Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23062 | −0.870182 | −0.435091 | − | 0.900387i | \(-0.643284\pi\) | ||||
−0.435091 | + | 0.900387i | \(0.643284\pi\) | |||||||
\(3\) | −0.724033 | −0.418020 | −0.209010 | − | 0.977913i | \(-0.567024\pi\) | ||||
−0.209010 | + | 0.977913i | \(0.567024\pi\) | |||||||
\(4\) | −0.485567 | −0.242784 | ||||||||
\(5\) | 2.55129 | 1.14097 | 0.570486 | − | 0.821307i | \(-0.306755\pi\) | ||||
0.570486 | + | 0.821307i | \(0.306755\pi\) | |||||||
\(6\) | 0.891011 | 0.363754 | ||||||||
\(7\) | −2.06260 | −0.779588 | −0.389794 | − | 0.920902i | \(-0.627454\pi\) | ||||
−0.389794 | + | 0.920902i | \(0.627454\pi\) | |||||||
\(8\) | 3.05880 | 1.08145 | ||||||||
\(9\) | −2.47578 | −0.825259 | ||||||||
\(10\) | −3.13968 | −0.992854 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.351567 | 0.101489 | ||||||||
\(13\) | −1.70217 | −0.472098 | −0.236049 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236049 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(14\) | 2.53828 | 0.678383 | ||||||||
\(15\) | −1.84722 | −0.476950 | ||||||||
\(16\) | −2.79309 | −0.698272 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 3.04675 | 0.718125 | ||||||||
\(19\) | 1.33060 | 0.305261 | 0.152630 | − | 0.988283i | \(-0.451226\pi\) | ||||
0.152630 | + | 0.988283i | \(0.451226\pi\) | |||||||
\(20\) | −1.23882 | −0.277010 | ||||||||
\(21\) | 1.49339 | 0.325884 | ||||||||
\(22\) | −1.23062 | −0.262370 | ||||||||
\(23\) | −4.90235 | −1.02221 | −0.511106 | − | 0.859518i | \(-0.670764\pi\) | ||||
−0.511106 | + | 0.859518i | \(0.670764\pi\) | |||||||
\(24\) | −2.21467 | −0.452067 | ||||||||
\(25\) | 1.50910 | 0.301819 | ||||||||
\(26\) | 2.09473 | 0.410811 | ||||||||
\(27\) | 3.96464 | 0.762996 | ||||||||
\(28\) | 1.00153 | 0.189271 | ||||||||
\(29\) | 2.06707 | 0.383845 | 0.191923 | − | 0.981410i | \(-0.438528\pi\) | ||||
0.191923 | + | 0.981410i | \(0.438528\pi\) | |||||||
\(30\) | 2.27323 | 0.415033 | ||||||||
\(31\) | −4.76678 | −0.856139 | −0.428069 | − | 0.903746i | \(-0.640806\pi\) | ||||
−0.428069 | + | 0.903746i | \(0.640806\pi\) | |||||||
\(32\) | −2.68035 | −0.473824 | ||||||||
\(33\) | −0.724033 | −0.126038 | ||||||||
\(34\) | −1.23062 | −0.211050 | ||||||||
\(35\) | −5.26229 | −0.889489 | ||||||||
\(36\) | 1.20216 | 0.200359 | ||||||||
\(37\) | 8.52570 | 1.40162 | 0.700808 | − | 0.713350i | \(-0.252823\pi\) | ||||
0.700808 | + | 0.713350i | \(0.252823\pi\) | |||||||
\(38\) | −1.63747 | −0.265632 | ||||||||
\(39\) | 1.23243 | 0.197347 | ||||||||
\(40\) | 7.80388 | 1.23390 | ||||||||
\(41\) | 9.72974 | 1.51953 | 0.759765 | − | 0.650197i | \(-0.225314\pi\) | ||||
0.759765 | + | 0.650197i | \(0.225314\pi\) | |||||||
\(42\) | −1.83780 | −0.283578 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −0.485567 | −0.0732020 | ||||||||
\(45\) | −6.31643 | −0.941598 | ||||||||
\(46\) | 6.03295 | 0.889510 | ||||||||
\(47\) | 0.420371 | 0.0613173 | 0.0306587 | − | 0.999530i | \(-0.490240\pi\) | ||||
0.0306587 | + | 0.999530i | \(0.490240\pi\) | |||||||
\(48\) | 2.02229 | 0.291892 | ||||||||
\(49\) | −2.74570 | −0.392243 | ||||||||
\(50\) | −1.85713 | −0.262637 | ||||||||
\(51\) | −0.724033 | −0.101385 | ||||||||
\(52\) | 0.826519 | 0.114618 | ||||||||
\(53\) | 4.45312 | 0.611684 | 0.305842 | − | 0.952082i | \(-0.401062\pi\) | ||||
0.305842 | + | 0.952082i | \(0.401062\pi\) | |||||||
\(54\) | −4.87898 | −0.663945 | ||||||||
\(55\) | 2.55129 | 0.344016 | ||||||||
\(56\) | −6.30906 | −0.843084 | ||||||||
\(57\) | −0.963398 | −0.127605 | ||||||||
\(58\) | −2.54378 | −0.334015 | ||||||||
\(59\) | 4.74791 | 0.618126 | 0.309063 | − | 0.951042i | \(-0.399985\pi\) | ||||
0.309063 | + | 0.951042i | \(0.399985\pi\) | |||||||
\(60\) | 0.896949 | 0.115796 | ||||||||
\(61\) | 0.122923 | 0.0157387 | 0.00786937 | − | 0.999969i | \(-0.497495\pi\) | ||||
0.00786937 | + | 0.999969i | \(0.497495\pi\) | |||||||
\(62\) | 5.86611 | 0.744997 | ||||||||
\(63\) | 5.10653 | 0.643362 | ||||||||
\(64\) | 8.88468 | 1.11059 | ||||||||
\(65\) | −4.34274 | −0.538651 | ||||||||
\(66\) | 0.891011 | 0.109676 | ||||||||
\(67\) | 4.12490 | 0.503937 | 0.251969 | − | 0.967735i | \(-0.418922\pi\) | ||||
0.251969 | + | 0.967735i | \(0.418922\pi\) | |||||||
\(68\) | −0.485567 | −0.0588837 | ||||||||
\(69\) | 3.54946 | 0.427305 | ||||||||
\(70\) | 6.47589 | 0.774017 | ||||||||
\(71\) | −3.39468 | −0.402874 | −0.201437 | − | 0.979501i | \(-0.564561\pi\) | ||||
−0.201437 | + | 0.979501i | \(0.564561\pi\) | |||||||
\(72\) | −7.57290 | −0.892474 | ||||||||
\(73\) | −10.2343 | −1.19784 | −0.598920 | − | 0.800809i | \(-0.704403\pi\) | ||||
−0.598920 | + | 0.800809i | \(0.704403\pi\) | |||||||
\(74\) | −10.4919 | −1.21966 | ||||||||
\(75\) | −1.09263 | −0.126167 | ||||||||
\(76\) | −0.646096 | −0.0741123 | ||||||||
\(77\) | −2.06260 | −0.235055 | ||||||||
\(78\) | −1.51665 | −0.171727 | ||||||||
\(79\) | −13.3023 | −1.49663 | −0.748313 | − | 0.663346i | \(-0.769136\pi\) | ||||
−0.748313 | + | 0.663346i | \(0.769136\pi\) | |||||||
\(80\) | −7.12599 | −0.796710 | ||||||||
\(81\) | 4.55680 | 0.506311 | ||||||||
\(82\) | −11.9736 | −1.32227 | ||||||||
\(83\) | −0.161520 | −0.0177292 | −0.00886459 | − | 0.999961i | \(-0.502822\pi\) | ||||
−0.00886459 | + | 0.999961i | \(0.502822\pi\) | |||||||
\(84\) | −0.725140 | −0.0791192 | ||||||||
\(85\) | 2.55129 | 0.276727 | ||||||||
\(86\) | 1.23062 | 0.132701 | ||||||||
\(87\) | −1.49663 | −0.160455 | ||||||||
\(88\) | 3.05880 | 0.326069 | ||||||||
\(89\) | −0.138476 | −0.0146784 | −0.00733921 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733921 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(90\) | 7.77314 | 0.819361 | ||||||||
\(91\) | 3.51089 | 0.368042 | ||||||||
\(92\) | 2.38042 | 0.248176 | ||||||||
\(93\) | 3.45130 | 0.357884 | ||||||||
\(94\) | −0.517318 | −0.0533572 | ||||||||
\(95\) | 3.39475 | 0.348294 | ||||||||
\(96\) | 1.94066 | 0.198068 | ||||||||
\(97\) | 4.10477 | 0.416777 | 0.208388 | − | 0.978046i | \(-0.433178\pi\) | ||||
0.208388 | + | 0.978046i | \(0.433178\pi\) | |||||||
\(98\) | 3.37892 | 0.341322 | ||||||||
\(99\) | −2.47578 | −0.248825 | ||||||||
\(100\) | −0.732767 | −0.0732767 | ||||||||
\(101\) | 0.242466 | 0.0241263 | 0.0120632 | − | 0.999927i | \(-0.496160\pi\) | ||||
0.0120632 | + | 0.999927i | \(0.496160\pi\) | |||||||
\(102\) | 0.891011 | 0.0882233 | ||||||||
\(103\) | −9.25304 | −0.911729 | −0.455865 | − | 0.890049i | \(-0.650670\pi\) | ||||
−0.455865 | + | 0.890049i | \(0.650670\pi\) | |||||||
\(104\) | −5.20660 | −0.510549 | ||||||||
\(105\) | 3.81007 | 0.371824 | ||||||||
\(106\) | −5.48012 | −0.532276 | ||||||||
\(107\) | −7.91468 | −0.765141 | −0.382571 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382571 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(108\) | −1.92510 | −0.185243 | ||||||||
\(109\) | 7.83282 | 0.750248 | 0.375124 | − | 0.926975i | \(-0.377600\pi\) | ||||
0.375124 | + | 0.926975i | \(0.377600\pi\) | |||||||
\(110\) | −3.13968 | −0.299357 | ||||||||
\(111\) | −6.17288 | −0.585904 | ||||||||
\(112\) | 5.76101 | 0.544365 | ||||||||
\(113\) | 13.3261 | 1.25361 | 0.626805 | − | 0.779176i | \(-0.284362\pi\) | ||||
0.626805 | + | 0.779176i | \(0.284362\pi\) | |||||||
\(114\) | 1.18558 | 0.111040 | ||||||||
\(115\) | −12.5073 | −1.16632 | ||||||||
\(116\) | −1.00370 | −0.0931914 | ||||||||
\(117\) | 4.21420 | 0.389603 | ||||||||
\(118\) | −5.84289 | −0.537882 | ||||||||
\(119\) | −2.06260 | −0.189078 | ||||||||
\(120\) | −5.65027 | −0.515796 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.151272 | −0.0136956 | ||||||||
\(123\) | −7.04465 | −0.635195 | ||||||||
\(124\) | 2.31459 | 0.207857 | ||||||||
\(125\) | −8.90632 | −0.796606 | ||||||||
\(126\) | −6.28421 | −0.559842 | ||||||||
\(127\) | −11.0755 | −0.982790 | −0.491395 | − | 0.870937i | \(-0.663513\pi\) | ||||
−0.491395 | + | 0.870937i | \(0.663513\pi\) | |||||||
\(128\) | −5.57299 | −0.492587 | ||||||||
\(129\) | 0.724033 | 0.0637475 | ||||||||
\(130\) | 5.34428 | 0.468724 | ||||||||
\(131\) | 10.2749 | 0.897719 | 0.448860 | − | 0.893602i | \(-0.351830\pi\) | ||||
0.448860 | + | 0.893602i | \(0.351830\pi\) | |||||||
\(132\) | 0.351567 | 0.0305999 | ||||||||
\(133\) | −2.74449 | −0.237978 | ||||||||
\(134\) | −5.07620 | −0.438517 | ||||||||
\(135\) | 10.1150 | 0.870557 | ||||||||
\(136\) | 3.05880 | 0.262290 | ||||||||
\(137\) | 7.14912 | 0.610790 | 0.305395 | − | 0.952226i | \(-0.401211\pi\) | ||||
0.305395 | + | 0.952226i | \(0.401211\pi\) | |||||||
\(138\) | −4.36805 | −0.371833 | ||||||||
\(139\) | 12.3340 | 1.04615 | 0.523077 | − | 0.852285i | \(-0.324784\pi\) | ||||
0.523077 | + | 0.852285i | \(0.324784\pi\) | |||||||
\(140\) | 2.55519 | 0.215953 | ||||||||
\(141\) | −0.304362 | −0.0256319 | ||||||||
\(142\) | 4.17757 | 0.350574 | ||||||||
\(143\) | −1.70217 | −0.142343 | ||||||||
\(144\) | 6.91507 | 0.576256 | ||||||||
\(145\) | 5.27370 | 0.437957 | ||||||||
\(146\) | 12.5946 | 1.04234 | ||||||||
\(147\) | 1.98798 | 0.163965 | ||||||||
\(148\) | −4.13980 | −0.340289 | ||||||||
\(149\) | 1.10114 | 0.0902086 | 0.0451043 | − | 0.998982i | \(-0.485638\pi\) | ||||
0.0451043 | + | 0.998982i | \(0.485638\pi\) | |||||||
\(150\) | 1.34462 | 0.109788 | ||||||||
\(151\) | −17.9687 | −1.46227 | −0.731136 | − | 0.682231i | \(-0.761010\pi\) | ||||
−0.731136 | + | 0.682231i | \(0.761010\pi\) | |||||||
\(152\) | 4.07004 | 0.330123 | ||||||||
\(153\) | −2.47578 | −0.200155 | ||||||||
\(154\) | 2.53828 | 0.204540 | ||||||||
\(155\) | −12.1615 | −0.976831 | ||||||||
\(156\) | −0.598427 | −0.0479125 | ||||||||
\(157\) | 1.51222 | 0.120688 | 0.0603440 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603440 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(158\) | 16.3701 | 1.30234 | ||||||||
\(159\) | −3.22421 | −0.255696 | ||||||||
\(160\) | −6.83836 | −0.540620 | ||||||||
\(161\) | 10.1116 | 0.796904 | ||||||||
\(162\) | −5.60770 | −0.440583 | ||||||||
\(163\) | 4.62010 | 0.361874 | 0.180937 | − | 0.983495i | \(-0.442087\pi\) | ||||
0.180937 | + | 0.983495i | \(0.442087\pi\) | |||||||
\(164\) | −4.72445 | −0.368917 | ||||||||
\(165\) | −1.84722 | −0.143806 | ||||||||
\(166\) | 0.198771 | 0.0154276 | ||||||||
\(167\) | 22.7634 | 1.76148 | 0.880742 | − | 0.473597i | \(-0.157045\pi\) | ||||
0.880742 | + | 0.473597i | \(0.157045\pi\) | |||||||
\(168\) | 4.56797 | 0.352426 | ||||||||
\(169\) | −10.1026 | −0.777124 | ||||||||
\(170\) | −3.13968 | −0.240802 | ||||||||
\(171\) | −3.29427 | −0.251919 | ||||||||
\(172\) | 0.485567 | 0.0370242 | ||||||||
\(173\) | −4.79053 | −0.364217 | −0.182109 | − | 0.983278i | \(-0.558292\pi\) | ||||
−0.182109 | + | 0.983278i | \(0.558292\pi\) | |||||||
\(174\) | 1.84178 | 0.139625 | ||||||||
\(175\) | −3.11265 | −0.235294 | ||||||||
\(176\) | −2.79309 | −0.210537 | ||||||||
\(177\) | −3.43764 | −0.258389 | ||||||||
\(178\) | 0.170412 | 0.0127729 | ||||||||
\(179\) | 10.3155 | 0.771017 | 0.385509 | − | 0.922704i | \(-0.374026\pi\) | ||||
0.385509 | + | 0.922704i | \(0.374026\pi\) | |||||||
\(180\) | 3.06705 | 0.228605 | ||||||||
\(181\) | −16.4030 | −1.21923 | −0.609613 | − | 0.792699i | \(-0.708675\pi\) | ||||
−0.609613 | + | 0.792699i | \(0.708675\pi\) | |||||||
\(182\) | −4.32059 | −0.320263 | ||||||||
\(183\) | −0.0890006 | −0.00657912 | ||||||||
\(184\) | −14.9953 | −1.10547 | ||||||||
\(185\) | 21.7516 | 1.59921 | ||||||||
\(186\) | −4.24725 | −0.311424 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −0.204118 | −0.0148869 | ||||||||
\(189\) | −8.17745 | −0.594822 | ||||||||
\(190\) | −4.17766 | −0.303079 | ||||||||
\(191\) | 8.34721 | 0.603983 | 0.301991 | − | 0.953311i | \(-0.402349\pi\) | ||||
0.301991 | + | 0.953311i | \(0.402349\pi\) | |||||||
\(192\) | −6.43280 | −0.464247 | ||||||||
\(193\) | −10.6289 | −0.765084 | −0.382542 | − | 0.923938i | \(-0.624951\pi\) | ||||
−0.382542 | + | 0.923938i | \(0.624951\pi\) | |||||||
\(194\) | −5.05143 | −0.362671 | ||||||||
\(195\) | 3.14429 | 0.225167 | ||||||||
\(196\) | 1.33322 | 0.0952301 | ||||||||
\(197\) | −21.3637 | −1.52210 | −0.761049 | − | 0.648694i | \(-0.775315\pi\) | ||||
−0.761049 | + | 0.648694i | \(0.775315\pi\) | |||||||
\(198\) | 3.04675 | 0.216523 | ||||||||
\(199\) | −11.8966 | −0.843330 | −0.421665 | − | 0.906752i | \(-0.638554\pi\) | ||||
−0.421665 | + | 0.906752i | \(0.638554\pi\) | |||||||
\(200\) | 4.61601 | 0.326401 | ||||||||
\(201\) | −2.98657 | −0.210656 | ||||||||
\(202\) | −0.298385 | −0.0209943 | ||||||||
\(203\) | −4.26353 | −0.299241 | ||||||||
\(204\) | 0.351567 | 0.0246146 | ||||||||
\(205\) | 24.8234 | 1.73374 | ||||||||
\(206\) | 11.3870 | 0.793370 | ||||||||
\(207\) | 12.1371 | 0.843589 | ||||||||
\(208\) | 4.75432 | 0.329653 | ||||||||
\(209\) | 1.33060 | 0.0920396 | ||||||||
\(210\) | −4.68876 | −0.323555 | ||||||||
\(211\) | −8.70840 | −0.599511 | −0.299755 | − | 0.954016i | \(-0.596905\pi\) | ||||
−0.299755 | + | 0.954016i | \(0.596905\pi\) | |||||||
\(212\) | −2.16229 | −0.148507 | ||||||||
\(213\) | 2.45786 | 0.168410 | ||||||||
\(214\) | 9.73999 | 0.665812 | ||||||||
\(215\) | −2.55129 | −0.173997 | ||||||||
\(216\) | 12.1270 | 0.825140 | ||||||||
\(217\) | 9.83194 | 0.667436 | ||||||||
\(218\) | −9.63925 | −0.652852 | ||||||||
\(219\) | 7.41000 | 0.500722 | ||||||||
\(220\) | −1.23882 | −0.0835215 | ||||||||
\(221\) | −1.70217 | −0.114501 | ||||||||
\(222\) | 7.59649 | 0.509843 | ||||||||
\(223\) | 22.0040 | 1.47350 | 0.736748 | − | 0.676167i | \(-0.236360\pi\) | ||||
0.736748 | + | 0.676167i | \(0.236360\pi\) | |||||||
\(224\) | 5.52848 | 0.369387 | ||||||||
\(225\) | −3.73618 | −0.249079 | ||||||||
\(226\) | −16.3994 | −1.09087 | ||||||||
\(227\) | 3.92613 | 0.260586 | 0.130293 | − | 0.991476i | \(-0.458408\pi\) | ||||
0.130293 | + | 0.991476i | \(0.458408\pi\) | |||||||
\(228\) | 0.467795 | 0.0309805 | ||||||||
\(229\) | −27.1137 | −1.79173 | −0.895863 | − | 0.444330i | \(-0.853442\pi\) | ||||
−0.895863 | + | 0.444330i | \(0.853442\pi\) | |||||||
\(230\) | 15.3918 | 1.01491 | ||||||||
\(231\) | 1.49339 | 0.0982576 | ||||||||
\(232\) | 6.32275 | 0.415109 | ||||||||
\(233\) | 5.02256 | 0.329039 | 0.164519 | − | 0.986374i | \(-0.447393\pi\) | ||||
0.164519 | + | 0.986374i | \(0.447393\pi\) | |||||||
\(234\) | −5.18609 | −0.339025 | ||||||||
\(235\) | 1.07249 | 0.0699614 | ||||||||
\(236\) | −2.30543 | −0.150071 | ||||||||
\(237\) | 9.63130 | 0.625620 | ||||||||
\(238\) | 2.53828 | 0.164532 | ||||||||
\(239\) | 8.17257 | 0.528640 | 0.264320 | − | 0.964435i | \(-0.414853\pi\) | ||||
0.264320 | + | 0.964435i | \(0.414853\pi\) | |||||||
\(240\) | 5.15945 | 0.333041 | ||||||||
\(241\) | −8.43853 | −0.543573 | −0.271787 | − | 0.962358i | \(-0.587615\pi\) | ||||
−0.271787 | + | 0.962358i | \(0.587615\pi\) | |||||||
\(242\) | −1.23062 | −0.0791074 | ||||||||
\(243\) | −15.1932 | −0.974644 | ||||||||
\(244\) | −0.0596876 | −0.00382111 | ||||||||
\(245\) | −7.00508 | −0.447538 | ||||||||
\(246\) | 8.66931 | 0.552735 | ||||||||
\(247\) | −2.26491 | −0.144113 | ||||||||
\(248\) | −14.5806 | −0.925870 | ||||||||
\(249\) | 0.116946 | 0.00741116 | ||||||||
\(250\) | 10.9603 | 0.693192 | ||||||||
\(251\) | −21.9660 | −1.38648 | −0.693240 | − | 0.720707i | \(-0.743817\pi\) | ||||
−0.693240 | + | 0.720707i | \(0.743817\pi\) | |||||||
\(252\) | −2.47956 | −0.156198 | ||||||||
\(253\) | −4.90235 | −0.308208 | ||||||||
\(254\) | 13.6297 | 0.855206 | ||||||||
\(255\) | −1.84722 | −0.115677 | ||||||||
\(256\) | −10.9111 | −0.681945 | ||||||||
\(257\) | 17.1179 | 1.06779 | 0.533893 | − | 0.845552i | \(-0.320729\pi\) | ||||
0.533893 | + | 0.845552i | \(0.320729\pi\) | |||||||
\(258\) | −0.891011 | −0.0554719 | ||||||||
\(259\) | −17.5851 | −1.09268 | ||||||||
\(260\) | 2.10869 | 0.130776 | ||||||||
\(261\) | −5.11761 | −0.316772 | ||||||||
\(262\) | −12.6445 | −0.781179 | ||||||||
\(263\) | −27.1804 | −1.67602 | −0.838008 | − | 0.545658i | \(-0.816280\pi\) | ||||
−0.838008 | + | 0.545658i | \(0.816280\pi\) | |||||||
\(264\) | −2.21467 | −0.136303 | ||||||||
\(265\) | 11.3612 | 0.697915 | ||||||||
\(266\) | 3.37743 | 0.207084 | ||||||||
\(267\) | 0.100261 | 0.00613588 | ||||||||
\(268\) | −2.00292 | −0.122348 | ||||||||
\(269\) | 11.9880 | 0.730921 | 0.365460 | − | 0.930827i | \(-0.380912\pi\) | ||||
0.365460 | + | 0.930827i | \(0.380912\pi\) | |||||||
\(270\) | −12.4477 | −0.757543 | ||||||||
\(271\) | −27.7685 | −1.68682 | −0.843410 | − | 0.537271i | \(-0.819455\pi\) | ||||
−0.843410 | + | 0.537271i | \(0.819455\pi\) | |||||||
\(272\) | −2.79309 | −0.169356 | ||||||||
\(273\) | −2.54200 | −0.153849 | ||||||||
\(274\) | −8.79787 | −0.531498 | ||||||||
\(275\) | 1.50910 | 0.0910019 | ||||||||
\(276\) | −1.72350 | −0.103743 | ||||||||
\(277\) | −2.81410 | −0.169083 | −0.0845415 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845415 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(278\) | −15.1785 | −0.910345 | ||||||||
\(279\) | 11.8015 | 0.706536 | ||||||||
\(280\) | −16.0963 | −0.961935 | ||||||||
\(281\) | 27.7761 | 1.65698 | 0.828492 | − | 0.560001i | \(-0.189199\pi\) | ||||
0.828492 | + | 0.560001i | \(0.189199\pi\) | |||||||
\(282\) | 0.374555 | 0.0223044 | ||||||||
\(283\) | −18.1857 | −1.08103 | −0.540514 | − | 0.841335i | \(-0.681770\pi\) | ||||
−0.540514 | + | 0.841335i | \(0.681770\pi\) | |||||||
\(284\) | 1.64834 | 0.0978112 | ||||||||
\(285\) | −2.45791 | −0.145594 | ||||||||
\(286\) | 2.09473 | 0.123864 | ||||||||
\(287\) | −20.0685 | −1.18461 | ||||||||
\(288\) | 6.63595 | 0.391027 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.48994 | −0.381102 | ||||||||
\(291\) | −2.97199 | −0.174221 | ||||||||
\(292\) | 4.96947 | 0.290816 | ||||||||
\(293\) | 4.96145 | 0.289851 | 0.144925 | − | 0.989443i | \(-0.453706\pi\) | ||||
0.144925 | + | 0.989443i | \(0.453706\pi\) | |||||||
\(294\) | −2.44645 | −0.142680 | ||||||||
\(295\) | 12.1133 | 0.705265 | ||||||||
\(296\) | 26.0784 | 1.51577 | ||||||||
\(297\) | 3.96464 | 0.230052 | ||||||||
\(298\) | −1.35508 | −0.0784978 | ||||||||
\(299\) | 8.34465 | 0.482584 | ||||||||
\(300\) | 0.530547 | 0.0306312 | ||||||||
\(301\) | 2.06260 | 0.118886 | ||||||||
\(302\) | 22.1127 | 1.27244 | ||||||||
\(303\) | −0.175554 | −0.0100853 | ||||||||
\(304\) | −3.71649 | −0.213155 | ||||||||
\(305\) | 0.313614 | 0.0179575 | ||||||||
\(306\) | 3.04675 | 0.174171 | ||||||||
\(307\) | 9.94534 | 0.567610 | 0.283805 | − | 0.958882i | \(-0.408403\pi\) | ||||
0.283805 | + | 0.958882i | \(0.408403\pi\) | |||||||
\(308\) | 1.00153 | 0.0570674 | ||||||||
\(309\) | 6.69950 | 0.381121 | ||||||||
\(310\) | 14.9662 | 0.850021 | ||||||||
\(311\) | 11.9476 | 0.677484 | 0.338742 | − | 0.940879i | \(-0.389999\pi\) | ||||
0.338742 | + | 0.940879i | \(0.389999\pi\) | |||||||
\(312\) | 3.76975 | 0.213420 | ||||||||
\(313\) | 9.04759 | 0.511400 | 0.255700 | − | 0.966756i | \(-0.417694\pi\) | ||||
0.255700 | + | 0.966756i | \(0.417694\pi\) | |||||||
\(314\) | −1.86097 | −0.105020 | ||||||||
\(315\) | 13.0282 | 0.734058 | ||||||||
\(316\) | 6.45916 | 0.363356 | ||||||||
\(317\) | 2.31430 | 0.129984 | 0.0649920 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649920 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(318\) | 3.96778 | 0.222502 | ||||||||
\(319\) | 2.06707 | 0.115734 | ||||||||
\(320\) | 22.6674 | 1.26715 | ||||||||
\(321\) | 5.73049 | 0.319845 | ||||||||
\(322\) | −12.4435 | −0.693451 | ||||||||
\(323\) | 1.33060 | 0.0740366 | ||||||||
\(324\) | −2.21263 | −0.122924 | ||||||||
\(325\) | −2.56874 | −0.142488 | ||||||||
\(326\) | −5.68560 | −0.314896 | ||||||||
\(327\) | −5.67122 | −0.313619 | ||||||||
\(328\) | 29.7613 | 1.64329 | ||||||||
\(329\) | −0.867055 | −0.0478023 | ||||||||
\(330\) | 2.27323 | 0.125137 | ||||||||
\(331\) | 4.70110 | 0.258396 | 0.129198 | − | 0.991619i | \(-0.458760\pi\) | ||||
0.129198 | + | 0.991619i | \(0.458760\pi\) | |||||||
\(332\) | 0.0784291 | 0.00430435 | ||||||||
\(333\) | −21.1077 | −1.15670 | ||||||||
\(334\) | −28.0131 | −1.53281 | ||||||||
\(335\) | 10.5238 | 0.574979 | ||||||||
\(336\) | −4.17116 | −0.227556 | ||||||||
\(337\) | −11.1600 | −0.607925 | −0.303962 | − | 0.952684i | \(-0.598310\pi\) | ||||
−0.303962 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(338\) | 12.4325 | 0.676239 | ||||||||
\(339\) | −9.64850 | −0.524035 | ||||||||
\(340\) | −1.23882 | −0.0671847 | ||||||||
\(341\) | −4.76678 | −0.258136 | ||||||||
\(342\) | 4.05400 | 0.219215 | ||||||||
\(343\) | 20.1014 | 1.08538 | ||||||||
\(344\) | −3.05880 | −0.164919 | ||||||||
\(345\) | 9.05572 | 0.487544 | ||||||||
\(346\) | 5.89534 | 0.316935 | ||||||||
\(347\) | 24.1946 | 1.29884 | 0.649418 | − | 0.760432i | \(-0.275013\pi\) | ||||
0.649418 | + | 0.760432i | \(0.275013\pi\) | |||||||
\(348\) | 0.726713 | 0.0389559 | ||||||||
\(349\) | −12.9487 | −0.693127 | −0.346564 | − | 0.938026i | \(-0.612652\pi\) | ||||
−0.346564 | + | 0.938026i | \(0.612652\pi\) | |||||||
\(350\) | 3.83050 | 0.204749 | ||||||||
\(351\) | −6.74850 | −0.360209 | ||||||||
\(352\) | −2.68035 | −0.142863 | ||||||||
\(353\) | −0.749307 | −0.0398816 | −0.0199408 | − | 0.999801i | \(-0.506348\pi\) | ||||
−0.0199408 | + | 0.999801i | \(0.506348\pi\) | |||||||
\(354\) | 4.23044 | 0.224846 | ||||||||
\(355\) | −8.66081 | −0.459668 | ||||||||
\(356\) | 0.0672394 | 0.00356368 | ||||||||
\(357\) | 1.49339 | 0.0790384 | ||||||||
\(358\) | −12.6945 | −0.670925 | ||||||||
\(359\) | 18.6476 | 0.984183 | 0.492091 | − | 0.870544i | \(-0.336233\pi\) | ||||
0.492091 | + | 0.870544i | \(0.336233\pi\) | |||||||
\(360\) | −19.3207 | −1.01829 | ||||||||
\(361\) | −17.2295 | −0.906816 | ||||||||
\(362\) | 20.1859 | 1.06095 | ||||||||
\(363\) | −0.724033 | −0.0380019 | ||||||||
\(364\) | −1.70478 | −0.0893545 | ||||||||
\(365\) | −26.1108 | −1.36670 | ||||||||
\(366\) | 0.109526 | 0.00572503 | ||||||||
\(367\) | −34.2155 | −1.78603 | −0.893017 | − | 0.450022i | \(-0.851416\pi\) | ||||
−0.893017 | + | 0.450022i | \(0.851416\pi\) | |||||||
\(368\) | 13.6927 | 0.713782 | ||||||||
\(369\) | −24.0887 | −1.25401 | ||||||||
\(370\) | −26.7680 | −1.39160 | ||||||||
\(371\) | −9.18500 | −0.476861 | ||||||||
\(372\) | −1.67584 | −0.0868883 | ||||||||
\(373\) | 27.3694 | 1.41713 | 0.708567 | − | 0.705644i | \(-0.249342\pi\) | ||||
0.708567 | + | 0.705644i | \(0.249342\pi\) | |||||||
\(374\) | −1.23062 | −0.0636340 | ||||||||
\(375\) | 6.44847 | 0.332997 | ||||||||
\(376\) | 1.28583 | 0.0663115 | ||||||||
\(377\) | −3.51851 | −0.181213 | ||||||||
\(378\) | 10.0634 | 0.517603 | ||||||||
\(379\) | −12.0817 | −0.620593 | −0.310297 | − | 0.950640i | \(-0.600428\pi\) | ||||
−0.310297 | + | 0.950640i | \(0.600428\pi\) | |||||||
\(380\) | −1.64838 | −0.0845601 | ||||||||
\(381\) | 8.01901 | 0.410826 | ||||||||
\(382\) | −10.2723 | −0.525575 | ||||||||
\(383\) | −12.3332 | −0.630197 | −0.315099 | − | 0.949059i | \(-0.602038\pi\) | ||||
−0.315099 | + | 0.949059i | \(0.602038\pi\) | |||||||
\(384\) | 4.03503 | 0.205912 | ||||||||
\(385\) | −5.26229 | −0.268191 | ||||||||
\(386\) | 13.0802 | 0.665762 | ||||||||
\(387\) | 2.47578 | 0.125851 | ||||||||
\(388\) | −1.99314 | −0.101187 | ||||||||
\(389\) | 22.6996 | 1.15092 | 0.575458 | − | 0.817831i | \(-0.304824\pi\) | ||||
0.575458 | + | 0.817831i | \(0.304824\pi\) | |||||||
\(390\) | −3.86943 | −0.195936 | ||||||||
\(391\) | −4.90235 | −0.247923 | ||||||||
\(392\) | −8.39853 | −0.424190 | ||||||||
\(393\) | −7.43934 | −0.375265 | ||||||||
\(394\) | 26.2906 | 1.32450 | ||||||||
\(395\) | −33.9381 | −1.70761 | ||||||||
\(396\) | 1.20216 | 0.0604106 | ||||||||
\(397\) | −28.3781 | −1.42426 | −0.712128 | − | 0.702050i | \(-0.752268\pi\) | ||||
−0.712128 | + | 0.702050i | \(0.752268\pi\) | |||||||
\(398\) | 14.6403 | 0.733850 | ||||||||
\(399\) | 1.98710 | 0.0994795 | ||||||||
\(400\) | −4.21504 | −0.210752 | ||||||||
\(401\) | −34.1374 | −1.70474 | −0.852371 | − | 0.522938i | \(-0.824836\pi\) | ||||
−0.852371 | + | 0.522938i | \(0.824836\pi\) | |||||||
\(402\) | 3.67534 | 0.183309 | ||||||||
\(403\) | 8.11388 | 0.404181 | ||||||||
\(404\) | −0.117734 | −0.00585747 | ||||||||
\(405\) | 11.6257 | 0.577687 | ||||||||
\(406\) | 5.24680 | 0.260394 | ||||||||
\(407\) | 8.52570 | 0.422603 | ||||||||
\(408\) | −2.21467 | −0.109642 | ||||||||
\(409\) | 24.8229 | 1.22741 | 0.613706 | − | 0.789535i | \(-0.289678\pi\) | ||||
0.613706 | + | 0.789535i | \(0.289678\pi\) | |||||||
\(410\) | −30.5483 | −1.50867 | ||||||||
\(411\) | −5.17619 | −0.255323 | ||||||||
\(412\) | 4.49297 | 0.221353 | ||||||||
\(413\) | −9.79303 | −0.481883 | ||||||||
\(414\) | −14.9362 | −0.734076 | ||||||||
\(415\) | −0.412086 | −0.0202285 | ||||||||
\(416\) | 4.56242 | 0.223691 | ||||||||
\(417\) | −8.93021 | −0.437314 | ||||||||
\(418\) | −1.63747 | −0.0800911 | ||||||||
\(419\) | 32.2326 | 1.57467 | 0.787334 | − | 0.616527i | \(-0.211461\pi\) | ||||
0.787334 | + | 0.616527i | \(0.211461\pi\) | |||||||
\(420\) | −1.85004 | −0.0902729 | ||||||||
\(421\) | −10.2195 | −0.498067 | −0.249033 | − | 0.968495i | \(-0.580113\pi\) | ||||
−0.249033 | + | 0.968495i | \(0.580113\pi\) | |||||||
\(422\) | 10.7168 | 0.521683 | ||||||||
\(423\) | −1.04074 | −0.0506027 | ||||||||
\(424\) | 13.6212 | 0.661504 | ||||||||
\(425\) | 1.50910 | 0.0732019 | ||||||||
\(426\) | −3.02469 | −0.146547 | ||||||||
\(427\) | −0.253541 | −0.0122697 | ||||||||
\(428\) | 3.84311 | 0.185764 | ||||||||
\(429\) | 1.23243 | 0.0595022 | ||||||||
\(430\) | 3.13968 | 0.151409 | ||||||||
\(431\) | 19.6132 | 0.944733 | 0.472367 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472367 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(432\) | −11.0736 | −0.532779 | ||||||||
\(433\) | 10.3066 | 0.495305 | 0.247653 | − | 0.968849i | \(-0.420341\pi\) | ||||
0.247653 | + | 0.968849i | \(0.420341\pi\) | |||||||
\(434\) | −12.0994 | −0.580790 | ||||||||
\(435\) | −3.81833 | −0.183075 | ||||||||
\(436\) | −3.80336 | −0.182148 | ||||||||
\(437\) | −6.52307 | −0.312041 | ||||||||
\(438\) | −9.11892 | −0.435719 | ||||||||
\(439\) | 5.03484 | 0.240300 | 0.120150 | − | 0.992756i | \(-0.461662\pi\) | ||||
0.120150 | + | 0.992756i | \(0.461662\pi\) | |||||||
\(440\) | 7.80388 | 0.372036 | ||||||||
\(441\) | 6.79774 | 0.323702 | ||||||||
\(442\) | 2.09473 | 0.0996363 | ||||||||
\(443\) | −38.5195 | −1.83012 | −0.915059 | − | 0.403321i | \(-0.867856\pi\) | ||||
−0.915059 | + | 0.403321i | \(0.867856\pi\) | |||||||
\(444\) | 2.99735 | 0.142248 | ||||||||
\(445\) | −0.353292 | −0.0167477 | ||||||||
\(446\) | −27.0786 | −1.28221 | ||||||||
\(447\) | −0.797258 | −0.0377090 | ||||||||
\(448\) | −18.3255 | −0.865799 | ||||||||
\(449\) | −9.20981 | −0.434638 | −0.217319 | − | 0.976101i | \(-0.569731\pi\) | ||||
−0.217319 | + | 0.976101i | \(0.569731\pi\) | |||||||
\(450\) | 4.59783 | 0.216744 | ||||||||
\(451\) | 9.72974 | 0.458156 | ||||||||
\(452\) | −6.47070 | −0.304356 | ||||||||
\(453\) | 13.0099 | 0.611260 | ||||||||
\(454\) | −4.83159 | −0.226758 | ||||||||
\(455\) | 8.95732 | 0.419926 | ||||||||
\(456\) | −2.94684 | −0.137998 | ||||||||
\(457\) | 38.0073 | 1.77791 | 0.888953 | − | 0.457998i | \(-0.151433\pi\) | ||||
0.888953 | + | 0.457998i | \(0.151433\pi\) | |||||||
\(458\) | 33.3668 | 1.55913 | ||||||||
\(459\) | 3.96464 | 0.185054 | ||||||||
\(460\) | 6.07315 | 0.283162 | ||||||||
\(461\) | 29.9323 | 1.39408 | 0.697042 | − | 0.717030i | \(-0.254499\pi\) | ||||
0.697042 | + | 0.717030i | \(0.254499\pi\) | |||||||
\(462\) | −1.83780 | −0.0855020 | ||||||||
\(463\) | −18.7756 | −0.872575 | −0.436288 | − | 0.899807i | \(-0.643707\pi\) | ||||
−0.436288 | + | 0.899807i | \(0.643707\pi\) | |||||||
\(464\) | −5.77351 | −0.268029 | ||||||||
\(465\) | 8.80529 | 0.408335 | ||||||||
\(466\) | −6.18087 | −0.286323 | ||||||||
\(467\) | −30.9064 | −1.43018 | −0.715090 | − | 0.699032i | \(-0.753614\pi\) | ||||
−0.715090 | + | 0.699032i | \(0.753614\pi\) | |||||||
\(468\) | −2.04628 | −0.0945892 | ||||||||
\(469\) | −8.50801 | −0.392863 | ||||||||
\(470\) | −1.31983 | −0.0608792 | ||||||||
\(471\) | −1.09489 | −0.0504500 | ||||||||
\(472\) | 14.5229 | 0.668471 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −11.8525 | −0.544403 | ||||||||
\(475\) | 2.00800 | 0.0921335 | ||||||||
\(476\) | 1.00153 | 0.0459050 | ||||||||
\(477\) | −11.0249 | −0.504797 | ||||||||
\(478\) | −10.0574 | −0.460013 | ||||||||
\(479\) | 2.78364 | 0.127188 | 0.0635938 | − | 0.997976i | \(-0.479744\pi\) | ||||
0.0635938 | + | 0.997976i | \(0.479744\pi\) | |||||||
\(480\) | 4.95120 | 0.225990 | ||||||||
\(481\) | −14.5122 | −0.661700 | ||||||||
\(482\) | 10.3846 | 0.473008 | ||||||||
\(483\) | −7.32111 | −0.333122 | ||||||||
\(484\) | −0.485567 | −0.0220712 | ||||||||
\(485\) | 10.4725 | 0.475531 | ||||||||
\(486\) | 18.6971 | 0.848117 | ||||||||
\(487\) | −5.18595 | −0.234998 | −0.117499 | − | 0.993073i | \(-0.537488\pi\) | ||||
−0.117499 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(488\) | 0.375998 | 0.0170206 | ||||||||
\(489\) | −3.34510 | −0.151271 | ||||||||
\(490\) | 8.62061 | 0.389440 | ||||||||
\(491\) | 25.8437 | 1.16631 | 0.583155 | − | 0.812361i | \(-0.301818\pi\) | ||||
0.583155 | + | 0.812361i | \(0.301818\pi\) | |||||||
\(492\) | 3.42065 | 0.154215 | ||||||||
\(493\) | 2.06707 | 0.0930962 | ||||||||
\(494\) | 2.78725 | 0.125404 | ||||||||
\(495\) | −6.31643 | −0.283902 | ||||||||
\(496\) | 13.3140 | 0.597818 | ||||||||
\(497\) | 7.00185 | 0.314076 | ||||||||
\(498\) | −0.143917 | −0.00644905 | ||||||||
\(499\) | −28.0904 | −1.25750 | −0.628749 | − | 0.777608i | \(-0.716433\pi\) | ||||
−0.628749 | + | 0.777608i | \(0.716433\pi\) | |||||||
\(500\) | 4.32462 | 0.193403 | ||||||||
\(501\) | −16.4814 | −0.736336 | ||||||||
\(502\) | 27.0318 | 1.20649 | ||||||||
\(503\) | −29.3877 | −1.31033 | −0.655167 | − | 0.755484i | \(-0.727402\pi\) | ||||
−0.655167 | + | 0.755484i | \(0.727402\pi\) | |||||||
\(504\) | 15.6198 | 0.695762 | ||||||||
\(505\) | 0.618603 | 0.0275275 | ||||||||
\(506\) | 6.03295 | 0.268197 | ||||||||
\(507\) | 7.31462 | 0.324854 | ||||||||
\(508\) | 5.37789 | 0.238605 | ||||||||
\(509\) | 12.9918 | 0.575851 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(510\) | 2.27323 | 0.100660 | ||||||||
\(511\) | 21.1093 | 0.933822 | ||||||||
\(512\) | 24.5734 | 1.08600 | ||||||||
\(513\) | 5.27535 | 0.232913 | ||||||||
\(514\) | −21.0657 | −0.929167 | ||||||||
\(515\) | −23.6072 | −1.04026 | ||||||||
\(516\) | −0.351567 | −0.0154769 | ||||||||
\(517\) | 0.420371 | 0.0184879 | ||||||||
\(518\) | 21.6406 | 0.950833 | ||||||||
\(519\) | 3.46850 | 0.152250 | ||||||||
\(520\) | −13.2836 | −0.582523 | ||||||||
\(521\) | −6.96116 | −0.304974 | −0.152487 | − | 0.988305i | \(-0.548728\pi\) | ||||
−0.152487 | + | 0.988305i | \(0.548728\pi\) | |||||||
\(522\) | 6.29784 | 0.275649 | ||||||||
\(523\) | −6.81286 | −0.297905 | −0.148953 | − | 0.988844i | \(-0.547590\pi\) | ||||
−0.148953 | + | 0.988844i | \(0.547590\pi\) | |||||||
\(524\) | −4.98914 | −0.217952 | ||||||||
\(525\) | 2.25366 | 0.0983579 | ||||||||
\(526\) | 33.4488 | 1.45844 | ||||||||
\(527\) | −4.76678 | −0.207644 | ||||||||
\(528\) | 2.02229 | 0.0880088 | ||||||||
\(529\) | 1.03306 | 0.0449158 | ||||||||
\(530\) | −13.9814 | −0.607313 | ||||||||
\(531\) | −11.7548 | −0.510114 | ||||||||
\(532\) | 1.33264 | 0.0577771 | ||||||||
\(533\) | −16.5617 | −0.717367 | ||||||||
\(534\) | −0.123384 | −0.00533933 | ||||||||
\(535\) | −20.1927 | −0.873005 | ||||||||
\(536\) | 12.6172 | 0.544982 | ||||||||
\(537\) | −7.46877 | −0.322301 | ||||||||
\(538\) | −14.7527 | −0.636034 | ||||||||
\(539\) | −2.74570 | −0.118266 | ||||||||
\(540\) | −4.91149 | −0.211357 | ||||||||
\(541\) | −27.9635 | −1.20225 | −0.601123 | − | 0.799156i | \(-0.705280\pi\) | ||||
−0.601123 | + | 0.799156i | \(0.705280\pi\) | |||||||
\(542\) | 34.1726 | 1.46784 | ||||||||
\(543\) | 11.8763 | 0.509661 | ||||||||
\(544\) | −2.68035 | −0.114919 | ||||||||
\(545\) | 19.9838 | 0.856013 | ||||||||
\(546\) | 3.12825 | 0.133877 | ||||||||
\(547\) | 1.84789 | 0.0790100 | 0.0395050 | − | 0.999219i | \(-0.487422\pi\) | ||||
0.0395050 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(548\) | −3.47138 | −0.148290 | ||||||||
\(549\) | −0.304331 | −0.0129885 | ||||||||
\(550\) | −1.85713 | −0.0791882 | ||||||||
\(551\) | 2.75045 | 0.117173 | ||||||||
\(552\) | 10.8571 | 0.462108 | ||||||||
\(553\) | 27.4373 | 1.16675 | ||||||||
\(554\) | 3.46310 | 0.147133 | ||||||||
\(555\) | −15.7488 | −0.668501 | ||||||||
\(556\) | −5.98898 | −0.253989 | ||||||||
\(557\) | −29.4574 | −1.24815 | −0.624075 | − | 0.781364i | \(-0.714524\pi\) | ||||
−0.624075 | + | 0.781364i | \(0.714524\pi\) | |||||||
\(558\) | −14.5232 | −0.614815 | ||||||||
\(559\) | 1.70217 | 0.0719942 | ||||||||
\(560\) | 14.6980 | 0.621105 | ||||||||
\(561\) | −0.724033 | −0.0305687 | ||||||||
\(562\) | −34.1819 | −1.44188 | ||||||||
\(563\) | −42.1523 | −1.77651 | −0.888253 | − | 0.459355i | \(-0.848081\pi\) | ||||
−0.888253 | + | 0.459355i | \(0.848081\pi\) | |||||||
\(564\) | 0.147788 | 0.00622301 | ||||||||
\(565\) | 33.9987 | 1.43034 | ||||||||
\(566\) | 22.3797 | 0.940690 | ||||||||
\(567\) | −9.39884 | −0.394714 | ||||||||
\(568\) | −10.3836 | −0.435687 | ||||||||
\(569\) | −35.0523 | −1.46947 | −0.734735 | − | 0.678355i | \(-0.762693\pi\) | ||||
−0.734735 | + | 0.678355i | \(0.762693\pi\) | |||||||
\(570\) | 3.02476 | 0.126693 | ||||||||
\(571\) | 2.47386 | 0.103528 | 0.0517638 | − | 0.998659i | \(-0.483516\pi\) | ||||
0.0517638 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(572\) | 0.826519 | 0.0345585 | ||||||||
\(573\) | −6.04365 | −0.252477 | ||||||||
\(574\) | 24.6968 | 1.03082 | ||||||||
\(575\) | −7.39812 | −0.308523 | ||||||||
\(576\) | −21.9965 | −0.916520 | ||||||||
\(577\) | −34.1607 | −1.42213 | −0.711064 | − | 0.703128i | \(-0.751786\pi\) | ||||
−0.711064 | + | 0.703128i | \(0.751786\pi\) | |||||||
\(578\) | −1.23062 | −0.0511872 | ||||||||
\(579\) | 7.69566 | 0.319821 | ||||||||
\(580\) | −2.56074 | −0.106329 | ||||||||
\(581\) | 0.333151 | 0.0138215 | ||||||||
\(582\) | 3.65740 | 0.151604 | ||||||||
\(583\) | 4.45312 | 0.184430 | ||||||||
\(584\) | −31.3048 | −1.29540 | ||||||||
\(585\) | 10.7517 | 0.444526 | ||||||||
\(586\) | −6.10567 | −0.252223 | ||||||||
\(587\) | −2.00704 | −0.0828393 | −0.0414197 | − | 0.999142i | \(-0.513188\pi\) | ||||
−0.0414197 | + | 0.999142i | \(0.513188\pi\) | |||||||
\(588\) | −0.965296 | −0.0398081 | ||||||||
\(589\) | −6.34268 | −0.261346 | ||||||||
\(590\) | −14.9069 | −0.613708 | ||||||||
\(591\) | 15.4680 | 0.636268 | ||||||||
\(592\) | −23.8130 | −0.978710 | ||||||||
\(593\) | 43.8241 | 1.79964 | 0.899820 | − | 0.436261i | \(-0.143698\pi\) | ||||
0.899820 | + | 0.436261i | \(0.143698\pi\) | |||||||
\(594\) | −4.87898 | −0.200187 | ||||||||
\(595\) | −5.26229 | −0.215733 | ||||||||
\(596\) | −0.534676 | −0.0219012 | ||||||||
\(597\) | 8.61355 | 0.352529 | ||||||||
\(598\) | −10.2691 | −0.419935 | ||||||||
\(599\) | −27.6933 | −1.13152 | −0.565758 | − | 0.824571i | \(-0.691416\pi\) | ||||
−0.565758 | + | 0.824571i | \(0.691416\pi\) | |||||||
\(600\) | −3.34215 | −0.136443 | ||||||||
\(601\) | −42.4356 | −1.73099 | −0.865493 | − | 0.500921i | \(-0.832995\pi\) | ||||
−0.865493 | + | 0.500921i | \(0.832995\pi\) | |||||||
\(602\) | −2.53828 | −0.103452 | ||||||||
\(603\) | −10.2123 | −0.415879 | ||||||||
\(604\) | 8.72502 | 0.355016 | ||||||||
\(605\) | 2.55129 | 0.103725 | ||||||||
\(606\) | 0.216040 | 0.00877604 | ||||||||
\(607\) | −4.66797 | −0.189467 | −0.0947336 | − | 0.995503i | \(-0.530200\pi\) | ||||
−0.0947336 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(608\) | −3.56648 | −0.144640 | ||||||||
\(609\) | 3.08694 | 0.125089 | ||||||||
\(610\) | −0.385940 | −0.0156263 | ||||||||
\(611\) | −0.715543 | −0.0289478 | ||||||||
\(612\) | 1.20216 | 0.0485943 | ||||||||
\(613\) | −21.6534 | −0.874574 | −0.437287 | − | 0.899322i | \(-0.644061\pi\) | ||||
−0.437287 | + | 0.899322i | \(0.644061\pi\) | |||||||
\(614\) | −12.2390 | −0.493924 | ||||||||
\(615\) | −17.9730 | −0.724740 | ||||||||
\(616\) | −6.30906 | −0.254199 | ||||||||
\(617\) | 1.32307 | 0.0532647 | 0.0266323 | − | 0.999645i | \(-0.491522\pi\) | ||||
0.0266323 | + | 0.999645i | \(0.491522\pi\) | |||||||
\(618\) | −8.24456 | −0.331645 | ||||||||
\(619\) | 10.3077 | 0.414303 | 0.207151 | − | 0.978309i | \(-0.433581\pi\) | ||||
0.207151 | + | 0.978309i | \(0.433581\pi\) | |||||||
\(620\) | 5.90520 | 0.237159 | ||||||||
\(621\) | −19.4361 | −0.779943 | ||||||||
\(622\) | −14.7029 | −0.589534 | ||||||||
\(623\) | 0.285620 | 0.0114431 | ||||||||
\(624\) | −3.44228 | −0.137802 | ||||||||
\(625\) | −30.2681 | −1.21072 | ||||||||
\(626\) | −11.1342 | −0.445011 | ||||||||
\(627\) | −0.963398 | −0.0384744 | ||||||||
\(628\) | −0.734283 | −0.0293011 | ||||||||
\(629\) | 8.52570 | 0.339942 | ||||||||
\(630\) | −16.0329 | −0.638764 | ||||||||
\(631\) | −33.4364 | −1.33108 | −0.665541 | − | 0.746362i | \(-0.731799\pi\) | ||||
−0.665541 | + | 0.746362i | \(0.731799\pi\) | |||||||
\(632\) | −40.6890 | −1.61852 | ||||||||
\(633\) | 6.30517 | 0.250608 | ||||||||
\(634\) | −2.84803 | −0.113110 | ||||||||
\(635\) | −28.2568 | −1.12134 | ||||||||
\(636\) | 1.56557 | 0.0620789 | ||||||||
\(637\) | 4.67365 | 0.185177 | ||||||||
\(638\) | −2.54378 | −0.100709 | ||||||||
\(639\) | 8.40446 | 0.332475 | ||||||||
\(640\) | −14.2183 | −0.562029 | ||||||||
\(641\) | 23.8883 | 0.943532 | 0.471766 | − | 0.881724i | \(-0.343617\pi\) | ||||
0.471766 | + | 0.881724i | \(0.343617\pi\) | |||||||
\(642\) | −7.05207 | −0.278323 | ||||||||
\(643\) | 4.89038 | 0.192858 | 0.0964289 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964289 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(644\) | −4.90985 | −0.193475 | ||||||||
\(645\) | 1.84722 | 0.0727342 | ||||||||
\(646\) | −1.63747 | −0.0644253 | ||||||||
\(647\) | 14.4863 | 0.569515 | 0.284758 | − | 0.958600i | \(-0.408087\pi\) | ||||
0.284758 | + | 0.958600i | \(0.408087\pi\) | |||||||
\(648\) | 13.9383 | 0.547549 | ||||||||
\(649\) | 4.74791 | 0.186372 | ||||||||
\(650\) | 3.16115 | 0.123991 | ||||||||
\(651\) | −7.11865 | −0.279002 | ||||||||
\(652\) | −2.24337 | −0.0878571 | ||||||||
\(653\) | −17.3742 | −0.679904 | −0.339952 | − | 0.940443i | \(-0.610411\pi\) | ||||
−0.339952 | + | 0.940443i | \(0.610411\pi\) | |||||||
\(654\) | 6.97913 | 0.272906 | ||||||||
\(655\) | 26.2142 | 1.02427 | ||||||||
\(656\) | −27.1760 | −1.06105 | ||||||||
\(657\) | 25.3380 | 0.988528 | ||||||||
\(658\) | 1.06702 | 0.0415967 | ||||||||
\(659\) | −17.3649 | −0.676439 | −0.338219 | − | 0.941067i | \(-0.609825\pi\) | ||||
−0.338219 | + | 0.941067i | \(0.609825\pi\) | |||||||
\(660\) | 0.896949 | 0.0349137 | ||||||||
\(661\) | −18.3523 | −0.713824 | −0.356912 | − | 0.934138i | \(-0.616170\pi\) | ||||
−0.356912 | + | 0.934138i | \(0.616170\pi\) | |||||||
\(662\) | −5.78529 | −0.224852 | ||||||||
\(663\) | 1.23243 | 0.0478636 | ||||||||
\(664\) | −0.494058 | −0.0191732 | ||||||||
\(665\) | −7.00200 | −0.271526 | ||||||||
\(666\) | 25.9756 | 1.00654 | ||||||||
\(667\) | −10.1335 | −0.392371 | ||||||||
\(668\) | −11.0532 | −0.427659 | ||||||||
\(669\) | −15.9316 | −0.615952 | ||||||||
\(670\) | −12.9509 | −0.500336 | ||||||||
\(671\) | 0.122923 | 0.00474541 | ||||||||
\(672\) | −4.00280 | −0.154411 | ||||||||
\(673\) | −9.53814 | −0.367668 | −0.183834 | − | 0.982957i | \(-0.558851\pi\) | ||||
−0.183834 | + | 0.982957i | \(0.558851\pi\) | |||||||
\(674\) | 13.7338 | 0.529005 | ||||||||
\(675\) | 5.98302 | 0.230287 | ||||||||
\(676\) | 4.90550 | 0.188673 | ||||||||
\(677\) | −2.57181 | −0.0988429 | −0.0494214 | − | 0.998778i | \(-0.515738\pi\) | ||||
−0.0494214 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(678\) | 11.8737 | 0.456005 | ||||||||
\(679\) | −8.46649 | −0.324914 | ||||||||
\(680\) | 7.80388 | 0.299265 | ||||||||
\(681\) | −2.84265 | −0.108930 | ||||||||
\(682\) | 5.86611 | 0.224625 | ||||||||
\(683\) | −38.8665 | −1.48719 | −0.743593 | − | 0.668632i | \(-0.766880\pi\) | ||||
−0.743593 | + | 0.668632i | \(0.766880\pi\) | |||||||
\(684\) | 1.59959 | 0.0611618 | ||||||||
\(685\) | 18.2395 | 0.696895 | ||||||||
\(686\) | −24.7373 | −0.944474 | ||||||||
\(687\) | 19.6312 | 0.748978 | ||||||||
\(688\) | 2.79309 | 0.106486 | ||||||||
\(689\) | −7.57999 | −0.288775 | ||||||||
\(690\) | −11.1442 | −0.424252 | ||||||||
\(691\) | −46.6076 | −1.77304 | −0.886518 | − | 0.462694i | \(-0.846883\pi\) | ||||
−0.886518 | + | 0.462694i | \(0.846883\pi\) | |||||||
\(692\) | 2.32612 | 0.0884260 | ||||||||
\(693\) | 5.10653 | 0.193981 | ||||||||
\(694\) | −29.7744 | −1.13022 | ||||||||
\(695\) | 31.4676 | 1.19363 | ||||||||
\(696\) | −4.57788 | −0.173524 | ||||||||
\(697\) | 9.72974 | 0.368540 | ||||||||
\(698\) | 15.9350 | 0.603147 | ||||||||
\(699\) | −3.63649 | −0.137545 | ||||||||
\(700\) | 1.51140 | 0.0571257 | ||||||||
\(701\) | −20.3251 | −0.767670 | −0.383835 | − | 0.923402i | \(-0.625397\pi\) | ||||
−0.383835 | + | 0.923402i | \(0.625397\pi\) | |||||||
\(702\) | 8.30486 | 0.313447 | ||||||||
\(703\) | 11.3443 | 0.427858 | ||||||||
\(704\) | 8.88468 | 0.334854 | ||||||||
\(705\) | −0.776517 | −0.0292453 | ||||||||
\(706\) | 0.922115 | 0.0347042 | ||||||||
\(707\) | −0.500110 | −0.0188086 | ||||||||
\(708\) | 1.66921 | 0.0627327 | ||||||||
\(709\) | −38.5723 | −1.44861 | −0.724307 | − | 0.689478i | \(-0.757840\pi\) | ||||
−0.724307 | + | 0.689478i | \(0.757840\pi\) | |||||||
\(710\) | 10.6582 | 0.399995 | ||||||||
\(711\) | 32.9335 | 1.23510 | ||||||||
\(712\) | −0.423569 | −0.0158739 | ||||||||
\(713\) | 23.3684 | 0.875155 | ||||||||
\(714\) | −1.83780 | −0.0687778 | ||||||||
\(715\) | −4.34274 | −0.162409 | ||||||||
\(716\) | −5.00887 | −0.187190 | ||||||||
\(717\) | −5.91721 | −0.220982 | ||||||||
\(718\) | −22.9482 | −0.856418 | ||||||||
\(719\) | −39.8883 | −1.48758 | −0.743792 | − | 0.668412i | \(-0.766974\pi\) | ||||
−0.743792 | + | 0.668412i | \(0.766974\pi\) | |||||||
\(720\) | 17.6424 | 0.657492 | ||||||||
\(721\) | 19.0853 | 0.710773 | ||||||||
\(722\) | 21.2030 | 0.789095 | ||||||||
\(723\) | 6.10977 | 0.227225 | ||||||||
\(724\) | 7.96476 | 0.296008 | ||||||||
\(725\) | 3.11941 | 0.115852 | ||||||||
\(726\) | 0.891011 | 0.0330685 | ||||||||
\(727\) | −44.3011 | −1.64304 | −0.821518 | − | 0.570183i | \(-0.806872\pi\) | ||||
−0.821518 | + | 0.570183i | \(0.806872\pi\) | |||||||
\(728\) | 10.7391 | 0.398018 | ||||||||
\(729\) | −2.67003 | −0.0988899 | ||||||||
\(730\) | 32.1326 | 1.18928 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 0.0432158 | 0.00159730 | ||||||||
\(733\) | 19.4722 | 0.719223 | 0.359611 | − | 0.933102i | \(-0.382909\pi\) | ||||
0.359611 | + | 0.933102i | \(0.382909\pi\) | |||||||
\(734\) | 42.1064 | 1.55417 | ||||||||
\(735\) | 5.07191 | 0.187080 | ||||||||
\(736\) | 13.1400 | 0.484348 | ||||||||
\(737\) | 4.12490 | 0.151943 | ||||||||
\(738\) | 29.6441 | 1.09121 | ||||||||
\(739\) | −21.7893 | −0.801532 | −0.400766 | − | 0.916180i | \(-0.631256\pi\) | ||||
−0.400766 | + | 0.916180i | \(0.631256\pi\) | |||||||
\(740\) | −10.5618 | −0.388261 | ||||||||
\(741\) | 1.63987 | 0.0602421 | ||||||||
\(742\) | 11.3033 | 0.414956 | ||||||||
\(743\) | 1.39570 | 0.0512033 | 0.0256016 | − | 0.999672i | \(-0.491850\pi\) | ||||
0.0256016 | + | 0.999672i | \(0.491850\pi\) | |||||||
\(744\) | 10.5568 | 0.387032 | ||||||||
\(745\) | 2.80932 | 0.102926 | ||||||||
\(746\) | −33.6814 | −1.23316 | ||||||||
\(747\) | 0.399889 | 0.0146312 | ||||||||
\(748\) | −0.485567 | −0.0177541 | ||||||||
\(749\) | 16.3248 | 0.596495 | ||||||||
\(750\) | −7.93563 | −0.289768 | ||||||||
\(751\) | −42.1287 | −1.53730 | −0.768649 | − | 0.639671i | \(-0.779071\pi\) | ||||
−0.768649 | + | 0.639671i | \(0.779071\pi\) | |||||||
\(752\) | −1.17413 | −0.0428162 | ||||||||
\(753\) | 15.9041 | 0.579577 | ||||||||
\(754\) | 4.32996 | 0.157688 | ||||||||
\(755\) | −45.8434 | −1.66841 | ||||||||
\(756\) | 3.97070 | 0.144413 | ||||||||
\(757\) | 17.0395 | 0.619311 | 0.309655 | − | 0.950849i | \(-0.399786\pi\) | ||||
0.309655 | + | 0.950849i | \(0.399786\pi\) | |||||||
\(758\) | 14.8680 | 0.540029 | ||||||||
\(759\) | 3.54946 | 0.128837 | ||||||||
\(760\) | 10.3839 | 0.376662 | ||||||||
\(761\) | 15.3709 | 0.557194 | 0.278597 | − | 0.960408i | \(-0.410131\pi\) | ||||
0.278597 | + | 0.960408i | \(0.410131\pi\) | |||||||
\(762\) | −9.86837 | −0.357493 | ||||||||
\(763\) | −16.1559 | −0.584884 | ||||||||
\(764\) | −4.05313 | −0.146637 | ||||||||
\(765\) | −6.31643 | −0.228371 | ||||||||
\(766\) | 15.1775 | 0.548386 | ||||||||
\(767\) | −8.08177 | −0.291816 | ||||||||
\(768\) | 7.90000 | 0.285067 | ||||||||
\(769\) | 18.8483 | 0.679689 | 0.339844 | − | 0.940482i | \(-0.389626\pi\) | ||||
0.339844 | + | 0.940482i | \(0.389626\pi\) | |||||||
\(770\) | 6.47589 | 0.233375 | ||||||||
\(771\) | −12.3939 | −0.446356 | ||||||||
\(772\) | 5.16104 | 0.185750 | ||||||||
\(773\) | −23.9245 | −0.860503 | −0.430251 | − | 0.902709i | \(-0.641575\pi\) | ||||
−0.430251 | + | 0.902709i | \(0.641575\pi\) | |||||||
\(774\) | −3.04675 | −0.109513 | ||||||||
\(775\) | −7.19352 | −0.258399 | ||||||||
\(776\) | 12.5557 | 0.450722 | ||||||||
\(777\) | 12.7322 | 0.456764 | ||||||||
\(778\) | −27.9347 | −1.00151 | ||||||||
\(779\) | 12.9464 | 0.463853 | ||||||||
\(780\) | −1.52676 | −0.0546669 | ||||||||
\(781\) | −3.39468 | −0.121471 | ||||||||
\(782\) | 6.03295 | 0.215738 | ||||||||
\(783\) | 8.19519 | 0.292872 | ||||||||
\(784\) | 7.66898 | 0.273892 | ||||||||
\(785\) | 3.85811 | 0.137702 | ||||||||
\(786\) | 9.15502 | 0.326549 | ||||||||
\(787\) | 10.4619 | 0.372925 | 0.186463 | − | 0.982462i | \(-0.440298\pi\) | ||||
0.186463 | + | 0.982462i | \(0.440298\pi\) | |||||||
\(788\) | 10.3735 | 0.369541 | ||||||||
\(789\) | 19.6795 | 0.700609 | ||||||||
\(790\) | 41.7650 | 1.48593 | ||||||||
\(791\) | −27.4863 | −0.977299 | ||||||||
\(792\) | −7.57290 | −0.269091 | ||||||||
\(793\) | −0.209237 | −0.00743022 | ||||||||
\(794\) | 34.9227 | 1.23936 | ||||||||
\(795\) | −8.22590 | −0.291743 | ||||||||
\(796\) | 5.77662 | 0.204747 | ||||||||
\(797\) | −29.1601 | −1.03291 | −0.516453 | − | 0.856316i | \(-0.672748\pi\) | ||||
−0.516453 | + | 0.856316i | \(0.672748\pi\) | |||||||
\(798\) | −2.44537 | −0.0865652 | ||||||||
\(799\) | 0.420371 | 0.0148716 | ||||||||
\(800\) | −4.04491 | −0.143009 | ||||||||
\(801\) | 0.342835 | 0.0121135 | ||||||||
\(802\) | 42.0103 | 1.48344 | ||||||||
\(803\) | −10.2343 | −0.361162 | ||||||||
\(804\) | 1.45018 | 0.0511439 | ||||||||
\(805\) | 25.7976 | 0.909245 | ||||||||
\(806\) | −9.98513 | −0.351711 | ||||||||
\(807\) | −8.67970 | −0.305540 | ||||||||
\(808\) | 0.741655 | 0.0260913 | ||||||||
\(809\) | 2.03074 | 0.0713970 | 0.0356985 | − | 0.999363i | \(-0.488634\pi\) | ||||
0.0356985 | + | 0.999363i | \(0.488634\pi\) | |||||||
\(810\) | −14.3069 | −0.502693 | ||||||||
\(811\) | −10.3763 | −0.364362 | −0.182181 | − | 0.983265i | \(-0.558316\pi\) | ||||
−0.182181 | + | 0.983265i | \(0.558316\pi\) | |||||||
\(812\) | 2.07023 | 0.0726509 | ||||||||
\(813\) | 20.1053 | 0.705125 | ||||||||
\(814\) | −10.4919 | −0.367742 | ||||||||
\(815\) | 11.7872 | 0.412888 | ||||||||
\(816\) | 2.02229 | 0.0707943 | ||||||||
\(817\) | −1.33060 | −0.0465518 | ||||||||
\(818\) | −30.5476 | −1.06807 | ||||||||
\(819\) | −8.69219 | −0.303730 | ||||||||
\(820\) | −12.0534 | −0.420924 | ||||||||
\(821\) | −45.5802 | −1.59076 | −0.795381 | − | 0.606110i | \(-0.792729\pi\) | ||||
−0.795381 | + | 0.606110i | \(0.792729\pi\) | |||||||
\(822\) | 6.36994 | 0.222177 | ||||||||
\(823\) | −13.8649 | −0.483301 | −0.241650 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241650 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(824\) | −28.3032 | −0.985987 | ||||||||
\(825\) | −1.09263 | −0.0380406 | ||||||||
\(826\) | 12.0515 | 0.419326 | ||||||||
\(827\) | 14.8901 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(828\) | −5.89339 | −0.204810 | ||||||||
\(829\) | 13.4956 | 0.468722 | 0.234361 | − | 0.972150i | \(-0.424700\pi\) | ||||
0.234361 | + | 0.972150i | \(0.424700\pi\) | |||||||
\(830\) | 0.507122 | 0.0176025 | ||||||||
\(831\) | 2.03750 | 0.0706802 | ||||||||
\(832\) | −15.1233 | −0.524305 | ||||||||
\(833\) | −2.74570 | −0.0951328 | ||||||||
\(834\) | 10.9897 | 0.380543 | ||||||||
\(835\) | 58.0761 | 2.00980 | ||||||||
\(836\) | −0.646096 | −0.0223457 | ||||||||
\(837\) | −18.8986 | −0.653230 | ||||||||
\(838\) | −39.6662 | −1.37025 | ||||||||
\(839\) | 46.3349 | 1.59966 | 0.799829 | − | 0.600228i | \(-0.204924\pi\) | ||||
0.799829 | + | 0.600228i | \(0.204924\pi\) | |||||||
\(840\) | 11.6542 | 0.402109 | ||||||||
\(841\) | −24.7272 | −0.852663 | ||||||||
\(842\) | 12.5763 | 0.433408 | ||||||||
\(843\) | −20.1108 | −0.692653 | ||||||||
\(844\) | 4.22851 | 0.145551 | ||||||||
\(845\) | −25.7747 | −0.886677 | ||||||||
\(846\) | 1.28076 | 0.0440335 | ||||||||
\(847\) | −2.06260 | −0.0708716 | ||||||||
\(848\) | −12.4380 | −0.427122 | ||||||||
\(849\) | 13.1670 | 0.451892 | ||||||||
\(850\) | −1.85713 | −0.0636989 | ||||||||
\(851\) | −41.7960 | −1.43275 | ||||||||
\(852\) | −1.19345 | −0.0408871 | ||||||||
\(853\) | −14.6074 | −0.500148 | −0.250074 | − | 0.968227i | \(-0.580455\pi\) | ||||
−0.250074 | + | 0.968227i | \(0.580455\pi\) | |||||||
\(854\) | 0.312014 | 0.0106769 | ||||||||
\(855\) | −8.40465 | −0.287433 | ||||||||
\(856\) | −24.2094 | −0.827460 | ||||||||
\(857\) | −41.6128 | −1.42147 | −0.710733 | − | 0.703462i | \(-0.751637\pi\) | ||||
−0.710733 | + | 0.703462i | \(0.751637\pi\) | |||||||
\(858\) | −1.51665 | −0.0517777 | ||||||||
\(859\) | −39.1949 | −1.33731 | −0.668656 | − | 0.743571i | \(-0.733130\pi\) | ||||
−0.668656 | + | 0.743571i | \(0.733130\pi\) | |||||||
\(860\) | 1.23882 | 0.0422436 | ||||||||
\(861\) | 14.5303 | 0.495190 | ||||||||
\(862\) | −24.1364 | −0.822090 | ||||||||
\(863\) | −32.2281 | −1.09706 | −0.548528 | − | 0.836132i | \(-0.684812\pi\) | ||||
−0.548528 | + | 0.836132i | \(0.684812\pi\) | |||||||
\(864\) | −10.6266 | −0.361525 | ||||||||
\(865\) | −12.2220 | −0.415562 | ||||||||
\(866\) | −12.6836 | −0.431006 | ||||||||
\(867\) | −0.724033 | −0.0245894 | ||||||||
\(868\) | −4.77407 | −0.162042 | ||||||||
\(869\) | −13.3023 | −0.451250 | ||||||||
\(870\) | 4.69893 | 0.159309 | ||||||||
\(871\) | −7.02130 | −0.237908 | ||||||||
\(872\) | 23.9590 | 0.811354 | ||||||||
\(873\) | −10.1625 | −0.343949 | ||||||||
\(874\) | 8.02744 | 0.271532 | ||||||||
\(875\) | 18.3701 | 0.621024 | ||||||||
\(876\) | −3.59806 | −0.121567 | ||||||||
\(877\) | 52.7060 | 1.77976 | 0.889878 | − | 0.456198i | \(-0.150789\pi\) | ||||
0.889878 | + | 0.456198i | \(0.150789\pi\) | |||||||
\(878\) | −6.19599 | −0.209105 | ||||||||
\(879\) | −3.59225 | −0.121164 | ||||||||
\(880\) | −7.12599 | −0.240217 | ||||||||
\(881\) | −28.1073 | −0.946958 | −0.473479 | − | 0.880805i | \(-0.657002\pi\) | ||||
−0.473479 | + | 0.880805i | \(0.657002\pi\) | |||||||
\(882\) | −8.36545 | −0.281679 | ||||||||
\(883\) | 21.2667 | 0.715682 | 0.357841 | − | 0.933782i | \(-0.383513\pi\) | ||||
0.357841 | + | 0.933782i | \(0.383513\pi\) | |||||||
\(884\) | 0.826519 | 0.0277989 | ||||||||
\(885\) | −8.77044 | −0.294815 | ||||||||
\(886\) | 47.4030 | 1.59253 | ||||||||
\(887\) | −9.51264 | −0.319403 | −0.159702 | − | 0.987165i | \(-0.551053\pi\) | ||||
−0.159702 | + | 0.987165i | \(0.551053\pi\) | |||||||
\(888\) | −18.8816 | −0.633625 | ||||||||
\(889\) | 22.8442 | 0.766171 | ||||||||
\(890\) | 0.434770 | 0.0145735 | ||||||||
\(891\) | 4.55680 | 0.152659 | ||||||||
\(892\) | −10.6844 | −0.357741 | ||||||||
\(893\) | 0.559345 | 0.0187178 | ||||||||
\(894\) | 0.981124 | 0.0328137 | ||||||||
\(895\) | 26.3179 | 0.879710 | ||||||||
\(896\) | 11.4948 | 0.384015 | ||||||||
\(897\) | −6.04180 | −0.201730 | ||||||||
\(898\) | 11.3338 | 0.378214 | ||||||||
\(899\) | −9.85327 | −0.328625 | ||||||||
\(900\) | 1.81417 | 0.0604723 | ||||||||
\(901\) | 4.45312 | 0.148355 | ||||||||
\(902\) | −11.9736 | −0.398679 | ||||||||
\(903\) | −1.49339 | −0.0496968 | ||||||||
\(904\) | 40.7617 | 1.35571 | ||||||||
\(905\) | −41.8489 | −1.39110 | ||||||||
\(906\) | −16.0103 | −0.531907 | ||||||||
\(907\) | 18.9644 | 0.629701 | 0.314851 | − | 0.949141i | \(-0.398046\pi\) | ||||
0.314851 | + | 0.949141i | \(0.398046\pi\) | |||||||
\(908\) | −1.90640 | −0.0632661 | ||||||||
\(909\) | −0.600293 | −0.0199104 | ||||||||
\(910\) | −11.0231 | −0.365412 | ||||||||
\(911\) | −26.4939 | −0.877783 | −0.438891 | − | 0.898540i | \(-0.644629\pi\) | ||||
−0.438891 | + | 0.898540i | \(0.644629\pi\) | |||||||
\(912\) | 2.69086 | 0.0891032 | ||||||||
\(913\) | −0.161520 | −0.00534555 | ||||||||
\(914\) | −46.7726 | −1.54710 | ||||||||
\(915\) | −0.227067 | −0.00750659 | ||||||||
\(916\) | 13.1655 | 0.435002 | ||||||||
\(917\) | −21.1929 | −0.699851 | ||||||||
\(918\) | −4.87898 | −0.161030 | ||||||||
\(919\) | −28.8068 | −0.950248 | −0.475124 | − | 0.879919i | \(-0.657597\pi\) | ||||
−0.475124 | + | 0.879919i | \(0.657597\pi\) | |||||||
\(920\) | −38.2574 | −1.26131 | ||||||||
\(921\) | −7.20075 | −0.237273 | ||||||||
\(922\) | −36.8353 | −1.21311 | ||||||||
\(923\) | 5.77833 | 0.190196 | ||||||||
\(924\) | −0.725140 | −0.0238553 | ||||||||
\(925\) | 12.8661 | 0.423034 | ||||||||
\(926\) | 23.1057 | 0.759299 | ||||||||
\(927\) | 22.9085 | 0.752412 | ||||||||
\(928\) | −5.54048 | −0.181875 | ||||||||
\(929\) | 24.3981 | 0.800476 | 0.400238 | − | 0.916411i | \(-0.368928\pi\) | ||||
0.400238 | + | 0.916411i | \(0.368928\pi\) | |||||||
\(930\) | −10.8360 | −0.355326 | ||||||||
\(931\) | −3.65343 | −0.119736 | ||||||||
\(932\) | −2.43879 | −0.0798852 | ||||||||
\(933\) | −8.65042 | −0.283202 | ||||||||
\(934\) | 38.0342 | 1.24452 | ||||||||
\(935\) | 2.55129 | 0.0834362 | ||||||||
\(936\) | 12.8904 | 0.421335 | ||||||||
\(937\) | −29.7178 | −0.970840 | −0.485420 | − | 0.874281i | \(-0.661333\pi\) | ||||
−0.485420 | + | 0.874281i | \(0.661333\pi\) | |||||||
\(938\) | 10.4702 | 0.341863 | ||||||||
\(939\) | −6.55075 | −0.213776 | ||||||||
\(940\) | −0.520765 | −0.0169855 | ||||||||
\(941\) | −51.7810 | −1.68801 | −0.844007 | − | 0.536332i | \(-0.819809\pi\) | ||||
−0.844007 | + | 0.536332i | \(0.819809\pi\) | |||||||
\(942\) | 1.34740 | 0.0439007 | ||||||||
\(943\) | −47.6986 | −1.55328 | ||||||||
\(944\) | −13.2613 | −0.431620 | ||||||||
\(945\) | −20.8631 | −0.678676 | ||||||||
\(946\) | 1.23062 | 0.0400110 | ||||||||
\(947\) | 10.7142 | 0.348165 | 0.174083 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174083 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(948\) | −4.67664 | −0.151890 | ||||||||
\(949\) | 17.4206 | 0.565498 | ||||||||
\(950\) | −2.47109 | −0.0801729 | ||||||||
\(951\) | −1.67563 | −0.0543360 | ||||||||
\(952\) | −6.30906 | −0.204478 | ||||||||
\(953\) | 29.2251 | 0.946695 | 0.473347 | − | 0.880876i | \(-0.343046\pi\) | ||||
0.473347 | + | 0.880876i | \(0.343046\pi\) | |||||||
\(954\) | 13.5675 | 0.439266 | ||||||||
\(955\) | 21.2962 | 0.689128 | ||||||||
\(956\) | −3.96833 | −0.128345 | ||||||||
\(957\) | −1.49663 | −0.0483791 | ||||||||
\(958\) | −3.42561 | −0.110676 | ||||||||
\(959\) | −14.7457 | −0.476165 | ||||||||
\(960\) | −16.4120 | −0.529694 | ||||||||
\(961\) | −8.27781 | −0.267026 | ||||||||
\(962\) | 17.8591 | 0.575799 | ||||||||
\(963\) | 19.5950 | 0.631439 | ||||||||
\(964\) | 4.09747 | 0.131971 | ||||||||
\(965\) | −27.1174 | −0.872940 | ||||||||
\(966\) | 9.00952 | 0.289877 | ||||||||
\(967\) | 34.6058 | 1.11285 | 0.556424 | − | 0.830899i | \(-0.312173\pi\) | ||||
0.556424 | + | 0.830899i | \(0.312173\pi\) | |||||||
\(968\) | 3.05880 | 0.0983134 | ||||||||
\(969\) | −0.963398 | −0.0309488 | ||||||||
\(970\) | −12.8877 | −0.413798 | ||||||||
\(971\) | 6.38228 | 0.204817 | 0.102409 | − | 0.994742i | \(-0.467345\pi\) | ||||
0.102409 | + | 0.994742i | \(0.467345\pi\) | |||||||
\(972\) | 7.37732 | 0.236628 | ||||||||
\(973\) | −25.4400 | −0.815570 | ||||||||
\(974\) | 6.38195 | 0.204491 | ||||||||
\(975\) | 1.85985 | 0.0595629 | ||||||||
\(976\) | −0.343336 | −0.0109899 | ||||||||
\(977\) | −15.1300 | −0.484052 | −0.242026 | − | 0.970270i | \(-0.577812\pi\) | ||||
−0.242026 | + | 0.970270i | \(0.577812\pi\) | |||||||
\(978\) | 4.11656 | 0.131633 | ||||||||
\(979\) | −0.138476 | −0.00442571 | ||||||||
\(980\) | 3.40144 | 0.108655 | ||||||||
\(981\) | −19.3923 | −0.619149 | ||||||||
\(982\) | −31.8038 | −1.01490 | ||||||||
\(983\) | 42.6640 | 1.36077 | 0.680386 | − | 0.732854i | \(-0.261812\pi\) | ||||
0.680386 | + | 0.732854i | \(0.261812\pi\) | |||||||
\(984\) | −21.5482 | −0.686930 | ||||||||
\(985\) | −54.5050 | −1.73667 | ||||||||
\(986\) | −2.54378 | −0.0810106 | ||||||||
\(987\) | 0.627776 | 0.0199823 | ||||||||
\(988\) | 1.09977 | 0.0349883 | ||||||||
\(989\) | 4.90235 | 0.155886 | ||||||||
\(990\) | 7.77314 | 0.247047 | ||||||||
\(991\) | 58.5872 | 1.86108 | 0.930542 | − | 0.366185i | \(-0.119336\pi\) | ||||
0.930542 | + | 0.366185i | \(0.119336\pi\) | |||||||
\(992\) | 12.7766 | 0.405659 | ||||||||
\(993\) | −3.40375 | −0.108015 | ||||||||
\(994\) | −8.61663 | −0.273303 | ||||||||
\(995\) | −30.3518 | −0.962216 | ||||||||
\(996\) | −0.0567852 | −0.00179931 | ||||||||
\(997\) | 39.7825 | 1.25993 | 0.629963 | − | 0.776625i | \(-0.283070\pi\) | ||||
0.629963 | + | 0.776625i | \(0.283070\pi\) | |||||||
\(998\) | 34.5687 | 1.09425 | ||||||||
\(999\) | 33.8013 | 1.06943 |
(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 | 8041.2.a.c.1.20 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.c.1.20 | ✓ | 60 | 1.1 | even | 1 | trivial |