Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57274 | −1.81920 | −0.909600 | − | 0.415485i | \(-0.863612\pi\) | ||||
−0.909600 | + | 0.415485i | \(0.863612\pi\) | |||||||
\(3\) | −3.14788 | −1.81743 | −0.908716 | − | 0.417416i | \(-0.862936\pi\) | ||||
−0.908716 | + | 0.417416i | \(0.862936\pi\) | |||||||
\(4\) | 4.61898 | 2.30949 | ||||||||
\(5\) | −2.11075 | −0.943957 | −0.471979 | − | 0.881610i | \(-0.656460\pi\) | ||||
−0.471979 | + | 0.881610i | \(0.656460\pi\) | |||||||
\(6\) | 8.09868 | 3.30627 | ||||||||
\(7\) | −0.361357 | −0.136580 | −0.0682900 | − | 0.997666i | \(-0.521754\pi\) | ||||
−0.0682900 | + | 0.997666i | \(0.521754\pi\) | |||||||
\(8\) | −6.73794 | −2.38222 | ||||||||
\(9\) | 6.90917 | 2.30306 | ||||||||
\(10\) | 5.43041 | 1.71725 | ||||||||
\(11\) | 6.02489 | 1.81657 | 0.908287 | − | 0.418348i | \(-0.137391\pi\) | ||||
0.908287 | + | 0.418348i | \(0.137391\pi\) | |||||||
\(12\) | −14.5400 | −4.19734 | ||||||||
\(13\) | −5.65995 | −1.56979 | −0.784894 | − | 0.619630i | \(-0.787283\pi\) | ||||
−0.784894 | + | 0.619630i | \(0.787283\pi\) | |||||||
\(14\) | 0.929676 | 0.248466 | ||||||||
\(15\) | 6.64440 | 1.71558 | ||||||||
\(16\) | 8.09699 | 2.02425 | ||||||||
\(17\) | −1.42134 | −0.344727 | −0.172363 | − | 0.985033i | \(-0.555140\pi\) | ||||
−0.172363 | + | 0.985033i | \(0.555140\pi\) | |||||||
\(18\) | −17.7755 | −4.18972 | ||||||||
\(19\) | 6.49301 | 1.48960 | 0.744800 | − | 0.667288i | \(-0.232545\pi\) | ||||
0.744800 | + | 0.667288i | \(0.232545\pi\) | |||||||
\(20\) | −9.74952 | −2.18006 | ||||||||
\(21\) | 1.13751 | 0.248225 | ||||||||
\(22\) | −15.5005 | −3.30471 | ||||||||
\(23\) | 7.36071 | 1.53481 | 0.767407 | − | 0.641161i | \(-0.221547\pi\) | ||||
0.767407 | + | 0.641161i | \(0.221547\pi\) | |||||||
\(24\) | 21.2102 | 4.32952 | ||||||||
\(25\) | −0.544723 | −0.108945 | ||||||||
\(26\) | 14.5616 | 2.85576 | ||||||||
\(27\) | −12.3056 | −2.36821 | ||||||||
\(28\) | −1.66910 | −0.315430 | ||||||||
\(29\) | −9.80257 | −1.82029 | −0.910146 | − | 0.414287i | \(-0.864031\pi\) | ||||
−0.910146 | + | 0.414287i | \(0.864031\pi\) | |||||||
\(30\) | −17.0943 | −3.12098 | ||||||||
\(31\) | −1.31642 | −0.236436 | −0.118218 | − | 0.992988i | \(-0.537718\pi\) | ||||
−0.118218 | + | 0.992988i | \(0.537718\pi\) | |||||||
\(32\) | −7.35555 | −1.30029 | ||||||||
\(33\) | −18.9657 | −3.30150 | ||||||||
\(34\) | 3.65675 | 0.627127 | ||||||||
\(35\) | 0.762735 | 0.128926 | ||||||||
\(36\) | 31.9133 | 5.31888 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −16.7048 | −2.70988 | ||||||||
\(39\) | 17.8169 | 2.85298 | ||||||||
\(40\) | 14.2221 | 2.24871 | ||||||||
\(41\) | −3.12744 | −0.488425 | −0.244212 | − | 0.969722i | \(-0.578529\pi\) | ||||
−0.244212 | + | 0.969722i | \(0.578529\pi\) | |||||||
\(42\) | −2.92651 | −0.451570 | ||||||||
\(43\) | 12.1352 | 1.85061 | 0.925304 | − | 0.379227i | \(-0.123810\pi\) | ||||
0.925304 | + | 0.379227i | \(0.123810\pi\) | |||||||
\(44\) | 27.8288 | 4.19536 | ||||||||
\(45\) | −14.5835 | −2.17399 | ||||||||
\(46\) | −18.9372 | −2.79213 | ||||||||
\(47\) | −10.1468 | −1.48007 | −0.740034 | − | 0.672569i | \(-0.765191\pi\) | ||||
−0.740034 | + | 0.672569i | \(0.765191\pi\) | |||||||
\(48\) | −25.4884 | −3.67893 | ||||||||
\(49\) | −6.86942 | −0.981346 | ||||||||
\(50\) | 1.40143 | 0.198192 | ||||||||
\(51\) | 4.47423 | 0.626517 | ||||||||
\(52\) | −26.1432 | −3.62541 | ||||||||
\(53\) | −3.72654 | −0.511880 | −0.255940 | − | 0.966693i | \(-0.582385\pi\) | ||||
−0.255940 | + | 0.966693i | \(0.582385\pi\) | |||||||
\(54\) | 31.6591 | 4.30825 | ||||||||
\(55\) | −12.7171 | −1.71477 | ||||||||
\(56\) | 2.43480 | 0.325364 | ||||||||
\(57\) | −20.4392 | −2.70724 | ||||||||
\(58\) | 25.2194 | 3.31148 | ||||||||
\(59\) | −5.13640 | −0.668702 | −0.334351 | − | 0.942449i | \(-0.608517\pi\) | ||||
−0.334351 | + | 0.942449i | \(0.608517\pi\) | |||||||
\(60\) | 30.6903 | 3.96211 | ||||||||
\(61\) | 4.78639 | 0.612834 | 0.306417 | − | 0.951897i | \(-0.400870\pi\) | ||||
0.306417 | + | 0.951897i | \(0.400870\pi\) | |||||||
\(62\) | 3.38680 | 0.430124 | ||||||||
\(63\) | −2.49667 | −0.314551 | ||||||||
\(64\) | 2.72991 | 0.341239 | ||||||||
\(65\) | 11.9468 | 1.48181 | ||||||||
\(66\) | 48.7937 | 6.00608 | ||||||||
\(67\) | 2.48641 | 0.303763 | 0.151882 | − | 0.988399i | \(-0.451467\pi\) | ||||
0.151882 | + | 0.988399i | \(0.451467\pi\) | |||||||
\(68\) | −6.56516 | −0.796142 | ||||||||
\(69\) | −23.1706 | −2.78942 | ||||||||
\(70\) | −1.96232 | −0.234542 | ||||||||
\(71\) | −9.23380 | −1.09585 | −0.547925 | − | 0.836527i | \(-0.684582\pi\) | ||||
−0.547925 | + | 0.836527i | \(0.684582\pi\) | |||||||
\(72\) | −46.5535 | −5.48639 | ||||||||
\(73\) | 4.42815 | 0.518276 | 0.259138 | − | 0.965840i | \(-0.416562\pi\) | ||||
0.259138 | + | 0.965840i | \(0.416562\pi\) | |||||||
\(74\) | −2.57274 | −0.299075 | ||||||||
\(75\) | 1.71472 | 0.197999 | ||||||||
\(76\) | 29.9911 | 3.44021 | ||||||||
\(77\) | −2.17714 | −0.248108 | ||||||||
\(78\) | −45.8381 | −5.19014 | ||||||||
\(79\) | 5.02268 | 0.565096 | 0.282548 | − | 0.959253i | \(-0.408820\pi\) | ||||
0.282548 | + | 0.959253i | \(0.408820\pi\) | |||||||
\(80\) | −17.0907 | −1.91080 | ||||||||
\(81\) | 18.0091 | 2.00101 | ||||||||
\(82\) | 8.04609 | 0.888542 | ||||||||
\(83\) | −10.4629 | −1.14846 | −0.574228 | − | 0.818695i | \(-0.694698\pi\) | ||||
−0.574228 | + | 0.818695i | \(0.694698\pi\) | |||||||
\(84\) | 5.25413 | 0.573272 | ||||||||
\(85\) | 3.00011 | 0.325407 | ||||||||
\(86\) | −31.2208 | −3.36663 | ||||||||
\(87\) | 30.8574 | 3.30826 | ||||||||
\(88\) | −40.5954 | −4.32748 | ||||||||
\(89\) | 8.14651 | 0.863528 | 0.431764 | − | 0.901987i | \(-0.357891\pi\) | ||||
0.431764 | + | 0.901987i | \(0.357891\pi\) | |||||||
\(90\) | 37.5196 | 3.95492 | ||||||||
\(91\) | 2.04526 | 0.214402 | ||||||||
\(92\) | 33.9989 | 3.54463 | ||||||||
\(93\) | 4.14393 | 0.429706 | ||||||||
\(94\) | 26.1051 | 2.69254 | ||||||||
\(95\) | −13.7051 | −1.40612 | ||||||||
\(96\) | 23.1544 | 2.36319 | ||||||||
\(97\) | 8.63894 | 0.877152 | 0.438576 | − | 0.898694i | \(-0.355483\pi\) | ||||
0.438576 | + | 0.898694i | \(0.355483\pi\) | |||||||
\(98\) | 17.6732 | 1.78526 | ||||||||
\(99\) | 41.6270 | 4.18367 | ||||||||
\(100\) | −2.51606 | −0.251606 | ||||||||
\(101\) | −5.51163 | −0.548428 | −0.274214 | − | 0.961669i | \(-0.588418\pi\) | ||||
−0.274214 | + | 0.961669i | \(0.588418\pi\) | |||||||
\(102\) | −11.5110 | −1.13976 | ||||||||
\(103\) | −2.22124 | −0.218866 | −0.109433 | − | 0.993994i | \(-0.534903\pi\) | ||||
−0.109433 | + | 0.993994i | \(0.534903\pi\) | |||||||
\(104\) | 38.1364 | 3.73958 | ||||||||
\(105\) | −2.40100 | −0.234314 | ||||||||
\(106\) | 9.58741 | 0.931212 | ||||||||
\(107\) | 16.7560 | 1.61987 | 0.809934 | − | 0.586521i | \(-0.199503\pi\) | ||||
0.809934 | + | 0.586521i | \(0.199503\pi\) | |||||||
\(108\) | −56.8393 | −5.46936 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 32.7177 | 3.11951 | ||||||||
\(111\) | −3.14788 | −0.298784 | ||||||||
\(112\) | −2.92590 | −0.276472 | ||||||||
\(113\) | −16.5451 | −1.55643 | −0.778217 | − | 0.627996i | \(-0.783875\pi\) | ||||
−0.778217 | + | 0.627996i | \(0.783875\pi\) | |||||||
\(114\) | 52.5848 | 4.92502 | ||||||||
\(115\) | −15.5366 | −1.44880 | ||||||||
\(116\) | −45.2779 | −4.20394 | ||||||||
\(117\) | −39.1056 | −3.61531 | ||||||||
\(118\) | 13.2146 | 1.21650 | ||||||||
\(119\) | 0.513612 | 0.0470828 | ||||||||
\(120\) | −44.7696 | −4.08688 | ||||||||
\(121\) | 25.2993 | 2.29994 | ||||||||
\(122\) | −12.3141 | −1.11487 | ||||||||
\(123\) | 9.84483 | 0.887678 | ||||||||
\(124\) | −6.08050 | −0.546045 | ||||||||
\(125\) | 11.7035 | 1.04680 | ||||||||
\(126\) | 6.42329 | 0.572232 | ||||||||
\(127\) | −6.09011 | −0.540410 | −0.270205 | − | 0.962803i | \(-0.587092\pi\) | ||||
−0.270205 | + | 0.962803i | \(0.587092\pi\) | |||||||
\(128\) | 7.68775 | 0.679507 | ||||||||
\(129\) | −38.2003 | −3.36335 | ||||||||
\(130\) | −30.7359 | −2.69571 | ||||||||
\(131\) | 7.66576 | 0.669761 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(132\) | −87.6019 | −7.62477 | ||||||||
\(133\) | −2.34629 | −0.203449 | ||||||||
\(134\) | −6.39688 | −0.552606 | ||||||||
\(135\) | 25.9741 | 2.23549 | ||||||||
\(136\) | 9.57693 | 0.821215 | ||||||||
\(137\) | 5.38160 | 0.459781 | 0.229891 | − | 0.973216i | \(-0.426163\pi\) | ||||
0.229891 | + | 0.973216i | \(0.426163\pi\) | |||||||
\(138\) | 59.6120 | 5.07451 | ||||||||
\(139\) | −1.50088 | −0.127303 | −0.0636515 | − | 0.997972i | \(-0.520275\pi\) | ||||
−0.0636515 | + | 0.997972i | \(0.520275\pi\) | |||||||
\(140\) | 3.52305 | 0.297752 | ||||||||
\(141\) | 31.9411 | 2.68992 | ||||||||
\(142\) | 23.7561 | 1.99357 | ||||||||
\(143\) | −34.1006 | −2.85164 | ||||||||
\(144\) | 55.9434 | 4.66195 | ||||||||
\(145\) | 20.6908 | 1.71828 | ||||||||
\(146\) | −11.3925 | −0.942847 | ||||||||
\(147\) | 21.6241 | 1.78353 | ||||||||
\(148\) | 4.61898 | 0.379677 | ||||||||
\(149\) | −2.99909 | −0.245695 | −0.122847 | − | 0.992426i | \(-0.539203\pi\) | ||||
−0.122847 | + | 0.992426i | \(0.539203\pi\) | |||||||
\(150\) | −4.41153 | −0.360200 | ||||||||
\(151\) | −3.49006 | −0.284017 | −0.142008 | − | 0.989865i | \(-0.545356\pi\) | ||||
−0.142008 | + | 0.989865i | \(0.545356\pi\) | |||||||
\(152\) | −43.7495 | −3.54855 | ||||||||
\(153\) | −9.82030 | −0.793925 | ||||||||
\(154\) | 5.60120 | 0.451358 | ||||||||
\(155\) | 2.77863 | 0.223185 | ||||||||
\(156\) | 82.2957 | 6.58893 | ||||||||
\(157\) | 14.3183 | 1.14272 | 0.571362 | − | 0.820698i | \(-0.306415\pi\) | ||||
0.571362 | + | 0.820698i | \(0.306415\pi\) | |||||||
\(158\) | −12.9220 | −1.02802 | ||||||||
\(159\) | 11.7307 | 0.930307 | ||||||||
\(160\) | 15.5257 | 1.22742 | ||||||||
\(161\) | −2.65984 | −0.209625 | ||||||||
\(162\) | −46.3326 | −3.64024 | ||||||||
\(163\) | 22.9105 | 1.79449 | 0.897246 | − | 0.441531i | \(-0.145564\pi\) | ||||
0.897246 | + | 0.441531i | \(0.145564\pi\) | |||||||
\(164\) | −14.4456 | −1.12801 | ||||||||
\(165\) | 40.0318 | 3.11647 | ||||||||
\(166\) | 26.9184 | 2.08927 | ||||||||
\(167\) | 7.38929 | 0.571801 | 0.285900 | − | 0.958259i | \(-0.407707\pi\) | ||||
0.285900 | + | 0.958259i | \(0.407707\pi\) | |||||||
\(168\) | −7.66446 | −0.591326 | ||||||||
\(169\) | 19.0351 | 1.46423 | ||||||||
\(170\) | −7.71848 | −0.591981 | ||||||||
\(171\) | 44.8613 | 3.43063 | ||||||||
\(172\) | 56.0524 | 4.27396 | ||||||||
\(173\) | −25.0782 | −1.90666 | −0.953329 | − | 0.301934i | \(-0.902368\pi\) | ||||
−0.953329 | + | 0.301934i | \(0.902368\pi\) | |||||||
\(174\) | −79.3879 | −6.01838 | ||||||||
\(175\) | 0.196839 | 0.0148797 | ||||||||
\(176\) | 48.7835 | 3.67719 | ||||||||
\(177\) | 16.1688 | 1.21532 | ||||||||
\(178\) | −20.9588 | −1.57093 | ||||||||
\(179\) | 24.9587 | 1.86550 | 0.932749 | − | 0.360526i | \(-0.117403\pi\) | ||||
0.932749 | + | 0.360526i | \(0.117403\pi\) | |||||||
\(180\) | −67.3610 | −5.02080 | ||||||||
\(181\) | −5.75277 | −0.427600 | −0.213800 | − | 0.976877i | \(-0.568584\pi\) | ||||
−0.213800 | + | 0.976877i | \(0.568584\pi\) | |||||||
\(182\) | −5.26192 | −0.390040 | ||||||||
\(183\) | −15.0670 | −1.11378 | ||||||||
\(184\) | −49.5960 | −3.65626 | ||||||||
\(185\) | −2.11075 | −0.155186 | ||||||||
\(186\) | −10.6612 | −0.781720 | ||||||||
\(187\) | −8.56345 | −0.626221 | ||||||||
\(188\) | −46.8680 | −3.41820 | ||||||||
\(189\) | 4.44671 | 0.323451 | ||||||||
\(190\) | 35.2597 | 2.55801 | ||||||||
\(191\) | −5.01845 | −0.363123 | −0.181561 | − | 0.983380i | \(-0.558115\pi\) | ||||
−0.181561 | + | 0.983380i | \(0.558115\pi\) | |||||||
\(192\) | −8.59345 | −0.620179 | ||||||||
\(193\) | 3.53640 | 0.254556 | 0.127278 | − | 0.991867i | \(-0.459376\pi\) | ||||
0.127278 | + | 0.991867i | \(0.459376\pi\) | |||||||
\(194\) | −22.2257 | −1.59571 | ||||||||
\(195\) | −37.6070 | −2.69309 | ||||||||
\(196\) | −31.7297 | −2.26641 | ||||||||
\(197\) | −8.67106 | −0.617788 | −0.308894 | − | 0.951097i | \(-0.599959\pi\) | ||||
−0.308894 | + | 0.951097i | \(0.599959\pi\) | |||||||
\(198\) | −107.095 | −7.61093 | ||||||||
\(199\) | 7.09379 | 0.502865 | 0.251433 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251433 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(200\) | 3.67031 | 0.259530 | ||||||||
\(201\) | −7.82693 | −0.552069 | ||||||||
\(202\) | 14.1800 | 0.997699 | ||||||||
\(203\) | 3.54223 | 0.248616 | ||||||||
\(204\) | 20.6663 | 1.44693 | ||||||||
\(205\) | 6.60126 | 0.461052 | ||||||||
\(206\) | 5.71467 | 0.398160 | ||||||||
\(207\) | 50.8563 | 3.53476 | ||||||||
\(208\) | −45.8286 | −3.17764 | ||||||||
\(209\) | 39.1197 | 2.70597 | ||||||||
\(210\) | 6.17714 | 0.426263 | ||||||||
\(211\) | 12.6517 | 0.870979 | 0.435489 | − | 0.900194i | \(-0.356575\pi\) | ||||
0.435489 | + | 0.900194i | \(0.356575\pi\) | |||||||
\(212\) | −17.2128 | −1.18218 | ||||||||
\(213\) | 29.0669 | 1.99163 | ||||||||
\(214\) | −43.1089 | −2.94686 | ||||||||
\(215\) | −25.6145 | −1.74689 | ||||||||
\(216\) | 82.9144 | 5.64161 | ||||||||
\(217\) | 0.475697 | 0.0322924 | ||||||||
\(218\) | −2.57274 | −0.174248 | ||||||||
\(219\) | −13.9393 | −0.941930 | ||||||||
\(220\) | −58.7398 | −3.96024 | ||||||||
\(221\) | 8.04474 | 0.541148 | ||||||||
\(222\) | 8.09868 | 0.543547 | ||||||||
\(223\) | 11.1399 | 0.745981 | 0.372990 | − | 0.927835i | \(-0.378332\pi\) | ||||
0.372990 | + | 0.927835i | \(0.378332\pi\) | |||||||
\(224\) | 2.65798 | 0.177594 | ||||||||
\(225\) | −3.76358 | −0.250905 | ||||||||
\(226\) | 42.5662 | 2.83146 | ||||||||
\(227\) | −2.82180 | −0.187289 | −0.0936447 | − | 0.995606i | \(-0.529852\pi\) | ||||
−0.0936447 | + | 0.995606i | \(0.529852\pi\) | |||||||
\(228\) | −94.4084 | −6.25235 | ||||||||
\(229\) | −21.8370 | −1.44303 | −0.721516 | − | 0.692398i | \(-0.756554\pi\) | ||||
−0.721516 | + | 0.692398i | \(0.756554\pi\) | |||||||
\(230\) | 39.9717 | 2.63565 | ||||||||
\(231\) | 6.85337 | 0.450919 | ||||||||
\(232\) | 66.0491 | 4.33634 | ||||||||
\(233\) | 9.44507 | 0.618767 | 0.309384 | − | 0.950937i | \(-0.399877\pi\) | ||||
0.309384 | + | 0.950937i | \(0.399877\pi\) | |||||||
\(234\) | 100.608 | 6.57697 | ||||||||
\(235\) | 21.4175 | 1.39712 | ||||||||
\(236\) | −23.7249 | −1.54436 | ||||||||
\(237\) | −15.8108 | −1.02702 | ||||||||
\(238\) | −1.32139 | −0.0856530 | ||||||||
\(239\) | 4.67138 | 0.302166 | 0.151083 | − | 0.988521i | \(-0.451724\pi\) | ||||
0.151083 | + | 0.988521i | \(0.451724\pi\) | |||||||
\(240\) | 53.7996 | 3.47275 | ||||||||
\(241\) | −30.2526 | −1.94874 | −0.974371 | − | 0.224946i | \(-0.927779\pi\) | ||||
−0.974371 | + | 0.224946i | \(0.927779\pi\) | |||||||
\(242\) | −65.0886 | −4.18405 | ||||||||
\(243\) | −19.7737 | −1.26848 | ||||||||
\(244\) | 22.1082 | 1.41533 | ||||||||
\(245\) | 14.4996 | 0.926349 | ||||||||
\(246\) | −25.3282 | −1.61486 | ||||||||
\(247\) | −36.7501 | −2.33835 | ||||||||
\(248\) | 8.86994 | 0.563242 | ||||||||
\(249\) | 32.9361 | 2.08724 | ||||||||
\(250\) | −30.1101 | −1.90433 | ||||||||
\(251\) | 3.70982 | 0.234162 | 0.117081 | − | 0.993122i | \(-0.462646\pi\) | ||||
0.117081 | + | 0.993122i | \(0.462646\pi\) | |||||||
\(252\) | −11.5321 | −0.726453 | ||||||||
\(253\) | 44.3475 | 2.78810 | ||||||||
\(254\) | 15.6683 | 0.983114 | ||||||||
\(255\) | −9.44398 | −0.591405 | ||||||||
\(256\) | −25.2384 | −1.57740 | ||||||||
\(257\) | 15.5303 | 0.968751 | 0.484376 | − | 0.874860i | \(-0.339047\pi\) | ||||
0.484376 | + | 0.874860i | \(0.339047\pi\) | |||||||
\(258\) | 98.2794 | 6.11861 | ||||||||
\(259\) | −0.361357 | −0.0224536 | ||||||||
\(260\) | 55.1818 | 3.42223 | ||||||||
\(261\) | −67.7276 | −4.19223 | ||||||||
\(262\) | −19.7220 | −1.21843 | ||||||||
\(263\) | −14.3488 | −0.884786 | −0.442393 | − | 0.896821i | \(-0.645870\pi\) | ||||
−0.442393 | + | 0.896821i | \(0.645870\pi\) | |||||||
\(264\) | 127.789 | 7.86490 | ||||||||
\(265\) | 7.86581 | 0.483193 | ||||||||
\(266\) | 6.03640 | 0.370115 | ||||||||
\(267\) | −25.6443 | −1.56940 | ||||||||
\(268\) | 11.4847 | 0.701538 | ||||||||
\(269\) | 10.9408 | 0.667072 | 0.333536 | − | 0.942737i | \(-0.391758\pi\) | ||||
0.333536 | + | 0.942737i | \(0.391758\pi\) | |||||||
\(270\) | −66.8245 | −4.06681 | ||||||||
\(271\) | 1.45386 | 0.0883158 | 0.0441579 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441579 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(272\) | −11.5086 | −0.697812 | ||||||||
\(273\) | −6.43824 | −0.389660 | ||||||||
\(274\) | −13.8455 | −0.836434 | ||||||||
\(275\) | −3.28190 | −0.197906 | ||||||||
\(276\) | −107.025 | −6.44213 | ||||||||
\(277\) | −20.2827 | −1.21867 | −0.609334 | − | 0.792914i | \(-0.708563\pi\) | ||||
−0.609334 | + | 0.792914i | \(0.708563\pi\) | |||||||
\(278\) | 3.86137 | 0.231590 | ||||||||
\(279\) | −9.09535 | −0.544525 | ||||||||
\(280\) | −5.13926 | −0.307129 | ||||||||
\(281\) | −28.9772 | −1.72863 | −0.864317 | − | 0.502947i | \(-0.832249\pi\) | ||||
−0.864317 | + | 0.502947i | \(0.832249\pi\) | |||||||
\(282\) | −82.1759 | −4.89351 | ||||||||
\(283\) | 19.6897 | 1.17043 | 0.585216 | − | 0.810878i | \(-0.301010\pi\) | ||||
0.585216 | + | 0.810878i | \(0.301010\pi\) | |||||||
\(284\) | −42.6507 | −2.53085 | ||||||||
\(285\) | 43.1422 | 2.55552 | ||||||||
\(286\) | 87.7319 | 5.18770 | ||||||||
\(287\) | 1.13012 | 0.0667091 | ||||||||
\(288\) | −50.8207 | −2.99464 | ||||||||
\(289\) | −14.9798 | −0.881164 | ||||||||
\(290\) | −53.2320 | −3.12589 | ||||||||
\(291\) | −27.1944 | −1.59416 | ||||||||
\(292\) | 20.4535 | 1.19695 | ||||||||
\(293\) | 1.08123 | 0.0631663 | 0.0315832 | − | 0.999501i | \(-0.489945\pi\) | ||||
0.0315832 | + | 0.999501i | \(0.489945\pi\) | |||||||
\(294\) | −55.6332 | −3.24459 | ||||||||
\(295\) | 10.8417 | 0.631227 | ||||||||
\(296\) | −6.73794 | −0.391635 | ||||||||
\(297\) | −74.1399 | −4.30204 | ||||||||
\(298\) | 7.71586 | 0.446968 | ||||||||
\(299\) | −41.6612 | −2.40933 | ||||||||
\(300\) | 7.92027 | 0.457277 | ||||||||
\(301\) | −4.38515 | −0.252756 | ||||||||
\(302\) | 8.97900 | 0.516684 | ||||||||
\(303\) | 17.3500 | 0.996729 | ||||||||
\(304\) | 52.5738 | 3.01532 | ||||||||
\(305\) | −10.1029 | −0.578489 | ||||||||
\(306\) | 25.2651 | 1.44431 | ||||||||
\(307\) | 10.3642 | 0.591518 | 0.295759 | − | 0.955263i | \(-0.404427\pi\) | ||||
0.295759 | + | 0.955263i | \(0.404427\pi\) | |||||||
\(308\) | −10.0561 | −0.573002 | ||||||||
\(309\) | 6.99221 | 0.397773 | ||||||||
\(310\) | −7.14869 | −0.406019 | ||||||||
\(311\) | 9.03585 | 0.512376 | 0.256188 | − | 0.966627i | \(-0.417533\pi\) | ||||
0.256188 | + | 0.966627i | \(0.417533\pi\) | |||||||
\(312\) | −120.049 | −6.79643 | ||||||||
\(313\) | −12.9425 | −0.731553 | −0.365776 | − | 0.930703i | \(-0.619197\pi\) | ||||
−0.365776 | + | 0.930703i | \(0.619197\pi\) | |||||||
\(314\) | −36.8372 | −2.07884 | ||||||||
\(315\) | 5.26986 | 0.296923 | ||||||||
\(316\) | 23.1996 | 1.30508 | ||||||||
\(317\) | 4.99636 | 0.280624 | 0.140312 | − | 0.990107i | \(-0.455189\pi\) | ||||
0.140312 | + | 0.990107i | \(0.455189\pi\) | |||||||
\(318\) | −30.1801 | −1.69241 | ||||||||
\(319\) | −59.0595 | −3.30670 | ||||||||
\(320\) | −5.76217 | −0.322115 | ||||||||
\(321\) | −52.7461 | −2.94400 | ||||||||
\(322\) | 6.84307 | 0.381349 | ||||||||
\(323\) | −9.22880 | −0.513504 | ||||||||
\(324\) | 83.1835 | 4.62131 | ||||||||
\(325\) | 3.08311 | 0.171020 | ||||||||
\(326\) | −58.9428 | −3.26454 | ||||||||
\(327\) | −3.14788 | −0.174078 | ||||||||
\(328\) | 21.0725 | 1.16354 | ||||||||
\(329\) | 3.66663 | 0.202148 | ||||||||
\(330\) | −102.991 | −5.66949 | ||||||||
\(331\) | 18.5412 | 1.01912 | 0.509559 | − | 0.860435i | \(-0.329808\pi\) | ||||
0.509559 | + | 0.860435i | \(0.329808\pi\) | |||||||
\(332\) | −48.3281 | −2.65235 | ||||||||
\(333\) | 6.90917 | 0.378620 | ||||||||
\(334\) | −19.0107 | −1.04022 | ||||||||
\(335\) | −5.24820 | −0.286740 | ||||||||
\(336\) | 9.21040 | 0.502468 | ||||||||
\(337\) | 12.5914 | 0.685895 | 0.342948 | − | 0.939355i | \(-0.388575\pi\) | ||||
0.342948 | + | 0.939355i | \(0.388575\pi\) | |||||||
\(338\) | −48.9722 | −2.66374 | ||||||||
\(339\) | 52.0821 | 2.82871 | ||||||||
\(340\) | 13.8574 | 0.751524 | ||||||||
\(341\) | −7.93128 | −0.429503 | ||||||||
\(342\) | −115.416 | −6.24100 | ||||||||
\(343\) | 5.01181 | 0.270612 | ||||||||
\(344\) | −81.7665 | −4.40856 | ||||||||
\(345\) | 48.9075 | 2.63309 | ||||||||
\(346\) | 64.5195 | 3.46859 | ||||||||
\(347\) | −28.3632 | −1.52262 | −0.761308 | − | 0.648391i | \(-0.775442\pi\) | ||||
−0.761308 | + | 0.648391i | \(0.775442\pi\) | |||||||
\(348\) | 142.529 | 7.64038 | ||||||||
\(349\) | 25.1264 | 1.34498 | 0.672492 | − | 0.740105i | \(-0.265224\pi\) | ||||
0.672492 | + | 0.740105i | \(0.265224\pi\) | |||||||
\(350\) | −0.506416 | −0.0270691 | ||||||||
\(351\) | 69.6491 | 3.71759 | ||||||||
\(352\) | −44.3164 | −2.36207 | ||||||||
\(353\) | −6.76895 | −0.360275 | −0.180137 | − | 0.983641i | \(-0.557654\pi\) | ||||
−0.180137 | + | 0.983641i | \(0.557654\pi\) | |||||||
\(354\) | −41.5980 | −2.21091 | ||||||||
\(355\) | 19.4903 | 1.03444 | ||||||||
\(356\) | 37.6285 | 1.99431 | ||||||||
\(357\) | −1.61679 | −0.0855697 | ||||||||
\(358\) | −64.2121 | −3.39371 | ||||||||
\(359\) | −19.0913 | −1.00760 | −0.503800 | − | 0.863820i | \(-0.668065\pi\) | ||||
−0.503800 | + | 0.863820i | \(0.668065\pi\) | |||||||
\(360\) | 98.2630 | 5.17891 | ||||||||
\(361\) | 23.1592 | 1.21891 | ||||||||
\(362\) | 14.8004 | 0.777890 | ||||||||
\(363\) | −79.6394 | −4.17998 | ||||||||
\(364\) | 9.44702 | 0.495158 | ||||||||
\(365\) | −9.34673 | −0.489230 | ||||||||
\(366\) | 38.7634 | 2.02620 | ||||||||
\(367\) | −23.7962 | −1.24215 | −0.621075 | − | 0.783751i | \(-0.713304\pi\) | ||||
−0.621075 | + | 0.783751i | \(0.713304\pi\) | |||||||
\(368\) | 59.5995 | 3.10684 | ||||||||
\(369\) | −21.6080 | −1.12487 | ||||||||
\(370\) | 5.43041 | 0.282314 | ||||||||
\(371\) | 1.34661 | 0.0699126 | ||||||||
\(372\) | 19.1407 | 0.992400 | ||||||||
\(373\) | 10.0157 | 0.518592 | 0.259296 | − | 0.965798i | \(-0.416509\pi\) | ||||
0.259296 | + | 0.965798i | \(0.416509\pi\) | |||||||
\(374\) | 22.0315 | 1.13922 | ||||||||
\(375\) | −36.8414 | −1.90248 | ||||||||
\(376\) | 68.3688 | 3.52585 | ||||||||
\(377\) | 55.4821 | 2.85747 | ||||||||
\(378\) | −11.4402 | −0.588421 | ||||||||
\(379\) | −25.0787 | −1.28821 | −0.644103 | − | 0.764939i | \(-0.722769\pi\) | ||||
−0.644103 | + | 0.764939i | \(0.722769\pi\) | |||||||
\(380\) | −63.3037 | −3.24741 | ||||||||
\(381\) | 19.1710 | 0.982158 | ||||||||
\(382\) | 12.9112 | 0.660592 | ||||||||
\(383\) | −5.11922 | −0.261580 | −0.130790 | − | 0.991410i | \(-0.541751\pi\) | ||||
−0.130790 | + | 0.991410i | \(0.541751\pi\) | |||||||
\(384\) | −24.2001 | −1.23496 | ||||||||
\(385\) | 4.59540 | 0.234203 | ||||||||
\(386\) | −9.09823 | −0.463088 | ||||||||
\(387\) | 83.8444 | 4.26205 | ||||||||
\(388\) | 39.9031 | 2.02577 | ||||||||
\(389\) | 25.7759 | 1.30689 | 0.653445 | − | 0.756974i | \(-0.273323\pi\) | ||||
0.653445 | + | 0.756974i | \(0.273323\pi\) | |||||||
\(390\) | 96.7529 | 4.89927 | ||||||||
\(391\) | −10.4621 | −0.529091 | ||||||||
\(392\) | 46.2857 | 2.33778 | ||||||||
\(393\) | −24.1309 | −1.21724 | ||||||||
\(394\) | 22.3084 | 1.12388 | ||||||||
\(395\) | −10.6016 | −0.533426 | ||||||||
\(396\) | 192.274 | 9.66214 | ||||||||
\(397\) | −32.9421 | −1.65332 | −0.826659 | − | 0.562703i | \(-0.809761\pi\) | ||||
−0.826659 | + | 0.562703i | \(0.809761\pi\) | |||||||
\(398\) | −18.2505 | −0.914813 | ||||||||
\(399\) | 7.38586 | 0.369755 | ||||||||
\(400\) | −4.41061 | −0.220531 | ||||||||
\(401\) | 24.8764 | 1.24227 | 0.621133 | − | 0.783705i | \(-0.286673\pi\) | ||||
0.621133 | + | 0.783705i | \(0.286673\pi\) | |||||||
\(402\) | 20.1366 | 1.00432 | ||||||||
\(403\) | 7.45086 | 0.371154 | ||||||||
\(404\) | −25.4581 | −1.26659 | ||||||||
\(405\) | −38.0127 | −1.88887 | ||||||||
\(406\) | −9.11322 | −0.452281 | ||||||||
\(407\) | 6.02489 | 0.298643 | ||||||||
\(408\) | −30.1470 | −1.49250 | ||||||||
\(409\) | 20.9581 | 1.03631 | 0.518155 | − | 0.855287i | \(-0.326619\pi\) | ||||
0.518155 | + | 0.855287i | \(0.326619\pi\) | |||||||
\(410\) | −16.9833 | −0.838746 | ||||||||
\(411\) | −16.9407 | −0.835621 | ||||||||
\(412\) | −10.2599 | −0.505467 | ||||||||
\(413\) | 1.85607 | 0.0913314 | ||||||||
\(414\) | −130.840 | −6.43044 | ||||||||
\(415\) | 22.0847 | 1.08409 | ||||||||
\(416\) | 41.6320 | 2.04118 | ||||||||
\(417\) | 4.72460 | 0.231365 | ||||||||
\(418\) | −100.645 | −4.92269 | ||||||||
\(419\) | −28.5675 | −1.39561 | −0.697806 | − | 0.716287i | \(-0.745840\pi\) | ||||
−0.697806 | + | 0.716287i | \(0.745840\pi\) | |||||||
\(420\) | −11.0902 | −0.541144 | ||||||||
\(421\) | 31.1856 | 1.51990 | 0.759948 | − | 0.649984i | \(-0.225225\pi\) | ||||
0.759948 | + | 0.649984i | \(0.225225\pi\) | |||||||
\(422\) | −32.5495 | −1.58448 | ||||||||
\(423\) | −70.1062 | −3.40868 | ||||||||
\(424\) | 25.1092 | 1.21941 | ||||||||
\(425\) | 0.774239 | 0.0375561 | ||||||||
\(426\) | −74.7815 | −3.62318 | ||||||||
\(427\) | −1.72959 | −0.0837009 | ||||||||
\(428\) | 77.3958 | 3.74107 | ||||||||
\(429\) | 107.345 | 5.18265 | ||||||||
\(430\) | 65.8994 | 3.17795 | ||||||||
\(431\) | −5.79032 | −0.278910 | −0.139455 | − | 0.990228i | \(-0.544535\pi\) | ||||
−0.139455 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(432\) | −99.6383 | −4.79385 | ||||||||
\(433\) | −14.1746 | −0.681187 | −0.340593 | − | 0.940211i | \(-0.610628\pi\) | ||||
−0.340593 | + | 0.940211i | \(0.610628\pi\) | |||||||
\(434\) | −1.22384 | −0.0587463 | ||||||||
\(435\) | −65.1322 | −3.12285 | ||||||||
\(436\) | 4.61898 | 0.221209 | ||||||||
\(437\) | 47.7931 | 2.28626 | ||||||||
\(438\) | 35.8621 | 1.71356 | ||||||||
\(439\) | −6.10292 | −0.291276 | −0.145638 | − | 0.989338i | \(-0.546524\pi\) | ||||
−0.145638 | + | 0.989338i | \(0.546524\pi\) | |||||||
\(440\) | 85.6868 | 4.08496 | ||||||||
\(441\) | −47.4620 | −2.26009 | ||||||||
\(442\) | −20.6970 | −0.984456 | ||||||||
\(443\) | −12.8666 | −0.611311 | −0.305656 | − | 0.952142i | \(-0.598876\pi\) | ||||
−0.305656 | + | 0.952142i | \(0.598876\pi\) | |||||||
\(444\) | −14.5400 | −0.690038 | ||||||||
\(445\) | −17.1953 | −0.815134 | ||||||||
\(446\) | −28.6600 | −1.35709 | ||||||||
\(447\) | 9.44078 | 0.446533 | ||||||||
\(448\) | −0.986472 | −0.0466064 | ||||||||
\(449\) | −20.6886 | −0.976354 | −0.488177 | − | 0.872745i | \(-0.662338\pi\) | ||||
−0.488177 | + | 0.872745i | \(0.662338\pi\) | |||||||
\(450\) | 9.68271 | 0.456447 | ||||||||
\(451\) | −18.8425 | −0.887260 | ||||||||
\(452\) | −76.4215 | −3.59456 | ||||||||
\(453\) | 10.9863 | 0.516181 | ||||||||
\(454\) | 7.25975 | 0.340717 | ||||||||
\(455\) | −4.31704 | −0.202386 | ||||||||
\(456\) | 137.718 | 6.44925 | ||||||||
\(457\) | −18.6793 | −0.873782 | −0.436891 | − | 0.899514i | \(-0.643921\pi\) | ||||
−0.436891 | + | 0.899514i | \(0.643921\pi\) | |||||||
\(458\) | 56.1809 | 2.62516 | ||||||||
\(459\) | 17.4905 | 0.816386 | ||||||||
\(460\) | −71.7633 | −3.34598 | ||||||||
\(461\) | 3.84650 | 0.179150 | 0.0895748 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895748 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(462\) | −17.6319 | −0.820311 | ||||||||
\(463\) | −2.09063 | −0.0971596 | −0.0485798 | − | 0.998819i | \(-0.515470\pi\) | ||||
−0.0485798 | + | 0.998819i | \(0.515470\pi\) | |||||||
\(464\) | −79.3713 | −3.68472 | ||||||||
\(465\) | −8.74681 | −0.405624 | ||||||||
\(466\) | −24.2997 | −1.12566 | ||||||||
\(467\) | −0.664455 | −0.0307473 | −0.0153737 | − | 0.999882i | \(-0.504894\pi\) | ||||
−0.0153737 | + | 0.999882i | \(0.504894\pi\) | |||||||
\(468\) | −180.628 | −8.34951 | ||||||||
\(469\) | −0.898482 | −0.0414880 | ||||||||
\(470\) | −55.1015 | −2.54164 | ||||||||
\(471\) | −45.0723 | −2.07682 | ||||||||
\(472\) | 34.6087 | 1.59300 | ||||||||
\(473\) | 73.1136 | 3.36177 | ||||||||
\(474\) | 40.6771 | 1.86836 | ||||||||
\(475\) | −3.53689 | −0.162284 | ||||||||
\(476\) | 2.37236 | 0.108737 | ||||||||
\(477\) | −25.7473 | −1.17889 | ||||||||
\(478\) | −12.0182 | −0.549701 | ||||||||
\(479\) | −31.2081 | −1.42594 | −0.712968 | − | 0.701196i | \(-0.752650\pi\) | ||||
−0.712968 | + | 0.701196i | \(0.752650\pi\) | |||||||
\(480\) | −48.8732 | −2.23075 | ||||||||
\(481\) | −5.65995 | −0.258072 | ||||||||
\(482\) | 77.8320 | 3.54515 | ||||||||
\(483\) | 8.37287 | 0.380979 | ||||||||
\(484\) | 116.857 | 5.31169 | ||||||||
\(485\) | −18.2347 | −0.827994 | ||||||||
\(486\) | 50.8725 | 2.30762 | ||||||||
\(487\) | −3.80054 | −0.172219 | −0.0861095 | − | 0.996286i | \(-0.527443\pi\) | ||||
−0.0861095 | + | 0.996286i | \(0.527443\pi\) | |||||||
\(488\) | −32.2504 | −1.45991 | ||||||||
\(489\) | −72.1197 | −3.26137 | ||||||||
\(490\) | −37.3038 | −1.68521 | ||||||||
\(491\) | −26.9962 | −1.21832 | −0.609160 | − | 0.793047i | \(-0.708493\pi\) | ||||
−0.609160 | + | 0.793047i | \(0.708493\pi\) | |||||||
\(492\) | 45.4730 | 2.05008 | ||||||||
\(493\) | 13.9328 | 0.627503 | ||||||||
\(494\) | 94.5484 | 4.25393 | ||||||||
\(495\) | −87.8643 | −3.94921 | ||||||||
\(496\) | −10.6590 | −0.478604 | ||||||||
\(497\) | 3.33670 | 0.149671 | ||||||||
\(498\) | −84.7360 | −3.79711 | ||||||||
\(499\) | −33.4899 | −1.49921 | −0.749607 | − | 0.661883i | \(-0.769758\pi\) | ||||
−0.749607 | + | 0.661883i | \(0.769758\pi\) | |||||||
\(500\) | 54.0584 | 2.41756 | ||||||||
\(501\) | −23.2606 | −1.03921 | ||||||||
\(502\) | −9.54439 | −0.425987 | ||||||||
\(503\) | −29.4808 | −1.31448 | −0.657242 | − | 0.753680i | \(-0.728277\pi\) | ||||
−0.657242 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(504\) | 16.8224 | 0.749331 | ||||||||
\(505\) | 11.6337 | 0.517692 | ||||||||
\(506\) | −114.094 | −5.07211 | ||||||||
\(507\) | −59.9201 | −2.66115 | ||||||||
\(508\) | −28.1301 | −1.24807 | ||||||||
\(509\) | −16.7184 | −0.741031 | −0.370516 | − | 0.928826i | \(-0.620819\pi\) | ||||
−0.370516 | + | 0.928826i | \(0.620819\pi\) | |||||||
\(510\) | 24.2969 | 1.07588 | ||||||||
\(511\) | −1.60014 | −0.0707861 | ||||||||
\(512\) | 49.5562 | 2.19010 | ||||||||
\(513\) | −79.9004 | −3.52769 | ||||||||
\(514\) | −39.9553 | −1.76235 | ||||||||
\(515\) | 4.68849 | 0.206600 | ||||||||
\(516\) | −176.446 | −7.76762 | ||||||||
\(517\) | −61.1336 | −2.68865 | ||||||||
\(518\) | 0.929676 | 0.0408476 | ||||||||
\(519\) | 78.9431 | 3.46522 | ||||||||
\(520\) | −80.4965 | −3.53001 | ||||||||
\(521\) | −30.9648 | −1.35659 | −0.678296 | − | 0.734789i | \(-0.737281\pi\) | ||||
−0.678296 | + | 0.734789i | \(0.737281\pi\) | |||||||
\(522\) | 174.245 | 7.62651 | ||||||||
\(523\) | 4.10598 | 0.179542 | 0.0897710 | − | 0.995962i | \(-0.471386\pi\) | ||||
0.0897710 | + | 0.995962i | \(0.471386\pi\) | |||||||
\(524\) | 35.4080 | 1.54680 | ||||||||
\(525\) | −0.619627 | −0.0270427 | ||||||||
\(526\) | 36.9157 | 1.60960 | ||||||||
\(527\) | 1.87108 | 0.0815057 | ||||||||
\(528\) | −153.565 | −6.68305 | ||||||||
\(529\) | 31.1800 | 1.35565 | ||||||||
\(530\) | −20.2367 | −0.879024 | ||||||||
\(531\) | −35.4883 | −1.54006 | ||||||||
\(532\) | −10.8375 | −0.469864 | ||||||||
\(533\) | 17.7012 | 0.766723 | ||||||||
\(534\) | 65.9759 | 2.85506 | ||||||||
\(535\) | −35.3679 | −1.52909 | ||||||||
\(536\) | −16.7533 | −0.723632 | ||||||||
\(537\) | −78.5670 | −3.39041 | ||||||||
\(538\) | −28.1478 | −1.21354 | ||||||||
\(539\) | −41.3875 | −1.78269 | ||||||||
\(540\) | 119.974 | 5.16284 | ||||||||
\(541\) | 19.8016 | 0.851337 | 0.425669 | − | 0.904879i | \(-0.360039\pi\) | ||||
0.425669 | + | 0.904879i | \(0.360039\pi\) | |||||||
\(542\) | −3.74040 | −0.160664 | ||||||||
\(543\) | 18.1091 | 0.777134 | ||||||||
\(544\) | 10.4548 | 0.448244 | ||||||||
\(545\) | −2.11075 | −0.0904147 | ||||||||
\(546\) | 16.5639 | 0.708870 | ||||||||
\(547\) | −16.0675 | −0.686995 | −0.343498 | − | 0.939154i | \(-0.611612\pi\) | ||||
−0.343498 | + | 0.939154i | \(0.611612\pi\) | |||||||
\(548\) | 24.8575 | 1.06186 | ||||||||
\(549\) | 33.0700 | 1.41139 | ||||||||
\(550\) | 8.44346 | 0.360030 | ||||||||
\(551\) | −63.6482 | −2.71151 | ||||||||
\(552\) | 156.122 | 6.64501 | ||||||||
\(553\) | −1.81498 | −0.0771808 | ||||||||
\(554\) | 52.1820 | 2.21700 | ||||||||
\(555\) | 6.64440 | 0.282039 | ||||||||
\(556\) | −6.93253 | −0.294005 | ||||||||
\(557\) | −8.52073 | −0.361035 | −0.180518 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180518 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(558\) | 23.4000 | 0.990599 | ||||||||
\(559\) | −68.6849 | −2.90506 | ||||||||
\(560\) | 6.17585 | 0.260977 | ||||||||
\(561\) | 26.9567 | 1.13811 | ||||||||
\(562\) | 74.5507 | 3.14473 | ||||||||
\(563\) | 36.6604 | 1.54505 | 0.772525 | − | 0.634984i | \(-0.218993\pi\) | ||||
0.772525 | + | 0.634984i | \(0.218993\pi\) | |||||||
\(564\) | 147.535 | 6.21234 | ||||||||
\(565\) | 34.9226 | 1.46921 | ||||||||
\(566\) | −50.6564 | −2.12925 | ||||||||
\(567\) | −6.50771 | −0.273298 | ||||||||
\(568\) | 62.2168 | 2.61056 | ||||||||
\(569\) | −18.7379 | −0.785535 | −0.392768 | − | 0.919638i | \(-0.628482\pi\) | ||||
−0.392768 | + | 0.919638i | \(0.628482\pi\) | |||||||
\(570\) | −110.993 | −4.64901 | ||||||||
\(571\) | 7.49718 | 0.313747 | 0.156874 | − | 0.987619i | \(-0.449858\pi\) | ||||
0.156874 | + | 0.987619i | \(0.449858\pi\) | |||||||
\(572\) | −157.510 | −6.58582 | ||||||||
\(573\) | 15.7975 | 0.659950 | ||||||||
\(574\) | −2.90751 | −0.121357 | ||||||||
\(575\) | −4.00955 | −0.167210 | ||||||||
\(576\) | 18.8614 | 0.785893 | ||||||||
\(577\) | 15.7852 | 0.657145 | 0.328572 | − | 0.944479i | \(-0.393433\pi\) | ||||
0.328572 | + | 0.944479i | \(0.393433\pi\) | |||||||
\(578\) | 38.5390 | 1.60301 | ||||||||
\(579\) | −11.1322 | −0.462637 | ||||||||
\(580\) | 95.5703 | 3.96834 | ||||||||
\(581\) | 3.78085 | 0.156856 | ||||||||
\(582\) | 69.9640 | 2.90010 | ||||||||
\(583\) | −22.4520 | −0.929868 | ||||||||
\(584\) | −29.8366 | −1.23465 | ||||||||
\(585\) | 82.5421 | 3.41270 | ||||||||
\(586\) | −2.78173 | −0.114912 | ||||||||
\(587\) | 30.5177 | 1.25960 | 0.629801 | − | 0.776756i | \(-0.283136\pi\) | ||||
0.629801 | + | 0.776756i | \(0.283136\pi\) | |||||||
\(588\) | 99.8814 | 4.11904 | ||||||||
\(589\) | −8.54752 | −0.352194 | ||||||||
\(590\) | −27.8928 | −1.14833 | ||||||||
\(591\) | 27.2955 | 1.12279 | ||||||||
\(592\) | 8.09699 | 0.332784 | ||||||||
\(593\) | 45.2409 | 1.85782 | 0.928911 | − | 0.370303i | \(-0.120746\pi\) | ||||
0.928911 | + | 0.370303i | \(0.120746\pi\) | |||||||
\(594\) | 190.743 | 7.82626 | ||||||||
\(595\) | −1.08411 | −0.0444441 | ||||||||
\(596\) | −13.8527 | −0.567429 | ||||||||
\(597\) | −22.3304 | −0.913923 | ||||||||
\(598\) | 107.183 | 4.38306 | ||||||||
\(599\) | −12.1439 | −0.496187 | −0.248094 | − | 0.968736i | \(-0.579804\pi\) | ||||
−0.248094 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(600\) | −11.5537 | −0.471678 | ||||||||
\(601\) | −27.5013 | −1.12180 | −0.560900 | − | 0.827883i | \(-0.689545\pi\) | ||||
−0.560900 | + | 0.827883i | \(0.689545\pi\) | |||||||
\(602\) | 11.2818 | 0.459814 | ||||||||
\(603\) | 17.1790 | 0.699584 | ||||||||
\(604\) | −16.1205 | −0.655934 | ||||||||
\(605\) | −53.4007 | −2.17105 | ||||||||
\(606\) | −44.6369 | −1.81325 | ||||||||
\(607\) | 19.2574 | 0.781633 | 0.390817 | − | 0.920469i | \(-0.372193\pi\) | ||||
0.390817 | + | 0.920469i | \(0.372193\pi\) | |||||||
\(608\) | −47.7597 | −1.93691 | ||||||||
\(609\) | −11.1505 | −0.451842 | ||||||||
\(610\) | 25.9921 | 1.05239 | ||||||||
\(611\) | 57.4306 | 2.32339 | ||||||||
\(612\) | −45.3598 | −1.83356 | ||||||||
\(613\) | 4.69155 | 0.189490 | 0.0947450 | − | 0.995502i | \(-0.469796\pi\) | ||||
0.0947450 | + | 0.995502i | \(0.469796\pi\) | |||||||
\(614\) | −26.6645 | −1.07609 | ||||||||
\(615\) | −20.7800 | −0.837931 | ||||||||
\(616\) | 14.6694 | 0.591047 | ||||||||
\(617\) | −40.9627 | −1.64909 | −0.824547 | − | 0.565793i | \(-0.808570\pi\) | ||||
−0.824547 | + | 0.565793i | \(0.808570\pi\) | |||||||
\(618\) | −17.9891 | −0.723629 | ||||||||
\(619\) | 34.9099 | 1.40315 | 0.701574 | − | 0.712596i | \(-0.252481\pi\) | ||||
0.701574 | + | 0.712596i | \(0.252481\pi\) | |||||||
\(620\) | 12.8344 | 0.515444 | ||||||||
\(621\) | −90.5779 | −3.63477 | ||||||||
\(622\) | −23.2469 | −0.932115 | ||||||||
\(623\) | −2.94380 | −0.117941 | ||||||||
\(624\) | 144.263 | 5.77514 | ||||||||
\(625\) | −21.9797 | −0.879186 | ||||||||
\(626\) | 33.2976 | 1.33084 | ||||||||
\(627\) | −123.144 | −4.91791 | ||||||||
\(628\) | 66.1359 | 2.63911 | ||||||||
\(629\) | −1.42134 | −0.0566727 | ||||||||
\(630\) | −13.5580 | −0.540162 | ||||||||
\(631\) | 8.72381 | 0.347289 | 0.173645 | − | 0.984808i | \(-0.444446\pi\) | ||||
0.173645 | + | 0.984808i | \(0.444446\pi\) | |||||||
\(632\) | −33.8425 | −1.34618 | ||||||||
\(633\) | −39.8261 | −1.58294 | ||||||||
\(634\) | −12.8543 | −0.510511 | ||||||||
\(635\) | 12.8547 | 0.510124 | ||||||||
\(636\) | 54.1839 | 2.14853 | ||||||||
\(637\) | 38.8806 | 1.54051 | ||||||||
\(638\) | 151.944 | 6.01554 | ||||||||
\(639\) | −63.7979 | −2.52380 | ||||||||
\(640\) | −16.2269 | −0.641426 | ||||||||
\(641\) | 10.9052 | 0.430728 | 0.215364 | − | 0.976534i | \(-0.430906\pi\) | ||||
0.215364 | + | 0.976534i | \(0.430906\pi\) | |||||||
\(642\) | 135.702 | 5.35572 | ||||||||
\(643\) | −10.9230 | −0.430761 | −0.215381 | − | 0.976530i | \(-0.569099\pi\) | ||||
−0.215381 | + | 0.976530i | \(0.569099\pi\) | |||||||
\(644\) | −12.2857 | −0.484126 | ||||||||
\(645\) | 80.6315 | 3.17486 | ||||||||
\(646\) | 23.7433 | 0.934167 | ||||||||
\(647\) | 18.1368 | 0.713030 | 0.356515 | − | 0.934290i | \(-0.383965\pi\) | ||||
0.356515 | + | 0.934290i | \(0.383965\pi\) | |||||||
\(648\) | −121.344 | −4.76685 | ||||||||
\(649\) | −30.9463 | −1.21475 | ||||||||
\(650\) | −7.93202 | −0.311119 | ||||||||
\(651\) | −1.49744 | −0.0586892 | ||||||||
\(652\) | 105.823 | 4.14436 | ||||||||
\(653\) | 5.34357 | 0.209110 | 0.104555 | − | 0.994519i | \(-0.466658\pi\) | ||||
0.104555 | + | 0.994519i | \(0.466658\pi\) | |||||||
\(654\) | 8.09868 | 0.316683 | ||||||||
\(655\) | −16.1805 | −0.632225 | ||||||||
\(656\) | −25.3229 | −0.988692 | ||||||||
\(657\) | 30.5948 | 1.19362 | ||||||||
\(658\) | −9.43327 | −0.367747 | ||||||||
\(659\) | 12.5265 | 0.487965 | 0.243983 | − | 0.969780i | \(-0.421546\pi\) | ||||
0.243983 | + | 0.969780i | \(0.421546\pi\) | |||||||
\(660\) | 184.906 | 7.19746 | ||||||||
\(661\) | 0.208838 | 0.00812288 | 0.00406144 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406144 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(662\) | −47.7017 | −1.85398 | ||||||||
\(663\) | −25.3239 | −0.983499 | ||||||||
\(664\) | 70.4986 | 2.73588 | ||||||||
\(665\) | 4.95245 | 0.192048 | ||||||||
\(666\) | −17.7755 | −0.688785 | ||||||||
\(667\) | −72.1539 | −2.79381 | ||||||||
\(668\) | 34.1310 | 1.32057 | ||||||||
\(669\) | −35.0670 | −1.35577 | ||||||||
\(670\) | 13.5022 | 0.521637 | ||||||||
\(671\) | 28.8375 | 1.11326 | ||||||||
\(672\) | −8.36700 | −0.322764 | ||||||||
\(673\) | −4.33561 | −0.167125 | −0.0835627 | − | 0.996503i | \(-0.526630\pi\) | ||||
−0.0835627 | + | 0.996503i | \(0.526630\pi\) | |||||||
\(674\) | −32.3943 | −1.24778 | ||||||||
\(675\) | 6.70314 | 0.258004 | ||||||||
\(676\) | 87.9225 | 3.38163 | ||||||||
\(677\) | 29.3308 | 1.12728 | 0.563638 | − | 0.826022i | \(-0.309401\pi\) | ||||
0.563638 | + | 0.826022i | \(0.309401\pi\) | |||||||
\(678\) | −133.994 | −5.14599 | ||||||||
\(679\) | −3.12174 | −0.119801 | ||||||||
\(680\) | −20.2145 | −0.775192 | ||||||||
\(681\) | 8.88270 | 0.340386 | ||||||||
\(682\) | 20.4051 | 0.781352 | ||||||||
\(683\) | 9.44450 | 0.361384 | 0.180692 | − | 0.983540i | \(-0.442166\pi\) | ||||
0.180692 | + | 0.983540i | \(0.442166\pi\) | |||||||
\(684\) | 207.213 | 7.92300 | ||||||||
\(685\) | −11.3592 | −0.434014 | ||||||||
\(686\) | −12.8941 | −0.492298 | ||||||||
\(687\) | 68.7404 | 2.62261 | ||||||||
\(688\) | 98.2589 | 3.74609 | ||||||||
\(689\) | 21.0921 | 0.803543 | ||||||||
\(690\) | −125.826 | −4.79012 | ||||||||
\(691\) | 8.03341 | 0.305605 | 0.152803 | − | 0.988257i | \(-0.451170\pi\) | ||||
0.152803 | + | 0.988257i | \(0.451170\pi\) | |||||||
\(692\) | −115.835 | −4.40340 | ||||||||
\(693\) | −15.0422 | −0.571406 | ||||||||
\(694\) | 72.9710 | 2.76994 | ||||||||
\(695\) | 3.16799 | 0.120169 | ||||||||
\(696\) | −207.915 | −7.88099 | ||||||||
\(697\) | 4.44518 | 0.168373 | ||||||||
\(698\) | −64.6435 | −2.44679 | ||||||||
\(699\) | −29.7320 | −1.12457 | ||||||||
\(700\) | 0.909196 | 0.0343644 | ||||||||
\(701\) | 30.7632 | 1.16191 | 0.580956 | − | 0.813935i | \(-0.302679\pi\) | ||||
0.580956 | + | 0.813935i | \(0.302679\pi\) | |||||||
\(702\) | −179.189 | −6.76305 | ||||||||
\(703\) | 6.49301 | 0.244889 | ||||||||
\(704\) | 16.4474 | 0.619886 | ||||||||
\(705\) | −67.4197 | −2.53917 | ||||||||
\(706\) | 17.4147 | 0.655412 | ||||||||
\(707\) | 1.99166 | 0.0749042 | ||||||||
\(708\) | 74.6833 | 2.80677 | ||||||||
\(709\) | −20.4700 | −0.768768 | −0.384384 | − | 0.923173i | \(-0.625586\pi\) | ||||
−0.384384 | + | 0.923173i | \(0.625586\pi\) | |||||||
\(710\) | −50.1433 | −1.88185 | ||||||||
\(711\) | 34.7025 | 1.30145 | ||||||||
\(712\) | −54.8907 | −2.05711 | ||||||||
\(713\) | −9.68977 | −0.362885 | ||||||||
\(714\) | 4.15958 | 0.155668 | ||||||||
\(715\) | 71.9780 | 2.69182 | ||||||||
\(716\) | 115.283 | 4.30835 | ||||||||
\(717\) | −14.7049 | −0.549166 | ||||||||
\(718\) | 49.1169 | 1.83303 | ||||||||
\(719\) | −1.64073 | −0.0611888 | −0.0305944 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305944 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(720\) | −118.083 | −4.40069 | ||||||||
\(721\) | 0.802661 | 0.0298927 | ||||||||
\(722\) | −59.5825 | −2.21743 | ||||||||
\(723\) | 95.2317 | 3.54170 | ||||||||
\(724\) | −26.5719 | −0.987537 | ||||||||
\(725\) | 5.33969 | 0.198311 | ||||||||
\(726\) | 204.891 | 7.60423 | ||||||||
\(727\) | −19.2673 | −0.714583 | −0.357292 | − | 0.933993i | \(-0.616300\pi\) | ||||
−0.357292 | + | 0.933993i | \(0.616300\pi\) | |||||||
\(728\) | −13.7808 | −0.510752 | ||||||||
\(729\) | 8.21803 | 0.304371 | ||||||||
\(730\) | 24.0467 | 0.890007 | ||||||||
\(731\) | −17.2484 | −0.637954 | ||||||||
\(732\) | −69.5941 | −2.57227 | ||||||||
\(733\) | 47.2261 | 1.74434 | 0.872168 | − | 0.489206i | \(-0.162713\pi\) | ||||
0.872168 | + | 0.489206i | \(0.162713\pi\) | |||||||
\(734\) | 61.2213 | 2.25972 | ||||||||
\(735\) | −45.6432 | −1.68357 | ||||||||
\(736\) | −54.1420 | −1.99570 | ||||||||
\(737\) | 14.9804 | 0.551809 | ||||||||
\(738\) | 55.5918 | 2.04636 | ||||||||
\(739\) | 3.88514 | 0.142917 | 0.0714587 | − | 0.997444i | \(-0.477235\pi\) | ||||
0.0714587 | + | 0.997444i | \(0.477235\pi\) | |||||||
\(740\) | −9.74952 | −0.358399 | ||||||||
\(741\) | 115.685 | 4.24980 | ||||||||
\(742\) | −3.46448 | −0.127185 | ||||||||
\(743\) | 52.4388 | 1.92379 | 0.961897 | − | 0.273413i | \(-0.0881524\pi\) | ||||
0.961897 | + | 0.273413i | \(0.0881524\pi\) | |||||||
\(744\) | −27.9215 | −1.02365 | ||||||||
\(745\) | 6.33033 | 0.231925 | ||||||||
\(746\) | −25.7677 | −0.943423 | ||||||||
\(747\) | −72.2902 | −2.64496 | ||||||||
\(748\) | −39.5544 | −1.44625 | ||||||||
\(749\) | −6.05491 | −0.221242 | ||||||||
\(750\) | 94.7832 | 3.46099 | ||||||||
\(751\) | 13.0876 | 0.477574 | 0.238787 | − | 0.971072i | \(-0.423250\pi\) | ||||
0.238787 | + | 0.971072i | \(0.423250\pi\) | |||||||
\(752\) | −82.1588 | −2.99602 | ||||||||
\(753\) | −11.6781 | −0.425573 | ||||||||
\(754\) | −142.741 | −5.19831 | ||||||||
\(755\) | 7.36665 | 0.268100 | ||||||||
\(756\) | 20.5393 | 0.747006 | ||||||||
\(757\) | 12.3486 | 0.448819 | 0.224410 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224410 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(758\) | 64.5209 | 2.34351 | ||||||||
\(759\) | −139.601 | −5.06718 | ||||||||
\(760\) | 92.3444 | 3.34968 | ||||||||
\(761\) | −14.2912 | −0.518055 | −0.259028 | − | 0.965870i | \(-0.583402\pi\) | ||||
−0.259028 | + | 0.965870i | \(0.583402\pi\) | |||||||
\(762\) | −49.3219 | −1.78674 | ||||||||
\(763\) | −0.361357 | −0.0130820 | ||||||||
\(764\) | −23.1801 | −0.838627 | ||||||||
\(765\) | 20.7282 | 0.749431 | ||||||||
\(766\) | 13.1704 | 0.475866 | ||||||||
\(767\) | 29.0718 | 1.04972 | ||||||||
\(768\) | 79.4474 | 2.86681 | ||||||||
\(769\) | 23.3553 | 0.842213 | 0.421106 | − | 0.907011i | \(-0.361642\pi\) | ||||
0.421106 | + | 0.907011i | \(0.361642\pi\) | |||||||
\(770\) | −11.8227 | −0.426062 | ||||||||
\(771\) | −48.8875 | −1.76064 | ||||||||
\(772\) | 16.3345 | 0.587893 | ||||||||
\(773\) | −24.4042 | −0.877758 | −0.438879 | − | 0.898546i | \(-0.644624\pi\) | ||||
−0.438879 | + | 0.898546i | \(0.644624\pi\) | |||||||
\(774\) | −215.710 | −7.75353 | ||||||||
\(775\) | 0.717083 | 0.0257584 | ||||||||
\(776\) | −58.2087 | −2.08957 | ||||||||
\(777\) | 1.13751 | 0.0408079 | ||||||||
\(778\) | −66.3146 | −2.37749 | ||||||||
\(779\) | −20.3065 | −0.727557 | ||||||||
\(780\) | −173.706 | −6.21967 | ||||||||
\(781\) | −55.6327 | −1.99069 | ||||||||
\(782\) | 26.9162 | 0.962522 | ||||||||
\(783\) | 120.627 | 4.31084 | ||||||||
\(784\) | −55.6216 | −1.98649 | ||||||||
\(785\) | −30.2224 | −1.07868 | ||||||||
\(786\) | 62.0825 | 2.21441 | ||||||||
\(787\) | −21.1116 | −0.752549 | −0.376274 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376274 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(788\) | −40.0514 | −1.42677 | ||||||||
\(789\) | 45.1684 | 1.60804 | ||||||||
\(790\) | 27.2752 | 0.970409 | ||||||||
\(791\) | 5.97869 | 0.212578 | ||||||||
\(792\) | −280.480 | −9.96643 | ||||||||
\(793\) | −27.0907 | −0.962020 | ||||||||
\(794\) | 84.7514 | 3.00772 | ||||||||
\(795\) | −24.7607 | −0.878170 | ||||||||
\(796\) | 32.7660 | 1.16136 | ||||||||
\(797\) | 17.9877 | 0.637157 | 0.318578 | − | 0.947897i | \(-0.396795\pi\) | ||||
0.318578 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(798\) | −19.0019 | −0.672659 | ||||||||
\(799\) | 14.4222 | 0.510219 | ||||||||
\(800\) | 4.00673 | 0.141659 | ||||||||
\(801\) | 56.2856 | 1.98875 | ||||||||
\(802\) | −64.0003 | −2.25993 | ||||||||
\(803\) | 26.6791 | 0.941486 | ||||||||
\(804\) | −36.1524 | −1.27500 | ||||||||
\(805\) | 5.61427 | 0.197877 | ||||||||
\(806\) | −19.1691 | −0.675203 | ||||||||
\(807\) | −34.4403 | −1.21236 | ||||||||
\(808\) | 37.1370 | 1.30648 | ||||||||
\(809\) | −0.322349 | −0.0113332 | −0.00566659 | − | 0.999984i | \(-0.501804\pi\) | ||||
−0.00566659 | + | 0.999984i | \(0.501804\pi\) | |||||||
\(810\) | 97.7968 | 3.43623 | ||||||||
\(811\) | 14.4791 | 0.508430 | 0.254215 | − | 0.967148i | \(-0.418183\pi\) | ||||
0.254215 | + | 0.967148i | \(0.418183\pi\) | |||||||
\(812\) | 16.3615 | 0.574175 | ||||||||
\(813\) | −4.57659 | −0.160508 | ||||||||
\(814\) | −15.5005 | −0.543291 | ||||||||
\(815\) | −48.3585 | −1.69392 | ||||||||
\(816\) | 36.2277 | 1.26822 | ||||||||
\(817\) | 78.7943 | 2.75666 | ||||||||
\(818\) | −53.9196 | −1.88525 | ||||||||
\(819\) | 14.1311 | 0.493779 | ||||||||
\(820\) | 30.4911 | 1.06479 | ||||||||
\(821\) | −11.5570 | −0.403342 | −0.201671 | − | 0.979453i | \(-0.564637\pi\) | ||||
−0.201671 | + | 0.979453i | \(0.564637\pi\) | |||||||
\(822\) | 43.5839 | 1.52016 | ||||||||
\(823\) | 45.2217 | 1.57633 | 0.788165 | − | 0.615464i | \(-0.211031\pi\) | ||||
0.788165 | + | 0.615464i | \(0.211031\pi\) | |||||||
\(824\) | 14.9666 | 0.521386 | ||||||||
\(825\) | 10.3310 | 0.359680 | ||||||||
\(826\) | −4.77519 | −0.166150 | ||||||||
\(827\) | 0.519011 | 0.0180478 | 0.00902389 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902389 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(828\) | 234.904 | 8.16349 | ||||||||
\(829\) | 1.69161 | 0.0587520 | 0.0293760 | − | 0.999568i | \(-0.490648\pi\) | ||||
0.0293760 | + | 0.999568i | \(0.490648\pi\) | |||||||
\(830\) | −56.8181 | −1.97218 | ||||||||
\(831\) | 63.8475 | 2.21485 | ||||||||
\(832\) | −15.4512 | −0.535673 | ||||||||
\(833\) | 9.76381 | 0.338296 | ||||||||
\(834\) | −12.1551 | −0.420898 | ||||||||
\(835\) | −15.5970 | −0.539755 | ||||||||
\(836\) | 180.693 | 6.24940 | ||||||||
\(837\) | 16.1993 | 0.559930 | ||||||||
\(838\) | 73.4965 | 2.53890 | ||||||||
\(839\) | −2.74416 | −0.0947388 | −0.0473694 | − | 0.998877i | \(-0.515084\pi\) | ||||
−0.0473694 | + | 0.998877i | \(0.515084\pi\) | |||||||
\(840\) | 16.1778 | 0.558187 | ||||||||
\(841\) | 67.0904 | 2.31346 | ||||||||
\(842\) | −80.2325 | −2.76499 | ||||||||
\(843\) | 91.2168 | 3.14167 | ||||||||
\(844\) | 58.4379 | 2.01152 | ||||||||
\(845\) | −40.1783 | −1.38218 | ||||||||
\(846\) | 180.365 | 6.20107 | ||||||||
\(847\) | −9.14209 | −0.314126 | ||||||||
\(848\) | −30.1738 | −1.03617 | ||||||||
\(849\) | −61.9809 | −2.12718 | ||||||||
\(850\) | −1.99191 | −0.0683220 | ||||||||
\(851\) | 7.36071 | 0.252322 | ||||||||
\(852\) | 134.259 | 4.59965 | ||||||||
\(853\) | −16.4082 | −0.561806 | −0.280903 | − | 0.959736i | \(-0.590634\pi\) | ||||
−0.280903 | + | 0.959736i | \(0.590634\pi\) | |||||||
\(854\) | 4.44979 | 0.152269 | ||||||||
\(855\) | −94.6911 | −3.23837 | ||||||||
\(856\) | −112.901 | −3.85888 | ||||||||
\(857\) | 20.9390 | 0.715262 | 0.357631 | − | 0.933863i | \(-0.383585\pi\) | ||||
0.357631 | + | 0.933863i | \(0.383585\pi\) | |||||||
\(858\) | −276.170 | −9.42828 | ||||||||
\(859\) | −31.0093 | −1.05802 | −0.529011 | − | 0.848615i | \(-0.677437\pi\) | ||||
−0.529011 | + | 0.848615i | \(0.677437\pi\) | |||||||
\(860\) | −118.313 | −4.03443 | ||||||||
\(861\) | −3.55750 | −0.121239 | ||||||||
\(862\) | 14.8970 | 0.507393 | ||||||||
\(863\) | −4.04705 | −0.137763 | −0.0688817 | − | 0.997625i | \(-0.521943\pi\) | ||||
−0.0688817 | + | 0.997625i | \(0.521943\pi\) | |||||||
\(864\) | 90.5144 | 3.07936 | ||||||||
\(865\) | 52.9338 | 1.79980 | ||||||||
\(866\) | 36.4675 | 1.23921 | ||||||||
\(867\) | 47.1546 | 1.60145 | ||||||||
\(868\) | 2.19723 | 0.0745789 | ||||||||
\(869\) | 30.2611 | 1.02654 | ||||||||
\(870\) | 167.568 | 5.68109 | ||||||||
\(871\) | −14.0730 | −0.476844 | ||||||||
\(872\) | −6.73794 | −0.228175 | ||||||||
\(873\) | 59.6879 | 2.02013 | ||||||||
\(874\) | −122.959 | −4.15916 | ||||||||
\(875\) | −4.22915 | −0.142971 | ||||||||
\(876\) | −64.3853 | −2.17538 | ||||||||
\(877\) | −34.6771 | −1.17096 | −0.585481 | − | 0.810686i | \(-0.699095\pi\) | ||||
−0.585481 | + | 0.810686i | \(0.699095\pi\) | |||||||
\(878\) | 15.7012 | 0.529890 | ||||||||
\(879\) | −3.40359 | −0.114800 | ||||||||
\(880\) | −102.970 | −3.47111 | ||||||||
\(881\) | −7.55028 | −0.254375 | −0.127188 | − | 0.991879i | \(-0.540595\pi\) | ||||
−0.127188 | + | 0.991879i | \(0.540595\pi\) | |||||||
\(882\) | 122.107 | 4.11156 | ||||||||
\(883\) | −9.27157 | −0.312013 | −0.156007 | − | 0.987756i | \(-0.549862\pi\) | ||||
−0.156007 | + | 0.987756i | \(0.549862\pi\) | |||||||
\(884\) | 37.1585 | 1.24977 | ||||||||
\(885\) | −34.1283 | −1.14721 | ||||||||
\(886\) | 33.1024 | 1.11210 | ||||||||
\(887\) | −9.33134 | −0.313316 | −0.156658 | − | 0.987653i | \(-0.550072\pi\) | ||||
−0.156658 | + | 0.987653i | \(0.550072\pi\) | |||||||
\(888\) | 21.2102 | 0.711769 | ||||||||
\(889\) | 2.20070 | 0.0738092 | ||||||||
\(890\) | 44.2389 | 1.48289 | ||||||||
\(891\) | 108.503 | 3.63498 | ||||||||
\(892\) | 51.4548 | 1.72283 | ||||||||
\(893\) | −65.8835 | −2.20471 | ||||||||
\(894\) | −24.2886 | −0.812334 | ||||||||
\(895\) | −52.6816 | −1.76095 | ||||||||
\(896\) | −2.77802 | −0.0928071 | ||||||||
\(897\) | 131.145 | 4.37879 | ||||||||
\(898\) | 53.2262 | 1.77618 | ||||||||
\(899\) | 12.9043 | 0.430382 | ||||||||
\(900\) | −17.3839 | −0.579463 | ||||||||
\(901\) | 5.29670 | 0.176459 | ||||||||
\(902\) | 48.4769 | 1.61410 | ||||||||
\(903\) | 13.8039 | 0.459367 | ||||||||
\(904\) | 111.480 | 3.70777 | ||||||||
\(905\) | 12.1427 | 0.403636 | ||||||||
\(906\) | −28.2649 | −0.939037 | ||||||||
\(907\) | −43.9512 | −1.45937 | −0.729687 | − | 0.683781i | \(-0.760334\pi\) | ||||
−0.729687 | + | 0.683781i | \(0.760334\pi\) | |||||||
\(908\) | −13.0338 | −0.432543 | ||||||||
\(909\) | −38.0808 | −1.26306 | ||||||||
\(910\) | 11.1066 | 0.368181 | ||||||||
\(911\) | 13.7011 | 0.453937 | 0.226968 | − | 0.973902i | \(-0.427119\pi\) | ||||
0.226968 | + | 0.973902i | \(0.427119\pi\) | |||||||
\(912\) | −165.496 | −5.48013 | ||||||||
\(913\) | −63.0381 | −2.08626 | ||||||||
\(914\) | 48.0570 | 1.58958 | ||||||||
\(915\) | 31.8027 | 1.05136 | ||||||||
\(916\) | −100.865 | −3.33266 | ||||||||
\(917\) | −2.77007 | −0.0914759 | ||||||||
\(918\) | −44.9984 | −1.48517 | ||||||||
\(919\) | −53.5232 | −1.76557 | −0.882783 | − | 0.469781i | \(-0.844333\pi\) | ||||
−0.882783 | + | 0.469781i | \(0.844333\pi\) | |||||||
\(920\) | 104.685 | 3.45136 | ||||||||
\(921\) | −32.6254 | −1.07504 | ||||||||
\(922\) | −9.89604 | −0.325909 | ||||||||
\(923\) | 52.2629 | 1.72025 | ||||||||
\(924\) | 31.6556 | 1.04139 | ||||||||
\(925\) | −0.544723 | −0.0179104 | ||||||||
\(926\) | 5.37863 | 0.176753 | ||||||||
\(927\) | −15.3469 | −0.504060 | ||||||||
\(928\) | 72.1033 | 2.36691 | ||||||||
\(929\) | −39.7919 | −1.30553 | −0.652765 | − | 0.757560i | \(-0.726391\pi\) | ||||
−0.652765 | + | 0.757560i | \(0.726391\pi\) | |||||||
\(930\) | 22.5033 | 0.737911 | ||||||||
\(931\) | −44.6032 | −1.46181 | ||||||||
\(932\) | 43.6266 | 1.42904 | ||||||||
\(933\) | −28.4438 | −0.931209 | ||||||||
\(934\) | 1.70947 | 0.0559355 | ||||||||
\(935\) | 18.0753 | 0.591126 | ||||||||
\(936\) | 263.491 | 8.61246 | ||||||||
\(937\) | −19.8514 | −0.648518 | −0.324259 | − | 0.945968i | \(-0.605115\pi\) | ||||
−0.324259 | + | 0.945968i | \(0.605115\pi\) | |||||||
\(938\) | 2.31156 | 0.0754750 | ||||||||
\(939\) | 40.7414 | 1.32955 | ||||||||
\(940\) | 98.9268 | 3.22664 | ||||||||
\(941\) | −23.0351 | −0.750924 | −0.375462 | − | 0.926838i | \(-0.622516\pi\) | ||||
−0.375462 | + | 0.926838i | \(0.622516\pi\) | |||||||
\(942\) | 115.959 | 3.77816 | ||||||||
\(943\) | −23.0202 | −0.749641 | ||||||||
\(944\) | −41.5894 | −1.35362 | ||||||||
\(945\) | −9.38591 | −0.305324 | ||||||||
\(946\) | −188.102 | −6.11572 | ||||||||
\(947\) | −39.8512 | −1.29499 | −0.647495 | − | 0.762070i | \(-0.724183\pi\) | ||||
−0.647495 | + | 0.762070i | \(0.724183\pi\) | |||||||
\(948\) | −73.0298 | −2.37190 | ||||||||
\(949\) | −25.0631 | −0.813583 | ||||||||
\(950\) | 9.09949 | 0.295227 | ||||||||
\(951\) | −15.7280 | −0.510014 | ||||||||
\(952\) | −3.46069 | −0.112162 | ||||||||
\(953\) | 25.9279 | 0.839887 | 0.419944 | − | 0.907550i | \(-0.362050\pi\) | ||||
0.419944 | + | 0.907550i | \(0.362050\pi\) | |||||||
\(954\) | 66.2411 | 2.14463 | ||||||||
\(955\) | 10.5927 | 0.342772 | ||||||||
\(956\) | 21.5770 | 0.697849 | ||||||||
\(957\) | 185.912 | 6.00969 | ||||||||
\(958\) | 80.2904 | 2.59406 | ||||||||
\(959\) | −1.94468 | −0.0627970 | ||||||||
\(960\) | 18.1386 | 0.585422 | ||||||||
\(961\) | −29.2670 | −0.944098 | ||||||||
\(962\) | 14.5616 | 0.469484 | ||||||||
\(963\) | 115.770 | 3.73065 | ||||||||
\(964\) | −139.736 | −4.50060 | ||||||||
\(965\) | −7.46446 | −0.240290 | ||||||||
\(966\) | −21.5412 | −0.693076 | ||||||||
\(967\) | 41.1762 | 1.32414 | 0.662069 | − | 0.749443i | \(-0.269679\pi\) | ||||
0.662069 | + | 0.749443i | \(0.269679\pi\) | |||||||
\(968\) | −170.465 | −5.47897 | ||||||||
\(969\) | 29.0512 | 0.933259 | ||||||||
\(970\) | 46.9130 | 1.50629 | ||||||||
\(971\) | 58.8135 | 1.88742 | 0.943708 | − | 0.330779i | \(-0.107312\pi\) | ||||
0.943708 | + | 0.330779i | \(0.107312\pi\) | |||||||
\(972\) | −91.3342 | −2.92955 | ||||||||
\(973\) | 0.542354 | 0.0173871 | ||||||||
\(974\) | 9.77779 | 0.313301 | ||||||||
\(975\) | −9.70525 | −0.310817 | ||||||||
\(976\) | 38.7553 | 1.24053 | ||||||||
\(977\) | 33.5927 | 1.07473 | 0.537363 | − | 0.843351i | \(-0.319420\pi\) | ||||
0.537363 | + | 0.843351i | \(0.319420\pi\) | |||||||
\(978\) | 185.545 | 5.93308 | ||||||||
\(979\) | 49.0819 | 1.56866 | ||||||||
\(980\) | 66.9735 | 2.13939 | ||||||||
\(981\) | 6.90917 | 0.220593 | ||||||||
\(982\) | 69.4541 | 2.21637 | ||||||||
\(983\) | 35.3837 | 1.12856 | 0.564282 | − | 0.825582i | \(-0.309153\pi\) | ||||
0.564282 | + | 0.825582i | \(0.309153\pi\) | |||||||
\(984\) | −66.3338 | −2.11465 | ||||||||
\(985\) | 18.3025 | 0.583165 | ||||||||
\(986\) | −35.8455 | −1.14155 | ||||||||
\(987\) | −11.5421 | −0.367390 | ||||||||
\(988\) | −169.748 | −5.40040 | ||||||||
\(989\) | 89.3240 | 2.84034 | ||||||||
\(990\) | 226.052 | 7.18440 | ||||||||
\(991\) | 42.0547 | 1.33591 | 0.667956 | − | 0.744201i | \(-0.267170\pi\) | ||||
0.667956 | + | 0.744201i | \(0.267170\pi\) | |||||||
\(992\) | 9.68298 | 0.307435 | ||||||||
\(993\) | −58.3657 | −1.85218 | ||||||||
\(994\) | −8.58444 | −0.272282 | ||||||||
\(995\) | −14.9732 | −0.474683 | ||||||||
\(996\) | 152.131 | 4.82046 | ||||||||
\(997\) | −49.8311 | −1.57817 | −0.789083 | − | 0.614286i | \(-0.789444\pi\) | ||||
−0.789083 | + | 0.614286i | \(0.789444\pi\) | |||||||
\(998\) | 86.1607 | 2.72737 | ||||||||
\(999\) | −12.3056 | −0.389332 |
(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 | 4033.2.a.c.1.6 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.6 | ✓ | 77 | 1.1 | even | 1 | trivial |