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: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69431 | −1.90517 | −0.952583 | − | 0.304280i | \(-0.901584\pi\) | ||||
−0.952583 | + | 0.304280i | \(0.901584\pi\) | |||||||
\(3\) | 0.251057 | 0.144948 | 0.0724739 | − | 0.997370i | \(-0.476911\pi\) | ||||
0.0724739 | + | 0.997370i | \(0.476911\pi\) | |||||||
\(4\) | 5.25931 | 2.62966 | ||||||||
\(5\) | 0.178464 | 0.0798117 | 0.0399059 | − | 0.999203i | \(-0.487294\pi\) | ||||
0.0399059 | + | 0.999203i | \(0.487294\pi\) | |||||||
\(6\) | −0.676426 | −0.276150 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −8.78160 | −3.10476 | ||||||||
\(9\) | −2.93697 | −0.978990 | ||||||||
\(10\) | −0.480839 | −0.152055 | ||||||||
\(11\) | 3.66197 | 1.10413 | 0.552063 | − | 0.833802i | \(-0.313841\pi\) | ||||
0.552063 | + | 0.833802i | \(0.313841\pi\) | |||||||
\(12\) | 1.32039 | 0.381163 | ||||||||
\(13\) | 2.67742 | 0.742582 | 0.371291 | − | 0.928517i | \(-0.378915\pi\) | ||||
0.371291 | + | 0.928517i | \(0.378915\pi\) | |||||||
\(14\) | 2.69431 | 0.720085 | ||||||||
\(15\) | 0.0448048 | 0.0115685 | ||||||||
\(16\) | 13.1417 | 3.28543 | ||||||||
\(17\) | 4.46232 | 1.08227 | 0.541136 | − | 0.840935i | \(-0.317994\pi\) | ||||
0.541136 | + | 0.840935i | \(0.317994\pi\) | |||||||
\(18\) | 7.91311 | 1.86514 | ||||||||
\(19\) | 4.96953 | 1.14009 | 0.570045 | − | 0.821614i | \(-0.306926\pi\) | ||||
0.570045 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(20\) | 0.938600 | 0.209877 | ||||||||
\(21\) | −0.251057 | −0.0547851 | ||||||||
\(22\) | −9.86649 | −2.10354 | ||||||||
\(23\) | −1.77881 | −0.370907 | −0.185454 | − | 0.982653i | \(-0.559375\pi\) | ||||
−0.185454 | + | 0.982653i | \(0.559375\pi\) | |||||||
\(24\) | −2.20468 | −0.450029 | ||||||||
\(25\) | −4.96815 | −0.993630 | ||||||||
\(26\) | −7.21379 | −1.41474 | ||||||||
\(27\) | −1.49052 | −0.286850 | ||||||||
\(28\) | −5.25931 | −0.993916 | ||||||||
\(29\) | 9.19377 | 1.70724 | 0.853621 | − | 0.520895i | \(-0.174402\pi\) | ||||
0.853621 | + | 0.520895i | \(0.174402\pi\) | |||||||
\(30\) | −0.120718 | −0.0220400 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −17.8447 | −3.15453 | ||||||||
\(33\) | 0.919364 | 0.160041 | ||||||||
\(34\) | −12.0229 | −2.06191 | ||||||||
\(35\) | −0.178464 | −0.0301660 | ||||||||
\(36\) | −15.4464 | −2.57441 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −13.3895 | −2.17206 | ||||||||
\(39\) | 0.672184 | 0.107636 | ||||||||
\(40\) | −1.56720 | −0.247797 | ||||||||
\(41\) | 2.12262 | 0.331497 | 0.165748 | − | 0.986168i | \(-0.446996\pi\) | ||||
0.165748 | + | 0.986168i | \(0.446996\pi\) | |||||||
\(42\) | 0.676426 | 0.104375 | ||||||||
\(43\) | 10.2905 | 1.56928 | 0.784641 | − | 0.619951i | \(-0.212847\pi\) | ||||
0.784641 | + | 0.619951i | \(0.212847\pi\) | |||||||
\(44\) | 19.2594 | 2.90347 | ||||||||
\(45\) | −0.524145 | −0.0781349 | ||||||||
\(46\) | 4.79266 | 0.706639 | ||||||||
\(47\) | −7.05947 | −1.02973 | −0.514864 | − | 0.857272i | \(-0.672158\pi\) | ||||
−0.514864 | + | 0.857272i | \(0.672158\pi\) | |||||||
\(48\) | 3.29932 | 0.476216 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 13.3857 | 1.89303 | ||||||||
\(51\) | 1.12030 | 0.156873 | ||||||||
\(52\) | 14.0814 | 1.95273 | ||||||||
\(53\) | 2.62856 | 0.361060 | 0.180530 | − | 0.983569i | \(-0.442219\pi\) | ||||
0.180530 | + | 0.983569i | \(0.442219\pi\) | |||||||
\(54\) | 4.01592 | 0.546497 | ||||||||
\(55\) | 0.653532 | 0.0881222 | ||||||||
\(56\) | 8.78160 | 1.17349 | ||||||||
\(57\) | 1.24764 | 0.165253 | ||||||||
\(58\) | −24.7709 | −3.25258 | ||||||||
\(59\) | 14.2418 | 1.85413 | 0.927063 | − | 0.374905i | \(-0.122325\pi\) | ||||
0.927063 | + | 0.374905i | \(0.122325\pi\) | |||||||
\(60\) | 0.235642 | 0.0304213 | ||||||||
\(61\) | 4.95002 | 0.633785 | 0.316893 | − | 0.948461i | \(-0.397361\pi\) | ||||
0.316893 | + | 0.948461i | \(0.397361\pi\) | |||||||
\(62\) | 2.69431 | 0.342178 | ||||||||
\(63\) | 2.93697 | 0.370023 | ||||||||
\(64\) | 21.7957 | 2.72447 | ||||||||
\(65\) | 0.477824 | 0.0592667 | ||||||||
\(66\) | −2.47705 | −0.304904 | ||||||||
\(67\) | 5.53909 | 0.676707 | 0.338354 | − | 0.941019i | \(-0.390130\pi\) | ||||
0.338354 | + | 0.941019i | \(0.390130\pi\) | |||||||
\(68\) | 23.4687 | 2.84600 | ||||||||
\(69\) | −0.446582 | −0.0537622 | ||||||||
\(70\) | 0.480839 | 0.0574712 | ||||||||
\(71\) | 6.97179 | 0.827400 | 0.413700 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413700 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(72\) | 25.7913 | 3.03953 | ||||||||
\(73\) | −9.60295 | −1.12394 | −0.561970 | − | 0.827158i | \(-0.689956\pi\) | ||||
−0.561970 | + | 0.827158i | \(0.689956\pi\) | |||||||
\(74\) | −2.69431 | −0.313207 | ||||||||
\(75\) | −1.24729 | −0.144025 | ||||||||
\(76\) | 26.1363 | 2.99804 | ||||||||
\(77\) | −3.66197 | −0.417320 | ||||||||
\(78\) | −1.81107 | −0.205064 | ||||||||
\(79\) | −10.3299 | −1.16221 | −0.581105 | − | 0.813829i | \(-0.697379\pi\) | ||||
−0.581105 | + | 0.813829i | \(0.697379\pi\) | |||||||
\(80\) | 2.34533 | 0.262216 | ||||||||
\(81\) | 8.43671 | 0.937412 | ||||||||
\(82\) | −5.71899 | −0.631556 | ||||||||
\(83\) | 0.0564772 | 0.00619918 | 0.00309959 | − | 0.999995i | \(-0.499013\pi\) | ||||
0.00309959 | + | 0.999995i | \(0.499013\pi\) | |||||||
\(84\) | −1.32039 | −0.144066 | ||||||||
\(85\) | 0.796366 | 0.0863780 | ||||||||
\(86\) | −27.7257 | −2.98974 | ||||||||
\(87\) | 2.30816 | 0.247461 | ||||||||
\(88\) | −32.1580 | −3.42805 | ||||||||
\(89\) | −10.2245 | −1.08379 | −0.541897 | − | 0.840445i | \(-0.682294\pi\) | ||||
−0.541897 | + | 0.840445i | \(0.682294\pi\) | |||||||
\(90\) | 1.41221 | 0.148860 | ||||||||
\(91\) | −2.67742 | −0.280670 | ||||||||
\(92\) | −9.35530 | −0.975358 | ||||||||
\(93\) | −0.251057 | −0.0260334 | ||||||||
\(94\) | 19.0204 | 1.96180 | ||||||||
\(95\) | 0.886885 | 0.0909925 | ||||||||
\(96\) | −4.48004 | −0.457242 | ||||||||
\(97\) | −16.4804 | −1.67333 | −0.836665 | − | 0.547714i | \(-0.815498\pi\) | ||||
−0.836665 | + | 0.547714i | \(0.815498\pi\) | |||||||
\(98\) | −2.69431 | −0.272166 | ||||||||
\(99\) | −10.7551 | −1.08093 | ||||||||
\(100\) | −26.1290 | −2.61290 | ||||||||
\(101\) | 11.7195 | 1.16614 | 0.583069 | − | 0.812423i | \(-0.301852\pi\) | ||||
0.583069 | + | 0.812423i | \(0.301852\pi\) | |||||||
\(102\) | −3.01843 | −0.298869 | ||||||||
\(103\) | 1.40605 | 0.138542 | 0.0692709 | − | 0.997598i | \(-0.477933\pi\) | ||||
0.0692709 | + | 0.997598i | \(0.477933\pi\) | |||||||
\(104\) | −23.5120 | −2.30554 | ||||||||
\(105\) | −0.0448048 | −0.00437250 | ||||||||
\(106\) | −7.08216 | −0.687880 | ||||||||
\(107\) | −18.2428 | −1.76360 | −0.881800 | − | 0.471623i | \(-0.843668\pi\) | ||||
−0.881800 | + | 0.471623i | \(0.843668\pi\) | |||||||
\(108\) | −7.83910 | −0.754318 | ||||||||
\(109\) | 10.0749 | 0.965003 | 0.482501 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482501 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(110\) | −1.76082 | −0.167887 | ||||||||
\(111\) | 0.251057 | 0.0238293 | ||||||||
\(112\) | −13.1417 | −1.24178 | ||||||||
\(113\) | −4.56902 | −0.429817 | −0.214908 | − | 0.976634i | \(-0.568945\pi\) | ||||
−0.214908 | + | 0.976634i | \(0.568945\pi\) | |||||||
\(114\) | −3.36152 | −0.314835 | ||||||||
\(115\) | −0.317454 | −0.0296027 | ||||||||
\(116\) | 48.3529 | 4.48946 | ||||||||
\(117\) | −7.86349 | −0.726980 | ||||||||
\(118\) | −38.3719 | −3.53242 | ||||||||
\(119\) | −4.46232 | −0.409061 | ||||||||
\(120\) | −0.393457 | −0.0359176 | ||||||||
\(121\) | 2.41004 | 0.219095 | ||||||||
\(122\) | −13.3369 | −1.20747 | ||||||||
\(123\) | 0.532898 | 0.0480498 | ||||||||
\(124\) | −5.25931 | −0.472300 | ||||||||
\(125\) | −1.77896 | −0.159115 | ||||||||
\(126\) | −7.91311 | −0.704956 | ||||||||
\(127\) | 8.46035 | 0.750734 | 0.375367 | − | 0.926876i | \(-0.377517\pi\) | ||||
0.375367 | + | 0.926876i | \(0.377517\pi\) | |||||||
\(128\) | −23.0351 | −2.03603 | ||||||||
\(129\) | 2.58349 | 0.227464 | ||||||||
\(130\) | −1.28741 | −0.112913 | ||||||||
\(131\) | 12.5494 | 1.09645 | 0.548223 | − | 0.836332i | \(-0.315304\pi\) | ||||
0.548223 | + | 0.836332i | \(0.315304\pi\) | |||||||
\(132\) | 4.83522 | 0.420852 | ||||||||
\(133\) | −4.96953 | −0.430913 | ||||||||
\(134\) | −14.9240 | −1.28924 | ||||||||
\(135\) | −0.266005 | −0.0228940 | ||||||||
\(136\) | −39.1863 | −3.36020 | ||||||||
\(137\) | 7.41292 | 0.633328 | 0.316664 | − | 0.948538i | \(-0.397437\pi\) | ||||
0.316664 | + | 0.948538i | \(0.397437\pi\) | |||||||
\(138\) | 1.20323 | 0.102426 | ||||||||
\(139\) | −14.8282 | −1.25771 | −0.628857 | − | 0.777521i | \(-0.716477\pi\) | ||||
−0.628857 | + | 0.777521i | \(0.716477\pi\) | |||||||
\(140\) | −0.938600 | −0.0793262 | ||||||||
\(141\) | −1.77233 | −0.149257 | ||||||||
\(142\) | −18.7842 | −1.57633 | ||||||||
\(143\) | 9.80463 | 0.819904 | ||||||||
\(144\) | −38.5969 | −3.21641 | ||||||||
\(145\) | 1.64076 | 0.136258 | ||||||||
\(146\) | 25.8733 | 2.14129 | ||||||||
\(147\) | 0.251057 | 0.0207068 | ||||||||
\(148\) | 5.25931 | 0.432313 | ||||||||
\(149\) | 17.0936 | 1.40036 | 0.700179 | − | 0.713967i | \(-0.253103\pi\) | ||||
0.700179 | + | 0.713967i | \(0.253103\pi\) | |||||||
\(150\) | 3.36058 | 0.274391 | ||||||||
\(151\) | 3.87739 | 0.315538 | 0.157769 | − | 0.987476i | \(-0.449570\pi\) | ||||
0.157769 | + | 0.987476i | \(0.449570\pi\) | |||||||
\(152\) | −43.6404 | −3.53971 | ||||||||
\(153\) | −13.1057 | −1.05953 | ||||||||
\(154\) | 9.86649 | 0.795064 | ||||||||
\(155\) | −0.178464 | −0.0143346 | ||||||||
\(156\) | 3.53523 | 0.283045 | ||||||||
\(157\) | −1.40374 | −0.112031 | −0.0560154 | − | 0.998430i | \(-0.517840\pi\) | ||||
−0.0560154 | + | 0.998430i | \(0.517840\pi\) | |||||||
\(158\) | 27.8321 | 2.21420 | ||||||||
\(159\) | 0.659918 | 0.0523349 | ||||||||
\(160\) | −3.18465 | −0.251768 | ||||||||
\(161\) | 1.77881 | 0.140190 | ||||||||
\(162\) | −22.7311 | −1.78592 | ||||||||
\(163\) | −12.9645 | −1.01546 | −0.507730 | − | 0.861516i | \(-0.669515\pi\) | ||||
−0.507730 | + | 0.861516i | \(0.669515\pi\) | |||||||
\(164\) | 11.1635 | 0.871723 | ||||||||
\(165\) | 0.164074 | 0.0127731 | ||||||||
\(166\) | −0.152167 | −0.0118105 | ||||||||
\(167\) | 1.63568 | 0.126573 | 0.0632863 | − | 0.997995i | \(-0.479842\pi\) | ||||
0.0632863 | + | 0.997995i | \(0.479842\pi\) | |||||||
\(168\) | 2.20468 | 0.170095 | ||||||||
\(169\) | −5.83144 | −0.448572 | ||||||||
\(170\) | −2.14566 | −0.164564 | ||||||||
\(171\) | −14.5954 | −1.11614 | ||||||||
\(172\) | 54.1208 | 4.12667 | ||||||||
\(173\) | 8.28553 | 0.629937 | 0.314968 | − | 0.949102i | \(-0.398006\pi\) | ||||
0.314968 | + | 0.949102i | \(0.398006\pi\) | |||||||
\(174\) | −6.21890 | −0.471454 | ||||||||
\(175\) | 4.96815 | 0.375557 | ||||||||
\(176\) | 48.1246 | 3.62753 | ||||||||
\(177\) | 3.57551 | 0.268752 | ||||||||
\(178\) | 27.5480 | 2.06481 | ||||||||
\(179\) | −3.26741 | −0.244218 | −0.122109 | − | 0.992517i | \(-0.538966\pi\) | ||||
−0.122109 | + | 0.992517i | \(0.538966\pi\) | |||||||
\(180\) | −2.75664 | −0.205468 | ||||||||
\(181\) | −14.7212 | −1.09421 | −0.547107 | − | 0.837062i | \(-0.684271\pi\) | ||||
−0.547107 | + | 0.837062i | \(0.684271\pi\) | |||||||
\(182\) | 7.21379 | 0.534722 | ||||||||
\(183\) | 1.24274 | 0.0918658 | ||||||||
\(184\) | 15.6208 | 1.15158 | ||||||||
\(185\) | 0.178464 | 0.0131210 | ||||||||
\(186\) | 0.676426 | 0.0495979 | ||||||||
\(187\) | 16.3409 | 1.19497 | ||||||||
\(188\) | −37.1279 | −2.70783 | ||||||||
\(189\) | 1.49052 | 0.108419 | ||||||||
\(190\) | −2.38954 | −0.173356 | ||||||||
\(191\) | −21.3203 | −1.54268 | −0.771341 | − | 0.636422i | \(-0.780414\pi\) | ||||
−0.771341 | + | 0.636422i | \(0.780414\pi\) | |||||||
\(192\) | 5.47197 | 0.394905 | ||||||||
\(193\) | −0.222014 | −0.0159809 | −0.00799044 | − | 0.999968i | \(-0.502543\pi\) | ||||
−0.00799044 | + | 0.999968i | \(0.502543\pi\) | |||||||
\(194\) | 44.4033 | 3.18797 | ||||||||
\(195\) | 0.119961 | 0.00859059 | ||||||||
\(196\) | 5.25931 | 0.375665 | ||||||||
\(197\) | 23.4663 | 1.67191 | 0.835954 | − | 0.548800i | \(-0.184915\pi\) | ||||
0.835954 | + | 0.548800i | \(0.184915\pi\) | |||||||
\(198\) | 28.9776 | 2.05935 | ||||||||
\(199\) | 14.9999 | 1.06331 | 0.531657 | − | 0.846960i | \(-0.321570\pi\) | ||||
0.531657 | + | 0.846960i | \(0.321570\pi\) | |||||||
\(200\) | 43.6283 | 3.08499 | ||||||||
\(201\) | 1.39063 | 0.0980872 | ||||||||
\(202\) | −31.5761 | −2.22169 | ||||||||
\(203\) | −9.19377 | −0.645276 | ||||||||
\(204\) | 5.89199 | 0.412522 | ||||||||
\(205\) | 0.378812 | 0.0264573 | ||||||||
\(206\) | −3.78833 | −0.263945 | ||||||||
\(207\) | 5.22431 | 0.363114 | ||||||||
\(208\) | 35.1859 | 2.43970 | ||||||||
\(209\) | 18.1983 | 1.25880 | ||||||||
\(210\) | 0.120718 | 0.00833033 | ||||||||
\(211\) | −10.2685 | −0.706915 | −0.353457 | − | 0.935451i | \(-0.614994\pi\) | ||||
−0.353457 | + | 0.935451i | \(0.614994\pi\) | |||||||
\(212\) | 13.8244 | 0.949465 | ||||||||
\(213\) | 1.75032 | 0.119930 | ||||||||
\(214\) | 49.1518 | 3.35995 | ||||||||
\(215\) | 1.83648 | 0.125247 | ||||||||
\(216\) | 13.0891 | 0.890602 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | −27.1450 | −1.83849 | ||||||||
\(219\) | −2.41089 | −0.162913 | ||||||||
\(220\) | 3.43713 | 0.231731 | ||||||||
\(221\) | 11.9475 | 0.803676 | ||||||||
\(222\) | −0.676426 | −0.0453987 | ||||||||
\(223\) | 9.76360 | 0.653819 | 0.326909 | − | 0.945056i | \(-0.393993\pi\) | ||||
0.326909 | + | 0.945056i | \(0.393993\pi\) | |||||||
\(224\) | 17.8447 | 1.19230 | ||||||||
\(225\) | 14.5913 | 0.972754 | ||||||||
\(226\) | 12.3104 | 0.818872 | ||||||||
\(227\) | −12.3276 | −0.818210 | −0.409105 | − | 0.912487i | \(-0.634159\pi\) | ||||
−0.409105 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(228\) | 6.56171 | 0.434560 | ||||||||
\(229\) | −13.3595 | −0.882818 | −0.441409 | − | 0.897306i | \(-0.645521\pi\) | ||||
−0.441409 | + | 0.897306i | \(0.645521\pi\) | |||||||
\(230\) | 0.855320 | 0.0563981 | ||||||||
\(231\) | −0.919364 | −0.0604897 | ||||||||
\(232\) | −80.7360 | −5.30058 | ||||||||
\(233\) | 27.3040 | 1.78874 | 0.894371 | − | 0.447325i | \(-0.147623\pi\) | ||||
0.894371 | + | 0.447325i | \(0.147623\pi\) | |||||||
\(234\) | 21.1867 | 1.38502 | ||||||||
\(235\) | −1.25986 | −0.0821844 | ||||||||
\(236\) | 74.9021 | 4.87571 | ||||||||
\(237\) | −2.59341 | −0.168460 | ||||||||
\(238\) | 12.0229 | 0.779328 | ||||||||
\(239\) | −14.1941 | −0.918139 | −0.459069 | − | 0.888400i | \(-0.651817\pi\) | ||||
−0.459069 | + | 0.888400i | \(0.651817\pi\) | |||||||
\(240\) | 0.588812 | 0.0380076 | ||||||||
\(241\) | −1.35010 | −0.0869678 | −0.0434839 | − | 0.999054i | \(-0.513846\pi\) | ||||
−0.0434839 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(242\) | −6.49340 | −0.417411 | ||||||||
\(243\) | 6.58965 | 0.422726 | ||||||||
\(244\) | 26.0337 | 1.66664 | ||||||||
\(245\) | 0.178464 | 0.0114017 | ||||||||
\(246\) | −1.43579 | −0.0915427 | ||||||||
\(247\) | 13.3055 | 0.846609 | ||||||||
\(248\) | 8.78160 | 0.557632 | ||||||||
\(249\) | 0.0141790 | 0.000898557 0 | ||||||||
\(250\) | 4.79307 | 0.303141 | ||||||||
\(251\) | −13.8546 | −0.874492 | −0.437246 | − | 0.899342i | \(-0.644046\pi\) | ||||
−0.437246 | + | 0.899342i | \(0.644046\pi\) | |||||||
\(252\) | 15.4464 | 0.973034 | ||||||||
\(253\) | −6.51394 | −0.409528 | ||||||||
\(254\) | −22.7948 | −1.43027 | ||||||||
\(255\) | 0.199933 | 0.0125203 | ||||||||
\(256\) | 18.4721 | 1.15451 | ||||||||
\(257\) | 23.5301 | 1.46777 | 0.733883 | − | 0.679276i | \(-0.237706\pi\) | ||||
0.733883 | + | 0.679276i | \(0.237706\pi\) | |||||||
\(258\) | −6.96074 | −0.433356 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | 2.51302 | 0.155851 | ||||||||
\(261\) | −27.0018 | −1.67137 | ||||||||
\(262\) | −33.8120 | −2.08891 | ||||||||
\(263\) | −3.46948 | −0.213937 | −0.106969 | − | 0.994262i | \(-0.534114\pi\) | ||||
−0.106969 | + | 0.994262i | \(0.534114\pi\) | |||||||
\(264\) | −8.07348 | −0.496888 | ||||||||
\(265\) | 0.469105 | 0.0288169 | ||||||||
\(266\) | 13.3895 | 0.820961 | ||||||||
\(267\) | −2.56693 | −0.157094 | ||||||||
\(268\) | 29.1318 | 1.77951 | ||||||||
\(269\) | −20.8782 | −1.27297 | −0.636483 | − | 0.771291i | \(-0.719611\pi\) | ||||
−0.636483 | + | 0.771291i | \(0.719611\pi\) | |||||||
\(270\) | 0.716699 | 0.0436169 | ||||||||
\(271\) | 31.9346 | 1.93989 | 0.969946 | − | 0.243321i | \(-0.0782369\pi\) | ||||
0.969946 | + | 0.243321i | \(0.0782369\pi\) | |||||||
\(272\) | 58.6426 | 3.55573 | ||||||||
\(273\) | −0.672184 | −0.0406824 | ||||||||
\(274\) | −19.9727 | −1.20660 | ||||||||
\(275\) | −18.1932 | −1.09709 | ||||||||
\(276\) | −2.34871 | −0.141376 | ||||||||
\(277\) | −31.4435 | −1.88926 | −0.944630 | − | 0.328139i | \(-0.893579\pi\) | ||||
−0.944630 | + | 0.328139i | \(0.893579\pi\) | |||||||
\(278\) | 39.9519 | 2.39615 | ||||||||
\(279\) | 2.93697 | 0.175832 | ||||||||
\(280\) | 1.56720 | 0.0936583 | ||||||||
\(281\) | −6.49411 | −0.387406 | −0.193703 | − | 0.981060i | \(-0.562050\pi\) | ||||
−0.193703 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(282\) | 4.77520 | 0.284359 | ||||||||
\(283\) | 14.8968 | 0.885523 | 0.442762 | − | 0.896639i | \(-0.353999\pi\) | ||||
0.442762 | + | 0.896639i | \(0.353999\pi\) | |||||||
\(284\) | 36.6668 | 2.17578 | ||||||||
\(285\) | 0.222659 | 0.0131892 | ||||||||
\(286\) | −26.4167 | −1.56205 | ||||||||
\(287\) | −2.12262 | −0.125294 | ||||||||
\(288\) | 52.4094 | 3.08825 | ||||||||
\(289\) | 2.91233 | 0.171314 | ||||||||
\(290\) | −4.42072 | −0.259594 | ||||||||
\(291\) | −4.13752 | −0.242546 | ||||||||
\(292\) | −50.5049 | −2.95558 | ||||||||
\(293\) | 5.35259 | 0.312702 | 0.156351 | − | 0.987702i | \(-0.450027\pi\) | ||||
0.156351 | + | 0.987702i | \(0.450027\pi\) | |||||||
\(294\) | −0.676426 | −0.0394499 | ||||||||
\(295\) | 2.54166 | 0.147981 | ||||||||
\(296\) | −8.78160 | −0.510420 | ||||||||
\(297\) | −5.45824 | −0.316719 | ||||||||
\(298\) | −46.0553 | −2.66791 | ||||||||
\(299\) | −4.76261 | −0.275429 | ||||||||
\(300\) | −6.55988 | −0.378735 | ||||||||
\(301\) | −10.2905 | −0.593133 | ||||||||
\(302\) | −10.4469 | −0.601151 | ||||||||
\(303\) | 2.94227 | 0.169029 | ||||||||
\(304\) | 65.3083 | 3.74569 | ||||||||
\(305\) | 0.883403 | 0.0505835 | ||||||||
\(306\) | 35.3109 | 2.01859 | ||||||||
\(307\) | 9.86897 | 0.563252 | 0.281626 | − | 0.959524i | \(-0.409126\pi\) | ||||
0.281626 | + | 0.959524i | \(0.409126\pi\) | |||||||
\(308\) | −19.2594 | −1.09741 | ||||||||
\(309\) | 0.352998 | 0.0200813 | ||||||||
\(310\) | 0.480839 | 0.0273098 | ||||||||
\(311\) | 8.89263 | 0.504255 | 0.252127 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252127 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(312\) | −5.90285 | −0.334183 | ||||||||
\(313\) | 3.89005 | 0.219879 | 0.109939 | − | 0.993938i | \(-0.464934\pi\) | ||||
0.109939 | + | 0.993938i | \(0.464934\pi\) | |||||||
\(314\) | 3.78211 | 0.213437 | ||||||||
\(315\) | 0.524145 | 0.0295322 | ||||||||
\(316\) | −54.3284 | −3.05621 | ||||||||
\(317\) | −2.84496 | −0.159789 | −0.0798945 | − | 0.996803i | \(-0.525458\pi\) | ||||
−0.0798945 | + | 0.996803i | \(0.525458\pi\) | |||||||
\(318\) | −1.77803 | −0.0997067 | ||||||||
\(319\) | 33.6673 | 1.88501 | ||||||||
\(320\) | 3.88976 | 0.217444 | ||||||||
\(321\) | −4.57999 | −0.255630 | ||||||||
\(322\) | −4.79266 | −0.267085 | ||||||||
\(323\) | 22.1757 | 1.23389 | ||||||||
\(324\) | 44.3713 | 2.46507 | ||||||||
\(325\) | −13.3018 | −0.737852 | ||||||||
\(326\) | 34.9304 | 1.93462 | ||||||||
\(327\) | 2.52938 | 0.139875 | ||||||||
\(328\) | −18.6400 | −1.02922 | ||||||||
\(329\) | 7.05947 | 0.389201 | ||||||||
\(330\) | −0.442066 | −0.0243349 | ||||||||
\(331\) | −3.23889 | −0.178025 | −0.0890127 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890127 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(332\) | 0.297031 | 0.0163017 | ||||||||
\(333\) | −2.93697 | −0.160945 | ||||||||
\(334\) | −4.40703 | −0.241142 | ||||||||
\(335\) | 0.988530 | 0.0540092 | ||||||||
\(336\) | −3.29932 | −0.179993 | ||||||||
\(337\) | 12.8106 | 0.697839 | 0.348920 | − | 0.937153i | \(-0.386549\pi\) | ||||
0.348920 | + | 0.937153i | \(0.386549\pi\) | |||||||
\(338\) | 15.7117 | 0.854604 | ||||||||
\(339\) | −1.14708 | −0.0623010 | ||||||||
\(340\) | 4.18834 | 0.227144 | ||||||||
\(341\) | −3.66197 | −0.198307 | ||||||||
\(342\) | 39.3245 | 2.12642 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −90.3667 | −4.87225 | ||||||||
\(345\) | −0.0796991 | −0.00429085 | ||||||||
\(346\) | −22.3238 | −1.20013 | ||||||||
\(347\) | 2.50700 | 0.134583 | 0.0672915 | − | 0.997733i | \(-0.478564\pi\) | ||||
0.0672915 | + | 0.997733i | \(0.478564\pi\) | |||||||
\(348\) | 12.1393 | 0.650737 | ||||||||
\(349\) | −4.11264 | −0.220144 | −0.110072 | − | 0.993924i | \(-0.535108\pi\) | ||||
−0.110072 | + | 0.993924i | \(0.535108\pi\) | |||||||
\(350\) | −13.3857 | −0.715498 | ||||||||
\(351\) | −3.99074 | −0.213010 | ||||||||
\(352\) | −65.3468 | −3.48300 | ||||||||
\(353\) | 16.8364 | 0.896112 | 0.448056 | − | 0.894005i | \(-0.352116\pi\) | ||||
0.448056 | + | 0.894005i | \(0.352116\pi\) | |||||||
\(354\) | −9.63353 | −0.512016 | ||||||||
\(355\) | 1.24422 | 0.0660362 | ||||||||
\(356\) | −53.7738 | −2.85001 | ||||||||
\(357\) | −1.12030 | −0.0592924 | ||||||||
\(358\) | 8.80342 | 0.465275 | ||||||||
\(359\) | 8.63293 | 0.455628 | 0.227814 | − | 0.973705i | \(-0.426842\pi\) | ||||
0.227814 | + | 0.973705i | \(0.426842\pi\) | |||||||
\(360\) | 4.60283 | 0.242590 | ||||||||
\(361\) | 5.69626 | 0.299803 | ||||||||
\(362\) | 39.6634 | 2.08466 | ||||||||
\(363\) | 0.605057 | 0.0317573 | ||||||||
\(364\) | −14.0814 | −0.738064 | ||||||||
\(365\) | −1.71379 | −0.0897036 | ||||||||
\(366\) | −3.34832 | −0.175019 | ||||||||
\(367\) | 23.5229 | 1.22789 | 0.613944 | − | 0.789350i | \(-0.289582\pi\) | ||||
0.613944 | + | 0.789350i | \(0.289582\pi\) | |||||||
\(368\) | −23.3766 | −1.21859 | ||||||||
\(369\) | −6.23406 | −0.324532 | ||||||||
\(370\) | −0.480839 | −0.0249976 | ||||||||
\(371\) | −2.62856 | −0.136468 | ||||||||
\(372\) | −1.32039 | −0.0684589 | ||||||||
\(373\) | −22.0977 | −1.14418 | −0.572088 | − | 0.820192i | \(-0.693867\pi\) | ||||
−0.572088 | + | 0.820192i | \(0.693867\pi\) | |||||||
\(374\) | −44.0275 | −2.27661 | ||||||||
\(375\) | −0.446621 | −0.0230634 | ||||||||
\(376\) | 61.9934 | 3.19706 | ||||||||
\(377\) | 24.6156 | 1.26777 | ||||||||
\(378\) | −4.01592 | −0.206557 | ||||||||
\(379\) | 7.65737 | 0.393332 | 0.196666 | − | 0.980470i | \(-0.436988\pi\) | ||||
0.196666 | + | 0.980470i | \(0.436988\pi\) | |||||||
\(380\) | 4.66440 | 0.239279 | ||||||||
\(381\) | 2.12403 | 0.108817 | ||||||||
\(382\) | 57.4435 | 2.93907 | ||||||||
\(383\) | −3.82347 | −0.195370 | −0.0976852 | − | 0.995217i | \(-0.531144\pi\) | ||||
−0.0976852 | + | 0.995217i | \(0.531144\pi\) | |||||||
\(384\) | −5.78311 | −0.295118 | ||||||||
\(385\) | −0.653532 | −0.0333071 | ||||||||
\(386\) | 0.598174 | 0.0304462 | ||||||||
\(387\) | −30.2228 | −1.53631 | ||||||||
\(388\) | −86.6755 | −4.40028 | ||||||||
\(389\) | 23.4442 | 1.18867 | 0.594334 | − | 0.804218i | \(-0.297416\pi\) | ||||
0.594334 | + | 0.804218i | \(0.297416\pi\) | |||||||
\(390\) | −0.323212 | −0.0163665 | ||||||||
\(391\) | −7.93762 | −0.401423 | ||||||||
\(392\) | −8.78160 | −0.443538 | ||||||||
\(393\) | 3.15062 | 0.158928 | ||||||||
\(394\) | −63.2256 | −3.18526 | ||||||||
\(395\) | −1.84353 | −0.0927580 | ||||||||
\(396\) | −56.5644 | −2.84247 | ||||||||
\(397\) | −20.2982 | −1.01874 | −0.509368 | − | 0.860549i | \(-0.670121\pi\) | ||||
−0.509368 | + | 0.860549i | \(0.670121\pi\) | |||||||
\(398\) | −40.4143 | −2.02579 | ||||||||
\(399\) | −1.24764 | −0.0624599 | ||||||||
\(400\) | −65.2901 | −3.26450 | ||||||||
\(401\) | −25.3918 | −1.26801 | −0.634003 | − | 0.773330i | \(-0.718589\pi\) | ||||
−0.634003 | + | 0.773330i | \(0.718589\pi\) | |||||||
\(402\) | −3.74678 | −0.186872 | ||||||||
\(403\) | −2.67742 | −0.133372 | ||||||||
\(404\) | 61.6367 | 3.06654 | ||||||||
\(405\) | 1.50565 | 0.0748165 | ||||||||
\(406\) | 24.7709 | 1.22936 | ||||||||
\(407\) | 3.66197 | 0.181517 | ||||||||
\(408\) | −9.83800 | −0.487054 | ||||||||
\(409\) | 7.86515 | 0.388907 | 0.194453 | − | 0.980912i | \(-0.437707\pi\) | ||||
0.194453 | + | 0.980912i | \(0.437707\pi\) | |||||||
\(410\) | −1.02064 | −0.0504056 | ||||||||
\(411\) | 1.86107 | 0.0917996 | ||||||||
\(412\) | 7.39484 | 0.364317 | ||||||||
\(413\) | −14.2418 | −0.700794 | ||||||||
\(414\) | −14.0759 | −0.691793 | ||||||||
\(415\) | 0.0100792 | 0.000494767 0 | ||||||||
\(416\) | −47.7777 | −2.34249 | ||||||||
\(417\) | −3.72273 | −0.182303 | ||||||||
\(418\) | −49.0319 | −2.39823 | ||||||||
\(419\) | 14.7585 | 0.721001 | 0.360500 | − | 0.932759i | \(-0.382606\pi\) | ||||
0.360500 | + | 0.932759i | \(0.382606\pi\) | |||||||
\(420\) | −0.235642 | −0.0114982 | ||||||||
\(421\) | −28.8854 | −1.40779 | −0.703894 | − | 0.710305i | \(-0.748557\pi\) | ||||
−0.703894 | + | 0.710305i | \(0.748557\pi\) | |||||||
\(422\) | 27.6666 | 1.34679 | ||||||||
\(423\) | 20.7334 | 1.00809 | ||||||||
\(424\) | −23.0830 | −1.12101 | ||||||||
\(425\) | −22.1695 | −1.07538 | ||||||||
\(426\) | −4.71590 | −0.228486 | ||||||||
\(427\) | −4.95002 | −0.239548 | ||||||||
\(428\) | −95.9447 | −4.63766 | ||||||||
\(429\) | 2.46152 | 0.118843 | ||||||||
\(430\) | −4.94806 | −0.238616 | ||||||||
\(431\) | 32.6594 | 1.57315 | 0.786575 | − | 0.617495i | \(-0.211852\pi\) | ||||
0.786575 | + | 0.617495i | \(0.211852\pi\) | |||||||
\(432\) | −19.5880 | −0.942427 | ||||||||
\(433\) | 14.3364 | 0.688966 | 0.344483 | − | 0.938793i | \(-0.388054\pi\) | ||||
0.344483 | + | 0.938793i | \(0.388054\pi\) | |||||||
\(434\) | −2.69431 | −0.129331 | ||||||||
\(435\) | 0.411925 | 0.0197503 | ||||||||
\(436\) | 52.9872 | 2.53763 | ||||||||
\(437\) | −8.83985 | −0.422867 | ||||||||
\(438\) | 6.49568 | 0.310376 | ||||||||
\(439\) | −17.3154 | −0.826421 | −0.413211 | − | 0.910635i | \(-0.635593\pi\) | ||||
−0.413211 | + | 0.910635i | \(0.635593\pi\) | |||||||
\(440\) | −5.73905 | −0.273599 | ||||||||
\(441\) | −2.93697 | −0.139856 | ||||||||
\(442\) | −32.1903 | −1.53114 | ||||||||
\(443\) | −17.4383 | −0.828520 | −0.414260 | − | 0.910159i | \(-0.635960\pi\) | ||||
−0.414260 | + | 0.910159i | \(0.635960\pi\) | |||||||
\(444\) | 1.32039 | 0.0626628 | ||||||||
\(445\) | −1.82471 | −0.0864995 | ||||||||
\(446\) | −26.3062 | −1.24563 | ||||||||
\(447\) | 4.29146 | 0.202979 | ||||||||
\(448\) | −21.7957 | −1.02975 | ||||||||
\(449\) | −3.82243 | −0.180392 | −0.0901959 | − | 0.995924i | \(-0.528749\pi\) | ||||
−0.0901959 | + | 0.995924i | \(0.528749\pi\) | |||||||
\(450\) | −39.3135 | −1.85326 | ||||||||
\(451\) | 7.77296 | 0.366014 | ||||||||
\(452\) | −24.0299 | −1.13027 | ||||||||
\(453\) | 0.973446 | 0.0457365 | ||||||||
\(454\) | 33.2143 | 1.55883 | ||||||||
\(455\) | −0.477824 | −0.0224007 | ||||||||
\(456\) | −10.9562 | −0.513073 | ||||||||
\(457\) | −2.76990 | −0.129571 | −0.0647853 | − | 0.997899i | \(-0.520636\pi\) | ||||
−0.0647853 | + | 0.997899i | \(0.520636\pi\) | |||||||
\(458\) | 35.9945 | 1.68191 | ||||||||
\(459\) | −6.65117 | −0.310450 | ||||||||
\(460\) | −1.66959 | −0.0778450 | ||||||||
\(461\) | −3.98753 | −0.185718 | −0.0928589 | − | 0.995679i | \(-0.529601\pi\) | ||||
−0.0928589 | + | 0.995679i | \(0.529601\pi\) | |||||||
\(462\) | 2.47705 | 0.115243 | ||||||||
\(463\) | −12.7326 | −0.591734 | −0.295867 | − | 0.955229i | \(-0.595608\pi\) | ||||
−0.295867 | + | 0.955229i | \(0.595608\pi\) | |||||||
\(464\) | 120.822 | 5.60902 | ||||||||
\(465\) | −0.0448048 | −0.00207777 | ||||||||
\(466\) | −73.5654 | −3.40785 | ||||||||
\(467\) | −3.02487 | −0.139974 | −0.0699872 | − | 0.997548i | \(-0.522296\pi\) | ||||
−0.0699872 | + | 0.997548i | \(0.522296\pi\) | |||||||
\(468\) | −41.3566 | −1.91171 | ||||||||
\(469\) | −5.53909 | −0.255771 | ||||||||
\(470\) | 3.39446 | 0.156575 | ||||||||
\(471\) | −0.352419 | −0.0162386 | ||||||||
\(472\) | −125.066 | −5.75662 | ||||||||
\(473\) | 37.6834 | 1.73268 | ||||||||
\(474\) | 6.98744 | 0.320944 | ||||||||
\(475\) | −24.6894 | −1.13283 | ||||||||
\(476\) | −23.4687 | −1.07569 | ||||||||
\(477\) | −7.72000 | −0.353475 | ||||||||
\(478\) | 38.2433 | 1.74921 | ||||||||
\(479\) | 9.28028 | 0.424027 | 0.212013 | − | 0.977267i | \(-0.431998\pi\) | ||||
0.212013 | + | 0.977267i | \(0.431998\pi\) | |||||||
\(480\) | −0.799528 | −0.0364933 | ||||||||
\(481\) | 2.67742 | 0.122080 | ||||||||
\(482\) | 3.63760 | 0.165688 | ||||||||
\(483\) | 0.446582 | 0.0203202 | ||||||||
\(484\) | 12.6751 | 0.576143 | ||||||||
\(485\) | −2.94117 | −0.133551 | ||||||||
\(486\) | −17.7546 | −0.805363 | ||||||||
\(487\) | −19.2271 | −0.871264 | −0.435632 | − | 0.900125i | \(-0.643475\pi\) | ||||
−0.435632 | + | 0.900125i | \(0.643475\pi\) | |||||||
\(488\) | −43.4691 | −1.96775 | ||||||||
\(489\) | −3.25483 | −0.147189 | ||||||||
\(490\) | −0.480839 | −0.0217221 | ||||||||
\(491\) | 16.8385 | 0.759910 | 0.379955 | − | 0.925005i | \(-0.375940\pi\) | ||||
0.379955 | + | 0.925005i | \(0.375940\pi\) | |||||||
\(492\) | 2.80267 | 0.126354 | ||||||||
\(493\) | 41.0256 | 1.84770 | ||||||||
\(494\) | −35.8492 | −1.61293 | ||||||||
\(495\) | −1.91940 | −0.0862708 | ||||||||
\(496\) | −13.1417 | −0.590081 | ||||||||
\(497\) | −6.97179 | −0.312728 | ||||||||
\(498\) | −0.0382026 | −0.00171190 | ||||||||
\(499\) | 24.6499 | 1.10348 | 0.551741 | − | 0.834015i | \(-0.313964\pi\) | ||||
0.551741 | + | 0.834015i | \(0.313964\pi\) | |||||||
\(500\) | −9.35611 | −0.418418 | ||||||||
\(501\) | 0.410649 | 0.0183464 | ||||||||
\(502\) | 37.3285 | 1.66605 | ||||||||
\(503\) | 0.925447 | 0.0412637 | 0.0206318 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206318 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(504\) | −25.7913 | −1.14884 | ||||||||
\(505\) | 2.09152 | 0.0930715 | ||||||||
\(506\) | 17.5506 | 0.780219 | ||||||||
\(507\) | −1.46402 | −0.0650196 | ||||||||
\(508\) | 44.4956 | 1.97417 | ||||||||
\(509\) | 41.2831 | 1.82984 | 0.914920 | − | 0.403635i | \(-0.132253\pi\) | ||||
0.914920 | + | 0.403635i | \(0.132253\pi\) | |||||||
\(510\) | −0.538683 | −0.0238533 | ||||||||
\(511\) | 9.60295 | 0.424809 | ||||||||
\(512\) | −3.69957 | −0.163500 | ||||||||
\(513\) | −7.40718 | −0.327035 | ||||||||
\(514\) | −63.3974 | −2.79634 | ||||||||
\(515\) | 0.250929 | 0.0110573 | ||||||||
\(516\) | 13.5874 | 0.598152 | ||||||||
\(517\) | −25.8516 | −1.13695 | ||||||||
\(518\) | 2.69431 | 0.118381 | ||||||||
\(519\) | 2.08014 | 0.0913080 | ||||||||
\(520\) | −4.19605 | −0.184009 | ||||||||
\(521\) | 34.5280 | 1.51270 | 0.756349 | − | 0.654168i | \(-0.226981\pi\) | ||||
0.756349 | + | 0.654168i | \(0.226981\pi\) | |||||||
\(522\) | 72.7514 | 3.18424 | ||||||||
\(523\) | 16.1455 | 0.705991 | 0.352996 | − | 0.935625i | \(-0.385163\pi\) | ||||
0.352996 | + | 0.935625i | \(0.385163\pi\) | |||||||
\(524\) | 66.0012 | 2.88328 | ||||||||
\(525\) | 1.24729 | 0.0544362 | ||||||||
\(526\) | 9.34786 | 0.407586 | ||||||||
\(527\) | −4.46232 | −0.194382 | ||||||||
\(528\) | 12.0820 | 0.525803 | ||||||||
\(529\) | −19.8358 | −0.862428 | ||||||||
\(530\) | −1.26391 | −0.0549009 | ||||||||
\(531\) | −41.8278 | −1.81517 | ||||||||
\(532\) | −26.1363 | −1.13315 | ||||||||
\(533\) | 5.68313 | 0.246164 | ||||||||
\(534\) | 6.91611 | 0.299289 | ||||||||
\(535\) | −3.25570 | −0.140756 | ||||||||
\(536\) | −48.6420 | −2.10102 | ||||||||
\(537\) | −0.820306 | −0.0353988 | ||||||||
\(538\) | 56.2524 | 2.42521 | ||||||||
\(539\) | 3.66197 | 0.157732 | ||||||||
\(540\) | −1.39900 | −0.0602034 | ||||||||
\(541\) | 15.0906 | 0.648794 | 0.324397 | − | 0.945921i | \(-0.394839\pi\) | ||||
0.324397 | + | 0.945921i | \(0.394839\pi\) | |||||||
\(542\) | −86.0419 | −3.69581 | ||||||||
\(543\) | −3.69585 | −0.158604 | ||||||||
\(544\) | −79.6288 | −3.41406 | ||||||||
\(545\) | 1.79802 | 0.0770186 | ||||||||
\(546\) | 1.81107 | 0.0775068 | ||||||||
\(547\) | −32.8676 | −1.40532 | −0.702659 | − | 0.711527i | \(-0.748004\pi\) | ||||
−0.702659 | + | 0.711527i | \(0.748004\pi\) | |||||||
\(548\) | 38.9868 | 1.66544 | ||||||||
\(549\) | −14.5381 | −0.620469 | ||||||||
\(550\) | 49.0182 | 2.09014 | ||||||||
\(551\) | 45.6888 | 1.94641 | ||||||||
\(552\) | 3.92170 | 0.166919 | ||||||||
\(553\) | 10.3299 | 0.439274 | ||||||||
\(554\) | 84.7187 | 3.59935 | ||||||||
\(555\) | 0.0448048 | 0.00190186 | ||||||||
\(556\) | −77.9863 | −3.30736 | ||||||||
\(557\) | 13.7036 | 0.580640 | 0.290320 | − | 0.956930i | \(-0.406238\pi\) | ||||
0.290320 | + | 0.956930i | \(0.406238\pi\) | |||||||
\(558\) | −7.91311 | −0.334989 | ||||||||
\(559\) | 27.5519 | 1.16532 | ||||||||
\(560\) | −2.34533 | −0.0991083 | ||||||||
\(561\) | 4.10250 | 0.173208 | ||||||||
\(562\) | 17.4971 | 0.738073 | ||||||||
\(563\) | 5.11925 | 0.215751 | 0.107875 | − | 0.994164i | \(-0.465595\pi\) | ||||
0.107875 | + | 0.994164i | \(0.465595\pi\) | |||||||
\(564\) | −9.32122 | −0.392494 | ||||||||
\(565\) | −0.815407 | −0.0343044 | ||||||||
\(566\) | −40.1366 | −1.68707 | ||||||||
\(567\) | −8.43671 | −0.354308 | ||||||||
\(568\) | −61.2235 | −2.56888 | ||||||||
\(569\) | 20.9523 | 0.878367 | 0.439184 | − | 0.898397i | \(-0.355268\pi\) | ||||
0.439184 | + | 0.898397i | \(0.355268\pi\) | |||||||
\(570\) | −0.599912 | −0.0251275 | ||||||||
\(571\) | −32.9140 | −1.37741 | −0.688704 | − | 0.725042i | \(-0.741820\pi\) | ||||
−0.688704 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(572\) | 51.5656 | 2.15606 | ||||||||
\(573\) | −5.35261 | −0.223608 | ||||||||
\(574\) | 5.71899 | 0.238706 | ||||||||
\(575\) | 8.83739 | 0.368544 | ||||||||
\(576\) | −64.0134 | −2.66723 | ||||||||
\(577\) | −21.5461 | −0.896978 | −0.448489 | − | 0.893788i | \(-0.648038\pi\) | ||||
−0.448489 | + | 0.893788i | \(0.648038\pi\) | |||||||
\(578\) | −7.84673 | −0.326381 | ||||||||
\(579\) | −0.0557381 | −0.00231640 | ||||||||
\(580\) | 8.62928 | 0.358311 | ||||||||
\(581\) | −0.0564772 | −0.00234307 | ||||||||
\(582\) | 11.1478 | 0.462090 | ||||||||
\(583\) | 9.62571 | 0.398656 | ||||||||
\(584\) | 84.3292 | 3.48957 | ||||||||
\(585\) | −1.40335 | −0.0580216 | ||||||||
\(586\) | −14.4216 | −0.595749 | ||||||||
\(587\) | −1.32271 | −0.0545942 | −0.0272971 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272971 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(588\) | 1.32039 | 0.0544518 | ||||||||
\(589\) | −4.96953 | −0.204766 | ||||||||
\(590\) | −6.84802 | −0.281928 | ||||||||
\(591\) | 5.89139 | 0.242339 | ||||||||
\(592\) | 13.1417 | 0.540122 | ||||||||
\(593\) | −17.2230 | −0.707264 | −0.353632 | − | 0.935385i | \(-0.615053\pi\) | ||||
−0.353632 | + | 0.935385i | \(0.615053\pi\) | |||||||
\(594\) | 14.7062 | 0.603402 | ||||||||
\(595\) | −0.796366 | −0.0326478 | ||||||||
\(596\) | 89.9003 | 3.68246 | ||||||||
\(597\) | 3.76582 | 0.154125 | ||||||||
\(598\) | 12.8320 | 0.524737 | ||||||||
\(599\) | −9.67484 | −0.395303 | −0.197652 | − | 0.980272i | \(-0.563331\pi\) | ||||
−0.197652 | + | 0.980272i | \(0.563331\pi\) | |||||||
\(600\) | 10.9532 | 0.447162 | ||||||||
\(601\) | 27.5006 | 1.12177 | 0.560886 | − | 0.827893i | \(-0.310461\pi\) | ||||
0.560886 | + | 0.827893i | \(0.310461\pi\) | |||||||
\(602\) | 27.7257 | 1.13002 | ||||||||
\(603\) | −16.2681 | −0.662490 | ||||||||
\(604\) | 20.3924 | 0.829755 | ||||||||
\(605\) | 0.430106 | 0.0174863 | ||||||||
\(606\) | −7.92740 | −0.322029 | ||||||||
\(607\) | −39.9500 | −1.62152 | −0.810761 | − | 0.585377i | \(-0.800947\pi\) | ||||
−0.810761 | + | 0.585377i | \(0.800947\pi\) | |||||||
\(608\) | −88.6799 | −3.59644 | ||||||||
\(609\) | −2.30816 | −0.0935314 | ||||||||
\(610\) | −2.38016 | −0.0963699 | ||||||||
\(611\) | −18.9011 | −0.764658 | ||||||||
\(612\) | −68.9270 | −2.78621 | ||||||||
\(613\) | −12.1820 | −0.492026 | −0.246013 | − | 0.969267i | \(-0.579121\pi\) | ||||
−0.246013 | + | 0.969267i | \(0.579121\pi\) | |||||||
\(614\) | −26.5901 | −1.07309 | ||||||||
\(615\) | 0.0951033 | 0.00383493 | ||||||||
\(616\) | 32.1580 | 1.29568 | ||||||||
\(617\) | 9.28903 | 0.373962 | 0.186981 | − | 0.982364i | \(-0.440130\pi\) | ||||
0.186981 | + | 0.982364i | \(0.440130\pi\) | |||||||
\(618\) | −0.951086 | −0.0382583 | ||||||||
\(619\) | 26.9927 | 1.08493 | 0.542465 | − | 0.840078i | \(-0.317491\pi\) | ||||
0.542465 | + | 0.840078i | \(0.317491\pi\) | |||||||
\(620\) | −0.938600 | −0.0376951 | ||||||||
\(621\) | 2.65135 | 0.106395 | ||||||||
\(622\) | −23.9595 | −0.960689 | ||||||||
\(623\) | 10.2245 | 0.409636 | ||||||||
\(624\) | 8.83366 | 0.353629 | ||||||||
\(625\) | 24.5233 | 0.980931 | ||||||||
\(626\) | −10.4810 | −0.418905 | ||||||||
\(627\) | 4.56881 | 0.182461 | ||||||||
\(628\) | −7.38271 | −0.294602 | ||||||||
\(629\) | 4.46232 | 0.177924 | ||||||||
\(630\) | −1.41221 | −0.0562638 | ||||||||
\(631\) | 23.1780 | 0.922703 | 0.461351 | − | 0.887217i | \(-0.347365\pi\) | ||||
0.461351 | + | 0.887217i | \(0.347365\pi\) | |||||||
\(632\) | 90.7134 | 3.60839 | ||||||||
\(633\) | −2.57799 | −0.102466 | ||||||||
\(634\) | 7.66522 | 0.304425 | ||||||||
\(635\) | 1.50987 | 0.0599174 | ||||||||
\(636\) | 3.47072 | 0.137623 | ||||||||
\(637\) | 2.67742 | 0.106083 | ||||||||
\(638\) | −90.7103 | −3.59125 | ||||||||
\(639\) | −20.4759 | −0.810016 | ||||||||
\(640\) | −4.11094 | −0.162499 | ||||||||
\(641\) | 17.8433 | 0.704767 | 0.352383 | − | 0.935856i | \(-0.385371\pi\) | ||||
0.352383 | + | 0.935856i | \(0.385371\pi\) | |||||||
\(642\) | 12.3399 | 0.487018 | ||||||||
\(643\) | −16.7184 | −0.659308 | −0.329654 | − | 0.944102i | \(-0.606932\pi\) | ||||
−0.329654 | + | 0.944102i | \(0.606932\pi\) | |||||||
\(644\) | 9.35530 | 0.368651 | ||||||||
\(645\) | 0.461062 | 0.0181543 | ||||||||
\(646\) | −59.7481 | −2.35076 | ||||||||
\(647\) | −24.1380 | −0.948962 | −0.474481 | − | 0.880266i | \(-0.657364\pi\) | ||||
−0.474481 | + | 0.880266i | \(0.657364\pi\) | |||||||
\(648\) | −74.0877 | −2.91044 | ||||||||
\(649\) | 52.1531 | 2.04719 | ||||||||
\(650\) | 35.8392 | 1.40573 | ||||||||
\(651\) | 0.251057 | 0.00983970 | ||||||||
\(652\) | −68.1844 | −2.67031 | ||||||||
\(653\) | −47.3406 | −1.85258 | −0.926291 | − | 0.376810i | \(-0.877021\pi\) | ||||
−0.926291 | + | 0.376810i | \(0.877021\pi\) | |||||||
\(654\) | −6.81494 | −0.266485 | ||||||||
\(655\) | 2.23962 | 0.0875093 | ||||||||
\(656\) | 27.8948 | 1.08911 | ||||||||
\(657\) | 28.2036 | 1.10033 | ||||||||
\(658\) | −19.0204 | −0.741492 | ||||||||
\(659\) | 0.00202863 | 7.90240e−5 0 | 3.95120e−5 | − | 1.00000i | \(-0.499987\pi\) | ||||
3.95120e−5 | 1.00000i | \(0.499987\pi\) | ||||||||
\(660\) | 0.862915 | 0.0335889 | ||||||||
\(661\) | 19.3540 | 0.752783 | 0.376392 | − | 0.926461i | \(-0.377165\pi\) | ||||
0.376392 | + | 0.926461i | \(0.377165\pi\) | |||||||
\(662\) | 8.72657 | 0.339168 | ||||||||
\(663\) | 2.99950 | 0.116491 | ||||||||
\(664\) | −0.495960 | −0.0192470 | ||||||||
\(665\) | −0.886885 | −0.0343919 | ||||||||
\(666\) | 7.91311 | 0.306627 | ||||||||
\(667\) | −16.3540 | −0.633228 | ||||||||
\(668\) | 8.60254 | 0.332842 | ||||||||
\(669\) | 2.45122 | 0.0947696 | ||||||||
\(670\) | −2.66341 | −0.102896 | ||||||||
\(671\) | 18.1268 | 0.699779 | ||||||||
\(672\) | 4.48004 | 0.172821 | ||||||||
\(673\) | 7.06381 | 0.272290 | 0.136145 | − | 0.990689i | \(-0.456529\pi\) | ||||
0.136145 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(674\) | −34.5158 | −1.32950 | ||||||||
\(675\) | 7.40512 | 0.285023 | ||||||||
\(676\) | −30.6694 | −1.17959 | ||||||||
\(677\) | 7.80024 | 0.299788 | 0.149894 | − | 0.988702i | \(-0.452107\pi\) | ||||
0.149894 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(678\) | 3.09060 | 0.118694 | ||||||||
\(679\) | 16.4804 | 0.632460 | ||||||||
\(680\) | −6.99337 | −0.268183 | ||||||||
\(681\) | −3.09493 | −0.118598 | ||||||||
\(682\) | 9.86649 | 0.377807 | ||||||||
\(683\) | 29.9541 | 1.14616 | 0.573081 | − | 0.819498i | \(-0.305748\pi\) | ||||
0.573081 | + | 0.819498i | \(0.305748\pi\) | |||||||
\(684\) | −76.7616 | −2.93505 | ||||||||
\(685\) | 1.32294 | 0.0505470 | ||||||||
\(686\) | 2.69431 | 0.102869 | ||||||||
\(687\) | −3.35399 | −0.127963 | ||||||||
\(688\) | 135.235 | 5.15577 | ||||||||
\(689\) | 7.03775 | 0.268117 | ||||||||
\(690\) | 0.214734 | 0.00817478 | ||||||||
\(691\) | 14.2316 | 0.541394 | 0.270697 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270697 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(692\) | 43.5762 | 1.65652 | ||||||||
\(693\) | 10.7551 | 0.408553 | ||||||||
\(694\) | −6.75464 | −0.256403 | ||||||||
\(695\) | −2.64631 | −0.100380 | ||||||||
\(696\) | −20.2693 | −0.768307 | ||||||||
\(697\) | 9.47180 | 0.358770 | ||||||||
\(698\) | 11.0807 | 0.419411 | ||||||||
\(699\) | 6.85485 | 0.259274 | ||||||||
\(700\) | 26.1290 | 0.987585 | ||||||||
\(701\) | 5.38225 | 0.203285 | 0.101642 | − | 0.994821i | \(-0.467590\pi\) | ||||
0.101642 | + | 0.994821i | \(0.467590\pi\) | |||||||
\(702\) | 10.7523 | 0.405819 | ||||||||
\(703\) | 4.96953 | 0.187430 | ||||||||
\(704\) | 79.8153 | 3.00815 | ||||||||
\(705\) | −0.316298 | −0.0119125 | ||||||||
\(706\) | −45.3626 | −1.70724 | ||||||||
\(707\) | −11.7195 | −0.440759 | ||||||||
\(708\) | 18.8047 | 0.706724 | ||||||||
\(709\) | 10.4232 | 0.391451 | 0.195725 | − | 0.980659i | \(-0.437294\pi\) | ||||
0.195725 | + | 0.980659i | \(0.437294\pi\) | |||||||
\(710\) | −3.35231 | −0.125810 | ||||||||
\(711\) | 30.3388 | 1.13779 | ||||||||
\(712\) | 89.7874 | 3.36492 | ||||||||
\(713\) | 1.77881 | 0.0666169 | ||||||||
\(714\) | 3.01843 | 0.112962 | ||||||||
\(715\) | 1.74978 | 0.0654380 | ||||||||
\(716\) | −17.1843 | −0.642209 | ||||||||
\(717\) | −3.56352 | −0.133082 | ||||||||
\(718\) | −23.2598 | −0.868048 | ||||||||
\(719\) | 28.3091 | 1.05575 | 0.527875 | − | 0.849322i | \(-0.322989\pi\) | ||||
0.527875 | + | 0.849322i | \(0.322989\pi\) | |||||||
\(720\) | −6.88817 | −0.256707 | ||||||||
\(721\) | −1.40605 | −0.0523639 | ||||||||
\(722\) | −15.3475 | −0.571175 | ||||||||
\(723\) | −0.338953 | −0.0126058 | ||||||||
\(724\) | −77.4231 | −2.87741 | ||||||||
\(725\) | −45.6761 | −1.69637 | ||||||||
\(726\) | −1.63021 | −0.0605029 | ||||||||
\(727\) | 4.42240 | 0.164018 | 0.0820088 | − | 0.996632i | \(-0.473866\pi\) | ||||
0.0820088 | + | 0.996632i | \(0.473866\pi\) | |||||||
\(728\) | 23.5120 | 0.871412 | ||||||||
\(729\) | −23.6557 | −0.876139 | ||||||||
\(730\) | 4.61747 | 0.170900 | ||||||||
\(731\) | 45.9194 | 1.69839 | ||||||||
\(732\) | 6.53594 | 0.241575 | ||||||||
\(733\) | −26.4098 | −0.975469 | −0.487735 | − | 0.872992i | \(-0.662177\pi\) | ||||
−0.487735 | + | 0.872992i | \(0.662177\pi\) | |||||||
\(734\) | −63.3781 | −2.33933 | ||||||||
\(735\) | 0.0448048 | 0.00165265 | ||||||||
\(736\) | 31.7423 | 1.17004 | ||||||||
\(737\) | 20.2840 | 0.747170 | ||||||||
\(738\) | 16.7965 | 0.618288 | ||||||||
\(739\) | 25.9483 | 0.954522 | 0.477261 | − | 0.878762i | \(-0.341630\pi\) | ||||
0.477261 | + | 0.878762i | \(0.341630\pi\) | |||||||
\(740\) | 0.938600 | 0.0345036 | ||||||||
\(741\) | 3.34044 | 0.122714 | ||||||||
\(742\) | 7.08216 | 0.259994 | ||||||||
\(743\) | −16.6151 | −0.609547 | −0.304774 | − | 0.952425i | \(-0.598581\pi\) | ||||
−0.304774 | + | 0.952425i | \(0.598581\pi\) | |||||||
\(744\) | 2.20468 | 0.0808275 | ||||||||
\(745\) | 3.05059 | 0.111765 | ||||||||
\(746\) | 59.5381 | 2.17985 | ||||||||
\(747\) | −0.165872 | −0.00606893 | ||||||||
\(748\) | 85.9419 | 3.14235 | ||||||||
\(749\) | 18.2428 | 0.666578 | ||||||||
\(750\) | 1.20333 | 0.0439396 | ||||||||
\(751\) | 20.2353 | 0.738398 | 0.369199 | − | 0.929350i | \(-0.379632\pi\) | ||||
0.369199 | + | 0.929350i | \(0.379632\pi\) | |||||||
\(752\) | −92.7736 | −3.38310 | ||||||||
\(753\) | −3.47828 | −0.126756 | ||||||||
\(754\) | −66.3220 | −2.41530 | ||||||||
\(755\) | 0.691977 | 0.0251836 | ||||||||
\(756\) | 7.83910 | 0.285105 | ||||||||
\(757\) | 2.06517 | 0.0750597 | 0.0375299 | − | 0.999296i | \(-0.488051\pi\) | ||||
0.0375299 | + | 0.999296i | \(0.488051\pi\) | |||||||
\(758\) | −20.6313 | −0.749363 | ||||||||
\(759\) | −1.63537 | −0.0593602 | ||||||||
\(760\) | −7.78827 | −0.282510 | ||||||||
\(761\) | 32.0730 | 1.16265 | 0.581324 | − | 0.813672i | \(-0.302535\pi\) | ||||
0.581324 | + | 0.813672i | \(0.302535\pi\) | |||||||
\(762\) | −5.72280 | −0.207315 | ||||||||
\(763\) | −10.0749 | −0.364737 | ||||||||
\(764\) | −112.130 | −4.05672 | ||||||||
\(765\) | −2.33890 | −0.0845633 | ||||||||
\(766\) | 10.3016 | 0.372213 | ||||||||
\(767\) | 38.1313 | 1.37684 | ||||||||
\(768\) | 4.63756 | 0.167344 | ||||||||
\(769\) | −16.8162 | −0.606408 | −0.303204 | − | 0.952926i | \(-0.598056\pi\) | ||||
−0.303204 | + | 0.952926i | \(0.598056\pi\) | |||||||
\(770\) | 1.76082 | 0.0634555 | ||||||||
\(771\) | 5.90739 | 0.212750 | ||||||||
\(772\) | −1.16764 | −0.0420242 | ||||||||
\(773\) | −40.4245 | −1.45397 | −0.726985 | − | 0.686654i | \(-0.759079\pi\) | ||||
−0.726985 | + | 0.686654i | \(0.759079\pi\) | |||||||
\(774\) | 81.4296 | 2.92693 | ||||||||
\(775\) | 4.96815 | 0.178461 | ||||||||
\(776\) | 144.724 | 5.19530 | ||||||||
\(777\) | −0.251057 | −0.00900662 | ||||||||
\(778\) | −63.1659 | −2.26461 | ||||||||
\(779\) | 10.5484 | 0.377936 | ||||||||
\(780\) | 0.630912 | 0.0225903 | ||||||||
\(781\) | 25.5305 | 0.913553 | ||||||||
\(782\) | 21.3864 | 0.764776 | ||||||||
\(783\) | −13.7035 | −0.489723 | ||||||||
\(784\) | 13.1417 | 0.469347 | ||||||||
\(785\) | −0.250518 | −0.00894137 | ||||||||
\(786\) | −8.48874 | −0.302783 | ||||||||
\(787\) | 37.4797 | 1.33601 | 0.668004 | − | 0.744157i | \(-0.267149\pi\) | ||||
0.668004 | + | 0.744157i | \(0.267149\pi\) | |||||||
\(788\) | 123.417 | 4.39654 | ||||||||
\(789\) | −0.871037 | −0.0310097 | ||||||||
\(790\) | 4.96704 | 0.176719 | ||||||||
\(791\) | 4.56902 | 0.162456 | ||||||||
\(792\) | 94.4470 | 3.35603 | ||||||||
\(793\) | 13.2533 | 0.470637 | ||||||||
\(794\) | 54.6896 | 1.94086 | ||||||||
\(795\) | 0.117772 | 0.00417694 | ||||||||
\(796\) | 78.8890 | 2.79615 | ||||||||
\(797\) | −10.2577 | −0.363346 | −0.181673 | − | 0.983359i | \(-0.558151\pi\) | ||||
−0.181673 | + | 0.983359i | \(0.558151\pi\) | |||||||
\(798\) | 3.36152 | 0.118997 | ||||||||
\(799\) | −31.5016 | −1.11445 | ||||||||
\(800\) | 88.6552 | 3.13443 | ||||||||
\(801\) | 30.0290 | 1.06102 | ||||||||
\(802\) | 68.4134 | 2.41576 | ||||||||
\(803\) | −35.1657 | −1.24097 | ||||||||
\(804\) | 7.31374 | 0.257936 | ||||||||
\(805\) | 0.317454 | 0.0111888 | ||||||||
\(806\) | 7.21379 | 0.254095 | ||||||||
\(807\) | −5.24162 | −0.184514 | ||||||||
\(808\) | −102.916 | −3.62058 | ||||||||
\(809\) | 13.4253 | 0.472007 | 0.236004 | − | 0.971752i | \(-0.424162\pi\) | ||||
0.236004 | + | 0.971752i | \(0.424162\pi\) | |||||||
\(810\) | −4.05670 | −0.142538 | ||||||||
\(811\) | 2.93197 | 0.102955 | 0.0514777 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514777 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(812\) | −48.3529 | −1.69685 | ||||||||
\(813\) | 8.01742 | 0.281183 | ||||||||
\(814\) | −9.86649 | −0.345820 | ||||||||
\(815\) | −2.31371 | −0.0810456 | ||||||||
\(816\) | 14.7226 | 0.515396 | ||||||||
\(817\) | 51.1388 | 1.78912 | ||||||||
\(818\) | −21.1912 | −0.740932 | ||||||||
\(819\) | 7.86349 | 0.274773 | ||||||||
\(820\) | 1.99229 | 0.0695737 | ||||||||
\(821\) | −0.967206 | −0.0337557 | −0.0168779 | − | 0.999858i | \(-0.505373\pi\) | ||||
−0.0168779 | + | 0.999858i | \(0.505373\pi\) | |||||||
\(822\) | −5.01429 | −0.174893 | ||||||||
\(823\) | −33.4575 | −1.16626 | −0.583128 | − | 0.812380i | \(-0.698171\pi\) | ||||
−0.583128 | + | 0.812380i | \(0.698171\pi\) | |||||||
\(824\) | −12.3473 | −0.430140 | ||||||||
\(825\) | −4.56754 | −0.159021 | ||||||||
\(826\) | 38.3719 | 1.33513 | ||||||||
\(827\) | 24.8260 | 0.863284 | 0.431642 | − | 0.902045i | \(-0.357934\pi\) | ||||
0.431642 | + | 0.902045i | \(0.357934\pi\) | |||||||
\(828\) | 27.4762 | 0.954866 | ||||||||
\(829\) | 51.9693 | 1.80497 | 0.902485 | − | 0.430722i | \(-0.141741\pi\) | ||||
0.902485 | + | 0.430722i | \(0.141741\pi\) | |||||||
\(830\) | −0.0271564 | −0.000942613 0 | ||||||||
\(831\) | −7.89412 | −0.273844 | ||||||||
\(832\) | 58.3562 | 2.02314 | ||||||||
\(833\) | 4.46232 | 0.154610 | ||||||||
\(834\) | 10.0302 | 0.347317 | ||||||||
\(835\) | 0.291911 | 0.0101020 | ||||||||
\(836\) | 95.7105 | 3.31022 | ||||||||
\(837\) | 1.49052 | 0.0515198 | ||||||||
\(838\) | −39.7640 | −1.37363 | ||||||||
\(839\) | 32.0290 | 1.10576 | 0.552882 | − | 0.833260i | \(-0.313528\pi\) | ||||
0.552882 | + | 0.833260i | \(0.313528\pi\) | |||||||
\(840\) | 0.393457 | 0.0135756 | ||||||||
\(841\) | 55.5255 | 1.91467 | ||||||||
\(842\) | 77.8263 | 2.68207 | ||||||||
\(843\) | −1.63039 | −0.0561537 | ||||||||
\(844\) | −54.0054 | −1.85894 | ||||||||
\(845\) | −1.04070 | −0.0358013 | ||||||||
\(846\) | −55.8623 | −1.92059 | ||||||||
\(847\) | −2.41004 | −0.0828099 | ||||||||
\(848\) | 34.5438 | 1.18624 | ||||||||
\(849\) | 3.73995 | 0.128355 | ||||||||
\(850\) | 59.7315 | 2.04877 | ||||||||
\(851\) | −1.77881 | −0.0609767 | ||||||||
\(852\) | 9.20546 | 0.315374 | ||||||||
\(853\) | 20.3896 | 0.698127 | 0.349063 | − | 0.937099i | \(-0.386500\pi\) | ||||
0.349063 | + | 0.937099i | \(0.386500\pi\) | |||||||
\(854\) | 13.3369 | 0.456379 | ||||||||
\(855\) | −2.60476 | −0.0890808 | ||||||||
\(856\) | 160.201 | 5.47556 | ||||||||
\(857\) | 28.7801 | 0.983109 | 0.491554 | − | 0.870847i | \(-0.336429\pi\) | ||||
0.491554 | + | 0.870847i | \(0.336429\pi\) | |||||||
\(858\) | −6.63210 | −0.226416 | ||||||||
\(859\) | −7.78592 | −0.265652 | −0.132826 | − | 0.991139i | \(-0.542405\pi\) | ||||
−0.132826 | + | 0.991139i | \(0.542405\pi\) | |||||||
\(860\) | 9.65863 | 0.329357 | ||||||||
\(861\) | −0.532898 | −0.0181611 | ||||||||
\(862\) | −87.9947 | −2.99711 | ||||||||
\(863\) | −4.21370 | −0.143436 | −0.0717180 | − | 0.997425i | \(-0.522848\pi\) | ||||
−0.0717180 | + | 0.997425i | \(0.522848\pi\) | |||||||
\(864\) | 26.5979 | 0.904877 | ||||||||
\(865\) | 1.47867 | 0.0502764 | ||||||||
\(866\) | −38.6268 | −1.31259 | ||||||||
\(867\) | 0.731161 | 0.0248315 | ||||||||
\(868\) | 5.25931 | 0.178513 | ||||||||
\(869\) | −37.8280 | −1.28323 | ||||||||
\(870\) | −1.10985 | −0.0376276 | ||||||||
\(871\) | 14.8304 | 0.502510 | ||||||||
\(872\) | −88.4739 | −2.99611 | ||||||||
\(873\) | 48.4024 | 1.63817 | ||||||||
\(874\) | 23.8173 | 0.805632 | ||||||||
\(875\) | 1.77896 | 0.0601398 | ||||||||
\(876\) | −12.6796 | −0.428404 | ||||||||
\(877\) | 2.17778 | 0.0735384 | 0.0367692 | − | 0.999324i | \(-0.488293\pi\) | ||||
0.0367692 | + | 0.999324i | \(0.488293\pi\) | |||||||
\(878\) | 46.6532 | 1.57447 | ||||||||
\(879\) | 1.34381 | 0.0453255 | ||||||||
\(880\) | 8.58854 | 0.289520 | ||||||||
\(881\) | 1.18433 | 0.0399010 | 0.0199505 | − | 0.999801i | \(-0.493649\pi\) | ||||
0.0199505 | + | 0.999801i | \(0.493649\pi\) | |||||||
\(882\) | 7.91311 | 0.266448 | ||||||||
\(883\) | 56.4191 | 1.89865 | 0.949327 | − | 0.314289i | \(-0.101766\pi\) | ||||
0.949327 | + | 0.314289i | \(0.101766\pi\) | |||||||
\(884\) | 62.8356 | 2.11339 | ||||||||
\(885\) | 0.638101 | 0.0214495 | ||||||||
\(886\) | 46.9843 | 1.57847 | ||||||||
\(887\) | −45.5257 | −1.52860 | −0.764301 | − | 0.644860i | \(-0.776916\pi\) | ||||
−0.764301 | + | 0.644860i | \(0.776916\pi\) | |||||||
\(888\) | −2.20468 | −0.0739843 | ||||||||
\(889\) | −8.46035 | −0.283751 | ||||||||
\(890\) | 4.91633 | 0.164796 | ||||||||
\(891\) | 30.8950 | 1.03502 | ||||||||
\(892\) | 51.3498 | 1.71932 | ||||||||
\(893\) | −35.0822 | −1.17398 | ||||||||
\(894\) | −11.5625 | −0.386708 | ||||||||
\(895\) | −0.583117 | −0.0194914 | ||||||||
\(896\) | 23.0351 | 0.769547 | ||||||||
\(897\) | −1.19569 | −0.0399228 | ||||||||
\(898\) | 10.2988 | 0.343676 | ||||||||
\(899\) | −9.19377 | −0.306630 | ||||||||
\(900\) | 76.7402 | 2.55801 | ||||||||
\(901\) | 11.7295 | 0.390766 | ||||||||
\(902\) | −20.9428 | −0.697318 | ||||||||
\(903\) | −2.58349 | −0.0859733 | ||||||||
\(904\) | 40.1233 | 1.33448 | ||||||||
\(905\) | −2.62720 | −0.0873312 | ||||||||
\(906\) | −2.62277 | −0.0871356 | ||||||||
\(907\) | −11.8334 | −0.392920 | −0.196460 | − | 0.980512i | \(-0.562945\pi\) | ||||
−0.196460 | + | 0.980512i | \(0.562945\pi\) | |||||||
\(908\) | −64.8346 | −2.15161 | ||||||||
\(909\) | −34.4199 | −1.14164 | ||||||||
\(910\) | 1.28741 | 0.0426771 | ||||||||
\(911\) | −2.64070 | −0.0874903 | −0.0437452 | − | 0.999043i | \(-0.513929\pi\) | ||||
−0.0437452 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(912\) | 16.3961 | 0.542929 | ||||||||
\(913\) | 0.206818 | 0.00684467 | ||||||||
\(914\) | 7.46298 | 0.246853 | ||||||||
\(915\) | 0.221784 | 0.00733197 | ||||||||
\(916\) | −70.2616 | −2.32151 | ||||||||
\(917\) | −12.5494 | −0.414418 | ||||||||
\(918\) | 17.9203 | 0.591459 | ||||||||
\(919\) | −24.6791 | −0.814088 | −0.407044 | − | 0.913409i | \(-0.633440\pi\) | ||||
−0.407044 | + | 0.913409i | \(0.633440\pi\) | |||||||
\(920\) | 2.78775 | 0.0919095 | ||||||||
\(921\) | 2.47767 | 0.0816422 | ||||||||
\(922\) | 10.7437 | 0.353823 | ||||||||
\(923\) | 18.6664 | 0.614412 | ||||||||
\(924\) | −4.83522 | −0.159067 | ||||||||
\(925\) | −4.96815 | −0.163352 | ||||||||
\(926\) | 34.3056 | 1.12735 | ||||||||
\(927\) | −4.12952 | −0.135631 | ||||||||
\(928\) | −164.060 | −5.38554 | ||||||||
\(929\) | −49.9616 | −1.63919 | −0.819593 | − | 0.572947i | \(-0.805800\pi\) | ||||
−0.819593 | + | 0.572947i | \(0.805800\pi\) | |||||||
\(930\) | 0.120718 | 0.00395850 | ||||||||
\(931\) | 4.96953 | 0.162870 | ||||||||
\(932\) | 143.600 | 4.70378 | ||||||||
\(933\) | 2.23256 | 0.0730907 | ||||||||
\(934\) | 8.14994 | 0.266674 | ||||||||
\(935\) | 2.91627 | 0.0953723 | ||||||||
\(936\) | 69.0540 | 2.25710 | ||||||||
\(937\) | −17.0283 | −0.556291 | −0.278146 | − | 0.960539i | \(-0.589720\pi\) | ||||
−0.278146 | + | 0.960539i | \(0.589720\pi\) | |||||||
\(938\) | 14.9240 | 0.487287 | ||||||||
\(939\) | 0.976624 | 0.0318709 | ||||||||
\(940\) | −6.62601 | −0.216117 | ||||||||
\(941\) | −8.38286 | −0.273273 | −0.136637 | − | 0.990621i | \(-0.543629\pi\) | ||||
−0.136637 | + | 0.990621i | \(0.543629\pi\) | |||||||
\(942\) | 0.949526 | 0.0309372 | ||||||||
\(943\) | −3.77573 | −0.122955 | ||||||||
\(944\) | 187.162 | 6.09161 | ||||||||
\(945\) | 0.266005 | 0.00865313 | ||||||||
\(946\) | −101.531 | −3.30105 | ||||||||
\(947\) | 53.6014 | 1.74181 | 0.870905 | − | 0.491451i | \(-0.163533\pi\) | ||||
0.870905 | + | 0.491451i | \(0.163533\pi\) | |||||||
\(948\) | −13.6395 | −0.442991 | ||||||||
\(949\) | −25.7111 | −0.834617 | ||||||||
\(950\) | 66.5209 | 2.15822 | ||||||||
\(951\) | −0.714248 | −0.0231611 | ||||||||
\(952\) | 39.1863 | 1.27004 | ||||||||
\(953\) | 41.3747 | 1.34026 | 0.670128 | − | 0.742245i | \(-0.266239\pi\) | ||||
0.670128 | + | 0.742245i | \(0.266239\pi\) | |||||||
\(954\) | 20.8001 | 0.673428 | ||||||||
\(955\) | −3.80492 | −0.123124 | ||||||||
\(956\) | −74.6511 | −2.41439 | ||||||||
\(957\) | 8.45242 | 0.273228 | ||||||||
\(958\) | −25.0039 | −0.807841 | ||||||||
\(959\) | −7.41292 | −0.239376 | ||||||||
\(960\) | 0.976552 | 0.0315181 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −7.21379 | −0.232582 | ||||||||
\(963\) | 53.5786 | 1.72655 | ||||||||
\(964\) | −7.10062 | −0.228695 | ||||||||
\(965\) | −0.0396215 | −0.00127546 | ||||||||
\(966\) | −1.20323 | −0.0387133 | ||||||||
\(967\) | −46.7824 | −1.50442 | −0.752210 | − | 0.658923i | \(-0.771012\pi\) | ||||
−0.752210 | + | 0.658923i | \(0.771012\pi\) | |||||||
\(968\) | −21.1640 | −0.680237 | ||||||||
\(969\) | 5.56736 | 0.178849 | ||||||||
\(970\) | 7.92441 | 0.254438 | ||||||||
\(971\) | 45.4403 | 1.45825 | 0.729124 | − | 0.684382i | \(-0.239928\pi\) | ||||
0.729124 | + | 0.684382i | \(0.239928\pi\) | |||||||
\(972\) | 34.6570 | 1.11162 | ||||||||
\(973\) | 14.8282 | 0.475372 | ||||||||
\(974\) | 51.8038 | 1.65990 | ||||||||
\(975\) | −3.33951 | −0.106950 | ||||||||
\(976\) | 65.0518 | 2.08226 | ||||||||
\(977\) | −24.8823 | −0.796056 | −0.398028 | − | 0.917373i | \(-0.630305\pi\) | ||||
−0.398028 | + | 0.917373i | \(0.630305\pi\) | |||||||
\(978\) | 8.76953 | 0.280419 | ||||||||
\(979\) | −37.4418 | −1.19665 | ||||||||
\(980\) | 0.938600 | 0.0299825 | ||||||||
\(981\) | −29.5898 | −0.944728 | ||||||||
\(982\) | −45.3681 | −1.44775 | ||||||||
\(983\) | −43.7462 | −1.39529 | −0.697644 | − | 0.716445i | \(-0.745768\pi\) | ||||
−0.697644 | + | 0.716445i | \(0.745768\pi\) | |||||||
\(984\) | −4.67969 | −0.149183 | ||||||||
\(985\) | 4.18791 | 0.133438 | ||||||||
\(986\) | −110.536 | −3.52017 | ||||||||
\(987\) | 1.77233 | 0.0564138 | ||||||||
\(988\) | 69.9778 | 2.22629 | ||||||||
\(989\) | −18.3048 | −0.582058 | ||||||||
\(990\) | 5.17147 | 0.164360 | ||||||||
\(991\) | 17.9494 | 0.570183 | 0.285091 | − | 0.958500i | \(-0.407976\pi\) | ||||
0.285091 | + | 0.958500i | \(0.407976\pi\) | |||||||
\(992\) | 17.8447 | 0.566570 | ||||||||
\(993\) | −0.813145 | −0.0258044 | ||||||||
\(994\) | 18.7842 | 0.595798 | ||||||||
\(995\) | 2.67695 | 0.0848649 | ||||||||
\(996\) | 0.0745717 | 0.00236290 | ||||||||
\(997\) | 4.12101 | 0.130514 | 0.0652568 | − | 0.997869i | \(-0.479213\pi\) | ||||
0.0652568 | + | 0.997869i | \(0.479213\pi\) | |||||||
\(998\) | −66.4146 | −2.10232 | ||||||||
\(999\) | −1.49052 | −0.0471579 |
(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.h.1.2 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8029.2.a.h.1.2 | ✓ | 71 | 1.1 | even | 1 | trivial |