Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, 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("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.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: | \(48.0859120972\) |
Analytic rank: | \(0\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-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 | ||||||||
\(3\) | −2.51016 | −1.44924 | −0.724622 | − | 0.689147i | \(-0.757985\pi\) | ||||
−0.724622 | + | 0.689147i | \(0.757985\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.21389 | 0.542868 | 0.271434 | − | 0.962457i | \(-0.412502\pi\) | ||||
0.271434 | + | 0.962457i | \(0.412502\pi\) | |||||||
\(6\) | 2.51016 | 1.02477 | ||||||||
\(7\) | 4.01976 | 1.51933 | 0.759664 | − | 0.650316i | \(-0.225363\pi\) | ||||
0.759664 | + | 0.650316i | \(0.225363\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.30092 | 1.10031 | ||||||||
\(10\) | −1.21389 | −0.383865 | ||||||||
\(11\) | 4.67270 | 1.40887 | 0.704436 | − | 0.709768i | \(-0.251200\pi\) | ||||
0.704436 | + | 0.709768i | \(0.251200\pi\) | |||||||
\(12\) | −2.51016 | −0.724622 | ||||||||
\(13\) | 3.24878 | 0.901050 | 0.450525 | − | 0.892764i | \(-0.351237\pi\) | ||||
0.450525 | + | 0.892764i | \(0.351237\pi\) | |||||||
\(14\) | −4.01976 | −1.07433 | ||||||||
\(15\) | −3.04706 | −0.786747 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.81620 | −1.65317 | −0.826586 | − | 0.562811i | \(-0.809720\pi\) | ||||
−0.826586 | + | 0.562811i | \(0.809720\pi\) | |||||||
\(18\) | −3.30092 | −0.778034 | ||||||||
\(19\) | −6.37578 | −1.46270 | −0.731352 | − | 0.682000i | \(-0.761110\pi\) | ||||
−0.731352 | + | 0.682000i | \(0.761110\pi\) | |||||||
\(20\) | 1.21389 | 0.271434 | ||||||||
\(21\) | −10.0903 | −2.20188 | ||||||||
\(22\) | −4.67270 | −0.996222 | ||||||||
\(23\) | 2.73733 | 0.570772 | 0.285386 | − | 0.958413i | \(-0.407878\pi\) | ||||
0.285386 | + | 0.958413i | \(0.407878\pi\) | |||||||
\(24\) | 2.51016 | 0.512385 | ||||||||
\(25\) | −3.52647 | −0.705295 | ||||||||
\(26\) | −3.24878 | −0.637138 | ||||||||
\(27\) | −0.755352 | −0.145368 | ||||||||
\(28\) | 4.01976 | 0.759664 | ||||||||
\(29\) | 1.51171 | 0.280718 | 0.140359 | − | 0.990101i | \(-0.455174\pi\) | ||||
0.140359 | + | 0.990101i | \(0.455174\pi\) | |||||||
\(30\) | 3.04706 | 0.556314 | ||||||||
\(31\) | −2.65133 | −0.476193 | −0.238097 | − | 0.971241i | \(-0.576523\pi\) | ||||
−0.238097 | + | 0.971241i | \(0.576523\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −11.7292 | −2.04180 | ||||||||
\(34\) | 6.81620 | 1.16897 | ||||||||
\(35\) | 4.87955 | 0.824794 | ||||||||
\(36\) | 3.30092 | 0.550153 | ||||||||
\(37\) | −4.72196 | −0.776286 | −0.388143 | − | 0.921599i | \(-0.626883\pi\) | ||||
−0.388143 | + | 0.921599i | \(0.626883\pi\) | |||||||
\(38\) | 6.37578 | 1.03429 | ||||||||
\(39\) | −8.15497 | −1.30584 | ||||||||
\(40\) | −1.21389 | −0.191933 | ||||||||
\(41\) | 5.91381 | 0.923582 | 0.461791 | − | 0.886989i | \(-0.347207\pi\) | ||||
0.461791 | + | 0.886989i | \(0.347207\pi\) | |||||||
\(42\) | 10.0903 | 1.55696 | ||||||||
\(43\) | 7.72089 | 1.17743 | 0.588713 | − | 0.808342i | \(-0.299635\pi\) | ||||
0.588713 | + | 0.808342i | \(0.299635\pi\) | |||||||
\(44\) | 4.67270 | 0.704436 | ||||||||
\(45\) | 4.00695 | 0.597321 | ||||||||
\(46\) | −2.73733 | −0.403597 | ||||||||
\(47\) | 12.9408 | 1.88761 | 0.943804 | − | 0.330507i | \(-0.107220\pi\) | ||||
0.943804 | + | 0.330507i | \(0.107220\pi\) | |||||||
\(48\) | −2.51016 | −0.362311 | ||||||||
\(49\) | 9.15850 | 1.30836 | ||||||||
\(50\) | 3.52647 | 0.498719 | ||||||||
\(51\) | 17.1098 | 2.39585 | ||||||||
\(52\) | 3.24878 | 0.450525 | ||||||||
\(53\) | −10.7353 | −1.47460 | −0.737301 | − | 0.675564i | \(-0.763900\pi\) | ||||
−0.737301 | + | 0.675564i | \(0.763900\pi\) | |||||||
\(54\) | 0.755352 | 0.102790 | ||||||||
\(55\) | 5.67214 | 0.764831 | ||||||||
\(56\) | −4.01976 | −0.537164 | ||||||||
\(57\) | 16.0043 | 2.11981 | ||||||||
\(58\) | −1.51171 | −0.198498 | ||||||||
\(59\) | 2.48541 | 0.323572 | 0.161786 | − | 0.986826i | \(-0.448275\pi\) | ||||
0.161786 | + | 0.986826i | \(0.448275\pi\) | |||||||
\(60\) | −3.04706 | −0.393374 | ||||||||
\(61\) | 11.0215 | 1.41115 | 0.705577 | − | 0.708633i | \(-0.250688\pi\) | ||||
0.705577 | + | 0.708633i | \(0.250688\pi\) | |||||||
\(62\) | 2.65133 | 0.336719 | ||||||||
\(63\) | 13.2689 | 1.67173 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.94366 | 0.489151 | ||||||||
\(66\) | 11.7292 | 1.44377 | ||||||||
\(67\) | −5.99089 | −0.731903 | −0.365952 | − | 0.930634i | \(-0.619256\pi\) | ||||
−0.365952 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(68\) | −6.81620 | −0.826586 | ||||||||
\(69\) | −6.87114 | −0.827188 | ||||||||
\(70\) | −4.87955 | −0.583218 | ||||||||
\(71\) | −6.95570 | −0.825490 | −0.412745 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412745 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(72\) | −3.30092 | −0.389017 | ||||||||
\(73\) | 11.9851 | 1.40275 | 0.701377 | − | 0.712791i | \(-0.252569\pi\) | ||||
0.701377 | + | 0.712791i | \(0.252569\pi\) | |||||||
\(74\) | 4.72196 | 0.548917 | ||||||||
\(75\) | 8.85202 | 1.02214 | ||||||||
\(76\) | −6.37578 | −0.731352 | ||||||||
\(77\) | 18.7831 | 2.14054 | ||||||||
\(78\) | 8.15497 | 0.923368 | ||||||||
\(79\) | −0.820280 | −0.0922887 | −0.0461444 | − | 0.998935i | \(-0.514693\pi\) | ||||
−0.0461444 | + | 0.998935i | \(0.514693\pi\) | |||||||
\(80\) | 1.21389 | 0.135717 | ||||||||
\(81\) | −8.00670 | −0.889633 | ||||||||
\(82\) | −5.91381 | −0.653071 | ||||||||
\(83\) | 6.75066 | 0.740981 | 0.370490 | − | 0.928836i | \(-0.379190\pi\) | ||||
0.370490 | + | 0.928836i | \(0.379190\pi\) | |||||||
\(84\) | −10.0903 | −1.10094 | ||||||||
\(85\) | −8.27411 | −0.897454 | ||||||||
\(86\) | −7.72089 | −0.832565 | ||||||||
\(87\) | −3.79465 | −0.406829 | ||||||||
\(88\) | −4.67270 | −0.498111 | ||||||||
\(89\) | 2.03257 | 0.215452 | 0.107726 | − | 0.994181i | \(-0.465643\pi\) | ||||
0.107726 | + | 0.994181i | \(0.465643\pi\) | |||||||
\(90\) | −4.00695 | −0.422369 | ||||||||
\(91\) | 13.0593 | 1.36899 | ||||||||
\(92\) | 2.73733 | 0.285386 | ||||||||
\(93\) | 6.65527 | 0.690120 | ||||||||
\(94\) | −12.9408 | −1.33474 | ||||||||
\(95\) | −7.73949 | −0.794055 | ||||||||
\(96\) | 2.51016 | 0.256192 | ||||||||
\(97\) | −8.73748 | −0.887157 | −0.443578 | − | 0.896236i | \(-0.646291\pi\) | ||||
−0.443578 | + | 0.896236i | \(0.646291\pi\) | |||||||
\(98\) | −9.15850 | −0.925148 | ||||||||
\(99\) | 15.4242 | 1.55019 | ||||||||
\(100\) | −3.52647 | −0.352647 | ||||||||
\(101\) | 4.95801 | 0.493341 | 0.246670 | − | 0.969099i | \(-0.420663\pi\) | ||||
0.246670 | + | 0.969099i | \(0.420663\pi\) | |||||||
\(102\) | −17.1098 | −1.69412 | ||||||||
\(103\) | 6.96802 | 0.686579 | 0.343290 | − | 0.939230i | \(-0.388459\pi\) | ||||
0.343290 | + | 0.939230i | \(0.388459\pi\) | |||||||
\(104\) | −3.24878 | −0.318569 | ||||||||
\(105\) | −12.2485 | −1.19533 | ||||||||
\(106\) | 10.7353 | 1.04270 | ||||||||
\(107\) | −7.43212 | −0.718490 | −0.359245 | − | 0.933243i | \(-0.616966\pi\) | ||||
−0.359245 | + | 0.933243i | \(0.616966\pi\) | |||||||
\(108\) | −0.755352 | −0.0726838 | ||||||||
\(109\) | 13.7246 | 1.31458 | 0.657289 | − | 0.753639i | \(-0.271703\pi\) | ||||
0.657289 | + | 0.753639i | \(0.271703\pi\) | |||||||
\(110\) | −5.67214 | −0.540817 | ||||||||
\(111\) | 11.8529 | 1.12503 | ||||||||
\(112\) | 4.01976 | 0.379832 | ||||||||
\(113\) | 10.6786 | 1.00455 | 0.502277 | − | 0.864707i | \(-0.332496\pi\) | ||||
0.502277 | + | 0.864707i | \(0.332496\pi\) | |||||||
\(114\) | −16.0043 | −1.49894 | ||||||||
\(115\) | 3.32281 | 0.309854 | ||||||||
\(116\) | 1.51171 | 0.140359 | ||||||||
\(117\) | 10.7240 | 0.991430 | ||||||||
\(118\) | −2.48541 | −0.228800 | ||||||||
\(119\) | −27.3995 | −2.51171 | ||||||||
\(120\) | 3.04706 | 0.278157 | ||||||||
\(121\) | 10.8341 | 0.984918 | ||||||||
\(122\) | −11.0215 | −0.997837 | ||||||||
\(123\) | −14.8446 | −1.33849 | ||||||||
\(124\) | −2.65133 | −0.238097 | ||||||||
\(125\) | −10.3502 | −0.925749 | ||||||||
\(126\) | −13.2689 | −1.18209 | ||||||||
\(127\) | −6.74879 | −0.598858 | −0.299429 | − | 0.954119i | \(-0.596796\pi\) | ||||
−0.299429 | + | 0.954119i | \(0.596796\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −19.3807 | −1.70638 | ||||||||
\(130\) | −3.94366 | −0.345882 | ||||||||
\(131\) | −15.4181 | −1.34709 | −0.673545 | − | 0.739146i | \(-0.735229\pi\) | ||||
−0.673545 | + | 0.739146i | \(0.735229\pi\) | |||||||
\(132\) | −11.7292 | −1.02090 | ||||||||
\(133\) | −25.6291 | −2.22233 | ||||||||
\(134\) | 5.99089 | 0.517534 | ||||||||
\(135\) | −0.916913 | −0.0789153 | ||||||||
\(136\) | 6.81620 | 0.584484 | ||||||||
\(137\) | −4.39322 | −0.375338 | −0.187669 | − | 0.982232i | \(-0.560093\pi\) | ||||
−0.187669 | + | 0.982232i | \(0.560093\pi\) | |||||||
\(138\) | 6.87114 | 0.584910 | ||||||||
\(139\) | −19.2144 | −1.62974 | −0.814872 | − | 0.579642i | \(-0.803193\pi\) | ||||
−0.814872 | + | 0.579642i | \(0.803193\pi\) | |||||||
\(140\) | 4.87955 | 0.412397 | ||||||||
\(141\) | −32.4835 | −2.73560 | ||||||||
\(142\) | 6.95570 | 0.583709 | ||||||||
\(143\) | 15.1806 | 1.26946 | ||||||||
\(144\) | 3.30092 | 0.275076 | ||||||||
\(145\) | 1.83505 | 0.152393 | ||||||||
\(146\) | −11.9851 | −0.991897 | ||||||||
\(147\) | −22.9893 | −1.89613 | ||||||||
\(148\) | −4.72196 | −0.388143 | ||||||||
\(149\) | 13.2134 | 1.08249 | 0.541243 | − | 0.840866i | \(-0.317954\pi\) | ||||
0.541243 | + | 0.840866i | \(0.317954\pi\) | |||||||
\(150\) | −8.85202 | −0.722765 | ||||||||
\(151\) | 21.3556 | 1.73790 | 0.868948 | − | 0.494904i | \(-0.164797\pi\) | ||||
0.868948 | + | 0.494904i | \(0.164797\pi\) | |||||||
\(152\) | 6.37578 | 0.517144 | ||||||||
\(153\) | −22.4997 | −1.81899 | ||||||||
\(154\) | −18.7831 | −1.51359 | ||||||||
\(155\) | −3.21842 | −0.258510 | ||||||||
\(156\) | −8.15497 | −0.652920 | ||||||||
\(157\) | 18.0969 | 1.44429 | 0.722145 | − | 0.691742i | \(-0.243156\pi\) | ||||
0.722145 | + | 0.691742i | \(0.243156\pi\) | |||||||
\(158\) | 0.820280 | 0.0652580 | ||||||||
\(159\) | 26.9473 | 2.13706 | ||||||||
\(160\) | −1.21389 | −0.0959664 | ||||||||
\(161\) | 11.0034 | 0.867190 | ||||||||
\(162\) | 8.00670 | 0.629065 | ||||||||
\(163\) | 15.4959 | 1.21373 | 0.606867 | − | 0.794803i | \(-0.292426\pi\) | ||||
0.606867 | + | 0.794803i | \(0.292426\pi\) | |||||||
\(164\) | 5.91381 | 0.461791 | ||||||||
\(165\) | −14.2380 | −1.10843 | ||||||||
\(166\) | −6.75066 | −0.523953 | ||||||||
\(167\) | 11.2723 | 0.872278 | 0.436139 | − | 0.899879i | \(-0.356346\pi\) | ||||
0.436139 | + | 0.899879i | \(0.356346\pi\) | |||||||
\(168\) | 10.0903 | 0.778481 | ||||||||
\(169\) | −2.44542 | −0.188110 | ||||||||
\(170\) | 8.27411 | 0.634596 | ||||||||
\(171\) | −21.0459 | −1.60942 | ||||||||
\(172\) | 7.72089 | 0.588713 | ||||||||
\(173\) | 1.11114 | 0.0844787 | 0.0422393 | − | 0.999108i | \(-0.486551\pi\) | ||||
0.0422393 | + | 0.999108i | \(0.486551\pi\) | |||||||
\(174\) | 3.79465 | 0.287671 | ||||||||
\(175\) | −14.1756 | −1.07157 | ||||||||
\(176\) | 4.67270 | 0.352218 | ||||||||
\(177\) | −6.23878 | −0.468935 | ||||||||
\(178\) | −2.03257 | −0.152347 | ||||||||
\(179\) | 9.19618 | 0.687355 | 0.343677 | − | 0.939088i | \(-0.388327\pi\) | ||||
0.343677 | + | 0.939088i | \(0.388327\pi\) | |||||||
\(180\) | 4.00695 | 0.298660 | ||||||||
\(181\) | −17.9710 | −1.33578 | −0.667888 | − | 0.744262i | \(-0.732801\pi\) | ||||
−0.667888 | + | 0.744262i | \(0.732801\pi\) | |||||||
\(182\) | −13.0593 | −0.968022 | ||||||||
\(183\) | −27.6657 | −2.04511 | ||||||||
\(184\) | −2.73733 | −0.201798 | ||||||||
\(185\) | −5.73194 | −0.421420 | ||||||||
\(186\) | −6.65527 | −0.487988 | ||||||||
\(187\) | −31.8500 | −2.32911 | ||||||||
\(188\) | 12.9408 | 0.943804 | ||||||||
\(189\) | −3.03634 | −0.220861 | ||||||||
\(190\) | 7.73949 | 0.561482 | ||||||||
\(191\) | 24.2424 | 1.75412 | 0.877060 | − | 0.480380i | \(-0.159501\pi\) | ||||
0.877060 | + | 0.480380i | \(0.159501\pi\) | |||||||
\(192\) | −2.51016 | −0.181155 | ||||||||
\(193\) | 8.80361 | 0.633697 | 0.316849 | − | 0.948476i | \(-0.397375\pi\) | ||||
0.316849 | + | 0.948476i | \(0.397375\pi\) | |||||||
\(194\) | 8.73748 | 0.627314 | ||||||||
\(195\) | −9.89923 | −0.708898 | ||||||||
\(196\) | 9.15850 | 0.654179 | ||||||||
\(197\) | 22.5605 | 1.60737 | 0.803684 | − | 0.595056i | \(-0.202870\pi\) | ||||
0.803684 | + | 0.595056i | \(0.202870\pi\) | |||||||
\(198\) | −15.4242 | −1.09615 | ||||||||
\(199\) | −12.7595 | −0.904494 | −0.452247 | − | 0.891893i | \(-0.649377\pi\) | ||||
−0.452247 | + | 0.891893i | \(0.649377\pi\) | |||||||
\(200\) | 3.52647 | 0.249359 | ||||||||
\(201\) | 15.0381 | 1.06071 | ||||||||
\(202\) | −4.95801 | −0.348845 | ||||||||
\(203\) | 6.07673 | 0.426503 | ||||||||
\(204\) | 17.1098 | 1.19792 | ||||||||
\(205\) | 7.17871 | 0.501383 | ||||||||
\(206\) | −6.96802 | −0.485485 | ||||||||
\(207\) | 9.03569 | 0.628024 | ||||||||
\(208\) | 3.24878 | 0.225262 | ||||||||
\(209\) | −29.7921 | −2.06076 | ||||||||
\(210\) | 12.2485 | 0.845224 | ||||||||
\(211\) | −21.9026 | −1.50784 | −0.753920 | − | 0.656966i | \(-0.771840\pi\) | ||||
−0.753920 | + | 0.656966i | \(0.771840\pi\) | |||||||
\(212\) | −10.7353 | −0.737301 | ||||||||
\(213\) | 17.4599 | 1.19634 | ||||||||
\(214\) | 7.43212 | 0.508049 | ||||||||
\(215\) | 9.37231 | 0.639186 | ||||||||
\(216\) | 0.755352 | 0.0513952 | ||||||||
\(217\) | −10.6577 | −0.723493 | ||||||||
\(218\) | −13.7246 | −0.929547 | ||||||||
\(219\) | −30.0846 | −2.03293 | ||||||||
\(220\) | 5.67214 | 0.382415 | ||||||||
\(221\) | −22.1443 | −1.48959 | ||||||||
\(222\) | −11.8529 | −0.795514 | ||||||||
\(223\) | −16.3532 | −1.09509 | −0.547547 | − | 0.836775i | \(-0.684438\pi\) | ||||
−0.547547 | + | 0.836775i | \(0.684438\pi\) | |||||||
\(224\) | −4.01976 | −0.268582 | ||||||||
\(225\) | −11.6406 | −0.776040 | ||||||||
\(226\) | −10.6786 | −0.710327 | ||||||||
\(227\) | 12.4998 | 0.829640 | 0.414820 | − | 0.909903i | \(-0.363844\pi\) | ||||
0.414820 | + | 0.909903i | \(0.363844\pi\) | |||||||
\(228\) | 16.0043 | 1.05991 | ||||||||
\(229\) | 18.2669 | 1.20711 | 0.603556 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603556 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(230\) | −3.32281 | −0.219100 | ||||||||
\(231\) | −47.1487 | −3.10216 | ||||||||
\(232\) | −1.51171 | −0.0992489 | ||||||||
\(233\) | 11.4372 | 0.749279 | 0.374639 | − | 0.927171i | \(-0.377767\pi\) | ||||
0.374639 | + | 0.927171i | \(0.377767\pi\) | |||||||
\(234\) | −10.7240 | −0.701047 | ||||||||
\(235\) | 15.7087 | 1.02472 | ||||||||
\(236\) | 2.48541 | 0.161786 | ||||||||
\(237\) | 2.05904 | 0.133749 | ||||||||
\(238\) | 27.3995 | 1.77605 | ||||||||
\(239\) | −9.03889 | −0.584677 | −0.292339 | − | 0.956315i | \(-0.594433\pi\) | ||||
−0.292339 | + | 0.956315i | \(0.594433\pi\) | |||||||
\(240\) | −3.04706 | −0.196687 | ||||||||
\(241\) | −13.9464 | −0.898368 | −0.449184 | − | 0.893439i | \(-0.648285\pi\) | ||||
−0.449184 | + | 0.893439i | \(0.648285\pi\) | |||||||
\(242\) | −10.8341 | −0.696442 | ||||||||
\(243\) | 22.3642 | 1.43466 | ||||||||
\(244\) | 11.0215 | 0.705577 | ||||||||
\(245\) | 11.1174 | 0.710265 | ||||||||
\(246\) | 14.8446 | 0.946459 | ||||||||
\(247\) | −20.7135 | −1.31797 | ||||||||
\(248\) | 2.65133 | 0.168360 | ||||||||
\(249\) | −16.9452 | −1.07386 | ||||||||
\(250\) | 10.3502 | 0.654604 | ||||||||
\(251\) | −13.1105 | −0.827525 | −0.413763 | − | 0.910385i | \(-0.635786\pi\) | ||||
−0.413763 | + | 0.910385i | \(0.635786\pi\) | |||||||
\(252\) | 13.2689 | 0.835863 | ||||||||
\(253\) | 12.7907 | 0.804144 | ||||||||
\(254\) | 6.74879 | 0.423457 | ||||||||
\(255\) | 20.7694 | 1.30063 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.8690 | 1.11464 | 0.557318 | − | 0.830299i | \(-0.311830\pi\) | ||||
0.557318 | + | 0.830299i | \(0.311830\pi\) | |||||||
\(258\) | 19.3807 | 1.20659 | ||||||||
\(259\) | −18.9812 | −1.17943 | ||||||||
\(260\) | 3.94366 | 0.244575 | ||||||||
\(261\) | 4.99004 | 0.308876 | ||||||||
\(262\) | 15.4181 | 0.952536 | ||||||||
\(263\) | −5.81471 | −0.358551 | −0.179275 | − | 0.983799i | \(-0.557375\pi\) | ||||
−0.179275 | + | 0.983799i | \(0.557375\pi\) | |||||||
\(264\) | 11.7292 | 0.721884 | ||||||||
\(265\) | −13.0314 | −0.800514 | ||||||||
\(266\) | 25.6291 | 1.57142 | ||||||||
\(267\) | −5.10207 | −0.312242 | ||||||||
\(268\) | −5.99089 | −0.365952 | ||||||||
\(269\) | 24.5522 | 1.49697 | 0.748487 | − | 0.663150i | \(-0.230781\pi\) | ||||
0.748487 | + | 0.663150i | \(0.230781\pi\) | |||||||
\(270\) | 0.916913 | 0.0558016 | ||||||||
\(271\) | 13.9621 | 0.848136 | 0.424068 | − | 0.905630i | \(-0.360602\pi\) | ||||
0.424068 | + | 0.905630i | \(0.360602\pi\) | |||||||
\(272\) | −6.81620 | −0.413293 | ||||||||
\(273\) | −32.7810 | −1.98400 | ||||||||
\(274\) | 4.39322 | 0.265404 | ||||||||
\(275\) | −16.4781 | −0.993669 | ||||||||
\(276\) | −6.87114 | −0.413594 | ||||||||
\(277\) | −6.71887 | −0.403698 | −0.201849 | − | 0.979417i | \(-0.564695\pi\) | ||||
−0.201849 | + | 0.979417i | \(0.564695\pi\) | |||||||
\(278\) | 19.2144 | 1.15240 | ||||||||
\(279\) | −8.75182 | −0.523958 | ||||||||
\(280\) | −4.87955 | −0.291609 | ||||||||
\(281\) | −5.63094 | −0.335913 | −0.167957 | − | 0.985794i | \(-0.553717\pi\) | ||||
−0.167957 | + | 0.985794i | \(0.553717\pi\) | |||||||
\(282\) | 32.4835 | 1.93436 | ||||||||
\(283\) | −15.3746 | −0.913924 | −0.456962 | − | 0.889486i | \(-0.651063\pi\) | ||||
−0.456962 | + | 0.889486i | \(0.651063\pi\) | |||||||
\(284\) | −6.95570 | −0.412745 | ||||||||
\(285\) | 19.4274 | 1.15078 | ||||||||
\(286\) | −15.1806 | −0.897646 | ||||||||
\(287\) | 23.7721 | 1.40322 | ||||||||
\(288\) | −3.30092 | −0.194508 | ||||||||
\(289\) | 29.4606 | 1.73298 | ||||||||
\(290\) | −1.83505 | −0.107758 | ||||||||
\(291\) | 21.9325 | 1.28571 | ||||||||
\(292\) | 11.9851 | 0.701377 | ||||||||
\(293\) | −5.87022 | −0.342942 | −0.171471 | − | 0.985189i | \(-0.554852\pi\) | ||||
−0.171471 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(294\) | 22.9893 | 1.34076 | ||||||||
\(295\) | 3.01701 | 0.175657 | ||||||||
\(296\) | 4.72196 | 0.274458 | ||||||||
\(297\) | −3.52953 | −0.204804 | ||||||||
\(298\) | −13.2134 | −0.765433 | ||||||||
\(299\) | 8.89297 | 0.514294 | ||||||||
\(300\) | 8.85202 | 0.511072 | ||||||||
\(301\) | 31.0362 | 1.78889 | ||||||||
\(302\) | −21.3556 | −1.22888 | ||||||||
\(303\) | −12.4454 | −0.714971 | ||||||||
\(304\) | −6.37578 | −0.365676 | ||||||||
\(305\) | 13.3788 | 0.766070 | ||||||||
\(306\) | 22.4997 | 1.28622 | ||||||||
\(307\) | −12.0524 | −0.687868 | −0.343934 | − | 0.938994i | \(-0.611760\pi\) | ||||
−0.343934 | + | 0.938994i | \(0.611760\pi\) | |||||||
\(308\) | 18.7831 | 1.07027 | ||||||||
\(309\) | −17.4909 | −0.995020 | ||||||||
\(310\) | 3.21842 | 0.182794 | ||||||||
\(311\) | 29.3871 | 1.66639 | 0.833196 | − | 0.552978i | \(-0.186509\pi\) | ||||
0.833196 | + | 0.552978i | \(0.186509\pi\) | |||||||
\(312\) | 8.15497 | 0.461684 | ||||||||
\(313\) | −1.93762 | −0.109521 | −0.0547603 | − | 0.998500i | \(-0.517439\pi\) | ||||
−0.0547603 | + | 0.998500i | \(0.517439\pi\) | |||||||
\(314\) | −18.0969 | −1.02127 | ||||||||
\(315\) | 16.1070 | 0.907526 | ||||||||
\(316\) | −0.820280 | −0.0461444 | ||||||||
\(317\) | 14.8682 | 0.835080 | 0.417540 | − | 0.908658i | \(-0.362892\pi\) | ||||
0.417540 | + | 0.908658i | \(0.362892\pi\) | |||||||
\(318\) | −26.9473 | −1.51113 | ||||||||
\(319\) | 7.06378 | 0.395496 | ||||||||
\(320\) | 1.21389 | 0.0678585 | ||||||||
\(321\) | 18.6558 | 1.04127 | ||||||||
\(322\) | −11.0034 | −0.613196 | ||||||||
\(323\) | 43.4586 | 2.41810 | ||||||||
\(324\) | −8.00670 | −0.444816 | ||||||||
\(325\) | −11.4567 | −0.635505 | ||||||||
\(326\) | −15.4959 | −0.858239 | ||||||||
\(327\) | −34.4510 | −1.90514 | ||||||||
\(328\) | −5.91381 | −0.326535 | ||||||||
\(329\) | 52.0189 | 2.86789 | ||||||||
\(330\) | 14.2380 | 0.783775 | ||||||||
\(331\) | 5.44635 | 0.299358 | 0.149679 | − | 0.988735i | \(-0.452176\pi\) | ||||
0.149679 | + | 0.988735i | \(0.452176\pi\) | |||||||
\(332\) | 6.75066 | 0.370490 | ||||||||
\(333\) | −15.5868 | −0.854152 | ||||||||
\(334\) | −11.2723 | −0.616793 | ||||||||
\(335\) | −7.27227 | −0.397327 | ||||||||
\(336\) | −10.0903 | −0.550469 | ||||||||
\(337\) | −23.5626 | −1.28354 | −0.641768 | − | 0.766899i | \(-0.721799\pi\) | ||||
−0.641768 | + | 0.766899i | \(0.721799\pi\) | |||||||
\(338\) | 2.44542 | 0.133014 | ||||||||
\(339\) | −26.8049 | −1.45584 | ||||||||
\(340\) | −8.27411 | −0.448727 | ||||||||
\(341\) | −12.3889 | −0.670895 | ||||||||
\(342\) | 21.0459 | 1.13803 | ||||||||
\(343\) | 8.67666 | 0.468496 | ||||||||
\(344\) | −7.72089 | −0.416283 | ||||||||
\(345\) | −8.34080 | −0.449053 | ||||||||
\(346\) | −1.11114 | −0.0597354 | ||||||||
\(347\) | 26.3506 | 1.41457 | 0.707286 | − | 0.706928i | \(-0.249919\pi\) | ||||
0.707286 | + | 0.706928i | \(0.249919\pi\) | |||||||
\(348\) | −3.79465 | −0.203414 | ||||||||
\(349\) | −0.161549 | −0.00864752 | −0.00432376 | − | 0.999991i | \(-0.501376\pi\) | ||||
−0.00432376 | + | 0.999991i | \(0.501376\pi\) | |||||||
\(350\) | 14.1756 | 0.757717 | ||||||||
\(351\) | −2.45397 | −0.130983 | ||||||||
\(352\) | −4.67270 | −0.249056 | ||||||||
\(353\) | 21.0100 | 1.11825 | 0.559124 | − | 0.829084i | \(-0.311138\pi\) | ||||
0.559124 | + | 0.829084i | \(0.311138\pi\) | |||||||
\(354\) | 6.23878 | 0.331587 | ||||||||
\(355\) | −8.44345 | −0.448132 | ||||||||
\(356\) | 2.03257 | 0.107726 | ||||||||
\(357\) | 68.7773 | 3.64008 | ||||||||
\(358\) | −9.19618 | −0.486033 | ||||||||
\(359\) | −32.9008 | −1.73644 | −0.868218 | − | 0.496183i | \(-0.834734\pi\) | ||||
−0.868218 | + | 0.496183i | \(0.834734\pi\) | |||||||
\(360\) | −4.00695 | −0.211185 | ||||||||
\(361\) | 21.6506 | 1.13951 | ||||||||
\(362\) | 17.9710 | 0.944536 | ||||||||
\(363\) | −27.1954 | −1.42739 | ||||||||
\(364\) | 13.0593 | 0.684495 | ||||||||
\(365\) | 14.5486 | 0.761510 | ||||||||
\(366\) | 27.6657 | 1.44611 | ||||||||
\(367\) | −8.81948 | −0.460373 | −0.230187 | − | 0.973146i | \(-0.573934\pi\) | ||||
−0.230187 | + | 0.973146i | \(0.573934\pi\) | |||||||
\(368\) | 2.73733 | 0.142693 | ||||||||
\(369\) | 19.5210 | 1.01622 | ||||||||
\(370\) | 5.73194 | 0.297989 | ||||||||
\(371\) | −43.1532 | −2.24040 | ||||||||
\(372\) | 6.65527 | 0.345060 | ||||||||
\(373\) | −28.0095 | −1.45028 | −0.725139 | − | 0.688603i | \(-0.758224\pi\) | ||||
−0.725139 | + | 0.688603i | \(0.758224\pi\) | |||||||
\(374\) | 31.8500 | 1.64693 | ||||||||
\(375\) | 25.9807 | 1.34164 | ||||||||
\(376\) | −12.9408 | −0.667370 | ||||||||
\(377\) | 4.91123 | 0.252941 | ||||||||
\(378\) | 3.03634 | 0.156172 | ||||||||
\(379\) | 9.41084 | 0.483403 | 0.241701 | − | 0.970351i | \(-0.422295\pi\) | ||||
0.241701 | + | 0.970351i | \(0.422295\pi\) | |||||||
\(380\) | −7.73949 | −0.397028 | ||||||||
\(381\) | 16.9406 | 0.867891 | ||||||||
\(382\) | −24.2424 | −1.24035 | ||||||||
\(383\) | 23.1857 | 1.18473 | 0.592367 | − | 0.805668i | \(-0.298193\pi\) | ||||
0.592367 | + | 0.805668i | \(0.298193\pi\) | |||||||
\(384\) | 2.51016 | 0.128096 | ||||||||
\(385\) | 22.8006 | 1.16203 | ||||||||
\(386\) | −8.80361 | −0.448092 | ||||||||
\(387\) | 25.4860 | 1.29553 | ||||||||
\(388\) | −8.73748 | −0.443578 | ||||||||
\(389\) | 10.2703 | 0.520726 | 0.260363 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260363 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(390\) | 9.89923 | 0.501267 | ||||||||
\(391\) | −18.6582 | −0.943584 | ||||||||
\(392\) | −9.15850 | −0.462574 | ||||||||
\(393\) | 38.7021 | 1.95226 | ||||||||
\(394\) | −22.5605 | −1.13658 | ||||||||
\(395\) | −0.995729 | −0.0501006 | ||||||||
\(396\) | 15.4242 | 0.775095 | ||||||||
\(397\) | 22.5607 | 1.13229 | 0.566145 | − | 0.824306i | \(-0.308434\pi\) | ||||
0.566145 | + | 0.824306i | \(0.308434\pi\) | |||||||
\(398\) | 12.7595 | 0.639574 | ||||||||
\(399\) | 64.3333 | 3.22069 | ||||||||
\(400\) | −3.52647 | −0.176324 | ||||||||
\(401\) | −0.914761 | −0.0456810 | −0.0228405 | − | 0.999739i | \(-0.507271\pi\) | ||||
−0.0228405 | + | 0.999739i | \(0.507271\pi\) | |||||||
\(402\) | −15.0381 | −0.750032 | ||||||||
\(403\) | −8.61359 | −0.429074 | ||||||||
\(404\) | 4.95801 | 0.246670 | ||||||||
\(405\) | −9.71924 | −0.482953 | ||||||||
\(406\) | −6.07673 | −0.301583 | ||||||||
\(407\) | −22.0643 | −1.09369 | ||||||||
\(408\) | −17.1098 | −0.847060 | ||||||||
\(409\) | 3.49032 | 0.172585 | 0.0862927 | − | 0.996270i | \(-0.472498\pi\) | ||||
0.0862927 | + | 0.996270i | \(0.472498\pi\) | |||||||
\(410\) | −7.17871 | −0.354531 | ||||||||
\(411\) | 11.0277 | 0.543957 | ||||||||
\(412\) | 6.96802 | 0.343290 | ||||||||
\(413\) | 9.99075 | 0.491613 | ||||||||
\(414\) | −9.03569 | −0.444080 | ||||||||
\(415\) | 8.19455 | 0.402255 | ||||||||
\(416\) | −3.24878 | −0.159285 | ||||||||
\(417\) | 48.2312 | 2.36189 | ||||||||
\(418\) | 29.7921 | 1.45718 | ||||||||
\(419\) | −10.2557 | −0.501023 | −0.250512 | − | 0.968114i | \(-0.580599\pi\) | ||||
−0.250512 | + | 0.968114i | \(0.580599\pi\) | |||||||
\(420\) | −12.2485 | −0.597664 | ||||||||
\(421\) | 7.17374 | 0.349627 | 0.174813 | − | 0.984602i | \(-0.444068\pi\) | ||||
0.174813 | + | 0.984602i | \(0.444068\pi\) | |||||||
\(422\) | 21.9026 | 1.06620 | ||||||||
\(423\) | 42.7165 | 2.07695 | ||||||||
\(424\) | 10.7353 | 0.521351 | ||||||||
\(425\) | 24.0371 | 1.16597 | ||||||||
\(426\) | −17.4599 | −0.845937 | ||||||||
\(427\) | 44.3037 | 2.14401 | ||||||||
\(428\) | −7.43212 | −0.359245 | ||||||||
\(429\) | −38.1057 | −1.83976 | ||||||||
\(430\) | −9.37231 | −0.451973 | ||||||||
\(431\) | −25.5762 | −1.23196 | −0.615982 | − | 0.787760i | \(-0.711241\pi\) | ||||
−0.615982 | + | 0.787760i | \(0.711241\pi\) | |||||||
\(432\) | −0.755352 | −0.0363419 | ||||||||
\(433\) | 14.5028 | 0.696958 | 0.348479 | − | 0.937317i | \(-0.386698\pi\) | ||||
0.348479 | + | 0.937317i | \(0.386698\pi\) | |||||||
\(434\) | 10.6577 | 0.511587 | ||||||||
\(435\) | −4.60628 | −0.220854 | ||||||||
\(436\) | 13.7246 | 0.657289 | ||||||||
\(437\) | −17.4526 | −0.834871 | ||||||||
\(438\) | 30.0846 | 1.43750 | ||||||||
\(439\) | −20.7583 | −0.990739 | −0.495370 | − | 0.868682i | \(-0.664967\pi\) | ||||
−0.495370 | + | 0.868682i | \(0.664967\pi\) | |||||||
\(440\) | −5.67214 | −0.270409 | ||||||||
\(441\) | 30.2315 | 1.43959 | ||||||||
\(442\) | 22.1443 | 1.05330 | ||||||||
\(443\) | −24.5702 | −1.16736 | −0.583682 | − | 0.811982i | \(-0.698388\pi\) | ||||
−0.583682 | + | 0.811982i | \(0.698388\pi\) | |||||||
\(444\) | 11.8529 | 0.562513 | ||||||||
\(445\) | 2.46731 | 0.116962 | ||||||||
\(446\) | 16.3532 | 0.774348 | ||||||||
\(447\) | −33.1678 | −1.56878 | ||||||||
\(448\) | 4.01976 | 0.189916 | ||||||||
\(449\) | −37.6451 | −1.77658 | −0.888292 | − | 0.459279i | \(-0.848108\pi\) | ||||
−0.888292 | + | 0.459279i | \(0.848108\pi\) | |||||||
\(450\) | 11.6406 | 0.548743 | ||||||||
\(451\) | 27.6334 | 1.30121 | ||||||||
\(452\) | 10.6786 | 0.502277 | ||||||||
\(453\) | −53.6061 | −2.51863 | ||||||||
\(454\) | −12.4998 | −0.586644 | ||||||||
\(455\) | 15.8526 | 0.743180 | ||||||||
\(456\) | −16.0043 | −0.749468 | ||||||||
\(457\) | 7.18013 | 0.335872 | 0.167936 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167936 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(458\) | −18.2669 | −0.853557 | ||||||||
\(459\) | 5.14863 | 0.240317 | ||||||||
\(460\) | 3.32281 | 0.154927 | ||||||||
\(461\) | −30.2705 | −1.40984 | −0.704918 | − | 0.709288i | \(-0.749016\pi\) | ||||
−0.704918 | + | 0.709288i | \(0.749016\pi\) | |||||||
\(462\) | 47.1487 | 2.19356 | ||||||||
\(463\) | −28.2538 | −1.31307 | −0.656533 | − | 0.754297i | \(-0.727978\pi\) | ||||
−0.656533 | + | 0.754297i | \(0.727978\pi\) | |||||||
\(464\) | 1.51171 | 0.0701795 | ||||||||
\(465\) | 8.07876 | 0.374644 | ||||||||
\(466\) | −11.4372 | −0.529820 | ||||||||
\(467\) | −8.30473 | −0.384297 | −0.192148 | − | 0.981366i | \(-0.561546\pi\) | ||||
−0.192148 | + | 0.981366i | \(0.561546\pi\) | |||||||
\(468\) | 10.7240 | 0.495715 | ||||||||
\(469\) | −24.0820 | −1.11200 | ||||||||
\(470\) | −15.7087 | −0.724587 | ||||||||
\(471\) | −45.4262 | −2.09313 | ||||||||
\(472\) | −2.48541 | −0.114400 | ||||||||
\(473\) | 36.0774 | 1.65884 | ||||||||
\(474\) | −2.05904 | −0.0945747 | ||||||||
\(475\) | 22.4840 | 1.03164 | ||||||||
\(476\) | −27.3995 | −1.25585 | ||||||||
\(477\) | −35.4362 | −1.62251 | ||||||||
\(478\) | 9.03889 | 0.413429 | ||||||||
\(479\) | −22.1687 | −1.01291 | −0.506456 | − | 0.862266i | \(-0.669045\pi\) | ||||
−0.506456 | + | 0.862266i | \(0.669045\pi\) | |||||||
\(480\) | 3.04706 | 0.139079 | ||||||||
\(481\) | −15.3406 | −0.699472 | ||||||||
\(482\) | 13.9464 | 0.635242 | ||||||||
\(483\) | −27.6203 | −1.25677 | ||||||||
\(484\) | 10.8341 | 0.492459 | ||||||||
\(485\) | −10.6063 | −0.481609 | ||||||||
\(486\) | −22.3642 | −1.01446 | ||||||||
\(487\) | −28.0909 | −1.27292 | −0.636460 | − | 0.771309i | \(-0.719602\pi\) | ||||
−0.636460 | + | 0.771309i | \(0.719602\pi\) | |||||||
\(488\) | −11.0215 | −0.498918 | ||||||||
\(489\) | −38.8973 | −1.75900 | ||||||||
\(490\) | −11.1174 | −0.502233 | ||||||||
\(491\) | 12.7026 | 0.573258 | 0.286629 | − | 0.958042i | \(-0.407465\pi\) | ||||
0.286629 | + | 0.958042i | \(0.407465\pi\) | |||||||
\(492\) | −14.8446 | −0.669247 | ||||||||
\(493\) | −10.3041 | −0.464075 | ||||||||
\(494\) | 20.7135 | 0.931945 | ||||||||
\(495\) | 18.7233 | 0.841548 | ||||||||
\(496\) | −2.65133 | −0.119048 | ||||||||
\(497\) | −27.9603 | −1.25419 | ||||||||
\(498\) | 16.9452 | 0.759335 | ||||||||
\(499\) | 41.7976 | 1.87112 | 0.935560 | − | 0.353168i | \(-0.114896\pi\) | ||||
0.935560 | + | 0.353168i | \(0.114896\pi\) | |||||||
\(500\) | −10.3502 | −0.462875 | ||||||||
\(501\) | −28.2953 | −1.26414 | ||||||||
\(502\) | 13.1105 | 0.585149 | ||||||||
\(503\) | 28.8523 | 1.28646 | 0.643231 | − | 0.765672i | \(-0.277593\pi\) | ||||
0.643231 | + | 0.765672i | \(0.277593\pi\) | |||||||
\(504\) | −13.2689 | −0.591044 | ||||||||
\(505\) | 6.01848 | 0.267819 | ||||||||
\(506\) | −12.7907 | −0.568616 | ||||||||
\(507\) | 6.13841 | 0.272616 | ||||||||
\(508\) | −6.74879 | −0.299429 | ||||||||
\(509\) | 39.8489 | 1.76627 | 0.883135 | − | 0.469118i | \(-0.155428\pi\) | ||||
0.883135 | + | 0.469118i | \(0.155428\pi\) | |||||||
\(510\) | −20.7694 | −0.919683 | ||||||||
\(511\) | 48.1774 | 2.13124 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.81596 | 0.212630 | ||||||||
\(514\) | −17.8690 | −0.788167 | ||||||||
\(515\) | 8.45840 | 0.372722 | ||||||||
\(516\) | −19.3807 | −0.853188 | ||||||||
\(517\) | 60.4684 | 2.65940 | ||||||||
\(518\) | 18.9812 | 0.833985 | ||||||||
\(519\) | −2.78915 | −0.122430 | ||||||||
\(520\) | −3.94366 | −0.172941 | ||||||||
\(521\) | −22.2964 | −0.976822 | −0.488411 | − | 0.872614i | \(-0.662423\pi\) | ||||
−0.488411 | + | 0.872614i | \(0.662423\pi\) | |||||||
\(522\) | −4.99004 | −0.218408 | ||||||||
\(523\) | −14.8565 | −0.649629 | −0.324815 | − | 0.945778i | \(-0.605302\pi\) | ||||
−0.324815 | + | 0.945778i | \(0.605302\pi\) | |||||||
\(524\) | −15.4181 | −0.673545 | ||||||||
\(525\) | 35.5830 | 1.55297 | ||||||||
\(526\) | 5.81471 | 0.253534 | ||||||||
\(527\) | 18.0720 | 0.787229 | ||||||||
\(528\) | −11.7292 | −0.510449 | ||||||||
\(529\) | −15.5070 | −0.674219 | ||||||||
\(530\) | 13.0314 | 0.566049 | ||||||||
\(531\) | 8.20412 | 0.356029 | ||||||||
\(532\) | −25.6291 | −1.11116 | ||||||||
\(533\) | 19.2127 | 0.832193 | ||||||||
\(534\) | 5.10207 | 0.220788 | ||||||||
\(535\) | −9.02177 | −0.390045 | ||||||||
\(536\) | 5.99089 | 0.258767 | ||||||||
\(537\) | −23.0839 | −0.996144 | ||||||||
\(538\) | −24.5522 | −1.05852 | ||||||||
\(539\) | 42.7949 | 1.84331 | ||||||||
\(540\) | −0.916913 | −0.0394577 | ||||||||
\(541\) | 22.9543 | 0.986882 | 0.493441 | − | 0.869779i | \(-0.335739\pi\) | ||||
0.493441 | + | 0.869779i | \(0.335739\pi\) | |||||||
\(542\) | −13.9621 | −0.599723 | ||||||||
\(543\) | 45.1102 | 1.93586 | ||||||||
\(544\) | 6.81620 | 0.292242 | ||||||||
\(545\) | 16.6601 | 0.713642 | ||||||||
\(546\) | 32.7810 | 1.40290 | ||||||||
\(547\) | −5.38432 | −0.230217 | −0.115109 | − | 0.993353i | \(-0.536722\pi\) | ||||
−0.115109 | + | 0.993353i | \(0.536722\pi\) | |||||||
\(548\) | −4.39322 | −0.187669 | ||||||||
\(549\) | 36.3809 | 1.55270 | ||||||||
\(550\) | 16.4781 | 0.702630 | ||||||||
\(551\) | −9.63836 | −0.410608 | ||||||||
\(552\) | 6.87114 | 0.292455 | ||||||||
\(553\) | −3.29733 | −0.140217 | ||||||||
\(554\) | 6.71887 | 0.285458 | ||||||||
\(555\) | 14.3881 | 0.610741 | ||||||||
\(556\) | −19.2144 | −0.814872 | ||||||||
\(557\) | 2.39840 | 0.101623 | 0.0508117 | − | 0.998708i | \(-0.483819\pi\) | ||||
0.0508117 | + | 0.998708i | \(0.483819\pi\) | |||||||
\(558\) | 8.75182 | 0.370494 | ||||||||
\(559\) | 25.0835 | 1.06092 | ||||||||
\(560\) | 4.87955 | 0.206199 | ||||||||
\(561\) | 79.9488 | 3.37544 | ||||||||
\(562\) | 5.63094 | 0.237527 | ||||||||
\(563\) | 45.7260 | 1.92712 | 0.963560 | − | 0.267492i | \(-0.0861950\pi\) | ||||
0.963560 | + | 0.267492i | \(0.0861950\pi\) | |||||||
\(564\) | −32.4835 | −1.36780 | ||||||||
\(565\) | 12.9626 | 0.545340 | ||||||||
\(566\) | 15.3746 | 0.646242 | ||||||||
\(567\) | −32.1850 | −1.35164 | ||||||||
\(568\) | 6.95570 | 0.291855 | ||||||||
\(569\) | 0.792583 | 0.0332268 | 0.0166134 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166134 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(570\) | −19.4274 | −0.813724 | ||||||||
\(571\) | 12.8133 | 0.536218 | 0.268109 | − | 0.963389i | \(-0.413601\pi\) | ||||
0.268109 | + | 0.963389i | \(0.413601\pi\) | |||||||
\(572\) | 15.1806 | 0.634731 | ||||||||
\(573\) | −60.8524 | −2.54215 | ||||||||
\(574\) | −23.7721 | −0.992229 | ||||||||
\(575\) | −9.65311 | −0.402562 | ||||||||
\(576\) | 3.30092 | 0.137538 | ||||||||
\(577\) | 1.21451 | 0.0505607 | 0.0252804 | − | 0.999680i | \(-0.491952\pi\) | ||||
0.0252804 | + | 0.999680i | \(0.491952\pi\) | |||||||
\(578\) | −29.4606 | −1.22540 | ||||||||
\(579\) | −22.0985 | −0.918382 | ||||||||
\(580\) | 1.83505 | 0.0761964 | ||||||||
\(581\) | 27.1360 | 1.12579 | ||||||||
\(582\) | −21.9325 | −0.909131 | ||||||||
\(583\) | −50.1627 | −2.07752 | ||||||||
\(584\) | −11.9851 | −0.495948 | ||||||||
\(585\) | 13.0177 | 0.538215 | ||||||||
\(586\) | 5.87022 | 0.242497 | ||||||||
\(587\) | −1.74261 | −0.0719251 | −0.0359625 | − | 0.999353i | \(-0.511450\pi\) | ||||
−0.0359625 | + | 0.999353i | \(0.511450\pi\) | |||||||
\(588\) | −22.9893 | −0.948064 | ||||||||
\(589\) | 16.9043 | 0.696530 | ||||||||
\(590\) | −3.01701 | −0.124208 | ||||||||
\(591\) | −56.6305 | −2.32947 | ||||||||
\(592\) | −4.72196 | −0.194071 | ||||||||
\(593\) | 34.7229 | 1.42590 | 0.712949 | − | 0.701216i | \(-0.247359\pi\) | ||||
0.712949 | + | 0.701216i | \(0.247359\pi\) | |||||||
\(594\) | 3.52953 | 0.144818 | ||||||||
\(595\) | −33.2600 | −1.36353 | ||||||||
\(596\) | 13.2134 | 0.541243 | ||||||||
\(597\) | 32.0283 | 1.31083 | ||||||||
\(598\) | −8.89297 | −0.363661 | ||||||||
\(599\) | 3.51978 | 0.143814 | 0.0719071 | − | 0.997411i | \(-0.477091\pi\) | ||||
0.0719071 | + | 0.997411i | \(0.477091\pi\) | |||||||
\(600\) | −8.85202 | −0.361382 | ||||||||
\(601\) | 5.77629 | 0.235620 | 0.117810 | − | 0.993036i | \(-0.462413\pi\) | ||||
0.117810 | + | 0.993036i | \(0.462413\pi\) | |||||||
\(602\) | −31.0362 | −1.26494 | ||||||||
\(603\) | −19.7754 | −0.805318 | ||||||||
\(604\) | 21.3556 | 0.868948 | ||||||||
\(605\) | 13.1514 | 0.534680 | ||||||||
\(606\) | 12.4454 | 0.505561 | ||||||||
\(607\) | 12.3287 | 0.500407 | 0.250203 | − | 0.968193i | \(-0.419503\pi\) | ||||
0.250203 | + | 0.968193i | \(0.419503\pi\) | |||||||
\(608\) | 6.37578 | 0.258572 | ||||||||
\(609\) | −15.2536 | −0.618107 | ||||||||
\(610\) | −13.3788 | −0.541693 | ||||||||
\(611\) | 42.0418 | 1.70083 | ||||||||
\(612\) | −22.4997 | −0.909497 | ||||||||
\(613\) | −0.349047 | −0.0140979 | −0.00704894 | − | 0.999975i | \(-0.502244\pi\) | ||||
−0.00704894 | + | 0.999975i | \(0.502244\pi\) | |||||||
\(614\) | 12.0524 | 0.486396 | ||||||||
\(615\) | −18.0197 | −0.726626 | ||||||||
\(616\) | −18.7831 | −0.756794 | ||||||||
\(617\) | 39.1621 | 1.57661 | 0.788303 | − | 0.615288i | \(-0.210960\pi\) | ||||
0.788303 | + | 0.615288i | \(0.210960\pi\) | |||||||
\(618\) | 17.4909 | 0.703586 | ||||||||
\(619\) | −41.8362 | −1.68154 | −0.840769 | − | 0.541394i | \(-0.817897\pi\) | ||||
−0.840769 | + | 0.541394i | \(0.817897\pi\) | |||||||
\(620\) | −3.21842 | −0.129255 | ||||||||
\(621\) | −2.06764 | −0.0829717 | ||||||||
\(622\) | −29.3871 | −1.17832 | ||||||||
\(623\) | 8.17044 | 0.327342 | ||||||||
\(624\) | −8.15497 | −0.326460 | ||||||||
\(625\) | 5.06838 | 0.202735 | ||||||||
\(626\) | 1.93762 | 0.0774427 | ||||||||
\(627\) | 74.7830 | 2.98655 | ||||||||
\(628\) | 18.0969 | 0.722145 | ||||||||
\(629\) | 32.1858 | 1.28333 | ||||||||
\(630\) | −16.1070 | −0.641718 | ||||||||
\(631\) | −28.8787 | −1.14964 | −0.574821 | − | 0.818280i | \(-0.694928\pi\) | ||||
−0.574821 | + | 0.818280i | \(0.694928\pi\) | |||||||
\(632\) | 0.820280 | 0.0326290 | ||||||||
\(633\) | 54.9792 | 2.18523 | ||||||||
\(634\) | −14.8682 | −0.590491 | ||||||||
\(635\) | −8.19229 | −0.325101 | ||||||||
\(636\) | 26.9473 | 1.06853 | ||||||||
\(637\) | 29.7540 | 1.17889 | ||||||||
\(638\) | −7.06378 | −0.279658 | ||||||||
\(639\) | −22.9602 | −0.908291 | ||||||||
\(640\) | −1.21389 | −0.0479832 | ||||||||
\(641\) | −1.86176 | −0.0735351 | −0.0367675 | − | 0.999324i | \(-0.511706\pi\) | ||||
−0.0367675 | + | 0.999324i | \(0.511706\pi\) | |||||||
\(642\) | −18.6558 | −0.736287 | ||||||||
\(643\) | 25.2592 | 0.996127 | 0.498064 | − | 0.867140i | \(-0.334045\pi\) | ||||
0.498064 | + | 0.867140i | \(0.334045\pi\) | |||||||
\(644\) | 11.0034 | 0.433595 | ||||||||
\(645\) | −23.5260 | −0.926336 | ||||||||
\(646\) | −43.4586 | −1.70986 | ||||||||
\(647\) | −7.39753 | −0.290827 | −0.145413 | − | 0.989371i | \(-0.546451\pi\) | ||||
−0.145413 | + | 0.989371i | \(0.546451\pi\) | |||||||
\(648\) | 8.00670 | 0.314533 | ||||||||
\(649\) | 11.6136 | 0.455872 | ||||||||
\(650\) | 11.4567 | 0.449370 | ||||||||
\(651\) | 26.7526 | 1.04852 | ||||||||
\(652\) | 15.4959 | 0.606867 | ||||||||
\(653\) | −27.1383 | −1.06200 | −0.531002 | − | 0.847370i | \(-0.678184\pi\) | ||||
−0.531002 | + | 0.847370i | \(0.678184\pi\) | |||||||
\(654\) | 34.4510 | 1.34714 | ||||||||
\(655\) | −18.7159 | −0.731291 | ||||||||
\(656\) | 5.91381 | 0.230895 | ||||||||
\(657\) | 39.5619 | 1.54346 | ||||||||
\(658\) | −52.0189 | −2.02791 | ||||||||
\(659\) | 2.22998 | 0.0868679 | 0.0434339 | − | 0.999056i | \(-0.486170\pi\) | ||||
0.0434339 | + | 0.999056i | \(0.486170\pi\) | |||||||
\(660\) | −14.2380 | −0.554213 | ||||||||
\(661\) | −3.14096 | −0.122169 | −0.0610846 | − | 0.998133i | \(-0.519456\pi\) | ||||
−0.0610846 | + | 0.998133i | \(0.519456\pi\) | |||||||
\(662\) | −5.44635 | −0.211678 | ||||||||
\(663\) | 55.5859 | 2.15878 | ||||||||
\(664\) | −6.75066 | −0.261976 | ||||||||
\(665\) | −31.1109 | −1.20643 | ||||||||
\(666\) | 15.5868 | 0.603976 | ||||||||
\(667\) | 4.13805 | 0.160226 | ||||||||
\(668\) | 11.2723 | 0.436139 | ||||||||
\(669\) | 41.0493 | 1.58706 | ||||||||
\(670\) | 7.27227 | 0.280952 | ||||||||
\(671\) | 51.5000 | 1.98813 | ||||||||
\(672\) | 10.0903 | 0.389240 | ||||||||
\(673\) | 31.9422 | 1.23128 | 0.615640 | − | 0.788027i | \(-0.288897\pi\) | ||||
0.615640 | + | 0.788027i | \(0.288897\pi\) | |||||||
\(674\) | 23.5626 | 0.907597 | ||||||||
\(675\) | 2.66373 | 0.102527 | ||||||||
\(676\) | −2.44542 | −0.0940548 | ||||||||
\(677\) | 38.5252 | 1.48064 | 0.740322 | − | 0.672253i | \(-0.234673\pi\) | ||||
0.740322 | + | 0.672253i | \(0.234673\pi\) | |||||||
\(678\) | 26.8049 | 1.02944 | ||||||||
\(679\) | −35.1226 | −1.34788 | ||||||||
\(680\) | 8.27411 | 0.317298 | ||||||||
\(681\) | −31.3765 | −1.20235 | ||||||||
\(682\) | 12.3889 | 0.474394 | ||||||||
\(683\) | 33.7516 | 1.29147 | 0.645734 | − | 0.763563i | \(-0.276552\pi\) | ||||
0.645734 | + | 0.763563i | \(0.276552\pi\) | |||||||
\(684\) | −21.0459 | −0.804711 | ||||||||
\(685\) | −5.33289 | −0.203759 | ||||||||
\(686\) | −8.67666 | −0.331276 | ||||||||
\(687\) | −45.8529 | −1.74940 | ||||||||
\(688\) | 7.72089 | 0.294356 | ||||||||
\(689\) | −34.8765 | −1.32869 | ||||||||
\(690\) | 8.34080 | 0.317529 | ||||||||
\(691\) | 27.7046 | 1.05393 | 0.526965 | − | 0.849887i | \(-0.323330\pi\) | ||||
0.526965 | + | 0.849887i | \(0.323330\pi\) | |||||||
\(692\) | 1.11114 | 0.0422393 | ||||||||
\(693\) | 62.0016 | 2.35525 | ||||||||
\(694\) | −26.3506 | −1.00025 | ||||||||
\(695\) | −23.3241 | −0.884735 | ||||||||
\(696\) | 3.79465 | 0.143836 | ||||||||
\(697\) | −40.3097 | −1.52684 | ||||||||
\(698\) | 0.161549 | 0.00611472 | ||||||||
\(699\) | −28.7093 | −1.08589 | ||||||||
\(700\) | −14.1756 | −0.535787 | ||||||||
\(701\) | 8.97566 | 0.339006 | 0.169503 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169503 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(702\) | 2.45397 | 0.0926192 | ||||||||
\(703\) | 30.1062 | 1.13548 | ||||||||
\(704\) | 4.67270 | 0.176109 | ||||||||
\(705\) | −39.4313 | −1.48507 | ||||||||
\(706\) | −21.0100 | −0.790721 | ||||||||
\(707\) | 19.9300 | 0.749547 | ||||||||
\(708\) | −6.23878 | −0.234468 | ||||||||
\(709\) | −11.0200 | −0.413866 | −0.206933 | − | 0.978355i | \(-0.566348\pi\) | ||||
−0.206933 | + | 0.978355i | \(0.566348\pi\) | |||||||
\(710\) | 8.44345 | 0.316877 | ||||||||
\(711\) | −2.70768 | −0.101546 | ||||||||
\(712\) | −2.03257 | −0.0761736 | ||||||||
\(713\) | −7.25756 | −0.271798 | ||||||||
\(714\) | −68.7773 | −2.57392 | ||||||||
\(715\) | 18.4275 | 0.689150 | ||||||||
\(716\) | 9.19618 | 0.343677 | ||||||||
\(717\) | 22.6891 | 0.847340 | ||||||||
\(718\) | 32.9008 | 1.22785 | ||||||||
\(719\) | −1.19184 | −0.0444480 | −0.0222240 | − | 0.999753i | \(-0.507075\pi\) | ||||
−0.0222240 | + | 0.999753i | \(0.507075\pi\) | |||||||
\(720\) | 4.00695 | 0.149330 | ||||||||
\(721\) | 28.0098 | 1.04314 | ||||||||
\(722\) | −21.6506 | −0.805752 | ||||||||
\(723\) | 35.0078 | 1.30195 | ||||||||
\(724\) | −17.9710 | −0.667888 | ||||||||
\(725\) | −5.33102 | −0.197989 | ||||||||
\(726\) | 27.1954 | 1.00931 | ||||||||
\(727\) | 15.5597 | 0.577079 | 0.288539 | − | 0.957468i | \(-0.406830\pi\) | ||||
0.288539 | + | 0.957468i | \(0.406830\pi\) | |||||||
\(728\) | −13.0593 | −0.484011 | ||||||||
\(729\) | −32.1176 | −1.18954 | ||||||||
\(730\) | −14.5486 | −0.538469 | ||||||||
\(731\) | −52.6272 | −1.94649 | ||||||||
\(732\) | −27.6657 | −1.02255 | ||||||||
\(733\) | 8.18329 | 0.302257 | 0.151128 | − | 0.988514i | \(-0.451709\pi\) | ||||
0.151128 | + | 0.988514i | \(0.451709\pi\) | |||||||
\(734\) | 8.81948 | 0.325533 | ||||||||
\(735\) | −27.9065 | −1.02935 | ||||||||
\(736\) | −2.73733 | −0.100899 | ||||||||
\(737\) | −27.9936 | −1.03116 | ||||||||
\(738\) | −19.5210 | −0.718578 | ||||||||
\(739\) | 2.99978 | 0.110349 | 0.0551744 | − | 0.998477i | \(-0.482429\pi\) | ||||
0.0551744 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(740\) | −5.73194 | −0.210710 | ||||||||
\(741\) | 51.9943 | 1.91006 | ||||||||
\(742\) | 43.1532 | 1.58421 | ||||||||
\(743\) | 8.31764 | 0.305145 | 0.152572 | − | 0.988292i | \(-0.451244\pi\) | ||||
0.152572 | + | 0.988292i | \(0.451244\pi\) | |||||||
\(744\) | −6.65527 | −0.243994 | ||||||||
\(745\) | 16.0396 | 0.587646 | ||||||||
\(746\) | 28.0095 | 1.02550 | ||||||||
\(747\) | 22.2834 | 0.815306 | ||||||||
\(748\) | −31.8500 | −1.16455 | ||||||||
\(749\) | −29.8754 | −1.09162 | ||||||||
\(750\) | −25.9807 | −0.948680 | ||||||||
\(751\) | 18.7289 | 0.683429 | 0.341714 | − | 0.939804i | \(-0.388992\pi\) | ||||
0.341714 | + | 0.939804i | \(0.388992\pi\) | |||||||
\(752\) | 12.9408 | 0.471902 | ||||||||
\(753\) | 32.9094 | 1.19928 | ||||||||
\(754\) | −4.91123 | −0.178856 | ||||||||
\(755\) | 25.9234 | 0.943447 | ||||||||
\(756\) | −3.03634 | −0.110430 | ||||||||
\(757\) | 42.9718 | 1.56183 | 0.780917 | − | 0.624634i | \(-0.214752\pi\) | ||||
0.780917 | + | 0.624634i | \(0.214752\pi\) | |||||||
\(758\) | −9.41084 | −0.341817 | ||||||||
\(759\) | −32.1067 | −1.16540 | ||||||||
\(760\) | 7.73949 | 0.280741 | ||||||||
\(761\) | 8.40161 | 0.304558 | 0.152279 | − | 0.988338i | \(-0.451339\pi\) | ||||
0.152279 | + | 0.988338i | \(0.451339\pi\) | |||||||
\(762\) | −16.9406 | −0.613692 | ||||||||
\(763\) | 55.1696 | 1.99728 | ||||||||
\(764\) | 24.2424 | 0.877060 | ||||||||
\(765\) | −27.3122 | −0.987473 | ||||||||
\(766\) | −23.1857 | −0.837734 | ||||||||
\(767\) | 8.07454 | 0.291555 | ||||||||
\(768\) | −2.51016 | −0.0905777 | ||||||||
\(769\) | −19.8721 | −0.716608 | −0.358304 | − | 0.933605i | \(-0.616645\pi\) | ||||
−0.358304 | + | 0.933605i | \(0.616645\pi\) | |||||||
\(770\) | −22.8006 | −0.821678 | ||||||||
\(771\) | −44.8540 | −1.61538 | ||||||||
\(772\) | 8.80361 | 0.316849 | ||||||||
\(773\) | −25.9813 | −0.934482 | −0.467241 | − | 0.884130i | \(-0.654752\pi\) | ||||
−0.467241 | + | 0.884130i | \(0.654752\pi\) | |||||||
\(774\) | −25.4860 | −0.916076 | ||||||||
\(775\) | 9.34985 | 0.335856 | ||||||||
\(776\) | 8.73748 | 0.313657 | ||||||||
\(777\) | 47.6458 | 1.70928 | ||||||||
\(778\) | −10.2703 | −0.368209 | ||||||||
\(779\) | −37.7052 | −1.35093 | ||||||||
\(780\) | −9.89923 | −0.354449 | ||||||||
\(781\) | −32.5019 | −1.16301 | ||||||||
\(782\) | 18.6582 | 0.667215 | ||||||||
\(783\) | −1.14188 | −0.0408073 | ||||||||
\(784\) | 9.15850 | 0.327089 | ||||||||
\(785\) | 21.9676 | 0.784059 | ||||||||
\(786\) | −38.7021 | −1.38046 | ||||||||
\(787\) | −6.96333 | −0.248216 | −0.124108 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124108 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(788\) | 22.5605 | 0.803684 | ||||||||
\(789\) | 14.5959 | 0.519627 | ||||||||
\(790\) | 0.995729 | 0.0354264 | ||||||||
\(791\) | 42.9253 | 1.52625 | ||||||||
\(792\) | −15.4242 | −0.548075 | ||||||||
\(793\) | 35.8063 | 1.27152 | ||||||||
\(794\) | −22.5607 | −0.800650 | ||||||||
\(795\) | 32.7110 | 1.16014 | ||||||||
\(796\) | −12.7595 | −0.452247 | ||||||||
\(797\) | 41.5681 | 1.47242 | 0.736209 | − | 0.676754i | \(-0.236614\pi\) | ||||
0.736209 | + | 0.676754i | \(0.236614\pi\) | |||||||
\(798\) | −64.3333 | −2.27737 | ||||||||
\(799\) | −88.2070 | −3.12054 | ||||||||
\(800\) | 3.52647 | 0.124680 | ||||||||
\(801\) | 6.70933 | 0.237063 | ||||||||
\(802\) | 0.914761 | 0.0323013 | ||||||||
\(803\) | 56.0029 | 1.97630 | ||||||||
\(804\) | 15.0381 | 0.530353 | ||||||||
\(805\) | 13.3569 | 0.470769 | ||||||||
\(806\) | 8.61359 | 0.303401 | ||||||||
\(807\) | −61.6300 | −2.16948 | ||||||||
\(808\) | −4.95801 | −0.174422 | ||||||||
\(809\) | 13.0635 | 0.459289 | 0.229644 | − | 0.973275i | \(-0.426244\pi\) | ||||
0.229644 | + | 0.973275i | \(0.426244\pi\) | |||||||
\(810\) | 9.71924 | 0.341499 | ||||||||
\(811\) | 14.6307 | 0.513752 | 0.256876 | − | 0.966444i | \(-0.417307\pi\) | ||||
0.256876 | + | 0.966444i | \(0.417307\pi\) | |||||||
\(812\) | 6.07673 | 0.213251 | ||||||||
\(813\) | −35.0471 | −1.22916 | ||||||||
\(814\) | 22.0643 | 0.773353 | ||||||||
\(815\) | 18.8103 | 0.658897 | ||||||||
\(816\) | 17.1098 | 0.598962 | ||||||||
\(817\) | −49.2267 | −1.72223 | ||||||||
\(818\) | −3.49032 | −0.122036 | ||||||||
\(819\) | 43.1078 | 1.50631 | ||||||||
\(820\) | 7.17871 | 0.250691 | ||||||||
\(821\) | −47.8079 | −1.66851 | −0.834254 | − | 0.551381i | \(-0.814101\pi\) | ||||
−0.834254 | + | 0.551381i | \(0.814101\pi\) | |||||||
\(822\) | −11.0277 | −0.384635 | ||||||||
\(823\) | 0.993723 | 0.0346390 | 0.0173195 | − | 0.999850i | \(-0.494487\pi\) | ||||
0.0173195 | + | 0.999850i | \(0.494487\pi\) | |||||||
\(824\) | −6.96802 | −0.242742 | ||||||||
\(825\) | 41.3628 | 1.44007 | ||||||||
\(826\) | −9.99075 | −0.347623 | ||||||||
\(827\) | 20.9711 | 0.729238 | 0.364619 | − | 0.931157i | \(-0.381199\pi\) | ||||
0.364619 | + | 0.931157i | \(0.381199\pi\) | |||||||
\(828\) | 9.03569 | 0.314012 | ||||||||
\(829\) | 42.3902 | 1.47227 | 0.736136 | − | 0.676834i | \(-0.236648\pi\) | ||||
0.736136 | + | 0.676834i | \(0.236648\pi\) | |||||||
\(830\) | −8.19455 | −0.284437 | ||||||||
\(831\) | 16.8655 | 0.585057 | ||||||||
\(832\) | 3.24878 | 0.112631 | ||||||||
\(833\) | −62.4262 | −2.16294 | ||||||||
\(834\) | −48.2312 | −1.67011 | ||||||||
\(835\) | 13.6833 | 0.473531 | ||||||||
\(836\) | −29.7921 | −1.03038 | ||||||||
\(837\) | 2.00269 | 0.0692230 | ||||||||
\(838\) | 10.2557 | 0.354277 | ||||||||
\(839\) | 5.84310 | 0.201726 | 0.100863 | − | 0.994900i | \(-0.467840\pi\) | ||||
0.100863 | + | 0.994900i | \(0.467840\pi\) | |||||||
\(840\) | 12.2485 | 0.422612 | ||||||||
\(841\) | −26.7147 | −0.921197 | ||||||||
\(842\) | −7.17374 | −0.247223 | ||||||||
\(843\) | 14.1346 | 0.486820 | ||||||||
\(844\) | −21.9026 | −0.753920 | ||||||||
\(845\) | −2.96847 | −0.102119 | ||||||||
\(846\) | −42.7165 | −1.46862 | ||||||||
\(847\) | 43.5505 | 1.49641 | ||||||||
\(848\) | −10.7353 | −0.368651 | ||||||||
\(849\) | 38.5927 | 1.32450 | ||||||||
\(850\) | −24.0371 | −0.824467 | ||||||||
\(851\) | −12.9256 | −0.443082 | ||||||||
\(852\) | 17.4599 | 0.598168 | ||||||||
\(853\) | 13.5369 | 0.463495 | 0.231748 | − | 0.972776i | \(-0.425556\pi\) | ||||
0.231748 | + | 0.972776i | \(0.425556\pi\) | |||||||
\(854\) | −44.3037 | −1.51604 | ||||||||
\(855\) | −25.5474 | −0.873704 | ||||||||
\(856\) | 7.43212 | 0.254025 | ||||||||
\(857\) | 0.00897015 | 0.000306414 0 | 0.000153207 | − | 1.00000i | \(-0.499951\pi\) | ||||
0.000153207 | 1.00000i | \(0.499951\pi\) | ||||||||
\(858\) | 38.1057 | 1.30091 | ||||||||
\(859\) | −53.3826 | −1.82139 | −0.910695 | − | 0.413080i | \(-0.864453\pi\) | ||||
−0.910695 | + | 0.413080i | \(0.864453\pi\) | |||||||
\(860\) | 9.37231 | 0.319593 | ||||||||
\(861\) | −59.6719 | −2.03361 | ||||||||
\(862\) | 25.5762 | 0.871130 | ||||||||
\(863\) | 33.9617 | 1.15607 | 0.578034 | − | 0.816013i | \(-0.303820\pi\) | ||||
0.578034 | + | 0.816013i | \(0.303820\pi\) | |||||||
\(864\) | 0.755352 | 0.0256976 | ||||||||
\(865\) | 1.34881 | 0.0458607 | ||||||||
\(866\) | −14.5028 | −0.492824 | ||||||||
\(867\) | −73.9509 | −2.51150 | ||||||||
\(868\) | −10.6577 | −0.361747 | ||||||||
\(869\) | −3.83292 | −0.130023 | ||||||||
\(870\) | 4.60628 | 0.156168 | ||||||||
\(871\) | −19.4631 | −0.659481 | ||||||||
\(872\) | −13.7246 | −0.464774 | ||||||||
\(873\) | −28.8417 | −0.976144 | ||||||||
\(874\) | 17.4526 | 0.590343 | ||||||||
\(875\) | −41.6053 | −1.40652 | ||||||||
\(876\) | −30.0846 | −1.01647 | ||||||||
\(877\) | −44.9270 | −1.51708 | −0.758538 | − | 0.651629i | \(-0.774086\pi\) | ||||
−0.758538 | + | 0.651629i | \(0.774086\pi\) | |||||||
\(878\) | 20.7583 | 0.700559 | ||||||||
\(879\) | 14.7352 | 0.497006 | ||||||||
\(880\) | 5.67214 | 0.191208 | ||||||||
\(881\) | 26.1150 | 0.879835 | 0.439918 | − | 0.898038i | \(-0.355008\pi\) | ||||
0.439918 | + | 0.898038i | \(0.355008\pi\) | |||||||
\(882\) | −30.2315 | −1.01795 | ||||||||
\(883\) | −0.528881 | −0.0177983 | −0.00889913 | − | 0.999960i | \(-0.502833\pi\) | ||||
−0.00889913 | + | 0.999960i | \(0.502833\pi\) | |||||||
\(884\) | −22.1443 | −0.744795 | ||||||||
\(885\) | −7.57318 | −0.254570 | ||||||||
\(886\) | 24.5702 | 0.825451 | ||||||||
\(887\) | −22.5205 | −0.756165 | −0.378083 | − | 0.925772i | \(-0.623416\pi\) | ||||
−0.378083 | + | 0.925772i | \(0.623416\pi\) | |||||||
\(888\) | −11.8529 | −0.397757 | ||||||||
\(889\) | −27.1285 | −0.909862 | ||||||||
\(890\) | −2.46731 | −0.0827044 | ||||||||
\(891\) | −37.4129 | −1.25338 | ||||||||
\(892\) | −16.3532 | −0.547547 | ||||||||
\(893\) | −82.5076 | −2.76101 | ||||||||
\(894\) | 33.1678 | 1.10930 | ||||||||
\(895\) | 11.1631 | 0.373143 | ||||||||
\(896\) | −4.01976 | −0.134291 | ||||||||
\(897\) | −22.3228 | −0.745337 | ||||||||
\(898\) | 37.6451 | 1.25623 | ||||||||
\(899\) | −4.00805 | −0.133676 | ||||||||
\(900\) | −11.6406 | −0.388020 | ||||||||
\(901\) | 73.1737 | 2.43777 | ||||||||
\(902\) | −27.6334 | −0.920093 | ||||||||
\(903\) | −77.9058 | −2.59254 | ||||||||
\(904\) | −10.6786 | −0.355164 | ||||||||
\(905\) | −21.8148 | −0.725149 | ||||||||
\(906\) | 53.6061 | 1.78094 | ||||||||
\(907\) | 9.43735 | 0.313362 | 0.156681 | − | 0.987649i | \(-0.449921\pi\) | ||||
0.156681 | + | 0.987649i | \(0.449921\pi\) | |||||||
\(908\) | 12.4998 | 0.414820 | ||||||||
\(909\) | 16.3660 | 0.542826 | ||||||||
\(910\) | −15.8526 | −0.525508 | ||||||||
\(911\) | 27.0224 | 0.895291 | 0.447646 | − | 0.894211i | \(-0.352263\pi\) | ||||
0.447646 | + | 0.894211i | \(0.352263\pi\) | |||||||
\(912\) | 16.0043 | 0.529954 | ||||||||
\(913\) | 31.5438 | 1.04395 | ||||||||
\(914\) | −7.18013 | −0.237497 | ||||||||
\(915\) | −33.5831 | −1.11022 | ||||||||
\(916\) | 18.2669 | 0.603556 | ||||||||
\(917\) | −61.9773 | −2.04667 | ||||||||
\(918\) | −5.14863 | −0.169930 | ||||||||
\(919\) | −49.0794 | −1.61898 | −0.809491 | − | 0.587133i | \(-0.800257\pi\) | ||||
−0.809491 | + | 0.587133i | \(0.800257\pi\) | |||||||
\(920\) | −3.32281 | −0.109550 | ||||||||
\(921\) | 30.2535 | 0.996887 | ||||||||
\(922\) | 30.2705 | 0.996905 | ||||||||
\(923\) | −22.5975 | −0.743807 | ||||||||
\(924\) | −47.1487 | −1.55108 | ||||||||
\(925\) | 16.6519 | 0.547510 | ||||||||
\(926\) | 28.2538 | 0.928478 | ||||||||
\(927\) | 23.0009 | 0.755447 | ||||||||
\(928\) | −1.51171 | −0.0496244 | ||||||||
\(929\) | 51.3861 | 1.68592 | 0.842962 | − | 0.537974i | \(-0.180810\pi\) | ||||
0.842962 | + | 0.537974i | \(0.180810\pi\) | |||||||
\(930\) | −8.07876 | −0.264913 | ||||||||
\(931\) | −58.3926 | −1.91374 | ||||||||
\(932\) | 11.4372 | 0.374639 | ||||||||
\(933\) | −73.7665 | −2.41501 | ||||||||
\(934\) | 8.30473 | 0.271739 | ||||||||
\(935\) | −38.6624 | −1.26440 | ||||||||
\(936\) | −10.7240 | −0.350523 | ||||||||
\(937\) | 37.4451 | 1.22328 | 0.611639 | − | 0.791137i | \(-0.290511\pi\) | ||||
0.611639 | + | 0.791137i | \(0.290511\pi\) | |||||||
\(938\) | 24.0820 | 0.786304 | ||||||||
\(939\) | 4.86373 | 0.158722 | ||||||||
\(940\) | 15.7087 | 0.512361 | ||||||||
\(941\) | −6.20414 | −0.202249 | −0.101125 | − | 0.994874i | \(-0.532244\pi\) | ||||
−0.101125 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(942\) | 45.4262 | 1.48006 | ||||||||
\(943\) | 16.1880 | 0.527155 | ||||||||
\(944\) | 2.48541 | 0.0808931 | ||||||||
\(945\) | −3.68578 | −0.119898 | ||||||||
\(946\) | −36.0774 | −1.17298 | ||||||||
\(947\) | −19.2298 | −0.624885 | −0.312442 | − | 0.949937i | \(-0.601147\pi\) | ||||
−0.312442 | + | 0.949937i | \(0.601147\pi\) | |||||||
\(948\) | 2.05904 | 0.0668744 | ||||||||
\(949\) | 38.9371 | 1.26395 | ||||||||
\(950\) | −22.4840 | −0.729478 | ||||||||
\(951\) | −37.3216 | −1.21023 | ||||||||
\(952\) | 27.3995 | 0.888023 | ||||||||
\(953\) | −13.7065 | −0.443997 | −0.221998 | − | 0.975047i | \(-0.571258\pi\) | ||||
−0.221998 | + | 0.975047i | \(0.571258\pi\) | |||||||
\(954\) | 35.4362 | 1.14729 | ||||||||
\(955\) | 29.4276 | 0.952256 | ||||||||
\(956\) | −9.03889 | −0.292339 | ||||||||
\(957\) | −17.7312 | −0.573170 | ||||||||
\(958\) | 22.1687 | 0.716238 | ||||||||
\(959\) | −17.6597 | −0.570262 | ||||||||
\(960\) | −3.04706 | −0.0983434 | ||||||||
\(961\) | −23.9704 | −0.773240 | ||||||||
\(962\) | 15.3406 | 0.494601 | ||||||||
\(963\) | −24.5328 | −0.790559 | ||||||||
\(964\) | −13.9464 | −0.449184 | ||||||||
\(965\) | 10.6866 | 0.344014 | ||||||||
\(966\) | 27.6203 | 0.888670 | ||||||||
\(967\) | −15.8001 | −0.508098 | −0.254049 | − | 0.967191i | \(-0.581762\pi\) | ||||
−0.254049 | + | 0.967191i | \(0.581762\pi\) | |||||||
\(968\) | −10.8341 | −0.348221 | ||||||||
\(969\) | −109.088 | −3.50442 | ||||||||
\(970\) | 10.6063 | 0.340549 | ||||||||
\(971\) | 51.7045 | 1.65928 | 0.829638 | − | 0.558302i | \(-0.188547\pi\) | ||||
0.829638 | + | 0.558302i | \(0.188547\pi\) | |||||||
\(972\) | 22.3642 | 0.717331 | ||||||||
\(973\) | −77.2373 | −2.47611 | ||||||||
\(974\) | 28.0909 | 0.900091 | ||||||||
\(975\) | 28.7583 | 0.921002 | ||||||||
\(976\) | 11.0215 | 0.352789 | ||||||||
\(977\) | −58.0074 | −1.85582 | −0.927911 | − | 0.372802i | \(-0.878397\pi\) | ||||
−0.927911 | + | 0.372802i | \(0.878397\pi\) | |||||||
\(978\) | 38.8973 | 1.24380 | ||||||||
\(979\) | 9.49757 | 0.303544 | ||||||||
\(980\) | 11.1174 | 0.355132 | ||||||||
\(981\) | 45.3038 | 1.44644 | ||||||||
\(982\) | −12.7026 | −0.405355 | ||||||||
\(983\) | −15.8172 | −0.504490 | −0.252245 | − | 0.967663i | \(-0.581169\pi\) | ||||
−0.252245 | + | 0.967663i | \(0.581169\pi\) | |||||||
\(984\) | 14.8446 | 0.473229 | ||||||||
\(985\) | 27.3859 | 0.872589 | ||||||||
\(986\) | 10.3041 | 0.328151 | ||||||||
\(987\) | −130.576 | −4.15628 | ||||||||
\(988\) | −20.7135 | −0.658985 | ||||||||
\(989\) | 21.1346 | 0.672041 | ||||||||
\(990\) | −18.7233 | −0.595064 | ||||||||
\(991\) | 18.7579 | 0.595865 | 0.297932 | − | 0.954587i | \(-0.403703\pi\) | ||||
0.297932 | + | 0.954587i | \(0.403703\pi\) | |||||||
\(992\) | 2.65133 | 0.0841798 | ||||||||
\(993\) | −13.6712 | −0.433843 | ||||||||
\(994\) | 27.9603 | 0.886846 | ||||||||
\(995\) | −15.4886 | −0.491021 | ||||||||
\(996\) | −16.9452 | −0.536931 | ||||||||
\(997\) | −13.3493 | −0.422777 | −0.211389 | − | 0.977402i | \(-0.567799\pi\) | ||||
−0.211389 | + | 0.977402i | \(0.567799\pi\) | |||||||
\(998\) | −41.7976 | −1.32308 | ||||||||
\(999\) | 3.56674 | 0.112847 |
(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 | 6022.2.a.c.1.9 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.c.1.9 | ✓ | 61 | 1.1 | even | 1 | trivial |