Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89616 | −1.34079 | −0.670393 | − | 0.742006i | \(-0.733874\pi\) | ||||
−0.670393 | + | 0.742006i | \(0.733874\pi\) | |||||||
\(3\) | 2.32800 | 1.34407 | 0.672037 | − | 0.740517i | \(-0.265420\pi\) | ||||
0.672037 | + | 0.740517i | \(0.265420\pi\) | |||||||
\(4\) | 1.59541 | 0.797707 | ||||||||
\(5\) | −3.08512 | −1.37971 | −0.689853 | − | 0.723950i | \(-0.742325\pi\) | ||||
−0.689853 | + | 0.723950i | \(0.742325\pi\) | |||||||
\(6\) | −4.41426 | −1.80212 | ||||||||
\(7\) | 2.27635 | 0.860381 | 0.430190 | − | 0.902738i | \(-0.358446\pi\) | ||||
0.430190 | + | 0.902738i | \(0.358446\pi\) | |||||||
\(8\) | 0.767159 | 0.271232 | ||||||||
\(9\) | 2.41961 | 0.806535 | ||||||||
\(10\) | 5.84987 | 1.84989 | ||||||||
\(11\) | 5.52272 | 1.66516 | 0.832581 | − | 0.553904i | \(-0.186862\pi\) | ||||
0.832581 | + | 0.553904i | \(0.186862\pi\) | |||||||
\(12\) | 3.71413 | 1.07218 | ||||||||
\(13\) | −0.731648 | −0.202923 | −0.101461 | − | 0.994839i | \(-0.532352\pi\) | ||||
−0.101461 | + | 0.994839i | \(0.532352\pi\) | |||||||
\(14\) | −4.31632 | −1.15359 | ||||||||
\(15\) | −7.18216 | −1.85443 | ||||||||
\(16\) | −4.64548 | −1.16137 | ||||||||
\(17\) | −2.27098 | −0.550794 | −0.275397 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275397 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(18\) | −4.58796 | −1.08139 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.92204 | −1.10060 | ||||||||
\(21\) | 5.29936 | 1.15642 | ||||||||
\(22\) | −10.4719 | −2.23263 | ||||||||
\(23\) | −6.66671 | −1.39010 | −0.695052 | − | 0.718959i | \(-0.744619\pi\) | ||||
−0.695052 | + | 0.718959i | \(0.744619\pi\) | |||||||
\(24\) | 1.78595 | 0.364555 | ||||||||
\(25\) | 4.51794 | 0.903588 | ||||||||
\(26\) | 1.38732 | 0.272076 | ||||||||
\(27\) | −1.35116 | −0.260031 | ||||||||
\(28\) | 3.63173 | 0.686332 | ||||||||
\(29\) | −8.44492 | −1.56818 | −0.784091 | − | 0.620646i | \(-0.786871\pi\) | ||||
−0.784091 | + | 0.620646i | \(0.786871\pi\) | |||||||
\(30\) | 13.6185 | 2.48639 | ||||||||
\(31\) | −2.58578 | −0.464420 | −0.232210 | − | 0.972666i | \(-0.574596\pi\) | ||||
−0.232210 | + | 0.972666i | \(0.574596\pi\) | |||||||
\(32\) | 7.27425 | 1.28592 | ||||||||
\(33\) | 12.8569 | 2.23810 | ||||||||
\(34\) | 4.30614 | 0.738497 | ||||||||
\(35\) | −7.02281 | −1.18707 | ||||||||
\(36\) | 3.86027 | 0.643379 | ||||||||
\(37\) | −1.51001 | −0.248244 | −0.124122 | − | 0.992267i | \(-0.539611\pi\) | ||||
−0.124122 | + | 0.992267i | \(0.539611\pi\) | |||||||
\(38\) | −1.89616 | −0.307597 | ||||||||
\(39\) | −1.70328 | −0.272743 | ||||||||
\(40\) | −2.36677 | −0.374220 | ||||||||
\(41\) | 9.69034 | 1.51338 | 0.756688 | − | 0.653776i | \(-0.226816\pi\) | ||||
0.756688 | + | 0.653776i | \(0.226816\pi\) | |||||||
\(42\) | −10.0484 | −1.55051 | ||||||||
\(43\) | −4.59537 | −0.700787 | −0.350394 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350394 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(44\) | 8.81102 | 1.32831 | ||||||||
\(45\) | −7.46477 | −1.11278 | ||||||||
\(46\) | 12.6411 | 1.86383 | ||||||||
\(47\) | −6.50404 | −0.948711 | −0.474356 | − | 0.880333i | \(-0.657319\pi\) | ||||
−0.474356 | + | 0.880333i | \(0.657319\pi\) | |||||||
\(48\) | −10.8147 | −1.56097 | ||||||||
\(49\) | −1.81822 | −0.259745 | ||||||||
\(50\) | −8.56672 | −1.21152 | ||||||||
\(51\) | −5.28686 | −0.740309 | ||||||||
\(52\) | −1.16728 | −0.161873 | ||||||||
\(53\) | −5.13502 | −0.705350 | −0.352675 | − | 0.935746i | \(-0.614728\pi\) | ||||
−0.352675 | + | 0.935746i | \(0.614728\pi\) | |||||||
\(54\) | 2.56201 | 0.348646 | ||||||||
\(55\) | −17.0382 | −2.29743 | ||||||||
\(56\) | 1.74632 | 0.233362 | ||||||||
\(57\) | 2.32800 | 0.308352 | ||||||||
\(58\) | 16.0129 | 2.10260 | ||||||||
\(59\) | −10.8330 | −1.41034 | −0.705171 | − | 0.709037i | \(-0.749130\pi\) | ||||
−0.705171 | + | 0.709037i | \(0.749130\pi\) | |||||||
\(60\) | −11.4585 | −1.47929 | ||||||||
\(61\) | −4.96951 | −0.636281 | −0.318140 | − | 0.948044i | \(-0.603058\pi\) | ||||
−0.318140 | + | 0.948044i | \(0.603058\pi\) | |||||||
\(62\) | 4.90305 | 0.622688 | ||||||||
\(63\) | 5.50788 | 0.693927 | ||||||||
\(64\) | −4.50216 | −0.562770 | ||||||||
\(65\) | 2.25722 | 0.279973 | ||||||||
\(66\) | −24.3787 | −3.00081 | ||||||||
\(67\) | 7.19918 | 0.879520 | 0.439760 | − | 0.898115i | \(-0.355063\pi\) | ||||
0.439760 | + | 0.898115i | \(0.355063\pi\) | |||||||
\(68\) | −3.62316 | −0.439373 | ||||||||
\(69\) | −15.5201 | −1.86840 | ||||||||
\(70\) | 13.3164 | 1.59161 | ||||||||
\(71\) | 0.258044 | 0.0306242 | 0.0153121 | − | 0.999883i | \(-0.495126\pi\) | ||||
0.0153121 | + | 0.999883i | \(0.495126\pi\) | |||||||
\(72\) | 1.85622 | 0.218758 | ||||||||
\(73\) | 12.2945 | 1.43897 | 0.719483 | − | 0.694510i | \(-0.244379\pi\) | ||||
0.719483 | + | 0.694510i | \(0.244379\pi\) | |||||||
\(74\) | 2.86322 | 0.332843 | ||||||||
\(75\) | 10.5178 | 1.21449 | ||||||||
\(76\) | 1.59541 | 0.183007 | ||||||||
\(77\) | 12.5717 | 1.43267 | ||||||||
\(78\) | 3.22969 | 0.365690 | ||||||||
\(79\) | −4.96840 | −0.558989 | −0.279494 | − | 0.960147i | \(-0.590167\pi\) | ||||
−0.279494 | + | 0.960147i | \(0.590167\pi\) | |||||||
\(80\) | 14.3319 | 1.60235 | ||||||||
\(81\) | −10.4043 | −1.15604 | ||||||||
\(82\) | −18.3744 | −2.02911 | ||||||||
\(83\) | −3.29391 | −0.361553 | −0.180777 | − | 0.983524i | \(-0.557861\pi\) | ||||
−0.180777 | + | 0.983524i | \(0.557861\pi\) | |||||||
\(84\) | 8.45467 | 0.922481 | ||||||||
\(85\) | 7.00625 | 0.759934 | ||||||||
\(86\) | 8.71355 | 0.939606 | ||||||||
\(87\) | −19.6598 | −2.10775 | ||||||||
\(88\) | 4.23680 | 0.451644 | ||||||||
\(89\) | −10.6118 | −1.12485 | −0.562426 | − | 0.826848i | \(-0.690132\pi\) | ||||
−0.562426 | + | 0.826848i | \(0.690132\pi\) | |||||||
\(90\) | 14.1544 | 1.49200 | ||||||||
\(91\) | −1.66549 | −0.174591 | ||||||||
\(92\) | −10.6362 | −1.10890 | ||||||||
\(93\) | −6.01971 | −0.624215 | ||||||||
\(94\) | 12.3327 | 1.27202 | ||||||||
\(95\) | −3.08512 | −0.316526 | ||||||||
\(96\) | 16.9345 | 1.72837 | ||||||||
\(97\) | 10.2851 | 1.04430 | 0.522149 | − | 0.852854i | \(-0.325130\pi\) | ||||
0.522149 | + | 0.852854i | \(0.325130\pi\) | |||||||
\(98\) | 3.44763 | 0.348263 | ||||||||
\(99\) | 13.3628 | 1.34301 | ||||||||
\(100\) | 7.20798 | 0.720798 | ||||||||
\(101\) | 5.98023 | 0.595055 | 0.297527 | − | 0.954713i | \(-0.403838\pi\) | ||||
0.297527 | + | 0.954713i | \(0.403838\pi\) | |||||||
\(102\) | 10.0247 | 0.992595 | ||||||||
\(103\) | −11.8444 | −1.16707 | −0.583534 | − | 0.812089i | \(-0.698331\pi\) | ||||
−0.583534 | + | 0.812089i | \(0.698331\pi\) | |||||||
\(104\) | −0.561290 | −0.0550390 | ||||||||
\(105\) | −16.3491 | −1.59551 | ||||||||
\(106\) | 9.73682 | 0.945723 | ||||||||
\(107\) | 3.41724 | 0.330357 | 0.165178 | − | 0.986264i | \(-0.447180\pi\) | ||||
0.165178 | + | 0.986264i | \(0.447180\pi\) | |||||||
\(108\) | −2.15566 | −0.207428 | ||||||||
\(109\) | 18.8570 | 1.80617 | 0.903087 | − | 0.429459i | \(-0.141296\pi\) | ||||
0.903087 | + | 0.429459i | \(0.141296\pi\) | |||||||
\(110\) | 32.3071 | 3.08037 | ||||||||
\(111\) | −3.51532 | −0.333659 | ||||||||
\(112\) | −10.5748 | −0.999221 | ||||||||
\(113\) | 0.294066 | 0.0276634 | 0.0138317 | − | 0.999904i | \(-0.495597\pi\) | ||||
0.0138317 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(114\) | −4.41426 | −0.413434 | ||||||||
\(115\) | 20.5676 | 1.91793 | ||||||||
\(116\) | −13.4731 | −1.25095 | ||||||||
\(117\) | −1.77030 | −0.163664 | ||||||||
\(118\) | 20.5412 | 1.89097 | ||||||||
\(119\) | −5.16956 | −0.473893 | ||||||||
\(120\) | −5.50986 | −0.502979 | ||||||||
\(121\) | 19.5004 | 1.77276 | ||||||||
\(122\) | 9.42297 | 0.853116 | ||||||||
\(123\) | 22.5591 | 2.03409 | ||||||||
\(124\) | −4.12539 | −0.370471 | ||||||||
\(125\) | 1.48721 | 0.133021 | ||||||||
\(126\) | −10.4438 | −0.930408 | ||||||||
\(127\) | −1.84767 | −0.163955 | −0.0819773 | − | 0.996634i | \(-0.526124\pi\) | ||||
−0.0819773 | + | 0.996634i | \(0.526124\pi\) | |||||||
\(128\) | −6.01170 | −0.531364 | ||||||||
\(129\) | −10.6980 | −0.941910 | ||||||||
\(130\) | −4.28004 | −0.375385 | ||||||||
\(131\) | −8.77881 | −0.767008 | −0.383504 | − | 0.923539i | \(-0.625283\pi\) | ||||
−0.383504 | + | 0.923539i | \(0.625283\pi\) | |||||||
\(132\) | 20.5121 | 1.78535 | ||||||||
\(133\) | 2.27635 | 0.197385 | ||||||||
\(134\) | −13.6508 | −1.17925 | ||||||||
\(135\) | 4.16848 | 0.358766 | ||||||||
\(136\) | −1.74221 | −0.149393 | ||||||||
\(137\) | 10.6955 | 0.913776 | 0.456888 | − | 0.889524i | \(-0.348964\pi\) | ||||
0.456888 | + | 0.889524i | \(0.348964\pi\) | |||||||
\(138\) | 29.4286 | 2.50513 | ||||||||
\(139\) | 3.39576 | 0.288025 | 0.144012 | − | 0.989576i | \(-0.454000\pi\) | ||||
0.144012 | + | 0.989576i | \(0.454000\pi\) | |||||||
\(140\) | −11.2043 | −0.946936 | ||||||||
\(141\) | −15.1414 | −1.27514 | ||||||||
\(142\) | −0.489292 | −0.0410604 | ||||||||
\(143\) | −4.04068 | −0.337899 | ||||||||
\(144\) | −11.2402 | −0.936687 | ||||||||
\(145\) | 26.0536 | 2.16363 | ||||||||
\(146\) | −23.3124 | −1.92935 | ||||||||
\(147\) | −4.23282 | −0.349117 | ||||||||
\(148\) | −2.40909 | −0.198026 | ||||||||
\(149\) | −8.52775 | −0.698621 | −0.349310 | − | 0.937007i | \(-0.613584\pi\) | ||||
−0.349310 | + | 0.937007i | \(0.613584\pi\) | |||||||
\(150\) | −19.9434 | −1.62837 | ||||||||
\(151\) | 15.9320 | 1.29652 | 0.648262 | − | 0.761417i | \(-0.275496\pi\) | ||||
0.648262 | + | 0.761417i | \(0.275496\pi\) | |||||||
\(152\) | 0.767159 | 0.0622248 | ||||||||
\(153\) | −5.49489 | −0.444235 | ||||||||
\(154\) | −23.8378 | −1.92091 | ||||||||
\(155\) | 7.97743 | 0.640763 | ||||||||
\(156\) | −2.71744 | −0.217569 | ||||||||
\(157\) | 6.28085 | 0.501267 | 0.250633 | − | 0.968082i | \(-0.419361\pi\) | ||||
0.250633 | + | 0.968082i | \(0.419361\pi\) | |||||||
\(158\) | 9.42087 | 0.749484 | ||||||||
\(159\) | −11.9544 | −0.948042 | ||||||||
\(160\) | −22.4419 | −1.77419 | ||||||||
\(161\) | −15.1758 | −1.19602 | ||||||||
\(162\) | 19.7282 | 1.55000 | ||||||||
\(163\) | −17.3633 | −1.36000 | −0.680001 | − | 0.733211i | \(-0.738021\pi\) | ||||
−0.680001 | + | 0.733211i | \(0.738021\pi\) | |||||||
\(164\) | 15.4601 | 1.20723 | ||||||||
\(165\) | −39.6651 | −3.08792 | ||||||||
\(166\) | 6.24576 | 0.484765 | ||||||||
\(167\) | −19.0969 | −1.47776 | −0.738881 | − | 0.673836i | \(-0.764645\pi\) | ||||
−0.738881 | + | 0.673836i | \(0.764645\pi\) | |||||||
\(168\) | 4.06545 | 0.313656 | ||||||||
\(169\) | −12.4647 | −0.958822 | ||||||||
\(170\) | −13.2849 | −1.01891 | ||||||||
\(171\) | 2.41961 | 0.185032 | ||||||||
\(172\) | −7.33152 | −0.559023 | ||||||||
\(173\) | −11.2595 | −0.856046 | −0.428023 | − | 0.903768i | \(-0.640790\pi\) | ||||
−0.428023 | + | 0.903768i | \(0.640790\pi\) | |||||||
\(174\) | 37.2781 | 2.82605 | ||||||||
\(175\) | 10.2844 | 0.777429 | ||||||||
\(176\) | −25.6557 | −1.93387 | ||||||||
\(177\) | −25.2194 | −1.89560 | ||||||||
\(178\) | 20.1217 | 1.50819 | ||||||||
\(179\) | −23.7984 | −1.77878 | −0.889390 | − | 0.457150i | \(-0.848870\pi\) | ||||
−0.889390 | + | 0.457150i | \(0.848870\pi\) | |||||||
\(180\) | −11.9094 | −0.887674 | ||||||||
\(181\) | −11.4578 | −0.851650 | −0.425825 | − | 0.904806i | \(-0.640016\pi\) | ||||
−0.425825 | + | 0.904806i | \(0.640016\pi\) | |||||||
\(182\) | 3.15803 | 0.234089 | ||||||||
\(183\) | −11.5690 | −0.855208 | ||||||||
\(184\) | −5.11442 | −0.377040 | ||||||||
\(185\) | 4.65856 | 0.342504 | ||||||||
\(186\) | 11.4143 | 0.836939 | ||||||||
\(187\) | −12.5420 | −0.917162 | ||||||||
\(188\) | −10.3766 | −0.756793 | ||||||||
\(189\) | −3.07572 | −0.223725 | ||||||||
\(190\) | 5.84987 | 0.424394 | ||||||||
\(191\) | −20.3988 | −1.47601 | −0.738003 | − | 0.674798i | \(-0.764231\pi\) | ||||
−0.738003 | + | 0.674798i | \(0.764231\pi\) | |||||||
\(192\) | −10.4810 | −0.756404 | ||||||||
\(193\) | 1.58604 | 0.114166 | 0.0570828 | − | 0.998369i | \(-0.481820\pi\) | ||||
0.0570828 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(194\) | −19.5023 | −1.40018 | ||||||||
\(195\) | 5.25482 | 0.376305 | ||||||||
\(196\) | −2.90081 | −0.207201 | ||||||||
\(197\) | −6.09897 | −0.434533 | −0.217267 | − | 0.976112i | \(-0.569714\pi\) | ||||
−0.217267 | + | 0.976112i | \(0.569714\pi\) | |||||||
\(198\) | −25.3380 | −1.80069 | ||||||||
\(199\) | 0.998849 | 0.0708065 | 0.0354032 | − | 0.999373i | \(-0.488728\pi\) | ||||
0.0354032 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(200\) | 3.46598 | 0.245082 | ||||||||
\(201\) | 16.7597 | 1.18214 | ||||||||
\(202\) | −11.3395 | −0.797841 | ||||||||
\(203\) | −19.2236 | −1.34923 | ||||||||
\(204\) | −8.43473 | −0.590549 | ||||||||
\(205\) | −29.8958 | −2.08801 | ||||||||
\(206\) | 22.4589 | 1.56479 | ||||||||
\(207\) | −16.1308 | −1.12117 | ||||||||
\(208\) | 3.39886 | 0.235668 | ||||||||
\(209\) | 5.52272 | 0.382014 | ||||||||
\(210\) | 31.0005 | 2.13924 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −8.19249 | −0.562662 | ||||||||
\(213\) | 0.600727 | 0.0411611 | ||||||||
\(214\) | −6.47962 | −0.442938 | ||||||||
\(215\) | 14.1772 | 0.966880 | ||||||||
\(216\) | −1.03655 | −0.0705286 | ||||||||
\(217\) | −5.88615 | −0.399578 | ||||||||
\(218\) | −35.7558 | −2.42169 | ||||||||
\(219\) | 28.6217 | 1.93408 | ||||||||
\(220\) | −27.1830 | −1.83268 | ||||||||
\(221\) | 1.66156 | 0.111769 | ||||||||
\(222\) | 6.66559 | 0.447365 | ||||||||
\(223\) | −20.1905 | −1.35206 | −0.676029 | − | 0.736875i | \(-0.736301\pi\) | ||||
−0.676029 | + | 0.736875i | \(0.736301\pi\) | |||||||
\(224\) | 16.5588 | 1.10638 | ||||||||
\(225\) | 10.9316 | 0.728776 | ||||||||
\(226\) | −0.557596 | −0.0370907 | ||||||||
\(227\) | 20.4304 | 1.35602 | 0.678008 | − | 0.735055i | \(-0.262844\pi\) | ||||
0.678008 | + | 0.735055i | \(0.262844\pi\) | |||||||
\(228\) | 3.71413 | 0.245974 | ||||||||
\(229\) | −1.42438 | −0.0941255 | −0.0470627 | − | 0.998892i | \(-0.514986\pi\) | ||||
−0.0470627 | + | 0.998892i | \(0.514986\pi\) | |||||||
\(230\) | −38.9993 | −2.57154 | ||||||||
\(231\) | 29.2669 | 1.92562 | ||||||||
\(232\) | −6.47860 | −0.425341 | ||||||||
\(233\) | 9.24377 | 0.605580 | 0.302790 | − | 0.953057i | \(-0.402082\pi\) | ||||
0.302790 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(234\) | 3.35677 | 0.219439 | ||||||||
\(235\) | 20.0657 | 1.30894 | ||||||||
\(236\) | −17.2832 | −1.12504 | ||||||||
\(237\) | −11.5665 | −0.751323 | ||||||||
\(238\) | 9.80230 | 0.635389 | ||||||||
\(239\) | 14.8743 | 0.962140 | 0.481070 | − | 0.876682i | \(-0.340248\pi\) | ||||
0.481070 | + | 0.876682i | \(0.340248\pi\) | |||||||
\(240\) | 33.3646 | 2.15368 | ||||||||
\(241\) | −2.06142 | −0.132788 | −0.0663938 | − | 0.997793i | \(-0.521149\pi\) | ||||
−0.0663938 | + | 0.997793i | \(0.521149\pi\) | |||||||
\(242\) | −36.9758 | −2.37690 | ||||||||
\(243\) | −20.1678 | −1.29377 | ||||||||
\(244\) | −7.92843 | −0.507565 | ||||||||
\(245\) | 5.60941 | 0.358372 | ||||||||
\(246\) | −42.7757 | −2.72728 | ||||||||
\(247\) | −0.731648 | −0.0465536 | ||||||||
\(248\) | −1.98371 | −0.125965 | ||||||||
\(249\) | −7.66823 | −0.485954 | ||||||||
\(250\) | −2.81999 | −0.178352 | ||||||||
\(251\) | −15.9637 | −1.00762 | −0.503810 | − | 0.863814i | \(-0.668069\pi\) | ||||
−0.503810 | + | 0.863814i | \(0.668069\pi\) | |||||||
\(252\) | 8.78735 | 0.553551 | ||||||||
\(253\) | −36.8183 | −2.31475 | ||||||||
\(254\) | 3.50348 | 0.219828 | ||||||||
\(255\) | 16.3106 | 1.02141 | ||||||||
\(256\) | 20.4034 | 1.27521 | ||||||||
\(257\) | 29.3119 | 1.82843 | 0.914214 | − | 0.405231i | \(-0.132809\pi\) | ||||
0.914214 | + | 0.405231i | \(0.132809\pi\) | |||||||
\(258\) | 20.2852 | 1.26290 | ||||||||
\(259\) | −3.43732 | −0.213585 | ||||||||
\(260\) | 3.60120 | 0.223337 | ||||||||
\(261\) | −20.4334 | −1.26479 | ||||||||
\(262\) | 16.6460 | 1.02839 | ||||||||
\(263\) | 2.97145 | 0.183227 | 0.0916137 | − | 0.995795i | \(-0.470798\pi\) | ||||
0.0916137 | + | 0.995795i | \(0.470798\pi\) | |||||||
\(264\) | 9.86329 | 0.607044 | ||||||||
\(265\) | 15.8421 | 0.973175 | ||||||||
\(266\) | −4.31632 | −0.264651 | ||||||||
\(267\) | −24.7044 | −1.51188 | ||||||||
\(268\) | 11.4857 | 0.701600 | ||||||||
\(269\) | −7.69974 | −0.469461 | −0.234731 | − | 0.972060i | \(-0.575421\pi\) | ||||
−0.234731 | + | 0.972060i | \(0.575421\pi\) | |||||||
\(270\) | −7.90410 | −0.481028 | ||||||||
\(271\) | 1.13246 | 0.0687923 | 0.0343962 | − | 0.999408i | \(-0.489049\pi\) | ||||
0.0343962 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(272\) | 10.5498 | 0.639676 | ||||||||
\(273\) | −3.87727 | −0.234663 | ||||||||
\(274\) | −20.2803 | −1.22518 | ||||||||
\(275\) | 24.9513 | 1.50462 | ||||||||
\(276\) | −24.7610 | −1.49044 | ||||||||
\(277\) | 29.3481 | 1.76336 | 0.881679 | − | 0.471849i | \(-0.156413\pi\) | ||||
0.881679 | + | 0.471849i | \(0.156413\pi\) | |||||||
\(278\) | −6.43890 | −0.386179 | ||||||||
\(279\) | −6.25657 | −0.374571 | ||||||||
\(280\) | −5.38761 | −0.321971 | ||||||||
\(281\) | −30.1794 | −1.80035 | −0.900177 | − | 0.435524i | \(-0.856563\pi\) | ||||
−0.900177 | + | 0.435524i | \(0.856563\pi\) | |||||||
\(282\) | 28.7105 | 1.70969 | ||||||||
\(283\) | 13.3662 | 0.794537 | 0.397269 | − | 0.917702i | \(-0.369958\pi\) | ||||
0.397269 | + | 0.917702i | \(0.369958\pi\) | |||||||
\(284\) | 0.411687 | 0.0244291 | ||||||||
\(285\) | −7.18216 | −0.425435 | ||||||||
\(286\) | 7.66177 | 0.453050 | ||||||||
\(287\) | 22.0586 | 1.30208 | ||||||||
\(288\) | 17.6008 | 1.03714 | ||||||||
\(289\) | −11.8426 | −0.696626 | ||||||||
\(290\) | −49.4016 | −2.90096 | ||||||||
\(291\) | 23.9439 | 1.40361 | ||||||||
\(292\) | 19.6149 | 1.14787 | ||||||||
\(293\) | 23.7817 | 1.38934 | 0.694671 | − | 0.719328i | \(-0.255550\pi\) | ||||
0.694671 | + | 0.719328i | \(0.255550\pi\) | |||||||
\(294\) | 8.02609 | 0.468091 | ||||||||
\(295\) | 33.4212 | 1.94586 | ||||||||
\(296\) | −1.15842 | −0.0673318 | ||||||||
\(297\) | −7.46207 | −0.432993 | ||||||||
\(298\) | 16.1700 | 0.936701 | ||||||||
\(299\) | 4.87768 | 0.282084 | ||||||||
\(300\) | 16.7802 | 0.968806 | ||||||||
\(301\) | −10.4607 | −0.602944 | ||||||||
\(302\) | −30.2095 | −1.73836 | ||||||||
\(303\) | 13.9220 | 0.799798 | ||||||||
\(304\) | −4.64548 | −0.266437 | ||||||||
\(305\) | 15.3315 | 0.877880 | ||||||||
\(306\) | 10.4192 | 0.595624 | ||||||||
\(307\) | 14.8643 | 0.848352 | 0.424176 | − | 0.905580i | \(-0.360564\pi\) | ||||
0.424176 | + | 0.905580i | \(0.360564\pi\) | |||||||
\(308\) | 20.0570 | 1.14285 | ||||||||
\(309\) | −27.5739 | −1.56863 | ||||||||
\(310\) | −15.1265 | −0.859126 | ||||||||
\(311\) | −8.91498 | −0.505522 | −0.252761 | − | 0.967529i | \(-0.581339\pi\) | ||||
−0.252761 | + | 0.967529i | \(0.581339\pi\) | |||||||
\(312\) | −1.30669 | −0.0739766 | ||||||||
\(313\) | 2.31418 | 0.130805 | 0.0654027 | − | 0.997859i | \(-0.479167\pi\) | ||||
0.0654027 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(314\) | −11.9095 | −0.672091 | ||||||||
\(315\) | −16.9924 | −0.957416 | ||||||||
\(316\) | −7.92666 | −0.445909 | ||||||||
\(317\) | 13.4888 | 0.757608 | 0.378804 | − | 0.925477i | \(-0.376335\pi\) | ||||
0.378804 | + | 0.925477i | \(0.376335\pi\) | |||||||
\(318\) | 22.6674 | 1.27112 | ||||||||
\(319\) | −46.6389 | −2.61128 | ||||||||
\(320\) | 13.8897 | 0.776457 | ||||||||
\(321\) | 7.95535 | 0.444024 | ||||||||
\(322\) | 28.7757 | 1.60361 | ||||||||
\(323\) | −2.27098 | −0.126361 | ||||||||
\(324\) | −16.5992 | −0.922178 | ||||||||
\(325\) | −3.30554 | −0.183358 | ||||||||
\(326\) | 32.9236 | 1.82347 | ||||||||
\(327\) | 43.8992 | 2.42763 | ||||||||
\(328\) | 7.43403 | 0.410476 | ||||||||
\(329\) | −14.8055 | −0.816253 | ||||||||
\(330\) | 75.2112 | 4.14024 | ||||||||
\(331\) | 14.1487 | 0.777682 | 0.388841 | − | 0.921305i | \(-0.372876\pi\) | ||||
0.388841 | + | 0.921305i | \(0.372876\pi\) | |||||||
\(332\) | −5.25514 | −0.288413 | ||||||||
\(333\) | −3.65363 | −0.200218 | ||||||||
\(334\) | 36.2107 | 1.98136 | ||||||||
\(335\) | −22.2103 | −1.21348 | ||||||||
\(336\) | −24.6181 | −1.34303 | ||||||||
\(337\) | −33.2704 | −1.81235 | −0.906177 | − | 0.422899i | \(-0.861013\pi\) | ||||
−0.906177 | + | 0.422899i | \(0.861013\pi\) | |||||||
\(338\) | 23.6350 | 1.28558 | ||||||||
\(339\) | 0.684588 | 0.0371817 | ||||||||
\(340\) | 11.1779 | 0.606205 | ||||||||
\(341\) | −14.2805 | −0.773334 | ||||||||
\(342\) | −4.58796 | −0.248088 | ||||||||
\(343\) | −20.0734 | −1.08386 | ||||||||
\(344\) | −3.52538 | −0.190076 | ||||||||
\(345\) | 47.8814 | 2.57785 | ||||||||
\(346\) | 21.3498 | 1.14777 | ||||||||
\(347\) | −2.57656 | −0.138317 | −0.0691584 | − | 0.997606i | \(-0.522031\pi\) | ||||
−0.0691584 | + | 0.997606i | \(0.522031\pi\) | |||||||
\(348\) | −31.3655 | −1.68137 | ||||||||
\(349\) | 17.3529 | 0.928881 | 0.464440 | − | 0.885604i | \(-0.346256\pi\) | ||||
0.464440 | + | 0.885604i | \(0.346256\pi\) | |||||||
\(350\) | −19.5009 | −1.04237 | ||||||||
\(351\) | 0.988573 | 0.0527661 | ||||||||
\(352\) | 40.1736 | 2.14126 | ||||||||
\(353\) | −4.67870 | −0.249022 | −0.124511 | − | 0.992218i | \(-0.539736\pi\) | ||||
−0.124511 | + | 0.992218i | \(0.539736\pi\) | |||||||
\(354\) | 47.8199 | 2.54160 | ||||||||
\(355\) | −0.796095 | −0.0422523 | ||||||||
\(356\) | −16.9303 | −0.897302 | ||||||||
\(357\) | −12.0348 | −0.636947 | ||||||||
\(358\) | 45.1256 | 2.38496 | ||||||||
\(359\) | −26.0903 | −1.37699 | −0.688497 | − | 0.725239i | \(-0.741729\pi\) | ||||
−0.688497 | + | 0.725239i | \(0.741729\pi\) | |||||||
\(360\) | −5.72666 | −0.301822 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 21.7257 | 1.14188 | ||||||||
\(363\) | 45.3970 | 2.38272 | ||||||||
\(364\) | −2.65714 | −0.139272 | ||||||||
\(365\) | −37.9301 | −1.98535 | ||||||||
\(366\) | 21.9367 | 1.14665 | ||||||||
\(367\) | −16.6648 | −0.869897 | −0.434948 | − | 0.900455i | \(-0.643233\pi\) | ||||
−0.434948 | + | 0.900455i | \(0.643233\pi\) | |||||||
\(368\) | 30.9701 | 1.61443 | ||||||||
\(369\) | 23.4468 | 1.22059 | ||||||||
\(370\) | −8.83337 | −0.459225 | ||||||||
\(371\) | −11.6891 | −0.606869 | ||||||||
\(372\) | −9.60393 | −0.497941 | ||||||||
\(373\) | −13.9629 | −0.722971 | −0.361486 | − | 0.932378i | \(-0.617730\pi\) | ||||
−0.361486 | + | 0.932378i | \(0.617730\pi\) | |||||||
\(374\) | 23.7816 | 1.22972 | ||||||||
\(375\) | 3.46224 | 0.178789 | ||||||||
\(376\) | −4.98963 | −0.257320 | ||||||||
\(377\) | 6.17871 | 0.318220 | ||||||||
\(378\) | 5.83204 | 0.299968 | ||||||||
\(379\) | 12.2721 | 0.630377 | 0.315188 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315188 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(380\) | −4.92204 | −0.252495 | ||||||||
\(381\) | −4.30140 | −0.220367 | ||||||||
\(382\) | 38.6793 | 1.97901 | ||||||||
\(383\) | −23.6871 | −1.21035 | −0.605177 | − | 0.796091i | \(-0.706898\pi\) | ||||
−0.605177 | + | 0.796091i | \(0.706898\pi\) | |||||||
\(384\) | −13.9953 | −0.714192 | ||||||||
\(385\) | −38.7850 | −1.97667 | ||||||||
\(386\) | −3.00738 | −0.153072 | ||||||||
\(387\) | −11.1190 | −0.565210 | ||||||||
\(388\) | 16.4091 | 0.833044 | ||||||||
\(389\) | −25.6988 | −1.30298 | −0.651492 | − | 0.758656i | \(-0.725856\pi\) | ||||
−0.651492 | + | 0.758656i | \(0.725856\pi\) | |||||||
\(390\) | −9.96396 | −0.504545 | ||||||||
\(391\) | 15.1400 | 0.765662 | ||||||||
\(392\) | −1.39486 | −0.0704511 | ||||||||
\(393\) | −20.4371 | −1.03092 | ||||||||
\(394\) | 11.5646 | 0.582616 | ||||||||
\(395\) | 15.3281 | 0.771240 | ||||||||
\(396\) | 21.3192 | 1.07133 | ||||||||
\(397\) | −35.5477 | −1.78409 | −0.892045 | − | 0.451947i | \(-0.850729\pi\) | ||||
−0.892045 | + | 0.451947i | \(0.850729\pi\) | |||||||
\(398\) | −1.89397 | −0.0949364 | ||||||||
\(399\) | 5.29936 | 0.265300 | ||||||||
\(400\) | −20.9880 | −1.04940 | ||||||||
\(401\) | −25.8084 | −1.28881 | −0.644404 | − | 0.764685i | \(-0.722895\pi\) | ||||
−0.644404 | + | 0.764685i | \(0.722895\pi\) | |||||||
\(402\) | −31.7791 | −1.58500 | ||||||||
\(403\) | 1.89188 | 0.0942413 | ||||||||
\(404\) | 9.54094 | 0.474680 | ||||||||
\(405\) | 32.0985 | 1.59499 | ||||||||
\(406\) | 36.4510 | 1.80903 | ||||||||
\(407\) | −8.33937 | −0.413367 | ||||||||
\(408\) | −4.05586 | −0.200795 | ||||||||
\(409\) | −6.41379 | −0.317141 | −0.158571 | − | 0.987348i | \(-0.550689\pi\) | ||||
−0.158571 | + | 0.987348i | \(0.550689\pi\) | |||||||
\(410\) | 56.6872 | 2.79958 | ||||||||
\(411\) | 24.8991 | 1.22818 | ||||||||
\(412\) | −18.8968 | −0.930978 | ||||||||
\(413\) | −24.6598 | −1.21343 | ||||||||
\(414\) | 30.5865 | 1.50325 | ||||||||
\(415\) | 10.1621 | 0.498837 | ||||||||
\(416\) | −5.32219 | −0.260942 | ||||||||
\(417\) | 7.90535 | 0.387126 | ||||||||
\(418\) | −10.4719 | −0.512199 | ||||||||
\(419\) | 6.68004 | 0.326341 | 0.163171 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163171 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(420\) | −26.0836 | −1.27275 | ||||||||
\(421\) | 33.9308 | 1.65369 | 0.826843 | − | 0.562433i | \(-0.190135\pi\) | ||||
0.826843 | + | 0.562433i | \(0.190135\pi\) | |||||||
\(422\) | −1.89616 | −0.0923035 | ||||||||
\(423\) | −15.7372 | −0.765169 | ||||||||
\(424\) | −3.93938 | −0.191313 | ||||||||
\(425\) | −10.2602 | −0.497691 | ||||||||
\(426\) | −1.13907 | −0.0551883 | ||||||||
\(427\) | −11.3124 | −0.547443 | ||||||||
\(428\) | 5.45191 | 0.263528 | ||||||||
\(429\) | −9.40673 | −0.454161 | ||||||||
\(430\) | −26.8823 | −1.29638 | ||||||||
\(431\) | −25.9332 | −1.24916 | −0.624578 | − | 0.780962i | \(-0.714729\pi\) | ||||
−0.624578 | + | 0.780962i | \(0.714729\pi\) | |||||||
\(432\) | 6.27679 | 0.301992 | ||||||||
\(433\) | −27.0827 | −1.30151 | −0.650756 | − | 0.759287i | \(-0.725548\pi\) | ||||
−0.650756 | + | 0.759287i | \(0.725548\pi\) | |||||||
\(434\) | 11.1611 | 0.535748 | ||||||||
\(435\) | 60.6528 | 2.90808 | ||||||||
\(436\) | 30.0847 | 1.44080 | ||||||||
\(437\) | −6.66671 | −0.318912 | ||||||||
\(438\) | −54.2713 | −2.59318 | ||||||||
\(439\) | 34.5516 | 1.64906 | 0.824530 | − | 0.565818i | \(-0.191440\pi\) | ||||
0.824530 | + | 0.565818i | \(0.191440\pi\) | |||||||
\(440\) | −13.0710 | −0.623136 | ||||||||
\(441\) | −4.39937 | −0.209494 | ||||||||
\(442\) | −3.15058 | −0.149858 | ||||||||
\(443\) | −23.4107 | −1.11228 | −0.556139 | − | 0.831089i | \(-0.687718\pi\) | ||||
−0.556139 | + | 0.831089i | \(0.687718\pi\) | |||||||
\(444\) | −5.60838 | −0.266162 | ||||||||
\(445\) | 32.7387 | 1.55196 | ||||||||
\(446\) | 38.2844 | 1.81282 | ||||||||
\(447\) | −19.8526 | −0.938998 | ||||||||
\(448\) | −10.2485 | −0.484196 | ||||||||
\(449\) | −12.8034 | −0.604229 | −0.302114 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302114 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(450\) | −20.7281 | −0.977132 | ||||||||
\(451\) | 53.5170 | 2.52002 | ||||||||
\(452\) | 0.469157 | 0.0220673 | ||||||||
\(453\) | 37.0897 | 1.74262 | ||||||||
\(454\) | −38.7393 | −1.81813 | ||||||||
\(455\) | 5.13823 | 0.240884 | ||||||||
\(456\) | 1.78595 | 0.0836348 | ||||||||
\(457\) | 24.8653 | 1.16315 | 0.581575 | − | 0.813493i | \(-0.302437\pi\) | ||||
0.581575 | + | 0.813493i | \(0.302437\pi\) | |||||||
\(458\) | 2.70084 | 0.126202 | ||||||||
\(459\) | 3.06846 | 0.143223 | ||||||||
\(460\) | 32.8138 | 1.52995 | ||||||||
\(461\) | 1.47167 | 0.0685423 | 0.0342712 | − | 0.999413i | \(-0.489089\pi\) | ||||
0.0342712 | + | 0.999413i | \(0.489089\pi\) | |||||||
\(462\) | −55.4946 | −2.58184 | ||||||||
\(463\) | 21.9905 | 1.02198 | 0.510992 | − | 0.859585i | \(-0.329278\pi\) | ||||
0.510992 | + | 0.859585i | \(0.329278\pi\) | |||||||
\(464\) | 39.2307 | 1.82124 | ||||||||
\(465\) | 18.5715 | 0.861233 | ||||||||
\(466\) | −17.5277 | −0.811953 | ||||||||
\(467\) | 18.0761 | 0.836462 | 0.418231 | − | 0.908341i | \(-0.362650\pi\) | ||||
0.418231 | + | 0.908341i | \(0.362650\pi\) | |||||||
\(468\) | −2.82436 | −0.130556 | ||||||||
\(469\) | 16.3879 | 0.756722 | ||||||||
\(470\) | −38.0477 | −1.75501 | ||||||||
\(471\) | 14.6219 | 0.673740 | ||||||||
\(472\) | −8.31067 | −0.382529 | ||||||||
\(473\) | −25.3789 | −1.16692 | ||||||||
\(474\) | 21.9318 | 1.00736 | ||||||||
\(475\) | 4.51794 | 0.207297 | ||||||||
\(476\) | −8.24759 | −0.378028 | ||||||||
\(477\) | −12.4247 | −0.568890 | ||||||||
\(478\) | −28.2041 | −1.29002 | ||||||||
\(479\) | 38.0603 | 1.73902 | 0.869511 | − | 0.493914i | \(-0.164434\pi\) | ||||
0.869511 | + | 0.493914i | \(0.164434\pi\) | |||||||
\(480\) | −52.2448 | −2.38464 | ||||||||
\(481\) | 1.10480 | 0.0503744 | ||||||||
\(482\) | 3.90878 | 0.178040 | ||||||||
\(483\) | −35.3293 | −1.60754 | ||||||||
\(484\) | 31.1112 | 1.41415 | ||||||||
\(485\) | −31.7309 | −1.44082 | ||||||||
\(486\) | 38.2414 | 1.73467 | ||||||||
\(487\) | −13.3572 | −0.605270 | −0.302635 | − | 0.953106i | \(-0.597866\pi\) | ||||
−0.302635 | + | 0.953106i | \(0.597866\pi\) | |||||||
\(488\) | −3.81240 | −0.172579 | ||||||||
\(489\) | −40.4220 | −1.82794 | ||||||||
\(490\) | −10.6363 | −0.480500 | ||||||||
\(491\) | 4.18672 | 0.188944 | 0.0944720 | − | 0.995528i | \(-0.469884\pi\) | ||||
0.0944720 | + | 0.995528i | \(0.469884\pi\) | |||||||
\(492\) | 35.9912 | 1.62261 | ||||||||
\(493\) | 19.1783 | 0.863746 | ||||||||
\(494\) | 1.38732 | 0.0624185 | ||||||||
\(495\) | −41.2258 | −1.85296 | ||||||||
\(496\) | 12.0122 | 0.539364 | ||||||||
\(497\) | 0.587399 | 0.0263484 | ||||||||
\(498\) | 14.5402 | 0.651561 | ||||||||
\(499\) | 4.46601 | 0.199926 | 0.0999630 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999630 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(500\) | 2.37272 | 0.106111 | ||||||||
\(501\) | −44.4577 | −1.98622 | ||||||||
\(502\) | 30.2697 | 1.35100 | ||||||||
\(503\) | −34.7751 | −1.55055 | −0.775273 | − | 0.631626i | \(-0.782388\pi\) | ||||
−0.775273 | + | 0.631626i | \(0.782388\pi\) | |||||||
\(504\) | 4.22542 | 0.188215 | ||||||||
\(505\) | −18.4497 | −0.821001 | ||||||||
\(506\) | 69.8133 | 3.10358 | ||||||||
\(507\) | −29.0179 | −1.28873 | ||||||||
\(508\) | −2.94781 | −0.130788 | ||||||||
\(509\) | 24.4115 | 1.08202 | 0.541011 | − | 0.841015i | \(-0.318042\pi\) | ||||
0.541011 | + | 0.841015i | \(0.318042\pi\) | |||||||
\(510\) | −30.9274 | −1.36949 | ||||||||
\(511\) | 27.9867 | 1.23806 | ||||||||
\(512\) | −26.6647 | −1.17843 | ||||||||
\(513\) | −1.35116 | −0.0596551 | ||||||||
\(514\) | −55.5801 | −2.45153 | ||||||||
\(515\) | 36.5415 | 1.61021 | ||||||||
\(516\) | −17.0678 | −0.751368 | ||||||||
\(517\) | −35.9199 | −1.57976 | ||||||||
\(518\) | 6.51770 | 0.286371 | ||||||||
\(519\) | −26.2122 | −1.15059 | ||||||||
\(520\) | 1.73165 | 0.0759377 | ||||||||
\(521\) | −11.7435 | −0.514492 | −0.257246 | − | 0.966346i | \(-0.582815\pi\) | ||||
−0.257246 | + | 0.966346i | \(0.582815\pi\) | |||||||
\(522\) | 38.7449 | 1.69582 | ||||||||
\(523\) | −19.2320 | −0.840957 | −0.420479 | − | 0.907302i | \(-0.638138\pi\) | ||||
−0.420479 | + | 0.907302i | \(0.638138\pi\) | |||||||
\(524\) | −14.0058 | −0.611847 | ||||||||
\(525\) | 23.9422 | 1.04492 | ||||||||
\(526\) | −5.63433 | −0.245669 | ||||||||
\(527\) | 5.87227 | 0.255800 | ||||||||
\(528\) | −59.7265 | −2.59926 | ||||||||
\(529\) | 21.4450 | 0.932390 | ||||||||
\(530\) | −30.0392 | −1.30482 | ||||||||
\(531\) | −26.2117 | −1.13749 | ||||||||
\(532\) | 3.63173 | 0.157455 | ||||||||
\(533\) | −7.08991 | −0.307098 | ||||||||
\(534\) | 46.8434 | 2.02711 | ||||||||
\(535\) | −10.5426 | −0.455795 | ||||||||
\(536\) | 5.52292 | 0.238554 | ||||||||
\(537\) | −55.4029 | −2.39081 | ||||||||
\(538\) | 14.5999 | 0.629447 | ||||||||
\(539\) | −10.0415 | −0.432518 | ||||||||
\(540\) | 6.65046 | 0.286190 | ||||||||
\(541\) | 37.3126 | 1.60419 | 0.802096 | − | 0.597195i | \(-0.203718\pi\) | ||||
0.802096 | + | 0.597195i | \(0.203718\pi\) | |||||||
\(542\) | −2.14733 | −0.0922358 | ||||||||
\(543\) | −26.6738 | −1.14468 | ||||||||
\(544\) | −16.5197 | −0.708276 | ||||||||
\(545\) | −58.1760 | −2.49199 | ||||||||
\(546\) | 7.35191 | 0.314633 | ||||||||
\(547\) | 20.9268 | 0.894767 | 0.447383 | − | 0.894342i | \(-0.352356\pi\) | ||||
0.447383 | + | 0.894342i | \(0.352356\pi\) | |||||||
\(548\) | 17.0637 | 0.728925 | ||||||||
\(549\) | −12.0243 | −0.513183 | ||||||||
\(550\) | −47.3116 | −2.01737 | ||||||||
\(551\) | −8.44492 | −0.359766 | ||||||||
\(552\) | −11.9064 | −0.506770 | ||||||||
\(553\) | −11.3098 | −0.480943 | ||||||||
\(554\) | −55.6487 | −2.36429 | ||||||||
\(555\) | 10.8452 | 0.460351 | ||||||||
\(556\) | 5.41764 | 0.229759 | ||||||||
\(557\) | −0.778116 | −0.0329698 | −0.0164849 | − | 0.999864i | \(-0.505248\pi\) | ||||
−0.0164849 | + | 0.999864i | \(0.505248\pi\) | |||||||
\(558\) | 11.8634 | 0.502220 | ||||||||
\(559\) | 3.36219 | 0.142206 | ||||||||
\(560\) | 32.6244 | 1.37863 | ||||||||
\(561\) | −29.1978 | −1.23273 | ||||||||
\(562\) | 57.2250 | 2.41389 | ||||||||
\(563\) | 29.7582 | 1.25416 | 0.627080 | − | 0.778955i | \(-0.284250\pi\) | ||||
0.627080 | + | 0.778955i | \(0.284250\pi\) | |||||||
\(564\) | −24.1568 | −1.01719 | ||||||||
\(565\) | −0.907228 | −0.0381674 | ||||||||
\(566\) | −25.3444 | −1.06530 | ||||||||
\(567\) | −23.6839 | −0.994631 | ||||||||
\(568\) | 0.197961 | 0.00830624 | ||||||||
\(569\) | 28.7080 | 1.20350 | 0.601751 | − | 0.798684i | \(-0.294470\pi\) | ||||
0.601751 | + | 0.798684i | \(0.294470\pi\) | |||||||
\(570\) | 13.6185 | 0.570417 | ||||||||
\(571\) | −30.4712 | −1.27518 | −0.637590 | − | 0.770376i | \(-0.720069\pi\) | ||||
−0.637590 | + | 0.770376i | \(0.720069\pi\) | |||||||
\(572\) | −6.44656 | −0.269544 | ||||||||
\(573\) | −47.4885 | −1.98386 | ||||||||
\(574\) | −41.8266 | −1.74581 | ||||||||
\(575\) | −30.1198 | −1.25608 | ||||||||
\(576\) | −10.8935 | −0.453894 | ||||||||
\(577\) | 39.0238 | 1.62458 | 0.812291 | − | 0.583252i | \(-0.198220\pi\) | ||||
0.812291 | + | 0.583252i | \(0.198220\pi\) | |||||||
\(578\) | 22.4555 | 0.934026 | ||||||||
\(579\) | 3.69231 | 0.153447 | ||||||||
\(580\) | 41.5662 | 1.72594 | ||||||||
\(581\) | −7.49809 | −0.311073 | ||||||||
\(582\) | −45.4013 | −1.88195 | ||||||||
\(583\) | −28.3593 | −1.17452 | ||||||||
\(584\) | 9.43187 | 0.390293 | ||||||||
\(585\) | 5.46158 | 0.225809 | ||||||||
\(586\) | −45.0939 | −1.86281 | ||||||||
\(587\) | −23.4240 | −0.966811 | −0.483406 | − | 0.875396i | \(-0.660600\pi\) | ||||
−0.483406 | + | 0.875396i | \(0.660600\pi\) | |||||||
\(588\) | −6.75310 | −0.278493 | ||||||||
\(589\) | −2.58578 | −0.106545 | ||||||||
\(590\) | −63.3718 | −2.60898 | ||||||||
\(591\) | −14.1984 | −0.584045 | ||||||||
\(592\) | 7.01473 | 0.288304 | ||||||||
\(593\) | −18.9687 | −0.778952 | −0.389476 | − | 0.921037i | \(-0.627344\pi\) | ||||
−0.389476 | + | 0.921037i | \(0.627344\pi\) | |||||||
\(594\) | 14.1493 | 0.580551 | ||||||||
\(595\) | 15.9487 | 0.653833 | ||||||||
\(596\) | −13.6053 | −0.557295 | ||||||||
\(597\) | 2.32532 | 0.0951692 | ||||||||
\(598\) | −9.24885 | −0.378214 | ||||||||
\(599\) | 15.0986 | 0.616910 | 0.308455 | − | 0.951239i | \(-0.400188\pi\) | ||||
0.308455 | + | 0.951239i | \(0.400188\pi\) | |||||||
\(600\) | 8.06881 | 0.329408 | ||||||||
\(601\) | 10.5525 | 0.430447 | 0.215224 | − | 0.976565i | \(-0.430952\pi\) | ||||
0.215224 | + | 0.976565i | \(0.430952\pi\) | |||||||
\(602\) | 19.8351 | 0.808419 | ||||||||
\(603\) | 17.4192 | 0.709364 | ||||||||
\(604\) | 25.4181 | 1.03425 | ||||||||
\(605\) | −60.1610 | −2.44589 | ||||||||
\(606\) | −26.3983 | −1.07236 | ||||||||
\(607\) | 18.8087 | 0.763423 | 0.381712 | − | 0.924281i | \(-0.375335\pi\) | ||||
0.381712 | + | 0.924281i | \(0.375335\pi\) | |||||||
\(608\) | 7.27425 | 0.295010 | ||||||||
\(609\) | −44.7527 | −1.81347 | ||||||||
\(610\) | −29.0710 | −1.17705 | ||||||||
\(611\) | 4.75866 | 0.192515 | ||||||||
\(612\) | −8.76662 | −0.354370 | ||||||||
\(613\) | −40.1821 | −1.62294 | −0.811469 | − | 0.584395i | \(-0.801332\pi\) | ||||
−0.811469 | + | 0.584395i | \(0.801332\pi\) | |||||||
\(614\) | −28.1851 | −1.13746 | ||||||||
\(615\) | −69.5976 | −2.80645 | ||||||||
\(616\) | 9.64445 | 0.388586 | ||||||||
\(617\) | 16.6726 | 0.671212 | 0.335606 | − | 0.942002i | \(-0.391059\pi\) | ||||
0.335606 | + | 0.942002i | \(0.391059\pi\) | |||||||
\(618\) | 52.2845 | 2.10319 | ||||||||
\(619\) | 1.28075 | 0.0514776 | 0.0257388 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257388 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(620\) | 12.7273 | 0.511141 | ||||||||
\(621\) | 9.00778 | 0.361470 | ||||||||
\(622\) | 16.9042 | 0.677797 | ||||||||
\(623\) | −24.1563 | −0.967801 | ||||||||
\(624\) | 7.91256 | 0.316756 | ||||||||
\(625\) | −27.1779 | −1.08712 | ||||||||
\(626\) | −4.38806 | −0.175382 | ||||||||
\(627\) | 12.8569 | 0.513455 | ||||||||
\(628\) | 10.0206 | 0.399864 | ||||||||
\(629\) | 3.42921 | 0.136732 | ||||||||
\(630\) | 32.2203 | 1.28369 | ||||||||
\(631\) | 16.5735 | 0.659781 | 0.329890 | − | 0.944019i | \(-0.392988\pi\) | ||||
0.329890 | + | 0.944019i | \(0.392988\pi\) | |||||||
\(632\) | −3.81155 | −0.151615 | ||||||||
\(633\) | 2.32800 | 0.0925299 | ||||||||
\(634\) | −25.5769 | −1.01579 | ||||||||
\(635\) | 5.70029 | 0.226209 | ||||||||
\(636\) | −19.0722 | −0.756260 | ||||||||
\(637\) | 1.33029 | 0.0527082 | ||||||||
\(638\) | 88.4347 | 3.50116 | ||||||||
\(639\) | 0.624364 | 0.0246995 | ||||||||
\(640\) | 18.5468 | 0.733126 | ||||||||
\(641\) | 46.4913 | 1.83629 | 0.918147 | − | 0.396239i | \(-0.129685\pi\) | ||||
0.918147 | + | 0.396239i | \(0.129685\pi\) | |||||||
\(642\) | −15.0846 | −0.595341 | ||||||||
\(643\) | 10.2482 | 0.404148 | 0.202074 | − | 0.979370i | \(-0.435232\pi\) | ||||
0.202074 | + | 0.979370i | \(0.435232\pi\) | |||||||
\(644\) | −24.2116 | −0.954072 | ||||||||
\(645\) | 33.0047 | 1.29956 | ||||||||
\(646\) | 4.30614 | 0.169423 | ||||||||
\(647\) | −14.8252 | −0.582838 | −0.291419 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291419 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(648\) | −7.98177 | −0.313554 | ||||||||
\(649\) | −59.8278 | −2.34845 | ||||||||
\(650\) | 6.26783 | 0.245844 | ||||||||
\(651\) | −13.7030 | −0.537062 | ||||||||
\(652\) | −27.7017 | −1.08488 | ||||||||
\(653\) | −8.67967 | −0.339662 | −0.169831 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169831 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(654\) | −83.2398 | −3.25493 | ||||||||
\(655\) | 27.0836 | 1.05825 | ||||||||
\(656\) | −45.0163 | −1.75759 | ||||||||
\(657\) | 29.7479 | 1.16058 | ||||||||
\(658\) | 28.0735 | 1.09442 | ||||||||
\(659\) | 31.8841 | 1.24203 | 0.621015 | − | 0.783799i | \(-0.286721\pi\) | ||||
0.621015 | + | 0.783799i | \(0.286721\pi\) | |||||||
\(660\) | −63.2822 | −2.46326 | ||||||||
\(661\) | −37.1039 | −1.44318 | −0.721588 | − | 0.692323i | \(-0.756587\pi\) | ||||
−0.721588 | + | 0.692323i | \(0.756587\pi\) | |||||||
\(662\) | −26.8281 | −1.04271 | ||||||||
\(663\) | 3.86812 | 0.150225 | ||||||||
\(664\) | −2.52695 | −0.0980646 | ||||||||
\(665\) | −7.02281 | −0.272333 | ||||||||
\(666\) | 6.92787 | 0.268449 | ||||||||
\(667\) | 56.2998 | 2.17994 | ||||||||
\(668\) | −30.4674 | −1.17882 | ||||||||
\(669\) | −47.0036 | −1.81727 | ||||||||
\(670\) | 42.1143 | 1.62702 | ||||||||
\(671\) | −27.4452 | −1.05951 | ||||||||
\(672\) | 38.5489 | 1.48705 | ||||||||
\(673\) | −22.7946 | −0.878667 | −0.439334 | − | 0.898324i | \(-0.644785\pi\) | ||||
−0.439334 | + | 0.898324i | \(0.644785\pi\) | |||||||
\(674\) | 63.0859 | 2.42998 | ||||||||
\(675\) | −6.10445 | −0.234961 | ||||||||
\(676\) | −19.8863 | −0.764859 | ||||||||
\(677\) | 19.6061 | 0.753523 | 0.376761 | − | 0.926310i | \(-0.377038\pi\) | ||||
0.376761 | + | 0.926310i | \(0.377038\pi\) | |||||||
\(678\) | −1.29809 | −0.0498527 | ||||||||
\(679\) | 23.4126 | 0.898494 | ||||||||
\(680\) | 5.37491 | 0.206118 | ||||||||
\(681\) | 47.5621 | 1.82259 | ||||||||
\(682\) | 27.0781 | 1.03688 | ||||||||
\(683\) | −49.7870 | −1.90505 | −0.952523 | − | 0.304465i | \(-0.901522\pi\) | ||||
−0.952523 | + | 0.304465i | \(0.901522\pi\) | |||||||
\(684\) | 3.86027 | 0.147601 | ||||||||
\(685\) | −32.9968 | −1.26074 | ||||||||
\(686\) | 38.0623 | 1.45322 | ||||||||
\(687\) | −3.31596 | −0.126512 | ||||||||
\(688\) | 21.3477 | 0.813874 | ||||||||
\(689\) | 3.75703 | 0.143131 | ||||||||
\(690\) | −90.7906 | −3.45634 | ||||||||
\(691\) | 18.0653 | 0.687235 | 0.343617 | − | 0.939110i | \(-0.388348\pi\) | ||||
0.343617 | + | 0.939110i | \(0.388348\pi\) | |||||||
\(692\) | −17.9636 | −0.682874 | ||||||||
\(693\) | 30.4184 | 1.15550 | ||||||||
\(694\) | 4.88556 | 0.185453 | ||||||||
\(695\) | −10.4763 | −0.397389 | ||||||||
\(696\) | −15.0822 | −0.571689 | ||||||||
\(697\) | −22.0066 | −0.833559 | ||||||||
\(698\) | −32.9039 | −1.24543 | ||||||||
\(699\) | 21.5195 | 0.813944 | ||||||||
\(700\) | 16.4079 | 0.620161 | ||||||||
\(701\) | −9.62100 | −0.363380 | −0.181690 | − | 0.983356i | \(-0.558157\pi\) | ||||
−0.181690 | + | 0.983356i | \(0.558157\pi\) | |||||||
\(702\) | −1.87449 | −0.0707481 | ||||||||
\(703\) | −1.51001 | −0.0569512 | ||||||||
\(704\) | −24.8641 | −0.937103 | ||||||||
\(705\) | 46.7131 | 1.75932 | ||||||||
\(706\) | 8.87156 | 0.333886 | ||||||||
\(707\) | 13.6131 | 0.511974 | ||||||||
\(708\) | −40.2353 | −1.51214 | ||||||||
\(709\) | −1.77327 | −0.0665967 | −0.0332984 | − | 0.999445i | \(-0.510601\pi\) | ||||
−0.0332984 | + | 0.999445i | \(0.510601\pi\) | |||||||
\(710\) | 1.50952 | 0.0566513 | ||||||||
\(711\) | −12.0216 | −0.450844 | ||||||||
\(712\) | −8.14096 | −0.305095 | ||||||||
\(713\) | 17.2386 | 0.645592 | ||||||||
\(714\) | 22.8198 | 0.854010 | ||||||||
\(715\) | 12.4660 | 0.466201 | ||||||||
\(716\) | −37.9684 | −1.41894 | ||||||||
\(717\) | 34.6275 | 1.29319 | ||||||||
\(718\) | 49.4713 | 1.84625 | ||||||||
\(719\) | −14.8079 | −0.552241 | −0.276120 | − | 0.961123i | \(-0.589049\pi\) | ||||
−0.276120 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(720\) | 34.6774 | 1.29235 | ||||||||
\(721\) | −26.9621 | −1.00412 | ||||||||
\(722\) | −1.89616 | −0.0705677 | ||||||||
\(723\) | −4.79899 | −0.178477 | ||||||||
\(724\) | −18.2799 | −0.679367 | ||||||||
\(725\) | −38.1536 | −1.41699 | ||||||||
\(726\) | −86.0799 | −3.19472 | ||||||||
\(727\) | 21.6140 | 0.801618 | 0.400809 | − | 0.916162i | \(-0.368729\pi\) | ||||
0.400809 | + | 0.916162i | \(0.368729\pi\) | |||||||
\(728\) | −1.27769 | −0.0473545 | ||||||||
\(729\) | −15.7379 | −0.582883 | ||||||||
\(730\) | 71.9214 | 2.66193 | ||||||||
\(731\) | 10.4360 | 0.385990 | ||||||||
\(732\) | −18.4574 | −0.682206 | ||||||||
\(733\) | −28.3996 | −1.04896 | −0.524482 | − | 0.851421i | \(-0.675741\pi\) | ||||
−0.524482 | + | 0.851421i | \(0.675741\pi\) | |||||||
\(734\) | 31.5991 | 1.16635 | ||||||||
\(735\) | 13.0587 | 0.481679 | ||||||||
\(736\) | −48.4953 | −1.78756 | ||||||||
\(737\) | 39.7590 | 1.46454 | ||||||||
\(738\) | −44.4588 | −1.63655 | ||||||||
\(739\) | −46.2660 | −1.70192 | −0.850962 | − | 0.525227i | \(-0.823980\pi\) | ||||
−0.850962 | + | 0.525227i | \(0.823980\pi\) | |||||||
\(740\) | 7.43233 | 0.273218 | ||||||||
\(741\) | −1.70328 | −0.0625715 | ||||||||
\(742\) | 22.1644 | 0.813682 | ||||||||
\(743\) | 22.0359 | 0.808417 | 0.404209 | − | 0.914667i | \(-0.367547\pi\) | ||||
0.404209 | + | 0.914667i | \(0.367547\pi\) | |||||||
\(744\) | −4.61808 | −0.169307 | ||||||||
\(745\) | 26.3091 | 0.963891 | ||||||||
\(746\) | 26.4758 | 0.969350 | ||||||||
\(747\) | −7.96995 | −0.291605 | ||||||||
\(748\) | −20.0097 | −0.731626 | ||||||||
\(749\) | 7.77884 | 0.284233 | ||||||||
\(750\) | −6.56496 | −0.239718 | ||||||||
\(751\) | 40.5381 | 1.47926 | 0.739629 | − | 0.673015i | \(-0.235001\pi\) | ||||
0.739629 | + | 0.673015i | \(0.235001\pi\) | |||||||
\(752\) | 30.2144 | 1.10181 | ||||||||
\(753\) | −37.1636 | −1.35432 | ||||||||
\(754\) | −11.7158 | −0.426664 | ||||||||
\(755\) | −49.1519 | −1.78882 | ||||||||
\(756\) | −4.90704 | −0.178467 | ||||||||
\(757\) | 15.0943 | 0.548612 | 0.274306 | − | 0.961642i | \(-0.411552\pi\) | ||||
0.274306 | + | 0.961642i | \(0.411552\pi\) | |||||||
\(758\) | −23.2699 | −0.845200 | ||||||||
\(759\) | −85.7132 | −3.11119 | ||||||||
\(760\) | −2.36677 | −0.0858519 | ||||||||
\(761\) | 10.3171 | 0.373995 | 0.186997 | − | 0.982360i | \(-0.440124\pi\) | ||||
0.186997 | + | 0.982360i | \(0.440124\pi\) | |||||||
\(762\) | 8.15612 | 0.295465 | ||||||||
\(763\) | 42.9252 | 1.55400 | ||||||||
\(764\) | −32.5445 | −1.17742 | ||||||||
\(765\) | 16.9524 | 0.612914 | ||||||||
\(766\) | 44.9145 | 1.62283 | ||||||||
\(767\) | 7.92597 | 0.286190 | ||||||||
\(768\) | 47.4993 | 1.71398 | ||||||||
\(769\) | 4.10952 | 0.148193 | 0.0740966 | − | 0.997251i | \(-0.476393\pi\) | ||||
0.0740966 | + | 0.997251i | \(0.476393\pi\) | |||||||
\(770\) | 73.5425 | 2.65029 | ||||||||
\(771\) | 68.2383 | 2.45754 | ||||||||
\(772\) | 2.53039 | 0.0910707 | ||||||||
\(773\) | −9.62766 | −0.346283 | −0.173141 | − | 0.984897i | \(-0.555392\pi\) | ||||
−0.173141 | + | 0.984897i | \(0.555392\pi\) | |||||||
\(774\) | 21.0833 | 0.757825 | ||||||||
\(775\) | −11.6824 | −0.419644 | ||||||||
\(776\) | 7.89034 | 0.283247 | ||||||||
\(777\) | −8.00210 | −0.287074 | ||||||||
\(778\) | 48.7291 | 1.74702 | ||||||||
\(779\) | 9.69034 | 0.347192 | ||||||||
\(780\) | 8.38361 | 0.300181 | ||||||||
\(781\) | 1.42510 | 0.0509942 | ||||||||
\(782\) | −28.7078 | −1.02659 | ||||||||
\(783\) | 11.4104 | 0.407776 | ||||||||
\(784\) | 8.44649 | 0.301661 | ||||||||
\(785\) | −19.3772 | −0.691601 | ||||||||
\(786\) | 38.7520 | 1.38224 | ||||||||
\(787\) | −23.1976 | −0.826907 | −0.413453 | − | 0.910525i | \(-0.635678\pi\) | ||||
−0.413453 | + | 0.910525i | \(0.635678\pi\) | |||||||
\(788\) | −9.73038 | −0.346630 | ||||||||
\(789\) | 6.91755 | 0.246271 | ||||||||
\(790\) | −29.0645 | −1.03407 | ||||||||
\(791\) | 0.669399 | 0.0238011 | ||||||||
\(792\) | 10.2514 | 0.364267 | ||||||||
\(793\) | 3.63593 | 0.129116 | ||||||||
\(794\) | 67.4041 | 2.39208 | ||||||||
\(795\) | 36.8806 | 1.30802 | ||||||||
\(796\) | 1.59358 | 0.0564828 | ||||||||
\(797\) | −6.62765 | −0.234764 | −0.117382 | − | 0.993087i | \(-0.537450\pi\) | ||||
−0.117382 | + | 0.993087i | \(0.537450\pi\) | |||||||
\(798\) | −10.0484 | −0.355710 | ||||||||
\(799\) | 14.7706 | 0.522545 | ||||||||
\(800\) | 32.8646 | 1.16194 | ||||||||
\(801\) | −25.6765 | −0.907233 | ||||||||
\(802\) | 48.9367 | 1.72802 | ||||||||
\(803\) | 67.8992 | 2.39611 | ||||||||
\(804\) | 26.7387 | 0.943002 | ||||||||
\(805\) | 46.8190 | 1.65015 | ||||||||
\(806\) | −3.58731 | −0.126357 | ||||||||
\(807\) | −17.9250 | −0.630991 | ||||||||
\(808\) | 4.58779 | 0.161398 | ||||||||
\(809\) | −36.6407 | −1.28822 | −0.644109 | − | 0.764934i | \(-0.722772\pi\) | ||||
−0.644109 | + | 0.764934i | \(0.722772\pi\) | |||||||
\(810\) | −60.8639 | −2.13854 | ||||||||
\(811\) | −30.7968 | −1.08142 | −0.540711 | − | 0.841209i | \(-0.681845\pi\) | ||||
−0.540711 | + | 0.841209i | \(0.681845\pi\) | |||||||
\(812\) | −30.6696 | −1.07629 | ||||||||
\(813\) | 2.63638 | 0.0924620 | ||||||||
\(814\) | 15.8128 | 0.554237 | ||||||||
\(815\) | 53.5679 | 1.87640 | ||||||||
\(816\) | 24.5600 | 0.859773 | ||||||||
\(817\) | −4.59537 | −0.160772 | ||||||||
\(818\) | 12.1616 | 0.425219 | ||||||||
\(819\) | −4.02983 | −0.140814 | ||||||||
\(820\) | −47.6962 | −1.66562 | ||||||||
\(821\) | 17.2180 | 0.600912 | 0.300456 | − | 0.953796i | \(-0.402861\pi\) | ||||
0.300456 | + | 0.953796i | \(0.402861\pi\) | |||||||
\(822\) | −47.2126 | −1.64673 | ||||||||
\(823\) | 0.201869 | 0.00703672 | 0.00351836 | − | 0.999994i | \(-0.498880\pi\) | ||||
0.00351836 | + | 0.999994i | \(0.498880\pi\) | |||||||
\(824\) | −9.08657 | −0.316546 | ||||||||
\(825\) | 58.0867 | 2.02232 | ||||||||
\(826\) | 46.7589 | 1.62695 | ||||||||
\(827\) | 47.6328 | 1.65636 | 0.828178 | − | 0.560465i | \(-0.189378\pi\) | ||||
0.828178 | + | 0.560465i | \(0.189378\pi\) | |||||||
\(828\) | −25.7353 | −0.894364 | ||||||||
\(829\) | −17.2267 | −0.598306 | −0.299153 | − | 0.954205i | \(-0.596704\pi\) | ||||
−0.299153 | + | 0.954205i | \(0.596704\pi\) | |||||||
\(830\) | −19.2689 | −0.668833 | ||||||||
\(831\) | 68.3226 | 2.37008 | ||||||||
\(832\) | 3.29399 | 0.114199 | ||||||||
\(833\) | 4.12914 | 0.143066 | ||||||||
\(834\) | −14.9898 | −0.519054 | ||||||||
\(835\) | 58.9161 | 2.03888 | ||||||||
\(836\) | 8.81102 | 0.304735 | ||||||||
\(837\) | 3.49380 | 0.120763 | ||||||||
\(838\) | −12.6664 | −0.437554 | ||||||||
\(839\) | 23.0985 | 0.797450 | 0.398725 | − | 0.917070i | \(-0.369453\pi\) | ||||
0.398725 | + | 0.917070i | \(0.369453\pi\) | |||||||
\(840\) | −12.5424 | −0.432754 | ||||||||
\(841\) | 42.3167 | 1.45920 | ||||||||
\(842\) | −64.3381 | −2.21724 | ||||||||
\(843\) | −70.2579 | −2.41981 | ||||||||
\(844\) | 1.59541 | 0.0549164 | ||||||||
\(845\) | 38.4550 | 1.32289 | ||||||||
\(846\) | 29.8402 | 1.02593 | ||||||||
\(847\) | 44.3898 | 1.52525 | ||||||||
\(848\) | 23.8547 | 0.819172 | ||||||||
\(849\) | 31.1166 | 1.06792 | ||||||||
\(850\) | 19.4549 | 0.667297 | ||||||||
\(851\) | 10.0668 | 0.345086 | ||||||||
\(852\) | 0.958409 | 0.0328345 | ||||||||
\(853\) | 33.0192 | 1.13056 | 0.565279 | − | 0.824900i | \(-0.308769\pi\) | ||||
0.565279 | + | 0.824900i | \(0.308769\pi\) | |||||||
\(854\) | 21.4500 | 0.734004 | ||||||||
\(855\) | −7.46477 | −0.255290 | ||||||||
\(856\) | 2.62156 | 0.0896032 | ||||||||
\(857\) | 51.0797 | 1.74485 | 0.872425 | − | 0.488748i | \(-0.162546\pi\) | ||||
0.872425 | + | 0.488748i | \(0.162546\pi\) | |||||||
\(858\) | 17.8366 | 0.608933 | ||||||||
\(859\) | −42.8117 | −1.46072 | −0.730358 | − | 0.683065i | \(-0.760647\pi\) | ||||
−0.730358 | + | 0.683065i | \(0.760647\pi\) | |||||||
\(860\) | 22.6186 | 0.771287 | ||||||||
\(861\) | 51.3526 | 1.75009 | ||||||||
\(862\) | 49.1734 | 1.67485 | ||||||||
\(863\) | 45.0771 | 1.53444 | 0.767221 | − | 0.641383i | \(-0.221639\pi\) | ||||
0.767221 | + | 0.641383i | \(0.221639\pi\) | |||||||
\(864\) | −9.82867 | −0.334378 | ||||||||
\(865\) | 34.7369 | 1.18109 | ||||||||
\(866\) | 51.3531 | 1.74505 | ||||||||
\(867\) | −27.5697 | −0.936316 | ||||||||
\(868\) | −9.39085 | −0.318746 | ||||||||
\(869\) | −27.4391 | −0.930807 | ||||||||
\(870\) | −115.007 | −3.89911 | ||||||||
\(871\) | −5.26727 | −0.178475 | ||||||||
\(872\) | 14.4663 | 0.489891 | ||||||||
\(873\) | 24.8860 | 0.842263 | ||||||||
\(874\) | 12.6411 | 0.427592 | ||||||||
\(875\) | 3.38543 | 0.114448 | ||||||||
\(876\) | 45.6635 | 1.54283 | ||||||||
\(877\) | 5.97682 | 0.201823 | 0.100912 | − | 0.994895i | \(-0.467824\pi\) | ||||
0.100912 | + | 0.994895i | \(0.467824\pi\) | |||||||
\(878\) | −65.5154 | −2.21104 | ||||||||
\(879\) | 55.3639 | 1.86738 | ||||||||
\(880\) | 79.1507 | 2.66817 | ||||||||
\(881\) | −0.750727 | −0.0252926 | −0.0126463 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126463 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(882\) | 8.34190 | 0.280886 | ||||||||
\(883\) | −34.1174 | −1.14814 | −0.574071 | − | 0.818806i | \(-0.694636\pi\) | ||||
−0.574071 | + | 0.818806i | \(0.694636\pi\) | |||||||
\(884\) | 2.65088 | 0.0891586 | ||||||||
\(885\) | 77.8047 | 2.61538 | ||||||||
\(886\) | 44.3905 | 1.49133 | ||||||||
\(887\) | −27.8845 | −0.936271 | −0.468136 | − | 0.883657i | \(-0.655074\pi\) | ||||
−0.468136 | + | 0.883657i | \(0.655074\pi\) | |||||||
\(888\) | −2.69681 | −0.0904989 | ||||||||
\(889\) | −4.20596 | −0.141063 | ||||||||
\(890\) | −62.0778 | −2.08085 | ||||||||
\(891\) | −57.4601 | −1.92499 | ||||||||
\(892\) | −32.2122 | −1.07855 | ||||||||
\(893\) | −6.50404 | −0.217649 | ||||||||
\(894\) | 37.6438 | 1.25900 | ||||||||
\(895\) | 73.4210 | 2.45419 | ||||||||
\(896\) | −13.6847 | −0.457175 | ||||||||
\(897\) | 11.3553 | 0.379141 | ||||||||
\(898\) | 24.2772 | 0.810141 | ||||||||
\(899\) | 21.8367 | 0.728295 | ||||||||
\(900\) | 17.4405 | 0.581349 | ||||||||
\(901\) | 11.6616 | 0.388503 | ||||||||
\(902\) | −101.477 | −3.37880 | ||||||||
\(903\) | −24.3525 | −0.810401 | ||||||||
\(904\) | 0.225596 | 0.00750320 | ||||||||
\(905\) | 35.3486 | 1.17503 | ||||||||
\(906\) | −70.3279 | −2.33649 | ||||||||
\(907\) | −38.1114 | −1.26547 | −0.632734 | − | 0.774369i | \(-0.718067\pi\) | ||||
−0.632734 | + | 0.774369i | \(0.718067\pi\) | |||||||
\(908\) | 32.5950 | 1.08170 | ||||||||
\(909\) | 14.4698 | 0.479933 | ||||||||
\(910\) | −9.74289 | −0.322974 | ||||||||
\(911\) | −52.7748 | −1.74851 | −0.874253 | − | 0.485470i | \(-0.838648\pi\) | ||||
−0.874253 | + | 0.485470i | \(0.838648\pi\) | |||||||
\(912\) | −10.8147 | −0.358111 | ||||||||
\(913\) | −18.1913 | −0.602044 | ||||||||
\(914\) | −47.1486 | −1.55954 | ||||||||
\(915\) | 35.6918 | 1.17994 | ||||||||
\(916\) | −2.27247 | −0.0750846 | ||||||||
\(917\) | −19.9837 | −0.659919 | ||||||||
\(918\) | −5.81828 | −0.192032 | ||||||||
\(919\) | 5.34251 | 0.176233 | 0.0881165 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881165 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(920\) | 15.7786 | 0.520205 | ||||||||
\(921\) | 34.6042 | 1.14025 | ||||||||
\(922\) | −2.79051 | −0.0919006 | ||||||||
\(923\) | −0.188797 | −0.00621434 | ||||||||
\(924\) | 46.6928 | 1.53608 | ||||||||
\(925\) | −6.82214 | −0.224311 | ||||||||
\(926\) | −41.6974 | −1.37026 | ||||||||
\(927\) | −28.6589 | −0.941282 | ||||||||
\(928\) | −61.4304 | −2.01655 | ||||||||
\(929\) | −10.0406 | −0.329421 | −0.164711 | − | 0.986342i | \(-0.552669\pi\) | ||||
−0.164711 | + | 0.986342i | \(0.552669\pi\) | |||||||
\(930\) | −35.2145 | −1.15473 | ||||||||
\(931\) | −1.81822 | −0.0595897 | ||||||||
\(932\) | 14.7476 | 0.483075 | ||||||||
\(933\) | −20.7541 | −0.679460 | ||||||||
\(934\) | −34.2751 | −1.12152 | ||||||||
\(935\) | 38.6935 | 1.26541 | ||||||||
\(936\) | −1.35810 | −0.0443909 | ||||||||
\(937\) | 8.03962 | 0.262643 | 0.131321 | − | 0.991340i | \(-0.458078\pi\) | ||||
0.131321 | + | 0.991340i | \(0.458078\pi\) | |||||||
\(938\) | −31.0740 | −1.01460 | ||||||||
\(939\) | 5.38743 | 0.175812 | ||||||||
\(940\) | 32.0131 | 1.04415 | ||||||||
\(941\) | −3.92527 | −0.127960 | −0.0639801 | − | 0.997951i | \(-0.520379\pi\) | ||||
−0.0639801 | + | 0.997951i | \(0.520379\pi\) | |||||||
\(942\) | −27.7253 | −0.903341 | ||||||||
\(943\) | −64.6026 | −2.10375 | ||||||||
\(944\) | 50.3247 | 1.63793 | ||||||||
\(945\) | 9.48894 | 0.308675 | ||||||||
\(946\) | 48.1224 | 1.56460 | ||||||||
\(947\) | −35.5607 | −1.15557 | −0.577783 | − | 0.816190i | \(-0.696082\pi\) | ||||
−0.577783 | + | 0.816190i | \(0.696082\pi\) | |||||||
\(948\) | −18.4533 | −0.599335 | ||||||||
\(949\) | −8.99527 | −0.291999 | ||||||||
\(950\) | −8.56672 | −0.277941 | ||||||||
\(951\) | 31.4021 | 1.01828 | ||||||||
\(952\) | −3.96587 | −0.128535 | ||||||||
\(953\) | −26.5941 | −0.861467 | −0.430733 | − | 0.902479i | \(-0.641745\pi\) | ||||
−0.430733 | + | 0.902479i | \(0.641745\pi\) | |||||||
\(954\) | 23.5593 | 0.762759 | ||||||||
\(955\) | 62.9326 | 2.03645 | ||||||||
\(956\) | 23.7307 | 0.767505 | ||||||||
\(957\) | −108.576 | −3.50975 | ||||||||
\(958\) | −72.1684 | −2.33166 | ||||||||
\(959\) | 24.3467 | 0.786195 | ||||||||
\(960\) | 32.3352 | 1.04362 | ||||||||
\(961\) | −24.3137 | −0.784314 | ||||||||
\(962\) | −2.09487 | −0.0675413 | ||||||||
\(963\) | 8.26837 | 0.266444 | ||||||||
\(964\) | −3.28882 | −0.105926 | ||||||||
\(965\) | −4.89312 | −0.157515 | ||||||||
\(966\) | 66.9899 | 2.15536 | ||||||||
\(967\) | 11.7958 | 0.379328 | 0.189664 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189664 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(968\) | 14.9599 | 0.480829 | ||||||||
\(969\) | −5.28686 | −0.169838 | ||||||||
\(970\) | 60.1667 | 1.93184 | ||||||||
\(971\) | −22.8663 | −0.733814 | −0.366907 | − | 0.930258i | \(-0.619583\pi\) | ||||
−0.366907 | + | 0.930258i | \(0.619583\pi\) | |||||||
\(972\) | −32.1761 | −1.03205 | ||||||||
\(973\) | 7.72995 | 0.247811 | ||||||||
\(974\) | 25.3273 | 0.811538 | ||||||||
\(975\) | −7.69531 | −0.246447 | ||||||||
\(976\) | 23.0858 | 0.738957 | ||||||||
\(977\) | 30.5176 | 0.976346 | 0.488173 | − | 0.872747i | \(-0.337664\pi\) | ||||
0.488173 | + | 0.872747i | \(0.337664\pi\) | |||||||
\(978\) | 76.6464 | 2.45088 | ||||||||
\(979\) | −58.6061 | −1.87306 | ||||||||
\(980\) | 8.94933 | 0.285876 | ||||||||
\(981\) | 45.6265 | 1.45674 | ||||||||
\(982\) | −7.93868 | −0.253333 | ||||||||
\(983\) | 15.6256 | 0.498379 | 0.249190 | − | 0.968455i | \(-0.419836\pi\) | ||||
0.249190 | + | 0.968455i | \(0.419836\pi\) | |||||||
\(984\) | 17.3065 | 0.551710 | ||||||||
\(985\) | 18.8160 | 0.599528 | ||||||||
\(986\) | −36.3650 | −1.15810 | ||||||||
\(987\) | −34.4672 | −1.09710 | ||||||||
\(988\) | −1.16728 | −0.0371362 | ||||||||
\(989\) | 30.6360 | 0.974167 | ||||||||
\(990\) | 78.1706 | 2.48442 | ||||||||
\(991\) | −14.1388 | −0.449132 | −0.224566 | − | 0.974459i | \(-0.572097\pi\) | ||||
−0.224566 | + | 0.974459i | \(0.572097\pi\) | |||||||
\(992\) | −18.8096 | −0.597206 | ||||||||
\(993\) | 32.9382 | 1.04526 | ||||||||
\(994\) | −1.11380 | −0.0353276 | ||||||||
\(995\) | −3.08156 | −0.0976921 | ||||||||
\(996\) | −12.2340 | −0.387649 | ||||||||
\(997\) | 10.2771 | 0.325479 | 0.162739 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162739 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(998\) | −8.46826 | −0.268058 | ||||||||
\(999\) | 2.04027 | 0.0645512 |
(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 | 4009.2.a.c.1.17 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.17 | ✓ | 71 | 1.1 | even | 1 | trivial |