Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1118877829\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19859 | −1.55464 | −0.777320 | − | 0.629106i | \(-0.783421\pi\) | ||||
−0.777320 | + | 0.629106i | \(0.783421\pi\) | |||||||
\(3\) | 1.85317 | 1.06993 | 0.534963 | − | 0.844875i | \(-0.320326\pi\) | ||||
0.534963 | + | 0.844875i | \(0.320326\pi\) | |||||||
\(4\) | 2.83381 | 1.41690 | ||||||||
\(5\) | −0.955285 | −0.427216 | −0.213608 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213608 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(6\) | −4.07436 | −1.66335 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.83320 | −0.648134 | ||||||||
\(9\) | 0.434225 | 0.144742 | ||||||||
\(10\) | 2.10028 | 0.664167 | ||||||||
\(11\) | −2.49420 | −0.752030 | −0.376015 | − | 0.926614i | \(-0.622706\pi\) | ||||
−0.376015 | + | 0.926614i | \(0.622706\pi\) | |||||||
\(12\) | 5.25152 | 1.51598 | ||||||||
\(13\) | 2.80187 | 0.777099 | 0.388549 | − | 0.921428i | \(-0.372976\pi\) | ||||
0.388549 | + | 0.921428i | \(0.372976\pi\) | |||||||
\(14\) | −2.19859 | −0.587598 | ||||||||
\(15\) | −1.77030 | −0.457090 | ||||||||
\(16\) | −1.63715 | −0.409288 | ||||||||
\(17\) | −1.96972 | −0.477727 | −0.238863 | − | 0.971053i | \(-0.576775\pi\) | ||||
−0.238863 | + | 0.971053i | \(0.576775\pi\) | |||||||
\(18\) | −0.954684 | −0.225021 | ||||||||
\(19\) | 4.59598 | 1.05439 | 0.527196 | − | 0.849744i | \(-0.323244\pi\) | ||||
0.527196 | + | 0.849744i | \(0.323244\pi\) | |||||||
\(20\) | −2.70709 | −0.605324 | ||||||||
\(21\) | 1.85317 | 0.404394 | ||||||||
\(22\) | 5.48373 | 1.16914 | ||||||||
\(23\) | 2.07051 | 0.431732 | 0.215866 | − | 0.976423i | \(-0.430743\pi\) | ||||
0.215866 | + | 0.976423i | \(0.430743\pi\) | |||||||
\(24\) | −3.39723 | −0.693456 | ||||||||
\(25\) | −4.08743 | −0.817486 | ||||||||
\(26\) | −6.16017 | −1.20811 | ||||||||
\(27\) | −4.75481 | −0.915063 | ||||||||
\(28\) | 2.83381 | 0.535539 | ||||||||
\(29\) | 6.01329 | 1.11664 | 0.558320 | − | 0.829625i | \(-0.311446\pi\) | ||||
0.558320 | + | 0.829625i | \(0.311446\pi\) | |||||||
\(30\) | 3.89217 | 0.710610 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 7.26583 | 1.28443 | ||||||||
\(33\) | −4.62217 | −0.804617 | ||||||||
\(34\) | 4.33061 | 0.742693 | ||||||||
\(35\) | −0.955285 | −0.161473 | ||||||||
\(36\) | 1.23051 | 0.205085 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −10.1047 | −1.63920 | ||||||||
\(39\) | 5.19233 | 0.831438 | ||||||||
\(40\) | 1.75123 | 0.276894 | ||||||||
\(41\) | 11.5944 | 1.81075 | 0.905374 | − | 0.424615i | \(-0.139590\pi\) | ||||
0.905374 | + | 0.424615i | \(0.139590\pi\) | |||||||
\(42\) | −4.07436 | −0.628687 | ||||||||
\(43\) | −12.9703 | −1.97796 | −0.988979 | − | 0.148055i | \(-0.952699\pi\) | ||||
−0.988979 | + | 0.148055i | \(0.952699\pi\) | |||||||
\(44\) | −7.06809 | −1.06555 | ||||||||
\(45\) | −0.414809 | −0.0618360 | ||||||||
\(46\) | −4.55221 | −0.671187 | ||||||||
\(47\) | −7.24856 | −1.05731 | −0.528655 | − | 0.848837i | \(-0.677304\pi\) | ||||
−0.528655 | + | 0.848837i | \(0.677304\pi\) | |||||||
\(48\) | −3.03392 | −0.437908 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.98659 | 1.27090 | ||||||||
\(51\) | −3.65021 | −0.511132 | ||||||||
\(52\) | 7.93996 | 1.10107 | ||||||||
\(53\) | 7.71285 | 1.05944 | 0.529721 | − | 0.848172i | \(-0.322297\pi\) | ||||
0.529721 | + | 0.848172i | \(0.322297\pi\) | |||||||
\(54\) | 10.4539 | 1.42259 | ||||||||
\(55\) | 2.38267 | 0.321280 | ||||||||
\(56\) | −1.83320 | −0.244972 | ||||||||
\(57\) | 8.51712 | 1.12812 | ||||||||
\(58\) | −13.2208 | −1.73597 | ||||||||
\(59\) | 4.95210 | 0.644709 | 0.322354 | − | 0.946619i | \(-0.395526\pi\) | ||||
0.322354 | + | 0.946619i | \(0.395526\pi\) | |||||||
\(60\) | −5.01669 | −0.647652 | ||||||||
\(61\) | 5.30201 | 0.678853 | 0.339427 | − | 0.940633i | \(-0.389767\pi\) | ||||
0.339427 | + | 0.940633i | \(0.389767\pi\) | |||||||
\(62\) | −2.19859 | −0.279221 | ||||||||
\(63\) | 0.434225 | 0.0547072 | ||||||||
\(64\) | −12.7003 | −1.58754 | ||||||||
\(65\) | −2.67658 | −0.331989 | ||||||||
\(66\) | 10.1623 | 1.25089 | ||||||||
\(67\) | −2.90641 | −0.355075 | −0.177537 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177537 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(68\) | −5.58180 | −0.676893 | ||||||||
\(69\) | 3.83701 | 0.461921 | ||||||||
\(70\) | 2.10028 | 0.251032 | ||||||||
\(71\) | 9.73376 | 1.15518 | 0.577592 | − | 0.816325i | \(-0.303992\pi\) | ||||
0.577592 | + | 0.816325i | \(0.303992\pi\) | |||||||
\(72\) | −0.796022 | −0.0938121 | ||||||||
\(73\) | −7.47694 | −0.875109 | −0.437555 | − | 0.899192i | \(-0.644155\pi\) | ||||
−0.437555 | + | 0.899192i | \(0.644155\pi\) | |||||||
\(74\) | −2.19859 | −0.255581 | ||||||||
\(75\) | −7.57469 | −0.874650 | ||||||||
\(76\) | 13.0241 | 1.49397 | ||||||||
\(77\) | −2.49420 | −0.284241 | ||||||||
\(78\) | −11.4158 | −1.29259 | ||||||||
\(79\) | 1.83243 | 0.206165 | 0.103082 | − | 0.994673i | \(-0.467129\pi\) | ||||
0.103082 | + | 0.994673i | \(0.467129\pi\) | |||||||
\(80\) | 1.56395 | 0.174855 | ||||||||
\(81\) | −10.1141 | −1.12379 | ||||||||
\(82\) | −25.4915 | −2.81506 | ||||||||
\(83\) | −9.79963 | −1.07565 | −0.537825 | − | 0.843057i | \(-0.680754\pi\) | ||||
−0.537825 | + | 0.843057i | \(0.680754\pi\) | |||||||
\(84\) | 5.25152 | 0.572987 | ||||||||
\(85\) | 1.88164 | 0.204093 | ||||||||
\(86\) | 28.5165 | 3.07501 | ||||||||
\(87\) | 11.1436 | 1.19472 | ||||||||
\(88\) | 4.57237 | 0.487417 | ||||||||
\(89\) | 1.93059 | 0.204642 | 0.102321 | − | 0.994751i | \(-0.467373\pi\) | ||||
0.102321 | + | 0.994751i | \(0.467373\pi\) | |||||||
\(90\) | 0.911995 | 0.0961327 | ||||||||
\(91\) | 2.80187 | 0.293716 | ||||||||
\(92\) | 5.86743 | 0.611722 | ||||||||
\(93\) | 1.85317 | 0.192164 | ||||||||
\(94\) | 15.9366 | 1.64374 | ||||||||
\(95\) | −4.39047 | −0.450453 | ||||||||
\(96\) | 13.4648 | 1.37424 | ||||||||
\(97\) | −15.1426 | −1.53749 | −0.768747 | − | 0.639554i | \(-0.779119\pi\) | ||||
−0.768747 | + | 0.639554i | \(0.779119\pi\) | |||||||
\(98\) | −2.19859 | −0.222091 | ||||||||
\(99\) | −1.08304 | −0.108850 | ||||||||
\(100\) | −11.5830 | −1.15830 | ||||||||
\(101\) | 5.16341 | 0.513779 | 0.256889 | − | 0.966441i | \(-0.417302\pi\) | ||||
0.256889 | + | 0.966441i | \(0.417302\pi\) | |||||||
\(102\) | 8.02533 | 0.794626 | ||||||||
\(103\) | 3.75727 | 0.370215 | 0.185107 | − | 0.982718i | \(-0.440737\pi\) | ||||
0.185107 | + | 0.982718i | \(0.440737\pi\) | |||||||
\(104\) | −5.13639 | −0.503665 | ||||||||
\(105\) | −1.77030 | −0.172764 | ||||||||
\(106\) | −16.9574 | −1.64705 | ||||||||
\(107\) | 15.2724 | 1.47644 | 0.738218 | − | 0.674562i | \(-0.235667\pi\) | ||||
0.738218 | + | 0.674562i | \(0.235667\pi\) | |||||||
\(108\) | −13.4742 | −1.29656 | ||||||||
\(109\) | −13.4663 | −1.28984 | −0.644921 | − | 0.764249i | \(-0.723110\pi\) | ||||
−0.644921 | + | 0.764249i | \(0.723110\pi\) | |||||||
\(110\) | −5.23853 | −0.499474 | ||||||||
\(111\) | 1.85317 | 0.175895 | ||||||||
\(112\) | −1.63715 | −0.154696 | ||||||||
\(113\) | 17.0148 | 1.60062 | 0.800310 | − | 0.599586i | \(-0.204668\pi\) | ||||
0.800310 | + | 0.599586i | \(0.204668\pi\) | |||||||
\(114\) | −18.7257 | −1.75382 | ||||||||
\(115\) | −1.97793 | −0.184443 | ||||||||
\(116\) | 17.0405 | 1.58217 | ||||||||
\(117\) | 1.21664 | 0.112479 | ||||||||
\(118\) | −10.8877 | −1.00229 | ||||||||
\(119\) | −1.96972 | −0.180564 | ||||||||
\(120\) | 3.24532 | 0.296256 | ||||||||
\(121\) | −4.77896 | −0.434451 | ||||||||
\(122\) | −11.6570 | −1.05537 | ||||||||
\(123\) | 21.4864 | 1.93737 | ||||||||
\(124\) | 2.83381 | 0.254483 | ||||||||
\(125\) | 8.68109 | 0.776460 | ||||||||
\(126\) | −0.954684 | −0.0850500 | ||||||||
\(127\) | 7.71745 | 0.684813 | 0.342406 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342406 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(128\) | 13.3911 | 1.18362 | ||||||||
\(129\) | −24.0362 | −2.11627 | ||||||||
\(130\) | 5.88472 | 0.516124 | ||||||||
\(131\) | 22.4384 | 1.96046 | 0.980228 | − | 0.197870i | \(-0.0634025\pi\) | ||||
0.980228 | + | 0.197870i | \(0.0634025\pi\) | |||||||
\(132\) | −13.0983 | −1.14006 | ||||||||
\(133\) | 4.59598 | 0.398522 | ||||||||
\(134\) | 6.39002 | 0.552013 | ||||||||
\(135\) | 4.54220 | 0.390930 | ||||||||
\(136\) | 3.61089 | 0.309631 | ||||||||
\(137\) | −9.48857 | −0.810663 | −0.405332 | − | 0.914170i | \(-0.632844\pi\) | ||||
−0.405332 | + | 0.914170i | \(0.632844\pi\) | |||||||
\(138\) | −8.43601 | −0.718121 | ||||||||
\(139\) | 5.00351 | 0.424392 | 0.212196 | − | 0.977227i | \(-0.431938\pi\) | ||||
0.212196 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(140\) | −2.70709 | −0.228791 | ||||||||
\(141\) | −13.4328 | −1.13124 | ||||||||
\(142\) | −21.4006 | −1.79589 | ||||||||
\(143\) | −6.98843 | −0.584402 | ||||||||
\(144\) | −0.710892 | −0.0592410 | ||||||||
\(145\) | −5.74441 | −0.477047 | ||||||||
\(146\) | 16.4387 | 1.36048 | ||||||||
\(147\) | 1.85317 | 0.152847 | ||||||||
\(148\) | 2.83381 | 0.232937 | ||||||||
\(149\) | −2.41172 | −0.197576 | −0.0987879 | − | 0.995109i | \(-0.531497\pi\) | ||||
−0.0987879 | + | 0.995109i | \(0.531497\pi\) | |||||||
\(150\) | 16.6537 | 1.35976 | ||||||||
\(151\) | 1.52530 | 0.124127 | 0.0620635 | − | 0.998072i | \(-0.480232\pi\) | ||||
0.0620635 | + | 0.998072i | \(0.480232\pi\) | |||||||
\(152\) | −8.42536 | −0.683387 | ||||||||
\(153\) | −0.855301 | −0.0691470 | ||||||||
\(154\) | 5.48373 | 0.441892 | ||||||||
\(155\) | −0.955285 | −0.0767303 | ||||||||
\(156\) | 14.7141 | 1.17807 | ||||||||
\(157\) | −3.15123 | −0.251496 | −0.125748 | − | 0.992062i | \(-0.540133\pi\) | ||||
−0.125748 | + | 0.992062i | \(0.540133\pi\) | |||||||
\(158\) | −4.02877 | −0.320512 | ||||||||
\(159\) | 14.2932 | 1.13352 | ||||||||
\(160\) | −6.94094 | −0.548729 | ||||||||
\(161\) | 2.07051 | 0.163179 | ||||||||
\(162\) | 22.2368 | 1.74709 | ||||||||
\(163\) | −15.4167 | −1.20753 | −0.603765 | − | 0.797163i | \(-0.706333\pi\) | ||||
−0.603765 | + | 0.797163i | \(0.706333\pi\) | |||||||
\(164\) | 32.8564 | 2.56566 | ||||||||
\(165\) | 4.41549 | 0.343745 | ||||||||
\(166\) | 21.5454 | 1.67225 | ||||||||
\(167\) | 12.5797 | 0.973447 | 0.486723 | − | 0.873556i | \(-0.338192\pi\) | ||||
0.486723 | + | 0.873556i | \(0.338192\pi\) | |||||||
\(168\) | −3.39723 | −0.262102 | ||||||||
\(169\) | −5.14953 | −0.396117 | ||||||||
\(170\) | −4.13696 | −0.317291 | ||||||||
\(171\) | 1.99569 | 0.152614 | ||||||||
\(172\) | −36.7554 | −2.80258 | ||||||||
\(173\) | 12.2124 | 0.928490 | 0.464245 | − | 0.885707i | \(-0.346326\pi\) | ||||
0.464245 | + | 0.885707i | \(0.346326\pi\) | |||||||
\(174\) | −24.5003 | −1.85736 | ||||||||
\(175\) | −4.08743 | −0.308981 | ||||||||
\(176\) | 4.08339 | 0.307797 | ||||||||
\(177\) | 9.17707 | 0.689791 | ||||||||
\(178\) | −4.24458 | −0.318144 | ||||||||
\(179\) | −23.5882 | −1.76306 | −0.881531 | − | 0.472126i | \(-0.843487\pi\) | ||||
−0.881531 | + | 0.472126i | \(0.843487\pi\) | |||||||
\(180\) | −1.17549 | −0.0876157 | ||||||||
\(181\) | −7.24636 | −0.538617 | −0.269309 | − | 0.963054i | \(-0.586795\pi\) | ||||
−0.269309 | + | 0.963054i | \(0.586795\pi\) | |||||||
\(182\) | −6.16017 | −0.456622 | ||||||||
\(183\) | 9.82551 | 0.726323 | ||||||||
\(184\) | −3.79567 | −0.279820 | ||||||||
\(185\) | −0.955285 | −0.0702339 | ||||||||
\(186\) | −4.07436 | −0.298746 | ||||||||
\(187\) | 4.91287 | 0.359265 | ||||||||
\(188\) | −20.5410 | −1.49811 | ||||||||
\(189\) | −4.75481 | −0.345861 | ||||||||
\(190\) | 9.65286 | 0.700292 | ||||||||
\(191\) | 17.5985 | 1.27338 | 0.636692 | − | 0.771118i | \(-0.280302\pi\) | ||||
0.636692 | + | 0.771118i | \(0.280302\pi\) | |||||||
\(192\) | −23.5358 | −1.69855 | ||||||||
\(193\) | 2.80581 | 0.201966 | 0.100983 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100983 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(194\) | 33.2923 | 2.39025 | ||||||||
\(195\) | −4.96015 | −0.355204 | ||||||||
\(196\) | 2.83381 | 0.202415 | ||||||||
\(197\) | 5.90534 | 0.420738 | 0.210369 | − | 0.977622i | \(-0.432533\pi\) | ||||
0.210369 | + | 0.977622i | \(0.432533\pi\) | |||||||
\(198\) | 2.38117 | 0.169223 | ||||||||
\(199\) | 4.12179 | 0.292186 | 0.146093 | − | 0.989271i | \(-0.453330\pi\) | ||||
0.146093 | + | 0.989271i | \(0.453330\pi\) | |||||||
\(200\) | 7.49308 | 0.529841 | ||||||||
\(201\) | −5.38607 | −0.379904 | ||||||||
\(202\) | −11.3522 | −0.798741 | ||||||||
\(203\) | 6.01329 | 0.422050 | ||||||||
\(204\) | −10.3440 | −0.724225 | ||||||||
\(205\) | −11.0760 | −0.773581 | ||||||||
\(206\) | −8.26071 | −0.575551 | ||||||||
\(207\) | 0.899069 | 0.0624896 | ||||||||
\(208\) | −4.58709 | −0.318057 | ||||||||
\(209\) | −11.4633 | −0.792934 | ||||||||
\(210\) | 3.89217 | 0.268585 | ||||||||
\(211\) | 24.5050 | 1.68699 | 0.843496 | − | 0.537135i | \(-0.180494\pi\) | ||||
0.843496 | + | 0.537135i | \(0.180494\pi\) | |||||||
\(212\) | 21.8567 | 1.50113 | ||||||||
\(213\) | 18.0383 | 1.23596 | ||||||||
\(214\) | −33.5777 | −2.29533 | ||||||||
\(215\) | 12.3904 | 0.845016 | ||||||||
\(216\) | 8.71652 | 0.593084 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | 29.6070 | 2.00524 | ||||||||
\(219\) | −13.8560 | −0.936302 | ||||||||
\(220\) | 6.75204 | 0.455222 | ||||||||
\(221\) | −5.51889 | −0.371241 | ||||||||
\(222\) | −4.07436 | −0.273453 | ||||||||
\(223\) | 8.51780 | 0.570394 | 0.285197 | − | 0.958469i | \(-0.407941\pi\) | ||||
0.285197 | + | 0.958469i | \(0.407941\pi\) | |||||||
\(224\) | 7.26583 | 0.485469 | ||||||||
\(225\) | −1.77486 | −0.118324 | ||||||||
\(226\) | −37.4087 | −2.48839 | ||||||||
\(227\) | −19.7301 | −1.30953 | −0.654767 | − | 0.755831i | \(-0.727233\pi\) | ||||
−0.654767 | + | 0.755831i | \(0.727233\pi\) | |||||||
\(228\) | 24.1359 | 1.59844 | ||||||||
\(229\) | 18.6657 | 1.23346 | 0.616732 | − | 0.787173i | \(-0.288456\pi\) | ||||
0.616732 | + | 0.787173i | \(0.288456\pi\) | |||||||
\(230\) | 4.34866 | 0.286742 | ||||||||
\(231\) | −4.62217 | −0.304117 | ||||||||
\(232\) | −11.0236 | −0.723733 | ||||||||
\(233\) | 3.47288 | 0.227516 | 0.113758 | − | 0.993508i | \(-0.463711\pi\) | ||||
0.113758 | + | 0.993508i | \(0.463711\pi\) | |||||||
\(234\) | −2.67490 | −0.174864 | ||||||||
\(235\) | 6.92444 | 0.451700 | ||||||||
\(236\) | 14.0333 | 0.913490 | ||||||||
\(237\) | 3.39580 | 0.220581 | ||||||||
\(238\) | 4.33061 | 0.280711 | ||||||||
\(239\) | 12.3931 | 0.801643 | 0.400821 | − | 0.916156i | \(-0.368725\pi\) | ||||
0.400821 | + | 0.916156i | \(0.368725\pi\) | |||||||
\(240\) | 2.89825 | 0.187081 | ||||||||
\(241\) | 13.6180 | 0.877209 | 0.438605 | − | 0.898680i | \(-0.355473\pi\) | ||||
0.438605 | + | 0.898680i | \(0.355473\pi\) | |||||||
\(242\) | 10.5070 | 0.675414 | ||||||||
\(243\) | −4.47873 | −0.287311 | ||||||||
\(244\) | 15.0249 | 0.961869 | ||||||||
\(245\) | −0.955285 | −0.0610309 | ||||||||
\(246\) | −47.2399 | −3.01191 | ||||||||
\(247\) | 12.8773 | 0.819366 | ||||||||
\(248\) | −1.83320 | −0.116408 | ||||||||
\(249\) | −18.1604 | −1.15087 | ||||||||
\(250\) | −19.0862 | −1.20712 | ||||||||
\(251\) | −20.2771 | −1.27988 | −0.639939 | − | 0.768426i | \(-0.721040\pi\) | ||||
−0.639939 | + | 0.768426i | \(0.721040\pi\) | |||||||
\(252\) | 1.23051 | 0.0775148 | ||||||||
\(253\) | −5.16428 | −0.324675 | ||||||||
\(254\) | −16.9675 | −1.06464 | ||||||||
\(255\) | 3.48699 | 0.218364 | ||||||||
\(256\) | −4.04098 | −0.252562 | ||||||||
\(257\) | −26.3158 | −1.64153 | −0.820767 | − | 0.571264i | \(-0.806453\pi\) | ||||
−0.820767 | + | 0.571264i | \(0.806453\pi\) | |||||||
\(258\) | 52.8458 | 3.29004 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | −7.58492 | −0.470397 | ||||||||
\(261\) | 2.61112 | 0.161624 | ||||||||
\(262\) | −49.3330 | −3.04780 | ||||||||
\(263\) | 21.5477 | 1.32869 | 0.664344 | − | 0.747427i | \(-0.268711\pi\) | ||||
0.664344 | + | 0.747427i | \(0.268711\pi\) | |||||||
\(264\) | 8.47337 | 0.521500 | ||||||||
\(265\) | −7.36797 | −0.452611 | ||||||||
\(266\) | −10.1047 | −0.619559 | ||||||||
\(267\) | 3.57770 | 0.218952 | ||||||||
\(268\) | −8.23622 | −0.503107 | ||||||||
\(269\) | 14.1235 | 0.861124 | 0.430562 | − | 0.902561i | \(-0.358315\pi\) | ||||
0.430562 | + | 0.902561i | \(0.358315\pi\) | |||||||
\(270\) | −9.98644 | −0.607755 | ||||||||
\(271\) | 17.6776 | 1.07384 | 0.536918 | − | 0.843634i | \(-0.319588\pi\) | ||||
0.536918 | + | 0.843634i | \(0.319588\pi\) | |||||||
\(272\) | 3.22473 | 0.195528 | ||||||||
\(273\) | 5.19233 | 0.314254 | ||||||||
\(274\) | 20.8615 | 1.26029 | ||||||||
\(275\) | 10.1949 | 0.614774 | ||||||||
\(276\) | 10.8733 | 0.654498 | ||||||||
\(277\) | −0.851079 | −0.0511364 | −0.0255682 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255682 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(278\) | −11.0007 | −0.659777 | ||||||||
\(279\) | 0.434225 | 0.0259964 | ||||||||
\(280\) | 1.75123 | 0.104656 | ||||||||
\(281\) | 26.6197 | 1.58800 | 0.793999 | − | 0.607919i | \(-0.207995\pi\) | ||||
0.793999 | + | 0.607919i | \(0.207995\pi\) | |||||||
\(282\) | 29.5332 | 1.75868 | ||||||||
\(283\) | 20.1065 | 1.19520 | 0.597602 | − | 0.801793i | \(-0.296120\pi\) | ||||
0.597602 | + | 0.801793i | \(0.296120\pi\) | |||||||
\(284\) | 27.5836 | 1.63678 | ||||||||
\(285\) | −8.13628 | −0.481952 | ||||||||
\(286\) | 15.3647 | 0.908534 | ||||||||
\(287\) | 11.5944 | 0.684398 | ||||||||
\(288\) | 3.15501 | 0.185911 | ||||||||
\(289\) | −13.1202 | −0.771777 | ||||||||
\(290\) | 12.6296 | 0.741636 | ||||||||
\(291\) | −28.0617 | −1.64500 | ||||||||
\(292\) | −21.1882 | −1.23995 | ||||||||
\(293\) | 11.0586 | 0.646050 | 0.323025 | − | 0.946390i | \(-0.395300\pi\) | ||||
0.323025 | + | 0.946390i | \(0.395300\pi\) | |||||||
\(294\) | −4.07436 | −0.237621 | ||||||||
\(295\) | −4.73067 | −0.275430 | ||||||||
\(296\) | −1.83320 | −0.106553 | ||||||||
\(297\) | 11.8595 | 0.688155 | ||||||||
\(298\) | 5.30239 | 0.307159 | ||||||||
\(299\) | 5.80131 | 0.335498 | ||||||||
\(300\) | −21.4652 | −1.23929 | ||||||||
\(301\) | −12.9703 | −0.747598 | ||||||||
\(302\) | −3.35351 | −0.192973 | ||||||||
\(303\) | 9.56866 | 0.549705 | ||||||||
\(304\) | −7.52433 | −0.431550 | ||||||||
\(305\) | −5.06493 | −0.290017 | ||||||||
\(306\) | 1.88046 | 0.107499 | ||||||||
\(307\) | 25.4022 | 1.44978 | 0.724891 | − | 0.688863i | \(-0.241890\pi\) | ||||
0.724891 | + | 0.688863i | \(0.241890\pi\) | |||||||
\(308\) | −7.06809 | −0.402742 | ||||||||
\(309\) | 6.96285 | 0.396103 | ||||||||
\(310\) | 2.10028 | 0.119288 | ||||||||
\(311\) | −33.3328 | −1.89013 | −0.945066 | − | 0.326880i | \(-0.894003\pi\) | ||||
−0.945066 | + | 0.326880i | \(0.894003\pi\) | |||||||
\(312\) | −9.51859 | −0.538884 | ||||||||
\(313\) | 2.26593 | 0.128078 | 0.0640390 | − | 0.997947i | \(-0.479602\pi\) | ||||
0.0640390 | + | 0.997947i | \(0.479602\pi\) | |||||||
\(314\) | 6.92828 | 0.390985 | ||||||||
\(315\) | −0.414809 | −0.0233718 | ||||||||
\(316\) | 5.19276 | 0.292115 | ||||||||
\(317\) | 1.56466 | 0.0878802 | 0.0439401 | − | 0.999034i | \(-0.486009\pi\) | ||||
0.0439401 | + | 0.999034i | \(0.486009\pi\) | |||||||
\(318\) | −31.4249 | −1.76222 | ||||||||
\(319\) | −14.9984 | −0.839747 | ||||||||
\(320\) | 12.1324 | 0.678222 | ||||||||
\(321\) | 28.3023 | 1.57968 | ||||||||
\(322\) | −4.55221 | −0.253685 | ||||||||
\(323\) | −9.05279 | −0.503711 | ||||||||
\(324\) | −28.6615 | −1.59230 | ||||||||
\(325\) | −11.4524 | −0.635268 | ||||||||
\(326\) | 33.8950 | 1.87727 | ||||||||
\(327\) | −24.9554 | −1.38003 | ||||||||
\(328\) | −21.2549 | −1.17361 | ||||||||
\(329\) | −7.24856 | −0.399626 | ||||||||
\(330\) | −9.70786 | −0.534400 | ||||||||
\(331\) | 2.87851 | 0.158217 | 0.0791086 | − | 0.996866i | \(-0.474793\pi\) | ||||
0.0791086 | + | 0.996866i | \(0.474793\pi\) | |||||||
\(332\) | −27.7703 | −1.52409 | ||||||||
\(333\) | 0.434225 | 0.0237954 | ||||||||
\(334\) | −27.6576 | −1.51336 | ||||||||
\(335\) | 2.77645 | 0.151694 | ||||||||
\(336\) | −3.03392 | −0.165514 | ||||||||
\(337\) | −10.9335 | −0.595585 | −0.297792 | − | 0.954631i | \(-0.596250\pi\) | ||||
−0.297792 | + | 0.954631i | \(0.596250\pi\) | |||||||
\(338\) | 11.3217 | 0.615820 | ||||||||
\(339\) | 31.5313 | 1.71255 | ||||||||
\(340\) | 5.33221 | 0.289180 | ||||||||
\(341\) | −2.49420 | −0.135069 | ||||||||
\(342\) | −4.38771 | −0.237260 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 23.7772 | 1.28198 | ||||||||
\(345\) | −3.66543 | −0.197340 | ||||||||
\(346\) | −26.8500 | −1.44347 | ||||||||
\(347\) | −7.17422 | −0.385132 | −0.192566 | − | 0.981284i | \(-0.561681\pi\) | ||||
−0.192566 | + | 0.981284i | \(0.561681\pi\) | |||||||
\(348\) | 31.5789 | 1.69281 | ||||||||
\(349\) | 7.21846 | 0.386395 | 0.193198 | − | 0.981160i | \(-0.438114\pi\) | ||||
0.193198 | + | 0.981160i | \(0.438114\pi\) | |||||||
\(350\) | 8.98659 | 0.480354 | ||||||||
\(351\) | −13.3224 | −0.711094 | ||||||||
\(352\) | −18.1225 | −0.965930 | ||||||||
\(353\) | −10.2185 | −0.543878 | −0.271939 | − | 0.962315i | \(-0.587665\pi\) | ||||
−0.271939 | + | 0.962315i | \(0.587665\pi\) | |||||||
\(354\) | −20.1766 | −1.07238 | ||||||||
\(355\) | −9.29851 | −0.493514 | ||||||||
\(356\) | 5.47092 | 0.289958 | ||||||||
\(357\) | −3.65021 | −0.193190 | ||||||||
\(358\) | 51.8607 | 2.74093 | ||||||||
\(359\) | 9.53195 | 0.503077 | 0.251539 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251539 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(360\) | 0.760427 | 0.0400780 | ||||||||
\(361\) | 2.12307 | 0.111741 | ||||||||
\(362\) | 15.9318 | 0.837356 | ||||||||
\(363\) | −8.85620 | −0.464830 | ||||||||
\(364\) | 7.93996 | 0.416167 | ||||||||
\(365\) | 7.14260 | 0.373861 | ||||||||
\(366\) | −21.6023 | −1.12917 | ||||||||
\(367\) | 22.3848 | 1.16848 | 0.584239 | − | 0.811582i | \(-0.301393\pi\) | ||||
0.584239 | + | 0.811582i | \(0.301393\pi\) | |||||||
\(368\) | −3.38975 | −0.176703 | ||||||||
\(369\) | 5.03460 | 0.262091 | ||||||||
\(370\) | 2.10028 | 0.109188 | ||||||||
\(371\) | 7.71285 | 0.400431 | ||||||||
\(372\) | 5.25152 | 0.272278 | ||||||||
\(373\) | 20.5137 | 1.06216 | 0.531080 | − | 0.847321i | \(-0.321786\pi\) | ||||
0.531080 | + | 0.847321i | \(0.321786\pi\) | |||||||
\(374\) | −10.8014 | −0.558527 | ||||||||
\(375\) | 16.0875 | 0.830755 | ||||||||
\(376\) | 13.2881 | 0.685279 | ||||||||
\(377\) | 16.8485 | 0.867740 | ||||||||
\(378\) | 10.4539 | 0.537690 | ||||||||
\(379\) | 19.2641 | 0.989532 | 0.494766 | − | 0.869026i | \(-0.335254\pi\) | ||||
0.494766 | + | 0.869026i | \(0.335254\pi\) | |||||||
\(380\) | −12.4418 | −0.638249 | ||||||||
\(381\) | 14.3017 | 0.732699 | ||||||||
\(382\) | −38.6920 | −1.97965 | ||||||||
\(383\) | −2.26182 | −0.115574 | −0.0577869 | − | 0.998329i | \(-0.518404\pi\) | ||||
−0.0577869 | + | 0.998329i | \(0.518404\pi\) | |||||||
\(384\) | 24.8159 | 1.26638 | ||||||||
\(385\) | 2.38267 | 0.121432 | ||||||||
\(386\) | −6.16883 | −0.313985 | ||||||||
\(387\) | −5.63205 | −0.286293 | ||||||||
\(388\) | −42.9111 | −2.17848 | ||||||||
\(389\) | 29.1270 | 1.47680 | 0.738398 | − | 0.674365i | \(-0.235583\pi\) | ||||
0.738398 | + | 0.674365i | \(0.235583\pi\) | |||||||
\(390\) | 10.9054 | 0.552214 | ||||||||
\(391\) | −4.07833 | −0.206250 | ||||||||
\(392\) | −1.83320 | −0.0925906 | ||||||||
\(393\) | 41.5822 | 2.09754 | ||||||||
\(394\) | −12.9834 | −0.654096 | ||||||||
\(395\) | −1.75049 | −0.0880769 | ||||||||
\(396\) | −3.06914 | −0.154230 | ||||||||
\(397\) | −13.2975 | −0.667380 | −0.333690 | − | 0.942683i | \(-0.608294\pi\) | ||||
−0.333690 | + | 0.942683i | \(0.608294\pi\) | |||||||
\(398\) | −9.06214 | −0.454244 | ||||||||
\(399\) | 8.51712 | 0.426389 | ||||||||
\(400\) | 6.69175 | 0.334587 | ||||||||
\(401\) | 28.4911 | 1.42278 | 0.711388 | − | 0.702800i | \(-0.248067\pi\) | ||||
0.711388 | + | 0.702800i | \(0.248067\pi\) | |||||||
\(402\) | 11.8418 | 0.590614 | ||||||||
\(403\) | 2.80187 | 0.139571 | ||||||||
\(404\) | 14.6321 | 0.727975 | ||||||||
\(405\) | 9.66187 | 0.480102 | ||||||||
\(406\) | −13.2208 | −0.656136 | ||||||||
\(407\) | −2.49420 | −0.123633 | ||||||||
\(408\) | 6.69158 | 0.331282 | ||||||||
\(409\) | 6.87511 | 0.339952 | 0.169976 | − | 0.985448i | \(-0.445631\pi\) | ||||
0.169976 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(410\) | 24.3516 | 1.20264 | ||||||||
\(411\) | −17.5839 | −0.867350 | ||||||||
\(412\) | 10.6474 | 0.524559 | ||||||||
\(413\) | 4.95210 | 0.243677 | ||||||||
\(414\) | −1.97668 | −0.0971488 | ||||||||
\(415\) | 9.36144 | 0.459535 | ||||||||
\(416\) | 20.3579 | 0.998129 | ||||||||
\(417\) | 9.27233 | 0.454068 | ||||||||
\(418\) | 25.2031 | 1.23273 | ||||||||
\(419\) | −16.8820 | −0.824741 | −0.412370 | − | 0.911016i | \(-0.635299\pi\) | ||||
−0.412370 | + | 0.911016i | \(0.635299\pi\) | |||||||
\(420\) | −5.01669 | −0.244790 | ||||||||
\(421\) | 23.8728 | 1.16349 | 0.581744 | − | 0.813372i | \(-0.302371\pi\) | ||||
0.581744 | + | 0.813372i | \(0.302371\pi\) | |||||||
\(422\) | −53.8764 | −2.62266 | ||||||||
\(423\) | −3.14750 | −0.153037 | ||||||||
\(424\) | −14.1392 | −0.686661 | ||||||||
\(425\) | 8.05108 | 0.390535 | ||||||||
\(426\) | −39.6588 | −1.92147 | ||||||||
\(427\) | 5.30201 | 0.256582 | ||||||||
\(428\) | 43.2790 | 2.09197 | ||||||||
\(429\) | −12.9507 | −0.625267 | ||||||||
\(430\) | −27.2414 | −1.31370 | ||||||||
\(431\) | 1.86378 | 0.0897749 | 0.0448874 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448874 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(432\) | 7.78434 | 0.374524 | ||||||||
\(433\) | −1.30293 | −0.0626150 | −0.0313075 | − | 0.999510i | \(-0.509967\pi\) | ||||
−0.0313075 | + | 0.999510i | \(0.509967\pi\) | |||||||
\(434\) | −2.19859 | −0.105536 | ||||||||
\(435\) | −10.6453 | −0.510405 | ||||||||
\(436\) | −38.1610 | −1.82758 | ||||||||
\(437\) | 9.51605 | 0.455214 | ||||||||
\(438\) | 30.4637 | 1.45561 | ||||||||
\(439\) | −8.99193 | −0.429162 | −0.214581 | − | 0.976706i | \(-0.568839\pi\) | ||||
−0.214581 | + | 0.976706i | \(0.568839\pi\) | |||||||
\(440\) | −4.36792 | −0.208232 | ||||||||
\(441\) | 0.434225 | 0.0206774 | ||||||||
\(442\) | 12.1338 | 0.577146 | ||||||||
\(443\) | 24.7224 | 1.17460 | 0.587298 | − | 0.809371i | \(-0.300192\pi\) | ||||
0.587298 | + | 0.809371i | \(0.300192\pi\) | |||||||
\(444\) | 5.25152 | 0.249226 | ||||||||
\(445\) | −1.84426 | −0.0874264 | ||||||||
\(446\) | −18.7272 | −0.886757 | ||||||||
\(447\) | −4.46932 | −0.211391 | ||||||||
\(448\) | −12.7003 | −0.600033 | ||||||||
\(449\) | 13.3189 | 0.628556 | 0.314278 | − | 0.949331i | \(-0.398238\pi\) | ||||
0.314278 | + | 0.949331i | \(0.398238\pi\) | |||||||
\(450\) | 3.90220 | 0.183952 | ||||||||
\(451\) | −28.9189 | −1.36174 | ||||||||
\(452\) | 48.2167 | 2.26792 | ||||||||
\(453\) | 2.82663 | 0.132807 | ||||||||
\(454\) | 43.3785 | 2.03585 | ||||||||
\(455\) | −2.67658 | −0.125480 | ||||||||
\(456\) | −15.6136 | −0.731174 | ||||||||
\(457\) | −10.9991 | −0.514515 | −0.257258 | − | 0.966343i | \(-0.582819\pi\) | ||||
−0.257258 | + | 0.966343i | \(0.582819\pi\) | |||||||
\(458\) | −41.0383 | −1.91759 | ||||||||
\(459\) | 9.36563 | 0.437150 | ||||||||
\(460\) | −5.60507 | −0.261338 | ||||||||
\(461\) | −30.6682 | −1.42836 | −0.714181 | − | 0.699961i | \(-0.753201\pi\) | ||||
−0.714181 | + | 0.699961i | \(0.753201\pi\) | |||||||
\(462\) | 10.1623 | 0.472791 | ||||||||
\(463\) | 29.1366 | 1.35409 | 0.677047 | − | 0.735940i | \(-0.263260\pi\) | ||||
0.677047 | + | 0.735940i | \(0.263260\pi\) | |||||||
\(464\) | −9.84468 | −0.457028 | ||||||||
\(465\) | −1.77030 | −0.0820958 | ||||||||
\(466\) | −7.63545 | −0.353705 | ||||||||
\(467\) | 0.618808 | 0.0286350 | 0.0143175 | − | 0.999897i | \(-0.495442\pi\) | ||||
0.0143175 | + | 0.999897i | \(0.495442\pi\) | |||||||
\(468\) | 3.44773 | 0.159371 | ||||||||
\(469\) | −2.90641 | −0.134206 | ||||||||
\(470\) | −15.2240 | −0.702231 | ||||||||
\(471\) | −5.83976 | −0.269082 | ||||||||
\(472\) | −9.07820 | −0.417858 | ||||||||
\(473\) | 32.3506 | 1.48748 | ||||||||
\(474\) | −7.46598 | −0.342924 | ||||||||
\(475\) | −18.7858 | −0.861950 | ||||||||
\(476\) | −5.58180 | −0.255841 | ||||||||
\(477\) | 3.34911 | 0.153345 | ||||||||
\(478\) | −27.2474 | −1.24627 | ||||||||
\(479\) | −23.6043 | −1.07851 | −0.539254 | − | 0.842143i | \(-0.681294\pi\) | ||||
−0.539254 | + | 0.842143i | \(0.681294\pi\) | |||||||
\(480\) | −12.8627 | −0.587100 | ||||||||
\(481\) | 2.80187 | 0.127754 | ||||||||
\(482\) | −29.9403 | −1.36374 | ||||||||
\(483\) | 3.83701 | 0.174590 | ||||||||
\(484\) | −13.5426 | −0.615575 | ||||||||
\(485\) | 14.4654 | 0.656842 | ||||||||
\(486\) | 9.84690 | 0.446664 | ||||||||
\(487\) | 18.7706 | 0.850576 | 0.425288 | − | 0.905058i | \(-0.360173\pi\) | ||||
0.425288 | + | 0.905058i | \(0.360173\pi\) | |||||||
\(488\) | −9.71966 | −0.439988 | ||||||||
\(489\) | −28.5697 | −1.29197 | ||||||||
\(490\) | 2.10028 | 0.0948811 | ||||||||
\(491\) | 10.6085 | 0.478754 | 0.239377 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239377 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(492\) | 60.8884 | 2.74506 | ||||||||
\(493\) | −11.8445 | −0.533449 | ||||||||
\(494\) | −28.3120 | −1.27382 | ||||||||
\(495\) | 1.03462 | 0.0465025 | ||||||||
\(496\) | −1.63715 | −0.0735103 | ||||||||
\(497\) | 9.73376 | 0.436619 | ||||||||
\(498\) | 39.9272 | 1.78918 | ||||||||
\(499\) | −8.39414 | −0.375773 | −0.187887 | − | 0.982191i | \(-0.560164\pi\) | ||||
−0.187887 | + | 0.982191i | \(0.560164\pi\) | |||||||
\(500\) | 24.6005 | 1.10017 | ||||||||
\(501\) | 23.3123 | 1.04152 | ||||||||
\(502\) | 44.5810 | 1.98975 | ||||||||
\(503\) | 6.99951 | 0.312093 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(504\) | −0.796022 | −0.0354576 | ||||||||
\(505\) | −4.93253 | −0.219495 | ||||||||
\(506\) | 11.3541 | 0.504753 | ||||||||
\(507\) | −9.54293 | −0.423816 | ||||||||
\(508\) | 21.8698 | 0.970314 | ||||||||
\(509\) | −12.9940 | −0.575948 | −0.287974 | − | 0.957638i | \(-0.592982\pi\) | ||||
−0.287974 | + | 0.957638i | \(0.592982\pi\) | |||||||
\(510\) | −7.66648 | −0.339477 | ||||||||
\(511\) | −7.47694 | −0.330760 | ||||||||
\(512\) | −17.8977 | −0.790976 | ||||||||
\(513\) | −21.8530 | −0.964835 | ||||||||
\(514\) | 57.8577 | 2.55199 | ||||||||
\(515\) | −3.58926 | −0.158162 | ||||||||
\(516\) | −68.1139 | −2.99855 | ||||||||
\(517\) | 18.0794 | 0.795129 | ||||||||
\(518\) | −2.19859 | −0.0966006 | ||||||||
\(519\) | 22.6316 | 0.993416 | ||||||||
\(520\) | 4.90672 | 0.215174 | ||||||||
\(521\) | −20.2192 | −0.885821 | −0.442911 | − | 0.896566i | \(-0.646054\pi\) | ||||
−0.442911 | + | 0.896566i | \(0.646054\pi\) | |||||||
\(522\) | −5.74079 | −0.251268 | ||||||||
\(523\) | −32.6323 | −1.42691 | −0.713455 | − | 0.700701i | \(-0.752870\pi\) | ||||
−0.713455 | + | 0.700701i | \(0.752870\pi\) | |||||||
\(524\) | 63.5862 | 2.77778 | ||||||||
\(525\) | −7.57469 | −0.330587 | ||||||||
\(526\) | −47.3746 | −2.06563 | ||||||||
\(527\) | −1.96972 | −0.0858023 | ||||||||
\(528\) | 7.56720 | 0.329320 | ||||||||
\(529\) | −18.7130 | −0.813608 | ||||||||
\(530\) | 16.1992 | 0.703646 | ||||||||
\(531\) | 2.15033 | 0.0933162 | ||||||||
\(532\) | 13.0241 | 0.564668 | ||||||||
\(533\) | 32.4861 | 1.40713 | ||||||||
\(534\) | −7.86591 | −0.340391 | ||||||||
\(535\) | −14.5895 | −0.630758 | ||||||||
\(536\) | 5.32804 | 0.230136 | ||||||||
\(537\) | −43.7128 | −1.88635 | ||||||||
\(538\) | −31.0518 | −1.33874 | ||||||||
\(539\) | −2.49420 | −0.107433 | ||||||||
\(540\) | 12.8717 | 0.553910 | ||||||||
\(541\) | −16.4890 | −0.708917 | −0.354459 | − | 0.935072i | \(-0.615335\pi\) | ||||
−0.354459 | + | 0.935072i | \(0.615335\pi\) | |||||||
\(542\) | −38.8658 | −1.66943 | ||||||||
\(543\) | −13.4287 | −0.576281 | ||||||||
\(544\) | −14.3116 | −0.613606 | ||||||||
\(545\) | 12.8642 | 0.551041 | ||||||||
\(546\) | −11.4158 | −0.488552 | ||||||||
\(547\) | −13.5799 | −0.580633 | −0.290317 | − | 0.956931i | \(-0.593761\pi\) | ||||
−0.290317 | + | 0.956931i | \(0.593761\pi\) | |||||||
\(548\) | −26.8888 | −1.14863 | ||||||||
\(549\) | 2.30227 | 0.0982583 | ||||||||
\(550\) | −22.4144 | −0.955752 | ||||||||
\(551\) | 27.6370 | 1.17738 | ||||||||
\(552\) | −7.03400 | −0.299387 | ||||||||
\(553\) | 1.83243 | 0.0779229 | ||||||||
\(554\) | 1.87117 | 0.0794986 | ||||||||
\(555\) | −1.77030 | −0.0751451 | ||||||||
\(556\) | 14.1790 | 0.601323 | ||||||||
\(557\) | −22.4371 | −0.950690 | −0.475345 | − | 0.879799i | \(-0.657677\pi\) | ||||
−0.475345 | + | 0.879799i | \(0.657677\pi\) | |||||||
\(558\) | −0.954684 | −0.0404150 | ||||||||
\(559\) | −36.3412 | −1.53707 | ||||||||
\(560\) | 1.56395 | 0.0660888 | ||||||||
\(561\) | 9.10437 | 0.384387 | ||||||||
\(562\) | −58.5259 | −2.46877 | ||||||||
\(563\) | 11.0123 | 0.464112 | 0.232056 | − | 0.972702i | \(-0.425455\pi\) | ||||
0.232056 | + | 0.972702i | \(0.425455\pi\) | |||||||
\(564\) | −38.0659 | −1.60286 | ||||||||
\(565\) | −16.2540 | −0.683811 | ||||||||
\(566\) | −44.2059 | −1.85811 | ||||||||
\(567\) | −10.1141 | −0.424753 | ||||||||
\(568\) | −17.8439 | −0.748715 | ||||||||
\(569\) | 0.00711389 | 0.000298230 0 | 0.000149115 | − | 1.00000i | \(-0.499953\pi\) | ||||
0.000149115 | 1.00000i | \(0.499953\pi\) | ||||||||
\(570\) | 17.8884 | 0.749261 | ||||||||
\(571\) | −18.4964 | −0.774050 | −0.387025 | − | 0.922069i | \(-0.626497\pi\) | ||||
−0.387025 | + | 0.922069i | \(0.626497\pi\) | |||||||
\(572\) | −19.8039 | −0.828041 | ||||||||
\(573\) | 32.6130 | 1.36243 | ||||||||
\(574\) | −25.4915 | −1.06399 | ||||||||
\(575\) | −8.46308 | −0.352935 | ||||||||
\(576\) | −5.51479 | −0.229783 | ||||||||
\(577\) | −21.4461 | −0.892811 | −0.446406 | − | 0.894831i | \(-0.647296\pi\) | ||||
−0.446406 | + | 0.894831i | \(0.647296\pi\) | |||||||
\(578\) | 28.8460 | 1.19984 | ||||||||
\(579\) | 5.19963 | 0.216089 | ||||||||
\(580\) | −16.2785 | −0.675930 | ||||||||
\(581\) | −9.79963 | −0.406557 | ||||||||
\(582\) | 61.6961 | 2.55739 | ||||||||
\(583\) | −19.2374 | −0.796732 | ||||||||
\(584\) | 13.7067 | 0.567188 | ||||||||
\(585\) | −1.16224 | −0.0480527 | ||||||||
\(586\) | −24.3133 | −1.00437 | ||||||||
\(587\) | −17.7924 | −0.734373 | −0.367186 | − | 0.930147i | \(-0.619679\pi\) | ||||
−0.367186 | + | 0.930147i | \(0.619679\pi\) | |||||||
\(588\) | 5.25152 | 0.216569 | ||||||||
\(589\) | 4.59598 | 0.189374 | ||||||||
\(590\) | 10.4008 | 0.428195 | ||||||||
\(591\) | 10.9436 | 0.450159 | ||||||||
\(592\) | −1.63715 | −0.0672865 | ||||||||
\(593\) | −31.1575 | −1.27949 | −0.639743 | − | 0.768589i | \(-0.720959\pi\) | ||||
−0.639743 | + | 0.768589i | \(0.720959\pi\) | |||||||
\(594\) | −26.0741 | −1.06983 | ||||||||
\(595\) | 1.88164 | 0.0771398 | ||||||||
\(596\) | −6.83435 | −0.279946 | ||||||||
\(597\) | 7.63836 | 0.312617 | ||||||||
\(598\) | −12.7547 | −0.521579 | ||||||||
\(599\) | −30.2632 | −1.23652 | −0.618261 | − | 0.785973i | \(-0.712163\pi\) | ||||
−0.618261 | + | 0.785973i | \(0.712163\pi\) | |||||||
\(600\) | 13.8859 | 0.566891 | ||||||||
\(601\) | 24.6288 | 1.00463 | 0.502314 | − | 0.864685i | \(-0.332482\pi\) | ||||
0.502314 | + | 0.864685i | \(0.332482\pi\) | |||||||
\(602\) | 28.5165 | 1.16225 | ||||||||
\(603\) | −1.26204 | −0.0513941 | ||||||||
\(604\) | 4.32240 | 0.175876 | ||||||||
\(605\) | 4.56527 | 0.185604 | ||||||||
\(606\) | −21.0376 | −0.854594 | ||||||||
\(607\) | 16.1346 | 0.654882 | 0.327441 | − | 0.944872i | \(-0.393814\pi\) | ||||
0.327441 | + | 0.944872i | \(0.393814\pi\) | |||||||
\(608\) | 33.3937 | 1.35429 | ||||||||
\(609\) | 11.1436 | 0.451563 | ||||||||
\(610\) | 11.1357 | 0.450872 | ||||||||
\(611\) | −20.3095 | −0.821635 | ||||||||
\(612\) | −2.42376 | −0.0979746 | ||||||||
\(613\) | 23.7330 | 0.958567 | 0.479283 | − | 0.877660i | \(-0.340897\pi\) | ||||
0.479283 | + | 0.877660i | \(0.340897\pi\) | |||||||
\(614\) | −55.8492 | −2.25389 | ||||||||
\(615\) | −20.5257 | −0.827675 | ||||||||
\(616\) | 4.57237 | 0.184226 | ||||||||
\(617\) | 39.4088 | 1.58654 | 0.793268 | − | 0.608872i | \(-0.208378\pi\) | ||||
0.793268 | + | 0.608872i | \(0.208378\pi\) | |||||||
\(618\) | −15.3085 | −0.615797 | ||||||||
\(619\) | −0.433089 | −0.0174073 | −0.00870365 | − | 0.999962i | \(-0.502770\pi\) | ||||
−0.00870365 | + | 0.999962i | \(0.502770\pi\) | |||||||
\(620\) | −2.70709 | −0.108719 | ||||||||
\(621\) | −9.84489 | −0.395062 | ||||||||
\(622\) | 73.2853 | 2.93847 | ||||||||
\(623\) | 1.93059 | 0.0773474 | ||||||||
\(624\) | −8.50064 | −0.340298 | ||||||||
\(625\) | 12.1442 | 0.485770 | ||||||||
\(626\) | −4.98186 | −0.199115 | ||||||||
\(627\) | −21.2434 | −0.848381 | ||||||||
\(628\) | −8.92999 | −0.356345 | ||||||||
\(629\) | −1.96972 | −0.0785378 | ||||||||
\(630\) | 0.911995 | 0.0363347 | ||||||||
\(631\) | −11.3647 | −0.452421 | −0.226210 | − | 0.974078i | \(-0.572634\pi\) | ||||
−0.226210 | + | 0.974078i | \(0.572634\pi\) | |||||||
\(632\) | −3.35922 | −0.133622 | ||||||||
\(633\) | 45.4118 | 1.80496 | ||||||||
\(634\) | −3.44006 | −0.136622 | ||||||||
\(635\) | −7.37236 | −0.292563 | ||||||||
\(636\) | 40.5041 | 1.60609 | ||||||||
\(637\) | 2.80187 | 0.111014 | ||||||||
\(638\) | 32.9753 | 1.30550 | ||||||||
\(639\) | 4.22664 | 0.167203 | ||||||||
\(640\) | −12.7923 | −0.505661 | ||||||||
\(641\) | 14.6813 | 0.579876 | 0.289938 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289938 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(642\) | −62.2251 | −2.45583 | ||||||||
\(643\) | 3.72681 | 0.146971 | 0.0734854 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734854 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(644\) | 5.86743 | 0.231209 | ||||||||
\(645\) | 22.9614 | 0.904105 | ||||||||
\(646\) | 19.9034 | 0.783089 | ||||||||
\(647\) | 35.2122 | 1.38434 | 0.692168 | − | 0.721737i | \(-0.256656\pi\) | ||||
0.692168 | + | 0.721737i | \(0.256656\pi\) | |||||||
\(648\) | 18.5412 | 0.728368 | ||||||||
\(649\) | −12.3515 | −0.484841 | ||||||||
\(650\) | 25.1793 | 0.987612 | ||||||||
\(651\) | 1.85317 | 0.0726313 | ||||||||
\(652\) | −43.6880 | −1.71095 | ||||||||
\(653\) | −26.8133 | −1.04929 | −0.524643 | − | 0.851322i | \(-0.675801\pi\) | ||||
−0.524643 | + | 0.851322i | \(0.675801\pi\) | |||||||
\(654\) | 54.8667 | 2.14546 | ||||||||
\(655\) | −21.4351 | −0.837539 | ||||||||
\(656\) | −18.9819 | −0.741118 | ||||||||
\(657\) | −3.24667 | −0.126665 | ||||||||
\(658\) | 15.9366 | 0.621274 | ||||||||
\(659\) | −32.0899 | −1.25004 | −0.625022 | − | 0.780607i | \(-0.714910\pi\) | ||||
−0.625022 | + | 0.780607i | \(0.714910\pi\) | |||||||
\(660\) | 12.5126 | 0.487054 | ||||||||
\(661\) | 35.1302 | 1.36641 | 0.683203 | − | 0.730229i | \(-0.260587\pi\) | ||||
0.683203 | + | 0.730229i | \(0.260587\pi\) | |||||||
\(662\) | −6.32867 | −0.245971 | ||||||||
\(663\) | −10.2274 | −0.397200 | ||||||||
\(664\) | 17.9647 | 0.697166 | ||||||||
\(665\) | −4.39047 | −0.170255 | ||||||||
\(666\) | −0.954684 | −0.0369932 | ||||||||
\(667\) | 12.4506 | 0.482089 | ||||||||
\(668\) | 35.6485 | 1.37928 | ||||||||
\(669\) | 15.7849 | 0.610280 | ||||||||
\(670\) | −6.10429 | −0.235829 | ||||||||
\(671\) | −13.2243 | −0.510518 | ||||||||
\(672\) | 13.4648 | 0.519416 | ||||||||
\(673\) | 50.8665 | 1.96076 | 0.980379 | − | 0.197121i | \(-0.0631593\pi\) | ||||
0.980379 | + | 0.197121i | \(0.0631593\pi\) | |||||||
\(674\) | 24.0383 | 0.925919 | ||||||||
\(675\) | 19.4349 | 0.748051 | ||||||||
\(676\) | −14.5928 | −0.561260 | ||||||||
\(677\) | 3.14562 | 0.120896 | 0.0604479 | − | 0.998171i | \(-0.480747\pi\) | ||||
0.0604479 | + | 0.998171i | \(0.480747\pi\) | |||||||
\(678\) | −69.3245 | −2.66239 | ||||||||
\(679\) | −15.1426 | −0.581118 | ||||||||
\(680\) | −3.44943 | −0.132279 | ||||||||
\(681\) | −36.5632 | −1.40110 | ||||||||
\(682\) | 5.48373 | 0.209983 | ||||||||
\(683\) | −18.0902 | −0.692202 | −0.346101 | − | 0.938197i | \(-0.612495\pi\) | ||||
−0.346101 | + | 0.938197i | \(0.612495\pi\) | |||||||
\(684\) | 5.65540 | 0.216240 | ||||||||
\(685\) | 9.06429 | 0.346329 | ||||||||
\(686\) | −2.19859 | −0.0839426 | ||||||||
\(687\) | 34.5907 | 1.31972 | ||||||||
\(688\) | 21.2344 | 0.809555 | ||||||||
\(689\) | 21.6104 | 0.823291 | ||||||||
\(690\) | 8.05879 | 0.306793 | ||||||||
\(691\) | 14.9065 | 0.567071 | 0.283536 | − | 0.958962i | \(-0.408493\pi\) | ||||
0.283536 | + | 0.958962i | \(0.408493\pi\) | |||||||
\(692\) | 34.6075 | 1.31558 | ||||||||
\(693\) | −1.08304 | −0.0411415 | ||||||||
\(694\) | 15.7732 | 0.598742 | ||||||||
\(695\) | −4.77978 | −0.181307 | ||||||||
\(696\) | −20.4285 | −0.774341 | ||||||||
\(697\) | −22.8378 | −0.865043 | ||||||||
\(698\) | −15.8704 | −0.600705 | ||||||||
\(699\) | 6.43583 | 0.243425 | ||||||||
\(700\) | −11.5830 | −0.437796 | ||||||||
\(701\) | 11.4781 | 0.433520 | 0.216760 | − | 0.976225i | \(-0.430451\pi\) | ||||
0.216760 | + | 0.976225i | \(0.430451\pi\) | |||||||
\(702\) | 29.2904 | 1.10550 | ||||||||
\(703\) | 4.59598 | 0.173341 | ||||||||
\(704\) | 31.6771 | 1.19388 | ||||||||
\(705\) | 12.8321 | 0.483286 | ||||||||
\(706\) | 22.4664 | 0.845534 | ||||||||
\(707\) | 5.16341 | 0.194190 | ||||||||
\(708\) | 26.0060 | 0.977367 | ||||||||
\(709\) | −48.9123 | −1.83694 | −0.918470 | − | 0.395490i | \(-0.870575\pi\) | ||||
−0.918470 | + | 0.395490i | \(0.870575\pi\) | |||||||
\(710\) | 20.4436 | 0.767236 | ||||||||
\(711\) | 0.795688 | 0.0298406 | ||||||||
\(712\) | −3.53916 | −0.132636 | ||||||||
\(713\) | 2.07051 | 0.0775413 | ||||||||
\(714\) | 8.02533 | 0.300341 | ||||||||
\(715\) | 6.67594 | 0.249666 | ||||||||
\(716\) | −66.8443 | −2.49809 | ||||||||
\(717\) | 22.9665 | 0.857699 | ||||||||
\(718\) | −20.9569 | −0.782104 | ||||||||
\(719\) | 2.76192 | 0.103002 | 0.0515011 | − | 0.998673i | \(-0.483599\pi\) | ||||
0.0515011 | + | 0.998673i | \(0.483599\pi\) | |||||||
\(720\) | 0.679105 | 0.0253087 | ||||||||
\(721\) | 3.75727 | 0.139928 | ||||||||
\(722\) | −4.66777 | −0.173717 | ||||||||
\(723\) | 25.2363 | 0.938549 | ||||||||
\(724\) | −20.5348 | −0.763169 | ||||||||
\(725\) | −24.5789 | −0.912838 | ||||||||
\(726\) | 19.4712 | 0.722643 | ||||||||
\(727\) | −15.6408 | −0.580084 | −0.290042 | − | 0.957014i | \(-0.593669\pi\) | ||||
−0.290042 | + | 0.957014i | \(0.593669\pi\) | |||||||
\(728\) | −5.13639 | −0.190367 | ||||||||
\(729\) | 22.0425 | 0.816390 | ||||||||
\(730\) | −15.7037 | −0.581219 | ||||||||
\(731\) | 25.5479 | 0.944924 | ||||||||
\(732\) | 27.8436 | 1.02913 | ||||||||
\(733\) | 41.3953 | 1.52897 | 0.764485 | − | 0.644641i | \(-0.222993\pi\) | ||||
0.764485 | + | 0.644641i | \(0.222993\pi\) | |||||||
\(734\) | −49.2151 | −1.81656 | ||||||||
\(735\) | −1.77030 | −0.0652986 | ||||||||
\(736\) | 15.0440 | 0.554529 | ||||||||
\(737\) | 7.24918 | 0.267027 | ||||||||
\(738\) | −11.0690 | −0.407456 | ||||||||
\(739\) | 33.5368 | 1.23367 | 0.616835 | − | 0.787093i | \(-0.288415\pi\) | ||||
0.616835 | + | 0.787093i | \(0.288415\pi\) | |||||||
\(740\) | −2.70709 | −0.0995147 | ||||||||
\(741\) | 23.8639 | 0.876661 | ||||||||
\(742\) | −16.9574 | −0.622526 | ||||||||
\(743\) | 43.0576 | 1.57963 | 0.789815 | − | 0.613345i | \(-0.210176\pi\) | ||||
0.789815 | + | 0.613345i | \(0.210176\pi\) | |||||||
\(744\) | −3.39723 | −0.124548 | ||||||||
\(745\) | 2.30388 | 0.0844076 | ||||||||
\(746\) | −45.1013 | −1.65128 | ||||||||
\(747\) | −4.25525 | −0.155691 | ||||||||
\(748\) | 13.9221 | 0.509044 | ||||||||
\(749\) | 15.2724 | 0.558041 | ||||||||
\(750\) | −35.3698 | −1.29152 | ||||||||
\(751\) | −4.65828 | −0.169983 | −0.0849916 | − | 0.996382i | \(-0.527086\pi\) | ||||
−0.0849916 | + | 0.996382i | \(0.527086\pi\) | |||||||
\(752\) | 11.8670 | 0.432745 | ||||||||
\(753\) | −37.5768 | −1.36937 | ||||||||
\(754\) | −37.0429 | −1.34902 | ||||||||
\(755\) | −1.45709 | −0.0530291 | ||||||||
\(756\) | −13.4742 | −0.490052 | ||||||||
\(757\) | −22.7127 | −0.825506 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(758\) | −42.3540 | −1.53837 | ||||||||
\(759\) | −9.57027 | −0.347379 | ||||||||
\(760\) | 8.04862 | 0.291954 | ||||||||
\(761\) | 24.4353 | 0.885778 | 0.442889 | − | 0.896576i | \(-0.353954\pi\) | ||||
0.442889 | + | 0.896576i | \(0.353954\pi\) | |||||||
\(762\) | −31.4436 | −1.13908 | ||||||||
\(763\) | −13.4663 | −0.487514 | ||||||||
\(764\) | 49.8708 | 1.80426 | ||||||||
\(765\) | 0.817056 | 0.0295407 | ||||||||
\(766\) | 4.97283 | 0.179675 | ||||||||
\(767\) | 13.8751 | 0.501002 | ||||||||
\(768\) | −7.48862 | −0.270222 | ||||||||
\(769\) | 28.3689 | 1.02301 | 0.511505 | − | 0.859280i | \(-0.329088\pi\) | ||||
0.511505 | + | 0.859280i | \(0.329088\pi\) | |||||||
\(770\) | −5.23853 | −0.188783 | ||||||||
\(771\) | −48.7675 | −1.75632 | ||||||||
\(772\) | 7.95112 | 0.286167 | ||||||||
\(773\) | 23.8822 | 0.858982 | 0.429491 | − | 0.903071i | \(-0.358693\pi\) | ||||
0.429491 | + | 0.903071i | \(0.358693\pi\) | |||||||
\(774\) | 12.3826 | 0.445082 | ||||||||
\(775\) | −4.08743 | −0.146825 | ||||||||
\(776\) | 27.7593 | 0.996502 | ||||||||
\(777\) | 1.85317 | 0.0664820 | ||||||||
\(778\) | −64.0383 | −2.29589 | ||||||||
\(779\) | 53.2879 | 1.90924 | ||||||||
\(780\) | −14.0561 | −0.503290 | ||||||||
\(781\) | −24.2780 | −0.868733 | ||||||||
\(782\) | 8.96658 | 0.320644 | ||||||||
\(783\) | −28.5921 | −1.02180 | ||||||||
\(784\) | −1.63715 | −0.0584697 | ||||||||
\(785\) | 3.01033 | 0.107443 | ||||||||
\(786\) | −91.4222 | −3.26092 | ||||||||
\(787\) | −28.9143 | −1.03068 | −0.515341 | − | 0.856985i | \(-0.672335\pi\) | ||||
−0.515341 | + | 0.856985i | \(0.672335\pi\) | |||||||
\(788\) | 16.7346 | 0.596146 | ||||||||
\(789\) | 39.9315 | 1.42160 | ||||||||
\(790\) | 3.84862 | 0.136928 | ||||||||
\(791\) | 17.0148 | 0.604978 | ||||||||
\(792\) | 1.98544 | 0.0705495 | ||||||||
\(793\) | 14.8555 | 0.527536 | ||||||||
\(794\) | 29.2357 | 1.03754 | ||||||||
\(795\) | −13.6541 | −0.484260 | ||||||||
\(796\) | 11.6804 | 0.413999 | ||||||||
\(797\) | 40.2463 | 1.42560 | 0.712798 | − | 0.701369i | \(-0.247427\pi\) | ||||
0.712798 | + | 0.701369i | \(0.247427\pi\) | |||||||
\(798\) | −18.7257 | −0.662882 | ||||||||
\(799\) | 14.2776 | 0.505105 | ||||||||
\(800\) | −29.6986 | −1.05000 | ||||||||
\(801\) | 0.838310 | 0.0296202 | ||||||||
\(802\) | −62.6402 | −2.21190 | ||||||||
\(803\) | 18.6490 | 0.658108 | ||||||||
\(804\) | −15.2631 | −0.538287 | ||||||||
\(805\) | −1.97793 | −0.0697129 | ||||||||
\(806\) | −6.16017 | −0.216983 | ||||||||
\(807\) | 26.1732 | 0.921339 | ||||||||
\(808\) | −9.46558 | −0.332998 | ||||||||
\(809\) | −30.4580 | −1.07085 | −0.535424 | − | 0.844583i | \(-0.679848\pi\) | ||||
−0.535424 | + | 0.844583i | \(0.679848\pi\) | |||||||
\(810\) | −21.2425 | −0.746386 | ||||||||
\(811\) | 30.0477 | 1.05512 | 0.527559 | − | 0.849519i | \(-0.323108\pi\) | ||||
0.527559 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(812\) | 17.0405 | 0.598005 | ||||||||
\(813\) | 32.7595 | 1.14893 | ||||||||
\(814\) | 5.48373 | 0.192205 | ||||||||
\(815\) | 14.7273 | 0.515876 | ||||||||
\(816\) | 5.97596 | 0.209200 | ||||||||
\(817\) | −59.6115 | −2.08554 | ||||||||
\(818\) | −15.1156 | −0.528503 | ||||||||
\(819\) | 1.21664 | 0.0425129 | ||||||||
\(820\) | −31.3872 | −1.09609 | ||||||||
\(821\) | 4.47390 | 0.156140 | 0.0780700 | − | 0.996948i | \(-0.475124\pi\) | ||||
0.0780700 | + | 0.996948i | \(0.475124\pi\) | |||||||
\(822\) | 38.6598 | 1.34842 | ||||||||
\(823\) | −40.8024 | −1.42228 | −0.711141 | − | 0.703050i | \(-0.751821\pi\) | ||||
−0.711141 | + | 0.703050i | \(0.751821\pi\) | |||||||
\(824\) | −6.88783 | −0.239949 | ||||||||
\(825\) | 18.8928 | 0.657763 | ||||||||
\(826\) | −10.8877 | −0.378830 | ||||||||
\(827\) | 6.00055 | 0.208660 | 0.104330 | − | 0.994543i | \(-0.466730\pi\) | ||||
0.104330 | + | 0.994543i | \(0.466730\pi\) | |||||||
\(828\) | 2.54779 | 0.0885417 | ||||||||
\(829\) | 33.9750 | 1.18000 | 0.590000 | − | 0.807403i | \(-0.299128\pi\) | ||||
0.590000 | + | 0.807403i | \(0.299128\pi\) | |||||||
\(830\) | −20.5820 | −0.714411 | ||||||||
\(831\) | −1.57719 | −0.0547121 | ||||||||
\(832\) | −35.5846 | −1.23367 | ||||||||
\(833\) | −1.96972 | −0.0682467 | ||||||||
\(834\) | −20.3861 | −0.705912 | ||||||||
\(835\) | −12.0172 | −0.415872 | ||||||||
\(836\) | −32.4848 | −1.12351 | ||||||||
\(837\) | −4.75481 | −0.164350 | ||||||||
\(838\) | 37.1167 | 1.28217 | ||||||||
\(839\) | −47.7629 | −1.64896 | −0.824479 | − | 0.565892i | \(-0.808532\pi\) | ||||
−0.824479 | + | 0.565892i | \(0.808532\pi\) | |||||||
\(840\) | 3.24532 | 0.111974 | ||||||||
\(841\) | 7.15970 | 0.246886 | ||||||||
\(842\) | −52.4865 | −1.80880 | ||||||||
\(843\) | 49.3307 | 1.69904 | ||||||||
\(844\) | 69.4424 | 2.39030 | ||||||||
\(845\) | 4.91927 | 0.169228 | ||||||||
\(846\) | 6.92008 | 0.237917 | ||||||||
\(847\) | −4.77896 | −0.164207 | ||||||||
\(848\) | −12.6271 | −0.433617 | ||||||||
\(849\) | 37.2606 | 1.27878 | ||||||||
\(850\) | −17.7011 | −0.607141 | ||||||||
\(851\) | 2.07051 | 0.0709763 | ||||||||
\(852\) | 51.1170 | 1.75124 | ||||||||
\(853\) | 28.2353 | 0.966758 | 0.483379 | − | 0.875411i | \(-0.339409\pi\) | ||||
0.483379 | + | 0.875411i | \(0.339409\pi\) | |||||||
\(854\) | −11.6570 | −0.398893 | ||||||||
\(855\) | −1.90645 | −0.0651993 | ||||||||
\(856\) | −27.9973 | −0.956930 | ||||||||
\(857\) | −48.6481 | −1.66179 | −0.830893 | − | 0.556432i | \(-0.812170\pi\) | ||||
−0.830893 | + | 0.556432i | \(0.812170\pi\) | |||||||
\(858\) | 28.4733 | 0.972064 | ||||||||
\(859\) | 24.7667 | 0.845029 | 0.422515 | − | 0.906356i | \(-0.361148\pi\) | ||||
0.422515 | + | 0.906356i | \(0.361148\pi\) | |||||||
\(860\) | 35.1119 | 1.19731 | ||||||||
\(861\) | 21.4864 | 0.732256 | ||||||||
\(862\) | −4.09768 | −0.139568 | ||||||||
\(863\) | −41.2006 | −1.40249 | −0.701243 | − | 0.712922i | \(-0.747371\pi\) | ||||
−0.701243 | + | 0.712922i | \(0.747371\pi\) | |||||||
\(864\) | −34.5476 | −1.17533 | ||||||||
\(865\) | −11.6663 | −0.396666 | ||||||||
\(866\) | 2.86462 | 0.0973438 | ||||||||
\(867\) | −24.3139 | −0.825744 | ||||||||
\(868\) | 2.83381 | 0.0961857 | ||||||||
\(869\) | −4.57046 | −0.155042 | ||||||||
\(870\) | 23.4048 | 0.793496 | ||||||||
\(871\) | −8.14339 | −0.275928 | ||||||||
\(872\) | 24.6865 | 0.835991 | ||||||||
\(873\) | −6.57527 | −0.222539 | ||||||||
\(874\) | −20.9219 | −0.707694 | ||||||||
\(875\) | 8.68109 | 0.293474 | ||||||||
\(876\) | −39.2652 | −1.32665 | ||||||||
\(877\) | 2.72219 | 0.0919218 | 0.0459609 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459609 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(878\) | 19.7696 | 0.667192 | ||||||||
\(879\) | 20.4934 | 0.691225 | ||||||||
\(880\) | −3.90080 | −0.131496 | ||||||||
\(881\) | 49.4139 | 1.66480 | 0.832399 | − | 0.554177i | \(-0.186967\pi\) | ||||
0.832399 | + | 0.554177i | \(0.186967\pi\) | |||||||
\(882\) | −0.954684 | −0.0321459 | ||||||||
\(883\) | 47.8115 | 1.60898 | 0.804492 | − | 0.593964i | \(-0.202438\pi\) | ||||
0.804492 | + | 0.593964i | \(0.202438\pi\) | |||||||
\(884\) | −15.6395 | −0.526012 | ||||||||
\(885\) | −8.76672 | −0.294690 | ||||||||
\(886\) | −54.3544 | −1.82607 | ||||||||
\(887\) | 36.8807 | 1.23833 | 0.619166 | − | 0.785260i | \(-0.287471\pi\) | ||||
0.619166 | + | 0.785260i | \(0.287471\pi\) | |||||||
\(888\) | −3.39723 | −0.114003 | ||||||||
\(889\) | 7.71745 | 0.258835 | ||||||||
\(890\) | 4.05478 | 0.135917 | ||||||||
\(891\) | 25.2267 | 0.845125 | ||||||||
\(892\) | 24.1378 | 0.808194 | ||||||||
\(893\) | −33.3142 | −1.11482 | ||||||||
\(894\) | 9.82621 | 0.328637 | ||||||||
\(895\) | 22.5334 | 0.753209 | ||||||||
\(896\) | 13.3911 | 0.447365 | ||||||||
\(897\) | 10.7508 | 0.358958 | ||||||||
\(898\) | −29.2827 | −0.977178 | ||||||||
\(899\) | 6.01329 | 0.200555 | ||||||||
\(900\) | −5.02962 | −0.167654 | ||||||||
\(901\) | −15.1921 | −0.506123 | ||||||||
\(902\) | 63.5808 | 2.11701 | ||||||||
\(903\) | −24.0362 | −0.799875 | ||||||||
\(904\) | −31.1916 | −1.03742 | ||||||||
\(905\) | 6.92233 | 0.230106 | ||||||||
\(906\) | −6.21461 | −0.206467 | ||||||||
\(907\) | −2.62052 | −0.0870128 | −0.0435064 | − | 0.999053i | \(-0.513853\pi\) | ||||
−0.0435064 | + | 0.999053i | \(0.513853\pi\) | |||||||
\(908\) | −55.9114 | −1.85548 | ||||||||
\(909\) | 2.24208 | 0.0743652 | ||||||||
\(910\) | 5.88472 | 0.195076 | ||||||||
\(911\) | 45.5923 | 1.51054 | 0.755270 | − | 0.655414i | \(-0.227506\pi\) | ||||
0.755270 | + | 0.655414i | \(0.227506\pi\) | |||||||
\(912\) | −13.9438 | −0.461726 | ||||||||
\(913\) | 24.4423 | 0.808921 | ||||||||
\(914\) | 24.1825 | 0.799886 | ||||||||
\(915\) | −9.38616 | −0.310297 | ||||||||
\(916\) | 52.8950 | 1.74770 | ||||||||
\(917\) | 22.4384 | 0.740983 | ||||||||
\(918\) | −20.5912 | −0.679611 | ||||||||
\(919\) | 35.1019 | 1.15790 | 0.578952 | − | 0.815362i | \(-0.303462\pi\) | ||||
0.578952 | + | 0.815362i | \(0.303462\pi\) | |||||||
\(920\) | 3.62594 | 0.119544 | ||||||||
\(921\) | 47.0746 | 1.55116 | ||||||||
\(922\) | 67.4269 | 2.22059 | ||||||||
\(923\) | 27.2727 | 0.897692 | ||||||||
\(924\) | −13.0983 | −0.430904 | ||||||||
\(925\) | −4.08743 | −0.134394 | ||||||||
\(926\) | −64.0595 | −2.10513 | ||||||||
\(927\) | 1.63150 | 0.0535855 | ||||||||
\(928\) | 43.6916 | 1.43425 | ||||||||
\(929\) | 13.3281 | 0.437282 | 0.218641 | − | 0.975805i | \(-0.429838\pi\) | ||||
0.218641 | + | 0.975805i | \(0.429838\pi\) | |||||||
\(930\) | 3.89217 | 0.127629 | ||||||||
\(931\) | 4.59598 | 0.150627 | ||||||||
\(932\) | 9.84147 | 0.322368 | ||||||||
\(933\) | −61.7713 | −2.02230 | ||||||||
\(934\) | −1.36051 | −0.0445171 | ||||||||
\(935\) | −4.69319 | −0.153484 | ||||||||
\(936\) | −2.23035 | −0.0729012 | ||||||||
\(937\) | 14.3348 | 0.468299 | 0.234149 | − | 0.972201i | \(-0.424769\pi\) | ||||
0.234149 | + | 0.972201i | \(0.424769\pi\) | |||||||
\(938\) | 6.39002 | 0.208641 | ||||||||
\(939\) | 4.19915 | 0.137034 | ||||||||
\(940\) | 19.6225 | 0.640016 | ||||||||
\(941\) | 37.9448 | 1.23697 | 0.618483 | − | 0.785798i | \(-0.287748\pi\) | ||||
0.618483 | + | 0.785798i | \(0.287748\pi\) | |||||||
\(942\) | 12.8393 | 0.418325 | ||||||||
\(943\) | 24.0065 | 0.781758 | ||||||||
\(944\) | −8.10735 | −0.263872 | ||||||||
\(945\) | 4.54220 | 0.147758 | ||||||||
\(946\) | −71.1259 | −2.31250 | ||||||||
\(947\) | −15.0161 | −0.487959 | −0.243979 | − | 0.969780i | \(-0.578453\pi\) | ||||
−0.243979 | + | 0.969780i | \(0.578453\pi\) | |||||||
\(948\) | 9.62304 | 0.312542 | ||||||||
\(949\) | −20.9494 | −0.680046 | ||||||||
\(950\) | 41.3022 | 1.34002 | ||||||||
\(951\) | 2.89958 | 0.0940253 | ||||||||
\(952\) | 3.61089 | 0.117030 | ||||||||
\(953\) | −54.0075 | −1.74947 | −0.874736 | − | 0.484599i | \(-0.838966\pi\) | ||||
−0.874736 | + | 0.484599i | \(0.838966\pi\) | |||||||
\(954\) | −7.36333 | −0.238397 | ||||||||
\(955\) | −16.8116 | −0.544010 | ||||||||
\(956\) | 35.1196 | 1.13585 | ||||||||
\(957\) | −27.7945 | −0.898468 | ||||||||
\(958\) | 51.8962 | 1.67669 | ||||||||
\(959\) | −9.48857 | −0.306402 | ||||||||
\(960\) | 22.4834 | 0.725647 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −6.16017 | −0.198612 | ||||||||
\(963\) | 6.63165 | 0.213702 | ||||||||
\(964\) | 38.5906 | 1.24292 | ||||||||
\(965\) | −2.68035 | −0.0862834 | ||||||||
\(966\) | −8.43601 | −0.271424 | ||||||||
\(967\) | 51.7196 | 1.66319 | 0.831595 | − | 0.555383i | \(-0.187428\pi\) | ||||
0.831595 | + | 0.555383i | \(0.187428\pi\) | |||||||
\(968\) | 8.76079 | 0.281582 | ||||||||
\(969\) | −16.7763 | −0.538933 | ||||||||
\(970\) | −31.8036 | −1.02115 | ||||||||
\(971\) | 9.66179 | 0.310061 | 0.155031 | − | 0.987910i | \(-0.450452\pi\) | ||||
0.155031 | + | 0.987910i | \(0.450452\pi\) | |||||||
\(972\) | −12.6919 | −0.407091 | ||||||||
\(973\) | 5.00351 | 0.160405 | ||||||||
\(974\) | −41.2688 | −1.32234 | ||||||||
\(975\) | −21.2233 | −0.679689 | ||||||||
\(976\) | −8.68020 | −0.277847 | ||||||||
\(977\) | −5.44003 | −0.174042 | −0.0870210 | − | 0.996206i | \(-0.527735\pi\) | ||||
−0.0870210 | + | 0.996206i | \(0.527735\pi\) | |||||||
\(978\) | 62.8132 | 2.00854 | ||||||||
\(979\) | −4.81528 | −0.153897 | ||||||||
\(980\) | −2.70709 | −0.0864749 | ||||||||
\(981\) | −5.84742 | −0.186694 | ||||||||
\(982\) | −23.3237 | −0.744290 | ||||||||
\(983\) | −21.6558 | −0.690714 | −0.345357 | − | 0.938471i | \(-0.612242\pi\) | ||||
−0.345357 | + | 0.938471i | \(0.612242\pi\) | |||||||
\(984\) | −39.3890 | −1.25567 | ||||||||
\(985\) | −5.64129 | −0.179746 | ||||||||
\(986\) | 26.0412 | 0.829321 | ||||||||
\(987\) | −13.4328 | −0.427570 | ||||||||
\(988\) | 36.4919 | 1.16096 | ||||||||
\(989\) | −26.8553 | −0.853948 | ||||||||
\(990\) | −2.27470 | −0.0722947 | ||||||||
\(991\) | 53.1501 | 1.68837 | 0.844184 | − | 0.536054i | \(-0.180086\pi\) | ||||
0.844184 | + | 0.536054i | \(0.180086\pi\) | |||||||
\(992\) | 7.26583 | 0.230690 | ||||||||
\(993\) | 5.33436 | 0.169281 | ||||||||
\(994\) | −21.4006 | −0.678784 | ||||||||
\(995\) | −3.93748 | −0.124827 | ||||||||
\(996\) | −51.4629 | −1.63067 | ||||||||
\(997\) | −43.6898 | −1.38367 | −0.691835 | − | 0.722056i | \(-0.743197\pi\) | ||||
−0.691835 | + | 0.722056i | \(0.743197\pi\) | |||||||
\(998\) | 18.4553 | 0.584192 | ||||||||
\(999\) | −4.75481 | −0.150435 |
(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 | 8029.2.a.g.1.9 | ✓ | 70 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8029.2.a.g.1.9 | ✓ | 70 | 1.1 | even | 1 | trivial |