Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53200 | −1.79040 | −0.895198 | − | 0.445669i | \(-0.852966\pi\) | ||||
−0.895198 | + | 0.445669i | \(0.852966\pi\) | |||||||
\(3\) | 0.341990 | 0.197448 | 0.0987239 | − | 0.995115i | \(-0.468524\pi\) | ||||
0.0987239 | + | 0.995115i | \(0.468524\pi\) | |||||||
\(4\) | 4.41103 | 2.20552 | ||||||||
\(5\) | 2.95840 | 1.32304 | 0.661519 | − | 0.749928i | \(-0.269912\pi\) | ||||
0.661519 | + | 0.749928i | \(0.269912\pi\) | |||||||
\(6\) | −0.865919 | −0.353510 | ||||||||
\(7\) | 4.74675 | 1.79410 | 0.897051 | − | 0.441926i | \(-0.145705\pi\) | ||||
0.897051 | + | 0.441926i | \(0.145705\pi\) | |||||||
\(8\) | −6.10474 | −2.15835 | ||||||||
\(9\) | −2.88304 | −0.961014 | ||||||||
\(10\) | −7.49068 | −2.36876 | ||||||||
\(11\) | −0.409857 | −0.123576 | −0.0617882 | − | 0.998089i | \(-0.519680\pi\) | ||||
−0.0617882 | + | 0.998089i | \(0.519680\pi\) | |||||||
\(12\) | 1.50853 | 0.435475 | ||||||||
\(13\) | −2.52058 | −0.699083 | −0.349541 | − | 0.936921i | \(-0.613663\pi\) | ||||
−0.349541 | + | 0.936921i | \(0.613663\pi\) | |||||||
\(14\) | −12.0188 | −3.21215 | ||||||||
\(15\) | 1.01174 | 0.261231 | ||||||||
\(16\) | 6.63515 | 1.65879 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 7.29987 | 1.72060 | ||||||||
\(19\) | 7.19313 | 1.65022 | 0.825109 | − | 0.564974i | \(-0.191114\pi\) | ||||
0.825109 | + | 0.564974i | \(0.191114\pi\) | |||||||
\(20\) | 13.0496 | 2.91798 | ||||||||
\(21\) | 1.62334 | 0.354242 | ||||||||
\(22\) | 1.03776 | 0.221251 | ||||||||
\(23\) | 4.18683 | 0.873014 | 0.436507 | − | 0.899701i | \(-0.356215\pi\) | ||||
0.436507 | + | 0.899701i | \(0.356215\pi\) | |||||||
\(24\) | −2.08776 | −0.426162 | ||||||||
\(25\) | 3.75215 | 0.750430 | ||||||||
\(26\) | 6.38211 | 1.25163 | ||||||||
\(27\) | −2.01194 | −0.387198 | ||||||||
\(28\) | 20.9381 | 3.95692 | ||||||||
\(29\) | 7.77491 | 1.44377 | 0.721883 | − | 0.692016i | \(-0.243277\pi\) | ||||
0.721883 | + | 0.692016i | \(0.243277\pi\) | |||||||
\(30\) | −2.56174 | −0.467707 | ||||||||
\(31\) | 4.33420 | 0.778445 | 0.389222 | − | 0.921144i | \(-0.372744\pi\) | ||||
0.389222 | + | 0.921144i | \(0.372744\pi\) | |||||||
\(32\) | −4.59073 | −0.811535 | ||||||||
\(33\) | −0.140167 | −0.0243999 | ||||||||
\(34\) | 2.53200 | 0.434235 | ||||||||
\(35\) | 14.0428 | 2.37367 | ||||||||
\(36\) | −12.7172 | −2.11953 | ||||||||
\(37\) | −10.6364 | −1.74861 | −0.874305 | − | 0.485376i | \(-0.838683\pi\) | ||||
−0.874305 | + | 0.485376i | \(0.838683\pi\) | |||||||
\(38\) | −18.2130 | −2.95454 | ||||||||
\(39\) | −0.862012 | −0.138032 | ||||||||
\(40\) | −18.0603 | −2.85558 | ||||||||
\(41\) | 6.97135 | 1.08874 | 0.544371 | − | 0.838845i | \(-0.316768\pi\) | ||||
0.544371 | + | 0.838845i | \(0.316768\pi\) | |||||||
\(42\) | −4.11030 | −0.634233 | ||||||||
\(43\) | −3.13226 | −0.477665 | −0.238832 | − | 0.971061i | \(-0.576765\pi\) | ||||
−0.238832 | + | 0.971061i | \(0.576765\pi\) | |||||||
\(44\) | −1.80789 | −0.272550 | ||||||||
\(45\) | −8.52920 | −1.27146 | ||||||||
\(46\) | −10.6011 | −1.56304 | ||||||||
\(47\) | −1.13711 | −0.165864 | −0.0829321 | − | 0.996555i | \(-0.526428\pi\) | ||||
−0.0829321 | + | 0.996555i | \(0.526428\pi\) | |||||||
\(48\) | 2.26915 | 0.327524 | ||||||||
\(49\) | 15.5316 | 2.21880 | ||||||||
\(50\) | −9.50046 | −1.34357 | ||||||||
\(51\) | −0.341990 | −0.0478881 | ||||||||
\(52\) | −11.1184 | −1.54184 | ||||||||
\(53\) | 6.05777 | 0.832099 | 0.416050 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416050 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(54\) | 5.09424 | 0.693238 | ||||||||
\(55\) | −1.21252 | −0.163496 | ||||||||
\(56\) | −28.9777 | −3.87231 | ||||||||
\(57\) | 2.45998 | 0.325832 | ||||||||
\(58\) | −19.6861 | −2.58491 | ||||||||
\(59\) | −7.59327 | −0.988560 | −0.494280 | − | 0.869303i | \(-0.664568\pi\) | ||||
−0.494280 | + | 0.869303i | \(0.664568\pi\) | |||||||
\(60\) | 4.46284 | 0.576150 | ||||||||
\(61\) | −6.35868 | −0.814146 | −0.407073 | − | 0.913396i | \(-0.633451\pi\) | ||||
−0.407073 | + | 0.913396i | \(0.633451\pi\) | |||||||
\(62\) | −10.9742 | −1.39372 | ||||||||
\(63\) | −13.6851 | −1.72416 | ||||||||
\(64\) | −1.64656 | −0.205820 | ||||||||
\(65\) | −7.45689 | −0.924913 | ||||||||
\(66\) | 0.354902 | 0.0436855 | ||||||||
\(67\) | −2.28847 | −0.279581 | −0.139790 | − | 0.990181i | \(-0.544643\pi\) | ||||
−0.139790 | + | 0.990181i | \(0.544643\pi\) | |||||||
\(68\) | −4.41103 | −0.534916 | ||||||||
\(69\) | 1.43185 | 0.172375 | ||||||||
\(70\) | −35.5564 | −4.24980 | ||||||||
\(71\) | 16.4609 | 1.95355 | 0.976777 | − | 0.214258i | \(-0.0687332\pi\) | ||||
0.976777 | + | 0.214258i | \(0.0687332\pi\) | |||||||
\(72\) | 17.6002 | 2.07421 | ||||||||
\(73\) | 3.24981 | 0.380362 | 0.190181 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190181 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(74\) | 26.9313 | 3.13070 | ||||||||
\(75\) | 1.28320 | 0.148171 | ||||||||
\(76\) | 31.7291 | 3.63958 | ||||||||
\(77\) | −1.94549 | −0.221709 | ||||||||
\(78\) | 2.18262 | 0.247133 | ||||||||
\(79\) | −14.3364 | −1.61297 | −0.806483 | − | 0.591257i | \(-0.798632\pi\) | ||||
−0.806483 | + | 0.591257i | \(0.798632\pi\) | |||||||
\(80\) | 19.6295 | 2.19464 | ||||||||
\(81\) | 7.96107 | 0.884563 | ||||||||
\(82\) | −17.6515 | −1.94928 | ||||||||
\(83\) | −3.32716 | −0.365203 | −0.182602 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182602 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(84\) | 7.16061 | 0.781286 | ||||||||
\(85\) | −2.95840 | −0.320884 | ||||||||
\(86\) | 7.93088 | 0.855209 | ||||||||
\(87\) | 2.65894 | 0.285068 | ||||||||
\(88\) | 2.50207 | 0.266721 | ||||||||
\(89\) | 9.96866 | 1.05668 | 0.528338 | − | 0.849034i | \(-0.322815\pi\) | ||||
0.528338 | + | 0.849034i | \(0.322815\pi\) | |||||||
\(90\) | 21.5960 | 2.27641 | ||||||||
\(91\) | −11.9646 | −1.25423 | ||||||||
\(92\) | 18.4682 | 1.92545 | ||||||||
\(93\) | 1.48225 | 0.153702 | ||||||||
\(94\) | 2.87916 | 0.296962 | ||||||||
\(95\) | 21.2802 | 2.18330 | ||||||||
\(96\) | −1.56998 | −0.160236 | ||||||||
\(97\) | −2.28126 | −0.231626 | −0.115813 | − | 0.993271i | \(-0.536947\pi\) | ||||
−0.115813 | + | 0.993271i | \(0.536947\pi\) | |||||||
\(98\) | −39.3261 | −3.97254 | ||||||||
\(99\) | 1.18163 | 0.118759 | ||||||||
\(100\) | 16.5509 | 1.65509 | ||||||||
\(101\) | 4.26105 | 0.423990 | 0.211995 | − | 0.977271i | \(-0.432004\pi\) | ||||
0.211995 | + | 0.977271i | \(0.432004\pi\) | |||||||
\(102\) | 0.865919 | 0.0857387 | ||||||||
\(103\) | −14.4725 | −1.42602 | −0.713009 | − | 0.701155i | \(-0.752668\pi\) | ||||
−0.713009 | + | 0.701155i | \(0.752668\pi\) | |||||||
\(104\) | 15.3875 | 1.50887 | ||||||||
\(105\) | 4.80249 | 0.468675 | ||||||||
\(106\) | −15.3383 | −1.48979 | ||||||||
\(107\) | 15.6412 | 1.51209 | 0.756045 | − | 0.654520i | \(-0.227129\pi\) | ||||
0.756045 | + | 0.654520i | \(0.227129\pi\) | |||||||
\(108\) | −8.87474 | −0.853972 | ||||||||
\(109\) | 11.0554 | 1.05891 | 0.529457 | − | 0.848337i | \(-0.322396\pi\) | ||||
0.529457 | + | 0.848337i | \(0.322396\pi\) | |||||||
\(110\) | 3.07011 | 0.292723 | ||||||||
\(111\) | −3.63753 | −0.345259 | ||||||||
\(112\) | 31.4954 | 2.97604 | ||||||||
\(113\) | −6.11056 | −0.574833 | −0.287416 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287416 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(114\) | −6.22867 | −0.583368 | ||||||||
\(115\) | 12.3863 | 1.15503 | ||||||||
\(116\) | 34.2954 | 3.18425 | ||||||||
\(117\) | 7.26693 | 0.671828 | ||||||||
\(118\) | 19.2262 | 1.76991 | ||||||||
\(119\) | −4.74675 | −0.435134 | ||||||||
\(120\) | −6.17643 | −0.563829 | ||||||||
\(121\) | −10.8320 | −0.984729 | ||||||||
\(122\) | 16.1002 | 1.45764 | ||||||||
\(123\) | 2.38413 | 0.214970 | ||||||||
\(124\) | 19.1183 | 1.71687 | ||||||||
\(125\) | −3.69164 | −0.330190 | ||||||||
\(126\) | 34.6507 | 3.08693 | ||||||||
\(127\) | 16.8060 | 1.49129 | 0.745647 | − | 0.666341i | \(-0.232140\pi\) | ||||
0.745647 | + | 0.666341i | \(0.232140\pi\) | |||||||
\(128\) | 13.3506 | 1.18003 | ||||||||
\(129\) | −1.07120 | −0.0943139 | ||||||||
\(130\) | 18.8809 | 1.65596 | ||||||||
\(131\) | −11.0365 | −0.964261 | −0.482131 | − | 0.876099i | \(-0.660137\pi\) | ||||
−0.482131 | + | 0.876099i | \(0.660137\pi\) | |||||||
\(132\) | −0.618280 | −0.0538144 | ||||||||
\(133\) | 34.1440 | 2.96066 | ||||||||
\(134\) | 5.79440 | 0.500560 | ||||||||
\(135\) | −5.95213 | −0.512278 | ||||||||
\(136\) | 6.10474 | 0.523477 | ||||||||
\(137\) | 12.2670 | 1.04804 | 0.524019 | − | 0.851707i | \(-0.324432\pi\) | ||||
0.524019 | + | 0.851707i | \(0.324432\pi\) | |||||||
\(138\) | −3.62545 | −0.308619 | ||||||||
\(139\) | 2.27634 | 0.193076 | 0.0965381 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965381 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(140\) | 61.9433 | 5.23516 | ||||||||
\(141\) | −0.388879 | −0.0327495 | ||||||||
\(142\) | −41.6791 | −3.49764 | ||||||||
\(143\) | 1.03308 | 0.0863901 | ||||||||
\(144\) | −19.1294 | −1.59412 | ||||||||
\(145\) | 23.0013 | 1.91016 | ||||||||
\(146\) | −8.22853 | −0.680998 | ||||||||
\(147\) | 5.31166 | 0.438098 | ||||||||
\(148\) | −46.9174 | −3.85659 | ||||||||
\(149\) | −6.31227 | −0.517122 | −0.258561 | − | 0.965995i | \(-0.583248\pi\) | ||||
−0.258561 | + | 0.965995i | \(0.583248\pi\) | |||||||
\(150\) | −3.24906 | −0.265284 | ||||||||
\(151\) | 0.595975 | 0.0484997 | 0.0242499 | − | 0.999706i | \(-0.492280\pi\) | ||||
0.0242499 | + | 0.999706i | \(0.492280\pi\) | |||||||
\(152\) | −43.9122 | −3.56175 | ||||||||
\(153\) | 2.88304 | 0.233080 | ||||||||
\(154\) | 4.92597 | 0.396946 | ||||||||
\(155\) | 12.8223 | 1.02991 | ||||||||
\(156\) | −3.80236 | −0.304433 | ||||||||
\(157\) | 18.1956 | 1.45216 | 0.726082 | − | 0.687608i | \(-0.241339\pi\) | ||||
0.726082 | + | 0.687608i | \(0.241339\pi\) | |||||||
\(158\) | 36.2997 | 2.88785 | ||||||||
\(159\) | 2.07170 | 0.164296 | ||||||||
\(160\) | −13.5812 | −1.07369 | ||||||||
\(161\) | 19.8738 | 1.56628 | ||||||||
\(162\) | −20.1574 | −1.58372 | ||||||||
\(163\) | −12.0663 | −0.945106 | −0.472553 | − | 0.881302i | \(-0.656667\pi\) | ||||
−0.472553 | + | 0.881302i | \(0.656667\pi\) | |||||||
\(164\) | 30.7508 | 2.40124 | ||||||||
\(165\) | −0.414670 | −0.0322820 | ||||||||
\(166\) | 8.42438 | 0.653858 | ||||||||
\(167\) | 14.4440 | 1.11771 | 0.558856 | − | 0.829265i | \(-0.311240\pi\) | ||||
0.558856 | + | 0.829265i | \(0.311240\pi\) | |||||||
\(168\) | −9.91007 | −0.764579 | ||||||||
\(169\) | −6.64669 | −0.511284 | ||||||||
\(170\) | 7.49068 | 0.574509 | ||||||||
\(171\) | −20.7381 | −1.58588 | ||||||||
\(172\) | −13.8165 | −1.05350 | ||||||||
\(173\) | 9.69087 | 0.736783 | 0.368391 | − | 0.929671i | \(-0.379909\pi\) | ||||
0.368391 | + | 0.929671i | \(0.379909\pi\) | |||||||
\(174\) | −6.73244 | −0.510385 | ||||||||
\(175\) | 17.8105 | 1.34635 | ||||||||
\(176\) | −2.71946 | −0.204987 | ||||||||
\(177\) | −2.59682 | −0.195189 | ||||||||
\(178\) | −25.2407 | −1.89187 | ||||||||
\(179\) | −12.2123 | −0.912789 | −0.456394 | − | 0.889778i | \(-0.650859\pi\) | ||||
−0.456394 | + | 0.889778i | \(0.650859\pi\) | |||||||
\(180\) | −37.6226 | −2.80422 | ||||||||
\(181\) | −21.9847 | −1.63411 | −0.817055 | − | 0.576560i | \(-0.804395\pi\) | ||||
−0.817055 | + | 0.576560i | \(0.804395\pi\) | |||||||
\(182\) | 30.2943 | 2.24556 | ||||||||
\(183\) | −2.17460 | −0.160751 | ||||||||
\(184\) | −25.5595 | −1.88427 | ||||||||
\(185\) | −31.4667 | −2.31348 | ||||||||
\(186\) | −3.75306 | −0.275188 | ||||||||
\(187\) | 0.409857 | 0.0299717 | ||||||||
\(188\) | −5.01582 | −0.365816 | ||||||||
\(189\) | −9.55018 | −0.694673 | ||||||||
\(190\) | −53.8815 | −3.90897 | ||||||||
\(191\) | 1.37577 | 0.0995476 | 0.0497738 | − | 0.998761i | \(-0.484150\pi\) | ||||
0.0497738 | + | 0.998761i | \(0.484150\pi\) | |||||||
\(192\) | −0.563106 | −0.0406387 | ||||||||
\(193\) | −0.410100 | −0.0295197 | −0.0147598 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147598 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(194\) | 5.77614 | 0.414703 | ||||||||
\(195\) | −2.55018 | −0.182622 | ||||||||
\(196\) | 68.5106 | 4.89361 | ||||||||
\(197\) | −21.6674 | −1.54374 | −0.771870 | − | 0.635780i | \(-0.780679\pi\) | ||||
−0.771870 | + | 0.635780i | \(0.780679\pi\) | |||||||
\(198\) | −2.99190 | −0.212625 | ||||||||
\(199\) | −20.0987 | −1.42476 | −0.712381 | − | 0.701793i | \(-0.752383\pi\) | ||||
−0.712381 | + | 0.701793i | \(0.752383\pi\) | |||||||
\(200\) | −22.9059 | −1.61969 | ||||||||
\(201\) | −0.782632 | −0.0552026 | ||||||||
\(202\) | −10.7890 | −0.759111 | ||||||||
\(203\) | 36.9056 | 2.59026 | ||||||||
\(204\) | −1.50853 | −0.105618 | ||||||||
\(205\) | 20.6241 | 1.44045 | ||||||||
\(206\) | 36.6444 | 2.55314 | ||||||||
\(207\) | −12.0708 | −0.838979 | ||||||||
\(208\) | −16.7244 | −1.15963 | ||||||||
\(209\) | −2.94815 | −0.203928 | ||||||||
\(210\) | −12.1599 | −0.839114 | ||||||||
\(211\) | 14.9466 | 1.02897 | 0.514484 | − | 0.857500i | \(-0.327983\pi\) | ||||
0.514484 | + | 0.857500i | \(0.327983\pi\) | |||||||
\(212\) | 26.7210 | 1.83521 | ||||||||
\(213\) | 5.62947 | 0.385725 | ||||||||
\(214\) | −39.6035 | −2.70724 | ||||||||
\(215\) | −9.26648 | −0.631969 | ||||||||
\(216\) | 12.2824 | 0.835710 | ||||||||
\(217\) | 20.5734 | 1.39661 | ||||||||
\(218\) | −27.9922 | −1.89587 | ||||||||
\(219\) | 1.11140 | 0.0751016 | ||||||||
\(220\) | −5.34847 | −0.360594 | ||||||||
\(221\) | 2.52058 | 0.169552 | ||||||||
\(222\) | 9.21024 | 0.618151 | ||||||||
\(223\) | 8.23191 | 0.551250 | 0.275625 | − | 0.961265i | \(-0.411115\pi\) | ||||
0.275625 | + | 0.961265i | \(0.411115\pi\) | |||||||
\(224\) | −21.7911 | −1.45598 | ||||||||
\(225\) | −10.8176 | −0.721174 | ||||||||
\(226\) | 15.4719 | 1.02918 | ||||||||
\(227\) | −26.6748 | −1.77047 | −0.885235 | − | 0.465145i | \(-0.846002\pi\) | ||||
−0.885235 | + | 0.465145i | \(0.846002\pi\) | |||||||
\(228\) | 10.8510 | 0.718628 | ||||||||
\(229\) | 24.9900 | 1.65139 | 0.825694 | − | 0.564118i | \(-0.190784\pi\) | ||||
0.825694 | + | 0.564118i | \(0.190784\pi\) | |||||||
\(230\) | −31.3622 | −2.06796 | ||||||||
\(231\) | −0.665336 | −0.0437759 | ||||||||
\(232\) | −47.4638 | −3.11615 | ||||||||
\(233\) | 13.9733 | 0.915421 | 0.457710 | − | 0.889101i | \(-0.348670\pi\) | ||||
0.457710 | + | 0.889101i | \(0.348670\pi\) | |||||||
\(234\) | −18.3999 | −1.20284 | ||||||||
\(235\) | −3.36402 | −0.219445 | ||||||||
\(236\) | −33.4942 | −2.18029 | ||||||||
\(237\) | −4.90289 | −0.318477 | ||||||||
\(238\) | 12.0188 | 0.779062 | ||||||||
\(239\) | 29.4534 | 1.90518 | 0.952590 | − | 0.304256i | \(-0.0984078\pi\) | ||||
0.952590 | + | 0.304256i | \(0.0984078\pi\) | |||||||
\(240\) | 6.71307 | 0.433327 | ||||||||
\(241\) | 6.60081 | 0.425195 | 0.212598 | − | 0.977140i | \(-0.431808\pi\) | ||||
0.212598 | + | 0.977140i | \(0.431808\pi\) | |||||||
\(242\) | 27.4267 | 1.76305 | ||||||||
\(243\) | 8.75842 | 0.561853 | ||||||||
\(244\) | −28.0484 | −1.79561 | ||||||||
\(245\) | 45.9488 | 2.93556 | ||||||||
\(246\) | −6.03662 | −0.384881 | ||||||||
\(247\) | −18.1308 | −1.15364 | ||||||||
\(248\) | −26.4592 | −1.68016 | ||||||||
\(249\) | −1.13785 | −0.0721086 | ||||||||
\(250\) | 9.34724 | 0.591171 | ||||||||
\(251\) | 16.9869 | 1.07220 | 0.536101 | − | 0.844154i | \(-0.319897\pi\) | ||||
0.536101 | + | 0.844154i | \(0.319897\pi\) | |||||||
\(252\) | −60.3654 | −3.80266 | ||||||||
\(253\) | −1.71600 | −0.107884 | ||||||||
\(254\) | −42.5529 | −2.67001 | ||||||||
\(255\) | −1.01174 | −0.0633578 | ||||||||
\(256\) | −30.5105 | −1.90691 | ||||||||
\(257\) | −3.78822 | −0.236303 | −0.118151 | − | 0.992996i | \(-0.537697\pi\) | ||||
−0.118151 | + | 0.992996i | \(0.537697\pi\) | |||||||
\(258\) | 2.71228 | 0.168859 | ||||||||
\(259\) | −50.4882 | −3.13719 | ||||||||
\(260\) | −32.8926 | −2.03991 | ||||||||
\(261\) | −22.4154 | −1.38748 | ||||||||
\(262\) | 27.9444 | 1.72641 | ||||||||
\(263\) | −11.5568 | −0.712624 | −0.356312 | − | 0.934367i | \(-0.615966\pi\) | ||||
−0.356312 | + | 0.934367i | \(0.615966\pi\) | |||||||
\(264\) | 0.855682 | 0.0526636 | ||||||||
\(265\) | 17.9213 | 1.10090 | ||||||||
\(266\) | −86.4526 | −5.30075 | ||||||||
\(267\) | 3.40918 | 0.208638 | ||||||||
\(268\) | −10.0945 | −0.616620 | ||||||||
\(269\) | 22.4938 | 1.37147 | 0.685735 | − | 0.727851i | \(-0.259481\pi\) | ||||
0.685735 | + | 0.727851i | \(0.259481\pi\) | |||||||
\(270\) | 15.0708 | 0.917180 | ||||||||
\(271\) | 21.4222 | 1.30131 | 0.650653 | − | 0.759375i | \(-0.274495\pi\) | ||||
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(272\) | −6.63515 | −0.402315 | ||||||||
\(273\) | −4.09175 | −0.247644 | ||||||||
\(274\) | −31.0600 | −1.87640 | ||||||||
\(275\) | −1.53784 | −0.0927355 | ||||||||
\(276\) | 6.31595 | 0.380175 | ||||||||
\(277\) | 1.73374 | 0.104170 | 0.0520852 | − | 0.998643i | \(-0.483413\pi\) | ||||
0.0520852 | + | 0.998643i | \(0.483413\pi\) | |||||||
\(278\) | −5.76368 | −0.345683 | ||||||||
\(279\) | −12.4957 | −0.748097 | ||||||||
\(280\) | −85.7277 | −5.12321 | ||||||||
\(281\) | −8.68295 | −0.517981 | −0.258991 | − | 0.965880i | \(-0.583390\pi\) | ||||
−0.258991 | + | 0.965880i | \(0.583390\pi\) | |||||||
\(282\) | 0.984642 | 0.0586346 | ||||||||
\(283\) | −20.9842 | −1.24738 | −0.623689 | − | 0.781672i | \(-0.714367\pi\) | ||||
−0.623689 | + | 0.781672i | \(0.714367\pi\) | |||||||
\(284\) | 72.6098 | 4.30860 | ||||||||
\(285\) | 7.27760 | 0.431088 | ||||||||
\(286\) | −2.61575 | −0.154672 | ||||||||
\(287\) | 33.0912 | 1.95331 | ||||||||
\(288\) | 13.2353 | 0.779897 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −58.2394 | −3.41994 | ||||||||
\(291\) | −0.780166 | −0.0457341 | ||||||||
\(292\) | 14.3350 | 0.838895 | ||||||||
\(293\) | 0.782898 | 0.0457374 | 0.0228687 | − | 0.999738i | \(-0.492720\pi\) | ||||
0.0228687 | + | 0.999738i | \(0.492720\pi\) | |||||||
\(294\) | −13.4491 | −0.784369 | ||||||||
\(295\) | −22.4640 | −1.30790 | ||||||||
\(296\) | 64.9324 | 3.77412 | ||||||||
\(297\) | 0.824607 | 0.0478485 | ||||||||
\(298\) | 15.9827 | 0.925852 | ||||||||
\(299\) | −10.5532 | −0.610309 | ||||||||
\(300\) | 5.66023 | 0.326793 | ||||||||
\(301\) | −14.8680 | −0.856980 | ||||||||
\(302\) | −1.50901 | −0.0868337 | ||||||||
\(303\) | 1.45724 | 0.0837160 | ||||||||
\(304\) | 47.7275 | 2.73736 | ||||||||
\(305\) | −18.8116 | −1.07715 | ||||||||
\(306\) | −7.29987 | −0.417306 | ||||||||
\(307\) | −7.20908 | −0.411444 | −0.205722 | − | 0.978611i | \(-0.565954\pi\) | ||||
−0.205722 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(308\) | −8.58161 | −0.488982 | ||||||||
\(309\) | −4.94945 | −0.281564 | ||||||||
\(310\) | −32.4661 | −1.84395 | ||||||||
\(311\) | −12.0123 | −0.681157 | −0.340579 | − | 0.940216i | \(-0.610623\pi\) | ||||
−0.340579 | + | 0.940216i | \(0.610623\pi\) | |||||||
\(312\) | 5.26236 | 0.297922 | ||||||||
\(313\) | 32.9807 | 1.86418 | 0.932089 | − | 0.362231i | \(-0.117985\pi\) | ||||
0.932089 | + | 0.362231i | \(0.117985\pi\) | |||||||
\(314\) | −46.0712 | −2.59995 | ||||||||
\(315\) | −40.4860 | −2.28113 | ||||||||
\(316\) | −63.2381 | −3.55742 | ||||||||
\(317\) | 18.6264 | 1.04616 | 0.523080 | − | 0.852283i | \(-0.324783\pi\) | ||||
0.523080 | + | 0.852283i | \(0.324783\pi\) | |||||||
\(318\) | −5.24554 | −0.294155 | ||||||||
\(319\) | −3.18660 | −0.178415 | ||||||||
\(320\) | −4.87118 | −0.272307 | ||||||||
\(321\) | 5.34912 | 0.298559 | ||||||||
\(322\) | −50.3206 | −2.80426 | ||||||||
\(323\) | −7.19313 | −0.400236 | ||||||||
\(324\) | 35.1165 | 1.95092 | ||||||||
\(325\) | −9.45759 | −0.524613 | ||||||||
\(326\) | 30.5519 | 1.69211 | ||||||||
\(327\) | 3.78083 | 0.209080 | ||||||||
\(328\) | −42.5583 | −2.34989 | ||||||||
\(329\) | −5.39756 | −0.297577 | ||||||||
\(330\) | 1.04994 | 0.0577975 | ||||||||
\(331\) | −17.4541 | −0.959364 | −0.479682 | − | 0.877442i | \(-0.659248\pi\) | ||||
−0.479682 | + | 0.877442i | \(0.659248\pi\) | |||||||
\(332\) | −14.6762 | −0.805462 | ||||||||
\(333\) | 30.6651 | 1.68044 | ||||||||
\(334\) | −36.5723 | −2.00115 | ||||||||
\(335\) | −6.77020 | −0.369896 | ||||||||
\(336\) | 10.7711 | 0.587612 | ||||||||
\(337\) | −14.1556 | −0.771103 | −0.385551 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385551 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(338\) | 16.8294 | 0.915400 | ||||||||
\(339\) | −2.08975 | −0.113500 | ||||||||
\(340\) | −13.0496 | −0.707715 | ||||||||
\(341\) | −1.77640 | −0.0961974 | ||||||||
\(342\) | 52.5089 | 2.83936 | ||||||||
\(343\) | 40.4975 | 2.18666 | ||||||||
\(344\) | 19.1216 | 1.03097 | ||||||||
\(345\) | 4.23600 | 0.228058 | ||||||||
\(346\) | −24.5373 | −1.31913 | ||||||||
\(347\) | −25.8478 | −1.38758 | −0.693792 | − | 0.720176i | \(-0.744061\pi\) | ||||
−0.693792 | + | 0.720176i | \(0.744061\pi\) | |||||||
\(348\) | 11.7287 | 0.628723 | ||||||||
\(349\) | 6.77753 | 0.362793 | 0.181396 | − | 0.983410i | \(-0.441938\pi\) | ||||
0.181396 | + | 0.983410i | \(0.441938\pi\) | |||||||
\(350\) | −45.0963 | −2.41050 | ||||||||
\(351\) | 5.07125 | 0.270683 | ||||||||
\(352\) | 1.88154 | 0.100287 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 6.57516 | 0.349466 | ||||||||
\(355\) | 48.6981 | 2.58463 | ||||||||
\(356\) | 43.9721 | 2.33052 | ||||||||
\(357\) | −1.62334 | −0.0859162 | ||||||||
\(358\) | 30.9215 | 1.63425 | ||||||||
\(359\) | −12.7456 | −0.672687 | −0.336343 | − | 0.941739i | \(-0.609190\pi\) | ||||
−0.336343 | + | 0.941739i | \(0.609190\pi\) | |||||||
\(360\) | 52.0686 | 2.74426 | ||||||||
\(361\) | 32.7411 | 1.72322 | ||||||||
\(362\) | 55.6653 | 2.92570 | ||||||||
\(363\) | −3.70444 | −0.194433 | ||||||||
\(364\) | −52.7760 | −2.76622 | ||||||||
\(365\) | 9.61426 | 0.503233 | ||||||||
\(366\) | 5.50610 | 0.287809 | ||||||||
\(367\) | 4.22149 | 0.220360 | 0.110180 | − | 0.993912i | \(-0.464857\pi\) | ||||
0.110180 | + | 0.993912i | \(0.464857\pi\) | |||||||
\(368\) | 27.7802 | 1.44815 | ||||||||
\(369\) | −20.0987 | −1.04630 | ||||||||
\(370\) | 79.6738 | 4.14204 | ||||||||
\(371\) | 28.7547 | 1.49287 | ||||||||
\(372\) | 6.53826 | 0.338993 | ||||||||
\(373\) | 27.8829 | 1.44372 | 0.721861 | − | 0.692038i | \(-0.243287\pi\) | ||||
0.721861 | + | 0.692038i | \(0.243287\pi\) | |||||||
\(374\) | −1.03776 | −0.0536612 | ||||||||
\(375\) | −1.26250 | −0.0651953 | ||||||||
\(376\) | 6.94175 | 0.357993 | ||||||||
\(377\) | −19.5973 | −1.00931 | ||||||||
\(378\) | 24.1811 | 1.24374 | ||||||||
\(379\) | 14.0382 | 0.721094 | 0.360547 | − | 0.932741i | \(-0.382590\pi\) | ||||
0.360547 | + | 0.932741i | \(0.382590\pi\) | |||||||
\(380\) | 93.8676 | 4.81531 | ||||||||
\(381\) | 5.74749 | 0.294453 | ||||||||
\(382\) | −3.48346 | −0.178230 | ||||||||
\(383\) | 33.3653 | 1.70489 | 0.852443 | − | 0.522820i | \(-0.175120\pi\) | ||||
0.852443 | + | 0.522820i | \(0.175120\pi\) | |||||||
\(384\) | 4.56575 | 0.232995 | ||||||||
\(385\) | −5.75553 | −0.293329 | ||||||||
\(386\) | 1.03837 | 0.0528519 | ||||||||
\(387\) | 9.03043 | 0.459043 | ||||||||
\(388\) | −10.0627 | −0.510856 | ||||||||
\(389\) | −19.3089 | −0.978999 | −0.489499 | − | 0.872004i | \(-0.662820\pi\) | ||||
−0.489499 | + | 0.872004i | \(0.662820\pi\) | |||||||
\(390\) | 6.45706 | 0.326966 | ||||||||
\(391\) | −4.18683 | −0.211737 | ||||||||
\(392\) | −94.8166 | −4.78896 | ||||||||
\(393\) | −3.77436 | −0.190391 | ||||||||
\(394\) | 54.8620 | 2.76391 | ||||||||
\(395\) | −42.4127 | −2.13402 | ||||||||
\(396\) | 5.21223 | 0.261924 | ||||||||
\(397\) | −36.6621 | −1.84002 | −0.920008 | − | 0.391899i | \(-0.871818\pi\) | ||||
−0.920008 | + | 0.391899i | \(0.871818\pi\) | |||||||
\(398\) | 50.8901 | 2.55089 | ||||||||
\(399\) | 11.6769 | 0.584576 | ||||||||
\(400\) | 24.8961 | 1.24480 | ||||||||
\(401\) | −20.1902 | −1.00825 | −0.504124 | − | 0.863631i | \(-0.668185\pi\) | ||||
−0.504124 | + | 0.863631i | \(0.668185\pi\) | |||||||
\(402\) | 1.98162 | 0.0988345 | ||||||||
\(403\) | −10.9247 | −0.544197 | ||||||||
\(404\) | 18.7956 | 0.935118 | ||||||||
\(405\) | 23.5520 | 1.17031 | ||||||||
\(406\) | −93.4450 | −4.63760 | ||||||||
\(407\) | 4.35939 | 0.216087 | ||||||||
\(408\) | 2.08776 | 0.103359 | ||||||||
\(409\) | 16.0783 | 0.795021 | 0.397511 | − | 0.917598i | \(-0.369874\pi\) | ||||
0.397511 | + | 0.917598i | \(0.369874\pi\) | |||||||
\(410\) | −52.2202 | −2.57897 | ||||||||
\(411\) | 4.19517 | 0.206933 | ||||||||
\(412\) | −63.8387 | −3.14511 | ||||||||
\(413\) | −36.0434 | −1.77358 | ||||||||
\(414\) | 30.5633 | 1.50210 | ||||||||
\(415\) | −9.84308 | −0.483178 | ||||||||
\(416\) | 11.5713 | 0.567330 | ||||||||
\(417\) | 0.778483 | 0.0381225 | ||||||||
\(418\) | 7.46472 | 0.365112 | ||||||||
\(419\) | 23.9982 | 1.17239 | 0.586194 | − | 0.810170i | \(-0.300626\pi\) | ||||
0.586194 | + | 0.810170i | \(0.300626\pi\) | |||||||
\(420\) | 21.1840 | 1.03367 | ||||||||
\(421\) | −26.2973 | −1.28165 | −0.640827 | − | 0.767685i | \(-0.721408\pi\) | ||||
−0.640827 | + | 0.767685i | \(0.721408\pi\) | |||||||
\(422\) | −37.8449 | −1.84226 | ||||||||
\(423\) | 3.27833 | 0.159398 | ||||||||
\(424\) | −36.9812 | −1.79596 | ||||||||
\(425\) | −3.75215 | −0.182006 | ||||||||
\(426\) | −14.2538 | −0.690601 | ||||||||
\(427\) | −30.1831 | −1.46066 | ||||||||
\(428\) | 68.9938 | 3.33494 | ||||||||
\(429\) | 0.353301 | 0.0170575 | ||||||||
\(430\) | 23.4628 | 1.13147 | ||||||||
\(431\) | 0.426122 | 0.0205256 | 0.0102628 | − | 0.999947i | \(-0.496733\pi\) | ||||
0.0102628 | + | 0.999947i | \(0.496733\pi\) | |||||||
\(432\) | −13.3495 | −0.642280 | ||||||||
\(433\) | 28.9559 | 1.39153 | 0.695765 | − | 0.718269i | \(-0.255065\pi\) | ||||
0.695765 | + | 0.718269i | \(0.255065\pi\) | |||||||
\(434\) | −52.0918 | −2.50048 | ||||||||
\(435\) | 7.86622 | 0.377156 | ||||||||
\(436\) | 48.7656 | 2.33545 | ||||||||
\(437\) | 30.1164 | 1.44066 | ||||||||
\(438\) | −2.81407 | −0.134462 | ||||||||
\(439\) | 5.15871 | 0.246212 | 0.123106 | − | 0.992394i | \(-0.460714\pi\) | ||||
0.123106 | + | 0.992394i | \(0.460714\pi\) | |||||||
\(440\) | 7.40213 | 0.352883 | ||||||||
\(441\) | −44.7784 | −2.13230 | ||||||||
\(442\) | −6.38211 | −0.303566 | ||||||||
\(443\) | −11.7649 | −0.558966 | −0.279483 | − | 0.960151i | \(-0.590163\pi\) | ||||
−0.279483 | + | 0.960151i | \(0.590163\pi\) | |||||||
\(444\) | −16.0453 | −0.761475 | ||||||||
\(445\) | 29.4913 | 1.39802 | ||||||||
\(446\) | −20.8432 | −0.986955 | ||||||||
\(447\) | −2.15873 | −0.102105 | ||||||||
\(448\) | −7.81580 | −0.369262 | ||||||||
\(449\) | 27.3016 | 1.28844 | 0.644222 | − | 0.764839i | \(-0.277181\pi\) | ||||
0.644222 | + | 0.764839i | \(0.277181\pi\) | |||||||
\(450\) | 27.3902 | 1.29119 | ||||||||
\(451\) | −2.85725 | −0.134543 | ||||||||
\(452\) | −26.9539 | −1.26780 | ||||||||
\(453\) | 0.203817 | 0.00957617 | ||||||||
\(454\) | 67.5407 | 3.16984 | ||||||||
\(455\) | −35.3960 | −1.65939 | ||||||||
\(456\) | −15.0175 | −0.703260 | ||||||||
\(457\) | −7.11366 | −0.332763 | −0.166382 | − | 0.986061i | \(-0.553208\pi\) | ||||
−0.166382 | + | 0.986061i | \(0.553208\pi\) | |||||||
\(458\) | −63.2748 | −2.95664 | ||||||||
\(459\) | 2.01194 | 0.0939093 | ||||||||
\(460\) | 54.6365 | 2.54744 | ||||||||
\(461\) | 8.72953 | 0.406575 | 0.203287 | − | 0.979119i | \(-0.434837\pi\) | ||||
0.203287 | + | 0.979119i | \(0.434837\pi\) | |||||||
\(462\) | 1.68463 | 0.0783762 | ||||||||
\(463\) | −6.66026 | −0.309528 | −0.154764 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154764 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(464\) | 51.5877 | 2.39490 | ||||||||
\(465\) | 4.38510 | 0.203354 | ||||||||
\(466\) | −35.3804 | −1.63897 | ||||||||
\(467\) | −6.84422 | −0.316713 | −0.158356 | − | 0.987382i | \(-0.550619\pi\) | ||||
−0.158356 | + | 0.987382i | \(0.550619\pi\) | |||||||
\(468\) | 32.0547 | 1.48173 | ||||||||
\(469\) | −10.8628 | −0.501596 | ||||||||
\(470\) | 8.51771 | 0.392893 | ||||||||
\(471\) | 6.22270 | 0.286727 | ||||||||
\(472\) | 46.3550 | 2.13366 | ||||||||
\(473\) | 1.28378 | 0.0590281 | ||||||||
\(474\) | 12.4141 | 0.570199 | ||||||||
\(475\) | 26.9897 | 1.23837 | ||||||||
\(476\) | −20.9381 | −0.959695 | ||||||||
\(477\) | −17.4648 | −0.799659 | ||||||||
\(478\) | −74.5760 | −3.41103 | ||||||||
\(479\) | −6.21841 | −0.284126 | −0.142063 | − | 0.989858i | \(-0.545374\pi\) | ||||
−0.142063 | + | 0.989858i | \(0.545374\pi\) | |||||||
\(480\) | −4.64465 | −0.211998 | ||||||||
\(481\) | 26.8098 | 1.22242 | ||||||||
\(482\) | −16.7133 | −0.761268 | ||||||||
\(483\) | 6.79664 | 0.309258 | ||||||||
\(484\) | −47.7804 | −2.17184 | ||||||||
\(485\) | −6.74888 | −0.306451 | ||||||||
\(486\) | −22.1763 | −1.00594 | ||||||||
\(487\) | −10.1103 | −0.458140 | −0.229070 | − | 0.973410i | \(-0.573568\pi\) | ||||
−0.229070 | + | 0.973410i | \(0.573568\pi\) | |||||||
\(488\) | 38.8181 | 1.75721 | ||||||||
\(489\) | −4.12655 | −0.186609 | ||||||||
\(490\) | −116.343 | −5.25582 | ||||||||
\(491\) | −23.1841 | −1.04628 | −0.523142 | − | 0.852246i | \(-0.675240\pi\) | ||||
−0.523142 | + | 0.852246i | \(0.675240\pi\) | |||||||
\(492\) | 10.5165 | 0.474119 | ||||||||
\(493\) | −7.77491 | −0.350164 | ||||||||
\(494\) | 45.9073 | 2.06547 | ||||||||
\(495\) | 3.49575 | 0.157122 | ||||||||
\(496\) | 28.7581 | 1.29128 | ||||||||
\(497\) | 78.1360 | 3.50488 | ||||||||
\(498\) | 2.88105 | 0.129103 | ||||||||
\(499\) | −8.02004 | −0.359026 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(500\) | −16.2839 | −0.728240 | ||||||||
\(501\) | 4.93971 | 0.220690 | ||||||||
\(502\) | −43.0108 | −1.91967 | ||||||||
\(503\) | −40.2426 | −1.79433 | −0.897164 | − | 0.441697i | \(-0.854377\pi\) | ||||
−0.897164 | + | 0.441697i | \(0.854377\pi\) | |||||||
\(504\) | 83.5439 | 3.72134 | ||||||||
\(505\) | 12.6059 | 0.560956 | ||||||||
\(506\) | 4.34491 | 0.193155 | ||||||||
\(507\) | −2.27310 | −0.100952 | ||||||||
\(508\) | 74.1320 | 3.28908 | ||||||||
\(509\) | −36.6408 | −1.62408 | −0.812038 | − | 0.583604i | \(-0.801642\pi\) | ||||
−0.812038 | + | 0.583604i | \(0.801642\pi\) | |||||||
\(510\) | 2.56174 | 0.113436 | ||||||||
\(511\) | 15.4260 | 0.682408 | ||||||||
\(512\) | 50.5516 | 2.23409 | ||||||||
\(513\) | −14.4721 | −0.638961 | ||||||||
\(514\) | 9.59179 | 0.423076 | ||||||||
\(515\) | −42.8155 | −1.88668 | ||||||||
\(516\) | −4.72510 | −0.208011 | ||||||||
\(517\) | 0.466051 | 0.0204969 | ||||||||
\(518\) | 127.836 | 5.61681 | ||||||||
\(519\) | 3.31418 | 0.145476 | ||||||||
\(520\) | 45.5224 | 1.99629 | ||||||||
\(521\) | 6.10851 | 0.267619 | 0.133809 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133809 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(522\) | 56.7559 | 2.48414 | ||||||||
\(523\) | −2.29166 | −0.100207 | −0.0501036 | − | 0.998744i | \(-0.515955\pi\) | ||||
−0.0501036 | + | 0.998744i | \(0.515955\pi\) | |||||||
\(524\) | −48.6823 | −2.12669 | ||||||||
\(525\) | 6.09102 | 0.265834 | ||||||||
\(526\) | 29.2619 | 1.27588 | ||||||||
\(527\) | −4.33420 | −0.188801 | ||||||||
\(528\) | −0.930028 | −0.0404743 | ||||||||
\(529\) | −5.47046 | −0.237846 | ||||||||
\(530\) | −45.3769 | −1.97105 | ||||||||
\(531\) | 21.8917 | 0.950020 | ||||||||
\(532\) | 150.610 | 6.52978 | ||||||||
\(533\) | −17.5718 | −0.761120 | ||||||||
\(534\) | −8.63205 | −0.373545 | ||||||||
\(535\) | 46.2729 | 2.00055 | ||||||||
\(536\) | 13.9705 | 0.603433 | ||||||||
\(537\) | −4.17647 | −0.180228 | ||||||||
\(538\) | −56.9543 | −2.45548 | ||||||||
\(539\) | −6.36574 | −0.274192 | ||||||||
\(540\) | −26.2551 | −1.12984 | ||||||||
\(541\) | 19.3560 | 0.832179 | 0.416090 | − | 0.909324i | \(-0.363400\pi\) | ||||
0.416090 | + | 0.909324i | \(0.363400\pi\) | |||||||
\(542\) | −54.2411 | −2.32985 | ||||||||
\(543\) | −7.51854 | −0.322652 | ||||||||
\(544\) | 4.59073 | 0.196826 | ||||||||
\(545\) | 32.7063 | 1.40098 | ||||||||
\(546\) | 10.3603 | 0.443381 | ||||||||
\(547\) | −1.50650 | −0.0644134 | −0.0322067 | − | 0.999481i | \(-0.510253\pi\) | ||||
−0.0322067 | + | 0.999481i | \(0.510253\pi\) | |||||||
\(548\) | 54.1100 | 2.31146 | ||||||||
\(549\) | 18.3324 | 0.782406 | ||||||||
\(550\) | 3.89382 | 0.166033 | ||||||||
\(551\) | 55.9260 | 2.38253 | ||||||||
\(552\) | −8.74109 | −0.372046 | ||||||||
\(553\) | −68.0511 | −2.89383 | ||||||||
\(554\) | −4.38983 | −0.186506 | ||||||||
\(555\) | −10.7613 | −0.456791 | ||||||||
\(556\) | 10.0410 | 0.425833 | ||||||||
\(557\) | −25.6913 | −1.08857 | −0.544287 | − | 0.838899i | \(-0.683200\pi\) | ||||
−0.544287 | + | 0.838899i | \(0.683200\pi\) | |||||||
\(558\) | 31.6391 | 1.33939 | ||||||||
\(559\) | 7.89510 | 0.333927 | ||||||||
\(560\) | 93.1761 | 3.93741 | ||||||||
\(561\) | 0.140167 | 0.00591784 | ||||||||
\(562\) | 21.9852 | 0.927391 | ||||||||
\(563\) | 39.1193 | 1.64868 | 0.824341 | − | 0.566094i | \(-0.191546\pi\) | ||||
0.824341 | + | 0.566094i | \(0.191546\pi\) | |||||||
\(564\) | −1.71536 | −0.0722296 | ||||||||
\(565\) | −18.0775 | −0.760526 | ||||||||
\(566\) | 53.1319 | 2.23330 | ||||||||
\(567\) | 37.7892 | 1.58700 | ||||||||
\(568\) | −100.490 | −4.21646 | ||||||||
\(569\) | 2.67575 | 0.112173 | 0.0560867 | − | 0.998426i | \(-0.482138\pi\) | ||||
0.0560867 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(570\) | −18.4269 | −0.771818 | ||||||||
\(571\) | 20.2454 | 0.847246 | 0.423623 | − | 0.905839i | \(-0.360758\pi\) | ||||
0.423623 | + | 0.905839i | \(0.360758\pi\) | |||||||
\(572\) | 4.55693 | 0.190535 | ||||||||
\(573\) | 0.470501 | 0.0196555 | ||||||||
\(574\) | −83.7871 | −3.49720 | ||||||||
\(575\) | 15.7096 | 0.655136 | ||||||||
\(576\) | 4.74710 | 0.197796 | ||||||||
\(577\) | −6.21131 | −0.258580 | −0.129290 | − | 0.991607i | \(-0.541270\pi\) | ||||
−0.129290 | + | 0.991607i | \(0.541270\pi\) | |||||||
\(578\) | −2.53200 | −0.105317 | ||||||||
\(579\) | −0.140250 | −0.00582859 | ||||||||
\(580\) | 101.460 | 4.21288 | ||||||||
\(581\) | −15.7932 | −0.655212 | ||||||||
\(582\) | 1.97538 | 0.0818822 | ||||||||
\(583\) | −2.48282 | −0.102828 | ||||||||
\(584\) | −19.8393 | −0.820955 | ||||||||
\(585\) | 21.4985 | 0.888855 | ||||||||
\(586\) | −1.98230 | −0.0818880 | ||||||||
\(587\) | 2.46999 | 0.101948 | 0.0509738 | − | 0.998700i | \(-0.483768\pi\) | ||||
0.0509738 | + | 0.998700i | \(0.483768\pi\) | |||||||
\(588\) | 23.4299 | 0.966233 | ||||||||
\(589\) | 31.1764 | 1.28460 | ||||||||
\(590\) | 56.8788 | 2.34166 | ||||||||
\(591\) | −7.41004 | −0.304808 | ||||||||
\(592\) | −70.5740 | −2.90057 | ||||||||
\(593\) | −6.64938 | −0.273057 | −0.136529 | − | 0.990636i | \(-0.543595\pi\) | ||||
−0.136529 | + | 0.990636i | \(0.543595\pi\) | |||||||
\(594\) | −2.08791 | −0.0856678 | ||||||||
\(595\) | −14.0428 | −0.575699 | ||||||||
\(596\) | −27.8436 | −1.14052 | ||||||||
\(597\) | −6.87356 | −0.281316 | ||||||||
\(598\) | 26.7208 | 1.09269 | ||||||||
\(599\) | 32.4310 | 1.32509 | 0.662547 | − | 0.749020i | \(-0.269475\pi\) | ||||
0.662547 | + | 0.749020i | \(0.269475\pi\) | |||||||
\(600\) | −7.83359 | −0.319805 | ||||||||
\(601\) | 14.6369 | 0.597053 | 0.298527 | − | 0.954401i | \(-0.403505\pi\) | ||||
0.298527 | + | 0.954401i | \(0.403505\pi\) | |||||||
\(602\) | 37.6459 | 1.53433 | ||||||||
\(603\) | 6.59774 | 0.268681 | ||||||||
\(604\) | 2.62887 | 0.106967 | ||||||||
\(605\) | −32.0455 | −1.30283 | ||||||||
\(606\) | −3.68972 | −0.149885 | ||||||||
\(607\) | −5.94197 | −0.241177 | −0.120589 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120589 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(608\) | −33.0217 | −1.33921 | ||||||||
\(609\) | 12.6213 | 0.511442 | ||||||||
\(610\) | 47.6309 | 1.92852 | ||||||||
\(611\) | 2.86617 | 0.115953 | ||||||||
\(612\) | 12.7172 | 0.514062 | ||||||||
\(613\) | −23.6245 | −0.954183 | −0.477091 | − | 0.878854i | \(-0.658309\pi\) | ||||
−0.477091 | + | 0.878854i | \(0.658309\pi\) | |||||||
\(614\) | 18.2534 | 0.736647 | ||||||||
\(615\) | 7.05322 | 0.284413 | ||||||||
\(616\) | 11.8767 | 0.478526 | ||||||||
\(617\) | −31.6910 | −1.27583 | −0.637915 | − | 0.770106i | \(-0.720203\pi\) | ||||
−0.637915 | + | 0.770106i | \(0.720203\pi\) | |||||||
\(618\) | 12.5320 | 0.504112 | ||||||||
\(619\) | −6.63221 | −0.266571 | −0.133286 | − | 0.991078i | \(-0.542553\pi\) | ||||
−0.133286 | + | 0.991078i | \(0.542553\pi\) | |||||||
\(620\) | 56.5596 | 2.27149 | ||||||||
\(621\) | −8.42365 | −0.338029 | ||||||||
\(622\) | 30.4153 | 1.21954 | ||||||||
\(623\) | 47.3187 | 1.89579 | ||||||||
\(624\) | −5.71958 | −0.228966 | ||||||||
\(625\) | −29.6821 | −1.18728 | ||||||||
\(626\) | −83.5071 | −3.33761 | ||||||||
\(627\) | −1.00824 | −0.0402651 | ||||||||
\(628\) | 80.2612 | 3.20277 | ||||||||
\(629\) | 10.6364 | 0.424100 | ||||||||
\(630\) | 102.511 | 4.08412 | ||||||||
\(631\) | 41.9770 | 1.67108 | 0.835538 | − | 0.549432i | \(-0.185156\pi\) | ||||
0.835538 | + | 0.549432i | \(0.185156\pi\) | |||||||
\(632\) | 87.5198 | 3.48135 | ||||||||
\(633\) | 5.11160 | 0.203168 | ||||||||
\(634\) | −47.1620 | −1.87304 | ||||||||
\(635\) | 49.7190 | 1.97304 | ||||||||
\(636\) | 9.13832 | 0.362358 | ||||||||
\(637\) | −39.1487 | −1.55113 | ||||||||
\(638\) | 8.06847 | 0.319434 | ||||||||
\(639\) | −47.4576 | −1.87739 | ||||||||
\(640\) | 39.4963 | 1.56123 | ||||||||
\(641\) | 34.5377 | 1.36416 | 0.682078 | − | 0.731279i | \(-0.261076\pi\) | ||||
0.682078 | + | 0.731279i | \(0.261076\pi\) | |||||||
\(642\) | −13.5440 | −0.534539 | ||||||||
\(643\) | −33.6910 | −1.32864 | −0.664322 | − | 0.747447i | \(-0.731280\pi\) | ||||
−0.664322 | + | 0.747447i | \(0.731280\pi\) | |||||||
\(644\) | 87.6641 | 3.45445 | ||||||||
\(645\) | −3.16904 | −0.124781 | ||||||||
\(646\) | 18.2130 | 0.716582 | ||||||||
\(647\) | −39.8177 | −1.56540 | −0.782698 | − | 0.622402i | \(-0.786157\pi\) | ||||
−0.782698 | + | 0.622402i | \(0.786157\pi\) | |||||||
\(648\) | −48.6003 | −1.90920 | ||||||||
\(649\) | 3.11215 | 0.122163 | ||||||||
\(650\) | 23.9466 | 0.939265 | ||||||||
\(651\) | 7.03587 | 0.275758 | ||||||||
\(652\) | −53.2249 | −2.08445 | ||||||||
\(653\) | −36.9263 | −1.44504 | −0.722519 | − | 0.691351i | \(-0.757016\pi\) | ||||
−0.722519 | + | 0.691351i | \(0.757016\pi\) | |||||||
\(654\) | −9.57306 | −0.374336 | ||||||||
\(655\) | −32.6503 | −1.27575 | ||||||||
\(656\) | 46.2559 | 1.80599 | ||||||||
\(657\) | −9.36935 | −0.365533 | ||||||||
\(658\) | 13.6666 | 0.532781 | ||||||||
\(659\) | 30.0812 | 1.17180 | 0.585898 | − | 0.810385i | \(-0.300742\pi\) | ||||
0.585898 | + | 0.810385i | \(0.300742\pi\) | |||||||
\(660\) | −1.82912 | −0.0711985 | ||||||||
\(661\) | −3.32441 | −0.129305 | −0.0646524 | − | 0.997908i | \(-0.520594\pi\) | ||||
−0.0646524 | + | 0.997908i | \(0.520594\pi\) | |||||||
\(662\) | 44.1938 | 1.71764 | ||||||||
\(663\) | 0.862012 | 0.0334778 | ||||||||
\(664\) | 20.3115 | 0.788237 | ||||||||
\(665\) | 101.012 | 3.91707 | ||||||||
\(666\) | −77.6442 | −3.00865 | ||||||||
\(667\) | 32.5522 | 1.26043 | ||||||||
\(668\) | 63.7131 | 2.46513 | ||||||||
\(669\) | 2.81523 | 0.108843 | ||||||||
\(670\) | 17.1422 | 0.662260 | ||||||||
\(671\) | 2.60615 | 0.100609 | ||||||||
\(672\) | −7.45232 | −0.287479 | ||||||||
\(673\) | 0.727099 | 0.0280276 | 0.0140138 | − | 0.999902i | \(-0.495539\pi\) | ||||
0.0140138 | + | 0.999902i | \(0.495539\pi\) | |||||||
\(674\) | 35.8419 | 1.38058 | ||||||||
\(675\) | −7.54911 | −0.290565 | ||||||||
\(676\) | −29.3188 | −1.12764 | ||||||||
\(677\) | 47.3716 | 1.82064 | 0.910319 | − | 0.413908i | \(-0.135837\pi\) | ||||
0.910319 | + | 0.413908i | \(0.135837\pi\) | |||||||
\(678\) | 5.29124 | 0.203209 | ||||||||
\(679\) | −10.8286 | −0.415562 | ||||||||
\(680\) | 18.0603 | 0.692581 | ||||||||
\(681\) | −9.12251 | −0.349575 | ||||||||
\(682\) | 4.49785 | 0.172231 | ||||||||
\(683\) | −12.6897 | −0.485558 | −0.242779 | − | 0.970082i | \(-0.578059\pi\) | ||||
−0.242779 | + | 0.970082i | \(0.578059\pi\) | |||||||
\(684\) | −91.4765 | −3.49769 | ||||||||
\(685\) | 36.2906 | 1.38659 | ||||||||
\(686\) | −102.540 | −3.91499 | ||||||||
\(687\) | 8.54633 | 0.326063 | ||||||||
\(688\) | −20.7830 | −0.792345 | ||||||||
\(689\) | −15.2691 | −0.581706 | ||||||||
\(690\) | −10.7256 | −0.408315 | ||||||||
\(691\) | −37.5014 | −1.42662 | −0.713310 | − | 0.700848i | \(-0.752805\pi\) | ||||
−0.713310 | + | 0.700848i | \(0.752805\pi\) | |||||||
\(692\) | 42.7467 | 1.62499 | ||||||||
\(693\) | 5.60892 | 0.213065 | ||||||||
\(694\) | 65.4467 | 2.48432 | ||||||||
\(695\) | 6.73432 | 0.255447 | ||||||||
\(696\) | −16.2321 | −0.615278 | ||||||||
\(697\) | −6.97135 | −0.264059 | ||||||||
\(698\) | −17.1607 | −0.649543 | ||||||||
\(699\) | 4.77872 | 0.180748 | ||||||||
\(700\) | 78.5628 | 2.96940 | ||||||||
\(701\) | 30.9827 | 1.17020 | 0.585100 | − | 0.810961i | \(-0.301055\pi\) | ||||
0.585100 | + | 0.810961i | \(0.301055\pi\) | |||||||
\(702\) | −12.8404 | −0.484630 | ||||||||
\(703\) | −76.5089 | −2.88559 | ||||||||
\(704\) | 0.674852 | 0.0254345 | ||||||||
\(705\) | −1.15046 | −0.0433289 | ||||||||
\(706\) | −2.53200 | −0.0952932 | ||||||||
\(707\) | 20.2261 | 0.760682 | ||||||||
\(708\) | −11.4547 | −0.430493 | ||||||||
\(709\) | 26.2119 | 0.984409 | 0.492204 | − | 0.870480i | \(-0.336191\pi\) | ||||
0.492204 | + | 0.870480i | \(0.336191\pi\) | |||||||
\(710\) | −123.304 | −4.62751 | ||||||||
\(711\) | 41.3323 | 1.55008 | ||||||||
\(712\) | −60.8561 | −2.28068 | ||||||||
\(713\) | 18.1465 | 0.679593 | ||||||||
\(714\) | 4.11030 | 0.153824 | ||||||||
\(715\) | 3.05625 | 0.114297 | ||||||||
\(716\) | −53.8688 | −2.01317 | ||||||||
\(717\) | 10.0728 | 0.376174 | ||||||||
\(718\) | 32.2719 | 1.20438 | ||||||||
\(719\) | −10.3708 | −0.386766 | −0.193383 | − | 0.981123i | \(-0.561946\pi\) | ||||
−0.193383 | + | 0.981123i | \(0.561946\pi\) | |||||||
\(720\) | −56.5926 | −2.10908 | ||||||||
\(721\) | −68.6974 | −2.55842 | ||||||||
\(722\) | −82.9006 | −3.08524 | ||||||||
\(723\) | 2.25741 | 0.0839539 | ||||||||
\(724\) | −96.9753 | −3.60406 | ||||||||
\(725\) | 29.1727 | 1.08345 | ||||||||
\(726\) | 9.37965 | 0.348111 | ||||||||
\(727\) | −5.97667 | −0.221663 | −0.110831 | − | 0.993839i | \(-0.535351\pi\) | ||||
−0.110831 | + | 0.993839i | \(0.535351\pi\) | |||||||
\(728\) | 73.0405 | 2.70706 | ||||||||
\(729\) | −20.8879 | −0.773626 | ||||||||
\(730\) | −24.3433 | −0.900987 | ||||||||
\(731\) | 3.13226 | 0.115851 | ||||||||
\(732\) | −9.59226 | −0.354540 | ||||||||
\(733\) | 8.67316 | 0.320350 | 0.160175 | − | 0.987089i | \(-0.448794\pi\) | ||||
0.160175 | + | 0.987089i | \(0.448794\pi\) | |||||||
\(734\) | −10.6888 | −0.394532 | ||||||||
\(735\) | 15.7140 | 0.579621 | ||||||||
\(736\) | −19.2206 | −0.708481 | ||||||||
\(737\) | 0.937943 | 0.0345496 | ||||||||
\(738\) | 50.8899 | 1.87328 | ||||||||
\(739\) | −20.3093 | −0.747091 | −0.373546 | − | 0.927612i | \(-0.621858\pi\) | ||||
−0.373546 | + | 0.927612i | \(0.621858\pi\) | |||||||
\(740\) | −138.801 | −5.10242 | ||||||||
\(741\) | −6.20056 | −0.227783 | ||||||||
\(742\) | −72.8071 | −2.67283 | ||||||||
\(743\) | −16.6153 | −0.609557 | −0.304778 | − | 0.952423i | \(-0.598582\pi\) | ||||
−0.304778 | + | 0.952423i | \(0.598582\pi\) | |||||||
\(744\) | −9.04876 | −0.331744 | ||||||||
\(745\) | −18.6743 | −0.684172 | ||||||||
\(746\) | −70.5996 | −2.58484 | ||||||||
\(747\) | 9.59234 | 0.350966 | ||||||||
\(748\) | 1.80789 | 0.0661030 | ||||||||
\(749\) | 74.2448 | 2.71284 | ||||||||
\(750\) | 3.19666 | 0.116725 | ||||||||
\(751\) | 30.1638 | 1.10069 | 0.550347 | − | 0.834936i | \(-0.314495\pi\) | ||||
0.550347 | + | 0.834936i | \(0.314495\pi\) | |||||||
\(752\) | −7.54488 | −0.275133 | ||||||||
\(753\) | 5.80934 | 0.211704 | ||||||||
\(754\) | 49.6203 | 1.80707 | ||||||||
\(755\) | 1.76313 | 0.0641670 | ||||||||
\(756\) | −42.1262 | −1.53211 | ||||||||
\(757\) | 9.90884 | 0.360143 | 0.180071 | − | 0.983654i | \(-0.442367\pi\) | ||||
0.180071 | + | 0.983654i | \(0.442367\pi\) | |||||||
\(758\) | −35.5447 | −1.29104 | ||||||||
\(759\) | −0.586854 | −0.0213015 | ||||||||
\(760\) | −129.910 | −4.71233 | ||||||||
\(761\) | 1.65148 | 0.0598660 | 0.0299330 | − | 0.999552i | \(-0.490471\pi\) | ||||
0.0299330 | + | 0.999552i | \(0.490471\pi\) | |||||||
\(762\) | −14.5527 | −0.527187 | ||||||||
\(763\) | 52.4771 | 1.89980 | ||||||||
\(764\) | 6.06859 | 0.219554 | ||||||||
\(765\) | 8.52920 | 0.308374 | ||||||||
\(766\) | −84.4809 | −3.05242 | ||||||||
\(767\) | 19.1394 | 0.691085 | ||||||||
\(768\) | −10.4343 | −0.376515 | ||||||||
\(769\) | −40.4713 | −1.45943 | −0.729717 | − | 0.683750i | \(-0.760348\pi\) | ||||
−0.729717 | + | 0.683750i | \(0.760348\pi\) | |||||||
\(770\) | 14.5730 | 0.525175 | ||||||||
\(771\) | −1.29553 | −0.0466575 | ||||||||
\(772\) | −1.80897 | −0.0651061 | ||||||||
\(773\) | 6.38055 | 0.229492 | 0.114746 | − | 0.993395i | \(-0.463395\pi\) | ||||
0.114746 | + | 0.993395i | \(0.463395\pi\) | |||||||
\(774\) | −22.8651 | −0.821868 | ||||||||
\(775\) | 16.2626 | 0.584169 | ||||||||
\(776\) | 13.9265 | 0.499932 | ||||||||
\(777\) | −17.2665 | −0.619431 | ||||||||
\(778\) | 48.8901 | 1.75280 | ||||||||
\(779\) | 50.1458 | 1.79666 | ||||||||
\(780\) | −11.2489 | −0.402776 | ||||||||
\(781\) | −6.74662 | −0.241413 | ||||||||
\(782\) | 10.6011 | 0.379093 | ||||||||
\(783\) | −15.6427 | −0.559023 | ||||||||
\(784\) | 103.055 | 3.68053 | ||||||||
\(785\) | 53.8298 | 1.92127 | ||||||||
\(786\) | 9.55669 | 0.340876 | ||||||||
\(787\) | −32.1561 | −1.14624 | −0.573120 | − | 0.819471i | \(-0.694267\pi\) | ||||
−0.573120 | + | 0.819471i | \(0.694267\pi\) | |||||||
\(788\) | −95.5758 | −3.40475 | ||||||||
\(789\) | −3.95231 | −0.140706 | ||||||||
\(790\) | 107.389 | 3.82073 | ||||||||
\(791\) | −29.0053 | −1.03131 | ||||||||
\(792\) | −7.21357 | −0.256323 | ||||||||
\(793\) | 16.0276 | 0.569155 | ||||||||
\(794\) | 92.8284 | 3.29436 | ||||||||
\(795\) | 6.12891 | 0.217370 | ||||||||
\(796\) | −88.6563 | −3.14234 | ||||||||
\(797\) | 27.3217 | 0.967786 | 0.483893 | − | 0.875127i | \(-0.339222\pi\) | ||||
0.483893 | + | 0.875127i | \(0.339222\pi\) | |||||||
\(798\) | −29.5659 | −1.04662 | ||||||||
\(799\) | 1.13711 | 0.0402280 | ||||||||
\(800\) | −17.2251 | −0.609000 | ||||||||
\(801\) | −28.7401 | −1.01548 | ||||||||
\(802\) | 51.1215 | 1.80516 | ||||||||
\(803\) | −1.33196 | −0.0470037 | ||||||||
\(804\) | −3.45221 | −0.121750 | ||||||||
\(805\) | 58.7948 | 2.07224 | ||||||||
\(806\) | 27.6613 | 0.974328 | ||||||||
\(807\) | 7.69265 | 0.270794 | ||||||||
\(808\) | −26.0126 | −0.915121 | ||||||||
\(809\) | 36.3355 | 1.27749 | 0.638744 | − | 0.769419i | \(-0.279454\pi\) | ||||
0.638744 | + | 0.769419i | \(0.279454\pi\) | |||||||
\(810\) | −59.6338 | −2.09532 | ||||||||
\(811\) | −5.01312 | −0.176034 | −0.0880171 | − | 0.996119i | \(-0.528053\pi\) | ||||
−0.0880171 | + | 0.996119i | \(0.528053\pi\) | |||||||
\(812\) | 162.792 | 5.71287 | ||||||||
\(813\) | 7.32618 | 0.256940 | ||||||||
\(814\) | −11.0380 | −0.386881 | ||||||||
\(815\) | −35.6970 | −1.25041 | ||||||||
\(816\) | −2.26915 | −0.0794363 | ||||||||
\(817\) | −22.5307 | −0.788251 | ||||||||
\(818\) | −40.7103 | −1.42340 | ||||||||
\(819\) | 34.4943 | 1.20533 | ||||||||
\(820\) | 90.9734 | 3.17693 | ||||||||
\(821\) | −29.5605 | −1.03167 | −0.515835 | − | 0.856688i | \(-0.672518\pi\) | ||||
−0.515835 | + | 0.856688i | \(0.672518\pi\) | |||||||
\(822\) | −10.6222 | −0.370491 | ||||||||
\(823\) | −8.83593 | −0.308001 | −0.154001 | − | 0.988071i | \(-0.549216\pi\) | ||||
−0.154001 | + | 0.988071i | \(0.549216\pi\) | |||||||
\(824\) | 88.3509 | 3.07785 | ||||||||
\(825\) | −0.525927 | −0.0183104 | ||||||||
\(826\) | 91.2619 | 3.17541 | ||||||||
\(827\) | −0.669650 | −0.0232860 | −0.0116430 | − | 0.999932i | \(-0.503706\pi\) | ||||
−0.0116430 | + | 0.999932i | \(0.503706\pi\) | |||||||
\(828\) | −53.2447 | −1.85038 | ||||||||
\(829\) | −17.0754 | −0.593052 | −0.296526 | − | 0.955025i | \(-0.595828\pi\) | ||||
−0.296526 | + | 0.955025i | \(0.595828\pi\) | |||||||
\(830\) | 24.9227 | 0.865080 | ||||||||
\(831\) | 0.592921 | 0.0205682 | ||||||||
\(832\) | 4.15028 | 0.143885 | ||||||||
\(833\) | −15.5316 | −0.538139 | ||||||||
\(834\) | −1.97112 | −0.0682543 | ||||||||
\(835\) | 42.7313 | 1.47878 | ||||||||
\(836\) | −13.0044 | −0.449766 | ||||||||
\(837\) | −8.72015 | −0.301412 | ||||||||
\(838\) | −60.7635 | −2.09904 | ||||||||
\(839\) | 26.8408 | 0.926647 | 0.463324 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463324 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(840\) | −29.3180 | −1.01157 | ||||||||
\(841\) | 31.4493 | 1.08446 | ||||||||
\(842\) | 66.5849 | 2.29467 | ||||||||
\(843\) | −2.96948 | −0.102274 | ||||||||
\(844\) | 65.9301 | 2.26941 | ||||||||
\(845\) | −19.6636 | −0.676448 | ||||||||
\(846\) | −8.30073 | −0.285385 | ||||||||
\(847\) | −51.4169 | −1.76670 | ||||||||
\(848\) | 40.1943 | 1.38028 | ||||||||
\(849\) | −7.17636 | −0.246292 | ||||||||
\(850\) | 9.50046 | 0.325863 | ||||||||
\(851\) | −44.5327 | −1.52656 | ||||||||
\(852\) | 24.8318 | 0.850723 | ||||||||
\(853\) | −19.2153 | −0.657921 | −0.328960 | − | 0.944344i | \(-0.606698\pi\) | ||||
−0.328960 | + | 0.944344i | \(0.606698\pi\) | |||||||
\(854\) | 76.4236 | 2.61516 | ||||||||
\(855\) | −61.3517 | −2.09818 | ||||||||
\(856\) | −95.4854 | −3.26362 | ||||||||
\(857\) | −0.0237696 | −0.000811952 0 | −0.000405976 | − | 1.00000i | \(-0.500129\pi\) | ||||
−0.000405976 | 1.00000i | \(0.500129\pi\) | ||||||||
\(858\) | −0.894559 | −0.0305397 | ||||||||
\(859\) | 26.7019 | 0.911057 | 0.455529 | − | 0.890221i | \(-0.349450\pi\) | ||||
0.455529 | + | 0.890221i | \(0.349450\pi\) | |||||||
\(860\) | −40.8748 | −1.39382 | ||||||||
\(861\) | 11.3169 | 0.385678 | ||||||||
\(862\) | −1.07894 | −0.0367489 | ||||||||
\(863\) | 19.5962 | 0.667061 | 0.333531 | − | 0.942739i | \(-0.391760\pi\) | ||||
0.333531 | + | 0.942739i | \(0.391760\pi\) | |||||||
\(864\) | 9.23628 | 0.314225 | ||||||||
\(865\) | 28.6695 | 0.974792 | ||||||||
\(866\) | −73.3163 | −2.49139 | ||||||||
\(867\) | 0.341990 | 0.0116146 | ||||||||
\(868\) | 90.7498 | 3.08025 | ||||||||
\(869\) | 5.87585 | 0.199324 | ||||||||
\(870\) | −19.9173 | −0.675259 | ||||||||
\(871\) | 5.76826 | 0.195450 | ||||||||
\(872\) | −67.4902 | −2.28551 | ||||||||
\(873\) | 6.57696 | 0.222596 | ||||||||
\(874\) | −76.2548 | −2.57936 | ||||||||
\(875\) | −17.5233 | −0.592395 | ||||||||
\(876\) | 4.90243 | 0.165638 | ||||||||
\(877\) | −51.5392 | −1.74035 | −0.870177 | − | 0.492739i | \(-0.835996\pi\) | ||||
−0.870177 | + | 0.492739i | \(0.835996\pi\) | |||||||
\(878\) | −13.0619 | −0.440817 | ||||||||
\(879\) | 0.267743 | 0.00903075 | ||||||||
\(880\) | −8.04526 | −0.271206 | ||||||||
\(881\) | 14.8020 | 0.498693 | 0.249347 | − | 0.968414i | \(-0.419784\pi\) | ||||
0.249347 | + | 0.968414i | \(0.419784\pi\) | |||||||
\(882\) | 113.379 | 3.81767 | ||||||||
\(883\) | 53.7521 | 1.80890 | 0.904452 | − | 0.426576i | \(-0.140280\pi\) | ||||
0.904452 | + | 0.426576i | \(0.140280\pi\) | |||||||
\(884\) | 11.1184 | 0.373951 | ||||||||
\(885\) | −7.68245 | −0.258243 | ||||||||
\(886\) | 29.7887 | 1.00077 | ||||||||
\(887\) | −43.9478 | −1.47562 | −0.737811 | − | 0.675007i | \(-0.764140\pi\) | ||||
−0.737811 | + | 0.675007i | \(0.764140\pi\) | |||||||
\(888\) | 22.2062 | 0.745191 | ||||||||
\(889\) | 79.7741 | 2.67554 | ||||||||
\(890\) | −74.6721 | −2.50301 | ||||||||
\(891\) | −3.26289 | −0.109311 | ||||||||
\(892\) | 36.3112 | 1.21579 | ||||||||
\(893\) | −8.17936 | −0.273712 | ||||||||
\(894\) | 5.46591 | 0.182808 | ||||||||
\(895\) | −36.1289 | −1.20765 | ||||||||
\(896\) | 63.3717 | 2.11710 | ||||||||
\(897\) | −3.60910 | −0.120504 | ||||||||
\(898\) | −69.1278 | −2.30682 | ||||||||
\(899\) | 33.6980 | 1.12389 | ||||||||
\(900\) | −47.7169 | −1.59056 | ||||||||
\(901\) | −6.05777 | −0.201814 | ||||||||
\(902\) | 7.23457 | 0.240885 | ||||||||
\(903\) | −5.08472 | −0.169209 | ||||||||
\(904\) | 37.3034 | 1.24069 | ||||||||
\(905\) | −65.0396 | −2.16199 | ||||||||
\(906\) | −0.516066 | −0.0171451 | ||||||||
\(907\) | 54.1901 | 1.79935 | 0.899677 | − | 0.436556i | \(-0.143802\pi\) | ||||
0.899677 | + | 0.436556i | \(0.143802\pi\) | |||||||
\(908\) | −117.664 | −3.90480 | ||||||||
\(909\) | −12.2848 | −0.407461 | ||||||||
\(910\) | 89.6227 | 2.97096 | ||||||||
\(911\) | −35.4911 | −1.17587 | −0.587936 | − | 0.808907i | \(-0.700059\pi\) | ||||
−0.587936 | + | 0.808907i | \(0.700059\pi\) | |||||||
\(912\) | 16.3223 | 0.540486 | ||||||||
\(913\) | 1.36366 | 0.0451305 | ||||||||
\(914\) | 18.0118 | 0.595778 | ||||||||
\(915\) | −6.43336 | −0.212680 | ||||||||
\(916\) | 110.232 | 3.64216 | ||||||||
\(917\) | −52.3874 | −1.72998 | ||||||||
\(918\) | −5.09424 | −0.168135 | ||||||||
\(919\) | 48.0560 | 1.58522 | 0.792610 | − | 0.609728i | \(-0.208721\pi\) | ||||
0.792610 | + | 0.609728i | \(0.208721\pi\) | |||||||
\(920\) | −75.6154 | −2.49296 | ||||||||
\(921\) | −2.46543 | −0.0812387 | ||||||||
\(922\) | −22.1032 | −0.727930 | ||||||||
\(923\) | −41.4911 | −1.36570 | ||||||||
\(924\) | −2.93482 | −0.0965485 | ||||||||
\(925\) | −39.9093 | −1.31221 | ||||||||
\(926\) | 16.8638 | 0.554178 | ||||||||
\(927\) | 41.7249 | 1.37042 | ||||||||
\(928\) | −35.6926 | −1.17167 | ||||||||
\(929\) | 37.3467 | 1.22531 | 0.612653 | − | 0.790352i | \(-0.290102\pi\) | ||||
0.612653 | + | 0.790352i | \(0.290102\pi\) | |||||||
\(930\) | −11.1031 | −0.364084 | ||||||||
\(931\) | 111.721 | 3.66151 | ||||||||
\(932\) | 61.6367 | 2.01898 | ||||||||
\(933\) | −4.10810 | −0.134493 | ||||||||
\(934\) | 17.3296 | 0.567041 | ||||||||
\(935\) | 1.21252 | 0.0396537 | ||||||||
\(936\) | −44.3628 | −1.45004 | ||||||||
\(937\) | 22.5737 | 0.737451 | 0.368725 | − | 0.929538i | \(-0.379794\pi\) | ||||
0.368725 | + | 0.929538i | \(0.379794\pi\) | |||||||
\(938\) | 27.5046 | 0.898056 | ||||||||
\(939\) | 11.2790 | 0.368078 | ||||||||
\(940\) | −14.8388 | −0.483989 | ||||||||
\(941\) | −18.6755 | −0.608804 | −0.304402 | − | 0.952544i | \(-0.598457\pi\) | ||||
−0.304402 | + | 0.952544i | \(0.598457\pi\) | |||||||
\(942\) | −15.7559 | −0.513354 | ||||||||
\(943\) | 29.1878 | 0.950487 | ||||||||
\(944\) | −50.3825 | −1.63981 | ||||||||
\(945\) | −28.2533 | −0.919079 | ||||||||
\(946\) | −3.25052 | −0.105684 | ||||||||
\(947\) | 30.4023 | 0.987942 | 0.493971 | − | 0.869478i | \(-0.335545\pi\) | ||||
0.493971 | + | 0.869478i | \(0.335545\pi\) | |||||||
\(948\) | −21.6268 | −0.702406 | ||||||||
\(949\) | −8.19141 | −0.265904 | ||||||||
\(950\) | −68.3380 | −2.21718 | ||||||||
\(951\) | 6.37002 | 0.206562 | ||||||||
\(952\) | 28.9777 | 0.939172 | ||||||||
\(953\) | −4.08548 | −0.132342 | −0.0661708 | − | 0.997808i | \(-0.521078\pi\) | ||||
−0.0661708 | + | 0.997808i | \(0.521078\pi\) | |||||||
\(954\) | 44.2210 | 1.43171 | ||||||||
\(955\) | 4.07010 | 0.131705 | ||||||||
\(956\) | 129.920 | 4.20191 | ||||||||
\(957\) | −1.08978 | −0.0352277 | ||||||||
\(958\) | 15.7450 | 0.508699 | ||||||||
\(959\) | 58.2282 | 1.88029 | ||||||||
\(960\) | −1.66589 | −0.0537665 | ||||||||
\(961\) | −12.2147 | −0.394024 | ||||||||
\(962\) | −67.8826 | −2.18862 | ||||||||
\(963\) | −45.0942 | −1.45314 | ||||||||
\(964\) | 29.1164 | 0.937776 | ||||||||
\(965\) | −1.21324 | −0.0390556 | ||||||||
\(966\) | −17.2091 | −0.553694 | ||||||||
\(967\) | −54.3561 | −1.74797 | −0.873987 | − | 0.485950i | \(-0.838474\pi\) | ||||
−0.873987 | + | 0.485950i | \(0.838474\pi\) | |||||||
\(968\) | 66.1267 | 2.12539 | ||||||||
\(969\) | −2.45998 | −0.0790258 | ||||||||
\(970\) | 17.0882 | 0.548668 | ||||||||
\(971\) | 4.53285 | 0.145466 | 0.0727330 | − | 0.997351i | \(-0.476828\pi\) | ||||
0.0727330 | + | 0.997351i | \(0.476828\pi\) | |||||||
\(972\) | 38.6337 | 1.23918 | ||||||||
\(973\) | 10.8052 | 0.346399 | ||||||||
\(974\) | 25.5992 | 0.820252 | ||||||||
\(975\) | −3.23440 | −0.103584 | ||||||||
\(976\) | −42.1908 | −1.35050 | ||||||||
\(977\) | −0.939849 | −0.0300684 | −0.0150342 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150342 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(978\) | 10.4484 | 0.334104 | ||||||||
\(979\) | −4.08572 | −0.130580 | ||||||||
\(980\) | 202.682 | 6.47443 | ||||||||
\(981\) | −31.8731 | −1.01763 | ||||||||
\(982\) | 58.7022 | 1.87326 | ||||||||
\(983\) | 47.6806 | 1.52077 | 0.760387 | − | 0.649470i | \(-0.225009\pi\) | ||||
0.760387 | + | 0.649470i | \(0.225009\pi\) | |||||||
\(984\) | −14.5545 | −0.463980 | ||||||||
\(985\) | −64.1010 | −2.04243 | ||||||||
\(986\) | 19.6861 | 0.626933 | ||||||||
\(987\) | −1.84591 | −0.0587560 | ||||||||
\(988\) | −79.9758 | −2.54437 | ||||||||
\(989\) | −13.1142 | −0.417008 | ||||||||
\(990\) | −8.85125 | −0.281311 | ||||||||
\(991\) | 58.6709 | 1.86374 | 0.931871 | − | 0.362791i | \(-0.118176\pi\) | ||||
0.931871 | + | 0.362791i | \(0.118176\pi\) | |||||||
\(992\) | −19.8971 | −0.631735 | ||||||||
\(993\) | −5.96912 | −0.189424 | ||||||||
\(994\) | −197.840 | −6.27512 | ||||||||
\(995\) | −59.4602 | −1.88502 | ||||||||
\(996\) | −5.01911 | −0.159037 | ||||||||
\(997\) | 13.7179 | 0.434450 | 0.217225 | − | 0.976122i | \(-0.430299\pi\) | ||||
0.217225 | + | 0.976122i | \(0.430299\pi\) | |||||||
\(998\) | 20.3068 | 0.642799 | ||||||||
\(999\) | 21.3998 | 0.677059 |
(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 | 6001.2.a.c.1.9 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.c.1.9 | ✓ | 121 | 1.1 | even | 1 | trivial |