Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55462 | −1.80639 | −0.903196 | − | 0.429228i | \(-0.858786\pi\) | ||||
−0.903196 | + | 0.429228i | \(0.858786\pi\) | |||||||
\(3\) | 2.40673 | 1.38952 | 0.694762 | − | 0.719239i | \(-0.255510\pi\) | ||||
0.694762 | + | 0.719239i | \(0.255510\pi\) | |||||||
\(4\) | 4.52611 | 2.26305 | ||||||||
\(5\) | 3.51168 | 1.57047 | 0.785236 | − | 0.619196i | \(-0.212542\pi\) | ||||
0.785236 | + | 0.619196i | \(0.212542\pi\) | |||||||
\(6\) | −6.14829 | −2.51003 | ||||||||
\(7\) | 3.52515 | 1.33238 | 0.666191 | − | 0.745781i | \(-0.267923\pi\) | ||||
0.666191 | + | 0.745781i | \(0.267923\pi\) | |||||||
\(8\) | −6.45325 | −2.28157 | ||||||||
\(9\) | 2.79234 | 0.930779 | ||||||||
\(10\) | −8.97103 | −2.83689 | ||||||||
\(11\) | −5.09895 | −1.53739 | −0.768696 | − | 0.639615i | \(-0.779094\pi\) | ||||
−0.768696 | + | 0.639615i | \(0.779094\pi\) | |||||||
\(12\) | 10.8931 | 3.14457 | ||||||||
\(13\) | −0.353446 | −0.0980281 | −0.0490141 | − | 0.998798i | \(-0.515608\pi\) | ||||
−0.0490141 | + | 0.998798i | \(0.515608\pi\) | |||||||
\(14\) | −9.00544 | −2.40681 | ||||||||
\(15\) | 8.45166 | 2.18221 | ||||||||
\(16\) | 7.43343 | 1.85836 | ||||||||
\(17\) | 1.22514 | 0.297141 | 0.148571 | − | 0.988902i | \(-0.452533\pi\) | ||||
0.148571 | + | 0.988902i | \(0.452533\pi\) | |||||||
\(18\) | −7.13338 | −1.68135 | ||||||||
\(19\) | 0.445154 | 0.102125 | 0.0510627 | − | 0.998695i | \(-0.483739\pi\) | ||||
0.0510627 | + | 0.998695i | \(0.483739\pi\) | |||||||
\(20\) | 15.8942 | 3.55406 | ||||||||
\(21\) | 8.48408 | 1.85138 | ||||||||
\(22\) | 13.0259 | 2.77713 | ||||||||
\(23\) | 9.35822 | 1.95132 | 0.975662 | − | 0.219280i | \(-0.0703710\pi\) | ||||
0.975662 | + | 0.219280i | \(0.0703710\pi\) | |||||||
\(24\) | −15.5312 | −3.17030 | ||||||||
\(25\) | 7.33191 | 1.46638 | ||||||||
\(26\) | 0.902921 | 0.177077 | ||||||||
\(27\) | −0.499785 | −0.0961838 | ||||||||
\(28\) | 15.9552 | 3.01525 | ||||||||
\(29\) | −6.41904 | −1.19199 | −0.595993 | − | 0.802990i | \(-0.703241\pi\) | ||||
−0.595993 | + | 0.802990i | \(0.703241\pi\) | |||||||
\(30\) | −21.5908 | −3.94193 | ||||||||
\(31\) | 4.59805 | 0.825834 | 0.412917 | − | 0.910769i | \(-0.364510\pi\) | ||||
0.412917 | + | 0.910769i | \(0.364510\pi\) | |||||||
\(32\) | −6.08311 | −1.07535 | ||||||||
\(33\) | −12.2718 | −2.13624 | ||||||||
\(34\) | −3.12979 | −0.536754 | ||||||||
\(35\) | 12.3792 | 2.09247 | ||||||||
\(36\) | 12.6384 | 2.10640 | ||||||||
\(37\) | −0.0828449 | −0.0136196 | −0.00680981 | − | 0.999977i | \(-0.502168\pi\) | ||||
−0.00680981 | + | 0.999977i | \(0.502168\pi\) | |||||||
\(38\) | −1.13720 | −0.184478 | ||||||||
\(39\) | −0.850647 | −0.136213 | ||||||||
\(40\) | −22.6618 | −3.58314 | ||||||||
\(41\) | 4.27416 | 0.667512 | 0.333756 | − | 0.942660i | \(-0.391684\pi\) | ||||
0.333756 | + | 0.942660i | \(0.391684\pi\) | |||||||
\(42\) | −21.6736 | −3.34432 | ||||||||
\(43\) | −9.28723 | −1.41629 | −0.708144 | − | 0.706068i | \(-0.750467\pi\) | ||||
−0.708144 | + | 0.706068i | \(0.750467\pi\) | |||||||
\(44\) | −23.0784 | −3.47920 | ||||||||
\(45\) | 9.80581 | 1.46176 | ||||||||
\(46\) | −23.9067 | −3.52486 | ||||||||
\(47\) | 2.53171 | 0.369288 | 0.184644 | − | 0.982805i | \(-0.440887\pi\) | ||||
0.184644 | + | 0.982805i | \(0.440887\pi\) | |||||||
\(48\) | 17.8902 | 2.58223 | ||||||||
\(49\) | 5.42670 | 0.775243 | ||||||||
\(50\) | −18.7303 | −2.64886 | ||||||||
\(51\) | 2.94859 | 0.412885 | ||||||||
\(52\) | −1.59973 | −0.221843 | ||||||||
\(53\) | −1.29833 | −0.178339 | −0.0891694 | − | 0.996016i | \(-0.528421\pi\) | ||||
−0.0891694 | + | 0.996016i | \(0.528421\pi\) | |||||||
\(54\) | 1.27676 | 0.173746 | ||||||||
\(55\) | −17.9059 | −2.41443 | ||||||||
\(56\) | −22.7487 | −3.03992 | ||||||||
\(57\) | 1.07136 | 0.141906 | ||||||||
\(58\) | 16.3982 | 2.15319 | ||||||||
\(59\) | −7.77128 | −1.01173 | −0.505867 | − | 0.862611i | \(-0.668828\pi\) | ||||
−0.505867 | + | 0.862611i | \(0.668828\pi\) | |||||||
\(60\) | 38.2531 | 4.93846 | ||||||||
\(61\) | 7.07624 | 0.906020 | 0.453010 | − | 0.891505i | \(-0.350350\pi\) | ||||
0.453010 | + | 0.891505i | \(0.350350\pi\) | |||||||
\(62\) | −11.7463 | −1.49178 | ||||||||
\(63\) | 9.84342 | 1.24015 | ||||||||
\(64\) | 0.673206 | 0.0841507 | ||||||||
\(65\) | −1.24119 | −0.153950 | ||||||||
\(66\) | 31.3498 | 3.85889 | ||||||||
\(67\) | 15.5801 | 1.90341 | 0.951704 | − | 0.307017i | \(-0.0993310\pi\) | ||||
0.951704 | + | 0.307017i | \(0.0993310\pi\) | |||||||
\(68\) | 5.54514 | 0.672447 | ||||||||
\(69\) | 22.5227 | 2.71141 | ||||||||
\(70\) | −31.6243 | −3.77982 | ||||||||
\(71\) | 6.33364 | 0.751665 | 0.375832 | − | 0.926688i | \(-0.377357\pi\) | ||||
0.375832 | + | 0.926688i | \(0.377357\pi\) | |||||||
\(72\) | −18.0197 | −2.12364 | ||||||||
\(73\) | 12.7305 | 1.49000 | 0.744999 | − | 0.667066i | \(-0.232450\pi\) | ||||
0.744999 | + | 0.667066i | \(0.232450\pi\) | |||||||
\(74\) | 0.211638 | 0.0246024 | ||||||||
\(75\) | 17.6459 | 2.03758 | ||||||||
\(76\) | 2.01482 | 0.231115 | ||||||||
\(77\) | −17.9746 | −2.04839 | ||||||||
\(78\) | 2.17308 | 0.246053 | ||||||||
\(79\) | −0.799467 | −0.0899471 | −0.0449736 | − | 0.998988i | \(-0.514320\pi\) | ||||
−0.0449736 | + | 0.998988i | \(0.514320\pi\) | |||||||
\(80\) | 26.1038 | 2.91850 | ||||||||
\(81\) | −9.57986 | −1.06443 | ||||||||
\(82\) | −10.9189 | −1.20579 | ||||||||
\(83\) | 2.66341 | 0.292347 | 0.146174 | − | 0.989259i | \(-0.453304\pi\) | ||||
0.146174 | + | 0.989259i | \(0.453304\pi\) | |||||||
\(84\) | 38.3999 | 4.18977 | ||||||||
\(85\) | 4.30232 | 0.466652 | ||||||||
\(86\) | 23.7254 | 2.55837 | ||||||||
\(87\) | −15.4489 | −1.65629 | ||||||||
\(88\) | 32.9048 | 3.50767 | ||||||||
\(89\) | −12.6340 | −1.33920 | −0.669599 | − | 0.742723i | \(-0.733534\pi\) | ||||
−0.669599 | + | 0.742723i | \(0.733534\pi\) | |||||||
\(90\) | −25.0502 | −2.64052 | ||||||||
\(91\) | −1.24595 | −0.130611 | ||||||||
\(92\) | 42.3563 | 4.41595 | ||||||||
\(93\) | 11.0663 | 1.14752 | ||||||||
\(94\) | −6.46758 | −0.667080 | ||||||||
\(95\) | 1.56324 | 0.160385 | ||||||||
\(96\) | −14.6404 | −1.49423 | ||||||||
\(97\) | 7.86963 | 0.799040 | 0.399520 | − | 0.916725i | \(-0.369177\pi\) | ||||
0.399520 | + | 0.916725i | \(0.369177\pi\) | |||||||
\(98\) | −13.8632 | −1.40039 | ||||||||
\(99\) | −14.2380 | −1.43097 | ||||||||
\(100\) | 33.1850 | 3.31850 | ||||||||
\(101\) | −11.6404 | −1.15827 | −0.579133 | − | 0.815233i | \(-0.696609\pi\) | ||||
−0.579133 | + | 0.815233i | \(0.696609\pi\) | |||||||
\(102\) | −7.53254 | −0.745833 | ||||||||
\(103\) | 15.0025 | 1.47824 | 0.739119 | − | 0.673575i | \(-0.235242\pi\) | ||||
0.739119 | + | 0.673575i | \(0.235242\pi\) | |||||||
\(104\) | 2.28087 | 0.223658 | ||||||||
\(105\) | 29.7934 | 2.90754 | ||||||||
\(106\) | 3.31674 | 0.322150 | ||||||||
\(107\) | −9.94886 | −0.961792 | −0.480896 | − | 0.876778i | \(-0.659689\pi\) | ||||
−0.480896 | + | 0.876778i | \(0.659689\pi\) | |||||||
\(108\) | −2.26208 | −0.217669 | ||||||||
\(109\) | 11.2873 | 1.08113 | 0.540563 | − | 0.841304i | \(-0.318211\pi\) | ||||
0.540563 | + | 0.841304i | \(0.318211\pi\) | |||||||
\(110\) | 45.7428 | 4.36141 | ||||||||
\(111\) | −0.199385 | −0.0189248 | ||||||||
\(112\) | 26.2040 | 2.47604 | ||||||||
\(113\) | 14.6614 | 1.37923 | 0.689615 | − | 0.724176i | \(-0.257780\pi\) | ||||
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(114\) | −2.73693 | −0.256337 | ||||||||
\(115\) | 32.8631 | 3.06450 | ||||||||
\(116\) | −29.0533 | −2.69753 | ||||||||
\(117\) | −0.986939 | −0.0912426 | ||||||||
\(118\) | 19.8527 | 1.82759 | ||||||||
\(119\) | 4.31882 | 0.395906 | ||||||||
\(120\) | −54.5407 | −4.97886 | ||||||||
\(121\) | 14.9993 | 1.36357 | ||||||||
\(122\) | −18.0771 | −1.63663 | ||||||||
\(123\) | 10.2867 | 0.927524 | ||||||||
\(124\) | 20.8113 | 1.86891 | ||||||||
\(125\) | 8.18894 | 0.732441 | ||||||||
\(126\) | −25.1462 | −2.24021 | ||||||||
\(127\) | 0.785559 | 0.0697070 | 0.0348535 | − | 0.999392i | \(-0.488904\pi\) | ||||
0.0348535 | + | 0.999392i | \(0.488904\pi\) | |||||||
\(128\) | 10.4464 | 0.923343 | ||||||||
\(129\) | −22.3518 | −1.96797 | ||||||||
\(130\) | 3.17077 | 0.278095 | ||||||||
\(131\) | −8.11721 | −0.709204 | −0.354602 | − | 0.935017i | \(-0.615384\pi\) | ||||
−0.354602 | + | 0.935017i | \(0.615384\pi\) | |||||||
\(132\) | −55.5434 | −4.83443 | ||||||||
\(133\) | 1.56924 | 0.136070 | ||||||||
\(134\) | −39.8012 | −3.43830 | ||||||||
\(135\) | −1.75509 | −0.151054 | ||||||||
\(136\) | −7.90617 | −0.677949 | ||||||||
\(137\) | 5.38620 | 0.460174 | 0.230087 | − | 0.973170i | \(-0.426099\pi\) | ||||
0.230087 | + | 0.973170i | \(0.426099\pi\) | |||||||
\(138\) | −57.5370 | −4.89788 | ||||||||
\(139\) | −5.75940 | −0.488506 | −0.244253 | − | 0.969712i | \(-0.578543\pi\) | ||||
−0.244253 | + | 0.969712i | \(0.578543\pi\) | |||||||
\(140\) | 56.0297 | 4.73537 | ||||||||
\(141\) | 6.09314 | 0.513135 | ||||||||
\(142\) | −16.1801 | −1.35780 | ||||||||
\(143\) | 1.80220 | 0.150708 | ||||||||
\(144\) | 20.7566 | 1.72972 | ||||||||
\(145\) | −22.5416 | −1.87198 | ||||||||
\(146\) | −32.5218 | −2.69152 | ||||||||
\(147\) | 13.0606 | 1.07722 | ||||||||
\(148\) | −0.374965 | −0.0308219 | ||||||||
\(149\) | −16.8085 | −1.37701 | −0.688503 | − | 0.725234i | \(-0.741732\pi\) | ||||
−0.688503 | + | 0.725234i | \(0.741732\pi\) | |||||||
\(150\) | −45.0787 | −3.68066 | ||||||||
\(151\) | −2.73254 | −0.222371 | −0.111186 | − | 0.993800i | \(-0.535465\pi\) | ||||
−0.111186 | + | 0.993800i | \(0.535465\pi\) | |||||||
\(152\) | −2.87269 | −0.233006 | ||||||||
\(153\) | 3.42102 | 0.276573 | ||||||||
\(154\) | 45.9183 | 3.70020 | ||||||||
\(155\) | 16.1469 | 1.29695 | ||||||||
\(156\) | −3.85012 | −0.308256 | ||||||||
\(157\) | 6.77702 | 0.540865 | 0.270433 | − | 0.962739i | \(-0.412833\pi\) | ||||
0.270433 | + | 0.962739i | \(0.412833\pi\) | |||||||
\(158\) | 2.04234 | 0.162480 | ||||||||
\(159\) | −3.12472 | −0.247806 | ||||||||
\(160\) | −21.3620 | −1.68881 | ||||||||
\(161\) | 32.9892 | 2.59991 | ||||||||
\(162\) | 24.4730 | 1.92278 | ||||||||
\(163\) | −15.2624 | −1.19544 | −0.597720 | − | 0.801705i | \(-0.703927\pi\) | ||||
−0.597720 | + | 0.801705i | \(0.703927\pi\) | |||||||
\(164\) | 19.3453 | 1.51061 | ||||||||
\(165\) | −43.0946 | −3.35491 | ||||||||
\(166\) | −6.80402 | −0.528094 | ||||||||
\(167\) | 13.2940 | 1.02872 | 0.514360 | − | 0.857574i | \(-0.328029\pi\) | ||||
0.514360 | + | 0.857574i | \(0.328029\pi\) | |||||||
\(168\) | −54.7499 | −4.22405 | ||||||||
\(169\) | −12.8751 | −0.990390 | ||||||||
\(170\) | −10.9908 | −0.842957 | ||||||||
\(171\) | 1.24302 | 0.0950562 | ||||||||
\(172\) | −42.0350 | −3.20514 | ||||||||
\(173\) | 5.89000 | 0.447808 | 0.223904 | − | 0.974611i | \(-0.428120\pi\) | ||||
0.223904 | + | 0.974611i | \(0.428120\pi\) | |||||||
\(174\) | 39.4661 | 2.99192 | ||||||||
\(175\) | 25.8461 | 1.95378 | ||||||||
\(176\) | −37.9027 | −2.85702 | ||||||||
\(177\) | −18.7034 | −1.40583 | ||||||||
\(178\) | 32.2750 | 2.41912 | ||||||||
\(179\) | 13.4178 | 1.00290 | 0.501448 | − | 0.865188i | \(-0.332801\pi\) | ||||
0.501448 | + | 0.865188i | \(0.332801\pi\) | |||||||
\(180\) | 44.3821 | 3.30805 | ||||||||
\(181\) | 12.2281 | 0.908908 | 0.454454 | − | 0.890770i | \(-0.349834\pi\) | ||||
0.454454 | + | 0.890770i | \(0.349834\pi\) | |||||||
\(182\) | 3.18293 | 0.235935 | ||||||||
\(183\) | 17.0306 | 1.25894 | ||||||||
\(184\) | −60.3910 | −4.45208 | ||||||||
\(185\) | −0.290925 | −0.0213892 | ||||||||
\(186\) | −28.2701 | −2.07287 | ||||||||
\(187\) | −6.24695 | −0.456822 | ||||||||
\(188\) | 11.4588 | 0.835719 | ||||||||
\(189\) | −1.76182 | −0.128154 | ||||||||
\(190\) | −3.99349 | −0.289718 | ||||||||
\(191\) | −25.3620 | −1.83513 | −0.917565 | − | 0.397585i | \(-0.869848\pi\) | ||||
−0.917565 | + | 0.397585i | \(0.869848\pi\) | |||||||
\(192\) | 1.62022 | 0.116930 | ||||||||
\(193\) | −15.3996 | −1.10849 | −0.554244 | − | 0.832354i | \(-0.686993\pi\) | ||||
−0.554244 | + | 0.832354i | \(0.686993\pi\) | |||||||
\(194\) | −20.1039 | −1.44338 | ||||||||
\(195\) | −2.98720 | −0.213918 | ||||||||
\(196\) | 24.5618 | 1.75442 | ||||||||
\(197\) | 21.6149 | 1.54000 | 0.769998 | − | 0.638046i | \(-0.220257\pi\) | ||||
0.769998 | + | 0.638046i | \(0.220257\pi\) | |||||||
\(198\) | 36.3727 | 2.58490 | ||||||||
\(199\) | 0.935357 | 0.0663057 | 0.0331529 | − | 0.999450i | \(-0.489445\pi\) | ||||
0.0331529 | + | 0.999450i | \(0.489445\pi\) | |||||||
\(200\) | −47.3147 | −3.34565 | ||||||||
\(201\) | 37.4970 | 2.64483 | ||||||||
\(202\) | 29.7369 | 2.09228 | ||||||||
\(203\) | −22.6281 | −1.58818 | ||||||||
\(204\) | 13.3456 | 0.934381 | ||||||||
\(205\) | 15.0095 | 1.04831 | ||||||||
\(206\) | −38.3257 | −2.67028 | ||||||||
\(207\) | 26.1313 | 1.81625 | ||||||||
\(208\) | −2.62731 | −0.182171 | ||||||||
\(209\) | −2.26982 | −0.157007 | ||||||||
\(210\) | −76.1110 | −5.25216 | ||||||||
\(211\) | 19.6612 | 1.35353 | 0.676765 | − | 0.736199i | \(-0.263381\pi\) | ||||
0.676765 | + | 0.736199i | \(0.263381\pi\) | |||||||
\(212\) | −5.87636 | −0.403590 | ||||||||
\(213\) | 15.2433 | 1.04446 | ||||||||
\(214\) | 25.4156 | 1.73737 | ||||||||
\(215\) | −32.6138 | −2.22424 | ||||||||
\(216\) | 3.22524 | 0.219450 | ||||||||
\(217\) | 16.2088 | 1.10033 | ||||||||
\(218\) | −28.8348 | −1.95294 | ||||||||
\(219\) | 30.6390 | 2.07039 | ||||||||
\(220\) | −81.0440 | −5.46398 | ||||||||
\(221\) | −0.433022 | −0.0291282 | ||||||||
\(222\) | 0.509354 | 0.0341856 | ||||||||
\(223\) | −10.0202 | −0.671004 | −0.335502 | − | 0.942040i | \(-0.608906\pi\) | ||||
−0.335502 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(224\) | −21.4439 | −1.43278 | ||||||||
\(225\) | 20.4732 | 1.36488 | ||||||||
\(226\) | −37.4544 | −2.49143 | ||||||||
\(227\) | −6.75105 | −0.448083 | −0.224041 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224041 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(228\) | 4.84911 | 0.321140 | ||||||||
\(229\) | 14.7685 | 0.975932 | 0.487966 | − | 0.872863i | \(-0.337739\pi\) | ||||
0.487966 | + | 0.872863i | \(0.337739\pi\) | |||||||
\(230\) | −83.9529 | −5.53569 | ||||||||
\(231\) | −43.2599 | −2.84629 | ||||||||
\(232\) | 41.4237 | 2.71960 | ||||||||
\(233\) | 9.02909 | 0.591515 | 0.295758 | − | 0.955263i | \(-0.404428\pi\) | ||||
0.295758 | + | 0.955263i | \(0.404428\pi\) | |||||||
\(234\) | 2.52126 | 0.164820 | ||||||||
\(235\) | 8.89057 | 0.579957 | ||||||||
\(236\) | −35.1737 | −2.28961 | ||||||||
\(237\) | −1.92410 | −0.124984 | ||||||||
\(238\) | −11.0330 | −0.715161 | ||||||||
\(239\) | −7.53759 | −0.487566 | −0.243783 | − | 0.969830i | \(-0.578388\pi\) | ||||
−0.243783 | + | 0.969830i | \(0.578388\pi\) | |||||||
\(240\) | 62.8248 | 4.05533 | ||||||||
\(241\) | −0.590570 | −0.0380419 | −0.0190210 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190210 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(242\) | −38.3176 | −2.46315 | ||||||||
\(243\) | −21.5568 | −1.38287 | ||||||||
\(244\) | 32.0278 | 2.05037 | ||||||||
\(245\) | 19.0569 | 1.21750 | ||||||||
\(246\) | −26.2788 | −1.67547 | ||||||||
\(247\) | −0.157338 | −0.0100112 | ||||||||
\(248\) | −29.6724 | −1.88420 | ||||||||
\(249\) | 6.41011 | 0.406224 | ||||||||
\(250\) | −20.9197 | −1.32308 | ||||||||
\(251\) | 5.33818 | 0.336943 | 0.168471 | − | 0.985707i | \(-0.446117\pi\) | ||||
0.168471 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(252\) | 44.5524 | 2.80654 | ||||||||
\(253\) | −47.7171 | −2.99995 | ||||||||
\(254\) | −2.00681 | −0.125918 | ||||||||
\(255\) | 10.3545 | 0.648425 | ||||||||
\(256\) | −28.0331 | −1.75207 | ||||||||
\(257\) | 14.8048 | 0.923496 | 0.461748 | − | 0.887011i | \(-0.347222\pi\) | ||||
0.461748 | + | 0.887011i | \(0.347222\pi\) | |||||||
\(258\) | 57.1005 | 3.55492 | ||||||||
\(259\) | −0.292041 | −0.0181465 | ||||||||
\(260\) | −5.61775 | −0.348398 | ||||||||
\(261\) | −17.9241 | −1.10948 | ||||||||
\(262\) | 20.7364 | 1.28110 | ||||||||
\(263\) | −9.17985 | −0.566054 | −0.283027 | − | 0.959112i | \(-0.591339\pi\) | ||||
−0.283027 | + | 0.959112i | \(0.591339\pi\) | |||||||
\(264\) | 79.1929 | 4.87399 | ||||||||
\(265\) | −4.55931 | −0.280076 | ||||||||
\(266\) | −4.00881 | −0.245796 | ||||||||
\(267\) | −30.4065 | −1.86085 | ||||||||
\(268\) | 70.5170 | 4.30751 | ||||||||
\(269\) | −21.5102 | −1.31150 | −0.655751 | − | 0.754977i | \(-0.727648\pi\) | ||||
−0.655751 | + | 0.754977i | \(0.727648\pi\) | |||||||
\(270\) | 4.48359 | 0.272863 | ||||||||
\(271\) | −30.7485 | −1.86784 | −0.933920 | − | 0.357481i | \(-0.883636\pi\) | ||||
−0.933920 | + | 0.357481i | \(0.883636\pi\) | |||||||
\(272\) | 9.10703 | 0.552195 | ||||||||
\(273\) | −2.99866 | −0.181487 | ||||||||
\(274\) | −13.7597 | −0.831255 | ||||||||
\(275\) | −37.3851 | −2.25440 | ||||||||
\(276\) | 101.940 | 6.13607 | ||||||||
\(277\) | −0.316138 | −0.0189949 | −0.00949745 | − | 0.999955i | \(-0.503023\pi\) | ||||
−0.00949745 | + | 0.999955i | \(0.503023\pi\) | |||||||
\(278\) | 14.7131 | 0.882434 | ||||||||
\(279\) | 12.8393 | 0.768669 | ||||||||
\(280\) | −79.8862 | −4.77412 | ||||||||
\(281\) | −24.1824 | −1.44260 | −0.721302 | − | 0.692621i | \(-0.756456\pi\) | ||||
−0.721302 | + | 0.692621i | \(0.756456\pi\) | |||||||
\(282\) | −15.5657 | −0.926924 | ||||||||
\(283\) | 14.5123 | 0.862666 | 0.431333 | − | 0.902193i | \(-0.358043\pi\) | ||||
0.431333 | + | 0.902193i | \(0.358043\pi\) | |||||||
\(284\) | 28.6667 | 1.70106 | ||||||||
\(285\) | 3.76229 | 0.222859 | ||||||||
\(286\) | −4.60395 | −0.272237 | ||||||||
\(287\) | 15.0671 | 0.889381 | ||||||||
\(288\) | −16.9861 | −1.00092 | ||||||||
\(289\) | −15.4990 | −0.911707 | ||||||||
\(290\) | 57.5854 | 3.38153 | ||||||||
\(291\) | 18.9401 | 1.11029 | ||||||||
\(292\) | 57.6198 | 3.37194 | ||||||||
\(293\) | −12.8933 | −0.753232 | −0.376616 | − | 0.926369i | \(-0.622912\pi\) | ||||
−0.376616 | + | 0.926369i | \(0.622912\pi\) | |||||||
\(294\) | −33.3649 | −1.94588 | ||||||||
\(295\) | −27.2903 | −1.58890 | ||||||||
\(296\) | 0.534619 | 0.0310741 | ||||||||
\(297\) | 2.54838 | 0.147872 | ||||||||
\(298\) | 42.9394 | 2.48741 | ||||||||
\(299\) | −3.30762 | −0.191285 | ||||||||
\(300\) | 79.8673 | 4.61114 | ||||||||
\(301\) | −32.7389 | −1.88704 | ||||||||
\(302\) | 6.98062 | 0.401690 | ||||||||
\(303\) | −28.0153 | −1.60944 | ||||||||
\(304\) | 3.30902 | 0.189785 | ||||||||
\(305\) | 24.8495 | 1.42288 | ||||||||
\(306\) | −8.73942 | −0.499599 | ||||||||
\(307\) | −26.2910 | −1.50050 | −0.750252 | − | 0.661151i | \(-0.770068\pi\) | ||||
−0.750252 | + | 0.661151i | \(0.770068\pi\) | |||||||
\(308\) | −81.3549 | −4.63562 | ||||||||
\(309\) | 36.1069 | 2.05405 | ||||||||
\(310\) | −41.2492 | −2.34280 | ||||||||
\(311\) | −35.0596 | −1.98805 | −0.994024 | − | 0.109159i | \(-0.965184\pi\) | ||||
−0.994024 | + | 0.109159i | \(0.965184\pi\) | |||||||
\(312\) | 5.48944 | 0.310778 | ||||||||
\(313\) | 2.41352 | 0.136420 | 0.0682102 | − | 0.997671i | \(-0.478271\pi\) | ||||
0.0682102 | + | 0.997671i | \(0.478271\pi\) | |||||||
\(314\) | −17.3127 | −0.977015 | ||||||||
\(315\) | 34.5670 | 1.94763 | ||||||||
\(316\) | −3.61847 | −0.203555 | ||||||||
\(317\) | −17.0471 | −0.957460 | −0.478730 | − | 0.877962i | \(-0.658903\pi\) | ||||
−0.478730 | + | 0.877962i | \(0.658903\pi\) | |||||||
\(318\) | 7.98248 | 0.447635 | ||||||||
\(319\) | 32.7304 | 1.83255 | ||||||||
\(320\) | 2.36409 | 0.132156 | ||||||||
\(321\) | −23.9442 | −1.33643 | ||||||||
\(322\) | −84.2749 | −4.69646 | ||||||||
\(323\) | 0.545378 | 0.0303457 | ||||||||
\(324\) | −43.3595 | −2.40886 | ||||||||
\(325\) | −2.59143 | −0.143747 | ||||||||
\(326\) | 38.9896 | 2.15943 | ||||||||
\(327\) | 27.1654 | 1.50225 | ||||||||
\(328\) | −27.5822 | −1.52297 | ||||||||
\(329\) | 8.92468 | 0.492033 | ||||||||
\(330\) | 110.091 | 6.06029 | ||||||||
\(331\) | −2.47954 | −0.136288 | −0.0681440 | − | 0.997675i | \(-0.521708\pi\) | ||||
−0.0681440 | + | 0.997675i | \(0.521708\pi\) | |||||||
\(332\) | 12.0549 | 0.661598 | ||||||||
\(333\) | −0.231331 | −0.0126769 | ||||||||
\(334\) | −33.9612 | −1.85827 | ||||||||
\(335\) | 54.7122 | 2.98925 | ||||||||
\(336\) | 63.0658 | 3.44052 | ||||||||
\(337\) | 22.4278 | 1.22172 | 0.610861 | − | 0.791738i | \(-0.290823\pi\) | ||||
0.610861 | + | 0.791738i | \(0.290823\pi\) | |||||||
\(338\) | 32.8910 | 1.78903 | ||||||||
\(339\) | 35.2860 | 1.91647 | ||||||||
\(340\) | 19.4728 | 1.05606 | ||||||||
\(341\) | −23.4452 | −1.26963 | ||||||||
\(342\) | −3.17545 | −0.171709 | ||||||||
\(343\) | −5.54612 | −0.299462 | ||||||||
\(344\) | 59.9328 | 3.23136 | ||||||||
\(345\) | 79.0925 | 4.25820 | ||||||||
\(346\) | −15.0467 | −0.808918 | ||||||||
\(347\) | 5.51687 | 0.296161 | 0.148081 | − | 0.988975i | \(-0.452691\pi\) | ||||
0.148081 | + | 0.988975i | \(0.452691\pi\) | |||||||
\(348\) | −69.9233 | −3.74828 | ||||||||
\(349\) | −31.8235 | −1.70347 | −0.851737 | − | 0.523969i | \(-0.824451\pi\) | ||||
−0.851737 | + | 0.523969i | \(0.824451\pi\) | |||||||
\(350\) | −66.0271 | −3.52930 | ||||||||
\(351\) | 0.176647 | 0.00942872 | ||||||||
\(352\) | 31.0175 | 1.65324 | ||||||||
\(353\) | 8.64697 | 0.460232 | 0.230116 | − | 0.973163i | \(-0.426089\pi\) | ||||
0.230116 | + | 0.973163i | \(0.426089\pi\) | |||||||
\(354\) | 47.7801 | 2.53948 | ||||||||
\(355\) | 22.2417 | 1.18047 | ||||||||
\(356\) | −57.1827 | −3.03068 | ||||||||
\(357\) | 10.3942 | 0.550121 | ||||||||
\(358\) | −34.2776 | −1.81163 | ||||||||
\(359\) | −1.07069 | −0.0565090 | −0.0282545 | − | 0.999601i | \(-0.508995\pi\) | ||||
−0.0282545 | + | 0.999601i | \(0.508995\pi\) | |||||||
\(360\) | −63.2794 | −3.33511 | ||||||||
\(361\) | −18.8018 | −0.989570 | ||||||||
\(362\) | −31.2382 | −1.64185 | ||||||||
\(363\) | 36.0992 | 1.89472 | ||||||||
\(364\) | −5.63930 | −0.295580 | ||||||||
\(365\) | 44.7056 | 2.34000 | ||||||||
\(366\) | −43.5068 | −2.27414 | ||||||||
\(367\) | 14.4814 | 0.755923 | 0.377961 | − | 0.925821i | \(-0.376625\pi\) | ||||
0.377961 | + | 0.925821i | \(0.376625\pi\) | |||||||
\(368\) | 69.5637 | 3.62626 | ||||||||
\(369\) | 11.9349 | 0.621306 | ||||||||
\(370\) | 0.743204 | 0.0386374 | ||||||||
\(371\) | −4.57680 | −0.237616 | ||||||||
\(372\) | 50.0870 | 2.59689 | ||||||||
\(373\) | −4.76462 | −0.246703 | −0.123351 | − | 0.992363i | \(-0.539364\pi\) | ||||
−0.123351 | + | 0.992363i | \(0.539364\pi\) | |||||||
\(374\) | 15.9586 | 0.825201 | ||||||||
\(375\) | 19.7086 | 1.01775 | ||||||||
\(376\) | −16.3378 | −0.842557 | ||||||||
\(377\) | 2.26878 | 0.116848 | ||||||||
\(378\) | 4.50079 | 0.231496 | ||||||||
\(379\) | 28.7046 | 1.47446 | 0.737229 | − | 0.675643i | \(-0.236134\pi\) | ||||
0.737229 | + | 0.675643i | \(0.236134\pi\) | |||||||
\(380\) | 7.07539 | 0.362960 | ||||||||
\(381\) | 1.89063 | 0.0968597 | ||||||||
\(382\) | 64.7904 | 3.31497 | ||||||||
\(383\) | 10.3699 | 0.529876 | 0.264938 | − | 0.964265i | \(-0.414648\pi\) | ||||
0.264938 | + | 0.964265i | \(0.414648\pi\) | |||||||
\(384\) | 25.1417 | 1.28301 | ||||||||
\(385\) | −63.1210 | −3.21694 | ||||||||
\(386\) | 39.3402 | 2.00236 | ||||||||
\(387\) | −25.9331 | −1.31825 | ||||||||
\(388\) | 35.6188 | 1.80827 | ||||||||
\(389\) | 26.5424 | 1.34575 | 0.672876 | − | 0.739755i | \(-0.265059\pi\) | ||||
0.672876 | + | 0.739755i | \(0.265059\pi\) | |||||||
\(390\) | 7.63118 | 0.386420 | ||||||||
\(391\) | 11.4652 | 0.579819 | ||||||||
\(392\) | −35.0199 | −1.76877 | ||||||||
\(393\) | −19.5359 | −0.985457 | ||||||||
\(394\) | −55.2179 | −2.78184 | ||||||||
\(395\) | −2.80748 | −0.141259 | ||||||||
\(396\) | −64.4427 | −3.23837 | ||||||||
\(397\) | −18.8686 | −0.946989 | −0.473494 | − | 0.880797i | \(-0.657008\pi\) | ||||
−0.473494 | + | 0.880797i | \(0.657008\pi\) | |||||||
\(398\) | −2.38949 | −0.119774 | ||||||||
\(399\) | 3.77672 | 0.189073 | ||||||||
\(400\) | 54.5013 | 2.72506 | ||||||||
\(401\) | −18.8086 | −0.939258 | −0.469629 | − | 0.882864i | \(-0.655612\pi\) | ||||
−0.469629 | + | 0.882864i | \(0.655612\pi\) | |||||||
\(402\) | −95.7907 | −4.77761 | ||||||||
\(403\) | −1.62516 | −0.0809550 | ||||||||
\(404\) | −52.6858 | −2.62122 | ||||||||
\(405\) | −33.6414 | −1.67166 | ||||||||
\(406\) | 57.8063 | 2.86888 | ||||||||
\(407\) | 0.422422 | 0.0209387 | ||||||||
\(408\) | −19.0280 | −0.942026 | ||||||||
\(409\) | −16.2427 | −0.803148 | −0.401574 | − | 0.915826i | \(-0.631537\pi\) | ||||
−0.401574 | + | 0.915826i | \(0.631537\pi\) | |||||||
\(410\) | −38.3436 | −1.89366 | ||||||||
\(411\) | 12.9631 | 0.639424 | ||||||||
\(412\) | 67.9028 | 3.34533 | ||||||||
\(413\) | −27.3950 | −1.34802 | ||||||||
\(414\) | −66.7557 | −3.28086 | ||||||||
\(415\) | 9.35306 | 0.459124 | ||||||||
\(416\) | 2.15005 | 0.105415 | ||||||||
\(417\) | −13.8613 | −0.678791 | ||||||||
\(418\) | 5.79854 | 0.283616 | ||||||||
\(419\) | −5.03656 | −0.246052 | −0.123026 | − | 0.992403i | \(-0.539260\pi\) | ||||
−0.123026 | + | 0.992403i | \(0.539260\pi\) | |||||||
\(420\) | 134.848 | 6.57992 | ||||||||
\(421\) | −25.8441 | −1.25956 | −0.629782 | − | 0.776772i | \(-0.716856\pi\) | ||||
−0.629782 | + | 0.776772i | \(0.716856\pi\) | |||||||
\(422\) | −50.2269 | −2.44501 | ||||||||
\(423\) | 7.06940 | 0.343726 | ||||||||
\(424\) | 8.37843 | 0.406893 | ||||||||
\(425\) | 8.98266 | 0.435723 | ||||||||
\(426\) | −38.9410 | −1.88670 | ||||||||
\(427\) | 24.9448 | 1.20717 | ||||||||
\(428\) | −45.0296 | −2.17659 | ||||||||
\(429\) | 4.33741 | 0.209412 | ||||||||
\(430\) | 83.3160 | 4.01785 | ||||||||
\(431\) | 31.3134 | 1.50831 | 0.754157 | − | 0.656695i | \(-0.228046\pi\) | ||||
0.754157 | + | 0.656695i | \(0.228046\pi\) | |||||||
\(432\) | −3.71512 | −0.178744 | ||||||||
\(433\) | −9.53010 | −0.457988 | −0.228994 | − | 0.973428i | \(-0.573544\pi\) | ||||
−0.228994 | + | 0.973428i | \(0.573544\pi\) | |||||||
\(434\) | −41.4075 | −1.98762 | ||||||||
\(435\) | −54.2516 | −2.60116 | ||||||||
\(436\) | 51.0874 | 2.44664 | ||||||||
\(437\) | 4.16585 | 0.199280 | ||||||||
\(438\) | −78.2710 | −3.73993 | ||||||||
\(439\) | 28.4026 | 1.35558 | 0.677791 | − | 0.735254i | \(-0.262937\pi\) | ||||
0.677791 | + | 0.735254i | \(0.262937\pi\) | |||||||
\(440\) | 115.551 | 5.50869 | ||||||||
\(441\) | 15.1532 | 0.721580 | ||||||||
\(442\) | 1.10621 | 0.0526170 | ||||||||
\(443\) | −26.2582 | −1.24756 | −0.623782 | − | 0.781598i | \(-0.714405\pi\) | ||||
−0.623782 | + | 0.781598i | \(0.714405\pi\) | |||||||
\(444\) | −0.902438 | −0.0428278 | ||||||||
\(445\) | −44.3665 | −2.10317 | ||||||||
\(446\) | 25.5979 | 1.21210 | ||||||||
\(447\) | −40.4535 | −1.91338 | ||||||||
\(448\) | 2.37315 | 0.112121 | ||||||||
\(449\) | −19.5626 | −0.923215 | −0.461608 | − | 0.887084i | \(-0.652727\pi\) | ||||
−0.461608 | + | 0.887084i | \(0.652727\pi\) | |||||||
\(450\) | −52.3013 | −2.46551 | ||||||||
\(451\) | −21.7937 | −1.02623 | ||||||||
\(452\) | 66.3591 | 3.12127 | ||||||||
\(453\) | −6.57649 | −0.308990 | ||||||||
\(454\) | 17.2464 | 0.809413 | ||||||||
\(455\) | −4.37538 | −0.205121 | ||||||||
\(456\) | −6.91379 | −0.323768 | ||||||||
\(457\) | 5.10525 | 0.238813 | 0.119407 | − | 0.992845i | \(-0.461901\pi\) | ||||
0.119407 | + | 0.992845i | \(0.461901\pi\) | |||||||
\(458\) | −37.7280 | −1.76292 | ||||||||
\(459\) | −0.612310 | −0.0285802 | ||||||||
\(460\) | 148.742 | 6.93513 | ||||||||
\(461\) | −38.1937 | −1.77886 | −0.889430 | − | 0.457072i | \(-0.848898\pi\) | ||||
−0.889430 | + | 0.457072i | \(0.848898\pi\) | |||||||
\(462\) | 110.513 | 5.14152 | ||||||||
\(463\) | −3.88947 | −0.180759 | −0.0903796 | − | 0.995907i | \(-0.528808\pi\) | ||||
−0.0903796 | + | 0.995907i | \(0.528808\pi\) | |||||||
\(464\) | −47.7155 | −2.21514 | ||||||||
\(465\) | 38.8612 | 1.80214 | ||||||||
\(466\) | −23.0659 | −1.06851 | ||||||||
\(467\) | 10.8376 | 0.501504 | 0.250752 | − | 0.968051i | \(-0.419322\pi\) | ||||
0.250752 | + | 0.968051i | \(0.419322\pi\) | |||||||
\(468\) | −4.46699 | −0.206487 | ||||||||
\(469\) | 54.9221 | 2.53607 | ||||||||
\(470\) | −22.7121 | −1.04763 | ||||||||
\(471\) | 16.3104 | 0.751546 | ||||||||
\(472\) | 50.1501 | 2.30834 | ||||||||
\(473\) | 47.3551 | 2.17739 | ||||||||
\(474\) | 4.91535 | 0.225770 | ||||||||
\(475\) | 3.26383 | 0.149755 | ||||||||
\(476\) | 19.5475 | 0.895956 | ||||||||
\(477\) | −3.62537 | −0.165994 | ||||||||
\(478\) | 19.2557 | 0.880735 | ||||||||
\(479\) | 6.20721 | 0.283615 | 0.141807 | − | 0.989894i | \(-0.454709\pi\) | ||||
0.141807 | + | 0.989894i | \(0.454709\pi\) | |||||||
\(480\) | −51.4124 | −2.34664 | ||||||||
\(481\) | 0.0292812 | 0.00133511 | ||||||||
\(482\) | 1.50868 | 0.0687187 | ||||||||
\(483\) | 79.3959 | 3.61264 | ||||||||
\(484\) | 67.8884 | 3.08584 | ||||||||
\(485\) | 27.6356 | 1.25487 | ||||||||
\(486\) | 55.0694 | 2.49800 | ||||||||
\(487\) | −15.1882 | −0.688244 | −0.344122 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344122 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(488\) | −45.6648 | −2.06715 | ||||||||
\(489\) | −36.7324 | −1.66109 | ||||||||
\(490\) | −48.6831 | −2.19928 | ||||||||
\(491\) | −5.62931 | −0.254047 | −0.127024 | − | 0.991900i | \(-0.540542\pi\) | ||||
−0.127024 | + | 0.991900i | \(0.540542\pi\) | |||||||
\(492\) | 46.5589 | 2.09904 | ||||||||
\(493\) | −7.86425 | −0.354188 | ||||||||
\(494\) | 0.401939 | 0.0180841 | ||||||||
\(495\) | −49.9993 | −2.24730 | ||||||||
\(496\) | 34.1793 | 1.53469 | ||||||||
\(497\) | 22.3270 | 1.00150 | ||||||||
\(498\) | −16.3754 | −0.733800 | ||||||||
\(499\) | 38.9865 | 1.74527 | 0.872637 | − | 0.488369i | \(-0.162408\pi\) | ||||
0.872637 | + | 0.488369i | \(0.162408\pi\) | |||||||
\(500\) | 37.0640 | 1.65755 | ||||||||
\(501\) | 31.9950 | 1.42943 | ||||||||
\(502\) | −13.6370 | −0.608651 | ||||||||
\(503\) | −30.5385 | −1.36165 | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(504\) | −63.5221 | −2.82950 | ||||||||
\(505\) | −40.8775 | −1.81902 | ||||||||
\(506\) | 121.899 | 5.41908 | ||||||||
\(507\) | −30.9868 | −1.37617 | ||||||||
\(508\) | 3.55552 | 0.157751 | ||||||||
\(509\) | −17.2270 | −0.763572 | −0.381786 | − | 0.924251i | \(-0.624691\pi\) | ||||
−0.381786 | + | 0.924251i | \(0.624691\pi\) | |||||||
\(510\) | −26.4519 | −1.17131 | ||||||||
\(511\) | 44.8771 | 1.98525 | ||||||||
\(512\) | 50.7212 | 2.24158 | ||||||||
\(513\) | −0.222482 | −0.00982280 | ||||||||
\(514\) | −37.8206 | −1.66820 | ||||||||
\(515\) | 52.6840 | 2.32153 | ||||||||
\(516\) | −101.167 | −4.45362 | ||||||||
\(517\) | −12.9091 | −0.567741 | ||||||||
\(518\) | 0.746055 | 0.0327798 | ||||||||
\(519\) | 14.1756 | 0.622241 | ||||||||
\(520\) | 8.00970 | 0.351249 | ||||||||
\(521\) | 34.3181 | 1.50350 | 0.751751 | − | 0.659447i | \(-0.229209\pi\) | ||||
0.751751 | + | 0.659447i | \(0.229209\pi\) | |||||||
\(522\) | 45.7894 | 2.00415 | ||||||||
\(523\) | 27.8798 | 1.21910 | 0.609549 | − | 0.792748i | \(-0.291351\pi\) | ||||
0.609549 | + | 0.792748i | \(0.291351\pi\) | |||||||
\(524\) | −36.7394 | −1.60497 | ||||||||
\(525\) | 62.2046 | 2.71483 | ||||||||
\(526\) | 23.4511 | 1.02252 | ||||||||
\(527\) | 5.63328 | 0.245389 | ||||||||
\(528\) | −91.2214 | −3.96990 | ||||||||
\(529\) | 64.5763 | 2.80766 | ||||||||
\(530\) | 11.6473 | 0.505928 | ||||||||
\(531\) | −21.7001 | −0.941702 | ||||||||
\(532\) | 7.10253 | 0.307934 | ||||||||
\(533\) | −1.51068 | −0.0654349 | ||||||||
\(534\) | 77.6772 | 3.36142 | ||||||||
\(535\) | −34.9372 | −1.51047 | ||||||||
\(536\) | −100.542 | −4.34276 | ||||||||
\(537\) | 32.2931 | 1.39355 | ||||||||
\(538\) | 54.9505 | 2.36909 | ||||||||
\(539\) | −27.6705 | −1.19185 | ||||||||
\(540\) | −7.94372 | −0.341843 | ||||||||
\(541\) | −42.1269 | −1.81118 | −0.905588 | − | 0.424158i | \(-0.860570\pi\) | ||||
−0.905588 | + | 0.424158i | \(0.860570\pi\) | |||||||
\(542\) | 78.5510 | 3.37405 | ||||||||
\(543\) | 29.4297 | 1.26295 | ||||||||
\(544\) | −7.45269 | −0.319531 | ||||||||
\(545\) | 39.6373 | 1.69788 | ||||||||
\(546\) | 7.66045 | 0.327837 | ||||||||
\(547\) | −40.3783 | −1.72645 | −0.863226 | − | 0.504817i | \(-0.831560\pi\) | ||||
−0.863226 | + | 0.504817i | \(0.831560\pi\) | |||||||
\(548\) | 24.3785 | 1.04140 | ||||||||
\(549\) | 19.7593 | 0.843305 | ||||||||
\(550\) | 95.5048 | 4.07234 | ||||||||
\(551\) | −2.85746 | −0.121732 | ||||||||
\(552\) | −145.345 | −6.18628 | ||||||||
\(553\) | −2.81824 | −0.119844 | ||||||||
\(554\) | 0.807614 | 0.0343122 | ||||||||
\(555\) | −0.700177 | −0.0297209 | ||||||||
\(556\) | −26.0677 | −1.10552 | ||||||||
\(557\) | −14.4863 | −0.613802 | −0.306901 | − | 0.951741i | \(-0.599292\pi\) | ||||
−0.306901 | + | 0.951741i | \(0.599292\pi\) | |||||||
\(558\) | −32.7996 | −1.38852 | ||||||||
\(559\) | 3.28253 | 0.138836 | ||||||||
\(560\) | 92.0200 | 3.88856 | ||||||||
\(561\) | −15.0347 | −0.634766 | ||||||||
\(562\) | 61.7770 | 2.60591 | ||||||||
\(563\) | −16.6356 | −0.701108 | −0.350554 | − | 0.936543i | \(-0.614007\pi\) | ||||
−0.350554 | + | 0.936543i | \(0.614007\pi\) | |||||||
\(564\) | 27.5782 | 1.16125 | ||||||||
\(565\) | 51.4862 | 2.16604 | ||||||||
\(566\) | −37.0735 | −1.55831 | ||||||||
\(567\) | −33.7705 | −1.41823 | ||||||||
\(568\) | −40.8726 | −1.71498 | ||||||||
\(569\) | −30.2930 | −1.26995 | −0.634974 | − | 0.772534i | \(-0.718989\pi\) | ||||
−0.634974 | + | 0.772534i | \(0.718989\pi\) | |||||||
\(570\) | −9.61125 | −0.402571 | ||||||||
\(571\) | 31.3960 | 1.31388 | 0.656940 | − | 0.753943i | \(-0.271850\pi\) | ||||
0.656940 | + | 0.753943i | \(0.271850\pi\) | |||||||
\(572\) | 8.15695 | 0.341059 | ||||||||
\(573\) | −61.0395 | −2.54996 | ||||||||
\(574\) | −38.4907 | −1.60657 | ||||||||
\(575\) | 68.6137 | 2.86139 | ||||||||
\(576\) | 1.87982 | 0.0783258 | ||||||||
\(577\) | 36.1967 | 1.50689 | 0.753445 | − | 0.657511i | \(-0.228391\pi\) | ||||
0.753445 | + | 0.657511i | \(0.228391\pi\) | |||||||
\(578\) | 39.5942 | 1.64690 | ||||||||
\(579\) | −37.0627 | −1.54027 | ||||||||
\(580\) | −102.026 | −4.23639 | ||||||||
\(581\) | 9.38893 | 0.389519 | ||||||||
\(582\) | −48.3847 | −2.00561 | ||||||||
\(583\) | 6.62010 | 0.274177 | ||||||||
\(584\) | −82.1534 | −3.39953 | ||||||||
\(585\) | −3.46582 | −0.143294 | ||||||||
\(586\) | 32.9374 | 1.36063 | ||||||||
\(587\) | −10.1363 | −0.418370 | −0.209185 | − | 0.977876i | \(-0.567081\pi\) | ||||
−0.209185 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(588\) | 59.1136 | 2.43781 | ||||||||
\(589\) | 2.04684 | 0.0843386 | ||||||||
\(590\) | 69.7164 | 2.87018 | ||||||||
\(591\) | 52.0211 | 2.13986 | ||||||||
\(592\) | −0.615822 | −0.0253101 | ||||||||
\(593\) | −29.0057 | −1.19112 | −0.595560 | − | 0.803311i | \(-0.703070\pi\) | ||||
−0.595560 | + | 0.803311i | \(0.703070\pi\) | |||||||
\(594\) | −6.51016 | −0.267115 | ||||||||
\(595\) | 15.1663 | 0.621759 | ||||||||
\(596\) | −76.0770 | −3.11624 | ||||||||
\(597\) | 2.25115 | 0.0921335 | ||||||||
\(598\) | 8.44973 | 0.345535 | ||||||||
\(599\) | −6.04943 | −0.247173 | −0.123587 | − | 0.992334i | \(-0.539440\pi\) | ||||
−0.123587 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(600\) | −113.874 | −4.64887 | ||||||||
\(601\) | −13.7169 | −0.559526 | −0.279763 | − | 0.960069i | \(-0.590256\pi\) | ||||
−0.279763 | + | 0.960069i | \(0.590256\pi\) | |||||||
\(602\) | 83.6356 | 3.40873 | ||||||||
\(603\) | 43.5048 | 1.77165 | ||||||||
\(604\) | −12.3678 | −0.503238 | ||||||||
\(605\) | 52.6728 | 2.14145 | ||||||||
\(606\) | 71.5687 | 2.90728 | ||||||||
\(607\) | −14.0943 | −0.572069 | −0.286035 | − | 0.958219i | \(-0.592337\pi\) | ||||
−0.286035 | + | 0.958219i | \(0.592337\pi\) | |||||||
\(608\) | −2.70792 | −0.109821 | ||||||||
\(609\) | −54.4597 | −2.20682 | ||||||||
\(610\) | −63.4812 | −2.57028 | ||||||||
\(611\) | −0.894823 | −0.0362007 | ||||||||
\(612\) | 15.4839 | 0.625899 | ||||||||
\(613\) | −24.6314 | −0.994854 | −0.497427 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497427 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(614\) | 67.1636 | 2.71050 | ||||||||
\(615\) | 36.1238 | 1.45665 | ||||||||
\(616\) | 115.995 | 4.67355 | ||||||||
\(617\) | 10.3455 | 0.416492 | 0.208246 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208246 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(618\) | −92.2395 | −3.71042 | ||||||||
\(619\) | 10.9672 | 0.440809 | 0.220404 | − | 0.975409i | \(-0.429262\pi\) | ||||
0.220404 | + | 0.975409i | \(0.429262\pi\) | |||||||
\(620\) | 73.0826 | 2.93507 | ||||||||
\(621\) | −4.67710 | −0.187686 | ||||||||
\(622\) | 89.5642 | 3.59120 | ||||||||
\(623\) | −44.5367 | −1.78432 | ||||||||
\(624\) | −6.32322 | −0.253132 | ||||||||
\(625\) | −7.90260 | −0.316104 | ||||||||
\(626\) | −6.16564 | −0.246429 | ||||||||
\(627\) | −5.46284 | −0.218165 | ||||||||
\(628\) | 30.6735 | 1.22401 | ||||||||
\(629\) | −0.101497 | −0.00404695 | ||||||||
\(630\) | −88.3056 | −3.51818 | ||||||||
\(631\) | 0.888044 | 0.0353525 | 0.0176762 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176762 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(632\) | 5.15917 | 0.205221 | ||||||||
\(633\) | 47.3191 | 1.88076 | ||||||||
\(634\) | 43.5489 | 1.72955 | ||||||||
\(635\) | 2.75863 | 0.109473 | ||||||||
\(636\) | −14.1428 | −0.560799 | ||||||||
\(637\) | −1.91804 | −0.0759956 | ||||||||
\(638\) | −83.6138 | −3.31030 | ||||||||
\(639\) | 17.6857 | 0.699634 | ||||||||
\(640\) | 36.6846 | 1.45008 | ||||||||
\(641\) | 0.884608 | 0.0349399 | 0.0174700 | − | 0.999847i | \(-0.494439\pi\) | ||||
0.0174700 | + | 0.999847i | \(0.494439\pi\) | |||||||
\(642\) | 61.1684 | 2.41413 | ||||||||
\(643\) | 22.1672 | 0.874188 | 0.437094 | − | 0.899416i | \(-0.356008\pi\) | ||||
0.437094 | + | 0.899416i | \(0.356008\pi\) | |||||||
\(644\) | 149.312 | 5.88373 | ||||||||
\(645\) | −78.4925 | −3.09064 | ||||||||
\(646\) | −1.39324 | −0.0548162 | ||||||||
\(647\) | 9.43374 | 0.370879 | 0.185439 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185439 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(648\) | 61.8213 | 2.42857 | ||||||||
\(649\) | 39.6254 | 1.55543 | ||||||||
\(650\) | 6.62014 | 0.259663 | ||||||||
\(651\) | 39.0102 | 1.52893 | ||||||||
\(652\) | −69.0791 | −2.70535 | ||||||||
\(653\) | 17.8173 | 0.697245 | 0.348622 | − | 0.937263i | \(-0.386650\pi\) | ||||
0.348622 | + | 0.937263i | \(0.386650\pi\) | |||||||
\(654\) | −69.3974 | −2.71365 | ||||||||
\(655\) | −28.5051 | −1.11379 | ||||||||
\(656\) | 31.7717 | 1.24048 | ||||||||
\(657\) | 35.5480 | 1.38686 | ||||||||
\(658\) | −22.7992 | −0.888805 | ||||||||
\(659\) | 31.2464 | 1.21719 | 0.608593 | − | 0.793483i | \(-0.291734\pi\) | ||||
0.608593 | + | 0.793483i | \(0.291734\pi\) | |||||||
\(660\) | −195.051 | −7.59234 | ||||||||
\(661\) | 16.8636 | 0.655919 | 0.327960 | − | 0.944692i | \(-0.393639\pi\) | ||||
0.327960 | + | 0.944692i | \(0.393639\pi\) | |||||||
\(662\) | 6.33430 | 0.246190 | ||||||||
\(663\) | −1.04217 | −0.0404744 | ||||||||
\(664\) | −17.1877 | −0.667011 | ||||||||
\(665\) | 5.51066 | 0.213694 | ||||||||
\(666\) | 0.590964 | 0.0228994 | ||||||||
\(667\) | −60.0708 | −2.32595 | ||||||||
\(668\) | 60.1701 | 2.32805 | ||||||||
\(669\) | −24.1160 | −0.932377 | ||||||||
\(670\) | −139.769 | −5.39976 | ||||||||
\(671\) | −36.0814 | −1.39291 | ||||||||
\(672\) | −51.6096 | −1.99088 | ||||||||
\(673\) | 13.7763 | 0.531036 | 0.265518 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265518 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(674\) | −57.2947 | −2.20691 | ||||||||
\(675\) | −3.66438 | −0.141042 | ||||||||
\(676\) | −58.2740 | −2.24131 | ||||||||
\(677\) | 25.7184 | 0.988438 | 0.494219 | − | 0.869338i | \(-0.335454\pi\) | ||||
0.494219 | + | 0.869338i | \(0.335454\pi\) | |||||||
\(678\) | −90.1426 | −3.46190 | ||||||||
\(679\) | 27.7416 | 1.06463 | ||||||||
\(680\) | −27.7640 | −1.06470 | ||||||||
\(681\) | −16.2479 | −0.622622 | ||||||||
\(682\) | 59.8938 | 2.29345 | ||||||||
\(683\) | −49.8079 | −1.90584 | −0.952922 | − | 0.303214i | \(-0.901940\pi\) | ||||
−0.952922 | + | 0.303214i | \(0.901940\pi\) | |||||||
\(684\) | 5.62605 | 0.215117 | ||||||||
\(685\) | 18.9146 | 0.722691 | ||||||||
\(686\) | 14.1682 | 0.540946 | ||||||||
\(687\) | 35.5438 | 1.35608 | ||||||||
\(688\) | −69.0359 | −2.63197 | ||||||||
\(689\) | 0.458888 | 0.0174822 | ||||||||
\(690\) | −202.052 | −7.69198 | ||||||||
\(691\) | 9.33284 | 0.355038 | 0.177519 | − | 0.984117i | \(-0.443193\pi\) | ||||
0.177519 | + | 0.984117i | \(0.443193\pi\) | |||||||
\(692\) | 26.6588 | 1.01341 | ||||||||
\(693\) | −50.1911 | −1.90660 | ||||||||
\(694\) | −14.0935 | −0.534983 | ||||||||
\(695\) | −20.2252 | −0.767185 | ||||||||
\(696\) | 99.6956 | 3.77895 | ||||||||
\(697\) | 5.23647 | 0.198345 | ||||||||
\(698\) | 81.2972 | 3.07714 | ||||||||
\(699\) | 21.7306 | 0.821925 | ||||||||
\(700\) | 116.982 | 4.42151 | ||||||||
\(701\) | −35.9991 | −1.35967 | −0.679834 | − | 0.733366i | \(-0.737948\pi\) | ||||
−0.679834 | + | 0.733366i | \(0.737948\pi\) | |||||||
\(702\) | −0.451267 | −0.0170320 | ||||||||
\(703\) | −0.0368788 | −0.00139091 | ||||||||
\(704\) | −3.43264 | −0.129373 | ||||||||
\(705\) | 21.3972 | 0.805865 | ||||||||
\(706\) | −22.0898 | −0.831359 | ||||||||
\(707\) | −41.0343 | −1.54325 | ||||||||
\(708\) | −84.6534 | −3.18147 | ||||||||
\(709\) | −28.6493 | −1.07595 | −0.537973 | − | 0.842962i | \(-0.680810\pi\) | ||||
−0.537973 | + | 0.842962i | \(0.680810\pi\) | |||||||
\(710\) | −56.8193 | −2.13239 | ||||||||
\(711\) | −2.23238 | −0.0837209 | ||||||||
\(712\) | 81.5302 | 3.05547 | ||||||||
\(713\) | 43.0296 | 1.61147 | ||||||||
\(714\) | −26.5534 | −0.993734 | ||||||||
\(715\) | 6.32876 | 0.236682 | ||||||||
\(716\) | 60.7306 | 2.26961 | ||||||||
\(717\) | −18.1409 | −0.677485 | ||||||||
\(718\) | 2.73522 | 0.102077 | ||||||||
\(719\) | −16.0244 | −0.597608 | −0.298804 | − | 0.954315i | \(-0.596588\pi\) | ||||
−0.298804 | + | 0.954315i | \(0.596588\pi\) | |||||||
\(720\) | 72.8907 | 2.71648 | ||||||||
\(721\) | 52.8860 | 1.96958 | ||||||||
\(722\) | 48.0316 | 1.78755 | ||||||||
\(723\) | −1.42134 | −0.0528602 | ||||||||
\(724\) | 55.3457 | 2.05691 | ||||||||
\(725\) | −47.0639 | −1.74791 | ||||||||
\(726\) | −92.2199 | −3.42260 | ||||||||
\(727\) | −25.9717 | −0.963237 | −0.481618 | − | 0.876381i | \(-0.659951\pi\) | ||||
−0.481618 | + | 0.876381i | \(0.659951\pi\) | |||||||
\(728\) | 8.04043 | 0.297998 | ||||||||
\(729\) | −23.1417 | −0.857099 | ||||||||
\(730\) | −114.206 | −4.22696 | ||||||||
\(731\) | −11.3782 | −0.420838 | ||||||||
\(732\) | 77.0823 | 2.84904 | ||||||||
\(733\) | −2.78609 | −0.102906 | −0.0514532 | − | 0.998675i | \(-0.516385\pi\) | ||||
−0.0514532 | + | 0.998675i | \(0.516385\pi\) | |||||||
\(734\) | −36.9945 | −1.36549 | ||||||||
\(735\) | 45.8647 | 1.69174 | ||||||||
\(736\) | −56.9271 | −2.09836 | ||||||||
\(737\) | −79.4420 | −2.92628 | ||||||||
\(738\) | −30.4892 | −1.12232 | ||||||||
\(739\) | −30.7886 | −1.13258 | −0.566288 | − | 0.824208i | \(-0.691621\pi\) | ||||
−0.566288 | + | 0.824208i | \(0.691621\pi\) | |||||||
\(740\) | −1.31676 | −0.0484050 | ||||||||
\(741\) | −0.378669 | −0.0139108 | ||||||||
\(742\) | 11.6920 | 0.429227 | ||||||||
\(743\) | −14.2263 | −0.521911 | −0.260955 | − | 0.965351i | \(-0.584038\pi\) | ||||
−0.260955 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(744\) | −71.4133 | −2.61814 | ||||||||
\(745\) | −59.0261 | −2.16255 | ||||||||
\(746\) | 12.1718 | 0.445642 | ||||||||
\(747\) | 7.43715 | 0.272111 | ||||||||
\(748\) | −28.2744 | −1.03381 | ||||||||
\(749\) | −35.0712 | −1.28148 | ||||||||
\(750\) | −50.3480 | −1.83845 | ||||||||
\(751\) | 25.4622 | 0.929129 | 0.464564 | − | 0.885539i | \(-0.346211\pi\) | ||||
0.464564 | + | 0.885539i | \(0.346211\pi\) | |||||||
\(752\) | 18.8193 | 0.686270 | ||||||||
\(753\) | 12.8475 | 0.468190 | ||||||||
\(754\) | −5.79588 | −0.211074 | ||||||||
\(755\) | −9.59582 | −0.349228 | ||||||||
\(756\) | −7.97419 | −0.290018 | ||||||||
\(757\) | −3.16487 | −0.115029 | −0.0575145 | − | 0.998345i | \(-0.518318\pi\) | ||||
−0.0575145 | + | 0.998345i | \(0.518318\pi\) | |||||||
\(758\) | −73.3296 | −2.66345 | ||||||||
\(759\) | −114.842 | −4.16850 | ||||||||
\(760\) | −10.0880 | −0.365930 | ||||||||
\(761\) | 32.0100 | 1.16036 | 0.580181 | − | 0.814488i | \(-0.302982\pi\) | ||||
0.580181 | + | 0.814488i | \(0.302982\pi\) | |||||||
\(762\) | −4.82984 | −0.174967 | ||||||||
\(763\) | 39.7894 | 1.44047 | ||||||||
\(764\) | −114.791 | −4.15300 | ||||||||
\(765\) | 12.0135 | 0.434350 | ||||||||
\(766\) | −26.4912 | −0.957164 | ||||||||
\(767\) | 2.74673 | 0.0991785 | ||||||||
\(768\) | −67.4681 | −2.43455 | ||||||||
\(769\) | 6.79258 | 0.244947 | 0.122473 | − | 0.992472i | \(-0.460917\pi\) | ||||
0.122473 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(770\) | 161.250 | 5.81106 | ||||||||
\(771\) | 35.6310 | 1.28322 | ||||||||
\(772\) | −69.7003 | −2.50857 | ||||||||
\(773\) | −33.1736 | −1.19317 | −0.596587 | − | 0.802549i | \(-0.703477\pi\) | ||||
−0.596587 | + | 0.802549i | \(0.703477\pi\) | |||||||
\(774\) | 66.2493 | 2.38128 | ||||||||
\(775\) | 33.7125 | 1.21099 | ||||||||
\(776\) | −50.7847 | −1.82307 | ||||||||
\(777\) | −0.702863 | −0.0252151 | ||||||||
\(778\) | −67.8059 | −2.43096 | ||||||||
\(779\) | 1.90266 | 0.0681699 | ||||||||
\(780\) | −13.5204 | −0.484108 | ||||||||
\(781\) | −32.2949 | −1.15560 | ||||||||
\(782\) | −29.2892 | −1.04738 | ||||||||
\(783\) | 3.20814 | 0.114650 | ||||||||
\(784\) | 40.3390 | 1.44068 | ||||||||
\(785\) | 23.7988 | 0.849414 | ||||||||
\(786\) | 49.9069 | 1.78012 | ||||||||
\(787\) | −39.5558 | −1.41001 | −0.705006 | − | 0.709202i | \(-0.749056\pi\) | ||||
−0.705006 | + | 0.709202i | \(0.749056\pi\) | |||||||
\(788\) | 97.8313 | 3.48510 | ||||||||
\(789\) | −22.0934 | −0.786546 | ||||||||
\(790\) | 7.17205 | 0.255170 | ||||||||
\(791\) | 51.6837 | 1.83766 | ||||||||
\(792\) | 91.8814 | 3.26486 | ||||||||
\(793\) | −2.50107 | −0.0888155 | ||||||||
\(794\) | 48.2022 | 1.71063 | ||||||||
\(795\) | −10.9730 | −0.389173 | ||||||||
\(796\) | 4.23353 | 0.150053 | ||||||||
\(797\) | −10.3530 | −0.366722 | −0.183361 | − | 0.983046i | \(-0.558698\pi\) | ||||
−0.183361 | + | 0.983046i | \(0.558698\pi\) | |||||||
\(798\) | −9.64811 | −0.341540 | ||||||||
\(799\) | 3.10172 | 0.109731 | ||||||||
\(800\) | −44.6008 | −1.57688 | ||||||||
\(801\) | −35.2783 | −1.24650 | ||||||||
\(802\) | 48.0490 | 1.69667 | ||||||||
\(803\) | −64.9124 | −2.29071 | ||||||||
\(804\) | 169.715 | 5.98540 | ||||||||
\(805\) | 115.847 | 4.08309 | ||||||||
\(806\) | 4.15167 | 0.146236 | ||||||||
\(807\) | −51.7692 | −1.82236 | ||||||||
\(808\) | 75.1186 | 2.64266 | ||||||||
\(809\) | 1.86785 | 0.0656700 | 0.0328350 | − | 0.999461i | \(-0.489546\pi\) | ||||
0.0328350 | + | 0.999461i | \(0.489546\pi\) | |||||||
\(810\) | 85.9412 | 3.01967 | ||||||||
\(811\) | 51.6194 | 1.81260 | 0.906302 | − | 0.422632i | \(-0.138894\pi\) | ||||
0.906302 | + | 0.422632i | \(0.138894\pi\) | |||||||
\(812\) | −102.417 | −3.59414 | ||||||||
\(813\) | −74.0034 | −2.59541 | ||||||||
\(814\) | −1.07913 | −0.0378235 | ||||||||
\(815\) | −53.5966 | −1.87741 | ||||||||
\(816\) | 21.9181 | 0.767288 | ||||||||
\(817\) | −4.13425 | −0.144639 | ||||||||
\(818\) | 41.4939 | 1.45080 | ||||||||
\(819\) | −3.47911 | −0.121570 | ||||||||
\(820\) | 67.9346 | 2.37238 | ||||||||
\(821\) | 15.8072 | 0.551674 | 0.275837 | − | 0.961204i | \(-0.411045\pi\) | ||||
0.275837 | + | 0.961204i | \(0.411045\pi\) | |||||||
\(822\) | −33.1159 | −1.15505 | ||||||||
\(823\) | −0.0293980 | −0.00102475 | −0.000512376 | − | 1.00000i | \(-0.500163\pi\) | ||||
−0.000512376 | 1.00000i | \(0.500163\pi\) | ||||||||
\(824\) | −96.8148 | −3.37270 | ||||||||
\(825\) | −89.9757 | −3.13255 | ||||||||
\(826\) | 69.9838 | 2.43505 | ||||||||
\(827\) | 44.2492 | 1.53870 | 0.769349 | − | 0.638829i | \(-0.220581\pi\) | ||||
0.769349 | + | 0.638829i | \(0.220581\pi\) | |||||||
\(828\) | 118.273 | 4.11027 | ||||||||
\(829\) | 43.2558 | 1.50234 | 0.751168 | − | 0.660111i | \(-0.229491\pi\) | ||||
0.751168 | + | 0.660111i | \(0.229491\pi\) | |||||||
\(830\) | −23.8936 | −0.829357 | ||||||||
\(831\) | −0.760858 | −0.0263939 | ||||||||
\(832\) | −0.237942 | −0.00824914 | ||||||||
\(833\) | 6.64850 | 0.230357 | ||||||||
\(834\) | 35.4104 | 1.22616 | ||||||||
\(835\) | 46.6843 | 1.61558 | ||||||||
\(836\) | −10.2734 | −0.355314 | ||||||||
\(837\) | −2.29804 | −0.0794318 | ||||||||
\(838\) | 12.8665 | 0.444466 | ||||||||
\(839\) | −7.67883 | −0.265103 | −0.132551 | − | 0.991176i | \(-0.542317\pi\) | ||||
−0.132551 | + | 0.991176i | \(0.542317\pi\) | |||||||
\(840\) | −192.264 | −6.63375 | ||||||||
\(841\) | 12.2041 | 0.420831 | ||||||||
\(842\) | 66.0219 | 2.27527 | ||||||||
\(843\) | −58.2005 | −2.00453 | ||||||||
\(844\) | 88.9885 | 3.06311 | ||||||||
\(845\) | −45.2132 | −1.55538 | ||||||||
\(846\) | −18.0597 | −0.620904 | ||||||||
\(847\) | 52.8748 | 1.81680 | ||||||||
\(848\) | −9.65102 | −0.331417 | ||||||||
\(849\) | 34.9271 | 1.19870 | ||||||||
\(850\) | −22.9473 | −0.787086 | ||||||||
\(851\) | −0.775281 | −0.0265763 | ||||||||
\(852\) | 68.9930 | 2.36366 | ||||||||
\(853\) | −30.2289 | −1.03502 | −0.517508 | − | 0.855678i | \(-0.673140\pi\) | ||||
−0.517508 | + | 0.855678i | \(0.673140\pi\) | |||||||
\(854\) | −63.7247 | −2.18061 | ||||||||
\(855\) | 4.36509 | 0.149283 | ||||||||
\(856\) | 64.2025 | 2.19440 | ||||||||
\(857\) | −3.54349 | −0.121043 | −0.0605216 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605216 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(858\) | −11.0804 | −0.378280 | ||||||||
\(859\) | 20.8200 | 0.710370 | 0.355185 | − | 0.934796i | \(-0.384418\pi\) | ||||
0.355185 | + | 0.934796i | \(0.384418\pi\) | |||||||
\(860\) | −147.613 | −5.03358 | ||||||||
\(861\) | 36.2623 | 1.23582 | ||||||||
\(862\) | −79.9940 | −2.72461 | ||||||||
\(863\) | −44.3342 | −1.50915 | −0.754576 | − | 0.656212i | \(-0.772158\pi\) | ||||
−0.754576 | + | 0.656212i | \(0.772158\pi\) | |||||||
\(864\) | 3.04025 | 0.103431 | ||||||||
\(865\) | 20.6838 | 0.703271 | ||||||||
\(866\) | 24.3458 | 0.827305 | ||||||||
\(867\) | −37.3019 | −1.26684 | ||||||||
\(868\) | 73.3629 | 2.49010 | ||||||||
\(869\) | 4.07644 | 0.138284 | ||||||||
\(870\) | 138.592 | 4.69872 | ||||||||
\(871\) | −5.50670 | −0.186588 | ||||||||
\(872\) | −72.8397 | −2.46666 | ||||||||
\(873\) | 21.9747 | 0.743730 | ||||||||
\(874\) | −10.6422 | −0.359977 | ||||||||
\(875\) | 28.8673 | 0.975892 | ||||||||
\(876\) | 138.675 | 4.68540 | ||||||||
\(877\) | −4.57800 | −0.154588 | −0.0772940 | − | 0.997008i | \(-0.524628\pi\) | ||||
−0.0772940 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(878\) | −72.5580 | −2.44871 | ||||||||
\(879\) | −31.0306 | −1.04664 | ||||||||
\(880\) | −133.102 | −4.48687 | ||||||||
\(881\) | −19.7130 | −0.664147 | −0.332073 | − | 0.943254i | \(-0.607748\pi\) | ||||
−0.332073 | + | 0.943254i | \(0.607748\pi\) | |||||||
\(882\) | −38.7107 | −1.30346 | ||||||||
\(883\) | −55.6168 | −1.87165 | −0.935827 | − | 0.352460i | \(-0.885345\pi\) | ||||
−0.935827 | + | 0.352460i | \(0.885345\pi\) | |||||||
\(884\) | −1.95990 | −0.0659187 | ||||||||
\(885\) | −65.6803 | −2.20782 | ||||||||
\(886\) | 67.0798 | 2.25359 | ||||||||
\(887\) | 48.2233 | 1.61918 | 0.809590 | − | 0.586995i | \(-0.199689\pi\) | ||||
0.809590 | + | 0.586995i | \(0.199689\pi\) | |||||||
\(888\) | 1.28668 | 0.0431783 | ||||||||
\(889\) | 2.76921 | 0.0928765 | ||||||||
\(890\) | 113.340 | 3.79916 | ||||||||
\(891\) | 48.8472 | 1.63644 | ||||||||
\(892\) | −45.3526 | −1.51852 | ||||||||
\(893\) | 1.12700 | 0.0377137 | ||||||||
\(894\) | 103.343 | 3.45632 | ||||||||
\(895\) | 47.1192 | 1.57502 | ||||||||
\(896\) | 36.8253 | 1.23025 | ||||||||
\(897\) | −7.96054 | −0.265795 | ||||||||
\(898\) | 49.9750 | 1.66769 | ||||||||
\(899\) | −29.5151 | −0.984383 | ||||||||
\(900\) | 92.6638 | 3.08879 | ||||||||
\(901\) | −1.59064 | −0.0529918 | ||||||||
\(902\) | 55.6748 | 1.85377 | ||||||||
\(903\) | −78.7936 | −2.62209 | ||||||||
\(904\) | −94.6138 | −3.14681 | ||||||||
\(905\) | 42.9413 | 1.42742 | ||||||||
\(906\) | 16.8005 | 0.558158 | ||||||||
\(907\) | 33.4445 | 1.11051 | 0.555253 | − | 0.831682i | \(-0.312622\pi\) | ||||
0.555253 | + | 0.831682i | \(0.312622\pi\) | |||||||
\(908\) | −30.5560 | −1.01404 | ||||||||
\(909\) | −32.5040 | −1.07809 | ||||||||
\(910\) | 11.1775 | 0.370529 | ||||||||
\(911\) | 48.7372 | 1.61474 | 0.807368 | − | 0.590048i | \(-0.200891\pi\) | ||||
0.807368 | + | 0.590048i | \(0.200891\pi\) | |||||||
\(912\) | 7.96391 | 0.263712 | ||||||||
\(913\) | −13.5806 | −0.449452 | ||||||||
\(914\) | −13.0420 | −0.431391 | ||||||||
\(915\) | 59.8060 | 1.97713 | ||||||||
\(916\) | 66.8439 | 2.20859 | ||||||||
\(917\) | −28.6144 | −0.944931 | ||||||||
\(918\) | 1.56422 | 0.0516270 | ||||||||
\(919\) | −0.445218 | −0.0146864 | −0.00734319 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734319 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(920\) | −212.074 | −6.99187 | ||||||||
\(921\) | −63.2752 | −2.08499 | ||||||||
\(922\) | 97.5707 | 3.21332 | ||||||||
\(923\) | −2.23860 | −0.0736843 | ||||||||
\(924\) | −195.799 | −6.44131 | ||||||||
\(925\) | −0.607412 | −0.0199716 | ||||||||
\(926\) | 9.93614 | 0.326522 | ||||||||
\(927\) | 41.8920 | 1.37591 | ||||||||
\(928\) | 39.0477 | 1.28180 | ||||||||
\(929\) | −22.0155 | −0.722307 | −0.361153 | − | 0.932506i | \(-0.617617\pi\) | ||||
−0.361153 | + | 0.932506i | \(0.617617\pi\) | |||||||
\(930\) | −99.2757 | −3.25538 | ||||||||
\(931\) | 2.41572 | 0.0791720 | ||||||||
\(932\) | 40.8666 | 1.33863 | ||||||||
\(933\) | −84.3790 | −2.76244 | ||||||||
\(934\) | −27.6860 | −0.905913 | ||||||||
\(935\) | −21.9373 | −0.717427 | ||||||||
\(936\) | 6.36897 | 0.208176 | ||||||||
\(937\) | 14.3889 | 0.470064 | 0.235032 | − | 0.971988i | \(-0.424480\pi\) | ||||
0.235032 | + | 0.971988i | \(0.424480\pi\) | |||||||
\(938\) | −140.305 | −4.58113 | ||||||||
\(939\) | 5.80869 | 0.189559 | ||||||||
\(940\) | 40.2397 | 1.31247 | ||||||||
\(941\) | 21.1587 | 0.689754 | 0.344877 | − | 0.938648i | \(-0.387921\pi\) | ||||
0.344877 | + | 0.938648i | \(0.387921\pi\) | |||||||
\(942\) | −41.6671 | −1.35759 | ||||||||
\(943\) | 39.9985 | 1.30253 | ||||||||
\(944\) | −57.7673 | −1.88016 | ||||||||
\(945\) | −6.18695 | −0.201262 | ||||||||
\(946\) | −120.975 | −3.93322 | ||||||||
\(947\) | −44.4077 | −1.44306 | −0.721529 | − | 0.692384i | \(-0.756560\pi\) | ||||
−0.721529 | + | 0.692384i | \(0.756560\pi\) | |||||||
\(948\) | −8.70868 | −0.282845 | ||||||||
\(949\) | −4.49955 | −0.146062 | ||||||||
\(950\) | −8.33787 | −0.270516 | ||||||||
\(951\) | −41.0277 | −1.33041 | ||||||||
\(952\) | −27.8705 | −0.903287 | ||||||||
\(953\) | −9.16837 | −0.296993 | −0.148496 | − | 0.988913i | \(-0.547443\pi\) | ||||
−0.148496 | + | 0.988913i | \(0.547443\pi\) | |||||||
\(954\) | 9.26145 | 0.299851 | ||||||||
\(955\) | −89.0633 | −2.88202 | ||||||||
\(956\) | −34.1159 | −1.10339 | ||||||||
\(957\) | 78.7731 | 2.54637 | ||||||||
\(958\) | −15.8571 | −0.512319 | ||||||||
\(959\) | 18.9872 | 0.613128 | ||||||||
\(960\) | 5.68971 | 0.183635 | ||||||||
\(961\) | −9.85794 | −0.317998 | ||||||||
\(962\) | −0.0748024 | −0.00241173 | ||||||||
\(963\) | −27.7806 | −0.895217 | ||||||||
\(964\) | −2.67298 | −0.0860909 | ||||||||
\(965\) | −54.0785 | −1.74085 | ||||||||
\(966\) | −202.827 | −6.52584 | ||||||||
\(967\) | 0.604773 | 0.0194482 | 0.00972410 | − | 0.999953i | \(-0.496905\pi\) | ||||
0.00972410 | + | 0.999953i | \(0.496905\pi\) | |||||||
\(968\) | −96.7943 | −3.11109 | ||||||||
\(969\) | 1.31258 | 0.0421661 | ||||||||
\(970\) | −70.5987 | −2.26679 | ||||||||
\(971\) | −32.9034 | −1.05592 | −0.527960 | − | 0.849269i | \(-0.677043\pi\) | ||||
−0.527960 | + | 0.849269i | \(0.677043\pi\) | |||||||
\(972\) | −97.5682 | −3.12950 | ||||||||
\(973\) | −20.3028 | −0.650877 | ||||||||
\(974\) | 38.8002 | 1.24324 | ||||||||
\(975\) | −6.23687 | −0.199740 | ||||||||
\(976\) | 52.6008 | 1.68371 | ||||||||
\(977\) | −26.9227 | −0.861333 | −0.430666 | − | 0.902511i | \(-0.641721\pi\) | ||||
−0.430666 | + | 0.902511i | \(0.641721\pi\) | |||||||
\(978\) | 93.8374 | 3.00059 | ||||||||
\(979\) | 64.4200 | 2.05887 | ||||||||
\(980\) | 86.2534 | 2.75526 | ||||||||
\(981\) | 31.5179 | 1.00629 | ||||||||
\(982\) | 14.3808 | 0.458909 | ||||||||
\(983\) | −7.23485 | −0.230756 | −0.115378 | − | 0.993322i | \(-0.536808\pi\) | ||||
−0.115378 | + | 0.993322i | \(0.536808\pi\) | |||||||
\(984\) | −66.3829 | −2.11621 | ||||||||
\(985\) | 75.9046 | 2.41852 | ||||||||
\(986\) | 20.0902 | 0.639803 | ||||||||
\(987\) | 21.4793 | 0.683693 | ||||||||
\(988\) | −0.712127 | −0.0226558 | ||||||||
\(989\) | −86.9119 | −2.76364 | ||||||||
\(990\) | 127.729 | 4.05951 | ||||||||
\(991\) | 19.4088 | 0.616539 | 0.308270 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308270 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(992\) | −27.9704 | −0.888062 | ||||||||
\(993\) | −5.96759 | −0.189376 | ||||||||
\(994\) | −57.0372 | −1.80911 | ||||||||
\(995\) | 3.28468 | 0.104131 | ||||||||
\(996\) | 29.0128 | 0.919307 | ||||||||
\(997\) | −44.0654 | −1.39557 | −0.697783 | − | 0.716310i | \(-0.745830\pi\) | ||||
−0.697783 | + | 0.716310i | \(0.745830\pi\) | |||||||
\(998\) | −99.5958 | −3.15265 | ||||||||
\(999\) | 0.0414047 | 0.00130999 |
(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 | 4001.2.a.b.1.15 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.15 | ✓ | 184 | 1.1 | even | 1 | trivial |