Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.50 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.88899 | 1.33571 | 0.667857 | − | 0.744289i | \(-0.267212\pi\) | ||||
0.667857 | + | 0.744289i | \(0.267212\pi\) | |||||||
\(3\) | 0.0315486 | 0.0182146 | 0.00910729 | − | 0.999959i | \(-0.497101\pi\) | ||||
0.00910729 | + | 0.999959i | \(0.497101\pi\) | |||||||
\(4\) | 1.56827 | 0.784134 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.0595948 | 0.0243295 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.815535 | −0.288335 | ||||||||
\(9\) | −2.99900 | −0.999668 | ||||||||
\(10\) | −1.88899 | −0.597350 | ||||||||
\(11\) | 4.01229 | 1.20975 | 0.604875 | − | 0.796320i | \(-0.293223\pi\) | ||||
0.604875 | + | 0.796320i | \(0.293223\pi\) | |||||||
\(12\) | 0.0494767 | 0.0142827 | ||||||||
\(13\) | 2.50308 | 0.694228 | 0.347114 | − | 0.937823i | \(-0.387162\pi\) | ||||
0.347114 | + | 0.937823i | \(0.387162\pi\) | |||||||
\(14\) | −1.88899 | −0.504853 | ||||||||
\(15\) | −0.0315486 | −0.00814581 | ||||||||
\(16\) | −4.67707 | −1.16927 | ||||||||
\(17\) | −3.17133 | −0.769161 | −0.384581 | − | 0.923091i | \(-0.625654\pi\) | ||||
−0.384581 | + | 0.923091i | \(0.625654\pi\) | |||||||
\(18\) | −5.66508 | −1.33527 | ||||||||
\(19\) | 3.46368 | 0.794624 | 0.397312 | − | 0.917684i | \(-0.369943\pi\) | ||||
0.397312 | + | 0.917684i | \(0.369943\pi\) | |||||||
\(20\) | −1.56827 | −0.350675 | ||||||||
\(21\) | −0.0315486 | −0.00688447 | ||||||||
\(22\) | 7.57915 | 1.61588 | ||||||||
\(23\) | 4.68922 | 0.977769 | 0.488885 | − | 0.872348i | \(-0.337404\pi\) | ||||
0.488885 | + | 0.872348i | \(0.337404\pi\) | |||||||
\(24\) | −0.0257290 | −0.00525191 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.72827 | 0.927291 | ||||||||
\(27\) | −0.189260 | −0.0364231 | ||||||||
\(28\) | −1.56827 | −0.296375 | ||||||||
\(29\) | −1.42042 | −0.263765 | −0.131882 | − | 0.991265i | \(-0.542102\pi\) | ||||
−0.131882 | + | 0.991265i | \(0.542102\pi\) | |||||||
\(30\) | −0.0595948 | −0.0108805 | ||||||||
\(31\) | −5.08502 | −0.913296 | −0.456648 | − | 0.889647i | \(-0.650950\pi\) | ||||
−0.456648 | + | 0.889647i | \(0.650950\pi\) | |||||||
\(32\) | −7.20385 | −1.27347 | ||||||||
\(33\) | 0.126582 | 0.0220351 | ||||||||
\(34\) | −5.99060 | −1.02738 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −4.70324 | −0.783874 | ||||||||
\(37\) | 10.0009 | 1.64413 | 0.822065 | − | 0.569393i | \(-0.192822\pi\) | ||||
0.822065 | + | 0.569393i | \(0.192822\pi\) | |||||||
\(38\) | 6.54285 | 1.06139 | ||||||||
\(39\) | 0.0789685 | 0.0126451 | ||||||||
\(40\) | 0.815535 | 0.128947 | ||||||||
\(41\) | −2.20842 | −0.344897 | −0.172448 | − | 0.985019i | \(-0.555168\pi\) | ||||
−0.172448 | + | 0.985019i | \(0.555168\pi\) | |||||||
\(42\) | −0.0595948 | −0.00919568 | ||||||||
\(43\) | −9.76821 | −1.48964 | −0.744819 | − | 0.667267i | \(-0.767464\pi\) | ||||
−0.744819 | + | 0.667267i | \(0.767464\pi\) | |||||||
\(44\) | 6.29234 | 0.948606 | ||||||||
\(45\) | 2.99900 | 0.447065 | ||||||||
\(46\) | 8.85786 | 1.30602 | ||||||||
\(47\) | 11.5894 | 1.69049 | 0.845245 | − | 0.534379i | \(-0.179455\pi\) | ||||
0.845245 | + | 0.534379i | \(0.179455\pi\) | |||||||
\(48\) | −0.147555 | −0.0212977 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.88899 | 0.267143 | ||||||||
\(51\) | −0.100051 | −0.0140100 | ||||||||
\(52\) | 3.92549 | 0.544368 | ||||||||
\(53\) | −6.36751 | −0.874645 | −0.437322 | − | 0.899305i | \(-0.644073\pi\) | ||||
−0.437322 | + | 0.899305i | \(0.644073\pi\) | |||||||
\(54\) | −0.357510 | −0.0486509 | ||||||||
\(55\) | −4.01229 | −0.541017 | ||||||||
\(56\) | 0.815535 | 0.108980 | ||||||||
\(57\) | 0.109274 | 0.0144737 | ||||||||
\(58\) | −2.68315 | −0.352315 | ||||||||
\(59\) | −6.06626 | −0.789760 | −0.394880 | − | 0.918733i | \(-0.629214\pi\) | ||||
−0.394880 | + | 0.918733i | \(0.629214\pi\) | |||||||
\(60\) | −0.0494767 | −0.00638741 | ||||||||
\(61\) | 5.01200 | 0.641721 | 0.320860 | − | 0.947127i | \(-0.396028\pi\) | ||||
0.320860 | + | 0.947127i | \(0.396028\pi\) | |||||||
\(62\) | −9.60552 | −1.21990 | ||||||||
\(63\) | 2.99900 | 0.377839 | ||||||||
\(64\) | −4.25383 | −0.531729 | ||||||||
\(65\) | −2.50308 | −0.310468 | ||||||||
\(66\) | 0.239112 | 0.0294326 | ||||||||
\(67\) | −0.732304 | −0.0894652 | −0.0447326 | − | 0.998999i | \(-0.514244\pi\) | ||||
−0.0447326 | + | 0.998999i | \(0.514244\pi\) | |||||||
\(68\) | −4.97350 | −0.603126 | ||||||||
\(69\) | 0.147938 | 0.0178097 | ||||||||
\(70\) | 1.88899 | 0.225777 | ||||||||
\(71\) | 4.73138 | 0.561511 | 0.280756 | − | 0.959779i | \(-0.409415\pi\) | ||||
0.280756 | + | 0.959779i | \(0.409415\pi\) | |||||||
\(72\) | 2.44579 | 0.288240 | ||||||||
\(73\) | −9.03085 | −1.05698 | −0.528491 | − | 0.848939i | \(-0.677242\pi\) | ||||
−0.528491 | + | 0.848939i | \(0.677242\pi\) | |||||||
\(74\) | 18.8915 | 2.19609 | ||||||||
\(75\) | 0.0315486 | 0.00364292 | ||||||||
\(76\) | 5.43199 | 0.623092 | ||||||||
\(77\) | −4.01229 | −0.457243 | ||||||||
\(78\) | 0.149170 | 0.0168902 | ||||||||
\(79\) | 8.75647 | 0.985179 | 0.492590 | − | 0.870262i | \(-0.336050\pi\) | ||||
0.492590 | + | 0.870262i | \(0.336050\pi\) | |||||||
\(80\) | 4.67707 | 0.522912 | ||||||||
\(81\) | 8.99104 | 0.999005 | ||||||||
\(82\) | −4.17167 | −0.460684 | ||||||||
\(83\) | 15.2253 | 1.67120 | 0.835598 | − | 0.549342i | \(-0.185121\pi\) | ||||
0.835598 | + | 0.549342i | \(0.185121\pi\) | |||||||
\(84\) | −0.0494767 | −0.00539835 | ||||||||
\(85\) | 3.17133 | 0.343979 | ||||||||
\(86\) | −18.4520 | −1.98973 | ||||||||
\(87\) | −0.0448122 | −0.00480437 | ||||||||
\(88\) | −3.27216 | −0.348813 | ||||||||
\(89\) | −1.80560 | −0.191393 | −0.0956966 | − | 0.995411i | \(-0.530508\pi\) | ||||
−0.0956966 | + | 0.995411i | \(0.530508\pi\) | |||||||
\(90\) | 5.66508 | 0.597152 | ||||||||
\(91\) | −2.50308 | −0.262394 | ||||||||
\(92\) | 7.35395 | 0.766702 | ||||||||
\(93\) | −0.160425 | −0.0166353 | ||||||||
\(94\) | 21.8922 | 2.25801 | ||||||||
\(95\) | −3.46368 | −0.355367 | ||||||||
\(96\) | −0.227271 | −0.0231958 | ||||||||
\(97\) | 13.5165 | 1.37239 | 0.686195 | − | 0.727417i | \(-0.259280\pi\) | ||||
0.686195 | + | 0.727417i | \(0.259280\pi\) | |||||||
\(98\) | 1.88899 | 0.190816 | ||||||||
\(99\) | −12.0329 | −1.20935 | ||||||||
\(100\) | 1.56827 | 0.156827 | ||||||||
\(101\) | 12.7953 | 1.27318 | 0.636588 | − | 0.771204i | \(-0.280345\pi\) | ||||
0.636588 | + | 0.771204i | \(0.280345\pi\) | |||||||
\(102\) | −0.188995 | −0.0187133 | ||||||||
\(103\) | 18.4088 | 1.81387 | 0.906937 | − | 0.421267i | \(-0.138414\pi\) | ||||
0.906937 | + | 0.421267i | \(0.138414\pi\) | |||||||
\(104\) | −2.04135 | −0.200170 | ||||||||
\(105\) | 0.0315486 | 0.00307883 | ||||||||
\(106\) | −12.0281 | −1.16828 | ||||||||
\(107\) | −10.8279 | −1.04678 | −0.523389 | − | 0.852094i | \(-0.675332\pi\) | ||||
−0.523389 | + | 0.852094i | \(0.675332\pi\) | |||||||
\(108\) | −0.296811 | −0.0285606 | ||||||||
\(109\) | 9.90433 | 0.948663 | 0.474331 | − | 0.880346i | \(-0.342690\pi\) | ||||
0.474331 | + | 0.880346i | \(0.342690\pi\) | |||||||
\(110\) | −7.57915 | −0.722644 | ||||||||
\(111\) | 0.315513 | 0.0299472 | ||||||||
\(112\) | 4.67707 | 0.441942 | ||||||||
\(113\) | −8.72373 | −0.820659 | −0.410330 | − | 0.911937i | \(-0.634586\pi\) | ||||
−0.410330 | + | 0.911937i | \(0.634586\pi\) | |||||||
\(114\) | 0.206418 | 0.0193328 | ||||||||
\(115\) | −4.68922 | −0.437272 | ||||||||
\(116\) | −2.22760 | −0.206827 | ||||||||
\(117\) | −7.50674 | −0.693998 | ||||||||
\(118\) | −11.4591 | −1.05489 | ||||||||
\(119\) | 3.17133 | 0.290716 | ||||||||
\(120\) | 0.0257290 | 0.00234872 | ||||||||
\(121\) | 5.09844 | 0.463495 | ||||||||
\(122\) | 9.46759 | 0.857156 | ||||||||
\(123\) | −0.0696725 | −0.00628215 | ||||||||
\(124\) | −7.97467 | −0.716147 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 5.66508 | 0.504685 | ||||||||
\(127\) | 5.66591 | 0.502768 | 0.251384 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251384 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(128\) | 6.37227 | 0.563234 | ||||||||
\(129\) | −0.308173 | −0.0271331 | ||||||||
\(130\) | −4.72827 | −0.414697 | ||||||||
\(131\) | 19.3345 | 1.68926 | 0.844631 | − | 0.535349i | \(-0.179820\pi\) | ||||
0.844631 | + | 0.535349i | \(0.179820\pi\) | |||||||
\(132\) | 0.198515 | 0.0172785 | ||||||||
\(133\) | −3.46368 | −0.300340 | ||||||||
\(134\) | −1.38331 | −0.119500 | ||||||||
\(135\) | 0.189260 | 0.0162889 | ||||||||
\(136\) | 2.58633 | 0.221776 | ||||||||
\(137\) | 17.1644 | 1.46646 | 0.733229 | − | 0.679982i | \(-0.238012\pi\) | ||||
0.733229 | + | 0.679982i | \(0.238012\pi\) | |||||||
\(138\) | 0.279453 | 0.0237886 | ||||||||
\(139\) | 12.9681 | 1.09994 | 0.549970 | − | 0.835185i | \(-0.314639\pi\) | ||||
0.549970 | + | 0.835185i | \(0.314639\pi\) | |||||||
\(140\) | 1.56827 | 0.132543 | ||||||||
\(141\) | 0.365630 | 0.0307916 | ||||||||
\(142\) | 8.93751 | 0.750019 | ||||||||
\(143\) | 10.0431 | 0.839843 | ||||||||
\(144\) | 14.0266 | 1.16888 | ||||||||
\(145\) | 1.42042 | 0.117959 | ||||||||
\(146\) | −17.0592 | −1.41183 | ||||||||
\(147\) | 0.0315486 | 0.00260208 | ||||||||
\(148\) | 15.6840 | 1.28922 | ||||||||
\(149\) | 6.61572 | 0.541981 | 0.270991 | − | 0.962582i | \(-0.412649\pi\) | ||||
0.270991 | + | 0.962582i | \(0.412649\pi\) | |||||||
\(150\) | 0.0595948 | 0.00486590 | ||||||||
\(151\) | 15.5005 | 1.26141 | 0.630706 | − | 0.776022i | \(-0.282765\pi\) | ||||
0.630706 | + | 0.776022i | \(0.282765\pi\) | |||||||
\(152\) | −2.82476 | −0.229118 | ||||||||
\(153\) | 9.51084 | 0.768906 | ||||||||
\(154\) | −7.57915 | −0.610746 | ||||||||
\(155\) | 5.08502 | 0.408438 | ||||||||
\(156\) | 0.123844 | 0.00991544 | ||||||||
\(157\) | 2.15806 | 0.172232 | 0.0861160 | − | 0.996285i | \(-0.472554\pi\) | ||||
0.0861160 | + | 0.996285i | \(0.472554\pi\) | |||||||
\(158\) | 16.5408 | 1.31592 | ||||||||
\(159\) | −0.200886 | −0.0159313 | ||||||||
\(160\) | 7.20385 | 0.569515 | ||||||||
\(161\) | −4.68922 | −0.369562 | ||||||||
\(162\) | 16.9840 | 1.33439 | ||||||||
\(163\) | −12.9903 | −1.01748 | −0.508739 | − | 0.860921i | \(-0.669888\pi\) | ||||
−0.508739 | + | 0.860921i | \(0.669888\pi\) | |||||||
\(164\) | −3.46339 | −0.270445 | ||||||||
\(165\) | −0.126582 | −0.00985439 | ||||||||
\(166\) | 28.7604 | 2.23224 | ||||||||
\(167\) | −18.5483 | −1.43531 | −0.717655 | − | 0.696399i | \(-0.754785\pi\) | ||||
−0.717655 | + | 0.696399i | \(0.754785\pi\) | |||||||
\(168\) | 0.0257290 | 0.00198503 | ||||||||
\(169\) | −6.73461 | −0.518047 | ||||||||
\(170\) | 5.99060 | 0.459458 | ||||||||
\(171\) | −10.3876 | −0.794360 | ||||||||
\(172\) | −15.3192 | −1.16808 | ||||||||
\(173\) | 3.65932 | 0.278213 | 0.139106 | − | 0.990277i | \(-0.455577\pi\) | ||||
0.139106 | + | 0.990277i | \(0.455577\pi\) | |||||||
\(174\) | −0.0846496 | −0.00641727 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −18.7658 | −1.41452 | ||||||||
\(177\) | −0.191382 | −0.0143851 | ||||||||
\(178\) | −3.41075 | −0.255647 | ||||||||
\(179\) | 21.9680 | 1.64197 | 0.820983 | − | 0.570953i | \(-0.193426\pi\) | ||||
0.820983 | + | 0.570953i | \(0.193426\pi\) | |||||||
\(180\) | 4.70324 | 0.350559 | ||||||||
\(181\) | −16.9779 | −1.26195 | −0.630977 | − | 0.775801i | \(-0.717346\pi\) | ||||
−0.630977 | + | 0.775801i | \(0.717346\pi\) | |||||||
\(182\) | −4.72827 | −0.350483 | ||||||||
\(183\) | 0.158121 | 0.0116887 | ||||||||
\(184\) | −3.82422 | −0.281925 | ||||||||
\(185\) | −10.0009 | −0.735278 | ||||||||
\(186\) | −0.303041 | −0.0222200 | ||||||||
\(187\) | −12.7243 | −0.930493 | ||||||||
\(188\) | 18.1753 | 1.32557 | ||||||||
\(189\) | 0.189260 | 0.0137666 | ||||||||
\(190\) | −6.54285 | −0.474668 | ||||||||
\(191\) | 14.9220 | 1.07972 | 0.539858 | − | 0.841756i | \(-0.318478\pi\) | ||||
0.539858 | + | 0.841756i | \(0.318478\pi\) | |||||||
\(192\) | −0.134202 | −0.00968523 | ||||||||
\(193\) | −3.99218 | −0.287364 | −0.143682 | − | 0.989624i | \(-0.545894\pi\) | ||||
−0.143682 | + | 0.989624i | \(0.545894\pi\) | |||||||
\(194\) | 25.5324 | 1.83312 | ||||||||
\(195\) | −0.0789685 | −0.00565505 | ||||||||
\(196\) | 1.56827 | 0.112019 | ||||||||
\(197\) | 16.7388 | 1.19259 | 0.596296 | − | 0.802765i | \(-0.296639\pi\) | ||||
0.596296 | + | 0.802765i | \(0.296639\pi\) | |||||||
\(198\) | −22.7299 | −1.61534 | ||||||||
\(199\) | 0.831093 | 0.0589146 | 0.0294573 | − | 0.999566i | \(-0.490622\pi\) | ||||
0.0294573 | + | 0.999566i | \(0.490622\pi\) | |||||||
\(200\) | −0.815535 | −0.0576670 | ||||||||
\(201\) | −0.0231032 | −0.00162957 | ||||||||
\(202\) | 24.1701 | 1.70060 | ||||||||
\(203\) | 1.42042 | 0.0996938 | ||||||||
\(204\) | −0.156907 | −0.0109857 | ||||||||
\(205\) | 2.20842 | 0.154243 | ||||||||
\(206\) | 34.7740 | 2.42282 | ||||||||
\(207\) | −14.0630 | −0.977445 | ||||||||
\(208\) | −11.7071 | −0.811739 | ||||||||
\(209\) | 13.8973 | 0.961296 | ||||||||
\(210\) | 0.0595948 | 0.00411244 | ||||||||
\(211\) | −1.82089 | −0.125355 | −0.0626775 | − | 0.998034i | \(-0.519964\pi\) | ||||
−0.0626775 | + | 0.998034i | \(0.519964\pi\) | |||||||
\(212\) | −9.98597 | −0.685839 | ||||||||
\(213\) | 0.149268 | 0.0102277 | ||||||||
\(214\) | −20.4538 | −1.39820 | ||||||||
\(215\) | 9.76821 | 0.666186 | ||||||||
\(216\) | 0.154348 | 0.0105021 | ||||||||
\(217\) | 5.08502 | 0.345193 | ||||||||
\(218\) | 18.7091 | 1.26714 | ||||||||
\(219\) | −0.284911 | −0.0192525 | ||||||||
\(220\) | −6.29234 | −0.424230 | ||||||||
\(221\) | −7.93808 | −0.533973 | ||||||||
\(222\) | 0.596000 | 0.0400009 | ||||||||
\(223\) | 20.3774 | 1.36457 | 0.682285 | − | 0.731086i | \(-0.260986\pi\) | ||||
0.682285 | + | 0.731086i | \(0.260986\pi\) | |||||||
\(224\) | 7.20385 | 0.481328 | ||||||||
\(225\) | −2.99900 | −0.199934 | ||||||||
\(226\) | −16.4790 | −1.09617 | ||||||||
\(227\) | 11.0181 | 0.731296 | 0.365648 | − | 0.930753i | \(-0.380847\pi\) | ||||
0.365648 | + | 0.930753i | \(0.380847\pi\) | |||||||
\(228\) | 0.171372 | 0.0113494 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −8.85786 | −0.584070 | ||||||||
\(231\) | −0.126582 | −0.00832848 | ||||||||
\(232\) | 1.15840 | 0.0760527 | ||||||||
\(233\) | −13.7735 | −0.902333 | −0.451166 | − | 0.892440i | \(-0.648992\pi\) | ||||
−0.451166 | + | 0.892440i | \(0.648992\pi\) | |||||||
\(234\) | −14.1801 | −0.926983 | ||||||||
\(235\) | −11.5894 | −0.756010 | ||||||||
\(236\) | −9.51352 | −0.619278 | ||||||||
\(237\) | 0.276254 | 0.0179446 | ||||||||
\(238\) | 5.99060 | 0.388313 | ||||||||
\(239\) | −4.00164 | −0.258844 | −0.129422 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129422 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(240\) | 0.147555 | 0.00952463 | ||||||||
\(241\) | 4.08531 | 0.263158 | 0.131579 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131579 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(242\) | 9.63089 | 0.619097 | ||||||||
\(243\) | 0.851435 | 0.0546196 | ||||||||
\(244\) | 7.86016 | 0.503195 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −0.131610 | −0.00839117 | ||||||||
\(247\) | 8.66986 | 0.551650 | ||||||||
\(248\) | 4.14701 | 0.263335 | ||||||||
\(249\) | 0.480337 | 0.0304401 | ||||||||
\(250\) | −1.88899 | −0.119470 | ||||||||
\(251\) | −3.77584 | −0.238329 | −0.119164 | − | 0.992875i | \(-0.538022\pi\) | ||||
−0.119164 | + | 0.992875i | \(0.538022\pi\) | |||||||
\(252\) | 4.70324 | 0.296277 | ||||||||
\(253\) | 18.8145 | 1.18286 | ||||||||
\(254\) | 10.7028 | 0.671555 | ||||||||
\(255\) | 0.100051 | 0.00626544 | ||||||||
\(256\) | 20.5448 | 1.28405 | ||||||||
\(257\) | −1.13302 | −0.0706758 | −0.0353379 | − | 0.999375i | \(-0.511251\pi\) | ||||
−0.0353379 | + | 0.999375i | \(0.511251\pi\) | |||||||
\(258\) | −0.582135 | −0.0362421 | ||||||||
\(259\) | −10.0009 | −0.621423 | ||||||||
\(260\) | −3.92549 | −0.243449 | ||||||||
\(261\) | 4.25984 | 0.263677 | ||||||||
\(262\) | 36.5226 | 2.25637 | ||||||||
\(263\) | −2.19881 | −0.135584 | −0.0677922 | − | 0.997699i | \(-0.521595\pi\) | ||||
−0.0677922 | + | 0.997699i | \(0.521595\pi\) | |||||||
\(264\) | −0.103232 | −0.00635349 | ||||||||
\(265\) | 6.36751 | 0.391153 | ||||||||
\(266\) | −6.54285 | −0.401168 | ||||||||
\(267\) | −0.0569641 | −0.00348615 | ||||||||
\(268\) | −1.14845 | −0.0701527 | ||||||||
\(269\) | −29.0954 | −1.77398 | −0.886988 | − | 0.461793i | \(-0.847206\pi\) | ||||
−0.886988 | + | 0.461793i | \(0.847206\pi\) | |||||||
\(270\) | 0.357510 | 0.0217574 | ||||||||
\(271\) | −2.02262 | −0.122865 | −0.0614327 | − | 0.998111i | \(-0.519567\pi\) | ||||
−0.0614327 | + | 0.998111i | \(0.519567\pi\) | |||||||
\(272\) | 14.8325 | 0.899355 | ||||||||
\(273\) | −0.0789685 | −0.00477939 | ||||||||
\(274\) | 32.4234 | 1.95877 | ||||||||
\(275\) | 4.01229 | 0.241950 | ||||||||
\(276\) | 0.232007 | 0.0139652 | ||||||||
\(277\) | 17.1471 | 1.03027 | 0.515134 | − | 0.857110i | \(-0.327742\pi\) | ||||
0.515134 | + | 0.857110i | \(0.327742\pi\) | |||||||
\(278\) | 24.4966 | 1.46921 | ||||||||
\(279\) | 15.2500 | 0.912993 | ||||||||
\(280\) | −0.815535 | −0.0487375 | ||||||||
\(281\) | −0.385523 | −0.0229984 | −0.0114992 | − | 0.999934i | \(-0.503660\pi\) | ||||
−0.0114992 | + | 0.999934i | \(0.503660\pi\) | |||||||
\(282\) | 0.690669 | 0.0411288 | ||||||||
\(283\) | 7.80331 | 0.463859 | 0.231929 | − | 0.972733i | \(-0.425496\pi\) | ||||
0.231929 | + | 0.972733i | \(0.425496\pi\) | |||||||
\(284\) | 7.42007 | 0.440300 | ||||||||
\(285\) | −0.109274 | −0.00647285 | ||||||||
\(286\) | 18.9712 | 1.12179 | ||||||||
\(287\) | 2.20842 | 0.130359 | ||||||||
\(288\) | 21.6044 | 1.27305 | ||||||||
\(289\) | −6.94265 | −0.408391 | ||||||||
\(290\) | 2.68315 | 0.157560 | ||||||||
\(291\) | 0.426426 | 0.0249975 | ||||||||
\(292\) | −14.1628 | −0.828815 | ||||||||
\(293\) | −0.0911613 | −0.00532570 | −0.00266285 | − | 0.999996i | \(-0.500848\pi\) | ||||
−0.00266285 | + | 0.999996i | \(0.500848\pi\) | |||||||
\(294\) | 0.0595948 | 0.00347564 | ||||||||
\(295\) | 6.06626 | 0.353191 | ||||||||
\(296\) | −8.15605 | −0.474061 | ||||||||
\(297\) | −0.759366 | −0.0440629 | ||||||||
\(298\) | 12.4970 | 0.723932 | ||||||||
\(299\) | 11.7375 | 0.678795 | ||||||||
\(300\) | 0.0494767 | 0.00285654 | ||||||||
\(301\) | 9.76821 | 0.563030 | ||||||||
\(302\) | 29.2802 | 1.68489 | ||||||||
\(303\) | 0.403672 | 0.0231904 | ||||||||
\(304\) | −16.1999 | −0.929128 | ||||||||
\(305\) | −5.01200 | −0.286986 | ||||||||
\(306\) | 17.9658 | 1.02704 | ||||||||
\(307\) | 15.8747 | 0.906018 | 0.453009 | − | 0.891506i | \(-0.350351\pi\) | ||||
0.453009 | + | 0.891506i | \(0.350351\pi\) | |||||||
\(308\) | −6.29234 | −0.358539 | ||||||||
\(309\) | 0.580772 | 0.0330390 | ||||||||
\(310\) | 9.60552 | 0.545557 | ||||||||
\(311\) | −29.8891 | −1.69485 | −0.847427 | − | 0.530912i | \(-0.821849\pi\) | ||||
−0.847427 | + | 0.530912i | \(0.821849\pi\) | |||||||
\(312\) | −0.0644016 | −0.00364602 | ||||||||
\(313\) | −20.1835 | −1.14084 | −0.570418 | − | 0.821354i | \(-0.693219\pi\) | ||||
−0.570418 | + | 0.821354i | \(0.693219\pi\) | |||||||
\(314\) | 4.07655 | 0.230053 | ||||||||
\(315\) | −2.99900 | −0.168975 | ||||||||
\(316\) | 13.7325 | 0.772513 | ||||||||
\(317\) | −35.2914 | −1.98216 | −0.991082 | − | 0.133252i | \(-0.957458\pi\) | ||||
−0.991082 | + | 0.133252i | \(0.957458\pi\) | |||||||
\(318\) | −0.379471 | −0.0212797 | ||||||||
\(319\) | −5.69912 | −0.319090 | ||||||||
\(320\) | 4.25383 | 0.237797 | ||||||||
\(321\) | −0.341607 | −0.0190666 | ||||||||
\(322\) | −8.85786 | −0.493629 | ||||||||
\(323\) | −10.9845 | −0.611194 | ||||||||
\(324\) | 14.1004 | 0.783354 | ||||||||
\(325\) | 2.50308 | 0.138846 | ||||||||
\(326\) | −24.5385 | −1.35906 | ||||||||
\(327\) | 0.312468 | 0.0172795 | ||||||||
\(328\) | 1.80104 | 0.0994459 | ||||||||
\(329\) | −11.5894 | −0.638945 | ||||||||
\(330\) | −0.239112 | −0.0131627 | ||||||||
\(331\) | −14.9929 | −0.824086 | −0.412043 | − | 0.911164i | \(-0.635185\pi\) | ||||
−0.412043 | + | 0.911164i | \(0.635185\pi\) | |||||||
\(332\) | 23.8774 | 1.31044 | ||||||||
\(333\) | −29.9926 | −1.64359 | ||||||||
\(334\) | −35.0375 | −1.91716 | ||||||||
\(335\) | 0.732304 | 0.0400101 | ||||||||
\(336\) | 0.147555 | 0.00804979 | ||||||||
\(337\) | 0.0172887 | 0.000941773 0 | 0.000470887 | − | 1.00000i | \(-0.499850\pi\) | ||||
0.000470887 | 1.00000i | \(0.499850\pi\) | ||||||||
\(338\) | −12.7216 | −0.691963 | ||||||||
\(339\) | −0.275221 | −0.0149480 | ||||||||
\(340\) | 4.97350 | 0.269726 | ||||||||
\(341\) | −20.4025 | −1.10486 | ||||||||
\(342\) | −19.6220 | −1.06104 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.96632 | 0.429515 | ||||||||
\(345\) | −0.147938 | −0.00796472 | ||||||||
\(346\) | 6.91240 | 0.371613 | ||||||||
\(347\) | −9.93796 | −0.533498 | −0.266749 | − | 0.963766i | \(-0.585949\pi\) | ||||
−0.266749 | + | 0.963766i | \(0.585949\pi\) | |||||||
\(348\) | −0.0702775 | −0.00376727 | ||||||||
\(349\) | −12.5623 | −0.672444 | −0.336222 | − | 0.941783i | \(-0.609149\pi\) | ||||
−0.336222 | + | 0.941783i | \(0.609149\pi\) | |||||||
\(350\) | −1.88899 | −0.100971 | ||||||||
\(351\) | −0.473732 | −0.0252860 | ||||||||
\(352\) | −28.9039 | −1.54058 | ||||||||
\(353\) | 20.9123 | 1.11305 | 0.556526 | − | 0.830830i | \(-0.312134\pi\) | ||||
0.556526 | + | 0.830830i | \(0.312134\pi\) | |||||||
\(354\) | −0.361518 | −0.0192145 | ||||||||
\(355\) | −4.73138 | −0.251116 | ||||||||
\(356\) | −2.83167 | −0.150078 | ||||||||
\(357\) | 0.100051 | 0.00529526 | ||||||||
\(358\) | 41.4973 | 2.19320 | ||||||||
\(359\) | −18.3259 | −0.967202 | −0.483601 | − | 0.875288i | \(-0.660671\pi\) | ||||
−0.483601 | + | 0.875288i | \(0.660671\pi\) | |||||||
\(360\) | −2.44579 | −0.128905 | ||||||||
\(361\) | −7.00289 | −0.368573 | ||||||||
\(362\) | −32.0709 | −1.68561 | ||||||||
\(363\) | 0.160849 | 0.00844237 | ||||||||
\(364\) | −3.92549 | −0.205752 | ||||||||
\(365\) | 9.03085 | 0.472696 | ||||||||
\(366\) | 0.298689 | 0.0156127 | ||||||||
\(367\) | 19.2290 | 1.00375 | 0.501873 | − | 0.864942i | \(-0.332645\pi\) | ||||
0.501873 | + | 0.864942i | \(0.332645\pi\) | |||||||
\(368\) | −21.9318 | −1.14327 | ||||||||
\(369\) | 6.62305 | 0.344782 | ||||||||
\(370\) | −18.8915 | −0.982121 | ||||||||
\(371\) | 6.36751 | 0.330585 | ||||||||
\(372\) | −0.251590 | −0.0130443 | ||||||||
\(373\) | −19.4541 | −1.00730 | −0.503648 | − | 0.863909i | \(-0.668009\pi\) | ||||
−0.503648 | + | 0.863909i | \(0.668009\pi\) | |||||||
\(374\) | −24.0360 | −1.24287 | ||||||||
\(375\) | −0.0315486 | −0.00162916 | ||||||||
\(376\) | −9.45157 | −0.487428 | ||||||||
\(377\) | −3.55541 | −0.183113 | ||||||||
\(378\) | 0.357510 | 0.0183883 | ||||||||
\(379\) | −1.78098 | −0.0914828 | −0.0457414 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457414 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(380\) | −5.43199 | −0.278655 | ||||||||
\(381\) | 0.178751 | 0.00915771 | ||||||||
\(382\) | 28.1874 | 1.44219 | ||||||||
\(383\) | −9.78680 | −0.500082 | −0.250041 | − | 0.968235i | \(-0.580444\pi\) | ||||
−0.250041 | + | 0.968235i | \(0.580444\pi\) | |||||||
\(384\) | 0.201036 | 0.0102591 | ||||||||
\(385\) | 4.01229 | 0.204485 | ||||||||
\(386\) | −7.54118 | −0.383836 | ||||||||
\(387\) | 29.2949 | 1.48914 | ||||||||
\(388\) | 21.1975 | 1.07614 | ||||||||
\(389\) | 28.2386 | 1.43175 | 0.715876 | − | 0.698227i | \(-0.246027\pi\) | ||||
0.715876 | + | 0.698227i | \(0.246027\pi\) | |||||||
\(390\) | −0.149170 | −0.00755354 | ||||||||
\(391\) | −14.8711 | −0.752062 | ||||||||
\(392\) | −0.815535 | −0.0411907 | ||||||||
\(393\) | 0.609976 | 0.0307692 | ||||||||
\(394\) | 31.6194 | 1.59296 | ||||||||
\(395\) | −8.75647 | −0.440586 | ||||||||
\(396\) | −18.8708 | −0.948292 | ||||||||
\(397\) | 23.2115 | 1.16495 | 0.582477 | − | 0.812847i | \(-0.302084\pi\) | ||||
0.582477 | + | 0.812847i | \(0.302084\pi\) | |||||||
\(398\) | 1.56992 | 0.0786931 | ||||||||
\(399\) | −0.109274 | −0.00547056 | ||||||||
\(400\) | −4.67707 | −0.233854 | ||||||||
\(401\) | −30.9902 | −1.54758 | −0.773788 | − | 0.633444i | \(-0.781641\pi\) | ||||
−0.773788 | + | 0.633444i | \(0.781641\pi\) | |||||||
\(402\) | −0.0436416 | −0.00217664 | ||||||||
\(403\) | −12.7282 | −0.634036 | ||||||||
\(404\) | 20.0664 | 0.998341 | ||||||||
\(405\) | −8.99104 | −0.446769 | ||||||||
\(406\) | 2.68315 | 0.133162 | ||||||||
\(407\) | 40.1263 | 1.98899 | ||||||||
\(408\) | 0.0815952 | 0.00403956 | ||||||||
\(409\) | −17.2411 | −0.852515 | −0.426258 | − | 0.904602i | \(-0.640168\pi\) | ||||
−0.426258 | + | 0.904602i | \(0.640168\pi\) | |||||||
\(410\) | 4.17167 | 0.206024 | ||||||||
\(411\) | 0.541514 | 0.0267109 | ||||||||
\(412\) | 28.8699 | 1.42232 | ||||||||
\(413\) | 6.06626 | 0.298501 | ||||||||
\(414\) | −26.5648 | −1.30559 | ||||||||
\(415\) | −15.2253 | −0.747381 | ||||||||
\(416\) | −18.0318 | −0.884081 | ||||||||
\(417\) | 0.409125 | 0.0200349 | ||||||||
\(418\) | 26.2518 | 1.28402 | ||||||||
\(419\) | 18.2138 | 0.889802 | 0.444901 | − | 0.895580i | \(-0.353239\pi\) | ||||
0.444901 | + | 0.895580i | \(0.353239\pi\) | |||||||
\(420\) | 0.0494767 | 0.00241421 | ||||||||
\(421\) | 33.5234 | 1.63383 | 0.816916 | − | 0.576756i | \(-0.195682\pi\) | ||||
0.816916 | + | 0.576756i | \(0.195682\pi\) | |||||||
\(422\) | −3.43963 | −0.167439 | ||||||||
\(423\) | −34.7567 | −1.68993 | ||||||||
\(424\) | 5.19293 | 0.252191 | ||||||||
\(425\) | −3.17133 | −0.153832 | ||||||||
\(426\) | 0.281966 | 0.0136613 | ||||||||
\(427\) | −5.01200 | −0.242548 | ||||||||
\(428\) | −16.9811 | −0.820814 | ||||||||
\(429\) | 0.316844 | 0.0152974 | ||||||||
\(430\) | 18.4520 | 0.889835 | ||||||||
\(431\) | 32.0031 | 1.54154 | 0.770768 | − | 0.637116i | \(-0.219873\pi\) | ||||
0.770768 | + | 0.637116i | \(0.219873\pi\) | |||||||
\(432\) | 0.885183 | 0.0425884 | ||||||||
\(433\) | −33.3052 | −1.60055 | −0.800273 | − | 0.599636i | \(-0.795312\pi\) | ||||
−0.800273 | + | 0.599636i | \(0.795312\pi\) | |||||||
\(434\) | 9.60552 | 0.461080 | ||||||||
\(435\) | 0.0448122 | 0.00214858 | ||||||||
\(436\) | 15.5326 | 0.743879 | ||||||||
\(437\) | 16.2420 | 0.776959 | ||||||||
\(438\) | −0.538192 | −0.0257158 | ||||||||
\(439\) | 17.7760 | 0.848401 | 0.424200 | − | 0.905568i | \(-0.360555\pi\) | ||||
0.424200 | + | 0.905568i | \(0.360555\pi\) | |||||||
\(440\) | 3.27216 | 0.155994 | ||||||||
\(441\) | −2.99900 | −0.142810 | ||||||||
\(442\) | −14.9949 | −0.713236 | ||||||||
\(443\) | 2.91859 | 0.138666 | 0.0693332 | − | 0.997594i | \(-0.477913\pi\) | ||||
0.0693332 | + | 0.997594i | \(0.477913\pi\) | |||||||
\(444\) | 0.494809 | 0.0234826 | ||||||||
\(445\) | 1.80560 | 0.0855936 | ||||||||
\(446\) | 38.4926 | 1.82268 | ||||||||
\(447\) | 0.208717 | 0.00987196 | ||||||||
\(448\) | 4.25383 | 0.200975 | ||||||||
\(449\) | −2.05565 | −0.0970121 | −0.0485060 | − | 0.998823i | \(-0.515446\pi\) | ||||
−0.0485060 | + | 0.998823i | \(0.515446\pi\) | |||||||
\(450\) | −5.66508 | −0.267054 | ||||||||
\(451\) | −8.86080 | −0.417239 | ||||||||
\(452\) | −13.6811 | −0.643507 | ||||||||
\(453\) | 0.489019 | 0.0229761 | ||||||||
\(454\) | 20.8130 | 0.976803 | ||||||||
\(455\) | 2.50308 | 0.117346 | ||||||||
\(456\) | −0.0891171 | −0.00417329 | ||||||||
\(457\) | 7.63978 | 0.357374 | 0.178687 | − | 0.983906i | \(-0.442815\pi\) | ||||
0.178687 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(458\) | 1.88899 | 0.0882665 | ||||||||
\(459\) | 0.600207 | 0.0280153 | ||||||||
\(460\) | −7.35395 | −0.342880 | ||||||||
\(461\) | 24.4139 | 1.13707 | 0.568535 | − | 0.822659i | \(-0.307511\pi\) | ||||
0.568535 | + | 0.822659i | \(0.307511\pi\) | |||||||
\(462\) | −0.239112 | −0.0111245 | ||||||||
\(463\) | −28.9533 | −1.34557 | −0.672786 | − | 0.739837i | \(-0.734903\pi\) | ||||
−0.672786 | + | 0.739837i | \(0.734903\pi\) | |||||||
\(464\) | 6.64339 | 0.308412 | ||||||||
\(465\) | 0.160425 | 0.00743954 | ||||||||
\(466\) | −26.0180 | −1.20526 | ||||||||
\(467\) | −9.13290 | −0.422620 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(468\) | −11.7726 | −0.544187 | ||||||||
\(469\) | 0.732304 | 0.0338147 | ||||||||
\(470\) | −21.8922 | −1.00981 | ||||||||
\(471\) | 0.0680838 | 0.00313714 | ||||||||
\(472\) | 4.94725 | 0.227715 | ||||||||
\(473\) | −39.1929 | −1.80209 | ||||||||
\(474\) | 0.521840 | 0.0239689 | ||||||||
\(475\) | 3.46368 | 0.158925 | ||||||||
\(476\) | 4.97350 | 0.227960 | ||||||||
\(477\) | 19.0962 | 0.874355 | ||||||||
\(478\) | −7.55904 | −0.345742 | ||||||||
\(479\) | 8.63929 | 0.394739 | 0.197370 | − | 0.980329i | \(-0.436760\pi\) | ||||
0.197370 | + | 0.980329i | \(0.436760\pi\) | |||||||
\(480\) | 0.227271 | 0.0103735 | ||||||||
\(481\) | 25.0329 | 1.14140 | ||||||||
\(482\) | 7.71709 | 0.351504 | ||||||||
\(483\) | −0.147938 | −0.00673142 | ||||||||
\(484\) | 7.99573 | 0.363442 | ||||||||
\(485\) | −13.5165 | −0.613752 | ||||||||
\(486\) | 1.60835 | 0.0729562 | ||||||||
\(487\) | −6.68985 | −0.303146 | −0.151573 | − | 0.988446i | \(-0.548434\pi\) | ||||
−0.151573 | + | 0.988446i | \(0.548434\pi\) | |||||||
\(488\) | −4.08746 | −0.185031 | ||||||||
\(489\) | −0.409825 | −0.0185329 | ||||||||
\(490\) | −1.88899 | −0.0853357 | ||||||||
\(491\) | −28.6229 | −1.29173 | −0.645867 | − | 0.763450i | \(-0.723504\pi\) | ||||
−0.645867 | + | 0.763450i | \(0.723504\pi\) | |||||||
\(492\) | −0.109265 | −0.00492605 | ||||||||
\(493\) | 4.50462 | 0.202878 | ||||||||
\(494\) | 16.3773 | 0.736847 | ||||||||
\(495\) | 12.0329 | 0.540837 | ||||||||
\(496\) | 23.7830 | 1.06789 | ||||||||
\(497\) | −4.73138 | −0.212231 | ||||||||
\(498\) | 0.907350 | 0.0406593 | ||||||||
\(499\) | −31.8613 | −1.42631 | −0.713155 | − | 0.701007i | \(-0.752734\pi\) | ||||
−0.713155 | + | 0.701007i | \(0.752734\pi\) | |||||||
\(500\) | −1.56827 | −0.0701351 | ||||||||
\(501\) | −0.585173 | −0.0261436 | ||||||||
\(502\) | −7.13251 | −0.318339 | ||||||||
\(503\) | 39.5390 | 1.76296 | 0.881479 | − | 0.472224i | \(-0.156549\pi\) | ||||
0.881479 | + | 0.472224i | \(0.156549\pi\) | |||||||
\(504\) | −2.44579 | −0.108944 | ||||||||
\(505\) | −12.7953 | −0.569382 | ||||||||
\(506\) | 35.5403 | 1.57996 | ||||||||
\(507\) | −0.212468 | −0.00943602 | ||||||||
\(508\) | 8.88566 | 0.394238 | ||||||||
\(509\) | −22.6328 | −1.00318 | −0.501590 | − | 0.865106i | \(-0.667251\pi\) | ||||
−0.501590 | + | 0.865106i | \(0.667251\pi\) | |||||||
\(510\) | 0.188995 | 0.00836884 | ||||||||
\(511\) | 9.03085 | 0.399501 | ||||||||
\(512\) | 26.0643 | 1.15189 | ||||||||
\(513\) | −0.655537 | −0.0289427 | ||||||||
\(514\) | −2.14026 | −0.0944027 | ||||||||
\(515\) | −18.4088 | −0.811189 | ||||||||
\(516\) | −0.483298 | −0.0212760 | ||||||||
\(517\) | 46.5000 | 2.04507 | ||||||||
\(518\) | −18.8915 | −0.830044 | ||||||||
\(519\) | 0.115446 | 0.00506753 | ||||||||
\(520\) | 2.04135 | 0.0895189 | ||||||||
\(521\) | 31.2907 | 1.37087 | 0.685436 | − | 0.728133i | \(-0.259612\pi\) | ||||
0.685436 | + | 0.728133i | \(0.259612\pi\) | |||||||
\(522\) | 8.04678 | 0.352198 | ||||||||
\(523\) | 30.4109 | 1.32977 | 0.664887 | − | 0.746944i | \(-0.268480\pi\) | ||||
0.664887 | + | 0.746944i | \(0.268480\pi\) | |||||||
\(524\) | 30.3217 | 1.32461 | ||||||||
\(525\) | −0.0315486 | −0.00137689 | ||||||||
\(526\) | −4.15352 | −0.181102 | ||||||||
\(527\) | 16.1263 | 0.702472 | ||||||||
\(528\) | −0.592033 | −0.0257649 | ||||||||
\(529\) | −1.01126 | −0.0439676 | ||||||||
\(530\) | 12.0281 | 0.522469 | ||||||||
\(531\) | 18.1927 | 0.789498 | ||||||||
\(532\) | −5.43199 | −0.235507 | ||||||||
\(533\) | −5.52784 | −0.239437 | ||||||||
\(534\) | −0.107604 | −0.00465650 | ||||||||
\(535\) | 10.8279 | 0.468133 | ||||||||
\(536\) | 0.597220 | 0.0257960 | ||||||||
\(537\) | 0.693060 | 0.0299077 | ||||||||
\(538\) | −54.9607 | −2.36953 | ||||||||
\(539\) | 4.01229 | 0.172821 | ||||||||
\(540\) | 0.296811 | 0.0127727 | ||||||||
\(541\) | −22.3988 | −0.963001 | −0.481501 | − | 0.876446i | \(-0.659908\pi\) | ||||
−0.481501 | + | 0.876446i | \(0.659908\pi\) | |||||||
\(542\) | −3.82070 | −0.164113 | ||||||||
\(543\) | −0.535628 | −0.0229860 | ||||||||
\(544\) | 22.8458 | 0.979506 | ||||||||
\(545\) | −9.90433 | −0.424255 | ||||||||
\(546\) | −0.149170 | −0.00638390 | ||||||||
\(547\) | −19.6316 | −0.839387 | −0.419694 | − | 0.907666i | \(-0.637863\pi\) | ||||
−0.419694 | + | 0.907666i | \(0.637863\pi\) | |||||||
\(548\) | 26.9185 | 1.14990 | ||||||||
\(549\) | −15.0310 | −0.641508 | ||||||||
\(550\) | 7.57915 | 0.323176 | ||||||||
\(551\) | −4.91988 | −0.209594 | ||||||||
\(552\) | −0.120649 | −0.00513515 | ||||||||
\(553\) | −8.75647 | −0.372363 | ||||||||
\(554\) | 32.3906 | 1.37614 | ||||||||
\(555\) | −0.315513 | −0.0133928 | ||||||||
\(556\) | 20.3375 | 0.862500 | ||||||||
\(557\) | −33.4278 | −1.41638 | −0.708190 | − | 0.706022i | \(-0.750488\pi\) | ||||
−0.708190 | + | 0.706022i | \(0.750488\pi\) | |||||||
\(558\) | 28.8070 | 1.21950 | ||||||||
\(559\) | −24.4506 | −1.03415 | ||||||||
\(560\) | −4.67707 | −0.197642 | ||||||||
\(561\) | −0.401434 | −0.0169485 | ||||||||
\(562\) | −0.728247 | −0.0307192 | ||||||||
\(563\) | −0.512607 | −0.0216038 | −0.0108019 | − | 0.999942i | \(-0.503438\pi\) | ||||
−0.0108019 | + | 0.999942i | \(0.503438\pi\) | |||||||
\(564\) | 0.573405 | 0.0241447 | ||||||||
\(565\) | 8.72373 | 0.367010 | ||||||||
\(566\) | 14.7403 | 0.619583 | ||||||||
\(567\) | −8.99104 | −0.377588 | ||||||||
\(568\) | −3.85861 | −0.161903 | ||||||||
\(569\) | −32.9188 | −1.38003 | −0.690014 | − | 0.723796i | \(-0.742396\pi\) | ||||
−0.690014 | + | 0.723796i | \(0.742396\pi\) | |||||||
\(570\) | −0.206418 | −0.00864589 | ||||||||
\(571\) | 4.69982 | 0.196681 | 0.0983406 | − | 0.995153i | \(-0.468647\pi\) | ||||
0.0983406 | + | 0.995153i | \(0.468647\pi\) | |||||||
\(572\) | 15.7502 | 0.658549 | ||||||||
\(573\) | 0.470767 | 0.0196666 | ||||||||
\(574\) | 4.17167 | 0.174122 | ||||||||
\(575\) | 4.68922 | 0.195554 | ||||||||
\(576\) | 12.7573 | 0.531553 | ||||||||
\(577\) | 32.6345 | 1.35859 | 0.679296 | − | 0.733865i | \(-0.262285\pi\) | ||||
0.679296 | + | 0.733865i | \(0.262285\pi\) | |||||||
\(578\) | −13.1146 | −0.545494 | ||||||||
\(579\) | −0.125948 | −0.00523421 | ||||||||
\(580\) | 2.22760 | 0.0924959 | ||||||||
\(581\) | −15.2253 | −0.631653 | ||||||||
\(582\) | 0.805512 | 0.0333896 | ||||||||
\(583\) | −25.5483 | −1.05810 | ||||||||
\(584\) | 7.36498 | 0.304765 | ||||||||
\(585\) | 7.50674 | 0.310365 | ||||||||
\(586\) | −0.172202 | −0.00711362 | ||||||||
\(587\) | 2.03947 | 0.0841778 | 0.0420889 | − | 0.999114i | \(-0.486599\pi\) | ||||
0.0420889 | + | 0.999114i | \(0.486599\pi\) | |||||||
\(588\) | 0.0494767 | 0.00204038 | ||||||||
\(589\) | −17.6129 | −0.725727 | ||||||||
\(590\) | 11.4591 | 0.471763 | ||||||||
\(591\) | 0.528086 | 0.0217226 | ||||||||
\(592\) | −46.7747 | −1.92243 | ||||||||
\(593\) | 14.2347 | 0.584548 | 0.292274 | − | 0.956335i | \(-0.405588\pi\) | ||||
0.292274 | + | 0.956335i | \(0.405588\pi\) | |||||||
\(594\) | −1.43443 | −0.0588554 | ||||||||
\(595\) | −3.17133 | −0.130012 | ||||||||
\(596\) | 10.3752 | 0.424986 | ||||||||
\(597\) | 0.0262198 | 0.00107311 | ||||||||
\(598\) | 22.1719 | 0.906676 | ||||||||
\(599\) | 29.3609 | 1.19965 | 0.599827 | − | 0.800130i | \(-0.295236\pi\) | ||||
0.599827 | + | 0.800130i | \(0.295236\pi\) | |||||||
\(600\) | −0.0257290 | −0.00105038 | ||||||||
\(601\) | −45.8293 | −1.86941 | −0.934707 | − | 0.355418i | \(-0.884338\pi\) | ||||
−0.934707 | + | 0.355418i | \(0.884338\pi\) | |||||||
\(602\) | 18.4520 | 0.752048 | ||||||||
\(603\) | 2.19618 | 0.0894355 | ||||||||
\(604\) | 24.3089 | 0.989117 | ||||||||
\(605\) | −5.09844 | −0.207281 | ||||||||
\(606\) | 0.762532 | 0.0309757 | ||||||||
\(607\) | 22.4559 | 0.911459 | 0.455729 | − | 0.890118i | \(-0.349378\pi\) | ||||
0.455729 | + | 0.890118i | \(0.349378\pi\) | |||||||
\(608\) | −24.9519 | −1.01193 | ||||||||
\(609\) | 0.0448122 | 0.00181588 | ||||||||
\(610\) | −9.46759 | −0.383332 | ||||||||
\(611\) | 29.0092 | 1.17359 | ||||||||
\(612\) | 14.9156 | 0.602925 | ||||||||
\(613\) | −13.9880 | −0.564972 | −0.282486 | − | 0.959271i | \(-0.591159\pi\) | ||||
−0.282486 | + | 0.959271i | \(0.591159\pi\) | |||||||
\(614\) | 29.9871 | 1.21018 | ||||||||
\(615\) | 0.0696725 | 0.00280946 | ||||||||
\(616\) | 3.27216 | 0.131839 | ||||||||
\(617\) | −32.2400 | −1.29793 | −0.648967 | − | 0.760817i | \(-0.724799\pi\) | ||||
−0.648967 | + | 0.760817i | \(0.724799\pi\) | |||||||
\(618\) | 1.09707 | 0.0441306 | ||||||||
\(619\) | 25.7627 | 1.03549 | 0.517745 | − | 0.855535i | \(-0.326772\pi\) | ||||
0.517745 | + | 0.855535i | \(0.326772\pi\) | |||||||
\(620\) | 7.97467 | 0.320270 | ||||||||
\(621\) | −0.887482 | −0.0356134 | ||||||||
\(622\) | −56.4600 | −2.26384 | ||||||||
\(623\) | 1.80560 | 0.0723398 | ||||||||
\(624\) | −0.369341 | −0.0147855 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −38.1263 | −1.52383 | ||||||||
\(627\) | 0.438440 | 0.0175096 | ||||||||
\(628\) | 3.38442 | 0.135053 | ||||||||
\(629\) | −31.7160 | −1.26460 | ||||||||
\(630\) | −5.66508 | −0.225702 | ||||||||
\(631\) | 0.690217 | 0.0274771 | 0.0137385 | − | 0.999906i | \(-0.495627\pi\) | ||||
0.0137385 | + | 0.999906i | \(0.495627\pi\) | |||||||
\(632\) | −7.14120 | −0.284062 | ||||||||
\(633\) | −0.0574464 | −0.00228329 | ||||||||
\(634\) | −66.6650 | −2.64761 | ||||||||
\(635\) | −5.66591 | −0.224845 | ||||||||
\(636\) | −0.315043 | −0.0124923 | ||||||||
\(637\) | 2.50308 | 0.0991755 | ||||||||
\(638\) | −10.7656 | −0.426213 | ||||||||
\(639\) | −14.1894 | −0.561325 | ||||||||
\(640\) | −6.37227 | −0.251886 | ||||||||
\(641\) | −19.7692 | −0.780835 | −0.390417 | − | 0.920638i | \(-0.627669\pi\) | ||||
−0.390417 | + | 0.920638i | \(0.627669\pi\) | |||||||
\(642\) | −0.645290 | −0.0254676 | ||||||||
\(643\) | −12.6906 | −0.500467 | −0.250233 | − | 0.968186i | \(-0.580507\pi\) | ||||
−0.250233 | + | 0.968186i | \(0.580507\pi\) | |||||||
\(644\) | −7.35395 | −0.289786 | ||||||||
\(645\) | 0.308173 | 0.0121343 | ||||||||
\(646\) | −20.7496 | −0.816380 | ||||||||
\(647\) | −12.5124 | −0.491913 | −0.245957 | − | 0.969281i | \(-0.579102\pi\) | ||||
−0.245957 | + | 0.969281i | \(0.579102\pi\) | |||||||
\(648\) | −7.33251 | −0.288048 | ||||||||
\(649\) | −24.3396 | −0.955412 | ||||||||
\(650\) | 4.72827 | 0.185458 | ||||||||
\(651\) | 0.160425 | 0.00628756 | ||||||||
\(652\) | −20.3723 | −0.797840 | ||||||||
\(653\) | 28.4569 | 1.11360 | 0.556802 | − | 0.830646i | \(-0.312028\pi\) | ||||
0.556802 | + | 0.830646i | \(0.312028\pi\) | |||||||
\(654\) | 0.590247 | 0.0230805 | ||||||||
\(655\) | −19.3345 | −0.755461 | ||||||||
\(656\) | 10.3289 | 0.403277 | ||||||||
\(657\) | 27.0836 | 1.05663 | ||||||||
\(658\) | −21.8922 | −0.853448 | ||||||||
\(659\) | −48.2626 | −1.88004 | −0.940021 | − | 0.341116i | \(-0.889195\pi\) | ||||
−0.940021 | + | 0.341116i | \(0.889195\pi\) | |||||||
\(660\) | −0.198515 | −0.00772717 | ||||||||
\(661\) | 2.26440 | 0.0880751 | 0.0440375 | − | 0.999030i | \(-0.485978\pi\) | ||||
0.0440375 | + | 0.999030i | \(0.485978\pi\) | |||||||
\(662\) | −28.3214 | −1.10074 | ||||||||
\(663\) | −0.250435 | −0.00972610 | ||||||||
\(664\) | −12.4168 | −0.481864 | ||||||||
\(665\) | 3.46368 | 0.134316 | ||||||||
\(666\) | −56.6556 | −2.19536 | ||||||||
\(667\) | −6.66065 | −0.257901 | ||||||||
\(668\) | −29.0887 | −1.12548 | ||||||||
\(669\) | 0.642877 | 0.0248551 | ||||||||
\(670\) | 1.38331 | 0.0534420 | ||||||||
\(671\) | 20.1096 | 0.776321 | ||||||||
\(672\) | 0.227271 | 0.00876718 | ||||||||
\(673\) | 6.02284 | 0.232164 | 0.116082 | − | 0.993240i | \(-0.462967\pi\) | ||||
0.116082 | + | 0.993240i | \(0.462967\pi\) | |||||||
\(674\) | 0.0326580 | 0.00125794 | ||||||||
\(675\) | −0.189260 | −0.00728463 | ||||||||
\(676\) | −10.5617 | −0.406218 | ||||||||
\(677\) | 1.90815 | 0.0733362 | 0.0366681 | − | 0.999327i | \(-0.488326\pi\) | ||||
0.0366681 | + | 0.999327i | \(0.488326\pi\) | |||||||
\(678\) | −0.519889 | −0.0199662 | ||||||||
\(679\) | −13.5165 | −0.518715 | ||||||||
\(680\) | −2.58633 | −0.0991813 | ||||||||
\(681\) | 0.347605 | 0.0133203 | ||||||||
\(682\) | −38.5401 | −1.47578 | ||||||||
\(683\) | 4.77522 | 0.182719 | 0.0913593 | − | 0.995818i | \(-0.470879\pi\) | ||||
0.0913593 | + | 0.995818i | \(0.470879\pi\) | |||||||
\(684\) | −16.2906 | −0.622885 | ||||||||
\(685\) | −17.1644 | −0.655820 | ||||||||
\(686\) | −1.88899 | −0.0721218 | ||||||||
\(687\) | 0.0315486 | 0.00120365 | ||||||||
\(688\) | 45.6866 | 1.74179 | ||||||||
\(689\) | −15.9384 | −0.607203 | ||||||||
\(690\) | −0.279453 | −0.0106386 | ||||||||
\(691\) | 46.9873 | 1.78748 | 0.893741 | − | 0.448583i | \(-0.148071\pi\) | ||||
0.893741 | + | 0.448583i | \(0.148071\pi\) | |||||||
\(692\) | 5.73879 | 0.218156 | ||||||||
\(693\) | 12.0329 | 0.457091 | ||||||||
\(694\) | −18.7727 | −0.712601 | ||||||||
\(695\) | −12.9681 | −0.491908 | ||||||||
\(696\) | 0.0365459 | 0.00138527 | ||||||||
\(697\) | 7.00363 | 0.265281 | ||||||||
\(698\) | −23.7300 | −0.898194 | ||||||||
\(699\) | −0.434535 | −0.0164356 | ||||||||
\(700\) | −1.56827 | −0.0592750 | ||||||||
\(701\) | −6.71717 | −0.253704 | −0.126852 | − | 0.991922i | \(-0.540487\pi\) | ||||
−0.126852 | + | 0.991922i | \(0.540487\pi\) | |||||||
\(702\) | −0.894874 | −0.0337748 | ||||||||
\(703\) | 34.6398 | 1.30647 | ||||||||
\(704\) | −17.0676 | −0.643259 | ||||||||
\(705\) | −0.365630 | −0.0137704 | ||||||||
\(706\) | 39.5031 | 1.48672 | ||||||||
\(707\) | −12.7953 | −0.481215 | ||||||||
\(708\) | −0.300138 | −0.0112799 | ||||||||
\(709\) | 40.4078 | 1.51755 | 0.758773 | − | 0.651355i | \(-0.225799\pi\) | ||||
0.758773 | + | 0.651355i | \(0.225799\pi\) | |||||||
\(710\) | −8.93751 | −0.335419 | ||||||||
\(711\) | −26.2607 | −0.984853 | ||||||||
\(712\) | 1.47253 | 0.0551854 | ||||||||
\(713\) | −23.8447 | −0.892992 | ||||||||
\(714\) | 0.188995 | 0.00707296 | ||||||||
\(715\) | −10.0431 | −0.375589 | ||||||||
\(716\) | 34.4517 | 1.28752 | ||||||||
\(717\) | −0.126246 | −0.00471474 | ||||||||
\(718\) | −34.6173 | −1.29191 | ||||||||
\(719\) | −36.4578 | −1.35965 | −0.679824 | − | 0.733375i | \(-0.737944\pi\) | ||||
−0.679824 | + | 0.733375i | \(0.737944\pi\) | |||||||
\(720\) | −14.0266 | −0.522739 | ||||||||
\(721\) | −18.4088 | −0.685580 | ||||||||
\(722\) | −13.2284 | −0.492309 | ||||||||
\(723\) | 0.128886 | 0.00479331 | ||||||||
\(724\) | −26.6258 | −0.989542 | ||||||||
\(725\) | −1.42042 | −0.0527530 | ||||||||
\(726\) | 0.303841 | 0.0112766 | ||||||||
\(727\) | 28.9177 | 1.07250 | 0.536248 | − | 0.844060i | \(-0.319841\pi\) | ||||
0.536248 | + | 0.844060i | \(0.319841\pi\) | |||||||
\(728\) | 2.04135 | 0.0756573 | ||||||||
\(729\) | −26.9463 | −0.998010 | ||||||||
\(730\) | 17.0592 | 0.631388 | ||||||||
\(731\) | 30.9782 | 1.14577 | ||||||||
\(732\) | 0.247977 | 0.00916549 | ||||||||
\(733\) | −37.0269 | −1.36762 | −0.683809 | − | 0.729661i | \(-0.739678\pi\) | ||||
−0.683809 | + | 0.729661i | \(0.739678\pi\) | |||||||
\(734\) | 36.3233 | 1.34072 | ||||||||
\(735\) | −0.0315486 | −0.00116369 | ||||||||
\(736\) | −33.7804 | −1.24516 | ||||||||
\(737\) | −2.93821 | −0.108231 | ||||||||
\(738\) | 12.5109 | 0.460531 | ||||||||
\(739\) | −37.5752 | −1.38223 | −0.691113 | − | 0.722746i | \(-0.742880\pi\) | ||||
−0.691113 | + | 0.722746i | \(0.742880\pi\) | |||||||
\(740\) | −15.6840 | −0.576556 | ||||||||
\(741\) | 0.273522 | 0.0100481 | ||||||||
\(742\) | 12.0281 | 0.441567 | ||||||||
\(743\) | −4.25196 | −0.155989 | −0.0779947 | − | 0.996954i | \(-0.524852\pi\) | ||||
−0.0779947 | + | 0.996954i | \(0.524852\pi\) | |||||||
\(744\) | 0.130832 | 0.00479654 | ||||||||
\(745\) | −6.61572 | −0.242381 | ||||||||
\(746\) | −36.7485 | −1.34546 | ||||||||
\(747\) | −45.6608 | −1.67064 | ||||||||
\(748\) | −19.9551 | −0.729631 | ||||||||
\(749\) | 10.8279 | 0.395645 | ||||||||
\(750\) | −0.0595948 | −0.00217610 | ||||||||
\(751\) | 30.0051 | 1.09490 | 0.547451 | − | 0.836838i | \(-0.315598\pi\) | ||||
0.547451 | + | 0.836838i | \(0.315598\pi\) | |||||||
\(752\) | −54.2045 | −1.97663 | ||||||||
\(753\) | −0.119122 | −0.00434106 | ||||||||
\(754\) | −6.71613 | −0.244587 | ||||||||
\(755\) | −15.5005 | −0.564121 | ||||||||
\(756\) | 0.296811 | 0.0107949 | ||||||||
\(757\) | −2.22302 | −0.0807970 | −0.0403985 | − | 0.999184i | \(-0.512863\pi\) | ||||
−0.0403985 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(758\) | −3.36425 | −0.122195 | ||||||||
\(759\) | 0.593570 | 0.0215452 | ||||||||
\(760\) | 2.82476 | 0.102465 | ||||||||
\(761\) | 9.07688 | 0.329037 | 0.164518 | − | 0.986374i | \(-0.447393\pi\) | ||||
0.164518 | + | 0.986374i | \(0.447393\pi\) | |||||||
\(762\) | 0.337659 | 0.0122321 | ||||||||
\(763\) | −9.90433 | −0.358561 | ||||||||
\(764\) | 23.4017 | 0.846642 | ||||||||
\(765\) | −9.51084 | −0.343865 | ||||||||
\(766\) | −18.4871 | −0.667967 | ||||||||
\(767\) | −15.1843 | −0.548273 | ||||||||
\(768\) | 0.648159 | 0.0233884 | ||||||||
\(769\) | −1.03985 | −0.0374978 | −0.0187489 | − | 0.999824i | \(-0.505968\pi\) | ||||
−0.0187489 | + | 0.999824i | \(0.505968\pi\) | |||||||
\(770\) | 7.57915 | 0.273134 | ||||||||
\(771\) | −0.0357452 | −0.00128733 | ||||||||
\(772\) | −6.26081 | −0.225332 | ||||||||
\(773\) | −10.5324 | −0.378823 | −0.189411 | − | 0.981898i | \(-0.560658\pi\) | ||||
−0.189411 | + | 0.981898i | \(0.560658\pi\) | |||||||
\(774\) | 55.3377 | 1.98907 | ||||||||
\(775\) | −5.08502 | −0.182659 | ||||||||
\(776\) | −11.0232 | −0.395708 | ||||||||
\(777\) | −0.315513 | −0.0113190 | ||||||||
\(778\) | 53.3423 | 1.91241 | ||||||||
\(779\) | −7.64926 | −0.274063 | ||||||||
\(780\) | −0.123844 | −0.00443432 | ||||||||
\(781\) | 18.9836 | 0.679288 | ||||||||
\(782\) | −28.0912 | −1.00454 | ||||||||
\(783\) | 0.268828 | 0.00960715 | ||||||||
\(784\) | −4.67707 | −0.167038 | ||||||||
\(785\) | −2.15806 | −0.0770245 | ||||||||
\(786\) | 1.15224 | 0.0410989 | ||||||||
\(787\) | 38.8606 | 1.38523 | 0.692615 | − | 0.721307i | \(-0.256458\pi\) | ||||
0.692615 | + | 0.721307i | \(0.256458\pi\) | |||||||
\(788\) | 26.2510 | 0.935152 | ||||||||
\(789\) | −0.0693693 | −0.00246961 | ||||||||
\(790\) | −16.5408 | −0.588497 | ||||||||
\(791\) | 8.72373 | 0.310180 | ||||||||
\(792\) | 9.81322 | 0.348698 | ||||||||
\(793\) | 12.5454 | 0.445500 | ||||||||
\(794\) | 43.8463 | 1.55605 | ||||||||
\(795\) | 0.200886 | 0.00712469 | ||||||||
\(796\) | 1.30338 | 0.0461970 | ||||||||
\(797\) | −7.73964 | −0.274152 | −0.137076 | − | 0.990561i | \(-0.543770\pi\) | ||||
−0.137076 | + | 0.990561i | \(0.543770\pi\) | |||||||
\(798\) | −0.206418 | −0.00730711 | ||||||||
\(799\) | −36.7539 | −1.30026 | ||||||||
\(800\) | −7.20385 | −0.254695 | ||||||||
\(801\) | 5.41500 | 0.191330 | ||||||||
\(802\) | −58.5400 | −2.06712 | ||||||||
\(803\) | −36.2344 | −1.27868 | ||||||||
\(804\) | −0.0362320 | −0.00127780 | ||||||||
\(805\) | 4.68922 | 0.165273 | ||||||||
\(806\) | −24.0434 | −0.846891 | ||||||||
\(807\) | −0.917918 | −0.0323122 | ||||||||
\(808\) | −10.4350 | −0.367101 | ||||||||
\(809\) | 9.52161 | 0.334762 | 0.167381 | − | 0.985892i | \(-0.446469\pi\) | ||||
0.167381 | + | 0.985892i | \(0.446469\pi\) | |||||||
\(810\) | −16.9840 | −0.596755 | ||||||||
\(811\) | 37.4507 | 1.31507 | 0.657535 | − | 0.753424i | \(-0.271599\pi\) | ||||
0.657535 | + | 0.753424i | \(0.271599\pi\) | |||||||
\(812\) | 2.22760 | 0.0781733 | ||||||||
\(813\) | −0.0638108 | −0.00223794 | ||||||||
\(814\) | 75.7980 | 2.65672 | ||||||||
\(815\) | 12.9903 | 0.455030 | ||||||||
\(816\) | 0.467946 | 0.0163814 | ||||||||
\(817\) | −33.8340 | −1.18370 | ||||||||
\(818\) | −32.5681 | −1.13872 | ||||||||
\(819\) | 7.50674 | 0.262307 | ||||||||
\(820\) | 3.46339 | 0.120947 | ||||||||
\(821\) | −4.80751 | −0.167783 | −0.0838917 | − | 0.996475i | \(-0.526735\pi\) | ||||
−0.0838917 | + | 0.996475i | \(0.526735\pi\) | |||||||
\(822\) | 1.02291 | 0.0356782 | ||||||||
\(823\) | −29.3481 | −1.02301 | −0.511505 | − | 0.859280i | \(-0.670912\pi\) | ||||
−0.511505 | + | 0.859280i | \(0.670912\pi\) | |||||||
\(824\) | −15.0130 | −0.523004 | ||||||||
\(825\) | 0.126582 | 0.00440702 | ||||||||
\(826\) | 11.4591 | 0.398712 | ||||||||
\(827\) | 57.3984 | 1.99594 | 0.997969 | − | 0.0636961i | \(-0.0202888\pi\) | ||||
0.997969 | + | 0.0636961i | \(0.0202888\pi\) | |||||||
\(828\) | −22.0545 | −0.766448 | ||||||||
\(829\) | 23.3854 | 0.812207 | 0.406103 | − | 0.913827i | \(-0.366887\pi\) | ||||
0.406103 | + | 0.913827i | \(0.366887\pi\) | |||||||
\(830\) | −28.7604 | −0.998288 | ||||||||
\(831\) | 0.540966 | 0.0187659 | ||||||||
\(832\) | −10.6477 | −0.369141 | ||||||||
\(833\) | −3.17133 | −0.109880 | ||||||||
\(834\) | 0.772832 | 0.0267610 | ||||||||
\(835\) | 18.5483 | 0.641890 | ||||||||
\(836\) | 21.7947 | 0.753785 | ||||||||
\(837\) | 0.962391 | 0.0332651 | ||||||||
\(838\) | 34.4056 | 1.18852 | ||||||||
\(839\) | −40.9060 | −1.41223 | −0.706116 | − | 0.708096i | \(-0.749554\pi\) | ||||
−0.706116 | + | 0.708096i | \(0.749554\pi\) | |||||||
\(840\) | −0.0257290 | −0.000887734 0 | ||||||||
\(841\) | −26.9824 | −0.930428 | ||||||||
\(842\) | 63.3253 | 2.18233 | ||||||||
\(843\) | −0.0121627 | −0.000418905 0 | ||||||||
\(844\) | −2.85564 | −0.0982952 | ||||||||
\(845\) | 6.73461 | 0.231678 | ||||||||
\(846\) | −65.6549 | −2.25726 | ||||||||
\(847\) | −5.09844 | −0.175185 | ||||||||
\(848\) | 29.7813 | 1.02269 | ||||||||
\(849\) | 0.246183 | 0.00844899 | ||||||||
\(850\) | −5.99060 | −0.205476 | ||||||||
\(851\) | 46.8962 | 1.60758 | ||||||||
\(852\) | 0.234093 | 0.00801989 | ||||||||
\(853\) | 16.1112 | 0.551637 | 0.275819 | − | 0.961210i | \(-0.411051\pi\) | ||||
0.275819 | + | 0.961210i | \(0.411051\pi\) | |||||||
\(854\) | −9.46759 | −0.323974 | ||||||||
\(855\) | 10.3876 | 0.355249 | ||||||||
\(856\) | 8.83057 | 0.301823 | ||||||||
\(857\) | 3.08592 | 0.105413 | 0.0527066 | − | 0.998610i | \(-0.483215\pi\) | ||||
0.0527066 | + | 0.998610i | \(0.483215\pi\) | |||||||
\(858\) | 0.598514 | 0.0204329 | ||||||||
\(859\) | −34.7741 | −1.18648 | −0.593238 | − | 0.805027i | \(-0.702151\pi\) | ||||
−0.593238 | + | 0.805027i | \(0.702151\pi\) | |||||||
\(860\) | 15.3192 | 0.522379 | ||||||||
\(861\) | 0.0696725 | 0.00237443 | ||||||||
\(862\) | 60.4535 | 2.05905 | ||||||||
\(863\) | −20.1752 | −0.686772 | −0.343386 | − | 0.939194i | \(-0.611574\pi\) | ||||
−0.343386 | + | 0.939194i | \(0.611574\pi\) | |||||||
\(864\) | 1.36340 | 0.0463839 | ||||||||
\(865\) | −3.65932 | −0.124420 | ||||||||
\(866\) | −62.9131 | −2.13787 | ||||||||
\(867\) | −0.219031 | −0.00743868 | ||||||||
\(868\) | 7.97467 | 0.270678 | ||||||||
\(869\) | 35.1335 | 1.19182 | ||||||||
\(870\) | 0.0846496 | 0.00286989 | ||||||||
\(871\) | −1.83301 | −0.0621093 | ||||||||
\(872\) | −8.07733 | −0.273533 | ||||||||
\(873\) | −40.5360 | −1.37194 | ||||||||
\(874\) | 30.6808 | 1.03780 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −0.446816 | −0.0150965 | ||||||||
\(877\) | 22.9808 | 0.776005 | 0.388003 | − | 0.921658i | \(-0.373165\pi\) | ||||
0.388003 | + | 0.921658i | \(0.373165\pi\) | |||||||
\(878\) | 33.5786 | 1.13322 | ||||||||
\(879\) | −0.00287601 | −9.70054e−5 0 | ||||||||
\(880\) | 18.7658 | 0.632593 | ||||||||
\(881\) | 31.7615 | 1.07007 | 0.535037 | − | 0.844829i | \(-0.320298\pi\) | ||||
0.535037 | + | 0.844829i | \(0.320298\pi\) | |||||||
\(882\) | −5.66508 | −0.190753 | ||||||||
\(883\) | −44.8101 | −1.50798 | −0.753990 | − | 0.656886i | \(-0.771873\pi\) | ||||
−0.753990 | + | 0.656886i | \(0.771873\pi\) | |||||||
\(884\) | −12.4490 | −0.418707 | ||||||||
\(885\) | 0.191382 | 0.00643323 | ||||||||
\(886\) | 5.51318 | 0.185219 | ||||||||
\(887\) | 44.6061 | 1.49773 | 0.748863 | − | 0.662724i | \(-0.230600\pi\) | ||||
0.748863 | + | 0.662724i | \(0.230600\pi\) | |||||||
\(888\) | −0.257312 | −0.00863482 | ||||||||
\(889\) | −5.66591 | −0.190028 | ||||||||
\(890\) | 3.41075 | 0.114329 | ||||||||
\(891\) | 36.0746 | 1.20855 | ||||||||
\(892\) | 31.9572 | 1.07001 | ||||||||
\(893\) | 40.1421 | 1.34330 | ||||||||
\(894\) | 0.394263 | 0.0131861 | ||||||||
\(895\) | −21.9680 | −0.734310 | ||||||||
\(896\) | −6.37227 | −0.212883 | ||||||||
\(897\) | 0.370300 | 0.0123640 | ||||||||
\(898\) | −3.88309 | −0.129581 | ||||||||
\(899\) | 7.22285 | 0.240895 | ||||||||
\(900\) | −4.70324 | −0.156775 | ||||||||
\(901\) | 20.1935 | 0.672743 | ||||||||
\(902\) | −16.7379 | −0.557312 | ||||||||
\(903\) | 0.308173 | 0.0102554 | ||||||||
\(904\) | 7.11451 | 0.236625 | ||||||||
\(905\) | 16.9779 | 0.564363 | ||||||||
\(906\) | 0.923750 | 0.0306895 | ||||||||
\(907\) | 22.4249 | 0.744605 | 0.372303 | − | 0.928111i | \(-0.378568\pi\) | ||||
0.372303 | + | 0.928111i | \(0.378568\pi\) | |||||||
\(908\) | 17.2793 | 0.573434 | ||||||||
\(909\) | −38.3730 | −1.27275 | ||||||||
\(910\) | 4.72827 | 0.156741 | ||||||||
\(911\) | −31.0064 | −1.02729 | −0.513644 | − | 0.858004i | \(-0.671705\pi\) | ||||
−0.513644 | + | 0.858004i | \(0.671705\pi\) | |||||||
\(912\) | −0.511084 | −0.0169237 | ||||||||
\(913\) | 61.0883 | 2.02173 | ||||||||
\(914\) | 14.4314 | 0.477350 | ||||||||
\(915\) | −0.158121 | −0.00522733 | ||||||||
\(916\) | 1.56827 | 0.0518170 | ||||||||
\(917\) | −19.3345 | −0.638481 | ||||||||
\(918\) | 1.13378 | 0.0374204 | ||||||||
\(919\) | −28.3754 | −0.936018 | −0.468009 | − | 0.883724i | \(-0.655029\pi\) | ||||
−0.468009 | + | 0.883724i | \(0.655029\pi\) | |||||||
\(920\) | 3.82422 | 0.126081 | ||||||||
\(921\) | 0.500825 | 0.0165027 | ||||||||
\(922\) | 46.1175 | 1.51880 | ||||||||
\(923\) | 11.8430 | 0.389817 | ||||||||
\(924\) | −0.198515 | −0.00653065 | ||||||||
\(925\) | 10.0009 | 0.328826 | ||||||||
\(926\) | −54.6923 | −1.79730 | ||||||||
\(927\) | −55.2081 | −1.81327 | ||||||||
\(928\) | 10.2325 | 0.335898 | ||||||||
\(929\) | −21.8692 | −0.717504 | −0.358752 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358752 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(930\) | 0.303041 | 0.00993710 | ||||||||
\(931\) | 3.46368 | 0.113518 | ||||||||
\(932\) | −21.6006 | −0.707550 | ||||||||
\(933\) | −0.942958 | −0.0308711 | ||||||||
\(934\) | −17.2519 | −0.564500 | ||||||||
\(935\) | 12.7243 | 0.416129 | ||||||||
\(936\) | 6.12201 | 0.200104 | ||||||||
\(937\) | 41.5377 | 1.35698 | 0.678489 | − | 0.734610i | \(-0.262635\pi\) | ||||
0.678489 | + | 0.734610i | \(0.262635\pi\) | |||||||
\(938\) | 1.38331 | 0.0451668 | ||||||||
\(939\) | −0.636759 | −0.0207799 | ||||||||
\(940\) | −18.1753 | −0.592813 | ||||||||
\(941\) | 28.6104 | 0.932672 | 0.466336 | − | 0.884608i | \(-0.345574\pi\) | ||||
0.466336 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(942\) | 0.128609 | 0.00419032 | ||||||||
\(943\) | −10.3557 | −0.337229 | ||||||||
\(944\) | 28.3723 | 0.923441 | ||||||||
\(945\) | −0.189260 | −0.00615663 | ||||||||
\(946\) | −74.0348 | −2.40708 | ||||||||
\(947\) | 60.9523 | 1.98068 | 0.990342 | − | 0.138645i | \(-0.0442747\pi\) | ||||
0.990342 | + | 0.138645i | \(0.0442747\pi\) | |||||||
\(948\) | 0.433241 | 0.0140710 | ||||||||
\(949\) | −22.6049 | −0.733786 | ||||||||
\(950\) | 6.54285 | 0.212278 | ||||||||
\(951\) | −1.11339 | −0.0361043 | ||||||||
\(952\) | −2.58633 | −0.0838235 | ||||||||
\(953\) | −26.0057 | −0.842409 | −0.421204 | − | 0.906966i | \(-0.638392\pi\) | ||||
−0.421204 | + | 0.906966i | \(0.638392\pi\) | |||||||
\(954\) | 36.0724 | 1.16789 | ||||||||
\(955\) | −14.9220 | −0.482864 | ||||||||
\(956\) | −6.27564 | −0.202969 | ||||||||
\(957\) | −0.179799 | −0.00581209 | ||||||||
\(958\) | 16.3195 | 0.527259 | ||||||||
\(959\) | −17.1644 | −0.554269 | ||||||||
\(960\) | 0.134202 | 0.00433137 | ||||||||
\(961\) | −5.14261 | −0.165891 | ||||||||
\(962\) | 47.2868 | 1.52459 | ||||||||
\(963\) | 32.4731 | 1.04643 | ||||||||
\(964\) | 6.40686 | 0.206351 | ||||||||
\(965\) | 3.99218 | 0.128513 | ||||||||
\(966\) | −0.279453 | −0.00899126 | ||||||||
\(967\) | 9.19978 | 0.295845 | 0.147923 | − | 0.988999i | \(-0.452741\pi\) | ||||
0.147923 | + | 0.988999i | \(0.452741\pi\) | |||||||
\(968\) | −4.15796 | −0.133642 | ||||||||
\(969\) | −0.346545 | −0.0111326 | ||||||||
\(970\) | −25.5324 | −0.819797 | ||||||||
\(971\) | 41.1393 | 1.32022 | 0.660112 | − | 0.751167i | \(-0.270509\pi\) | ||||
0.660112 | + | 0.751167i | \(0.270509\pi\) | |||||||
\(972\) | 1.33528 | 0.0428291 | ||||||||
\(973\) | −12.9681 | −0.415738 | ||||||||
\(974\) | −12.6370 | −0.404917 | ||||||||
\(975\) | 0.0789685 | 0.00252902 | ||||||||
\(976\) | −23.4415 | −0.750343 | ||||||||
\(977\) | 24.2944 | 0.777248 | 0.388624 | − | 0.921396i | \(-0.372950\pi\) | ||||
0.388624 | + | 0.921396i | \(0.372950\pi\) | |||||||
\(978\) | −0.774155 | −0.0247547 | ||||||||
\(979\) | −7.24458 | −0.231538 | ||||||||
\(980\) | −1.56827 | −0.0500965 | ||||||||
\(981\) | −29.7031 | −0.948348 | ||||||||
\(982\) | −54.0683 | −1.72539 | ||||||||
\(983\) | 17.1856 | 0.548136 | 0.274068 | − | 0.961710i | \(-0.411631\pi\) | ||||
0.274068 | + | 0.961710i | \(0.411631\pi\) | |||||||
\(984\) | 0.0568203 | 0.00181137 | ||||||||
\(985\) | −16.7388 | −0.533343 | ||||||||
\(986\) | 8.50916 | 0.270987 | ||||||||
\(987\) | −0.365630 | −0.0116381 | ||||||||
\(988\) | 13.5967 | 0.432568 | ||||||||
\(989\) | −45.8052 | −1.45652 | ||||||||
\(990\) | 22.7299 | 0.722404 | ||||||||
\(991\) | 1.69894 | 0.0539687 | 0.0269844 | − | 0.999636i | \(-0.491410\pi\) | ||||
0.0269844 | + | 0.999636i | \(0.491410\pi\) | |||||||
\(992\) | 36.6317 | 1.16306 | ||||||||
\(993\) | −0.473006 | −0.0150104 | ||||||||
\(994\) | −8.93751 | −0.283481 | ||||||||
\(995\) | −0.831093 | −0.0263474 | ||||||||
\(996\) | 0.753298 | 0.0238692 | ||||||||
\(997\) | 38.4897 | 1.21898 | 0.609491 | − | 0.792793i | \(-0.291374\pi\) | ||||
0.609491 | + | 0.792793i | \(0.291374\pi\) | |||||||
\(998\) | −60.1856 | −1.90514 | ||||||||
\(999\) | −1.89276 | −0.0598844 |
(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 | 8015.2.a.l.1.50 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.50 | ✓ | 62 | 1.1 | even | 1 | trivial |