Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51181 | −1.77612 | −0.888060 | − | 0.459727i | \(-0.847947\pi\) | ||||
−0.888060 | + | 0.459727i | \(0.847947\pi\) | |||||||
\(3\) | −2.99105 | −1.72688 | −0.863440 | − | 0.504451i | \(-0.831695\pi\) | ||||
−0.863440 | + | 0.504451i | \(0.831695\pi\) | |||||||
\(4\) | 4.30921 | 2.15460 | ||||||||
\(5\) | 1.76112 | 0.787596 | 0.393798 | − | 0.919197i | \(-0.371161\pi\) | ||||
0.393798 | + | 0.919197i | \(0.371161\pi\) | |||||||
\(6\) | 7.51295 | 3.06715 | ||||||||
\(7\) | 3.89256 | 1.47125 | 0.735625 | − | 0.677389i | \(-0.236889\pi\) | ||||
0.735625 | + | 0.677389i | \(0.236889\pi\) | |||||||
\(8\) | −5.80031 | −2.05072 | ||||||||
\(9\) | 5.94635 | 1.98212 | ||||||||
\(10\) | −4.42360 | −1.39886 | ||||||||
\(11\) | −5.42983 | −1.63716 | −0.818578 | − | 0.574395i | \(-0.805237\pi\) | ||||
−0.818578 | + | 0.574395i | \(0.805237\pi\) | |||||||
\(12\) | −12.8890 | −3.72075 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −9.77739 | −2.61312 | ||||||||
\(15\) | −5.26758 | −1.36008 | ||||||||
\(16\) | 5.95087 | 1.48772 | ||||||||
\(17\) | 3.49734 | 0.848231 | 0.424115 | − | 0.905608i | \(-0.360585\pi\) | ||||
0.424115 | + | 0.905608i | \(0.360585\pi\) | |||||||
\(18\) | −14.9361 | −3.52048 | ||||||||
\(19\) | 4.03795 | 0.926368 | 0.463184 | − | 0.886262i | \(-0.346707\pi\) | ||||
0.463184 | + | 0.886262i | \(0.346707\pi\) | |||||||
\(20\) | 7.58902 | 1.69696 | ||||||||
\(21\) | −11.6428 | −2.54067 | ||||||||
\(22\) | 13.6387 | 2.90779 | ||||||||
\(23\) | −6.04800 | −1.26109 | −0.630547 | − | 0.776151i | \(-0.717169\pi\) | ||||
−0.630547 | + | 0.776151i | \(0.717169\pi\) | |||||||
\(24\) | 17.3490 | 3.54135 | ||||||||
\(25\) | −1.89847 | −0.379693 | ||||||||
\(26\) | 2.51181 | 0.492607 | ||||||||
\(27\) | −8.81267 | −1.69600 | ||||||||
\(28\) | 16.7739 | 3.16996 | ||||||||
\(29\) | −9.38630 | −1.74299 | −0.871497 | − | 0.490402i | \(-0.836850\pi\) | ||||
−0.871497 | + | 0.490402i | \(0.836850\pi\) | |||||||
\(30\) | 13.2312 | 2.41567 | ||||||||
\(31\) | 6.27218 | 1.12652 | 0.563258 | − | 0.826281i | \(-0.309548\pi\) | ||||
0.563258 | + | 0.826281i | \(0.309548\pi\) | |||||||
\(32\) | −3.34687 | −0.591648 | ||||||||
\(33\) | 16.2409 | 2.82717 | ||||||||
\(34\) | −8.78468 | −1.50656 | ||||||||
\(35\) | 6.85525 | 1.15875 | ||||||||
\(36\) | 25.6241 | 4.27068 | ||||||||
\(37\) | 7.54791 | 1.24087 | 0.620435 | − | 0.784258i | \(-0.286956\pi\) | ||||
0.620435 | + | 0.784258i | \(0.286956\pi\) | |||||||
\(38\) | −10.1426 | −1.64534 | ||||||||
\(39\) | 2.99105 | 0.478951 | ||||||||
\(40\) | −10.2150 | −1.61514 | ||||||||
\(41\) | 9.87852 | 1.54277 | 0.771383 | − | 0.636372i | \(-0.219565\pi\) | ||||
0.771383 | + | 0.636372i | \(0.219565\pi\) | |||||||
\(42\) | 29.2446 | 4.51254 | ||||||||
\(43\) | −5.32767 | −0.812462 | −0.406231 | − | 0.913770i | \(-0.633157\pi\) | ||||
−0.406231 | + | 0.913770i | \(0.633157\pi\) | |||||||
\(44\) | −23.3983 | −3.52743 | ||||||||
\(45\) | 10.4722 | 1.56111 | ||||||||
\(46\) | 15.1914 | 2.23986 | ||||||||
\(47\) | 8.51872 | 1.24258 | 0.621292 | − | 0.783579i | \(-0.286608\pi\) | ||||
0.621292 | + | 0.783579i | \(0.286608\pi\) | |||||||
\(48\) | −17.7993 | −2.56911 | ||||||||
\(49\) | 8.15202 | 1.16457 | ||||||||
\(50\) | 4.76859 | 0.674381 | ||||||||
\(51\) | −10.4607 | −1.46479 | ||||||||
\(52\) | −4.30921 | −0.597580 | ||||||||
\(53\) | −6.65992 | −0.914810 | −0.457405 | − | 0.889258i | \(-0.651221\pi\) | ||||
−0.457405 | + | 0.889258i | \(0.651221\pi\) | |||||||
\(54\) | 22.1358 | 3.01230 | ||||||||
\(55\) | −9.56257 | −1.28942 | ||||||||
\(56\) | −22.5780 | −3.01712 | ||||||||
\(57\) | −12.0777 | −1.59973 | ||||||||
\(58\) | 23.5767 | 3.09577 | ||||||||
\(59\) | −4.16499 | −0.542235 | −0.271118 | − | 0.962546i | \(-0.587393\pi\) | ||||
−0.271118 | + | 0.962546i | \(0.587393\pi\) | |||||||
\(60\) | −22.6991 | −2.93044 | ||||||||
\(61\) | −15.3368 | −1.96368 | −0.981838 | − | 0.189723i | \(-0.939241\pi\) | ||||
−0.981838 | + | 0.189723i | \(0.939241\pi\) | |||||||
\(62\) | −15.7545 | −2.00083 | ||||||||
\(63\) | 23.1465 | 2.91619 | ||||||||
\(64\) | −3.49503 | −0.436879 | ||||||||
\(65\) | −1.76112 | −0.218440 | ||||||||
\(66\) | −40.7941 | −5.02140 | ||||||||
\(67\) | 3.15830 | 0.385848 | 0.192924 | − | 0.981214i | \(-0.438203\pi\) | ||||
0.192924 | + | 0.981214i | \(0.438203\pi\) | |||||||
\(68\) | 15.0708 | 1.82760 | ||||||||
\(69\) | 18.0898 | 2.17776 | ||||||||
\(70\) | −17.2191 | −2.05808 | ||||||||
\(71\) | 10.8333 | 1.28568 | 0.642838 | − | 0.766002i | \(-0.277757\pi\) | ||||
0.642838 | + | 0.766002i | \(0.277757\pi\) | |||||||
\(72\) | −34.4907 | −4.06476 | ||||||||
\(73\) | −2.84051 | −0.332456 | −0.166228 | − | 0.986087i | \(-0.553159\pi\) | ||||
−0.166228 | + | 0.986087i | \(0.553159\pi\) | |||||||
\(74\) | −18.9590 | −2.20393 | ||||||||
\(75\) | 5.67840 | 0.655685 | ||||||||
\(76\) | 17.4004 | 1.99596 | ||||||||
\(77\) | −21.1360 | −2.40867 | ||||||||
\(78\) | −7.51295 | −0.850674 | ||||||||
\(79\) | 9.78667 | 1.10109 | 0.550543 | − | 0.834807i | \(-0.314421\pi\) | ||||
0.550543 | + | 0.834807i | \(0.314421\pi\) | |||||||
\(80\) | 10.4802 | 1.17172 | ||||||||
\(81\) | 8.52003 | 0.946670 | ||||||||
\(82\) | −24.8130 | −2.74014 | ||||||||
\(83\) | −2.31751 | −0.254379 | −0.127190 | − | 0.991878i | \(-0.540596\pi\) | ||||
−0.127190 | + | 0.991878i | \(0.540596\pi\) | |||||||
\(84\) | −50.1714 | −5.47414 | ||||||||
\(85\) | 6.15923 | 0.668063 | ||||||||
\(86\) | 13.3821 | 1.44303 | ||||||||
\(87\) | 28.0749 | 3.00994 | ||||||||
\(88\) | 31.4947 | 3.35735 | ||||||||
\(89\) | −13.4969 | −1.43067 | −0.715334 | − | 0.698783i | \(-0.753725\pi\) | ||||
−0.715334 | + | 0.698783i | \(0.753725\pi\) | |||||||
\(90\) | −26.3043 | −2.77271 | ||||||||
\(91\) | −3.89256 | −0.408051 | ||||||||
\(92\) | −26.0621 | −2.71716 | ||||||||
\(93\) | −18.7604 | −1.94536 | ||||||||
\(94\) | −21.3974 | −2.20698 | ||||||||
\(95\) | 7.11130 | 0.729604 | ||||||||
\(96\) | 10.0106 | 1.02171 | ||||||||
\(97\) | −12.2652 | −1.24534 | −0.622670 | − | 0.782485i | \(-0.713952\pi\) | ||||
−0.622670 | + | 0.782485i | \(0.713952\pi\) | |||||||
\(98\) | −20.4764 | −2.06843 | ||||||||
\(99\) | −32.2877 | −3.24504 | ||||||||
\(100\) | −8.18089 | −0.818089 | ||||||||
\(101\) | −13.5097 | −1.34427 | −0.672134 | − | 0.740429i | \(-0.734622\pi\) | ||||
−0.672134 | + | 0.740429i | \(0.734622\pi\) | |||||||
\(102\) | 26.2754 | 2.60165 | ||||||||
\(103\) | 8.28325 | 0.816173 | 0.408086 | − | 0.912943i | \(-0.366196\pi\) | ||||
0.408086 | + | 0.912943i | \(0.366196\pi\) | |||||||
\(104\) | 5.80031 | 0.568767 | ||||||||
\(105\) | −20.5044 | −2.00102 | ||||||||
\(106\) | 16.7285 | 1.62481 | ||||||||
\(107\) | −7.63331 | −0.737940 | −0.368970 | − | 0.929441i | \(-0.620289\pi\) | ||||
−0.368970 | + | 0.929441i | \(0.620289\pi\) | |||||||
\(108\) | −37.9756 | −3.65421 | ||||||||
\(109\) | 4.26933 | 0.408928 | 0.204464 | − | 0.978874i | \(-0.434455\pi\) | ||||
0.204464 | + | 0.978874i | \(0.434455\pi\) | |||||||
\(110\) | 24.0194 | 2.29016 | ||||||||
\(111\) | −22.5761 | −2.14283 | ||||||||
\(112\) | 23.1641 | 2.18880 | ||||||||
\(113\) | −11.6296 | −1.09402 | −0.547012 | − | 0.837125i | \(-0.684235\pi\) | ||||
−0.547012 | + | 0.837125i | \(0.684235\pi\) | |||||||
\(114\) | 30.3369 | 2.84131 | ||||||||
\(115\) | −10.6512 | −0.993232 | ||||||||
\(116\) | −40.4476 | −3.75546 | ||||||||
\(117\) | −5.94635 | −0.549740 | ||||||||
\(118\) | 10.4617 | 0.963075 | ||||||||
\(119\) | 13.6136 | 1.24796 | ||||||||
\(120\) | 30.5536 | 2.78915 | ||||||||
\(121\) | 18.4831 | 1.68028 | ||||||||
\(122\) | 38.5232 | 3.48772 | ||||||||
\(123\) | −29.5471 | −2.66417 | ||||||||
\(124\) | 27.0281 | 2.42720 | ||||||||
\(125\) | −12.1490 | −1.08664 | ||||||||
\(126\) | −58.1398 | −5.17950 | ||||||||
\(127\) | 4.77812 | 0.423990 | 0.211995 | − | 0.977271i | \(-0.432004\pi\) | ||||
0.211995 | + | 0.977271i | \(0.432004\pi\) | |||||||
\(128\) | 15.4726 | 1.36760 | ||||||||
\(129\) | 15.9353 | 1.40303 | ||||||||
\(130\) | 4.42360 | 0.387975 | ||||||||
\(131\) | 11.7456 | 1.02621 | 0.513107 | − | 0.858324i | \(-0.328494\pi\) | ||||
0.513107 | + | 0.858324i | \(0.328494\pi\) | |||||||
\(132\) | 69.9854 | 6.09144 | ||||||||
\(133\) | 15.7179 | 1.36292 | ||||||||
\(134\) | −7.93307 | −0.685313 | ||||||||
\(135\) | −15.5201 | −1.33576 | ||||||||
\(136\) | −20.2857 | −1.73948 | ||||||||
\(137\) | −4.13947 | −0.353659 | −0.176830 | − | 0.984241i | \(-0.556584\pi\) | ||||
−0.176830 | + | 0.984241i | \(0.556584\pi\) | |||||||
\(138\) | −45.4383 | −3.86796 | ||||||||
\(139\) | −12.8403 | −1.08910 | −0.544551 | − | 0.838728i | \(-0.683300\pi\) | ||||
−0.544551 | + | 0.838728i | \(0.683300\pi\) | |||||||
\(140\) | 29.5407 | 2.49665 | ||||||||
\(141\) | −25.4799 | −2.14579 | ||||||||
\(142\) | −27.2112 | −2.28352 | ||||||||
\(143\) | 5.42983 | 0.454066 | ||||||||
\(144\) | 35.3860 | 2.94883 | ||||||||
\(145\) | −16.5304 | −1.37277 | ||||||||
\(146\) | 7.13483 | 0.590483 | ||||||||
\(147\) | −24.3831 | −2.01108 | ||||||||
\(148\) | 32.5255 | 2.67358 | ||||||||
\(149\) | −16.8623 | −1.38142 | −0.690708 | − | 0.723134i | \(-0.742701\pi\) | ||||
−0.690708 | + | 0.723134i | \(0.742701\pi\) | |||||||
\(150\) | −14.2631 | −1.16458 | ||||||||
\(151\) | 11.5132 | 0.936930 | 0.468465 | − | 0.883482i | \(-0.344807\pi\) | ||||
0.468465 | + | 0.883482i | \(0.344807\pi\) | |||||||
\(152\) | −23.4213 | −1.89972 | ||||||||
\(153\) | 20.7964 | 1.68129 | ||||||||
\(154\) | 53.0896 | 4.27808 | ||||||||
\(155\) | 11.0460 | 0.887239 | ||||||||
\(156\) | 12.8890 | 1.03195 | ||||||||
\(157\) | 3.81230 | 0.304255 | 0.152127 | − | 0.988361i | \(-0.451388\pi\) | ||||
0.152127 | + | 0.988361i | \(0.451388\pi\) | |||||||
\(158\) | −24.5823 | −1.95566 | ||||||||
\(159\) | 19.9201 | 1.57977 | ||||||||
\(160\) | −5.89423 | −0.465980 | ||||||||
\(161\) | −23.5422 | −1.85538 | ||||||||
\(162\) | −21.4007 | −1.68140 | ||||||||
\(163\) | 13.2923 | 1.04113 | 0.520566 | − | 0.853822i | \(-0.325721\pi\) | ||||
0.520566 | + | 0.853822i | \(0.325721\pi\) | |||||||
\(164\) | 42.5686 | 3.32405 | ||||||||
\(165\) | 28.6021 | 2.22667 | ||||||||
\(166\) | 5.82115 | 0.451809 | ||||||||
\(167\) | −9.55572 | −0.739444 | −0.369722 | − | 0.929142i | \(-0.620547\pi\) | ||||
−0.369722 | + | 0.929142i | \(0.620547\pi\) | |||||||
\(168\) | 67.5319 | 5.21020 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −15.4708 | −1.18656 | ||||||||
\(171\) | 24.0110 | 1.83617 | ||||||||
\(172\) | −22.9581 | −1.75054 | ||||||||
\(173\) | 17.8207 | 1.35489 | 0.677443 | − | 0.735576i | \(-0.263088\pi\) | ||||
0.677443 | + | 0.735576i | \(0.263088\pi\) | |||||||
\(174\) | −70.5188 | −5.34602 | ||||||||
\(175\) | −7.38989 | −0.558623 | ||||||||
\(176\) | −32.3122 | −2.43563 | ||||||||
\(177\) | 12.4577 | 0.936376 | ||||||||
\(178\) | 33.9017 | 2.54104 | ||||||||
\(179\) | −16.5228 | −1.23497 | −0.617486 | − | 0.786582i | \(-0.711849\pi\) | ||||
−0.617486 | + | 0.786582i | \(0.711849\pi\) | |||||||
\(180\) | 45.1270 | 3.36357 | ||||||||
\(181\) | −13.5494 | −1.00712 | −0.503561 | − | 0.863960i | \(-0.667977\pi\) | ||||
−0.503561 | + | 0.863960i | \(0.667977\pi\) | |||||||
\(182\) | 9.77739 | 0.724748 | ||||||||
\(183\) | 45.8730 | 3.39103 | ||||||||
\(184\) | 35.0802 | 2.58615 | ||||||||
\(185\) | 13.2928 | 0.977303 | ||||||||
\(186\) | 47.1226 | 3.45519 | ||||||||
\(187\) | −18.9900 | −1.38869 | ||||||||
\(188\) | 36.7090 | 2.67728 | ||||||||
\(189\) | −34.3038 | −2.49524 | ||||||||
\(190\) | −17.8623 | −1.29586 | ||||||||
\(191\) | 1.18068 | 0.0854311 | 0.0427156 | − | 0.999087i | \(-0.486399\pi\) | ||||
0.0427156 | + | 0.999087i | \(0.486399\pi\) | |||||||
\(192\) | 10.4538 | 0.754437 | ||||||||
\(193\) | 7.24026 | 0.521166 | 0.260583 | − | 0.965452i | \(-0.416085\pi\) | ||||
0.260583 | + | 0.965452i | \(0.416085\pi\) | |||||||
\(194\) | 30.8078 | 2.21187 | ||||||||
\(195\) | 5.26758 | 0.377219 | ||||||||
\(196\) | 35.1288 | 2.50920 | ||||||||
\(197\) | 16.5870 | 1.18177 | 0.590887 | − | 0.806755i | \(-0.298778\pi\) | ||||
0.590887 | + | 0.806755i | \(0.298778\pi\) | |||||||
\(198\) | 81.1007 | 5.76358 | ||||||||
\(199\) | −24.2241 | −1.71720 | −0.858599 | − | 0.512647i | \(-0.828665\pi\) | ||||
−0.858599 | + | 0.512647i | \(0.828665\pi\) | |||||||
\(200\) | 11.0117 | 0.778644 | ||||||||
\(201\) | −9.44663 | −0.666314 | ||||||||
\(202\) | 33.9339 | 2.38758 | ||||||||
\(203\) | −36.5368 | −2.56438 | ||||||||
\(204\) | −45.0774 | −3.15605 | ||||||||
\(205\) | 17.3972 | 1.21508 | ||||||||
\(206\) | −20.8060 | −1.44962 | ||||||||
\(207\) | −35.9635 | −2.49964 | ||||||||
\(208\) | −5.95087 | −0.412619 | ||||||||
\(209\) | −21.9254 | −1.51661 | ||||||||
\(210\) | 51.5032 | 3.55406 | ||||||||
\(211\) | −14.2839 | −0.983342 | −0.491671 | − | 0.870781i | \(-0.663614\pi\) | ||||
−0.491671 | + | 0.870781i | \(0.663614\pi\) | |||||||
\(212\) | −28.6990 | −1.97105 | ||||||||
\(213\) | −32.4029 | −2.22021 | ||||||||
\(214\) | 19.1734 | 1.31067 | ||||||||
\(215\) | −9.38266 | −0.639892 | ||||||||
\(216\) | 51.1162 | 3.47801 | ||||||||
\(217\) | 24.4148 | 1.65739 | ||||||||
\(218\) | −10.7238 | −0.726306 | ||||||||
\(219\) | 8.49609 | 0.574112 | ||||||||
\(220\) | −41.2071 | −2.77818 | ||||||||
\(221\) | −3.49734 | −0.235257 | ||||||||
\(222\) | 56.7071 | 3.80593 | ||||||||
\(223\) | 18.5319 | 1.24099 | 0.620493 | − | 0.784212i | \(-0.286932\pi\) | ||||
0.620493 | + | 0.784212i | \(0.286932\pi\) | |||||||
\(224\) | −13.0279 | −0.870462 | ||||||||
\(225\) | −11.2889 | −0.752596 | ||||||||
\(226\) | 29.2115 | 1.94312 | ||||||||
\(227\) | 22.5663 | 1.49778 | 0.748890 | − | 0.662695i | \(-0.230587\pi\) | ||||
0.748890 | + | 0.662695i | \(0.230587\pi\) | |||||||
\(228\) | −52.0453 | −3.44678 | ||||||||
\(229\) | −1.74389 | −0.115239 | −0.0576196 | − | 0.998339i | \(-0.518351\pi\) | ||||
−0.0576196 | + | 0.998339i | \(0.518351\pi\) | |||||||
\(230\) | 26.7539 | 1.76410 | ||||||||
\(231\) | 63.2186 | 4.15948 | ||||||||
\(232\) | 54.4434 | 3.57439 | ||||||||
\(233\) | −14.8912 | −0.975558 | −0.487779 | − | 0.872967i | \(-0.662193\pi\) | ||||
−0.487779 | + | 0.872967i | \(0.662193\pi\) | |||||||
\(234\) | 14.9361 | 0.976405 | ||||||||
\(235\) | 15.0025 | 0.978653 | ||||||||
\(236\) | −17.9478 | −1.16830 | ||||||||
\(237\) | −29.2724 | −1.90144 | ||||||||
\(238\) | −34.1949 | −2.21653 | ||||||||
\(239\) | 19.1194 | 1.23673 | 0.618367 | − | 0.785889i | \(-0.287795\pi\) | ||||
0.618367 | + | 0.785889i | \(0.287795\pi\) | |||||||
\(240\) | −31.3467 | −2.02342 | ||||||||
\(241\) | −14.8340 | −0.955545 | −0.477772 | − | 0.878484i | \(-0.658556\pi\) | ||||
−0.477772 | + | 0.878484i | \(0.658556\pi\) | |||||||
\(242\) | −46.4261 | −2.98438 | ||||||||
\(243\) | 0.954196 | 0.0612117 | ||||||||
\(244\) | −66.0895 | −4.23094 | ||||||||
\(245\) | 14.3567 | 0.917214 | ||||||||
\(246\) | 74.2168 | 4.73189 | ||||||||
\(247\) | −4.03795 | −0.256928 | ||||||||
\(248\) | −36.3806 | −2.31017 | ||||||||
\(249\) | 6.93177 | 0.439283 | ||||||||
\(250\) | 30.5160 | 1.93000 | ||||||||
\(251\) | 3.01486 | 0.190296 | 0.0951480 | − | 0.995463i | \(-0.469668\pi\) | ||||
0.0951480 | + | 0.995463i | \(0.469668\pi\) | |||||||
\(252\) | 99.7432 | 6.28323 | ||||||||
\(253\) | 32.8396 | 2.06461 | ||||||||
\(254\) | −12.0017 | −0.753057 | ||||||||
\(255\) | −18.4225 | −1.15366 | ||||||||
\(256\) | −31.8742 | −1.99214 | ||||||||
\(257\) | 14.9671 | 0.933620 | 0.466810 | − | 0.884358i | \(-0.345403\pi\) | ||||
0.466810 | + | 0.884358i | \(0.345403\pi\) | |||||||
\(258\) | −40.0265 | −2.49194 | ||||||||
\(259\) | 29.3807 | 1.82563 | ||||||||
\(260\) | −7.58902 | −0.470651 | ||||||||
\(261\) | −55.8143 | −3.45482 | ||||||||
\(262\) | −29.5027 | −1.82268 | ||||||||
\(263\) | 27.2285 | 1.67898 | 0.839489 | − | 0.543376i | \(-0.182854\pi\) | ||||
0.839489 | + | 0.543376i | \(0.182854\pi\) | |||||||
\(264\) | −94.2021 | −5.79774 | ||||||||
\(265\) | −11.7289 | −0.720500 | ||||||||
\(266\) | −39.4806 | −2.42071 | ||||||||
\(267\) | 40.3698 | 2.47059 | ||||||||
\(268\) | 13.6098 | 0.831351 | ||||||||
\(269\) | −2.42331 | −0.147752 | −0.0738758 | − | 0.997267i | \(-0.523537\pi\) | ||||
−0.0738758 | + | 0.997267i | \(0.523537\pi\) | |||||||
\(270\) | 38.9837 | 2.37247 | ||||||||
\(271\) | −26.9724 | −1.63846 | −0.819229 | − | 0.573466i | \(-0.805598\pi\) | ||||
−0.819229 | + | 0.573466i | \(0.805598\pi\) | |||||||
\(272\) | 20.8122 | 1.26193 | ||||||||
\(273\) | 11.6428 | 0.704656 | ||||||||
\(274\) | 10.3976 | 0.628141 | ||||||||
\(275\) | 10.3084 | 0.621617 | ||||||||
\(276\) | 77.9529 | 4.69221 | ||||||||
\(277\) | 22.5664 | 1.35588 | 0.677942 | − | 0.735115i | \(-0.262872\pi\) | ||||
0.677942 | + | 0.735115i | \(0.262872\pi\) | |||||||
\(278\) | 32.2525 | 1.93438 | ||||||||
\(279\) | 37.2966 | 2.23289 | ||||||||
\(280\) | −39.7626 | −2.37627 | ||||||||
\(281\) | −29.9857 | −1.78880 | −0.894399 | − | 0.447270i | \(-0.852396\pi\) | ||||
−0.894399 | + | 0.447270i | \(0.852396\pi\) | |||||||
\(282\) | 64.0007 | 3.81119 | ||||||||
\(283\) | −22.2092 | −1.32020 | −0.660101 | − | 0.751177i | \(-0.729487\pi\) | ||||
−0.660101 | + | 0.751177i | \(0.729487\pi\) | |||||||
\(284\) | 46.6830 | 2.77012 | ||||||||
\(285\) | −21.2702 | −1.25994 | ||||||||
\(286\) | −13.6387 | −0.806475 | ||||||||
\(287\) | 38.4527 | 2.26979 | ||||||||
\(288\) | −19.9017 | −1.17272 | ||||||||
\(289\) | −4.76858 | −0.280505 | ||||||||
\(290\) | 41.5212 | 2.43821 | ||||||||
\(291\) | 36.6857 | 2.15055 | ||||||||
\(292\) | −12.2403 | −0.716312 | ||||||||
\(293\) | −0.859670 | −0.0502225 | −0.0251112 | − | 0.999685i | \(-0.507994\pi\) | ||||
−0.0251112 | + | 0.999685i | \(0.507994\pi\) | |||||||
\(294\) | 61.2457 | 3.57192 | ||||||||
\(295\) | −7.33503 | −0.427062 | ||||||||
\(296\) | −43.7802 | −2.54467 | ||||||||
\(297\) | 47.8513 | 2.77662 | ||||||||
\(298\) | 42.3550 | 2.45356 | ||||||||
\(299\) | 6.04800 | 0.349765 | ||||||||
\(300\) | 24.4694 | 1.41274 | ||||||||
\(301\) | −20.7383 | −1.19533 | ||||||||
\(302\) | −28.9190 | −1.66410 | ||||||||
\(303\) | 40.4082 | 2.32139 | ||||||||
\(304\) | 24.0293 | 1.37817 | ||||||||
\(305\) | −27.0099 | −1.54658 | ||||||||
\(306\) | −52.2368 | −2.98618 | ||||||||
\(307\) | −26.9448 | −1.53782 | −0.768911 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768911 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(308\) | −91.0793 | −5.18972 | ||||||||
\(309\) | −24.7756 | −1.40943 | ||||||||
\(310\) | −27.7456 | −1.57584 | ||||||||
\(311\) | −1.56447 | −0.0887131 | −0.0443565 | − | 0.999016i | \(-0.514124\pi\) | ||||
−0.0443565 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(312\) | −17.3490 | −0.982192 | ||||||||
\(313\) | 8.79620 | 0.497190 | 0.248595 | − | 0.968607i | \(-0.420031\pi\) | ||||
0.248595 | + | 0.968607i | \(0.420031\pi\) | |||||||
\(314\) | −9.57578 | −0.540393 | ||||||||
\(315\) | 40.7637 | 2.29678 | ||||||||
\(316\) | 42.1728 | 2.37241 | ||||||||
\(317\) | 32.7422 | 1.83898 | 0.919492 | − | 0.393108i | \(-0.128600\pi\) | ||||
0.919492 | + | 0.393108i | \(0.128600\pi\) | |||||||
\(318\) | −50.0356 | −2.80586 | ||||||||
\(319\) | 50.9661 | 2.85355 | ||||||||
\(320\) | −6.15516 | −0.344084 | ||||||||
\(321\) | 22.8316 | 1.27433 | ||||||||
\(322\) | 59.1336 | 3.29539 | ||||||||
\(323\) | 14.1221 | 0.785774 | ||||||||
\(324\) | 36.7146 | 2.03970 | ||||||||
\(325\) | 1.89847 | 0.105308 | ||||||||
\(326\) | −33.3877 | −1.84918 | ||||||||
\(327\) | −12.7698 | −0.706170 | ||||||||
\(328\) | −57.2984 | −3.16378 | ||||||||
\(329\) | 33.1596 | 1.82815 | ||||||||
\(330\) | −71.8431 | −3.95483 | ||||||||
\(331\) | −11.3480 | −0.623743 | −0.311871 | − | 0.950124i | \(-0.600956\pi\) | ||||
−0.311871 | + | 0.950124i | \(0.600956\pi\) | |||||||
\(332\) | −9.98662 | −0.548087 | ||||||||
\(333\) | 44.8825 | 2.45955 | ||||||||
\(334\) | 24.0022 | 1.31334 | ||||||||
\(335\) | 5.56214 | 0.303892 | ||||||||
\(336\) | −69.2849 | −3.77980 | ||||||||
\(337\) | −26.1101 | −1.42231 | −0.711155 | − | 0.703035i | \(-0.751828\pi\) | ||||
−0.711155 | + | 0.703035i | \(0.751828\pi\) | |||||||
\(338\) | −2.51181 | −0.136625 | ||||||||
\(339\) | 34.7847 | 1.88925 | ||||||||
\(340\) | 26.5414 | 1.43941 | ||||||||
\(341\) | −34.0569 | −1.84428 | ||||||||
\(342\) | −60.3113 | −3.26126 | ||||||||
\(343\) | 4.48432 | 0.242131 | ||||||||
\(344\) | 30.9021 | 1.66613 | ||||||||
\(345\) | 31.8583 | 1.71519 | ||||||||
\(346\) | −44.7624 | −2.40644 | ||||||||
\(347\) | 4.21683 | 0.226371 | 0.113186 | − | 0.993574i | \(-0.463895\pi\) | ||||
0.113186 | + | 0.993574i | \(0.463895\pi\) | |||||||
\(348\) | 120.980 | 6.48523 | ||||||||
\(349\) | 12.4441 | 0.666118 | 0.333059 | − | 0.942906i | \(-0.391919\pi\) | ||||
0.333059 | + | 0.942906i | \(0.391919\pi\) | |||||||
\(350\) | 18.5620 | 0.992183 | ||||||||
\(351\) | 8.81267 | 0.470385 | ||||||||
\(352\) | 18.1729 | 0.968621 | ||||||||
\(353\) | −36.3534 | −1.93490 | −0.967449 | − | 0.253066i | \(-0.918561\pi\) | ||||
−0.967449 | + | 0.253066i | \(0.918561\pi\) | |||||||
\(354\) | −31.2913 | −1.66312 | ||||||||
\(355\) | 19.0787 | 1.01259 | ||||||||
\(356\) | −58.1609 | −3.08252 | ||||||||
\(357\) | −40.7190 | −2.15508 | ||||||||
\(358\) | 41.5022 | 2.19346 | ||||||||
\(359\) | 18.5971 | 0.981517 | 0.490759 | − | 0.871296i | \(-0.336720\pi\) | ||||
0.490759 | + | 0.871296i | \(0.336720\pi\) | |||||||
\(360\) | −60.7421 | −3.20139 | ||||||||
\(361\) | −2.69499 | −0.141842 | ||||||||
\(362\) | 34.0337 | 1.78877 | ||||||||
\(363\) | −55.2838 | −2.90165 | ||||||||
\(364\) | −16.7739 | −0.879189 | ||||||||
\(365\) | −5.00247 | −0.261841 | ||||||||
\(366\) | −115.225 | −6.02288 | ||||||||
\(367\) | 26.7809 | 1.39795 | 0.698976 | − | 0.715145i | \(-0.253640\pi\) | ||||
0.698976 | + | 0.715145i | \(0.253640\pi\) | |||||||
\(368\) | −35.9908 | −1.87615 | ||||||||
\(369\) | 58.7411 | 3.05794 | ||||||||
\(370\) | −33.3889 | −1.73581 | ||||||||
\(371\) | −25.9241 | −1.34591 | ||||||||
\(372\) | −80.8424 | −4.19148 | ||||||||
\(373\) | −7.95613 | −0.411953 | −0.205976 | − | 0.978557i | \(-0.566037\pi\) | ||||
−0.205976 | + | 0.978557i | \(0.566037\pi\) | |||||||
\(374\) | 47.6994 | 2.46647 | ||||||||
\(375\) | 36.3382 | 1.87650 | ||||||||
\(376\) | −49.4112 | −2.54819 | ||||||||
\(377\) | 9.38630 | 0.483419 | ||||||||
\(378\) | 86.1649 | 4.43184 | ||||||||
\(379\) | −8.11162 | −0.416666 | −0.208333 | − | 0.978058i | \(-0.566804\pi\) | ||||
−0.208333 | + | 0.978058i | \(0.566804\pi\) | |||||||
\(380\) | 30.6441 | 1.57201 | ||||||||
\(381\) | −14.2916 | −0.732179 | ||||||||
\(382\) | −2.96565 | −0.151736 | ||||||||
\(383\) | 5.95164 | 0.304115 | 0.152057 | − | 0.988372i | \(-0.451410\pi\) | ||||
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(384\) | −46.2793 | −2.36168 | ||||||||
\(385\) | −37.2229 | −1.89705 | ||||||||
\(386\) | −18.1862 | −0.925653 | ||||||||
\(387\) | −31.6802 | −1.61040 | ||||||||
\(388\) | −52.8532 | −2.68322 | ||||||||
\(389\) | −21.1402 | −1.07185 | −0.535926 | − | 0.844265i | \(-0.680037\pi\) | ||||
−0.535926 | + | 0.844265i | \(0.680037\pi\) | |||||||
\(390\) | −13.2312 | −0.669987 | ||||||||
\(391\) | −21.1519 | −1.06970 | ||||||||
\(392\) | −47.2842 | −2.38821 | ||||||||
\(393\) | −35.1315 | −1.77215 | ||||||||
\(394\) | −41.6634 | −2.09897 | ||||||||
\(395\) | 17.2355 | 0.867211 | ||||||||
\(396\) | −139.134 | −6.99177 | ||||||||
\(397\) | −15.8358 | −0.794774 | −0.397387 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397387 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(398\) | 60.8464 | 3.04995 | ||||||||
\(399\) | −47.0131 | −2.35360 | ||||||||
\(400\) | −11.2975 | −0.564876 | ||||||||
\(401\) | −31.2313 | −1.55962 | −0.779808 | − | 0.626018i | \(-0.784683\pi\) | ||||
−0.779808 | + | 0.626018i | \(0.784683\pi\) | |||||||
\(402\) | 23.7282 | 1.18345 | ||||||||
\(403\) | −6.27218 | −0.312439 | ||||||||
\(404\) | −58.2163 | −2.89637 | ||||||||
\(405\) | 15.0048 | 0.745593 | ||||||||
\(406\) | 91.7735 | 4.55464 | ||||||||
\(407\) | −40.9839 | −2.03150 | ||||||||
\(408\) | 60.6753 | 3.00388 | ||||||||
\(409\) | 26.6186 | 1.31621 | 0.658103 | − | 0.752928i | \(-0.271359\pi\) | ||||
0.658103 | + | 0.752928i | \(0.271359\pi\) | |||||||
\(410\) | −43.6986 | −2.15812 | ||||||||
\(411\) | 12.3814 | 0.610727 | ||||||||
\(412\) | 35.6943 | 1.75853 | ||||||||
\(413\) | −16.2125 | −0.797763 | ||||||||
\(414\) | 90.3336 | 4.43966 | ||||||||
\(415\) | −4.08140 | −0.200348 | ||||||||
\(416\) | 3.34687 | 0.164094 | ||||||||
\(417\) | 38.4060 | 1.88075 | ||||||||
\(418\) | 55.0725 | 2.69368 | ||||||||
\(419\) | −1.24155 | −0.0606539 | −0.0303270 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303270 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(420\) | −88.3577 | −4.31141 | ||||||||
\(421\) | 29.1342 | 1.41992 | 0.709958 | − | 0.704244i | \(-0.248714\pi\) | ||||
0.709958 | + | 0.704244i | \(0.248714\pi\) | |||||||
\(422\) | 35.8784 | 1.74653 | ||||||||
\(423\) | 50.6553 | 2.46295 | ||||||||
\(424\) | 38.6296 | 1.87602 | ||||||||
\(425\) | −6.63959 | −0.322067 | ||||||||
\(426\) | 81.3900 | 3.94336 | ||||||||
\(427\) | −59.6994 | −2.88906 | ||||||||
\(428\) | −32.8935 | −1.58997 | ||||||||
\(429\) | −16.2409 | −0.784117 | ||||||||
\(430\) | 23.5675 | 1.13653 | ||||||||
\(431\) | −20.3554 | −0.980484 | −0.490242 | − | 0.871586i | \(-0.663092\pi\) | ||||
−0.490242 | + | 0.871586i | \(0.663092\pi\) | |||||||
\(432\) | −52.4430 | −2.52317 | ||||||||
\(433\) | −12.8686 | −0.618427 | −0.309213 | − | 0.950993i | \(-0.600066\pi\) | ||||
−0.309213 | + | 0.950993i | \(0.600066\pi\) | |||||||
\(434\) | −61.3255 | −2.94372 | ||||||||
\(435\) | 49.4431 | 2.37062 | ||||||||
\(436\) | 18.3975 | 0.881079 | ||||||||
\(437\) | −24.4215 | −1.16824 | ||||||||
\(438\) | −21.3406 | −1.01969 | ||||||||
\(439\) | −8.91008 | −0.425255 | −0.212628 | − | 0.977133i | \(-0.568202\pi\) | ||||
−0.212628 | + | 0.977133i | \(0.568202\pi\) | |||||||
\(440\) | 55.4659 | 2.64423 | ||||||||
\(441\) | 48.4748 | 2.30832 | ||||||||
\(442\) | 8.78468 | 0.417845 | ||||||||
\(443\) | 0.339655 | 0.0161375 | 0.00806876 | − | 0.999967i | \(-0.497432\pi\) | ||||
0.00806876 | + | 0.999967i | \(0.497432\pi\) | |||||||
\(444\) | −97.2853 | −4.61696 | ||||||||
\(445\) | −23.7696 | −1.12679 | ||||||||
\(446\) | −46.5486 | −2.20414 | ||||||||
\(447\) | 50.4360 | 2.38554 | ||||||||
\(448\) | −13.6046 | −0.642758 | ||||||||
\(449\) | 24.5888 | 1.16042 | 0.580210 | − | 0.814467i | \(-0.302971\pi\) | ||||
0.580210 | + | 0.814467i | \(0.302971\pi\) | |||||||
\(450\) | 28.3557 | 1.33670 | ||||||||
\(451\) | −53.6387 | −2.52575 | ||||||||
\(452\) | −50.1145 | −2.35719 | ||||||||
\(453\) | −34.4365 | −1.61797 | ||||||||
\(454\) | −56.6824 | −2.66024 | ||||||||
\(455\) | −6.85525 | −0.321379 | ||||||||
\(456\) | 70.0542 | 3.28059 | ||||||||
\(457\) | −18.0417 | −0.843955 | −0.421977 | − | 0.906606i | \(-0.638664\pi\) | ||||
−0.421977 | + | 0.906606i | \(0.638664\pi\) | |||||||
\(458\) | 4.38032 | 0.204679 | ||||||||
\(459\) | −30.8209 | −1.43860 | ||||||||
\(460\) | −45.8984 | −2.14002 | ||||||||
\(461\) | 2.58467 | 0.120380 | 0.0601901 | − | 0.998187i | \(-0.480829\pi\) | ||||
0.0601901 | + | 0.998187i | \(0.480829\pi\) | |||||||
\(462\) | −158.793 | −7.38774 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −55.8567 | −2.59308 | ||||||||
\(465\) | −33.0392 | −1.53216 | ||||||||
\(466\) | 37.4040 | 1.73271 | ||||||||
\(467\) | −32.0750 | −1.48425 | −0.742127 | − | 0.670259i | \(-0.766183\pi\) | ||||
−0.742127 | + | 0.670259i | \(0.766183\pi\) | |||||||
\(468\) | −25.6241 | −1.18447 | ||||||||
\(469\) | 12.2939 | 0.567679 | ||||||||
\(470\) | −37.6834 | −1.73821 | ||||||||
\(471\) | −11.4028 | −0.525411 | ||||||||
\(472\) | 24.1582 | 1.11197 | ||||||||
\(473\) | 28.9284 | 1.33013 | ||||||||
\(474\) | 73.5267 | 3.37720 | ||||||||
\(475\) | −7.66590 | −0.351736 | ||||||||
\(476\) | 58.6640 | 2.68886 | ||||||||
\(477\) | −39.6022 | −1.81326 | ||||||||
\(478\) | −48.0245 | −2.19659 | ||||||||
\(479\) | 1.54240 | 0.0704738 | 0.0352369 | − | 0.999379i | \(-0.488781\pi\) | ||||
0.0352369 | + | 0.999379i | \(0.488781\pi\) | |||||||
\(480\) | 17.6299 | 0.804691 | ||||||||
\(481\) | −7.54791 | −0.344155 | ||||||||
\(482\) | 37.2604 | 1.69716 | ||||||||
\(483\) | 70.4158 | 3.20403 | ||||||||
\(484\) | 79.6476 | 3.62034 | ||||||||
\(485\) | −21.6004 | −0.980824 | ||||||||
\(486\) | −2.39676 | −0.108719 | ||||||||
\(487\) | 12.9024 | 0.584662 | 0.292331 | − | 0.956317i | \(-0.405569\pi\) | ||||
0.292331 | + | 0.956317i | \(0.405569\pi\) | |||||||
\(488\) | 88.9581 | 4.02694 | ||||||||
\(489\) | −39.7578 | −1.79791 | ||||||||
\(490\) | −36.0613 | −1.62908 | ||||||||
\(491\) | −12.8284 | −0.578937 | −0.289468 | − | 0.957188i | \(-0.593478\pi\) | ||||
−0.289468 | + | 0.957188i | \(0.593478\pi\) | |||||||
\(492\) | −127.325 | −5.74024 | ||||||||
\(493\) | −32.8271 | −1.47846 | ||||||||
\(494\) | 10.1426 | 0.456336 | ||||||||
\(495\) | −56.8624 | −2.55578 | ||||||||
\(496\) | 37.3249 | 1.67594 | ||||||||
\(497\) | 42.1693 | 1.89155 | ||||||||
\(498\) | −17.4113 | −0.780220 | ||||||||
\(499\) | −8.39311 | −0.375727 | −0.187864 | − | 0.982195i | \(-0.560156\pi\) | ||||
−0.187864 | + | 0.982195i | \(0.560156\pi\) | |||||||
\(500\) | −52.3526 | −2.34128 | ||||||||
\(501\) | 28.5816 | 1.27693 | ||||||||
\(502\) | −7.57276 | −0.337989 | ||||||||
\(503\) | −34.9071 | −1.55643 | −0.778216 | − | 0.627997i | \(-0.783875\pi\) | ||||
−0.778216 | + | 0.627997i | \(0.783875\pi\) | |||||||
\(504\) | −134.257 | −5.98028 | ||||||||
\(505\) | −23.7922 | −1.05874 | ||||||||
\(506\) | −82.4870 | −3.66700 | ||||||||
\(507\) | −2.99105 | −0.132837 | ||||||||
\(508\) | 20.5899 | 0.913530 | ||||||||
\(509\) | −5.51098 | −0.244270 | −0.122135 | − | 0.992514i | \(-0.538974\pi\) | ||||
−0.122135 | + | 0.992514i | \(0.538974\pi\) | |||||||
\(510\) | 46.2740 | 2.04905 | ||||||||
\(511\) | −11.0568 | −0.489126 | ||||||||
\(512\) | 49.1170 | 2.17068 | ||||||||
\(513\) | −35.5851 | −1.57112 | ||||||||
\(514\) | −37.5945 | −1.65822 | ||||||||
\(515\) | 14.5878 | 0.642814 | ||||||||
\(516\) | 68.6686 | 3.02297 | ||||||||
\(517\) | −46.2552 | −2.03430 | ||||||||
\(518\) | −73.7989 | −3.24254 | ||||||||
\(519\) | −53.3026 | −2.33973 | ||||||||
\(520\) | 10.2150 | 0.447958 | ||||||||
\(521\) | 2.94477 | 0.129013 | 0.0645064 | − | 0.997917i | \(-0.479453\pi\) | ||||
0.0645064 | + | 0.997917i | \(0.479453\pi\) | |||||||
\(522\) | 140.195 | 6.13617 | ||||||||
\(523\) | 37.9436 | 1.65916 | 0.829580 | − | 0.558388i | \(-0.188580\pi\) | ||||
0.829580 | + | 0.558388i | \(0.188580\pi\) | |||||||
\(524\) | 50.6141 | 2.21109 | ||||||||
\(525\) | 22.1035 | 0.964676 | ||||||||
\(526\) | −68.3928 | −2.98207 | ||||||||
\(527\) | 21.9360 | 0.955546 | ||||||||
\(528\) | 96.6474 | 4.20604 | ||||||||
\(529\) | 13.5783 | 0.590359 | ||||||||
\(530\) | 29.4608 | 1.27970 | ||||||||
\(531\) | −24.7665 | −1.07477 | ||||||||
\(532\) | 67.7319 | 2.93655 | ||||||||
\(533\) | −9.87852 | −0.427886 | ||||||||
\(534\) | −101.401 | −4.38807 | ||||||||
\(535\) | −13.4431 | −0.581198 | ||||||||
\(536\) | −18.3191 | −0.791266 | ||||||||
\(537\) | 49.4205 | 2.13265 | ||||||||
\(538\) | 6.08689 | 0.262425 | ||||||||
\(539\) | −44.2641 | −1.90659 | ||||||||
\(540\) | −66.8795 | −2.87804 | ||||||||
\(541\) | 8.13089 | 0.349574 | 0.174787 | − | 0.984606i | \(-0.444076\pi\) | ||||
0.174787 | + | 0.984606i | \(0.444076\pi\) | |||||||
\(542\) | 67.7497 | 2.91010 | ||||||||
\(543\) | 40.5270 | 1.73918 | ||||||||
\(544\) | −11.7052 | −0.501854 | ||||||||
\(545\) | 7.51880 | 0.322070 | ||||||||
\(546\) | −29.2446 | −1.25155 | ||||||||
\(547\) | 2.35221 | 0.100573 | 0.0502866 | − | 0.998735i | \(-0.483987\pi\) | ||||
0.0502866 | + | 0.998735i | \(0.483987\pi\) | |||||||
\(548\) | −17.8379 | −0.761996 | ||||||||
\(549\) | −91.1980 | −3.89223 | ||||||||
\(550\) | −25.8927 | −1.10407 | ||||||||
\(551\) | −37.9014 | −1.61465 | ||||||||
\(552\) | −104.927 | −4.46597 | ||||||||
\(553\) | 38.0952 | 1.61997 | ||||||||
\(554\) | −56.6826 | −2.40821 | ||||||||
\(555\) | −39.7592 | −1.68769 | ||||||||
\(556\) | −55.3317 | −2.34659 | ||||||||
\(557\) | 12.2887 | 0.520688 | 0.260344 | − | 0.965516i | \(-0.416164\pi\) | ||||
0.260344 | + | 0.965516i | \(0.416164\pi\) | |||||||
\(558\) | −93.6821 | −3.96588 | ||||||||
\(559\) | 5.32767 | 0.225337 | ||||||||
\(560\) | 40.7947 | 1.72389 | ||||||||
\(561\) | 56.7999 | 2.39810 | ||||||||
\(562\) | 75.3185 | 3.17712 | ||||||||
\(563\) | 32.0547 | 1.35095 | 0.675473 | − | 0.737385i | \(-0.263940\pi\) | ||||
0.675473 | + | 0.737385i | \(0.263940\pi\) | |||||||
\(564\) | −109.798 | −4.62334 | ||||||||
\(565\) | −20.4811 | −0.861648 | ||||||||
\(566\) | 55.7855 | 2.34484 | ||||||||
\(567\) | 33.1647 | 1.39279 | ||||||||
\(568\) | −62.8365 | −2.63656 | ||||||||
\(569\) | −1.66385 | −0.0697521 | −0.0348761 | − | 0.999392i | \(-0.511104\pi\) | ||||
−0.0348761 | + | 0.999392i | \(0.511104\pi\) | |||||||
\(570\) | 53.4268 | 2.23780 | ||||||||
\(571\) | −5.95208 | −0.249087 | −0.124543 | − | 0.992214i | \(-0.539747\pi\) | ||||
−0.124543 | + | 0.992214i | \(0.539747\pi\) | |||||||
\(572\) | 23.3983 | 0.978332 | ||||||||
\(573\) | −3.53147 | −0.147529 | ||||||||
\(574\) | −96.5861 | −4.03143 | ||||||||
\(575\) | 11.4819 | 0.478829 | ||||||||
\(576\) | −20.7827 | −0.865945 | ||||||||
\(577\) | 15.7826 | 0.657038 | 0.328519 | − | 0.944497i | \(-0.393451\pi\) | ||||
0.328519 | + | 0.944497i | \(0.393451\pi\) | |||||||
\(578\) | 11.9778 | 0.498210 | ||||||||
\(579\) | −21.6560 | −0.899991 | ||||||||
\(580\) | −71.2329 | −2.95778 | ||||||||
\(581\) | −9.02103 | −0.374256 | ||||||||
\(582\) | −92.1476 | −3.81964 | ||||||||
\(583\) | 36.1622 | 1.49769 | ||||||||
\(584\) | 16.4758 | 0.681774 | ||||||||
\(585\) | −10.4722 | −0.432973 | ||||||||
\(586\) | 2.15933 | 0.0892012 | ||||||||
\(587\) | 34.5161 | 1.42463 | 0.712316 | − | 0.701859i | \(-0.247646\pi\) | ||||
0.712316 | + | 0.701859i | \(0.247646\pi\) | |||||||
\(588\) | −105.072 | −4.33309 | ||||||||
\(589\) | 25.3267 | 1.04357 | ||||||||
\(590\) | 18.4242 | 0.758514 | ||||||||
\(591\) | −49.6124 | −2.04078 | ||||||||
\(592\) | 44.9166 | 1.84606 | ||||||||
\(593\) | −42.1148 | −1.72945 | −0.864724 | − | 0.502247i | \(-0.832507\pi\) | ||||
−0.864724 | + | 0.502247i | \(0.832507\pi\) | |||||||
\(594\) | −120.194 | −4.93160 | ||||||||
\(595\) | 23.9752 | 0.982887 | ||||||||
\(596\) | −72.6633 | −2.97641 | ||||||||
\(597\) | 72.4553 | 2.96540 | ||||||||
\(598\) | −15.1914 | −0.621224 | ||||||||
\(599\) | 33.1014 | 1.35249 | 0.676243 | − | 0.736679i | \(-0.263607\pi\) | ||||
0.676243 | + | 0.736679i | \(0.263607\pi\) | |||||||
\(600\) | −32.9364 | −1.34462 | ||||||||
\(601\) | 47.5637 | 1.94017 | 0.970083 | − | 0.242775i | \(-0.0780576\pi\) | ||||
0.970083 | + | 0.242775i | \(0.0780576\pi\) | |||||||
\(602\) | 52.0907 | 2.12306 | ||||||||
\(603\) | 18.7804 | 0.764796 | ||||||||
\(604\) | 49.6127 | 2.01871 | ||||||||
\(605\) | 32.5509 | 1.32338 | ||||||||
\(606\) | −101.498 | −4.12307 | ||||||||
\(607\) | 5.03096 | 0.204200 | 0.102100 | − | 0.994774i | \(-0.467444\pi\) | ||||
0.102100 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(608\) | −13.5145 | −0.548084 | ||||||||
\(609\) | 109.283 | 4.42837 | ||||||||
\(610\) | 67.8438 | 2.74692 | ||||||||
\(611\) | −8.51872 | −0.344631 | ||||||||
\(612\) | 89.6162 | 3.62252 | ||||||||
\(613\) | 30.0597 | 1.21410 | 0.607050 | − | 0.794663i | \(-0.292353\pi\) | ||||
0.607050 | + | 0.794663i | \(0.292353\pi\) | |||||||
\(614\) | 67.6804 | 2.73136 | ||||||||
\(615\) | −52.0359 | −2.09829 | ||||||||
\(616\) | 122.595 | 4.93949 | ||||||||
\(617\) | −19.8182 | −0.797850 | −0.398925 | − | 0.916984i | \(-0.630617\pi\) | ||||
−0.398925 | + | 0.916984i | \(0.630617\pi\) | |||||||
\(618\) | 62.2316 | 2.50332 | ||||||||
\(619\) | 14.1960 | 0.570586 | 0.285293 | − | 0.958440i | \(-0.407909\pi\) | ||||
0.285293 | + | 0.958440i | \(0.407909\pi\) | |||||||
\(620\) | 47.5997 | 1.91165 | ||||||||
\(621\) | 53.2990 | 2.13881 | ||||||||
\(622\) | 3.92966 | 0.157565 | ||||||||
\(623\) | −52.5374 | −2.10487 | ||||||||
\(624\) | 17.7993 | 0.712543 | ||||||||
\(625\) | −11.9035 | −0.476140 | ||||||||
\(626\) | −22.0944 | −0.883070 | ||||||||
\(627\) | 65.5798 | 2.61900 | ||||||||
\(628\) | 16.4280 | 0.655548 | ||||||||
\(629\) | 26.3976 | 1.05254 | ||||||||
\(630\) | −102.391 | −4.07935 | ||||||||
\(631\) | −30.8457 | −1.22795 | −0.613974 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613974 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(632\) | −56.7657 | −2.25802 | ||||||||
\(633\) | 42.7237 | 1.69811 | ||||||||
\(634\) | −82.2423 | −3.26626 | ||||||||
\(635\) | 8.41483 | 0.333932 | ||||||||
\(636\) | 85.8400 | 3.40378 | ||||||||
\(637\) | −8.15202 | −0.322995 | ||||||||
\(638\) | −128.017 | −5.06825 | ||||||||
\(639\) | 64.4186 | 2.54836 | ||||||||
\(640\) | 27.2491 | 1.07711 | ||||||||
\(641\) | 19.9868 | 0.789432 | 0.394716 | − | 0.918803i | \(-0.370843\pi\) | ||||
0.394716 | + | 0.918803i | \(0.370843\pi\) | |||||||
\(642\) | −57.3486 | −2.26337 | ||||||||
\(643\) | −5.15777 | −0.203402 | −0.101701 | − | 0.994815i | \(-0.532429\pi\) | ||||
−0.101701 | + | 0.994815i | \(0.532429\pi\) | |||||||
\(644\) | −101.448 | −3.99762 | ||||||||
\(645\) | 28.0639 | 1.10502 | ||||||||
\(646\) | −35.4721 | −1.39563 | ||||||||
\(647\) | −32.4123 | −1.27426 | −0.637129 | − | 0.770757i | \(-0.719878\pi\) | ||||
−0.637129 | + | 0.770757i | \(0.719878\pi\) | |||||||
\(648\) | −49.4188 | −1.94135 | ||||||||
\(649\) | 22.6152 | 0.887724 | ||||||||
\(650\) | −4.76859 | −0.187040 | ||||||||
\(651\) | −73.0259 | −2.86211 | ||||||||
\(652\) | 57.2792 | 2.24323 | ||||||||
\(653\) | 22.1546 | 0.866975 | 0.433488 | − | 0.901159i | \(-0.357283\pi\) | ||||
0.433488 | + | 0.901159i | \(0.357283\pi\) | |||||||
\(654\) | 32.0753 | 1.25424 | ||||||||
\(655\) | 20.6853 | 0.808242 | ||||||||
\(656\) | 58.7858 | 2.29520 | ||||||||
\(657\) | −16.8907 | −0.658967 | ||||||||
\(658\) | −83.2908 | −3.24701 | ||||||||
\(659\) | −24.9857 | −0.973303 | −0.486652 | − | 0.873596i | \(-0.661782\pi\) | ||||
−0.486652 | + | 0.873596i | \(0.661782\pi\) | |||||||
\(660\) | 123.252 | 4.79759 | ||||||||
\(661\) | −1.78735 | −0.0695198 | −0.0347599 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347599 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(662\) | 28.5041 | 1.10784 | ||||||||
\(663\) | 10.4607 | 0.406261 | ||||||||
\(664\) | 13.4422 | 0.521660 | ||||||||
\(665\) | 27.6811 | 1.07343 | ||||||||
\(666\) | −112.737 | −4.36845 | ||||||||
\(667\) | 56.7683 | 2.19808 | ||||||||
\(668\) | −41.1776 | −1.59321 | ||||||||
\(669\) | −55.4297 | −2.14304 | ||||||||
\(670\) | −13.9711 | −0.539750 | ||||||||
\(671\) | 83.2763 | 3.21484 | ||||||||
\(672\) | 38.9670 | 1.50318 | ||||||||
\(673\) | −17.9655 | −0.692519 | −0.346260 | − | 0.938139i | \(-0.612548\pi\) | ||||
−0.346260 | + | 0.938139i | \(0.612548\pi\) | |||||||
\(674\) | 65.5838 | 2.52619 | ||||||||
\(675\) | 16.7306 | 0.643959 | ||||||||
\(676\) | 4.30921 | 0.165739 | ||||||||
\(677\) | 44.0681 | 1.69367 | 0.846837 | − | 0.531852i | \(-0.178504\pi\) | ||||
0.846837 | + | 0.531852i | \(0.178504\pi\) | |||||||
\(678\) | −87.3728 | −3.35553 | ||||||||
\(679\) | −47.7429 | −1.83221 | ||||||||
\(680\) | −35.7254 | −1.37001 | ||||||||
\(681\) | −67.4969 | −2.58649 | ||||||||
\(682\) | 85.5446 | 3.27567 | ||||||||
\(683\) | −25.6391 | −0.981053 | −0.490527 | − | 0.871426i | \(-0.663196\pi\) | ||||
−0.490527 | + | 0.871426i | \(0.663196\pi\) | |||||||
\(684\) | 103.469 | 3.95622 | ||||||||
\(685\) | −7.29010 | −0.278540 | ||||||||
\(686\) | −11.2638 | −0.430053 | ||||||||
\(687\) | 5.21604 | 0.199004 | ||||||||
\(688\) | −31.7043 | −1.20871 | ||||||||
\(689\) | 6.65992 | 0.253723 | ||||||||
\(690\) | −80.0222 | −3.04639 | ||||||||
\(691\) | −19.6313 | −0.746809 | −0.373404 | − | 0.927669i | \(-0.621810\pi\) | ||||
−0.373404 | + | 0.927669i | \(0.621810\pi\) | |||||||
\(692\) | 76.7933 | 2.91924 | ||||||||
\(693\) | −125.682 | −4.77426 | ||||||||
\(694\) | −10.5919 | −0.402062 | ||||||||
\(695\) | −22.6133 | −0.857772 | ||||||||
\(696\) | −162.843 | −6.17254 | ||||||||
\(697\) | 34.5486 | 1.30862 | ||||||||
\(698\) | −31.2573 | −1.18311 | ||||||||
\(699\) | 44.5404 | 1.68467 | ||||||||
\(700\) | −31.8446 | −1.20361 | ||||||||
\(701\) | −25.9632 | −0.980616 | −0.490308 | − | 0.871549i | \(-0.663116\pi\) | ||||
−0.490308 | + | 0.871549i | \(0.663116\pi\) | |||||||
\(702\) | −22.1358 | −0.835461 | ||||||||
\(703\) | 30.4781 | 1.14950 | ||||||||
\(704\) | 18.9774 | 0.715239 | ||||||||
\(705\) | −44.8731 | −1.69002 | ||||||||
\(706\) | 91.3131 | 3.43661 | ||||||||
\(707\) | −52.5874 | −1.97775 | ||||||||
\(708\) | 53.6827 | 2.01752 | ||||||||
\(709\) | 27.0719 | 1.01671 | 0.508353 | − | 0.861149i | \(-0.330254\pi\) | ||||
0.508353 | + | 0.861149i | \(0.330254\pi\) | |||||||
\(710\) | −47.9222 | −1.79849 | ||||||||
\(711\) | 58.1950 | 2.18248 | ||||||||
\(712\) | 78.2861 | 2.93389 | ||||||||
\(713\) | −37.9341 | −1.42064 | ||||||||
\(714\) | 102.278 | 3.82768 | ||||||||
\(715\) | 9.56257 | 0.357620 | ||||||||
\(716\) | −71.2003 | −2.66088 | ||||||||
\(717\) | −57.1871 | −2.13569 | ||||||||
\(718\) | −46.7125 | −1.74329 | ||||||||
\(719\) | −5.33076 | −0.198804 | −0.0994020 | − | 0.995047i | \(-0.531693\pi\) | ||||
−0.0994020 | + | 0.995047i | \(0.531693\pi\) | |||||||
\(720\) | 62.3188 | 2.32249 | ||||||||
\(721\) | 32.2430 | 1.20079 | ||||||||
\(722\) | 6.76932 | 0.251928 | ||||||||
\(723\) | 44.3693 | 1.65011 | ||||||||
\(724\) | −58.3874 | −2.16995 | ||||||||
\(725\) | 17.8196 | 0.661803 | ||||||||
\(726\) | 138.863 | 5.15367 | ||||||||
\(727\) | −7.59358 | −0.281630 | −0.140815 | − | 0.990036i | \(-0.544972\pi\) | ||||
−0.140815 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(728\) | 22.5780 | 0.836798 | ||||||||
\(729\) | −28.4141 | −1.05238 | ||||||||
\(730\) | 12.5653 | 0.465062 | ||||||||
\(731\) | −18.6327 | −0.689156 | ||||||||
\(732\) | 197.677 | 7.30634 | ||||||||
\(733\) | −11.9586 | −0.441701 | −0.220851 | − | 0.975308i | \(-0.570883\pi\) | ||||
−0.220851 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(734\) | −67.2686 | −2.48293 | ||||||||
\(735\) | −42.9414 | −1.58392 | ||||||||
\(736\) | 20.2419 | 0.746125 | ||||||||
\(737\) | −17.1491 | −0.631694 | ||||||||
\(738\) | −147.547 | −5.43127 | ||||||||
\(739\) | −13.5784 | −0.499488 | −0.249744 | − | 0.968312i | \(-0.580346\pi\) | ||||
−0.249744 | + | 0.968312i | \(0.580346\pi\) | |||||||
\(740\) | 57.2813 | 2.10570 | ||||||||
\(741\) | 12.0777 | 0.443685 | ||||||||
\(742\) | 65.1166 | 2.39051 | ||||||||
\(743\) | 0.116237 | 0.00426431 | 0.00213216 | − | 0.999998i | \(-0.499321\pi\) | ||||
0.00213216 | + | 0.999998i | \(0.499321\pi\) | |||||||
\(744\) | 108.816 | 3.98938 | ||||||||
\(745\) | −29.6965 | −1.08800 | ||||||||
\(746\) | 19.9843 | 0.731678 | ||||||||
\(747\) | −13.7807 | −0.504210 | ||||||||
\(748\) | −81.8319 | −2.99207 | ||||||||
\(749\) | −29.7131 | −1.08569 | ||||||||
\(750\) | −91.2749 | −3.33289 | ||||||||
\(751\) | −28.2045 | −1.02920 | −0.514598 | − | 0.857432i | \(-0.672059\pi\) | ||||
−0.514598 | + | 0.857432i | \(0.672059\pi\) | |||||||
\(752\) | 50.6938 | 1.84861 | ||||||||
\(753\) | −9.01757 | −0.328619 | ||||||||
\(754\) | −23.5767 | −0.858611 | ||||||||
\(755\) | 20.2761 | 0.737922 | ||||||||
\(756\) | −147.822 | −5.37625 | ||||||||
\(757\) | −27.5628 | −1.00179 | −0.500894 | − | 0.865509i | \(-0.666995\pi\) | ||||
−0.500894 | + | 0.865509i | \(0.666995\pi\) | |||||||
\(758\) | 20.3749 | 0.740049 | ||||||||
\(759\) | −98.2248 | −3.56533 | ||||||||
\(760\) | −41.2477 | −1.49621 | ||||||||
\(761\) | −14.5806 | −0.528545 | −0.264272 | − | 0.964448i | \(-0.585132\pi\) | ||||
−0.264272 | + | 0.964448i | \(0.585132\pi\) | |||||||
\(762\) | 35.8978 | 1.30044 | ||||||||
\(763\) | 16.6186 | 0.601635 | ||||||||
\(764\) | 5.08780 | 0.184070 | ||||||||
\(765\) | 36.6250 | 1.32418 | ||||||||
\(766\) | −14.9494 | −0.540144 | ||||||||
\(767\) | 4.16499 | 0.150389 | ||||||||
\(768\) | 95.3373 | 3.44019 | ||||||||
\(769\) | 13.1329 | 0.473586 | 0.236793 | − | 0.971560i | \(-0.423904\pi\) | ||||
0.236793 | + | 0.971560i | \(0.423904\pi\) | |||||||
\(770\) | 93.4970 | 3.36940 | ||||||||
\(771\) | −44.7672 | −1.61225 | ||||||||
\(772\) | 31.1998 | 1.12291 | ||||||||
\(773\) | 13.6355 | 0.490434 | 0.245217 | − | 0.969468i | \(-0.421141\pi\) | ||||
0.245217 | + | 0.969468i | \(0.421141\pi\) | |||||||
\(774\) | 79.5748 | 2.86026 | ||||||||
\(775\) | −11.9075 | −0.427731 | ||||||||
\(776\) | 71.1418 | 2.55384 | ||||||||
\(777\) | −87.8790 | −3.15264 | ||||||||
\(778\) | 53.1003 | 1.90374 | ||||||||
\(779\) | 39.8889 | 1.42917 | ||||||||
\(780\) | 22.6991 | 0.812759 | ||||||||
\(781\) | −58.8230 | −2.10485 | ||||||||
\(782\) | 53.1297 | 1.89991 | ||||||||
\(783\) | 82.7184 | 2.95611 | ||||||||
\(784\) | 48.5116 | 1.73256 | ||||||||
\(785\) | 6.71390 | 0.239630 | ||||||||
\(786\) | 88.2438 | 3.14755 | ||||||||
\(787\) | 1.73206 | 0.0617413 | 0.0308707 | − | 0.999523i | \(-0.490172\pi\) | ||||
0.0308707 | + | 0.999523i | \(0.490172\pi\) | |||||||
\(788\) | 71.4768 | 2.54625 | ||||||||
\(789\) | −81.4415 | −2.89940 | ||||||||
\(790\) | −43.2923 | −1.54027 | ||||||||
\(791\) | −45.2690 | −1.60958 | ||||||||
\(792\) | 187.279 | 6.65465 | ||||||||
\(793\) | 15.3368 | 0.544626 | ||||||||
\(794\) | 39.7765 | 1.41162 | ||||||||
\(795\) | 35.0817 | 1.24422 | ||||||||
\(796\) | −104.387 | −3.69989 | ||||||||
\(797\) | 4.01249 | 0.142130 | 0.0710648 | − | 0.997472i | \(-0.477360\pi\) | ||||
0.0710648 | + | 0.997472i | \(0.477360\pi\) | |||||||
\(798\) | 118.088 | 4.18027 | ||||||||
\(799\) | 29.7929 | 1.05400 | ||||||||
\(800\) | 6.35392 | 0.224645 | ||||||||
\(801\) | −80.2572 | −2.83575 | ||||||||
\(802\) | 78.4472 | 2.77007 | ||||||||
\(803\) | 15.4235 | 0.544283 | ||||||||
\(804\) | −40.7075 | −1.43564 | ||||||||
\(805\) | −41.4606 | −1.46129 | ||||||||
\(806\) | 15.7545 | 0.554930 | ||||||||
\(807\) | 7.24822 | 0.255149 | ||||||||
\(808\) | 78.3606 | 2.75672 | ||||||||
\(809\) | 21.3266 | 0.749803 | 0.374901 | − | 0.927065i | \(-0.377677\pi\) | ||||
0.374901 | + | 0.927065i | \(0.377677\pi\) | |||||||
\(810\) | −37.6892 | −1.32426 | ||||||||
\(811\) | 19.6544 | 0.690158 | 0.345079 | − | 0.938574i | \(-0.387852\pi\) | ||||
0.345079 | + | 0.938574i | \(0.387852\pi\) | |||||||
\(812\) | −157.445 | −5.52522 | ||||||||
\(813\) | 80.6757 | 2.82942 | ||||||||
\(814\) | 102.944 | 3.60818 | ||||||||
\(815\) | 23.4093 | 0.819991 | ||||||||
\(816\) | −62.2504 | −2.17920 | ||||||||
\(817\) | −21.5129 | −0.752639 | ||||||||
\(818\) | −66.8610 | −2.33774 | ||||||||
\(819\) | −23.1465 | −0.808805 | ||||||||
\(820\) | 74.9683 | 2.61801 | ||||||||
\(821\) | 42.1954 | 1.47263 | 0.736314 | − | 0.676640i | \(-0.236565\pi\) | ||||
0.736314 | + | 0.676640i | \(0.236565\pi\) | |||||||
\(822\) | −31.0997 | −1.08472 | ||||||||
\(823\) | −27.1347 | −0.945856 | −0.472928 | − | 0.881101i | \(-0.656803\pi\) | ||||
−0.472928 | + | 0.881101i | \(0.656803\pi\) | |||||||
\(824\) | −48.0454 | −1.67374 | ||||||||
\(825\) | −30.8328 | −1.07346 | ||||||||
\(826\) | 40.7227 | 1.41692 | ||||||||
\(827\) | −6.67973 | −0.232277 | −0.116139 | − | 0.993233i | \(-0.537052\pi\) | ||||
−0.116139 | + | 0.993233i | \(0.537052\pi\) | |||||||
\(828\) | −154.974 | −5.38573 | ||||||||
\(829\) | 11.3075 | 0.392724 | 0.196362 | − | 0.980531i | \(-0.437087\pi\) | ||||
0.196362 | + | 0.980531i | \(0.437087\pi\) | |||||||
\(830\) | 10.2517 | 0.355842 | ||||||||
\(831\) | −67.4971 | −2.34145 | ||||||||
\(832\) | 3.49503 | 0.121168 | ||||||||
\(833\) | 28.5104 | 0.987828 | ||||||||
\(834\) | −96.4687 | −3.34044 | ||||||||
\(835\) | −16.8288 | −0.582383 | ||||||||
\(836\) | −94.4811 | −3.26770 | ||||||||
\(837\) | −55.2746 | −1.91057 | ||||||||
\(838\) | 3.11855 | 0.107729 | ||||||||
\(839\) | −28.5879 | −0.986963 | −0.493481 | − | 0.869756i | \(-0.664276\pi\) | ||||
−0.493481 | + | 0.869756i | \(0.664276\pi\) | |||||||
\(840\) | 118.932 | 4.10353 | ||||||||
\(841\) | 59.1027 | 2.03802 | ||||||||
\(842\) | −73.1798 | −2.52194 | ||||||||
\(843\) | 89.6886 | 3.08904 | ||||||||
\(844\) | −61.5522 | −2.11871 | ||||||||
\(845\) | 1.76112 | 0.0605843 | ||||||||
\(846\) | −127.237 | −4.37449 | ||||||||
\(847\) | 71.9466 | 2.47211 | ||||||||
\(848\) | −39.6323 | −1.36098 | ||||||||
\(849\) | 66.4288 | 2.27983 | ||||||||
\(850\) | 16.6774 | 0.572031 | ||||||||
\(851\) | −45.6497 | −1.56485 | ||||||||
\(852\) | −139.631 | −4.78367 | ||||||||
\(853\) | 33.2008 | 1.13677 | 0.568387 | − | 0.822761i | \(-0.307568\pi\) | ||||
0.568387 | + | 0.822761i | \(0.307568\pi\) | |||||||
\(854\) | 149.954 | 5.13131 | ||||||||
\(855\) | 42.2863 | 1.44616 | ||||||||
\(856\) | 44.2755 | 1.51331 | ||||||||
\(857\) | −22.7121 | −0.775829 | −0.387915 | − | 0.921695i | \(-0.626804\pi\) | ||||
−0.387915 | + | 0.921695i | \(0.626804\pi\) | |||||||
\(858\) | 40.7941 | 1.39269 | ||||||||
\(859\) | −22.5069 | −0.767927 | −0.383964 | − | 0.923348i | \(-0.625441\pi\) | ||||
−0.383964 | + | 0.923348i | \(0.625441\pi\) | |||||||
\(860\) | −40.4318 | −1.37871 | ||||||||
\(861\) | −115.014 | −3.91966 | ||||||||
\(862\) | 51.1289 | 1.74146 | ||||||||
\(863\) | −1.69455 | −0.0576832 | −0.0288416 | − | 0.999584i | \(-0.509182\pi\) | ||||
−0.0288416 | + | 0.999584i | \(0.509182\pi\) | |||||||
\(864\) | 29.4948 | 1.00343 | ||||||||
\(865\) | 31.3844 | 1.06710 | ||||||||
\(866\) | 32.3236 | 1.09840 | ||||||||
\(867\) | 14.2630 | 0.484398 | ||||||||
\(868\) | 105.209 | 3.57101 | ||||||||
\(869\) | −53.1400 | −1.80265 | ||||||||
\(870\) | −124.192 | −4.21050 | ||||||||
\(871\) | −3.15830 | −0.107015 | ||||||||
\(872\) | −24.7634 | −0.838596 | ||||||||
\(873\) | −72.9330 | −2.46841 | ||||||||
\(874\) | 61.3422 | 2.07493 | ||||||||
\(875\) | −47.2907 | −1.59872 | ||||||||
\(876\) | 36.6114 | 1.23699 | ||||||||
\(877\) | −35.7899 | −1.20854 | −0.604269 | − | 0.796781i | \(-0.706535\pi\) | ||||
−0.604269 | + | 0.796781i | \(0.706535\pi\) | |||||||
\(878\) | 22.3805 | 0.755304 | ||||||||
\(879\) | 2.57131 | 0.0867282 | ||||||||
\(880\) | −56.9056 | −1.91829 | ||||||||
\(881\) | −21.8118 | −0.734859 | −0.367430 | − | 0.930051i | \(-0.619762\pi\) | ||||
−0.367430 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(882\) | −121.760 | −4.09986 | ||||||||
\(883\) | 45.7537 | 1.53973 | 0.769867 | − | 0.638204i | \(-0.220322\pi\) | ||||
0.769867 | + | 0.638204i | \(0.220322\pi\) | |||||||
\(884\) | −15.0708 | −0.506886 | ||||||||
\(885\) | 21.9394 | 0.737485 | ||||||||
\(886\) | −0.853151 | −0.0286622 | ||||||||
\(887\) | −42.1357 | −1.41478 | −0.707389 | − | 0.706825i | \(-0.750127\pi\) | ||||
−0.707389 | + | 0.706825i | \(0.750127\pi\) | |||||||
\(888\) | 130.949 | 4.39435 | ||||||||
\(889\) | 18.5991 | 0.623794 | ||||||||
\(890\) | 59.7048 | 2.00131 | ||||||||
\(891\) | −46.2624 | −1.54985 | ||||||||
\(892\) | 79.8578 | 2.67384 | ||||||||
\(893\) | 34.3981 | 1.15109 | ||||||||
\(894\) | −126.686 | −4.23701 | ||||||||
\(895\) | −29.0986 | −0.972659 | ||||||||
\(896\) | 60.2280 | 2.01208 | ||||||||
\(897\) | −18.0898 | −0.604002 | ||||||||
\(898\) | −61.7626 | −2.06105 | ||||||||
\(899\) | −58.8726 | −1.96351 | ||||||||
\(900\) | −48.6464 | −1.62155 | ||||||||
\(901\) | −23.2920 | −0.775970 | ||||||||
\(902\) | 134.730 | 4.48603 | ||||||||
\(903\) | 62.0291 | 2.06420 | ||||||||
\(904\) | 67.4554 | 2.24353 | ||||||||
\(905\) | −23.8621 | −0.793205 | ||||||||
\(906\) | 86.4980 | 2.87370 | ||||||||
\(907\) | 19.5909 | 0.650504 | 0.325252 | − | 0.945627i | \(-0.394551\pi\) | ||||
0.325252 | + | 0.945627i | \(0.394551\pi\) | |||||||
\(908\) | 97.2430 | 3.22712 | ||||||||
\(909\) | −80.3336 | −2.66450 | ||||||||
\(910\) | 17.2191 | 0.570808 | ||||||||
\(911\) | −18.7084 | −0.619837 | −0.309918 | − | 0.950763i | \(-0.600302\pi\) | ||||
−0.309918 | + | 0.950763i | \(0.600302\pi\) | |||||||
\(912\) | −71.8727 | −2.37994 | ||||||||
\(913\) | 12.5837 | 0.416459 | ||||||||
\(914\) | 45.3174 | 1.49897 | ||||||||
\(915\) | 80.7878 | 2.67076 | ||||||||
\(916\) | −7.51477 | −0.248295 | ||||||||
\(917\) | 45.7203 | 1.50982 | ||||||||
\(918\) | 77.4165 | 2.55512 | ||||||||
\(919\) | −26.3386 | −0.868830 | −0.434415 | − | 0.900713i | \(-0.643045\pi\) | ||||
−0.434415 | + | 0.900713i | \(0.643045\pi\) | |||||||
\(920\) | 61.7804 | 2.03684 | ||||||||
\(921\) | 80.5932 | 2.65564 | ||||||||
\(922\) | −6.49222 | −0.213810 | ||||||||
\(923\) | −10.8333 | −0.356582 | ||||||||
\(924\) | 272.422 | 8.96203 | ||||||||
\(925\) | −14.3295 | −0.471150 | ||||||||
\(926\) | 2.51181 | 0.0825433 | ||||||||
\(927\) | 49.2551 | 1.61775 | ||||||||
\(928\) | 31.4147 | 1.03124 | ||||||||
\(929\) | −22.6383 | −0.742737 | −0.371368 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371368 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(930\) | 82.9884 | 2.72130 | ||||||||
\(931\) | 32.9174 | 1.07883 | ||||||||
\(932\) | −64.1695 | −2.10194 | ||||||||
\(933\) | 4.67941 | 0.153197 | ||||||||
\(934\) | 80.5665 | 2.63622 | ||||||||
\(935\) | −33.4436 | −1.09372 | ||||||||
\(936\) | 34.4907 | 1.12736 | ||||||||
\(937\) | −30.5897 | −0.999323 | −0.499661 | − | 0.866221i | \(-0.666542\pi\) | ||||
−0.499661 | + | 0.866221i | \(0.666542\pi\) | |||||||
\(938\) | −30.8800 | −1.00827 | ||||||||
\(939\) | −26.3098 | −0.858589 | ||||||||
\(940\) | 64.6488 | 2.10861 | ||||||||
\(941\) | 0.170224 | 0.00554915 | 0.00277457 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277457 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(942\) | 28.6416 | 0.933194 | ||||||||
\(943\) | −59.7452 | −1.94557 | ||||||||
\(944\) | −24.7853 | −0.806693 | ||||||||
\(945\) | −60.4131 | −1.96524 | ||||||||
\(946\) | −72.6627 | −2.36247 | ||||||||
\(947\) | 1.32065 | 0.0429153 | 0.0214576 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214576 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(948\) | −126.141 | −4.09686 | ||||||||
\(949\) | 2.84051 | 0.0922068 | ||||||||
\(950\) | 19.2553 | 0.624725 | ||||||||
\(951\) | −97.9334 | −3.17571 | ||||||||
\(952\) | −78.9632 | −2.55921 | ||||||||
\(953\) | 3.28041 | 0.106263 | 0.0531314 | − | 0.998588i | \(-0.483080\pi\) | ||||
0.0531314 | + | 0.998588i | \(0.483080\pi\) | |||||||
\(954\) | 99.4734 | 3.22057 | ||||||||
\(955\) | 2.07932 | 0.0672852 | ||||||||
\(956\) | 82.3897 | 2.66467 | ||||||||
\(957\) | −152.442 | −4.92775 | ||||||||
\(958\) | −3.87421 | −0.125170 | ||||||||
\(959\) | −16.1131 | −0.520321 | ||||||||
\(960\) | 18.4104 | 0.594192 | ||||||||
\(961\) | 8.34023 | 0.269040 | ||||||||
\(962\) | 18.9590 | 0.611261 | ||||||||
\(963\) | −45.3903 | −1.46268 | ||||||||
\(964\) | −63.9230 | −2.05882 | ||||||||
\(965\) | 12.7510 | 0.410468 | ||||||||
\(966\) | −176.871 | −5.69074 | ||||||||
\(967\) | −14.4038 | −0.463195 | −0.231598 | − | 0.972812i | \(-0.574395\pi\) | ||||
−0.231598 | + | 0.972812i | \(0.574395\pi\) | |||||||
\(968\) | −107.208 | −3.44578 | ||||||||
\(969\) | −42.2398 | −1.35694 | ||||||||
\(970\) | 54.2562 | 1.74206 | ||||||||
\(971\) | 26.2939 | 0.843811 | 0.421905 | − | 0.906640i | \(-0.361361\pi\) | ||||
0.421905 | + | 0.906640i | \(0.361361\pi\) | |||||||
\(972\) | 4.11183 | 0.131887 | ||||||||
\(973\) | −49.9817 | −1.60234 | ||||||||
\(974\) | −32.4083 | −1.03843 | ||||||||
\(975\) | −5.67840 | −0.181854 | ||||||||
\(976\) | −91.2673 | −2.92139 | ||||||||
\(977\) | 0.996346 | 0.0318759 | 0.0159380 | − | 0.999873i | \(-0.494927\pi\) | ||||
0.0159380 | + | 0.999873i | \(0.494927\pi\) | |||||||
\(978\) | 99.8642 | 3.19331 | ||||||||
\(979\) | 73.2859 | 2.34223 | ||||||||
\(980\) | 61.8659 | 1.97623 | ||||||||
\(981\) | 25.3870 | 0.810543 | ||||||||
\(982\) | 32.2225 | 1.02826 | ||||||||
\(983\) | 29.4146 | 0.938181 | 0.469090 | − | 0.883150i | \(-0.344582\pi\) | ||||
0.469090 | + | 0.883150i | \(0.344582\pi\) | |||||||
\(984\) | 171.382 | 5.46346 | ||||||||
\(985\) | 29.2116 | 0.930759 | ||||||||
\(986\) | 82.4557 | 2.62592 | ||||||||
\(987\) | −99.1820 | −3.15700 | ||||||||
\(988\) | −17.4004 | −0.553579 | ||||||||
\(989\) | 32.2217 | 1.02459 | ||||||||
\(990\) | 142.828 | 4.53937 | ||||||||
\(991\) | −35.1949 | −1.11800 | −0.559001 | − | 0.829167i | \(-0.688815\pi\) | ||||
−0.559001 | + | 0.829167i | \(0.688815\pi\) | |||||||
\(992\) | −20.9922 | −0.666502 | ||||||||
\(993\) | 33.9424 | 1.07713 | ||||||||
\(994\) | −105.921 | −3.35962 | ||||||||
\(995\) | −42.6614 | −1.35246 | ||||||||
\(996\) | 29.8704 | 0.946481 | ||||||||
\(997\) | −15.7106 | −0.497561 | −0.248780 | − | 0.968560i | \(-0.580030\pi\) | ||||
−0.248780 | + | 0.968560i | \(0.580030\pi\) | |||||||
\(998\) | 21.0819 | 0.667337 | ||||||||
\(999\) | −66.5172 | −2.10451 |
(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 | 6019.2.a.c.1.10 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.10 | ✓ | 108 | 1.1 | even | 1 | trivial |