | ||||
0.109366 | + | 0.994002i | \(0.465118\pi\) | |||||||
\(444\) | 0.175516 | 0.00832962 | ||||||||
\(445\) | −7.10603 | −0.336858 | ||||||||
\(446\) | −31.2448 | −1.47949 | ||||||||
\(447\) | 1.30254 | 0.0616081 | ||||||||
\(448\) | −7.56325 | −0.357330 | ||||||||
\(449\) | 31.4977 | 1.48647 | 0.743233 | − | 0.669032i | \(-0.233291\pi\) | ||||
0.743233 | + | 0.669032i | \(0.233291\pi\) | |||||||
\(450\) | 4.18488 | 0.197277 | ||||||||
\(451\) | −5.09988 | −0.240144 | ||||||||
\(452\) | 1.39027 | 0.0653930 | ||||||||
\(453\) | 5.37501 | 0.252540 | ||||||||
\(454\) | −4.10415 | −0.192617 | ||||||||
\(455\) | −2.76676 | −0.129708 | ||||||||
\(456\) | −2.40255 | −0.112510 | ||||||||
\(457\) | −22.3912 | −1.04741 | −0.523707 | − | 0.851898i | \(-0.675451\pi\) | ||||
−0.523707 | + | 0.851898i | \(0.675451\pi\) | |||||||
\(458\) | −1.44897 | −0.0677062 | ||||||||
\(459\) | −10.7926 | −0.503756 | ||||||||
\(460\) | 0.651643 | 0.0303830 | ||||||||
\(461\) | −35.3570 | −1.64674 | −0.823369 | − | 0.567507i | \(-0.807908\pi\) | ||||
−0.823369 | + | 0.567507i | \(0.807908\pi\) | |||||||
\(462\) | −0.620585 | −0.0288722 | ||||||||
\(463\) | −3.68681 | −0.171341 | −0.0856703 | − | 0.996324i | \(-0.527303\pi\) | ||||
−0.0856703 | + | 0.996324i | \(0.527303\pi\) | |||||||
\(464\) | 29.6831 | 1.37801 | ||||||||
\(465\) | −3.03858 | −0.140911 | ||||||||
\(466\) | −6.32730 | −0.293106 | ||||||||
\(467\) | −1.28493 | −0.0594594 | −0.0297297 | − | 0.999558i | \(-0.509465\pi\) | ||||
−0.0297297 | + | 0.999558i | \(0.509465\pi\) | |||||||
\(468\) | 0.795316 | 0.0367635 | ||||||||
\(469\) | −1.19958 | −0.0553912 | ||||||||
\(470\) | 15.8764 | 0.732326 | ||||||||
\(471\) | 5.02877 | 0.231714 | ||||||||
\(472\) | −22.4441 | −1.03307 | ||||||||
\(473\) | 6.08992 | 0.280015 | ||||||||
\(474\) | −5.47165 | −0.251321 | ||||||||
\(475\) | 2.60890 | 0.119705 | ||||||||
\(476\) | 0.545508 | 0.0250033 | ||||||||
\(477\) | 33.0143 | 1.51162 | ||||||||
\(478\) | 10.7678 | 0.492508 | ||||||||
\(479\) | −23.0059 | −1.05117 | −0.525583 | − | 0.850743i | \(-0.676153\pi\) | ||||
−0.525583 | + | 0.850743i | \(0.676153\pi\) | |||||||
\(480\) | 0.188112 | 0.00858612 | ||||||||
\(481\) | 14.5898 | 0.665237 | ||||||||
\(482\) | 43.9207 | 2.00053 | ||||||||
\(483\) | −2.18955 | −0.0996280 | ||||||||
\(484\) | −0.931566 | −0.0423439 | ||||||||
\(485\) | 9.93147 | 0.450965 | ||||||||
\(486\) | 12.4390 | 0.564247 | ||||||||
\(487\) | 43.2864 | 1.96149 | 0.980747 | − | 0.195283i | \(-0.0625624\pi\) | ||||
0.980747 | + | 0.195283i | \(0.0625624\pi\) | |||||||
\(488\) | −40.2930 | −1.82398 | ||||||||
\(489\) | −7.78628 | −0.352108 | ||||||||
\(490\) | 1.44897 | 0.0654580 | ||||||||
\(491\) | 1.40108 | 0.0632296 | 0.0316148 | − | 0.999500i | \(-0.489935\pi\) | ||||
0.0316148 | + | 0.999500i | \(0.489935\pi\) | |||||||
\(492\) | 0.132541 | 0.00597542 | ||||||||
\(493\) | 38.8363 | 1.74910 | ||||||||
\(494\) | 10.4590 | 0.470573 | ||||||||
\(495\) | 3.69887 | 0.166252 | ||||||||
\(496\) | 38.0631 | 1.70908 | ||||||||
\(497\) | −8.09731 | −0.363214 | ||||||||
\(498\) | −6.89230 | −0.308851 | ||||||||
\(499\) | 12.8905 | 0.577057 | 0.288529 | − | 0.957471i | \(-0.406834\pi\) | ||||
0.288529 | + | 0.957471i | \(0.406834\pi\) | |||||||
\(500\) | −0.0995284 | −0.00445104 | ||||||||
\(501\) | −0.167982 | −0.00750490 | ||||||||
\(502\) | −10.9348 | −0.488044 | ||||||||
\(503\) | 32.8478 | 1.46461 | 0.732305 | − | 0.680977i | \(-0.238445\pi\) | ||||
0.732305 | + | 0.680977i | \(0.238445\pi\) | |||||||
\(504\) | 7.95324 | 0.354265 | ||||||||
\(505\) | 7.35364 | 0.327233 | ||||||||
\(506\) | 12.1499 | 0.540127 | ||||||||
\(507\) | 1.78749 | 0.0793853 | ||||||||
\(508\) | −0.322104 | −0.0142911 | ||||||||
\(509\) | 28.5619 | 1.26599 | 0.632993 | − | 0.774157i | \(-0.281826\pi\) | ||||
0.632993 | + | 0.774157i | \(0.281826\pi\) | |||||||
\(510\) | 2.65587 | 0.117604 | ||||||||
\(511\) | −14.8891 | −0.658656 | ||||||||
\(512\) | 20.7152 | 0.915492 | ||||||||
\(513\) | 5.13724 | 0.226815 | ||||||||
\(514\) | 36.9704 | 1.63070 | ||||||||
\(515\) | −3.52525 | −0.155341 | ||||||||
\(516\) | −0.158272 | −0.00696752 | ||||||||
\(517\) | 14.0327 | 0.617156 | ||||||||
\(518\) | −7.64079 | −0.335717 | ||||||||
\(519\) | 8.38292 | 0.367969 | ||||||||
\(520\) | 7.61892 | 0.334112 | ||||||||
\(521\) | 23.1733 | 1.01524 | 0.507620 | − | 0.861581i | \(-0.330525\pi\) | ||||
0.507620 | + | 0.861581i | \(0.330525\pi\) | |||||||
\(522\) | −29.6529 | −1.29787 | ||||||||
\(523\) | 13.0566 | 0.570925 | 0.285463 | − | 0.958390i | \(-0.407853\pi\) | ||||
0.285463 | + | 0.958390i | \(0.407853\pi\) | |||||||
\(524\) | −0.0436255 | −0.00190579 | ||||||||
\(525\) | 0.334420 | 0.0145953 | ||||||||
\(526\) | −0.172263 | −0.00751104 | ||||||||
\(527\) | 49.8004 | 2.16934 | ||||||||
\(528\) | 1.79418 | 0.0780817 | ||||||||
\(529\) | 19.8672 | 0.863793 | ||||||||
\(530\) | −16.5631 | −0.719456 | ||||||||
\(531\) | 23.5397 | 1.02154 | ||||||||
\(532\) | −0.259660 | −0.0112577 | ||||||||
\(533\) | 11.0175 | 0.477221 | ||||||||
\(534\) | 3.44334 | 0.149008 | ||||||||
\(535\) | 17.2285 | 0.744852 | ||||||||
\(536\) | 3.30331 | 0.142681 | ||||||||
\(537\) | −7.55450 | −0.326001 | ||||||||
\(538\) | 25.7285 | 1.10923 | ||||||||
\(539\) | 1.28070 | 0.0551637 | ||||||||
\(540\) | −0.195983 | −0.00843378 | ||||||||
\(541\) | 13.0025 | 0.559022 | 0.279511 | − | 0.960143i | \(-0.409828\pi\) | ||||
0.279511 | + | 0.960143i | \(0.409828\pi\) | |||||||
\(542\) | 41.2976 | 1.77388 | ||||||||
\(543\) | 5.25762 | 0.225626 | ||||||||
\(544\) | −3.08304 | −0.132184 | ||||||||
\(545\) | 4.63683 | 0.198620 | ||||||||
\(546\) | 1.34068 | 0.0573757 | ||||||||
\(547\) | −16.6444 | −0.711661 | −0.355831 | − | 0.934551i | \(-0.615802\pi\) | ||||
−0.355831 | + | 0.934551i | \(0.615802\pi\) | |||||||
\(548\) | −1.89668 | −0.0810220 | ||||||||
\(549\) | 42.2600 | 1.80361 | ||||||||
\(550\) | −1.85570 | −0.0791275 | ||||||||
\(551\) | −18.4860 | −0.787528 | ||||||||
\(552\) | 6.02945 | 0.256630 | ||||||||
\(553\) | 11.2918 | 0.480178 | ||||||||
\(554\) | 8.88972 | 0.377688 | ||||||||
\(555\) | −1.76348 | −0.0748554 | ||||||||
\(556\) | 0.760063 | 0.0322339 | ||||||||
\(557\) | 12.0159 | 0.509130 | 0.254565 | − | 0.967056i | \(-0.418068\pi\) | ||||
0.254565 | + | 0.967056i | \(0.418068\pi\) | |||||||
\(558\) | −38.0243 | −1.60970 | ||||||||
\(559\) | −13.1563 | −0.556453 | ||||||||
\(560\) | −4.18915 | −0.177024 | ||||||||
\(561\) | 2.34744 | 0.0991090 | ||||||||
\(562\) | 4.07896 | 0.172061 | ||||||||
\(563\) | 21.4417 | 0.903659 | 0.451830 | − | 0.892104i | \(-0.350771\pi\) | ||||
0.451830 | + | 0.892104i | \(0.350771\pi\) | |||||||
\(564\) | −0.364697 | −0.0153565 | ||||||||
\(565\) | −13.9686 | −0.587664 | ||||||||
\(566\) | −31.4314 | −1.32116 | ||||||||
\(567\) | −8.00598 | −0.336219 | ||||||||
\(568\) | 22.2979 | 0.935597 | ||||||||
\(569\) | −40.7414 | −1.70797 | −0.853985 | − | 0.520298i | \(-0.825821\pi\) | ||||
−0.853985 | + | 0.520298i | \(0.825821\pi\) | |||||||
\(570\) | −1.26419 | −0.0529510 | ||||||||
\(571\) | −31.7372 | −1.32816 | −0.664081 | − | 0.747661i | \(-0.731177\pi\) | ||||
−0.664081 | + | 0.747661i | \(0.731177\pi\) | |||||||
\(572\) | −0.352668 | −0.0147458 | ||||||||
\(573\) | −3.66503 | −0.153109 | ||||||||
\(574\) | −5.76996 | −0.240833 | ||||||||
\(575\) | −6.54731 | −0.273042 | ||||||||
\(576\) | −21.8439 | −0.910162 | ||||||||
\(577\) | 31.9765 | 1.33120 | 0.665600 | − | 0.746309i | \(-0.268176\pi\) | ||||
0.665600 | + | 0.746309i | \(0.268176\pi\) | |||||||
\(578\) | −18.8955 | −0.785949 | ||||||||
\(579\) | 4.34984 | 0.180773 | ||||||||
\(580\) | 0.705230 | 0.0292831 | ||||||||
\(581\) | 14.2236 | 0.590096 | ||||||||
\(582\) | −4.81246 | −0.199483 | ||||||||
\(583\) | −14.6396 | −0.606310 | ||||||||
\(584\) | 41.0007 | 1.69662 | ||||||||
\(585\) | −7.99085 | −0.330381 | ||||||||
\(586\) | −10.9214 | −0.451161 | ||||||||
\(587\) | −0.889352 | −0.0367075 | −0.0183538 | − | 0.999832i | \(-0.505843\pi\) | ||||
−0.0183538 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(588\) | −0.0332843 | −0.00137262 | ||||||||
\(589\) | −23.7048 | −0.976739 | ||||||||
\(590\) | −11.8097 | −0.486199 | ||||||||
\(591\) | −2.75790 | −0.113445 | ||||||||
\(592\) | 22.0904 | 0.907910 | ||||||||
\(593\) | 7.77931 | 0.319458 | 0.159729 | − | 0.987161i | \(-0.448938\pi\) | ||||
0.159729 | + | 0.987161i | \(0.448938\pi\) | |||||||
\(594\) | −3.65410 | −0.149930 | ||||||||
\(595\) | −5.48093 | −0.224696 | ||||||||
\(596\) | −0.387656 | −0.0158790 | ||||||||
\(597\) | −0.319332 | −0.0130694 | ||||||||
\(598\) | −26.2479 | −1.07336 | ||||||||
\(599\) | 41.6102 | 1.70015 | 0.850073 | − | 0.526665i | \(-0.176558\pi\) | ||||
0.850073 | + | 0.526665i | \(0.176558\pi\) | |||||||
\(600\) | −0.920905 | −0.0375958 | ||||||||
\(601\) | 25.6159 | 1.04489 | 0.522446 | − | 0.852672i | \(-0.325019\pi\) | ||||
0.522446 | + | 0.852672i | \(0.325019\pi\) | |||||||
\(602\) | 6.89008 | 0.280819 | ||||||||
\(603\) | −3.46457 | −0.141088 | ||||||||
\(604\) | −1.59968 | −0.0650901 | ||||||||
\(605\) | 9.35980 | 0.380530 | ||||||||
\(606\) | −3.56333 | −0.144750 | ||||||||
\(607\) | 20.6682 | 0.838895 | 0.419448 | − | 0.907780i | \(-0.362224\pi\) | ||||
0.419448 | + | 0.907780i | \(0.362224\pi\) | |||||||
\(608\) | 1.46752 | 0.0595156 | ||||||||
\(609\) | −2.36961 | −0.0960213 | ||||||||
\(610\) | −21.2016 | −0.858427 | ||||||||
\(611\) | −30.3154 | −1.22643 | ||||||||
\(612\) | 1.57552 | 0.0636865 | ||||||||
\(613\) | −28.9050 | −1.16746 | −0.583730 | − | 0.811948i | \(-0.698407\pi\) | ||||
−0.583730 | + | 0.811948i | \(0.698407\pi\) | |||||||
\(614\) | −32.7250 | −1.32067 | ||||||||
\(615\) | −1.33169 | −0.0536991 | ||||||||
\(616\) | −3.52671 | −0.142095 | ||||||||
\(617\) | 35.2831 | 1.42044 | 0.710221 | − | 0.703978i | \(-0.248595\pi\) | ||||
0.710221 | + | 0.703978i | \(0.248595\pi\) | |||||||
\(618\) | 1.70822 | 0.0687145 | ||||||||
\(619\) | −47.3886 | −1.90471 | −0.952355 | − | 0.304991i | \(-0.901347\pi\) | ||||
−0.952355 | + | 0.304991i | \(0.901347\pi\) | |||||||
\(620\) | 0.904327 | 0.0363186 | ||||||||
\(621\) | −12.8924 | −0.517356 | ||||||||
\(622\) | −29.2179 | −1.17153 | ||||||||
\(623\) | −7.10603 | −0.284697 | ||||||||
\(624\) | −3.87605 | −0.155166 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.0360 | −1.40032 | ||||||||
\(627\) | −1.11737 | −0.0446236 | ||||||||
\(628\) | −1.49664 | −0.0597223 | ||||||||
\(629\) | 28.9023 | 1.15241 | ||||||||
\(630\) | 4.18488 | 0.166729 | ||||||||
\(631\) | −43.5288 | −1.73285 | −0.866427 | − | 0.499303i | \(-0.833589\pi\) | ||||
−0.866427 | + | 0.499303i | \(0.833589\pi\) | |||||||
\(632\) | −31.0948 | −1.23688 | ||||||||
\(633\) | 3.54150 | 0.140762 | ||||||||
\(634\) | 46.6291 | 1.85188 | ||||||||
\(635\) | 3.23631 | 0.128429 | ||||||||
\(636\) | 0.380470 | 0.0150866 | ||||||||
\(637\) | −2.76676 | −0.109623 | ||||||||
\(638\) | 13.1490 | 0.520574 | ||||||||
\(639\) | −23.3864 | −0.925150 | ||||||||
\(640\) | 12.0840 | 0.477661 | ||||||||
\(641\) | −8.95842 | −0.353836 | −0.176918 | − | 0.984226i | \(-0.556613\pi\) | ||||
−0.176918 | + | 0.984226i | \(0.556613\pi\) | |||||||
\(642\) | −8.34834 | −0.329483 | ||||||||
\(643\) | −2.62887 | −0.103672 | −0.0518362 | − | 0.998656i | \(-0.516507\pi\) | ||||
−0.0518362 | + | 0.998656i | \(0.516507\pi\) | |||||||
\(644\) | 0.651643 | 0.0256783 | ||||||||
\(645\) | 1.59022 | 0.0626147 | ||||||||
\(646\) | 20.7192 | 0.815186 | ||||||||
\(647\) | −19.5396 | −0.768180 | −0.384090 | − | 0.923296i | \(-0.625485\pi\) | ||||
−0.384090 | + | 0.923296i | \(0.625485\pi\) | |||||||
\(648\) | 22.0463 | 0.866062 | ||||||||
\(649\) | −10.4382 | −0.409737 | ||||||||
\(650\) | 4.00896 | 0.157244 | ||||||||
\(651\) | −3.03858 | −0.119091 | ||||||||
\(652\) | 2.31731 | 0.0907529 | ||||||||
\(653\) | 32.0258 | 1.25327 | 0.626633 | − | 0.779315i | \(-0.284433\pi\) | ||||
0.626633 | + | 0.779315i | \(0.284433\pi\) | |||||||
\(654\) | −2.24685 | −0.0878589 | ||||||||
\(655\) | 0.438322 | 0.0171267 | ||||||||
\(656\) | 16.6816 | 0.651307 | ||||||||
\(657\) | −43.0022 | −1.67768 | ||||||||
\(658\) | 15.8764 | 0.618928 | ||||||||
\(659\) | 7.48380 | 0.291527 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(660\) | 0.0426272 | 0.00165926 | ||||||||
\(661\) | 42.4287 | 1.65028 | 0.825142 | − | 0.564926i | \(-0.191095\pi\) | ||||
0.825142 | + | 0.564926i | \(0.191095\pi\) | |||||||
\(662\) | −24.7829 | −0.963214 | ||||||||
\(663\) | −5.07128 | −0.196952 | ||||||||
\(664\) | −39.1681 | −1.52002 | ||||||||
\(665\) | 2.60890 | 0.101169 | ||||||||
\(666\) | −22.0679 | −0.855112 | ||||||||
\(667\) | 46.3924 | 1.79632 | ||||||||
\(668\) | 0.0499940 | 0.00193433 | ||||||||
\(669\) | −7.21124 | −0.278803 | ||||||||
\(670\) | 1.73815 | 0.0671508 | ||||||||
\(671\) | −18.7394 | −0.723426 | ||||||||
\(672\) | 0.188112 | 0.00725659 | ||||||||
\(673\) | 42.2405 | 1.62825 | 0.814126 | − | 0.580688i | \(-0.197216\pi\) | ||||
0.814126 | + | 0.580688i | \(0.197216\pi\) | |||||||
\(674\) | −18.7192 | −0.721037 | ||||||||
\(675\) | 1.96912 | 0.0757915 | ||||||||
\(676\) | −0.531984 | −0.0204609 | ||||||||
\(677\) | 0.714895 | 0.0274757 | 0.0137378 | − | 0.999906i | \(-0.495627\pi\) | ||||
0.0137378 | + | 0.999906i | \(0.495627\pi\) | |||||||
\(678\) | 6.76873 | 0.259951 | ||||||||
\(679\) | 9.93147 | 0.381135 | ||||||||
\(680\) | 15.0930 | 0.578791 | ||||||||
\(681\) | −0.947229 | −0.0362979 | ||||||||
\(682\) | 16.8611 | 0.645647 | ||||||||
\(683\) | −22.9528 | −0.878263 | −0.439132 | − | 0.898423i | \(-0.644714\pi\) | ||||
−0.439132 | + | 0.898423i | \(0.644714\pi\) | |||||||
\(684\) | −0.749940 | −0.0286747 | ||||||||
\(685\) | 19.0566 | 0.728117 | ||||||||
\(686\) | 1.44897 | 0.0553221 | ||||||||
\(687\) | −0.334420 | −0.0127589 | ||||||||
\(688\) | −19.9200 | −0.759443 | ||||||||
\(689\) | 31.6266 | 1.20488 | ||||||||
\(690\) | 3.17261 | 0.120779 | ||||||||
\(691\) | 19.0997 | 0.726588 | 0.363294 | − | 0.931675i | \(-0.381652\pi\) | ||||
0.363294 | + | 0.931675i | \(0.381652\pi\) | |||||||
\(692\) | −2.49488 | −0.0948411 | ||||||||
\(693\) | 3.69887 | 0.140509 | ||||||||
\(694\) | 23.8863 | 0.906712 | ||||||||
\(695\) | −7.63665 | −0.289675 | ||||||||
\(696\) | 6.52527 | 0.247340 | ||||||||
\(697\) | 21.8256 | 0.826703 | ||||||||
\(698\) | −26.3138 | −0.995993 | ||||||||
\(699\) | −1.46033 | −0.0552346 | ||||||||
\(700\) | −0.0995284 | −0.00376182 | ||||||||
\(701\) | −29.7326 | −1.12298 | −0.561492 | − | 0.827482i | \(-0.689772\pi\) | ||||
−0.561492 | + | 0.827482i | \(0.689772\pi\) | |||||||
\(702\) | 7.89413 | 0.297945 | ||||||||
\(703\) | −13.7574 | −0.518869 | ||||||||
\(704\) | 9.68626 | 0.365065 | ||||||||
\(705\) | 3.66425 | 0.138004 | ||||||||
\(706\) | −11.6204 | −0.437339 | ||||||||
\(707\) | 7.35364 | 0.276562 | ||||||||
\(708\) | 0.271281 | 0.0101954 | ||||||||
\(709\) | −28.0817 | −1.05463 | −0.527315 | − | 0.849670i | \(-0.676801\pi\) | ||||
−0.527315 | + | 0.849670i | \(0.676801\pi\) | |||||||
\(710\) | 11.7328 | 0.440324 | ||||||||
\(711\) | 32.6127 | 1.22307 | ||||||||
\(712\) | 19.5681 | 0.733346 | ||||||||
\(713\) | 59.4896 | 2.22790 | ||||||||
\(714\) | 2.65587 | 0.0993936 | ||||||||
\(715\) | 3.54339 | 0.132515 | ||||||||
\(716\) | 2.24833 | 0.0840241 | ||||||||
\(717\) | 2.48518 | 0.0928109 | ||||||||
\(718\) | 26.4493 | 0.987080 | ||||||||
\(719\) | −24.3876 | −0.909503 | −0.454751 | − | 0.890618i | \(-0.650272\pi\) | ||||
−0.454751 | + | 0.890618i | \(0.650272\pi\) | |||||||
\(720\) | −12.0990 | −0.450901 | ||||||||
\(721\) | −3.52525 | −0.131287 | ||||||||
\(722\) | 17.6683 | 0.657544 | ||||||||
\(723\) | 10.1368 | 0.376992 | ||||||||
\(724\) | −1.56475 | −0.0581533 | ||||||||
\(725\) | −7.08572 | −0.263157 | ||||||||
\(726\) | −4.53545 | −0.168326 | ||||||||
\(727\) | −12.8921 | −0.478143 | −0.239071 | − | 0.971002i | \(-0.576843\pi\) | ||||
−0.239071 | + | 0.971002i | \(0.576843\pi\) | |||||||
\(728\) | 7.61892 | 0.282376 | ||||||||
\(729\) | −21.1470 | −0.783223 | ||||||||
\(730\) | 21.5740 | 0.798489 | ||||||||
\(731\) | −26.0626 | −0.963960 | ||||||||
\(732\) | 0.487020 | 0.0180008 | ||||||||
\(733\) | 6.65434 | 0.245784 | 0.122892 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122892 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(734\) | 4.60690 | 0.170044 | ||||||||
\(735\) | 0.334420 | 0.0123353 | ||||||||
\(736\) | −3.68288 | −0.135753 | ||||||||
\(737\) | 1.53630 | 0.0565903 | ||||||||
\(738\) | −16.6646 | −0.613432 | ||||||||
\(739\) | −4.80076 | −0.176599 | −0.0882995 | − | 0.996094i | \(-0.528143\pi\) | ||||
−0.0882995 | + | 0.996094i | \(0.528143\pi\) | |||||||
\(740\) | 0.524837 | 0.0192934 | ||||||||
\(741\) | 2.41391 | 0.0886773 | ||||||||
\(742\) | −16.5631 | −0.608051 | ||||||||
\(743\) | −6.04337 | −0.221710 | −0.110855 | − | 0.993837i | \(-0.535359\pi\) | ||||
−0.110855 | + | 0.993837i | \(0.535359\pi\) | |||||||
\(744\) | 8.36745 | 0.306766 | ||||||||
\(745\) | 3.89493 | 0.142699 | ||||||||
\(746\) | −19.0880 | −0.698860 | ||||||||
\(747\) | 41.0802 | 1.50305 | ||||||||
\(748\) | −0.698633 | −0.0255445 | ||||||||
\(749\) | 17.2285 | 0.629515 | ||||||||
\(750\) | −0.484566 | −0.0176939 | ||||||||
\(751\) | −17.1640 | −0.626322 | −0.313161 | − | 0.949700i | \(-0.601388\pi\) | ||||
−0.313161 | + | 0.949700i | \(0.601388\pi\) | |||||||
\(752\) | −45.9006 | −1.67382 | ||||||||
\(753\) | −2.52373 | −0.0919697 | ||||||||
\(754\) | −28.4064 | −1.03450 | ||||||||
\(755\) | 16.0726 | 0.584942 | ||||||||
\(756\) | −0.195983 | −0.00712785 | ||||||||
\(757\) | 28.1755 | 1.02406 | 0.512028 | − | 0.858969i | \(-0.328894\pi\) | ||||
0.512028 | + | 0.858969i | \(0.328894\pi\) | |||||||
\(758\) | −32.2458 | −1.17122 | ||||||||
\(759\) | 2.80416 | 0.101785 | ||||||||
\(760\) | −7.18423 | −0.260599 | ||||||||
\(761\) | −47.6650 | −1.72786 | −0.863928 | − | 0.503615i | \(-0.832003\pi\) | ||||
−0.863928 | + | 0.503615i | \(0.832003\pi\) | |||||||
\(762\) | −1.56820 | −0.0568101 | ||||||||
\(763\) | 4.63683 | 0.167865 | ||||||||
\(764\) | 1.09077 | 0.0394626 | ||||||||
\(765\) | −15.8298 | −0.572328 | ||||||||
\(766\) | 7.09723 | 0.256433 | ||||||||
\(767\) | 22.5502 | 0.814241 | ||||||||
\(768\) | −0.796878 | −0.0287548 | ||||||||
\(769\) | 16.4901 | 0.594649 | 0.297324 | − | 0.954777i | \(-0.403906\pi\) | ||||
0.297324 | + | 0.954777i | \(0.403906\pi\) | |||||||
\(770\) | −1.85570 | −0.0668749 | ||||||||
\(771\) | 8.53270 | 0.307298 | ||||||||
\(772\) | −1.29458 | −0.0465928 | ||||||||
\(773\) | −17.6275 | −0.634017 | −0.317008 | − | 0.948423i | \(-0.602678\pi\) | ||||
−0.317008 | + | 0.948423i | \(0.602678\pi\) | |||||||
\(774\) | 19.8997 | 0.715279 | ||||||||
\(775\) | −9.08612 | −0.326383 | ||||||||
\(776\) | −27.3487 | −0.981760 | ||||||||
\(777\) | −1.76348 | −0.0632644 | ||||||||
\(778\) | 45.9147 | 1.64612 | ||||||||
\(779\) | −10.3889 | −0.372221 | ||||||||
\(780\) | −0.0920896 | −0.00329734 | ||||||||
\(781\) | 10.3702 | 0.371076 | ||||||||
\(782\) | −51.9969 | −1.85941 | ||||||||
\(783\) | −13.9526 | −0.498627 | ||||||||
\(784\) | −4.18915 | −0.149613 | ||||||||
\(785\) | 15.0373 | 0.536704 | ||||||||
\(786\) | −0.212396 | −0.00757592 | ||||||||
\(787\) | −1.84529 | −0.0657774 | −0.0328887 | − | 0.999459i | \(-0.510471\pi\) | ||||
−0.0328887 | + | 0.999459i | \(0.510471\pi\) | |||||||
\(788\) | 0.820792 | 0.0292395 | ||||||||
\(789\) | −0.0397580 | −0.00141542 | ||||||||
\(790\) | −16.3616 | −0.582120 | ||||||||
\(791\) | −13.9686 | −0.496667 | ||||||||
\(792\) | −10.1857 | −0.361934 | ||||||||
\(793\) | 40.4836 | 1.43761 | ||||||||
\(794\) | 14.4735 | 0.513646 | ||||||||
\(795\) | −3.82273 | −0.135578 | ||||||||
\(796\) | 0.0950379 | 0.00336853 | ||||||||
\(797\) | 7.61111 | 0.269599 | 0.134800 | − | 0.990873i | \(-0.456961\pi\) | ||||
0.134800 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(798\) | −1.26419 | −0.0447517 | ||||||||
\(799\) | −60.0547 | −2.12458 | ||||||||
\(800\) | 0.562503 | 0.0198875 | ||||||||
\(801\) | −20.5234 | −0.725158 | ||||||||
\(802\) | 30.3773 | 1.07266 | ||||||||
\(803\) | 19.0685 | 0.672914 | ||||||||
\(804\) | −0.0399270 | −0.00140812 | ||||||||
\(805\) | −6.54731 | −0.230762 | ||||||||
\(806\) | −36.4259 | −1.28305 | ||||||||
\(807\) | 5.93808 | 0.209030 | ||||||||
\(808\) | −20.2500 | −0.712392 | ||||||||
\(809\) | −5.68837 | −0.199992 | −0.0999961 | − | 0.994988i | \(-0.531883\pi\) | ||||
−0.0999961 | + | 0.994988i | \(0.531883\pi\) | |||||||
\(810\) | 11.6005 | 0.407599 | ||||||||
\(811\) | 43.8866 | 1.54107 | 0.770533 | − | 0.637401i | \(-0.219990\pi\) | ||||
0.770533 | + | 0.637401i | \(0.219990\pi\) | |||||||
\(812\) | 0.705230 | 0.0247487 | ||||||||
\(813\) | 9.53138 | 0.334280 | ||||||||
\(814\) | 9.78557 | 0.342984 | ||||||||
\(815\) | −23.2829 | −0.815565 | ||||||||
\(816\) | −7.67844 | −0.268799 | ||||||||
\(817\) | 12.4057 | 0.434021 | ||||||||
\(818\) | 6.48316 | 0.226679 | ||||||||
\(819\) | −7.99085 | −0.279223 | ||||||||
\(820\) | 0.396332 | 0.0138405 | ||||||||
\(821\) | 4.31248 | 0.150507 | 0.0752533 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752533 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(822\) | −9.23421 | −0.322080 | ||||||||
\(823\) | 22.5449 | 0.785865 | 0.392932 | − | 0.919567i | \(-0.371461\pi\) | ||||
0.392932 | + | 0.919567i | \(0.371461\pi\) | |||||||
\(824\) | 9.70760 | 0.338180 | ||||||||
\(825\) | −0.428292 | −0.0149112 | ||||||||
\(826\) | −11.8097 | −0.410913 | ||||||||
\(827\) | −16.8185 | −0.584836 | −0.292418 | − | 0.956291i | \(-0.594460\pi\) | ||||
−0.292418 | + | 0.956291i | \(0.594460\pi\) | |||||||
\(828\) | 1.88205 | 0.0654058 | ||||||||
\(829\) | −29.7592 | −1.03358 | −0.516790 | − | 0.856112i | \(-0.672873\pi\) | ||||
−0.516790 | + | 0.856112i | \(0.672873\pi\) | |||||||
\(830\) | −20.6097 | −0.715373 | ||||||||
\(831\) | 2.05173 | 0.0711736 | ||||||||
\(832\) | −20.9257 | −0.725468 | ||||||||
\(833\) | −5.48093 | −0.189903 | ||||||||
\(834\) | 3.70046 | 0.128137 | ||||||||
\(835\) | −0.502309 | −0.0173831 | ||||||||
\(836\) | 0.332547 | 0.0115014 | ||||||||
\(837\) | −17.8917 | −0.618426 | ||||||||
\(838\) | −21.9370 | −0.757800 | ||||||||
\(839\) | −22.8086 | −0.787439 | −0.393720 | − | 0.919231i | \(-0.628812\pi\) | ||||
−0.393720 | + | 0.919231i | \(0.628812\pi\) | |||||||
\(840\) | −0.920905 | −0.0317742 | ||||||||
\(841\) | 21.2074 | 0.731290 | ||||||||
\(842\) | 38.8775 | 1.33981 | ||||||||
\(843\) | 0.941416 | 0.0324241 | ||||||||
\(844\) | −1.05400 | −0.0362803 | ||||||||
\(845\) | 5.34505 | 0.183875 | ||||||||
\(846\) | 45.8538 | 1.57649 | ||||||||
\(847\) | 9.35980 | 0.321607 | ||||||||
\(848\) | 47.8858 | 1.64441 | ||||||||
\(849\) | −7.25429 | −0.248967 | ||||||||
\(850\) | 7.94173 | 0.272399 | ||||||||
\(851\) | 34.5255 | 1.18352 | ||||||||
\(852\) | −0.269513 | −0.00923337 | ||||||||
\(853\) | 18.8903 | 0.646790 | 0.323395 | − | 0.946264i | \(-0.395176\pi\) | ||||
0.323395 | + | 0.946264i | \(0.395176\pi\) | |||||||
\(854\) | −21.2016 | −0.725504 | ||||||||
\(855\) | 7.53494 | 0.257689 | ||||||||
\(856\) | −47.4427 | −1.62156 | ||||||||
\(857\) | 26.6372 | 0.909909 | 0.454955 | − | 0.890515i | \(-0.349655\pi\) | ||||
0.454955 | + | 0.890515i | \(0.349655\pi\) | |||||||
\(858\) | −1.71701 | −0.0586177 | ||||||||
\(859\) | 6.02854 | 0.205691 | 0.102845 | − | 0.994697i | \(-0.467205\pi\) | ||||
0.102845 | + | 0.994697i | \(0.467205\pi\) | |||||||
\(860\) | −0.473272 | −0.0161384 | ||||||||
\(861\) | −1.33169 | −0.0453840 | ||||||||
\(862\) | −24.6052 | −0.838058 | ||||||||
\(863\) | 27.4201 | 0.933391 | 0.466695 | − | 0.884418i | \(-0.345444\pi\) | ||||
0.466695 | + | 0.884418i | \(0.345444\pi\) | |||||||
\(864\) | 1.10764 | 0.0376826 | ||||||||
\(865\) | 25.0670 | 0.852304 | ||||||||
\(866\) | 11.1578 | 0.379157 | ||||||||
\(867\) | −4.36104 | −0.148109 | ||||||||
\(868\) | 0.904327 | 0.0306948 | ||||||||
\(869\) | −14.4615 | −0.490572 | ||||||||
\(870\) | 3.43350 | 0.116407 | ||||||||
\(871\) | −3.31894 | −0.112458 | ||||||||
\(872\) | −12.7686 | −0.432400 | ||||||||
\(873\) | 28.6837 | 0.970797 | ||||||||
\(874\) | 24.7504 | 0.837193 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −0.495574 | −0.0167439 | ||||||||
\(877\) | −23.0021 | −0.776725 | −0.388363 | − | 0.921507i | \(-0.626959\pi\) | ||||
−0.388363 | + | 0.921507i | \(0.626959\pi\) | |||||||
\(878\) | −16.7539 | −0.565417 | ||||||||
\(879\) | −2.52065 | −0.0850193 | ||||||||
\(880\) | 5.36505 | 0.180856 | ||||||||
\(881\) | −12.7993 | −0.431219 | −0.215610 | − | 0.976480i | \(-0.569174\pi\) | ||||
−0.215610 | + | 0.976480i | \(0.569174\pi\) | |||||||
\(882\) | 4.18488 | 0.140912 | ||||||||
\(883\) | −27.4825 | −0.924861 | −0.462431 | − | 0.886655i | \(-0.653023\pi\) | ||||
−0.462431 | + | 0.886655i | \(0.653023\pi\) | |||||||
\(884\) | 1.50929 | 0.0507629 | ||||||||
\(885\) | −2.72566 | −0.0916221 | ||||||||
\(886\) | −6.67076 | −0.224109 | ||||||||
\(887\) | 24.0207 | 0.806535 | 0.403268 | − | 0.915082i | \(-0.367874\pi\) | ||||
0.403268 | + | 0.915082i | \(0.367874\pi\) | |||||||
\(888\) | 4.85615 | 0.162962 | ||||||||
\(889\) | 3.23631 | 0.108542 | ||||||||
\(890\) | 10.2965 | 0.345138 | ||||||||
\(891\) | 10.2533 | 0.343497 | ||||||||
\(892\) | 2.14617 | 0.0718591 | ||||||||
\(893\) | 28.5858 | 0.956588 | ||||||||
\(894\) | −1.88735 | −0.0631225 | ||||||||
\(895\) | −22.5898 | −0.755095 | ||||||||
\(896\) | 12.0840 | 0.403697 | ||||||||
\(897\) | −6.05796 | −0.202269 | ||||||||
\(898\) | −45.6393 | −1.52300 | ||||||||
\(899\) | 64.3817 | 2.14725 | ||||||||
\(900\) | −0.287454 | −0.00958181 | ||||||||
\(901\) | 62.6520 | 2.08724 | ||||||||
\(902\) | 7.38959 | 0.246047 | ||||||||
\(903\) | 1.59022 | 0.0529191 | ||||||||
\(904\) | 38.4659 | 1.27936 | ||||||||
\(905\) | 15.7216 | 0.522604 | ||||||||
\(906\) | −7.78825 | −0.258747 | ||||||||
\(907\) | 26.1891 | 0.869595 | 0.434797 | − | 0.900528i | \(-0.356820\pi\) | ||||
0.434797 | + | 0.900528i | \(0.356820\pi\) | |||||||
\(908\) | 0.281909 | 0.00935549 | ||||||||
\(909\) | 21.2385 | 0.704437 | ||||||||
\(910\) | 4.00896 | 0.132896 | ||||||||
\(911\) | −29.6976 | −0.983924 | −0.491962 | − | 0.870617i | \(-0.663720\pi\) | ||||
−0.491962 | + | 0.870617i | \(0.663720\pi\) | |||||||
\(912\) | 3.65491 | 0.121026 | ||||||||
\(913\) | −18.2162 | −0.602869 | ||||||||
\(914\) | 32.4442 | 1.07316 | ||||||||
\(915\) | −4.89328 | −0.161767 | ||||||||
\(916\) | 0.0995284 | 0.00328851 | ||||||||
\(917\) | 0.438322 | 0.0144747 | ||||||||
\(918\) | 15.6382 | 0.516138 | ||||||||
\(919\) | −30.8884 | −1.01892 | −0.509458 | − | 0.860496i | \(-0.670154\pi\) | ||||
−0.509458 | + | 0.860496i | \(0.670154\pi\) | |||||||
\(920\) | 18.0296 | 0.594417 | ||||||||
\(921\) | −7.55286 | −0.248875 | ||||||||
\(922\) | 51.2313 | 1.68721 | ||||||||
\(923\) | −22.4033 | −0.737414 | ||||||||
\(924\) | 0.0426272 | 0.00140233 | ||||||||
\(925\) | −5.27324 | −0.173383 | ||||||||
\(926\) | 5.34209 | 0.175552 | ||||||||
\(927\) | −10.1815 | −0.334404 | ||||||||
\(928\) | −3.98574 | −0.130838 | ||||||||
\(929\) | −34.1081 | −1.11905 | −0.559526 | − | 0.828813i | \(-0.689017\pi\) | ||||
−0.559526 | + | 0.828813i | \(0.689017\pi\) | |||||||
\(930\) | 4.40283 | 0.144374 | ||||||||
\(931\) | 2.60890 | 0.0855033 | ||||||||
\(932\) | 0.434614 | 0.0142363 | ||||||||
\(933\) | −6.74342 | −0.220770 | ||||||||
\(934\) | 1.86183 | 0.0609210 | ||||||||
\(935\) | 7.01943 | 0.229560 | ||||||||
\(936\) | 22.0047 | 0.719246 | ||||||||
\(937\) | −38.9570 | −1.27267 | −0.636334 | − | 0.771413i | \(-0.719550\pi\) | ||||
−0.636334 | + | 0.771413i | \(0.719550\pi\) | |||||||
\(938\) | 1.73815 | 0.0567528 | ||||||||
\(939\) | −8.08624 | −0.263885 | ||||||||
\(940\) | −1.09053 | −0.0355693 | ||||||||
\(941\) | 7.17550 | 0.233914 | 0.116957 | − | 0.993137i | \(-0.462686\pi\) | ||||
0.116957 | + | 0.993137i | \(0.462686\pi\) | |||||||
\(942\) | −7.28657 | −0.237409 | ||||||||
\(943\) | 26.0720 | 0.849021 | ||||||||
\(944\) | 34.1433 | 1.11127 | ||||||||
\(945\) | 1.96912 | 0.0640555 | ||||||||
\(946\) | −8.82414 | −0.286897 | ||||||||
\(947\) | −20.8186 | −0.676515 | −0.338257 | − | 0.941054i | \(-0.609837\pi\) | ||||
−0.338257 | + | 0.941054i | \(0.609837\pi\) | |||||||
\(948\) | 0.375841 | 0.0122068 | ||||||||
\(949\) | −41.1946 | −1.33723 | ||||||||
\(950\) | −3.78024 | −0.122647 | ||||||||
\(951\) | 10.7619 | 0.348978 | ||||||||
\(952\) | 15.0930 | 0.489168 | ||||||||
\(953\) | −21.8539 | −0.707916 | −0.353958 | − | 0.935261i | \(-0.615164\pi\) | ||||
−0.353958 | + | 0.935261i | \(0.615164\pi\) | |||||||
\(954\) | −47.8370 | −1.54878 | ||||||||
\(955\) | −10.9594 | −0.354636 | ||||||||
\(956\) | −0.739627 | −0.0239213 | ||||||||
\(957\) | 3.03476 | 0.0980998 | ||||||||
\(958\) | 33.3349 | 1.07700 | ||||||||
\(959\) | 19.0566 | 0.615371 | ||||||||
\(960\) | 2.52930 | 0.0816329 | ||||||||
\(961\) | 51.5576 | 1.66315 | ||||||||
\(962\) | −21.1402 | −0.681588 | ||||||||
\(963\) | 49.7587 | 1.60345 | ||||||||
\(964\) | −3.01686 | −0.0971666 | ||||||||
\(965\) | 13.0071 | 0.418714 | ||||||||
\(966\) | 3.17261 | 0.102077 | ||||||||
\(967\) | 20.3076 | 0.653048 | 0.326524 | − | 0.945189i | \(-0.394123\pi\) | ||||
0.326524 | + | 0.945189i | \(0.394123\pi\) | |||||||
\(968\) | −25.7744 | −0.828421 | ||||||||
\(969\) | 4.78195 | 0.153618 | ||||||||
\(970\) | −14.3905 | −0.462050 | ||||||||
\(971\) | 7.00744 | 0.224880 | 0.112440 | − | 0.993659i | \(-0.464133\pi\) | ||||
0.112440 | + | 0.993659i | \(0.464133\pi\) | |||||||
\(972\) | −0.854423 | −0.0274056 | ||||||||
\(973\) | −7.63665 | −0.244820 | ||||||||
\(974\) | −62.7209 | −2.00971 | ||||||||
\(975\) | 0.925260 | 0.0296320 | ||||||||
\(976\) | 61.2962 | 1.96204 | ||||||||
\(977\) | −22.9913 | −0.735558 | −0.367779 | − | 0.929913i | \(-0.619882\pi\) | ||||
−0.367779 | + | 0.929913i | \(0.619882\pi\) | |||||||
\(978\) | 11.2821 | 0.360763 | ||||||||
\(979\) | 9.10070 | 0.290860 | ||||||||
\(980\) | −0.0995284 | −0.00317932 | ||||||||
\(981\) | 13.3919 | 0.427571 | ||||||||
\(982\) | −2.03012 | −0.0647838 | ||||||||
\(983\) | −44.9190 | −1.43269 | −0.716346 | − | 0.697745i | \(-0.754187\pi\) | ||||
−0.716346 | + | 0.697745i | \(0.754187\pi\) | |||||||
\(984\) | 3.66713 | 0.116904 | ||||||||
\(985\) | −8.24681 | −0.262765 | ||||||||
\(986\) | −56.2729 | −1.79209 | ||||||||
\(987\) | 3.66425 | 0.116634 | ||||||||
\(988\) | −0.718416 | −0.0228559 | ||||||||
\(989\) | −31.1334 | −0.989984 | ||||||||
\(990\) | −5.35958 | −0.170339 | ||||||||
\(991\) | 52.8419 | 1.67858 | 0.839290 | − | 0.543685i | \(-0.182971\pi\) | ||||
0.839290 | + | 0.543685i | \(0.182971\pi\) | |||||||
\(992\) | −5.11097 | −0.162273 | ||||||||
\(993\) | −5.71983 | −0.181513 | ||||||||
\(994\) | 11.7328 | 0.372142 | ||||||||
\(995\) | −0.954882 | −0.0302718 | ||||||||
\(996\) | 0.473424 | 0.0150010 | ||||||||
\(997\) | 40.5194 | 1.28326 | 0.641632 | − | 0.767013i | \(-0.278258\pi\) | ||||
0.641632 | + | 0.767013i | \(0.278258\pi\) | |||||||
\(998\) | −18.6780 | −0.591241 | ||||||||
\(999\) | −10.3836 | −0.328524 |
(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 | 8015.2.a.l.1.17 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.17 | ✓ | 62 | 1.1 | even | 1 | trivial |