Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.0611935 | −0.0353301 | −0.0176650 | − | 0.999844i | \(-0.505623\pi\) | ||||
−0.0176650 | + | 0.999844i | \(0.505623\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.49914 | −1.56486 | −0.782431 | − | 0.622738i | \(-0.786020\pi\) | ||||
−0.782431 | + | 0.622738i | \(0.786020\pi\) | |||||||
\(6\) | 0.0611935 | 0.0249821 | ||||||||
\(7\) | −5.08120 | −1.92051 | −0.960257 | − | 0.279119i | \(-0.909958\pi\) | ||||
−0.960257 | + | 0.279119i | \(0.909958\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.99626 | −0.998752 | ||||||||
\(10\) | 3.49914 | 1.10652 | ||||||||
\(11\) | −0.435748 | −0.131383 | −0.0656915 | − | 0.997840i | \(-0.520925\pi\) | ||||
−0.0656915 | + | 0.997840i | \(0.520925\pi\) | |||||||
\(12\) | −0.0611935 | −0.0176650 | ||||||||
\(13\) | 0.685830 | 0.190215 | 0.0951075 | − | 0.995467i | \(-0.469681\pi\) | ||||
0.0951075 | + | 0.995467i | \(0.469681\pi\) | |||||||
\(14\) | 5.08120 | 1.35801 | ||||||||
\(15\) | 0.214124 | 0.0552867 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.65973 | 1.13015 | 0.565075 | − | 0.825039i | \(-0.308847\pi\) | ||||
0.565075 | + | 0.825039i | \(0.308847\pi\) | |||||||
\(18\) | 2.99626 | 0.706224 | ||||||||
\(19\) | 8.26410 | 1.89592 | 0.947958 | − | 0.318397i | \(-0.103144\pi\) | ||||
0.947958 | + | 0.318397i | \(0.103144\pi\) | |||||||
\(20\) | −3.49914 | −0.782431 | ||||||||
\(21\) | 0.310936 | 0.0678518 | ||||||||
\(22\) | 0.435748 | 0.0929019 | ||||||||
\(23\) | −1.27945 | −0.266784 | −0.133392 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133392 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(24\) | 0.0611935 | 0.0124911 | ||||||||
\(25\) | 7.24396 | 1.44879 | ||||||||
\(26\) | −0.685830 | −0.134502 | ||||||||
\(27\) | 0.366932 | 0.0706160 | ||||||||
\(28\) | −5.08120 | −0.960257 | ||||||||
\(29\) | −0.893012 | −0.165828 | −0.0829141 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829141 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(30\) | −0.214124 | −0.0390936 | ||||||||
\(31\) | 4.10479 | 0.737242 | 0.368621 | − | 0.929580i | \(-0.379830\pi\) | ||||
0.368621 | + | 0.929580i | \(0.379830\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.0266650 | 0.00464177 | ||||||||
\(34\) | −4.65973 | −0.799137 | ||||||||
\(35\) | 17.7798 | 3.00534 | ||||||||
\(36\) | −2.99626 | −0.499376 | ||||||||
\(37\) | −10.6262 | −1.74694 | −0.873472 | − | 0.486875i | \(-0.838137\pi\) | ||||
−0.873472 | + | 0.486875i | \(0.838137\pi\) | |||||||
\(38\) | −8.26410 | −1.34061 | ||||||||
\(39\) | −0.0419683 | −0.00672031 | ||||||||
\(40\) | 3.49914 | 0.553262 | ||||||||
\(41\) | 8.20672 | 1.28167 | 0.640837 | − | 0.767677i | \(-0.278588\pi\) | ||||
0.640837 | + | 0.767677i | \(0.278588\pi\) | |||||||
\(42\) | −0.310936 | −0.0479785 | ||||||||
\(43\) | −3.04884 | −0.464944 | −0.232472 | − | 0.972603i | \(-0.574681\pi\) | ||||
−0.232472 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(44\) | −0.435748 | −0.0656915 | ||||||||
\(45\) | 10.4843 | 1.56291 | ||||||||
\(46\) | 1.27945 | 0.188645 | ||||||||
\(47\) | 4.10573 | 0.598883 | 0.299441 | − | 0.954115i | \(-0.403200\pi\) | ||||
0.299441 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(48\) | −0.0611935 | −0.00883251 | ||||||||
\(49\) | 18.8186 | 2.68837 | ||||||||
\(50\) | −7.24396 | −1.02445 | ||||||||
\(51\) | −0.285145 | −0.0399283 | ||||||||
\(52\) | 0.685830 | 0.0951075 | ||||||||
\(53\) | 9.92221 | 1.36292 | 0.681460 | − | 0.731855i | \(-0.261345\pi\) | ||||
0.681460 | + | 0.731855i | \(0.261345\pi\) | |||||||
\(54\) | −0.366932 | −0.0499331 | ||||||||
\(55\) | 1.52474 | 0.205596 | ||||||||
\(56\) | 5.08120 | 0.679004 | ||||||||
\(57\) | −0.505709 | −0.0669828 | ||||||||
\(58\) | 0.893012 | 0.117258 | ||||||||
\(59\) | −10.1672 | −1.32366 | −0.661831 | − | 0.749653i | \(-0.730220\pi\) | ||||
−0.661831 | + | 0.749653i | \(0.730220\pi\) | |||||||
\(60\) | 0.214124 | 0.0276433 | ||||||||
\(61\) | −11.7413 | −1.50332 | −0.751659 | − | 0.659552i | \(-0.770746\pi\) | ||||
−0.751659 | + | 0.659552i | \(0.770746\pi\) | |||||||
\(62\) | −4.10479 | −0.521309 | ||||||||
\(63\) | 15.2246 | 1.91812 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.39981 | −0.297660 | ||||||||
\(66\) | −0.0266650 | −0.00328223 | ||||||||
\(67\) | −8.02486 | −0.980392 | −0.490196 | − | 0.871612i | \(-0.663075\pi\) | ||||
−0.490196 | + | 0.871612i | \(0.663075\pi\) | |||||||
\(68\) | 4.65973 | 0.565075 | ||||||||
\(69\) | 0.0782940 | 0.00942549 | ||||||||
\(70\) | −17.7798 | −2.12509 | ||||||||
\(71\) | 1.52492 | 0.180975 | 0.0904873 | − | 0.995898i | \(-0.471158\pi\) | ||||
0.0904873 | + | 0.995898i | \(0.471158\pi\) | |||||||
\(72\) | 2.99626 | 0.353112 | ||||||||
\(73\) | 3.89753 | 0.456171 | 0.228085 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228085 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(74\) | 10.6262 | 1.23528 | ||||||||
\(75\) | −0.443283 | −0.0511859 | ||||||||
\(76\) | 8.26410 | 0.947958 | ||||||||
\(77\) | 2.21412 | 0.252323 | ||||||||
\(78\) | 0.0419683 | 0.00475198 | ||||||||
\(79\) | 0.879981 | 0.0990056 | 0.0495028 | − | 0.998774i | \(-0.484236\pi\) | ||||
0.0495028 | + | 0.998774i | \(0.484236\pi\) | |||||||
\(80\) | −3.49914 | −0.391215 | ||||||||
\(81\) | 8.96631 | 0.996257 | ||||||||
\(82\) | −8.20672 | −0.906280 | ||||||||
\(83\) | 16.3188 | 1.79122 | 0.895612 | − | 0.444836i | \(-0.146738\pi\) | ||||
0.895612 | + | 0.444836i | \(0.146738\pi\) | |||||||
\(84\) | 0.310936 | 0.0339259 | ||||||||
\(85\) | −16.3050 | −1.76853 | ||||||||
\(86\) | 3.04884 | 0.328765 | ||||||||
\(87\) | 0.0546465 | 0.00585872 | ||||||||
\(88\) | 0.435748 | 0.0464509 | ||||||||
\(89\) | −2.11755 | −0.224460 | −0.112230 | − | 0.993682i | \(-0.535799\pi\) | ||||
−0.112230 | + | 0.993682i | \(0.535799\pi\) | |||||||
\(90\) | −10.4843 | −1.10514 | ||||||||
\(91\) | −3.48484 | −0.365311 | ||||||||
\(92\) | −1.27945 | −0.133392 | ||||||||
\(93\) | −0.251186 | −0.0260468 | ||||||||
\(94\) | −4.10573 | −0.423474 | ||||||||
\(95\) | −28.9172 | −2.96684 | ||||||||
\(96\) | 0.0611935 | 0.00624553 | ||||||||
\(97\) | 1.77788 | 0.180516 | 0.0902581 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902581 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(98\) | −18.8186 | −1.90097 | ||||||||
\(99\) | 1.30561 | 0.131219 | ||||||||
\(100\) | 7.24396 | 0.724396 | ||||||||
\(101\) | 1.43584 | 0.142872 | 0.0714358 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714358 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(102\) | 0.285145 | 0.0282336 | ||||||||
\(103\) | −2.93501 | −0.289195 | −0.144597 | − | 0.989491i | \(-0.546189\pi\) | ||||
−0.144597 | + | 0.989491i | \(0.546189\pi\) | |||||||
\(104\) | −0.685830 | −0.0672512 | ||||||||
\(105\) | −1.08801 | −0.106179 | ||||||||
\(106\) | −9.92221 | −0.963730 | ||||||||
\(107\) | −5.29527 | −0.511913 | −0.255956 | − | 0.966688i | \(-0.582390\pi\) | ||||
−0.255956 | + | 0.966688i | \(0.582390\pi\) | |||||||
\(108\) | 0.366932 | 0.0353080 | ||||||||
\(109\) | −9.98409 | −0.956302 | −0.478151 | − | 0.878278i | \(-0.658693\pi\) | ||||
−0.478151 | + | 0.878278i | \(0.658693\pi\) | |||||||
\(110\) | −1.52474 | −0.145379 | ||||||||
\(111\) | 0.650256 | 0.0617196 | ||||||||
\(112\) | −5.08120 | −0.480128 | ||||||||
\(113\) | 2.51508 | 0.236599 | 0.118299 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118299 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(114\) | 0.505709 | 0.0473640 | ||||||||
\(115\) | 4.47697 | 0.417480 | ||||||||
\(116\) | −0.893012 | −0.0829141 | ||||||||
\(117\) | −2.05492 | −0.189978 | ||||||||
\(118\) | 10.1672 | 0.935970 | ||||||||
\(119\) | −23.6770 | −2.17047 | ||||||||
\(120\) | −0.214124 | −0.0195468 | ||||||||
\(121\) | −10.8101 | −0.982738 | ||||||||
\(122\) | 11.7413 | 1.06301 | ||||||||
\(123\) | −0.502197 | −0.0452816 | ||||||||
\(124\) | 4.10479 | 0.368621 | ||||||||
\(125\) | −7.85192 | −0.702297 | ||||||||
\(126\) | −15.2246 | −1.35631 | ||||||||
\(127\) | −18.2688 | −1.62110 | −0.810548 | − | 0.585672i | \(-0.800831\pi\) | ||||
−0.810548 | + | 0.585672i | \(0.800831\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.186569 | 0.0164265 | ||||||||
\(130\) | 2.39981 | 0.210478 | ||||||||
\(131\) | 6.84595 | 0.598133 | 0.299067 | − | 0.954232i | \(-0.403325\pi\) | ||||
0.299067 | + | 0.954232i | \(0.403325\pi\) | |||||||
\(132\) | 0.0266650 | 0.00232089 | ||||||||
\(133\) | −41.9916 | −3.64113 | ||||||||
\(134\) | 8.02486 | 0.693242 | ||||||||
\(135\) | −1.28394 | −0.110504 | ||||||||
\(136\) | −4.65973 | −0.399569 | ||||||||
\(137\) | −18.1594 | −1.55146 | −0.775732 | − | 0.631063i | \(-0.782619\pi\) | ||||
−0.775732 | + | 0.631063i | \(0.782619\pi\) | |||||||
\(138\) | −0.0782940 | −0.00666483 | ||||||||
\(139\) | 10.7728 | 0.913735 | 0.456868 | − | 0.889535i | \(-0.348971\pi\) | ||||
0.456868 | + | 0.889535i | \(0.348971\pi\) | |||||||
\(140\) | 17.7798 | 1.50267 | ||||||||
\(141\) | −0.251244 | −0.0211586 | ||||||||
\(142\) | −1.52492 | −0.127968 | ||||||||
\(143\) | −0.298849 | −0.0249910 | ||||||||
\(144\) | −2.99626 | −0.249688 | ||||||||
\(145\) | 3.12477 | 0.259498 | ||||||||
\(146\) | −3.89753 | −0.322562 | ||||||||
\(147\) | −1.15157 | −0.0949803 | ||||||||
\(148\) | −10.6262 | −0.873472 | ||||||||
\(149\) | −10.0866 | −0.826323 | −0.413161 | − | 0.910658i | \(-0.635575\pi\) | ||||
−0.413161 | + | 0.910658i | \(0.635575\pi\) | |||||||
\(150\) | 0.443283 | 0.0361939 | ||||||||
\(151\) | 11.2302 | 0.913903 | 0.456952 | − | 0.889492i | \(-0.348941\pi\) | ||||
0.456952 | + | 0.889492i | \(0.348941\pi\) | |||||||
\(152\) | −8.26410 | −0.670307 | ||||||||
\(153\) | −13.9617 | −1.12874 | ||||||||
\(154\) | −2.21412 | −0.178419 | ||||||||
\(155\) | −14.3632 | −1.15368 | ||||||||
\(156\) | −0.0419683 | −0.00336015 | ||||||||
\(157\) | 18.3948 | 1.46806 | 0.734031 | − | 0.679116i | \(-0.237637\pi\) | ||||
0.734031 | + | 0.679116i | \(0.237637\pi\) | |||||||
\(158\) | −0.879981 | −0.0700076 | ||||||||
\(159\) | −0.607174 | −0.0481520 | ||||||||
\(160\) | 3.49914 | 0.276631 | ||||||||
\(161\) | 6.50115 | 0.512362 | ||||||||
\(162\) | −8.96631 | −0.704460 | ||||||||
\(163\) | −18.9079 | −1.48098 | −0.740490 | − | 0.672067i | \(-0.765407\pi\) | ||||
−0.740490 | + | 0.672067i | \(0.765407\pi\) | |||||||
\(164\) | 8.20672 | 0.640837 | ||||||||
\(165\) | −0.0933043 | −0.00726373 | ||||||||
\(166\) | −16.3188 | −1.26659 | ||||||||
\(167\) | −8.29004 | −0.641502 | −0.320751 | − | 0.947164i | \(-0.603935\pi\) | ||||
−0.320751 | + | 0.947164i | \(0.603935\pi\) | |||||||
\(168\) | −0.310936 | −0.0239892 | ||||||||
\(169\) | −12.5296 | −0.963818 | ||||||||
\(170\) | 16.3050 | 1.25054 | ||||||||
\(171\) | −24.7614 | −1.89355 | ||||||||
\(172\) | −3.04884 | −0.232472 | ||||||||
\(173\) | 3.30808 | 0.251509 | 0.125754 | − | 0.992061i | \(-0.459865\pi\) | ||||
0.125754 | + | 0.992061i | \(0.459865\pi\) | |||||||
\(174\) | −0.0546465 | −0.00414274 | ||||||||
\(175\) | −36.8080 | −2.78242 | ||||||||
\(176\) | −0.435748 | −0.0328458 | ||||||||
\(177\) | 0.622168 | 0.0467650 | ||||||||
\(178\) | 2.11755 | 0.158717 | ||||||||
\(179\) | 17.3494 | 1.29676 | 0.648378 | − | 0.761319i | \(-0.275448\pi\) | ||||
0.648378 | + | 0.761319i | \(0.275448\pi\) | |||||||
\(180\) | 10.4843 | 0.781454 | ||||||||
\(181\) | 25.4989 | 1.89532 | 0.947658 | − | 0.319288i | \(-0.103444\pi\) | ||||
0.947658 | + | 0.319288i | \(0.103444\pi\) | |||||||
\(182\) | 3.48484 | 0.258314 | ||||||||
\(183\) | 0.718490 | 0.0531123 | ||||||||
\(184\) | 1.27945 | 0.0943224 | ||||||||
\(185\) | 37.1827 | 2.73372 | ||||||||
\(186\) | 0.251186 | 0.0184179 | ||||||||
\(187\) | −2.03047 | −0.148483 | ||||||||
\(188\) | 4.10573 | 0.299441 | ||||||||
\(189\) | −1.86445 | −0.135619 | ||||||||
\(190\) | 28.9172 | 2.09788 | ||||||||
\(191\) | 22.8773 | 1.65534 | 0.827671 | − | 0.561214i | \(-0.189665\pi\) | ||||
0.827671 | + | 0.561214i | \(0.189665\pi\) | |||||||
\(192\) | −0.0611935 | −0.00441626 | ||||||||
\(193\) | 6.99022 | 0.503167 | 0.251584 | − | 0.967836i | \(-0.419049\pi\) | ||||
0.251584 | + | 0.967836i | \(0.419049\pi\) | |||||||
\(194\) | −1.77788 | −0.127644 | ||||||||
\(195\) | 0.146853 | 0.0105164 | ||||||||
\(196\) | 18.8186 | 1.34419 | ||||||||
\(197\) | −2.50115 | −0.178200 | −0.0890998 | − | 0.996023i | \(-0.528399\pi\) | ||||
−0.0890998 | + | 0.996023i | \(0.528399\pi\) | |||||||
\(198\) | −1.30561 | −0.0927859 | ||||||||
\(199\) | 6.69601 | 0.474667 | 0.237334 | − | 0.971428i | \(-0.423727\pi\) | ||||
0.237334 | + | 0.971428i | \(0.423727\pi\) | |||||||
\(200\) | −7.24396 | −0.512225 | ||||||||
\(201\) | 0.491069 | 0.0346373 | ||||||||
\(202\) | −1.43584 | −0.101025 | ||||||||
\(203\) | 4.53757 | 0.318475 | ||||||||
\(204\) | −0.285145 | −0.0199641 | ||||||||
\(205\) | −28.7164 | −2.00564 | ||||||||
\(206\) | 2.93501 | 0.204492 | ||||||||
\(207\) | 3.83356 | 0.266451 | ||||||||
\(208\) | 0.685830 | 0.0475538 | ||||||||
\(209\) | −3.60107 | −0.249091 | ||||||||
\(210\) | 1.08801 | 0.0750797 | ||||||||
\(211\) | −26.0947 | −1.79643 | −0.898217 | − | 0.439553i | \(-0.855137\pi\) | ||||
−0.898217 | + | 0.439553i | \(0.855137\pi\) | |||||||
\(212\) | 9.92221 | 0.681460 | ||||||||
\(213\) | −0.0933150 | −0.00639384 | ||||||||
\(214\) | 5.29527 | 0.361977 | ||||||||
\(215\) | 10.6683 | 0.727573 | ||||||||
\(216\) | −0.366932 | −0.0249665 | ||||||||
\(217\) | −20.8572 | −1.41588 | ||||||||
\(218\) | 9.98409 | 0.676208 | ||||||||
\(219\) | −0.238503 | −0.0161165 | ||||||||
\(220\) | 1.52474 | 0.102798 | ||||||||
\(221\) | 3.19578 | 0.214972 | ||||||||
\(222\) | −0.650256 | −0.0436423 | ||||||||
\(223\) | −5.41806 | −0.362820 | −0.181410 | − | 0.983408i | \(-0.558066\pi\) | ||||
−0.181410 | + | 0.983408i | \(0.558066\pi\) | |||||||
\(224\) | 5.08120 | 0.339502 | ||||||||
\(225\) | −21.7048 | −1.44698 | ||||||||
\(226\) | −2.51508 | −0.167301 | ||||||||
\(227\) | −4.42350 | −0.293598 | −0.146799 | − | 0.989166i | \(-0.546897\pi\) | ||||
−0.146799 | + | 0.989166i | \(0.546897\pi\) | |||||||
\(228\) | −0.505709 | −0.0334914 | ||||||||
\(229\) | −0.821632 | −0.0542950 | −0.0271475 | − | 0.999631i | \(-0.508642\pi\) | ||||
−0.0271475 | + | 0.999631i | \(0.508642\pi\) | |||||||
\(230\) | −4.47697 | −0.295203 | ||||||||
\(231\) | −0.135490 | −0.00891458 | ||||||||
\(232\) | 0.893012 | 0.0586291 | ||||||||
\(233\) | 15.1979 | 0.995645 | 0.497822 | − | 0.867279i | \(-0.334133\pi\) | ||||
0.497822 | + | 0.867279i | \(0.334133\pi\) | |||||||
\(234\) | 2.05492 | 0.134334 | ||||||||
\(235\) | −14.3665 | −0.937169 | ||||||||
\(236\) | −10.1672 | −0.661831 | ||||||||
\(237\) | −0.0538491 | −0.00349788 | ||||||||
\(238\) | 23.6770 | 1.53475 | ||||||||
\(239\) | 4.92727 | 0.318719 | 0.159359 | − | 0.987221i | \(-0.449057\pi\) | ||||
0.159359 | + | 0.987221i | \(0.449057\pi\) | |||||||
\(240\) | 0.214124 | 0.0138217 | ||||||||
\(241\) | 18.4369 | 1.18762 | 0.593811 | − | 0.804604i | \(-0.297623\pi\) | ||||
0.593811 | + | 0.804604i | \(0.297623\pi\) | |||||||
\(242\) | 10.8101 | 0.694901 | ||||||||
\(243\) | −1.64947 | −0.105814 | ||||||||
\(244\) | −11.7413 | −0.751659 | ||||||||
\(245\) | −65.8488 | −4.20693 | ||||||||
\(246\) | 0.502197 | 0.0320189 | ||||||||
\(247\) | 5.66777 | 0.360632 | ||||||||
\(248\) | −4.10479 | −0.260654 | ||||||||
\(249\) | −0.998606 | −0.0632841 | ||||||||
\(250\) | 7.85192 | 0.496599 | ||||||||
\(251\) | 22.6972 | 1.43264 | 0.716318 | − | 0.697774i | \(-0.245826\pi\) | ||||
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(252\) | 15.2246 | 0.959058 | ||||||||
\(253\) | 0.557519 | 0.0350509 | ||||||||
\(254\) | 18.2688 | 1.14629 | ||||||||
\(255\) | 0.997762 | 0.0624823 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2930 | −0.766816 | −0.383408 | − | 0.923579i | \(-0.625250\pi\) | ||||
−0.383408 | + | 0.923579i | \(0.625250\pi\) | |||||||
\(258\) | −0.186569 | −0.0116153 | ||||||||
\(259\) | 53.9940 | 3.35503 | ||||||||
\(260\) | −2.39981 | −0.148830 | ||||||||
\(261\) | 2.67569 | 0.165621 | ||||||||
\(262\) | −6.84595 | −0.422944 | ||||||||
\(263\) | −28.1035 | −1.73293 | −0.866467 | − | 0.499234i | \(-0.833615\pi\) | ||||
−0.866467 | + | 0.499234i | \(0.833615\pi\) | |||||||
\(264\) | −0.0266650 | −0.00164111 | ||||||||
\(265\) | −34.7192 | −2.13278 | ||||||||
\(266\) | 41.9916 | 2.57467 | ||||||||
\(267\) | 0.129580 | 0.00793018 | ||||||||
\(268\) | −8.02486 | −0.490196 | ||||||||
\(269\) | −14.3762 | −0.876534 | −0.438267 | − | 0.898845i | \(-0.644408\pi\) | ||||
−0.438267 | + | 0.898845i | \(0.644408\pi\) | |||||||
\(270\) | 1.28394 | 0.0781383 | ||||||||
\(271\) | −10.6452 | −0.646651 | −0.323325 | − | 0.946288i | \(-0.604801\pi\) | ||||
−0.323325 | + | 0.946288i | \(0.604801\pi\) | |||||||
\(272\) | 4.65973 | 0.282538 | ||||||||
\(273\) | 0.213249 | 0.0129064 | ||||||||
\(274\) | 18.1594 | 1.09705 | ||||||||
\(275\) | −3.15654 | −0.190347 | ||||||||
\(276\) | 0.0782940 | 0.00471275 | ||||||||
\(277\) | −23.5976 | −1.41784 | −0.708921 | − | 0.705288i | \(-0.750818\pi\) | ||||
−0.708921 | + | 0.705288i | \(0.750818\pi\) | |||||||
\(278\) | −10.7728 | −0.646108 | ||||||||
\(279\) | −12.2990 | −0.736321 | ||||||||
\(280\) | −17.7798 | −1.06255 | ||||||||
\(281\) | −4.46587 | −0.266411 | −0.133206 | − | 0.991088i | \(-0.542527\pi\) | ||||
−0.133206 | + | 0.991088i | \(0.542527\pi\) | |||||||
\(282\) | 0.251244 | 0.0149614 | ||||||||
\(283\) | 30.4143 | 1.80794 | 0.903972 | − | 0.427592i | \(-0.140638\pi\) | ||||
0.903972 | + | 0.427592i | \(0.140638\pi\) | |||||||
\(284\) | 1.52492 | 0.0904873 | ||||||||
\(285\) | 1.76954 | 0.104819 | ||||||||
\(286\) | 0.298849 | 0.0176713 | ||||||||
\(287\) | −41.7000 | −2.46147 | ||||||||
\(288\) | 2.99626 | 0.176556 | ||||||||
\(289\) | 4.71309 | 0.277241 | ||||||||
\(290\) | −3.12477 | −0.183493 | ||||||||
\(291\) | −0.108795 | −0.00637765 | ||||||||
\(292\) | 3.89753 | 0.228085 | ||||||||
\(293\) | −29.8683 | −1.74493 | −0.872463 | − | 0.488680i | \(-0.837479\pi\) | ||||
−0.872463 | + | 0.488680i | \(0.837479\pi\) | |||||||
\(294\) | 1.15157 | 0.0671612 | ||||||||
\(295\) | 35.5766 | 2.07135 | ||||||||
\(296\) | 10.6262 | 0.617638 | ||||||||
\(297\) | −0.159890 | −0.00927775 | ||||||||
\(298\) | 10.0866 | 0.584298 | ||||||||
\(299\) | −0.877486 | −0.0507463 | ||||||||
\(300\) | −0.443283 | −0.0255929 | ||||||||
\(301\) | 15.4918 | 0.892931 | ||||||||
\(302\) | −11.2302 | −0.646227 | ||||||||
\(303\) | −0.0878641 | −0.00504766 | ||||||||
\(304\) | 8.26410 | 0.473979 | ||||||||
\(305\) | 41.0844 | 2.35248 | ||||||||
\(306\) | 13.9617 | 0.798140 | ||||||||
\(307\) | 21.2830 | 1.21468 | 0.607342 | − | 0.794441i | \(-0.292236\pi\) | ||||
0.607342 | + | 0.794441i | \(0.292236\pi\) | |||||||
\(308\) | 2.21412 | 0.126161 | ||||||||
\(309\) | 0.179603 | 0.0102173 | ||||||||
\(310\) | 14.3632 | 0.815776 | ||||||||
\(311\) | 22.1697 | 1.25713 | 0.628563 | − | 0.777758i | \(-0.283643\pi\) | ||||
0.628563 | + | 0.777758i | \(0.283643\pi\) | |||||||
\(312\) | 0.0419683 | 0.00237599 | ||||||||
\(313\) | −25.9576 | −1.46721 | −0.733604 | − | 0.679577i | \(-0.762163\pi\) | ||||
−0.733604 | + | 0.679577i | \(0.762163\pi\) | |||||||
\(314\) | −18.3948 | −1.03808 | ||||||||
\(315\) | −53.2729 | −3.00159 | ||||||||
\(316\) | 0.879981 | 0.0495028 | ||||||||
\(317\) | 26.5281 | 1.48997 | 0.744985 | − | 0.667082i | \(-0.232457\pi\) | ||||
0.744985 | + | 0.667082i | \(0.232457\pi\) | |||||||
\(318\) | 0.607174 | 0.0340486 | ||||||||
\(319\) | 0.389128 | 0.0217870 | ||||||||
\(320\) | −3.49914 | −0.195608 | ||||||||
\(321\) | 0.324036 | 0.0180859 | ||||||||
\(322\) | −6.50115 | −0.362295 | ||||||||
\(323\) | 38.5085 | 2.14267 | ||||||||
\(324\) | 8.96631 | 0.498128 | ||||||||
\(325\) | 4.96813 | 0.275582 | ||||||||
\(326\) | 18.9079 | 1.04721 | ||||||||
\(327\) | 0.610961 | 0.0337862 | ||||||||
\(328\) | −8.20672 | −0.453140 | ||||||||
\(329\) | −20.8621 | −1.15016 | ||||||||
\(330\) | 0.0933043 | 0.00513623 | ||||||||
\(331\) | 7.32483 | 0.402609 | 0.201304 | − | 0.979529i | \(-0.435482\pi\) | ||||
0.201304 | + | 0.979529i | \(0.435482\pi\) | |||||||
\(332\) | 16.3188 | 0.895612 | ||||||||
\(333\) | 31.8389 | 1.74476 | ||||||||
\(334\) | 8.29004 | 0.453611 | ||||||||
\(335\) | 28.0801 | 1.53418 | ||||||||
\(336\) | 0.310936 | 0.0169630 | ||||||||
\(337\) | 28.2581 | 1.53932 | 0.769658 | − | 0.638456i | \(-0.220427\pi\) | ||||
0.769658 | + | 0.638456i | \(0.220427\pi\) | |||||||
\(338\) | 12.5296 | 0.681522 | ||||||||
\(339\) | −0.153906 | −0.00835905 | ||||||||
\(340\) | −16.3050 | −0.884265 | ||||||||
\(341\) | −1.78865 | −0.0968611 | ||||||||
\(342\) | 24.7614 | 1.33894 | ||||||||
\(343\) | −60.0526 | −3.24254 | ||||||||
\(344\) | 3.04884 | 0.164382 | ||||||||
\(345\) | −0.273961 | −0.0147496 | ||||||||
\(346\) | −3.30808 | −0.177843 | ||||||||
\(347\) | −9.50897 | −0.510468 | −0.255234 | − | 0.966879i | \(-0.582153\pi\) | ||||
−0.255234 | + | 0.966879i | \(0.582153\pi\) | |||||||
\(348\) | 0.0546465 | 0.00292936 | ||||||||
\(349\) | −17.2692 | −0.924396 | −0.462198 | − | 0.886777i | \(-0.652939\pi\) | ||||
−0.462198 | + | 0.886777i | \(0.652939\pi\) | |||||||
\(350\) | 36.8080 | 1.96747 | ||||||||
\(351\) | 0.251653 | 0.0134322 | ||||||||
\(352\) | 0.435748 | 0.0232255 | ||||||||
\(353\) | −6.93260 | −0.368985 | −0.184493 | − | 0.982834i | \(-0.559064\pi\) | ||||
−0.184493 | + | 0.982834i | \(0.559064\pi\) | |||||||
\(354\) | −0.622168 | −0.0330679 | ||||||||
\(355\) | −5.33590 | −0.283200 | ||||||||
\(356\) | −2.11755 | −0.112230 | ||||||||
\(357\) | 1.44888 | 0.0766828 | ||||||||
\(358\) | −17.3494 | −0.916944 | ||||||||
\(359\) | 1.92339 | 0.101513 | 0.0507563 | − | 0.998711i | \(-0.483837\pi\) | ||||
0.0507563 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(360\) | −10.4843 | −0.552572 | ||||||||
\(361\) | 49.2954 | 2.59449 | ||||||||
\(362\) | −25.4989 | −1.34019 | ||||||||
\(363\) | 0.661509 | 0.0347202 | ||||||||
\(364\) | −3.48484 | −0.182655 | ||||||||
\(365\) | −13.6380 | −0.713844 | ||||||||
\(366\) | −0.718490 | −0.0375561 | ||||||||
\(367\) | 9.66206 | 0.504356 | 0.252178 | − | 0.967681i | \(-0.418853\pi\) | ||||
0.252178 | + | 0.967681i | \(0.418853\pi\) | |||||||
\(368\) | −1.27945 | −0.0666960 | ||||||||
\(369\) | −24.5894 | −1.28007 | ||||||||
\(370\) | −37.1827 | −1.93303 | ||||||||
\(371\) | −50.4167 | −2.61751 | ||||||||
\(372\) | −0.251186 | −0.0130234 | ||||||||
\(373\) | 1.27250 | 0.0658876 | 0.0329438 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329438 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(374\) | 2.03047 | 0.104993 | ||||||||
\(375\) | 0.480486 | 0.0248122 | ||||||||
\(376\) | −4.10573 | −0.211737 | ||||||||
\(377\) | −0.612454 | −0.0315430 | ||||||||
\(378\) | 1.86445 | 0.0958971 | ||||||||
\(379\) | −25.8845 | −1.32960 | −0.664798 | − | 0.747023i | \(-0.731483\pi\) | ||||
−0.664798 | + | 0.747023i | \(0.731483\pi\) | |||||||
\(380\) | −28.9172 | −1.48342 | ||||||||
\(381\) | 1.11793 | 0.0572734 | ||||||||
\(382\) | −22.8773 | −1.17050 | ||||||||
\(383\) | −7.70473 | −0.393693 | −0.196847 | − | 0.980434i | \(-0.563070\pi\) | ||||
−0.196847 | + | 0.980434i | \(0.563070\pi\) | |||||||
\(384\) | 0.0611935 | 0.00312277 | ||||||||
\(385\) | −7.74753 | −0.394850 | ||||||||
\(386\) | −6.99022 | −0.355793 | ||||||||
\(387\) | 9.13511 | 0.464364 | ||||||||
\(388\) | 1.77788 | 0.0902581 | ||||||||
\(389\) | −7.85027 | −0.398025 | −0.199012 | − | 0.979997i | \(-0.563773\pi\) | ||||
−0.199012 | + | 0.979997i | \(0.563773\pi\) | |||||||
\(390\) | −0.146853 | −0.00743619 | ||||||||
\(391\) | −5.96190 | −0.301506 | ||||||||
\(392\) | −18.8186 | −0.950483 | ||||||||
\(393\) | −0.418927 | −0.0211321 | ||||||||
\(394\) | 2.50115 | 0.126006 | ||||||||
\(395\) | −3.07918 | −0.154930 | ||||||||
\(396\) | 1.30561 | 0.0656095 | ||||||||
\(397\) | 6.42948 | 0.322686 | 0.161343 | − | 0.986898i | \(-0.448417\pi\) | ||||
0.161343 | + | 0.986898i | \(0.448417\pi\) | |||||||
\(398\) | −6.69601 | −0.335641 | ||||||||
\(399\) | 2.56961 | 0.128641 | ||||||||
\(400\) | 7.24396 | 0.362198 | ||||||||
\(401\) | −18.2141 | −0.909566 | −0.454783 | − | 0.890602i | \(-0.650283\pi\) | ||||
−0.454783 | + | 0.890602i | \(0.650283\pi\) | |||||||
\(402\) | −0.491069 | −0.0244923 | ||||||||
\(403\) | 2.81519 | 0.140234 | ||||||||
\(404\) | 1.43584 | 0.0714358 | ||||||||
\(405\) | −31.3744 | −1.55900 | ||||||||
\(406\) | −4.53757 | −0.225196 | ||||||||
\(407\) | 4.63037 | 0.229519 | ||||||||
\(408\) | 0.285145 | 0.0141168 | ||||||||
\(409\) | 24.2767 | 1.20041 | 0.600203 | − | 0.799848i | \(-0.295086\pi\) | ||||
0.600203 | + | 0.799848i | \(0.295086\pi\) | |||||||
\(410\) | 28.7164 | 1.41820 | ||||||||
\(411\) | 1.11124 | 0.0548133 | ||||||||
\(412\) | −2.93501 | −0.144597 | ||||||||
\(413\) | 51.6618 | 2.54211 | ||||||||
\(414\) | −3.83356 | −0.188409 | ||||||||
\(415\) | −57.1018 | −2.80302 | ||||||||
\(416\) | −0.685830 | −0.0336256 | ||||||||
\(417\) | −0.659224 | −0.0322823 | ||||||||
\(418\) | 3.60107 | 0.176134 | ||||||||
\(419\) | −3.50317 | −0.171141 | −0.0855706 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855706 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(420\) | −1.08801 | −0.0530894 | ||||||||
\(421\) | 14.3544 | 0.699589 | 0.349794 | − | 0.936827i | \(-0.386251\pi\) | ||||
0.349794 | + | 0.936827i | \(0.386251\pi\) | |||||||
\(422\) | 26.0947 | 1.27027 | ||||||||
\(423\) | −12.3018 | −0.598135 | ||||||||
\(424\) | −9.92221 | −0.481865 | ||||||||
\(425\) | 33.7549 | 1.63735 | ||||||||
\(426\) | 0.0933150 | 0.00452113 | ||||||||
\(427\) | 59.6598 | 2.88714 | ||||||||
\(428\) | −5.29527 | −0.255956 | ||||||||
\(429\) | 0.0182876 | 0.000882935 0 | ||||||||
\(430\) | −10.6683 | −0.514472 | ||||||||
\(431\) | 25.1471 | 1.21129 | 0.605646 | − | 0.795734i | \(-0.292915\pi\) | ||||
0.605646 | + | 0.795734i | \(0.292915\pi\) | |||||||
\(432\) | 0.366932 | 0.0176540 | ||||||||
\(433\) | −17.7019 | −0.850697 | −0.425348 | − | 0.905030i | \(-0.639848\pi\) | ||||
−0.425348 | + | 0.905030i | \(0.639848\pi\) | |||||||
\(434\) | 20.8572 | 1.00118 | ||||||||
\(435\) | −0.191216 | −0.00916808 | ||||||||
\(436\) | −9.98409 | −0.478151 | ||||||||
\(437\) | −10.5735 | −0.505800 | ||||||||
\(438\) | 0.238503 | 0.0113961 | ||||||||
\(439\) | −23.5557 | −1.12425 | −0.562127 | − | 0.827051i | \(-0.690017\pi\) | ||||
−0.562127 | + | 0.827051i | \(0.690017\pi\) | |||||||
\(440\) | −1.52474 | −0.0726893 | ||||||||
\(441\) | −56.3853 | −2.68501 | ||||||||
\(442\) | −3.19578 | −0.152008 | ||||||||
\(443\) | 9.43668 | 0.448350 | 0.224175 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224175 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(444\) | 0.650256 | 0.0308598 | ||||||||
\(445\) | 7.40959 | 0.351248 | ||||||||
\(446\) | 5.41806 | 0.256552 | ||||||||
\(447\) | 0.617231 | 0.0291940 | ||||||||
\(448\) | −5.08120 | −0.240064 | ||||||||
\(449\) | 0.654226 | 0.0308748 | 0.0154374 | − | 0.999881i | \(-0.495086\pi\) | ||||
0.0154374 | + | 0.999881i | \(0.495086\pi\) | |||||||
\(450\) | 21.7048 | 1.02317 | ||||||||
\(451\) | −3.57606 | −0.168390 | ||||||||
\(452\) | 2.51508 | 0.118299 | ||||||||
\(453\) | −0.687216 | −0.0322882 | ||||||||
\(454\) | 4.42350 | 0.207605 | ||||||||
\(455\) | 12.1939 | 0.571660 | ||||||||
\(456\) | 0.505709 | 0.0236820 | ||||||||
\(457\) | −37.5655 | −1.75724 | −0.878619 | − | 0.477523i | \(-0.841535\pi\) | ||||
−0.878619 | + | 0.477523i | \(0.841535\pi\) | |||||||
\(458\) | 0.821632 | 0.0383924 | ||||||||
\(459\) | 1.70980 | 0.0798067 | ||||||||
\(460\) | 4.47697 | 0.208740 | ||||||||
\(461\) | −14.4018 | −0.670758 | −0.335379 | − | 0.942083i | \(-0.608864\pi\) | ||||
−0.335379 | + | 0.942083i | \(0.608864\pi\) | |||||||
\(462\) | 0.135490 | 0.00630356 | ||||||||
\(463\) | −13.4904 | −0.626951 | −0.313475 | − | 0.949596i | \(-0.601493\pi\) | ||||
−0.313475 | + | 0.949596i | \(0.601493\pi\) | |||||||
\(464\) | −0.893012 | −0.0414570 | ||||||||
\(465\) | 0.878935 | 0.0407596 | ||||||||
\(466\) | −15.1979 | −0.704027 | ||||||||
\(467\) | 28.0903 | 1.29986 | 0.649932 | − | 0.759993i | \(-0.274797\pi\) | ||||
0.649932 | + | 0.759993i | \(0.274797\pi\) | |||||||
\(468\) | −2.05492 | −0.0949888 | ||||||||
\(469\) | 40.7759 | 1.88286 | ||||||||
\(470\) | 14.3665 | 0.662678 | ||||||||
\(471\) | −1.12564 | −0.0518667 | ||||||||
\(472\) | 10.1672 | 0.467985 | ||||||||
\(473\) | 1.32853 | 0.0610858 | ||||||||
\(474\) | 0.0538491 | 0.00247337 | ||||||||
\(475\) | 59.8648 | 2.74679 | ||||||||
\(476\) | −23.6770 | −1.08523 | ||||||||
\(477\) | −29.7295 | −1.36122 | ||||||||
\(478\) | −4.92727 | −0.225368 | ||||||||
\(479\) | 31.3288 | 1.43145 | 0.715724 | − | 0.698383i | \(-0.246097\pi\) | ||||
0.715724 | + | 0.698383i | \(0.246097\pi\) | |||||||
\(480\) | −0.214124 | −0.00977339 | ||||||||
\(481\) | −7.28780 | −0.332295 | ||||||||
\(482\) | −18.4369 | −0.839776 | ||||||||
\(483\) | −0.397828 | −0.0181018 | ||||||||
\(484\) | −10.8101 | −0.491369 | ||||||||
\(485\) | −6.22104 | −0.282483 | ||||||||
\(486\) | 1.64947 | 0.0748217 | ||||||||
\(487\) | −24.3563 | −1.10369 | −0.551844 | − | 0.833947i | \(-0.686076\pi\) | ||||
−0.551844 | + | 0.833947i | \(0.686076\pi\) | |||||||
\(488\) | 11.7413 | 0.531503 | ||||||||
\(489\) | 1.15704 | 0.0523231 | ||||||||
\(490\) | 65.8488 | 2.97475 | ||||||||
\(491\) | −6.03591 | −0.272397 | −0.136198 | − | 0.990682i | \(-0.543488\pi\) | ||||
−0.136198 | + | 0.990682i | \(0.543488\pi\) | |||||||
\(492\) | −0.502197 | −0.0226408 | ||||||||
\(493\) | −4.16119 | −0.187411 | ||||||||
\(494\) | −5.66777 | −0.255005 | ||||||||
\(495\) | −4.56852 | −0.205340 | ||||||||
\(496\) | 4.10479 | 0.184310 | ||||||||
\(497\) | −7.74842 | −0.347564 | ||||||||
\(498\) | 0.998606 | 0.0447486 | ||||||||
\(499\) | −28.7559 | −1.28729 | −0.643647 | − | 0.765323i | \(-0.722579\pi\) | ||||
−0.643647 | + | 0.765323i | \(0.722579\pi\) | |||||||
\(500\) | −7.85192 | −0.351149 | ||||||||
\(501\) | 0.507296 | 0.0226643 | ||||||||
\(502\) | −22.6972 | −1.01303 | ||||||||
\(503\) | −21.9100 | −0.976919 | −0.488460 | − | 0.872586i | \(-0.662441\pi\) | ||||
−0.488460 | + | 0.872586i | \(0.662441\pi\) | |||||||
\(504\) | −15.2246 | −0.678156 | ||||||||
\(505\) | −5.02421 | −0.223574 | ||||||||
\(506\) | −0.557519 | −0.0247847 | ||||||||
\(507\) | 0.766732 | 0.0340518 | ||||||||
\(508\) | −18.2688 | −0.810548 | ||||||||
\(509\) | −8.26373 | −0.366283 | −0.183142 | − | 0.983087i | \(-0.558627\pi\) | ||||
−0.183142 | + | 0.983087i | \(0.558627\pi\) | |||||||
\(510\) | −0.997762 | −0.0441816 | ||||||||
\(511\) | −19.8041 | −0.876082 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.03236 | 0.133882 | ||||||||
\(514\) | 12.2930 | 0.542221 | ||||||||
\(515\) | 10.2700 | 0.452550 | ||||||||
\(516\) | 0.186569 | 0.00821325 | ||||||||
\(517\) | −1.78907 | −0.0786831 | ||||||||
\(518\) | −53.9940 | −2.37236 | ||||||||
\(519\) | −0.202433 | −0.00888581 | ||||||||
\(520\) | 2.39981 | 0.105239 | ||||||||
\(521\) | 35.1737 | 1.54099 | 0.770495 | − | 0.637446i | \(-0.220009\pi\) | ||||
0.770495 | + | 0.637446i | \(0.220009\pi\) | |||||||
\(522\) | −2.67569 | −0.117112 | ||||||||
\(523\) | 3.65078 | 0.159638 | 0.0798188 | − | 0.996809i | \(-0.474566\pi\) | ||||
0.0798188 | + | 0.996809i | \(0.474566\pi\) | |||||||
\(524\) | 6.84595 | 0.299067 | ||||||||
\(525\) | 2.25241 | 0.0983032 | ||||||||
\(526\) | 28.1035 | 1.22537 | ||||||||
\(527\) | 19.1272 | 0.833194 | ||||||||
\(528\) | 0.0266650 | 0.00116044 | ||||||||
\(529\) | −21.3630 | −0.928826 | ||||||||
\(530\) | 34.7192 | 1.50810 | ||||||||
\(531\) | 30.4636 | 1.32201 | ||||||||
\(532\) | −41.9916 | −1.82056 | ||||||||
\(533\) | 5.62841 | 0.243794 | ||||||||
\(534\) | −0.129580 | −0.00560748 | ||||||||
\(535\) | 18.5289 | 0.801072 | ||||||||
\(536\) | 8.02486 | 0.346621 | ||||||||
\(537\) | −1.06167 | −0.0458144 | ||||||||
\(538\) | 14.3762 | 0.619803 | ||||||||
\(539\) | −8.20017 | −0.353206 | ||||||||
\(540\) | −1.28394 | −0.0552521 | ||||||||
\(541\) | 4.10374 | 0.176433 | 0.0882167 | − | 0.996101i | \(-0.471883\pi\) | ||||
0.0882167 | + | 0.996101i | \(0.471883\pi\) | |||||||
\(542\) | 10.6452 | 0.457251 | ||||||||
\(543\) | −1.56036 | −0.0669616 | ||||||||
\(544\) | −4.65973 | −0.199784 | ||||||||
\(545\) | 34.9357 | 1.49648 | ||||||||
\(546\) | −0.213249 | −0.00912623 | ||||||||
\(547\) | −32.7998 | −1.40242 | −0.701208 | − | 0.712957i | \(-0.747356\pi\) | ||||
−0.701208 | + | 0.712957i | \(0.747356\pi\) | |||||||
\(548\) | −18.1594 | −0.775732 | ||||||||
\(549\) | 35.1799 | 1.50144 | ||||||||
\(550\) | 3.15654 | 0.134595 | ||||||||
\(551\) | −7.37994 | −0.314396 | ||||||||
\(552\) | −0.0782940 | −0.00333241 | ||||||||
\(553\) | −4.47136 | −0.190142 | ||||||||
\(554\) | 23.5976 | 1.00257 | ||||||||
\(555\) | −2.27534 | −0.0965826 | ||||||||
\(556\) | 10.7728 | 0.456868 | ||||||||
\(557\) | −23.4568 | −0.993897 | −0.496949 | − | 0.867780i | \(-0.665546\pi\) | ||||
−0.496949 | + | 0.867780i | \(0.665546\pi\) | |||||||
\(558\) | 12.2990 | 0.520658 | ||||||||
\(559\) | −2.09099 | −0.0884393 | ||||||||
\(560\) | 17.7798 | 0.751334 | ||||||||
\(561\) | 0.124251 | 0.00524590 | ||||||||
\(562\) | 4.46587 | 0.188381 | ||||||||
\(563\) | 11.8134 | 0.497876 | 0.248938 | − | 0.968519i | \(-0.419918\pi\) | ||||
0.248938 | + | 0.968519i | \(0.419918\pi\) | |||||||
\(564\) | −0.251244 | −0.0105793 | ||||||||
\(565\) | −8.80061 | −0.370244 | ||||||||
\(566\) | −30.4143 | −1.27841 | ||||||||
\(567\) | −45.5596 | −1.91332 | ||||||||
\(568\) | −1.52492 | −0.0639842 | ||||||||
\(569\) | 2.62999 | 0.110255 | 0.0551274 | − | 0.998479i | \(-0.482444\pi\) | ||||
0.0551274 | + | 0.998479i | \(0.482444\pi\) | |||||||
\(570\) | −1.76954 | −0.0741181 | ||||||||
\(571\) | −32.6436 | −1.36609 | −0.683046 | − | 0.730375i | \(-0.739345\pi\) | ||||
−0.683046 | + | 0.730375i | \(0.739345\pi\) | |||||||
\(572\) | −0.298849 | −0.0124955 | ||||||||
\(573\) | −1.39994 | −0.0584833 | ||||||||
\(574\) | 41.7000 | 1.74052 | ||||||||
\(575\) | −9.26829 | −0.386514 | ||||||||
\(576\) | −2.99626 | −0.124844 | ||||||||
\(577\) | −11.0412 | −0.459650 | −0.229825 | − | 0.973232i | \(-0.573815\pi\) | ||||
−0.229825 | + | 0.973232i | \(0.573815\pi\) | |||||||
\(578\) | −4.71309 | −0.196039 | ||||||||
\(579\) | −0.427756 | −0.0177769 | ||||||||
\(580\) | 3.12477 | 0.129749 | ||||||||
\(581\) | −82.9192 | −3.44007 | ||||||||
\(582\) | 0.108795 | 0.00450968 | ||||||||
\(583\) | −4.32359 | −0.179065 | ||||||||
\(584\) | −3.89753 | −0.161281 | ||||||||
\(585\) | 7.19045 | 0.297289 | ||||||||
\(586\) | 29.8683 | 1.23385 | ||||||||
\(587\) | −37.3438 | −1.54134 | −0.770671 | − | 0.637233i | \(-0.780079\pi\) | ||||
−0.770671 | + | 0.637233i | \(0.780079\pi\) | |||||||
\(588\) | −1.15157 | −0.0474901 | ||||||||
\(589\) | 33.9224 | 1.39775 | ||||||||
\(590\) | −35.5766 | −1.46466 | ||||||||
\(591\) | 0.153054 | 0.00629580 | ||||||||
\(592\) | −10.6262 | −0.436736 | ||||||||
\(593\) | 13.2150 | 0.542675 | 0.271337 | − | 0.962484i | \(-0.412534\pi\) | ||||
0.271337 | + | 0.962484i | \(0.412534\pi\) | |||||||
\(594\) | 0.159890 | 0.00656036 | ||||||||
\(595\) | 82.8491 | 3.39648 | ||||||||
\(596\) | −10.0866 | −0.413161 | ||||||||
\(597\) | −0.409752 | −0.0167700 | ||||||||
\(598\) | 0.877486 | 0.0358831 | ||||||||
\(599\) | −25.9499 | −1.06028 | −0.530142 | − | 0.847909i | \(-0.677861\pi\) | ||||
−0.530142 | + | 0.847909i | \(0.677861\pi\) | |||||||
\(600\) | 0.443283 | 0.0180969 | ||||||||
\(601\) | −34.2177 | −1.39577 | −0.697885 | − | 0.716210i | \(-0.745875\pi\) | ||||
−0.697885 | + | 0.716210i | \(0.745875\pi\) | |||||||
\(602\) | −15.4918 | −0.631397 | ||||||||
\(603\) | 24.0445 | 0.979169 | ||||||||
\(604\) | 11.2302 | 0.456952 | ||||||||
\(605\) | 37.8261 | 1.53785 | ||||||||
\(606\) | 0.0878641 | 0.00356924 | ||||||||
\(607\) | −22.1999 | −0.901066 | −0.450533 | − | 0.892760i | \(-0.648766\pi\) | ||||
−0.450533 | + | 0.892760i | \(0.648766\pi\) | |||||||
\(608\) | −8.26410 | −0.335154 | ||||||||
\(609\) | −0.277670 | −0.0112517 | ||||||||
\(610\) | −41.0844 | −1.66346 | ||||||||
\(611\) | 2.81584 | 0.113917 | ||||||||
\(612\) | −13.9617 | −0.564370 | ||||||||
\(613\) | 25.2622 | 1.02033 | 0.510166 | − | 0.860076i | \(-0.329584\pi\) | ||||
0.510166 | + | 0.860076i | \(0.329584\pi\) | |||||||
\(614\) | −21.2830 | −0.858911 | ||||||||
\(615\) | 1.75726 | 0.0708594 | ||||||||
\(616\) | −2.21412 | −0.0892096 | ||||||||
\(617\) | 6.32614 | 0.254681 | 0.127340 | − | 0.991859i | \(-0.459356\pi\) | ||||
0.127340 | + | 0.991859i | \(0.459356\pi\) | |||||||
\(618\) | −0.179603 | −0.00722470 | ||||||||
\(619\) | −12.0759 | −0.485370 | −0.242685 | − | 0.970105i | \(-0.578028\pi\) | ||||
−0.242685 | + | 0.970105i | \(0.578028\pi\) | |||||||
\(620\) | −14.3632 | −0.576841 | ||||||||
\(621\) | −0.469471 | −0.0188392 | ||||||||
\(622\) | −22.1697 | −0.888923 | ||||||||
\(623\) | 10.7597 | 0.431078 | ||||||||
\(624\) | −0.0419683 | −0.00168008 | ||||||||
\(625\) | −8.74485 | −0.349794 | ||||||||
\(626\) | 25.9576 | 1.03747 | ||||||||
\(627\) | 0.220362 | 0.00880041 | ||||||||
\(628\) | 18.3948 | 0.734031 | ||||||||
\(629\) | −49.5154 | −1.97431 | ||||||||
\(630\) | 53.2729 | 2.12244 | ||||||||
\(631\) | −25.0928 | −0.998929 | −0.499464 | − | 0.866334i | \(-0.666470\pi\) | ||||
−0.499464 | + | 0.866334i | \(0.666470\pi\) | |||||||
\(632\) | −0.879981 | −0.0350038 | ||||||||
\(633\) | 1.59682 | 0.0634681 | ||||||||
\(634\) | −26.5281 | −1.05357 | ||||||||
\(635\) | 63.9251 | 2.53679 | ||||||||
\(636\) | −0.607174 | −0.0240760 | ||||||||
\(637\) | 12.9064 | 0.511369 | ||||||||
\(638\) | −0.389128 | −0.0154057 | ||||||||
\(639\) | −4.56905 | −0.180749 | ||||||||
\(640\) | 3.49914 | 0.138316 | ||||||||
\(641\) | 9.64622 | 0.381003 | 0.190501 | − | 0.981687i | \(-0.438989\pi\) | ||||
0.190501 | + | 0.981687i | \(0.438989\pi\) | |||||||
\(642\) | −0.324036 | −0.0127887 | ||||||||
\(643\) | 1.36328 | 0.0537624 | 0.0268812 | − | 0.999639i | \(-0.491442\pi\) | ||||
0.0268812 | + | 0.999639i | \(0.491442\pi\) | |||||||
\(644\) | 6.50115 | 0.256181 | ||||||||
\(645\) | −0.652831 | −0.0257052 | ||||||||
\(646\) | −38.5085 | −1.51510 | ||||||||
\(647\) | 31.6755 | 1.24529 | 0.622646 | − | 0.782504i | \(-0.286058\pi\) | ||||
0.622646 | + | 0.782504i | \(0.286058\pi\) | |||||||
\(648\) | −8.96631 | −0.352230 | ||||||||
\(649\) | 4.43036 | 0.173907 | ||||||||
\(650\) | −4.96813 | −0.194866 | ||||||||
\(651\) | 1.27633 | 0.0500232 | ||||||||
\(652\) | −18.9079 | −0.740490 | ||||||||
\(653\) | 31.5563 | 1.23489 | 0.617447 | − | 0.786612i | \(-0.288167\pi\) | ||||
0.617447 | + | 0.786612i | \(0.288167\pi\) | |||||||
\(654\) | −0.610961 | −0.0238905 | ||||||||
\(655\) | −23.9549 | −0.935996 | ||||||||
\(656\) | 8.20672 | 0.320418 | ||||||||
\(657\) | −11.6780 | −0.455602 | ||||||||
\(658\) | 20.8621 | 0.813287 | ||||||||
\(659\) | 7.24458 | 0.282209 | 0.141104 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141104 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(660\) | −0.0933043 | −0.00363187 | ||||||||
\(661\) | −5.77347 | −0.224562 | −0.112281 | − | 0.993677i | \(-0.535816\pi\) | ||||
−0.112281 | + | 0.993677i | \(0.535816\pi\) | |||||||
\(662\) | −7.32483 | −0.284687 | ||||||||
\(663\) | −0.195561 | −0.00759496 | ||||||||
\(664\) | −16.3188 | −0.633293 | ||||||||
\(665\) | 146.934 | 5.69786 | ||||||||
\(666\) | −31.8389 | −1.23373 | ||||||||
\(667\) | 1.14256 | 0.0442403 | ||||||||
\(668\) | −8.29004 | −0.320751 | ||||||||
\(669\) | 0.331550 | 0.0128184 | ||||||||
\(670\) | −28.0801 | −1.08483 | ||||||||
\(671\) | 5.11625 | 0.197511 | ||||||||
\(672\) | −0.310936 | −0.0119946 | ||||||||
\(673\) | −16.6691 | −0.642547 | −0.321273 | − | 0.946986i | \(-0.604111\pi\) | ||||
−0.321273 | + | 0.946986i | \(0.604111\pi\) | |||||||
\(674\) | −28.2581 | −1.08846 | ||||||||
\(675\) | 2.65804 | 0.102308 | ||||||||
\(676\) | −12.5296 | −0.481909 | ||||||||
\(677\) | −43.1623 | −1.65886 | −0.829430 | − | 0.558610i | \(-0.811335\pi\) | ||||
−0.829430 | + | 0.558610i | \(0.811335\pi\) | |||||||
\(678\) | 0.153906 | 0.00591074 | ||||||||
\(679\) | −9.03376 | −0.346684 | ||||||||
\(680\) | 16.3050 | 0.625270 | ||||||||
\(681\) | 0.270689 | 0.0103728 | ||||||||
\(682\) | 1.78865 | 0.0684911 | ||||||||
\(683\) | 40.4684 | 1.54848 | 0.774239 | − | 0.632893i | \(-0.218133\pi\) | ||||
0.774239 | + | 0.632893i | \(0.218133\pi\) | |||||||
\(684\) | −24.7614 | −0.946774 | ||||||||
\(685\) | 63.5423 | 2.42783 | ||||||||
\(686\) | 60.0526 | 2.29282 | ||||||||
\(687\) | 0.0502785 | 0.00191825 | ||||||||
\(688\) | −3.04884 | −0.116236 | ||||||||
\(689\) | 6.80495 | 0.259248 | ||||||||
\(690\) | 0.273961 | 0.0104295 | ||||||||
\(691\) | −49.2510 | −1.87359 | −0.936797 | − | 0.349873i | \(-0.886225\pi\) | ||||
−0.936797 | + | 0.349873i | \(0.886225\pi\) | |||||||
\(692\) | 3.30808 | 0.125754 | ||||||||
\(693\) | −6.63408 | −0.252008 | ||||||||
\(694\) | 9.50897 | 0.360955 | ||||||||
\(695\) | −37.6954 | −1.42987 | ||||||||
\(696\) | −0.0546465 | −0.00207137 | ||||||||
\(697\) | 38.2411 | 1.44848 | ||||||||
\(698\) | 17.2692 | 0.653647 | ||||||||
\(699\) | −0.930009 | −0.0351762 | ||||||||
\(700\) | −36.8080 | −1.39121 | ||||||||
\(701\) | −23.0826 | −0.871818 | −0.435909 | − | 0.899991i | \(-0.643573\pi\) | ||||
−0.435909 | + | 0.899991i | \(0.643573\pi\) | |||||||
\(702\) | −0.251653 | −0.00949802 | ||||||||
\(703\) | −87.8163 | −3.31206 | ||||||||
\(704\) | −0.435748 | −0.0164229 | ||||||||
\(705\) | 0.879137 | 0.0331102 | ||||||||
\(706\) | 6.93260 | 0.260912 | ||||||||
\(707\) | −7.29580 | −0.274387 | ||||||||
\(708\) | 0.622168 | 0.0233825 | ||||||||
\(709\) | −29.4652 | −1.10659 | −0.553294 | − | 0.832986i | \(-0.686629\pi\) | ||||
−0.553294 | + | 0.832986i | \(0.686629\pi\) | |||||||
\(710\) | 5.33590 | 0.200253 | ||||||||
\(711\) | −2.63665 | −0.0988821 | ||||||||
\(712\) | 2.11755 | 0.0793585 | ||||||||
\(713\) | −5.25187 | −0.196684 | ||||||||
\(714\) | −1.44888 | −0.0542229 | ||||||||
\(715\) | 1.04571 | 0.0391075 | ||||||||
\(716\) | 17.3494 | 0.648378 | ||||||||
\(717\) | −0.301517 | −0.0112604 | ||||||||
\(718\) | −1.92339 | −0.0717802 | ||||||||
\(719\) | −16.3129 | −0.608370 | −0.304185 | − | 0.952613i | \(-0.598384\pi\) | ||||
−0.304185 | + | 0.952613i | \(0.598384\pi\) | |||||||
\(720\) | 10.4843 | 0.390727 | ||||||||
\(721\) | 14.9134 | 0.555402 | ||||||||
\(722\) | −49.2954 | −1.83458 | ||||||||
\(723\) | −1.12822 | −0.0419588 | ||||||||
\(724\) | 25.4989 | 0.947658 | ||||||||
\(725\) | −6.46894 | −0.240250 | ||||||||
\(726\) | −0.661509 | −0.0245509 | ||||||||
\(727\) | 18.1167 | 0.671910 | 0.335955 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335955 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(728\) | 3.48484 | 0.129157 | ||||||||
\(729\) | −26.7980 | −0.992519 | ||||||||
\(730\) | 13.6380 | 0.504764 | ||||||||
\(731\) | −14.2068 | −0.525457 | ||||||||
\(732\) | 0.718490 | 0.0265562 | ||||||||
\(733\) | 18.9057 | 0.698298 | 0.349149 | − | 0.937067i | \(-0.386471\pi\) | ||||
0.349149 | + | 0.937067i | \(0.386471\pi\) | |||||||
\(734\) | −9.66206 | −0.356633 | ||||||||
\(735\) | 4.02952 | 0.148631 | ||||||||
\(736\) | 1.27945 | 0.0471612 | ||||||||
\(737\) | 3.49682 | 0.128807 | ||||||||
\(738\) | 24.5894 | 0.905149 | ||||||||
\(739\) | 53.3588 | 1.96283 | 0.981417 | − | 0.191887i | \(-0.0614607\pi\) | ||||
0.981417 | + | 0.191887i | \(0.0614607\pi\) | |||||||
\(740\) | 37.1827 | 1.36686 | ||||||||
\(741\) | −0.346830 | −0.0127411 | ||||||||
\(742\) | 50.4167 | 1.85086 | ||||||||
\(743\) | 26.4758 | 0.971304 | 0.485652 | − | 0.874152i | \(-0.338582\pi\) | ||||
0.485652 | + | 0.874152i | \(0.338582\pi\) | |||||||
\(744\) | 0.251186 | 0.00920893 | ||||||||
\(745\) | 35.2942 | 1.29308 | ||||||||
\(746\) | −1.27250 | −0.0465896 | ||||||||
\(747\) | −48.8954 | −1.78899 | ||||||||
\(748\) | −2.03047 | −0.0742413 | ||||||||
\(749\) | 26.9063 | 0.983135 | ||||||||
\(750\) | −0.480486 | −0.0175449 | ||||||||
\(751\) | −7.00119 | −0.255477 | −0.127738 | − | 0.991808i | \(-0.540772\pi\) | ||||
−0.127738 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(752\) | 4.10573 | 0.149721 | ||||||||
\(753\) | −1.38892 | −0.0506151 | ||||||||
\(754\) | 0.612454 | 0.0223043 | ||||||||
\(755\) | −39.2961 | −1.43013 | ||||||||
\(756\) | −1.86445 | −0.0678095 | ||||||||
\(757\) | −17.7201 | −0.644047 | −0.322024 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322024 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(758\) | 25.8845 | 0.940167 | ||||||||
\(759\) | −0.0341165 | −0.00123835 | ||||||||
\(760\) | 28.9172 | 1.04894 | ||||||||
\(761\) | −41.4532 | −1.50268 | −0.751339 | − | 0.659916i | \(-0.770592\pi\) | ||||
−0.751339 | + | 0.659916i | \(0.770592\pi\) | |||||||
\(762\) | −1.11793 | −0.0404984 | ||||||||
\(763\) | 50.7311 | 1.83659 | ||||||||
\(764\) | 22.8773 | 0.827671 | ||||||||
\(765\) | 48.8541 | 1.76632 | ||||||||
\(766\) | 7.70473 | 0.278383 | ||||||||
\(767\) | −6.97300 | −0.251780 | ||||||||
\(768\) | −0.0611935 | −0.00220813 | ||||||||
\(769\) | 32.3244 | 1.16565 | 0.582824 | − | 0.812599i | \(-0.301948\pi\) | ||||
0.582824 | + | 0.812599i | \(0.301948\pi\) | |||||||
\(770\) | 7.74753 | 0.279201 | ||||||||
\(771\) | 0.752251 | 0.0270917 | ||||||||
\(772\) | 6.99022 | 0.251584 | ||||||||
\(773\) | 7.51575 | 0.270323 | 0.135161 | − | 0.990824i | \(-0.456845\pi\) | ||||
0.135161 | + | 0.990824i | \(0.456845\pi\) | |||||||
\(774\) | −9.13511 | −0.328355 | ||||||||
\(775\) | 29.7349 | 1.06811 | ||||||||
\(776\) | −1.77788 | −0.0638221 | ||||||||
\(777\) | −3.30408 | −0.118533 | ||||||||
\(778\) | 7.85027 | 0.281446 | ||||||||
\(779\) | 67.8211 | 2.42994 | ||||||||
\(780\) | 0.146853 | 0.00525818 | ||||||||
\(781\) | −0.664481 | −0.0237770 | ||||||||
\(782\) | 5.96190 | 0.213197 | ||||||||
\(783\) | −0.327674 | −0.0117101 | ||||||||
\(784\) | 18.8186 | 0.672093 | ||||||||
\(785\) | −64.3658 | −2.29731 | ||||||||
\(786\) | 0.418927 | 0.0149426 | ||||||||
\(787\) | −24.0165 | −0.856095 | −0.428048 | − | 0.903756i | \(-0.640798\pi\) | ||||
−0.428048 | + | 0.903756i | \(0.640798\pi\) | |||||||
\(788\) | −2.50115 | −0.0890998 | ||||||||
\(789\) | 1.71975 | 0.0612247 | ||||||||
\(790\) | 3.07918 | 0.109552 | ||||||||
\(791\) | −12.7796 | −0.454391 | ||||||||
\(792\) | −1.30561 | −0.0463930 | ||||||||
\(793\) | −8.05253 | −0.285954 | ||||||||
\(794\) | −6.42948 | −0.228174 | ||||||||
\(795\) | 2.12459 | 0.0753513 | ||||||||
\(796\) | 6.69601 | 0.237334 | ||||||||
\(797\) | 1.82374 | 0.0646002 | 0.0323001 | − | 0.999478i | \(-0.489717\pi\) | ||||
0.0323001 | + | 0.999478i | \(0.489717\pi\) | |||||||
\(798\) | −2.56961 | −0.0909632 | ||||||||
\(799\) | 19.1316 | 0.676828 | ||||||||
\(800\) | −7.24396 | −0.256113 | ||||||||
\(801\) | 6.34472 | 0.224180 | ||||||||
\(802\) | 18.2141 | 0.643161 | ||||||||
\(803\) | −1.69834 | −0.0599332 | ||||||||
\(804\) | 0.491069 | 0.0173187 | ||||||||
\(805\) | −22.7484 | −0.801776 | ||||||||
\(806\) | −2.81519 | −0.0991607 | ||||||||
\(807\) | 0.879731 | 0.0309680 | ||||||||
\(808\) | −1.43584 | −0.0505127 | ||||||||
\(809\) | −37.5568 | −1.32043 | −0.660213 | − | 0.751079i | \(-0.729534\pi\) | ||||
−0.660213 | + | 0.751079i | \(0.729534\pi\) | |||||||
\(810\) | 31.3744 | 1.10238 | ||||||||
\(811\) | −40.5144 | −1.42265 | −0.711326 | − | 0.702862i | \(-0.751905\pi\) | ||||
−0.711326 | + | 0.702862i | \(0.751905\pi\) | |||||||
\(812\) | 4.53757 | 0.159238 | ||||||||
\(813\) | 0.651418 | 0.0228462 | ||||||||
\(814\) | −4.63037 | −0.162294 | ||||||||
\(815\) | 66.1613 | 2.31753 | ||||||||
\(816\) | −0.285145 | −0.00998207 | ||||||||
\(817\) | −25.1959 | −0.881494 | ||||||||
\(818\) | −24.2767 | −0.848815 | ||||||||
\(819\) | 10.4415 | 0.364855 | ||||||||
\(820\) | −28.7164 | −1.00282 | ||||||||
\(821\) | −40.1395 | −1.40088 | −0.700439 | − | 0.713712i | \(-0.747013\pi\) | ||||
−0.700439 | + | 0.713712i | \(0.747013\pi\) | |||||||
\(822\) | −1.11124 | −0.0387589 | ||||||||
\(823\) | 0.209763 | 0.00731188 | 0.00365594 | − | 0.999993i | \(-0.498836\pi\) | ||||
0.00365594 | + | 0.999993i | \(0.498836\pi\) | |||||||
\(824\) | 2.93501 | 0.102246 | ||||||||
\(825\) | 0.193160 | 0.00672496 | ||||||||
\(826\) | −51.6618 | −1.79754 | ||||||||
\(827\) | 30.6362 | 1.06532 | 0.532662 | − | 0.846328i | \(-0.321192\pi\) | ||||
0.532662 | + | 0.846328i | \(0.321192\pi\) | |||||||
\(828\) | 3.83356 | 0.133225 | ||||||||
\(829\) | 0.925440 | 0.0321419 | 0.0160709 | − | 0.999871i | \(-0.494884\pi\) | ||||
0.0160709 | + | 0.999871i | \(0.494884\pi\) | |||||||
\(830\) | 57.1018 | 1.98203 | ||||||||
\(831\) | 1.44402 | 0.0500925 | ||||||||
\(832\) | 0.685830 | 0.0237769 | ||||||||
\(833\) | 87.6896 | 3.03826 | ||||||||
\(834\) | 0.659224 | 0.0228270 | ||||||||
\(835\) | 29.0080 | 1.00386 | ||||||||
\(836\) | −3.60107 | −0.124546 | ||||||||
\(837\) | 1.50618 | 0.0520611 | ||||||||
\(838\) | 3.50317 | 0.121015 | ||||||||
\(839\) | 30.0803 | 1.03849 | 0.519244 | − | 0.854626i | \(-0.326213\pi\) | ||||
0.519244 | + | 0.854626i | \(0.326213\pi\) | |||||||
\(840\) | 1.08801 | 0.0375399 | ||||||||
\(841\) | −28.2025 | −0.972501 | ||||||||
\(842\) | −14.3544 | −0.494684 | ||||||||
\(843\) | 0.273282 | 0.00941233 | ||||||||
\(844\) | −26.0947 | −0.898217 | ||||||||
\(845\) | 43.8429 | 1.50824 | ||||||||
\(846\) | 12.3018 | 0.422945 | ||||||||
\(847\) | 54.9284 | 1.88736 | ||||||||
\(848\) | 9.92221 | 0.340730 | ||||||||
\(849\) | −1.86116 | −0.0638747 | ||||||||
\(850\) | −33.7549 | −1.15778 | ||||||||
\(851\) | 13.5958 | 0.466056 | ||||||||
\(852\) | −0.0933150 | −0.00319692 | ||||||||
\(853\) | −37.1863 | −1.27323 | −0.636617 | − | 0.771180i | \(-0.719667\pi\) | ||||
−0.636617 | + | 0.771180i | \(0.719667\pi\) | |||||||
\(854\) | −59.6598 | −2.04152 | ||||||||
\(855\) | 86.6434 | 2.96314 | ||||||||
\(856\) | 5.29527 | 0.180988 | ||||||||
\(857\) | −55.4575 | −1.89439 | −0.947197 | − | 0.320653i | \(-0.896098\pi\) | ||||
−0.947197 | + | 0.320653i | \(0.896098\pi\) | |||||||
\(858\) | −0.0182876 | −0.000624329 0 | ||||||||
\(859\) | −2.98923 | −0.101991 | −0.0509957 | − | 0.998699i | \(-0.516239\pi\) | ||||
−0.0509957 | + | 0.998699i | \(0.516239\pi\) | |||||||
\(860\) | 10.6683 | 0.363786 | ||||||||
\(861\) | 2.55176 | 0.0869639 | ||||||||
\(862\) | −25.1471 | −0.856513 | ||||||||
\(863\) | 4.99496 | 0.170030 | 0.0850152 | − | 0.996380i | \(-0.472906\pi\) | ||||
0.0850152 | + | 0.996380i | \(0.472906\pi\) | |||||||
\(864\) | −0.366932 | −0.0124833 | ||||||||
\(865\) | −11.5754 | −0.393576 | ||||||||
\(866\) | 17.7019 | 0.601533 | ||||||||
\(867\) | −0.288410 | −0.00979493 | ||||||||
\(868\) | −20.8572 | −0.707941 | ||||||||
\(869\) | −0.383451 | −0.0130077 | ||||||||
\(870\) | 0.191216 | 0.00648281 | ||||||||
\(871\) | −5.50369 | −0.186485 | ||||||||
\(872\) | 9.98409 | 0.338104 | ||||||||
\(873\) | −5.32698 | −0.180291 | ||||||||
\(874\) | 10.5735 | 0.357654 | ||||||||
\(875\) | 39.8972 | 1.34877 | ||||||||
\(876\) | −0.238503 | −0.00805827 | ||||||||
\(877\) | −14.5310 | −0.490678 | −0.245339 | − | 0.969437i | \(-0.578899\pi\) | ||||
−0.245339 | + | 0.969437i | \(0.578899\pi\) | |||||||
\(878\) | 23.5557 | 0.794967 | ||||||||
\(879\) | 1.82775 | 0.0616483 | ||||||||
\(880\) | 1.52474 | 0.0513991 | ||||||||
\(881\) | −5.88818 | −0.198378 | −0.0991890 | − | 0.995069i | \(-0.531625\pi\) | ||||
−0.0991890 | + | 0.995069i | \(0.531625\pi\) | |||||||
\(882\) | 56.3853 | 1.89859 | ||||||||
\(883\) | 39.3783 | 1.32519 | 0.662593 | − | 0.748980i | \(-0.269456\pi\) | ||||
0.662593 | + | 0.748980i | \(0.269456\pi\) | |||||||
\(884\) | 3.19578 | 0.107486 | ||||||||
\(885\) | −2.17705 | −0.0731808 | ||||||||
\(886\) | −9.43668 | −0.317031 | ||||||||
\(887\) | 16.5659 | 0.556228 | 0.278114 | − | 0.960548i | \(-0.410291\pi\) | ||||
0.278114 | + | 0.960548i | \(0.410291\pi\) | |||||||
\(888\) | −0.650256 | −0.0218212 | ||||||||
\(889\) | 92.8276 | 3.11334 | ||||||||
\(890\) | −7.40959 | −0.248370 | ||||||||
\(891\) | −3.90706 | −0.130891 | ||||||||
\(892\) | −5.41806 | −0.181410 | ||||||||
\(893\) | 33.9302 | 1.13543 | ||||||||
\(894\) | −0.617231 | −0.0206433 | ||||||||
\(895\) | −60.7079 | −2.02924 | ||||||||
\(896\) | 5.08120 | 0.169751 | ||||||||
\(897\) | 0.0536964 | 0.00179287 | ||||||||
\(898\) | −0.654226 | −0.0218318 | ||||||||
\(899\) | −3.66562 | −0.122255 | ||||||||
\(900\) | −21.7048 | −0.723492 | ||||||||
\(901\) | 46.2348 | 1.54030 | ||||||||
\(902\) | 3.57606 | 0.119070 | ||||||||
\(903\) | −0.947995 | −0.0315473 | ||||||||
\(904\) | −2.51508 | −0.0836503 | ||||||||
\(905\) | −89.2240 | −2.96591 | ||||||||
\(906\) | 0.687216 | 0.0228312 | ||||||||
\(907\) | −55.0964 | −1.82945 | −0.914723 | − | 0.404082i | \(-0.867591\pi\) | ||||
−0.914723 | + | 0.404082i | \(0.867591\pi\) | |||||||
\(908\) | −4.42350 | −0.146799 | ||||||||
\(909\) | −4.30215 | −0.142693 | ||||||||
\(910\) | −12.1939 | −0.404225 | ||||||||
\(911\) | 50.1208 | 1.66058 | 0.830288 | − | 0.557335i | \(-0.188176\pi\) | ||||
0.830288 | + | 0.557335i | \(0.188176\pi\) | |||||||
\(912\) | −0.505709 | −0.0167457 | ||||||||
\(913\) | −7.11090 | −0.235337 | ||||||||
\(914\) | 37.5655 | 1.24255 | ||||||||
\(915\) | −2.51409 | −0.0831134 | ||||||||
\(916\) | −0.821632 | −0.0271475 | ||||||||
\(917\) | −34.7856 | −1.14872 | ||||||||
\(918\) | −1.70980 | −0.0564319 | ||||||||
\(919\) | 34.7091 | 1.14495 | 0.572473 | − | 0.819923i | \(-0.305984\pi\) | ||||
0.572473 | + | 0.819923i | \(0.305984\pi\) | |||||||
\(920\) | −4.47697 | −0.147601 | ||||||||
\(921\) | −1.30238 | −0.0429148 | ||||||||
\(922\) | 14.4018 | 0.474298 | ||||||||
\(923\) | 1.04584 | 0.0344241 | ||||||||
\(924\) | −0.135490 | −0.00445729 | ||||||||
\(925\) | −76.9760 | −2.53096 | ||||||||
\(926\) | 13.4904 | 0.443321 | ||||||||
\(927\) | 8.79403 | 0.288834 | ||||||||
\(928\) | 0.893012 | 0.0293145 | ||||||||
\(929\) | 50.9562 | 1.67182 | 0.835910 | − | 0.548866i | \(-0.184940\pi\) | ||||
0.835910 | + | 0.548866i | \(0.184940\pi\) | |||||||
\(930\) | −0.878935 | −0.0288214 | ||||||||
\(931\) | 155.519 | 5.09692 | ||||||||
\(932\) | 15.1979 | 0.497822 | ||||||||
\(933\) | −1.35664 | −0.0444144 | ||||||||
\(934\) | −28.0903 | −0.919142 | ||||||||
\(935\) | 7.10489 | 0.232355 | ||||||||
\(936\) | 2.05492 | 0.0671672 | ||||||||
\(937\) | −33.7795 | −1.10353 | −0.551765 | − | 0.834000i | \(-0.686045\pi\) | ||||
−0.551765 | + | 0.834000i | \(0.686045\pi\) | |||||||
\(938\) | −40.7759 | −1.33138 | ||||||||
\(939\) | 1.58843 | 0.0518365 | ||||||||
\(940\) | −14.3665 | −0.468584 | ||||||||
\(941\) | −8.77729 | −0.286131 | −0.143066 | − | 0.989713i | \(-0.545696\pi\) | ||||
−0.143066 | + | 0.989713i | \(0.545696\pi\) | |||||||
\(942\) | 1.12564 | 0.0366753 | ||||||||
\(943\) | −10.5001 | −0.341930 | ||||||||
\(944\) | −10.1672 | −0.330915 | ||||||||
\(945\) | 6.52398 | 0.212225 | ||||||||
\(946\) | −1.32853 | −0.0431942 | ||||||||
\(947\) | −6.23151 | −0.202497 | −0.101248 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101248 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(948\) | −0.0538491 | −0.00174894 | ||||||||
\(949\) | 2.67304 | 0.0867706 | ||||||||
\(950\) | −59.8648 | −1.94227 | ||||||||
\(951\) | −1.62335 | −0.0526407 | ||||||||
\(952\) | 23.6770 | 0.767377 | ||||||||
\(953\) | 43.4502 | 1.40749 | 0.703745 | − | 0.710452i | \(-0.251510\pi\) | ||||
0.703745 | + | 0.710452i | \(0.251510\pi\) | |||||||
\(954\) | 29.7295 | 0.962527 | ||||||||
\(955\) | −80.0507 | −2.59038 | ||||||||
\(956\) | 4.92727 | 0.159359 | ||||||||
\(957\) | −0.0238121 | −0.000769736 0 | ||||||||
\(958\) | −31.3288 | −1.01219 | ||||||||
\(959\) | 92.2716 | 2.97961 | ||||||||
\(960\) | 0.214124 | 0.00691083 | ||||||||
\(961\) | −14.1507 | −0.456475 | ||||||||
\(962\) | 7.28780 | 0.234968 | ||||||||
\(963\) | 15.8660 | 0.511274 | ||||||||
\(964\) | 18.4369 | 0.593811 | ||||||||
\(965\) | −24.4597 | −0.787387 | ||||||||
\(966\) | 0.397828 | 0.0127999 | ||||||||
\(967\) | 55.5146 | 1.78523 | 0.892614 | − | 0.450821i | \(-0.148869\pi\) | ||||
0.892614 | + | 0.450821i | \(0.148869\pi\) | |||||||
\(968\) | 10.8101 | 0.347451 | ||||||||
\(969\) | −2.35647 | −0.0757007 | ||||||||
\(970\) | 6.22104 | 0.199746 | ||||||||
\(971\) | 11.4729 | 0.368184 | 0.184092 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184092 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(972\) | −1.64947 | −0.0529069 | ||||||||
\(973\) | −54.7387 | −1.75484 | ||||||||
\(974\) | 24.3563 | 0.780425 | ||||||||
\(975\) | −0.304017 | −0.00973633 | ||||||||
\(976\) | −11.7413 | −0.375829 | ||||||||
\(977\) | 28.5973 | 0.914910 | 0.457455 | − | 0.889233i | \(-0.348761\pi\) | ||||
0.457455 | + | 0.889233i | \(0.348761\pi\) | |||||||
\(978\) | −1.15704 | −0.0369980 | ||||||||
\(979\) | 0.922719 | 0.0294902 | ||||||||
\(980\) | −65.8488 | −2.10346 | ||||||||
\(981\) | 29.9149 | 0.955109 | ||||||||
\(982\) | 6.03591 | 0.192614 | ||||||||
\(983\) | −2.36378 | −0.0753927 | −0.0376964 | − | 0.999289i | \(-0.512002\pi\) | ||||
−0.0376964 | + | 0.999289i | \(0.512002\pi\) | |||||||
\(984\) | 0.502197 | 0.0160095 | ||||||||
\(985\) | 8.75187 | 0.278858 | ||||||||
\(986\) | 4.16119 | 0.132519 | ||||||||
\(987\) | 1.27662 | 0.0406353 | ||||||||
\(988\) | 5.66777 | 0.180316 | ||||||||
\(989\) | 3.90084 | 0.124040 | ||||||||
\(990\) | 4.56852 | 0.145197 | ||||||||
\(991\) | 18.1790 | 0.577474 | 0.288737 | − | 0.957408i | \(-0.406765\pi\) | ||||
0.288737 | + | 0.957408i | \(0.406765\pi\) | |||||||
\(992\) | −4.10479 | −0.130327 | ||||||||
\(993\) | −0.448231 | −0.0142242 | ||||||||
\(994\) | 7.74842 | 0.245765 | ||||||||
\(995\) | −23.4302 | −0.742789 | ||||||||
\(996\) | −0.998606 | −0.0316420 | ||||||||
\(997\) | 11.4428 | 0.362396 | 0.181198 | − | 0.983447i | \(-0.442002\pi\) | ||||
0.181198 | + | 0.983447i | \(0.442002\pi\) | |||||||
\(998\) | 28.7559 | 0.910254 | ||||||||
\(999\) | −3.89910 | −0.123362 |
(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 | 4022.2.a.d.1.18 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.18 | ✓ | 37 | 1.1 | even | 1 | trivial |