Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, 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("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(154\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51869 | −1.78098 | −0.890491 | − | 0.455000i | \(-0.849639\pi\) | ||||
−0.890491 | + | 0.455000i | \(0.849639\pi\) | |||||||
\(3\) | 0.856221 | 0.494340 | 0.247170 | − | 0.968972i | \(-0.420499\pi\) | ||||
0.247170 | + | 0.968972i | \(0.420499\pi\) | |||||||
\(4\) | 4.34380 | 2.17190 | ||||||||
\(5\) | 2.85854 | 1.27838 | 0.639190 | − | 0.769049i | \(-0.279270\pi\) | ||||
0.639190 | + | 0.769049i | \(0.279270\pi\) | |||||||
\(6\) | −2.15656 | −0.880410 | ||||||||
\(7\) | −2.09984 | −0.793666 | −0.396833 | − | 0.917891i | \(-0.629891\pi\) | ||||
−0.396833 | + | 0.917891i | \(0.629891\pi\) | |||||||
\(8\) | −5.90330 | −2.08713 | ||||||||
\(9\) | −2.26688 | −0.755628 | ||||||||
\(10\) | −7.19979 | −2.27677 | ||||||||
\(11\) | 4.13907 | 1.24798 | 0.623988 | − | 0.781434i | \(-0.285511\pi\) | ||||
0.623988 | + | 0.781434i | \(0.285511\pi\) | |||||||
\(12\) | 3.71925 | 1.07366 | ||||||||
\(13\) | −3.52588 | −0.977903 | −0.488951 | − | 0.872311i | \(-0.662620\pi\) | ||||
−0.488951 | + | 0.872311i | \(0.662620\pi\) | |||||||
\(14\) | 5.28885 | 1.41351 | ||||||||
\(15\) | 2.44755 | 0.631954 | ||||||||
\(16\) | 6.18098 | 1.54525 | ||||||||
\(17\) | −2.95728 | −0.717246 | −0.358623 | − | 0.933483i | \(-0.616754\pi\) | ||||
−0.358623 | + | 0.933483i | \(0.616754\pi\) | |||||||
\(18\) | 5.70958 | 1.34576 | ||||||||
\(19\) | 6.64980 | 1.52557 | 0.762785 | − | 0.646652i | \(-0.223832\pi\) | ||||
0.762785 | + | 0.646652i | \(0.223832\pi\) | |||||||
\(20\) | 12.4169 | 2.77651 | ||||||||
\(21\) | −1.79793 | −0.392341 | ||||||||
\(22\) | −10.4250 | −2.22262 | ||||||||
\(23\) | −1.55948 | −0.325174 | −0.162587 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162587 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(24\) | −5.05453 | −1.03175 | ||||||||
\(25\) | 3.17128 | 0.634255 | ||||||||
\(26\) | 8.88059 | 1.74163 | ||||||||
\(27\) | −4.50962 | −0.867877 | ||||||||
\(28\) | −9.12130 | −1.72376 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −6.16461 | −1.12550 | ||||||||
\(31\) | 5.39140 | 0.968323 | 0.484162 | − | 0.874979i | \(-0.339125\pi\) | ||||
0.484162 | + | 0.874979i | \(0.339125\pi\) | |||||||
\(32\) | −3.76138 | −0.664924 | ||||||||
\(33\) | 3.54396 | 0.616924 | ||||||||
\(34\) | 7.44847 | 1.27740 | ||||||||
\(35\) | −6.00250 | −1.01461 | ||||||||
\(36\) | −9.84689 | −1.64115 | ||||||||
\(37\) | 0.947797 | 0.155817 | 0.0779085 | − | 0.996961i | \(-0.475176\pi\) | ||||
0.0779085 | + | 0.996961i | \(0.475176\pi\) | |||||||
\(38\) | −16.7488 | −2.71701 | ||||||||
\(39\) | −3.01893 | −0.483416 | ||||||||
\(40\) | −16.8748 | −2.66815 | ||||||||
\(41\) | −2.18113 | −0.340636 | −0.170318 | − | 0.985389i | \(-0.554479\pi\) | ||||
−0.170318 | + | 0.985389i | \(0.554479\pi\) | |||||||
\(42\) | 4.52843 | 0.698752 | ||||||||
\(43\) | −10.4669 | −1.59619 | −0.798095 | − | 0.602532i | \(-0.794159\pi\) | ||||
−0.798095 | + | 0.602532i | \(0.794159\pi\) | |||||||
\(44\) | 17.9793 | 2.71048 | ||||||||
\(45\) | −6.47999 | −0.965980 | ||||||||
\(46\) | 3.92784 | 0.579129 | ||||||||
\(47\) | 5.38926 | 0.786105 | 0.393052 | − | 0.919516i | \(-0.371419\pi\) | ||||
0.393052 | + | 0.919516i | \(0.371419\pi\) | |||||||
\(48\) | 5.29229 | 0.763876 | ||||||||
\(49\) | −2.59066 | −0.370094 | ||||||||
\(50\) | −7.98746 | −1.12960 | ||||||||
\(51\) | −2.53209 | −0.354563 | ||||||||
\(52\) | −15.3157 | −2.12391 | ||||||||
\(53\) | −9.94779 | −1.36643 | −0.683217 | − | 0.730215i | \(-0.739420\pi\) | ||||
−0.683217 | + | 0.730215i | \(0.739420\pi\) | |||||||
\(54\) | 11.3583 | 1.54567 | ||||||||
\(55\) | 11.8317 | 1.59539 | ||||||||
\(56\) | 12.3960 | 1.65649 | ||||||||
\(57\) | 5.69370 | 0.754150 | ||||||||
\(58\) | −2.51869 | −0.330720 | ||||||||
\(59\) | −8.20758 | −1.06854 | −0.534268 | − | 0.845315i | \(-0.679413\pi\) | ||||
−0.534268 | + | 0.845315i | \(0.679413\pi\) | |||||||
\(60\) | 10.6316 | 1.37254 | ||||||||
\(61\) | 3.34496 | 0.428278 | 0.214139 | − | 0.976803i | \(-0.431305\pi\) | ||||
0.214139 | + | 0.976803i | \(0.431305\pi\) | |||||||
\(62\) | −13.5793 | −1.72457 | ||||||||
\(63\) | 4.76010 | 0.599717 | ||||||||
\(64\) | −2.88822 | −0.361028 | ||||||||
\(65\) | −10.0789 | −1.25013 | ||||||||
\(66\) | −8.92613 | −1.09873 | ||||||||
\(67\) | 0.413585 | 0.0505274 | 0.0252637 | − | 0.999681i | \(-0.491957\pi\) | ||||
0.0252637 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(68\) | −12.8458 | −1.55779 | ||||||||
\(69\) | −1.33526 | −0.160746 | ||||||||
\(70\) | 15.1184 | 1.80700 | ||||||||
\(71\) | −8.54828 | −1.01449 | −0.507247 | − | 0.861801i | \(-0.669337\pi\) | ||||
−0.507247 | + | 0.861801i | \(0.669337\pi\) | |||||||
\(72\) | 13.3821 | 1.57710 | ||||||||
\(73\) | −3.00400 | −0.351591 | −0.175796 | − | 0.984427i | \(-0.556250\pi\) | ||||
−0.175796 | + | 0.984427i | \(0.556250\pi\) | |||||||
\(74\) | −2.38721 | −0.277507 | ||||||||
\(75\) | 2.71531 | 0.313537 | ||||||||
\(76\) | 28.8854 | 3.31338 | ||||||||
\(77\) | −8.69140 | −0.990477 | ||||||||
\(78\) | 7.60376 | 0.860956 | ||||||||
\(79\) | 10.9773 | 1.23504 | 0.617522 | − | 0.786554i | \(-0.288137\pi\) | ||||
0.617522 | + | 0.786554i | \(0.288137\pi\) | |||||||
\(80\) | 17.6686 | 1.97541 | ||||||||
\(81\) | 2.93942 | 0.326602 | ||||||||
\(82\) | 5.49360 | 0.606666 | ||||||||
\(83\) | 1.69324 | 0.185858 | 0.0929289 | − | 0.995673i | \(-0.470377\pi\) | ||||
0.0929289 | + | 0.995673i | \(0.470377\pi\) | |||||||
\(84\) | −7.80985 | −0.852124 | ||||||||
\(85\) | −8.45352 | −0.916912 | ||||||||
\(86\) | 26.3629 | 2.84279 | ||||||||
\(87\) | 0.856221 | 0.0917966 | ||||||||
\(88\) | −24.4342 | −2.60469 | ||||||||
\(89\) | 0.555214 | 0.0588525 | 0.0294263 | − | 0.999567i | \(-0.490632\pi\) | ||||
0.0294263 | + | 0.999567i | \(0.490632\pi\) | |||||||
\(90\) | 16.3211 | 1.72039 | ||||||||
\(91\) | 7.40380 | 0.776129 | ||||||||
\(92\) | −6.77406 | −0.706244 | ||||||||
\(93\) | 4.61623 | 0.478681 | ||||||||
\(94\) | −13.5739 | −1.40004 | ||||||||
\(95\) | 19.0088 | 1.95026 | ||||||||
\(96\) | −3.22057 | −0.328698 | ||||||||
\(97\) | −11.5136 | −1.16903 | −0.584517 | − | 0.811381i | \(-0.698716\pi\) | ||||
−0.584517 | + | 0.811381i | \(0.698716\pi\) | |||||||
\(98\) | 6.52506 | 0.659130 | ||||||||
\(99\) | −9.38279 | −0.943006 | ||||||||
\(100\) | 13.7754 | 1.37754 | ||||||||
\(101\) | −8.39462 | −0.835295 | −0.417648 | − | 0.908609i | \(-0.637145\pi\) | ||||
−0.417648 | + | 0.908609i | \(0.637145\pi\) | |||||||
\(102\) | 6.37754 | 0.631470 | ||||||||
\(103\) | 13.3268 | 1.31313 | 0.656563 | − | 0.754272i | \(-0.272010\pi\) | ||||
0.656563 | + | 0.754272i | \(0.272010\pi\) | |||||||
\(104\) | 20.8143 | 2.04101 | ||||||||
\(105\) | −5.13947 | −0.501561 | ||||||||
\(106\) | 25.0554 | 2.43360 | ||||||||
\(107\) | 11.8470 | 1.14529 | 0.572647 | − | 0.819802i | \(-0.305917\pi\) | ||||
0.572647 | + | 0.819802i | \(0.305917\pi\) | |||||||
\(108\) | −19.5889 | −1.88494 | ||||||||
\(109\) | −11.6309 | −1.11404 | −0.557020 | − | 0.830499i | \(-0.688055\pi\) | ||||
−0.557020 | + | 0.830499i | \(0.688055\pi\) | |||||||
\(110\) | −29.8004 | −2.84136 | ||||||||
\(111\) | 0.811524 | 0.0770265 | ||||||||
\(112\) | −12.9791 | −1.22641 | ||||||||
\(113\) | 7.65618 | 0.720233 | 0.360117 | − | 0.932907i | \(-0.382737\pi\) | ||||
0.360117 | + | 0.932907i | \(0.382737\pi\) | |||||||
\(114\) | −14.3407 | −1.34313 | ||||||||
\(115\) | −4.45784 | −0.415696 | ||||||||
\(116\) | 4.34380 | 0.403311 | ||||||||
\(117\) | 7.99276 | 0.738931 | ||||||||
\(118\) | 20.6724 | 1.90304 | ||||||||
\(119\) | 6.20983 | 0.569254 | ||||||||
\(120\) | −14.4486 | −1.31897 | ||||||||
\(121\) | 6.13188 | 0.557444 | ||||||||
\(122\) | −8.42491 | −0.762755 | ||||||||
\(123\) | −1.86753 | −0.168390 | ||||||||
\(124\) | 23.4191 | 2.10310 | ||||||||
\(125\) | −5.22749 | −0.467561 | ||||||||
\(126\) | −11.9892 | −1.06809 | ||||||||
\(127\) | −8.15168 | −0.723344 | −0.361672 | − | 0.932305i | \(-0.617794\pi\) | ||||
−0.361672 | + | 0.932305i | \(0.617794\pi\) | |||||||
\(128\) | 14.7973 | 1.30791 | ||||||||
\(129\) | −8.96199 | −0.789060 | ||||||||
\(130\) | 25.3856 | 2.22646 | ||||||||
\(131\) | −2.99298 | −0.261498 | −0.130749 | − | 0.991415i | \(-0.541738\pi\) | ||||
−0.130749 | + | 0.991415i | \(0.541738\pi\) | |||||||
\(132\) | 15.3942 | 1.33990 | ||||||||
\(133\) | −13.9636 | −1.21079 | ||||||||
\(134\) | −1.04169 | −0.0899885 | ||||||||
\(135\) | −12.8909 | −1.10948 | ||||||||
\(136\) | 17.4577 | 1.49699 | ||||||||
\(137\) | −1.38832 | −0.118612 | −0.0593060 | − | 0.998240i | \(-0.518889\pi\) | ||||
−0.0593060 | + | 0.998240i | \(0.518889\pi\) | |||||||
\(138\) | 3.36310 | 0.286286 | ||||||||
\(139\) | 16.4252 | 1.39317 | 0.696583 | − | 0.717477i | \(-0.254703\pi\) | ||||
0.696583 | + | 0.717477i | \(0.254703\pi\) | |||||||
\(140\) | −26.0736 | −2.20362 | ||||||||
\(141\) | 4.61440 | 0.388603 | ||||||||
\(142\) | 21.5305 | 1.80680 | ||||||||
\(143\) | −14.5939 | −1.22040 | ||||||||
\(144\) | −14.0116 | −1.16763 | ||||||||
\(145\) | 2.85854 | 0.237389 | ||||||||
\(146\) | 7.56614 | 0.626178 | ||||||||
\(147\) | −2.21817 | −0.182952 | ||||||||
\(148\) | 4.11704 | 0.338419 | ||||||||
\(149\) | −4.28514 | −0.351052 | −0.175526 | − | 0.984475i | \(-0.556163\pi\) | ||||
−0.175526 | + | 0.984475i | \(0.556163\pi\) | |||||||
\(150\) | −6.83903 | −0.558405 | ||||||||
\(151\) | 8.85411 | 0.720537 | 0.360268 | − | 0.932849i | \(-0.382685\pi\) | ||||
0.360268 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(152\) | −39.2558 | −3.18406 | ||||||||
\(153\) | 6.70381 | 0.541971 | ||||||||
\(154\) | 21.8909 | 1.76402 | ||||||||
\(155\) | 15.4115 | 1.23789 | ||||||||
\(156\) | −13.1136 | −1.04993 | ||||||||
\(157\) | 0.155484 | 0.0124090 | 0.00620450 | − | 0.999981i | \(-0.498025\pi\) | ||||
0.00620450 | + | 0.999981i | \(0.498025\pi\) | |||||||
\(158\) | −27.6484 | −2.19959 | ||||||||
\(159\) | −8.51751 | −0.675483 | ||||||||
\(160\) | −10.7521 | −0.850025 | ||||||||
\(161\) | 3.27466 | 0.258079 | ||||||||
\(162\) | −7.40349 | −0.581673 | ||||||||
\(163\) | 2.04684 | 0.160321 | 0.0801604 | − | 0.996782i | \(-0.474457\pi\) | ||||
0.0801604 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(164\) | −9.47440 | −0.739826 | ||||||||
\(165\) | 10.1306 | 0.788663 | ||||||||
\(166\) | −4.26476 | −0.331009 | ||||||||
\(167\) | −16.9384 | −1.31073 | −0.655366 | − | 0.755311i | \(-0.727486\pi\) | ||||
−0.655366 | + | 0.755311i | \(0.727486\pi\) | |||||||
\(168\) | 10.6137 | 0.818867 | ||||||||
\(169\) | −0.568177 | −0.0437059 | ||||||||
\(170\) | 21.2918 | 1.63301 | ||||||||
\(171\) | −15.0743 | −1.15276 | ||||||||
\(172\) | −45.4661 | −3.46676 | ||||||||
\(173\) | −22.0549 | −1.67680 | −0.838401 | − | 0.545053i | \(-0.816509\pi\) | ||||
−0.838401 | + | 0.545053i | \(0.816509\pi\) | |||||||
\(174\) | −2.15656 | −0.163488 | ||||||||
\(175\) | −6.65918 | −0.503387 | ||||||||
\(176\) | 25.5835 | 1.92843 | ||||||||
\(177\) | −7.02751 | −0.528220 | ||||||||
\(178\) | −1.39841 | −0.104815 | ||||||||
\(179\) | 14.3666 | 1.07381 | 0.536907 | − | 0.843642i | \(-0.319593\pi\) | ||||
0.536907 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(180\) | −28.1478 | −2.09801 | ||||||||
\(181\) | −4.19106 | −0.311519 | −0.155760 | − | 0.987795i | \(-0.549783\pi\) | ||||
−0.155760 | + | 0.987795i | \(0.549783\pi\) | |||||||
\(182\) | −18.6479 | −1.38227 | ||||||||
\(183\) | 2.86402 | 0.211715 | ||||||||
\(184\) | 9.20607 | 0.678680 | ||||||||
\(185\) | 2.70932 | 0.199193 | ||||||||
\(186\) | −11.6268 | −0.852522 | ||||||||
\(187\) | −12.2404 | −0.895105 | ||||||||
\(188\) | 23.4099 | 1.70734 | ||||||||
\(189\) | 9.46950 | 0.688805 | ||||||||
\(190\) | −47.8772 | −3.47337 | ||||||||
\(191\) | −1.61806 | −0.117078 | −0.0585392 | − | 0.998285i | \(-0.518644\pi\) | ||||
−0.0585392 | + | 0.998285i | \(0.518644\pi\) | |||||||
\(192\) | −2.47296 | −0.178470 | ||||||||
\(193\) | −26.8863 | −1.93532 | −0.967660 | − | 0.252258i | \(-0.918827\pi\) | ||||
−0.967660 | + | 0.252258i | \(0.918827\pi\) | |||||||
\(194\) | 28.9993 | 2.08203 | ||||||||
\(195\) | −8.62975 | −0.617989 | ||||||||
\(196\) | −11.2533 | −0.803806 | ||||||||
\(197\) | 10.9753 | 0.781961 | 0.390980 | − | 0.920399i | \(-0.372136\pi\) | ||||
0.390980 | + | 0.920399i | \(0.372136\pi\) | |||||||
\(198\) | 23.6323 | 1.67948 | ||||||||
\(199\) | 1.50400 | 0.106616 | 0.0533079 | − | 0.998578i | \(-0.483024\pi\) | ||||
0.0533079 | + | 0.998578i | \(0.483024\pi\) | |||||||
\(200\) | −18.7210 | −1.32377 | ||||||||
\(201\) | 0.354120 | 0.0249777 | ||||||||
\(202\) | 21.1434 | 1.48765 | ||||||||
\(203\) | −2.09984 | −0.147380 | ||||||||
\(204\) | −10.9989 | −0.770075 | ||||||||
\(205\) | −6.23487 | −0.435462 | ||||||||
\(206\) | −33.5660 | −2.33865 | ||||||||
\(207\) | 3.53516 | 0.245710 | ||||||||
\(208\) | −21.7934 | −1.51110 | ||||||||
\(209\) | 27.5240 | 1.90387 | ||||||||
\(210\) | 12.9447 | 0.893270 | ||||||||
\(211\) | 8.39783 | 0.578130 | 0.289065 | − | 0.957309i | \(-0.406656\pi\) | ||||
0.289065 | + | 0.957309i | \(0.406656\pi\) | |||||||
\(212\) | −43.2112 | −2.96776 | ||||||||
\(213\) | −7.31922 | −0.501504 | ||||||||
\(214\) | −29.8389 | −2.03975 | ||||||||
\(215\) | −29.9201 | −2.04054 | ||||||||
\(216\) | 26.6216 | 1.81137 | ||||||||
\(217\) | −11.3211 | −0.768526 | ||||||||
\(218\) | 29.2947 | 1.98408 | ||||||||
\(219\) | −2.57209 | −0.173806 | ||||||||
\(220\) | 51.3945 | 3.46502 | ||||||||
\(221\) | 10.4270 | 0.701397 | ||||||||
\(222\) | −2.04398 | −0.137183 | ||||||||
\(223\) | 1.30233 | 0.0872105 | 0.0436052 | − | 0.999049i | \(-0.486116\pi\) | ||||
0.0436052 | + | 0.999049i | \(0.486116\pi\) | |||||||
\(224\) | 7.89830 | 0.527727 | ||||||||
\(225\) | −7.18892 | −0.479261 | ||||||||
\(226\) | −19.2835 | −1.28272 | ||||||||
\(227\) | −25.8320 | −1.71453 | −0.857265 | − | 0.514875i | \(-0.827838\pi\) | ||||
−0.857265 | + | 0.514875i | \(0.827838\pi\) | |||||||
\(228\) | 24.7323 | 1.63794 | ||||||||
\(229\) | 14.2816 | 0.943756 | 0.471878 | − | 0.881664i | \(-0.343576\pi\) | ||||
0.471878 | + | 0.881664i | \(0.343576\pi\) | |||||||
\(230\) | 11.2279 | 0.740346 | ||||||||
\(231\) | −7.44176 | −0.489632 | ||||||||
\(232\) | −5.90330 | −0.387570 | ||||||||
\(233\) | −16.0648 | −1.05244 | −0.526222 | − | 0.850348i | \(-0.676392\pi\) | ||||
−0.526222 | + | 0.850348i | \(0.676392\pi\) | |||||||
\(234\) | −20.1313 | −1.31602 | ||||||||
\(235\) | 15.4054 | 1.00494 | ||||||||
\(236\) | −35.6521 | −2.32075 | ||||||||
\(237\) | 9.39900 | 0.610531 | ||||||||
\(238\) | −15.6406 | −1.01383 | ||||||||
\(239\) | −10.0630 | −0.650922 | −0.325461 | − | 0.945556i | \(-0.605519\pi\) | ||||
−0.325461 | + | 0.945556i | \(0.605519\pi\) | |||||||
\(240\) | 15.1282 | 0.976524 | ||||||||
\(241\) | −24.7756 | −1.59594 | −0.797968 | − | 0.602700i | \(-0.794092\pi\) | ||||
−0.797968 | + | 0.602700i | \(0.794092\pi\) | |||||||
\(242\) | −15.4443 | −0.992798 | ||||||||
\(243\) | 16.0457 | 1.02933 | ||||||||
\(244\) | 14.5298 | 0.930176 | ||||||||
\(245\) | −7.40550 | −0.473120 | ||||||||
\(246\) | 4.70374 | 0.299899 | ||||||||
\(247\) | −23.4464 | −1.49186 | ||||||||
\(248\) | −31.8270 | −2.02102 | ||||||||
\(249\) | 1.44979 | 0.0918768 | ||||||||
\(250\) | 13.1664 | 0.832718 | ||||||||
\(251\) | 8.64192 | 0.545473 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(252\) | 20.6769 | 1.30252 | ||||||||
\(253\) | −6.45479 | −0.405809 | ||||||||
\(254\) | 20.5315 | 1.28826 | ||||||||
\(255\) | −7.23808 | −0.453266 | ||||||||
\(256\) | −31.4933 | −1.96833 | ||||||||
\(257\) | −3.65842 | −0.228206 | −0.114103 | − | 0.993469i | \(-0.536399\pi\) | ||||
−0.114103 | + | 0.993469i | \(0.536399\pi\) | |||||||
\(258\) | 22.5725 | 1.40530 | ||||||||
\(259\) | −1.99023 | −0.123667 | ||||||||
\(260\) | −43.7806 | −2.71516 | ||||||||
\(261\) | −2.26688 | −0.140317 | ||||||||
\(262\) | 7.53839 | 0.465724 | ||||||||
\(263\) | 0.266691 | 0.0164449 | 0.00822244 | − | 0.999966i | \(-0.497383\pi\) | ||||
0.00822244 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(264\) | −20.9210 | −1.28760 | ||||||||
\(265\) | −28.4362 | −1.74682 | ||||||||
\(266\) | 35.1698 | 2.15640 | ||||||||
\(267\) | 0.475386 | 0.0290931 | ||||||||
\(268\) | 1.79653 | 0.109740 | ||||||||
\(269\) | 12.6587 | 0.771813 | 0.385906 | − | 0.922538i | \(-0.373889\pi\) | ||||
0.385906 | + | 0.922538i | \(0.373889\pi\) | |||||||
\(270\) | 32.4683 | 1.97596 | ||||||||
\(271\) | −28.2643 | −1.71693 | −0.858467 | − | 0.512868i | \(-0.828583\pi\) | ||||
−0.858467 | + | 0.512868i | \(0.828583\pi\) | |||||||
\(272\) | −18.2789 | −1.10832 | ||||||||
\(273\) | 6.33929 | 0.383671 | ||||||||
\(274\) | 3.49674 | 0.211246 | ||||||||
\(275\) | 13.1261 | 0.791535 | ||||||||
\(276\) | −5.80009 | −0.349125 | ||||||||
\(277\) | 1.00000 | 0.0600842 | ||||||||
\(278\) | −41.3699 | −2.48120 | ||||||||
\(279\) | −12.2217 | −0.731693 | ||||||||
\(280\) | 35.4345 | 2.11762 | ||||||||
\(281\) | −12.8183 | −0.764675 | −0.382338 | − | 0.924023i | \(-0.624881\pi\) | ||||
−0.382338 | + | 0.924023i | \(0.624881\pi\) | |||||||
\(282\) | −11.6222 | −0.692095 | ||||||||
\(283\) | −24.5097 | −1.45695 | −0.728475 | − | 0.685072i | \(-0.759771\pi\) | ||||
−0.728475 | + | 0.685072i | \(0.759771\pi\) | |||||||
\(284\) | −37.1320 | −2.20338 | ||||||||
\(285\) | 16.2757 | 0.964090 | ||||||||
\(286\) | 36.7574 | 2.17351 | ||||||||
\(287\) | 4.58004 | 0.270351 | ||||||||
\(288\) | 8.52661 | 0.502435 | ||||||||
\(289\) | −8.25450 | −0.485559 | ||||||||
\(290\) | −7.19979 | −0.422786 | ||||||||
\(291\) | −9.85823 | −0.577900 | ||||||||
\(292\) | −13.0488 | −0.763621 | ||||||||
\(293\) | 30.2306 | 1.76609 | 0.883046 | − | 0.469287i | \(-0.155489\pi\) | ||||
0.883046 | + | 0.469287i | \(0.155489\pi\) | |||||||
\(294\) | 5.58689 | 0.325834 | ||||||||
\(295\) | −23.4617 | −1.36600 | ||||||||
\(296\) | −5.59513 | −0.325210 | ||||||||
\(297\) | −18.6656 | −1.08309 | ||||||||
\(298\) | 10.7929 | 0.625218 | ||||||||
\(299\) | 5.49853 | 0.317988 | ||||||||
\(300\) | 11.7948 | 0.680972 | ||||||||
\(301\) | 21.9789 | 1.26684 | ||||||||
\(302\) | −22.3007 | −1.28326 | ||||||||
\(303\) | −7.18765 | −0.412920 | ||||||||
\(304\) | 41.1023 | 2.35738 | ||||||||
\(305\) | 9.56171 | 0.547502 | ||||||||
\(306\) | −16.8848 | −0.965241 | ||||||||
\(307\) | −20.8466 | −1.18978 | −0.594890 | − | 0.803807i | \(-0.702804\pi\) | ||||
−0.594890 | + | 0.803807i | \(0.702804\pi\) | |||||||
\(308\) | −37.7537 | −2.15121 | ||||||||
\(309\) | 11.4107 | 0.649130 | ||||||||
\(310\) | −38.8169 | −2.20465 | ||||||||
\(311\) | 0.790747 | 0.0448392 | 0.0224196 | − | 0.999749i | \(-0.492863\pi\) | ||||
0.0224196 | + | 0.999749i | \(0.492863\pi\) | |||||||
\(312\) | 17.8217 | 1.00895 | ||||||||
\(313\) | −2.95234 | −0.166876 | −0.0834382 | − | 0.996513i | \(-0.526590\pi\) | ||||
−0.0834382 | + | 0.996513i | \(0.526590\pi\) | |||||||
\(314\) | −0.391617 | −0.0221002 | ||||||||
\(315\) | 13.6070 | 0.766666 | ||||||||
\(316\) | 47.6832 | 2.68239 | ||||||||
\(317\) | 18.9719 | 1.06557 | 0.532785 | − | 0.846251i | \(-0.321145\pi\) | ||||
0.532785 | + | 0.846251i | \(0.321145\pi\) | |||||||
\(318\) | 21.4530 | 1.20302 | ||||||||
\(319\) | 4.13907 | 0.231743 | ||||||||
\(320\) | −8.25612 | −0.461531 | ||||||||
\(321\) | 10.1437 | 0.566164 | ||||||||
\(322\) | −8.24785 | −0.459635 | ||||||||
\(323\) | −19.6653 | −1.09421 | ||||||||
\(324\) | 12.7683 | 0.709348 | ||||||||
\(325\) | −11.1815 | −0.620240 | ||||||||
\(326\) | −5.15535 | −0.285528 | ||||||||
\(327\) | −9.95864 | −0.550714 | ||||||||
\(328\) | 12.8759 | 0.710952 | ||||||||
\(329\) | −11.3166 | −0.623905 | ||||||||
\(330\) | −25.5157 | −1.40460 | ||||||||
\(331\) | 25.9752 | 1.42772 | 0.713862 | − | 0.700286i | \(-0.246944\pi\) | ||||
0.713862 | + | 0.700286i | \(0.246944\pi\) | |||||||
\(332\) | 7.35511 | 0.403664 | ||||||||
\(333\) | −2.14855 | −0.117740 | ||||||||
\(334\) | 42.6625 | 2.33439 | ||||||||
\(335\) | 1.18225 | 0.0645932 | ||||||||
\(336\) | −11.1130 | −0.606263 | ||||||||
\(337\) | −19.8561 | −1.08163 | −0.540817 | − | 0.841141i | \(-0.681885\pi\) | ||||
−0.540817 | + | 0.841141i | \(0.681885\pi\) | |||||||
\(338\) | 1.43106 | 0.0778395 | ||||||||
\(339\) | 6.55539 | 0.356040 | ||||||||
\(340\) | −36.7204 | −1.99144 | ||||||||
\(341\) | 22.3154 | 1.20844 | ||||||||
\(342\) | 37.9676 | 2.05305 | ||||||||
\(343\) | 20.1389 | 1.08740 | ||||||||
\(344\) | 61.7893 | 3.33146 | ||||||||
\(345\) | −3.81690 | −0.205495 | ||||||||
\(346\) | 55.5494 | 2.98636 | ||||||||
\(347\) | −10.1557 | −0.545185 | −0.272593 | − | 0.962130i | \(-0.587881\pi\) | ||||
−0.272593 | + | 0.962130i | \(0.587881\pi\) | |||||||
\(348\) | 3.71925 | 0.199373 | ||||||||
\(349\) | −25.9996 | −1.39173 | −0.695864 | − | 0.718174i | \(-0.744978\pi\) | ||||
−0.695864 | + | 0.718174i | \(0.744978\pi\) | |||||||
\(350\) | 16.7724 | 0.896523 | ||||||||
\(351\) | 15.9004 | 0.848699 | ||||||||
\(352\) | −15.5686 | −0.829809 | ||||||||
\(353\) | 2.89740 | 0.154213 | 0.0771064 | − | 0.997023i | \(-0.475432\pi\) | ||||
0.0771064 | + | 0.997023i | \(0.475432\pi\) | |||||||
\(354\) | 17.7001 | 0.940750 | ||||||||
\(355\) | −24.4356 | −1.29691 | ||||||||
\(356\) | 2.41174 | 0.127822 | ||||||||
\(357\) | 5.31699 | 0.281405 | ||||||||
\(358\) | −36.1851 | −1.91244 | ||||||||
\(359\) | 14.1255 | 0.745516 | 0.372758 | − | 0.927929i | \(-0.378412\pi\) | ||||
0.372758 | + | 0.927929i | \(0.378412\pi\) | |||||||
\(360\) | 38.2533 | 2.01613 | ||||||||
\(361\) | 25.2199 | 1.32736 | ||||||||
\(362\) | 10.5560 | 0.554811 | ||||||||
\(363\) | 5.25025 | 0.275567 | ||||||||
\(364\) | 32.1606 | 1.68567 | ||||||||
\(365\) | −8.58706 | −0.449467 | ||||||||
\(366\) | −7.21359 | −0.377060 | ||||||||
\(367\) | −19.2117 | −1.00284 | −0.501422 | − | 0.865203i | \(-0.667190\pi\) | ||||
−0.501422 | + | 0.865203i | \(0.667190\pi\) | |||||||
\(368\) | −9.63911 | −0.502473 | ||||||||
\(369\) | 4.94438 | 0.257394 | ||||||||
\(370\) | −6.82394 | −0.354760 | ||||||||
\(371\) | 20.8888 | 1.08449 | ||||||||
\(372\) | 20.0520 | 1.03965 | ||||||||
\(373\) | 1.79570 | 0.0929780 | 0.0464890 | − | 0.998919i | \(-0.485197\pi\) | ||||
0.0464890 | + | 0.998919i | \(0.485197\pi\) | |||||||
\(374\) | 30.8297 | 1.59417 | ||||||||
\(375\) | −4.47589 | −0.231134 | ||||||||
\(376\) | −31.8144 | −1.64070 | ||||||||
\(377\) | −3.52588 | −0.181592 | ||||||||
\(378\) | −23.8507 | −1.22675 | ||||||||
\(379\) | −3.36426 | −0.172810 | −0.0864051 | − | 0.996260i | \(-0.527538\pi\) | ||||
−0.0864051 | + | 0.996260i | \(0.527538\pi\) | |||||||
\(380\) | 82.5702 | 4.23576 | ||||||||
\(381\) | −6.97964 | −0.357578 | ||||||||
\(382\) | 4.07538 | 0.208515 | ||||||||
\(383\) | −1.04995 | −0.0536498 | −0.0268249 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268249 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(384\) | 12.6698 | 0.646551 | ||||||||
\(385\) | −24.8447 | −1.26621 | ||||||||
\(386\) | 67.7183 | 3.44677 | ||||||||
\(387\) | 23.7273 | 1.20613 | ||||||||
\(388\) | −50.0130 | −2.53902 | ||||||||
\(389\) | 17.3425 | 0.879301 | 0.439650 | − | 0.898169i | \(-0.355102\pi\) | ||||
0.439650 | + | 0.898169i | \(0.355102\pi\) | |||||||
\(390\) | 21.7357 | 1.10063 | ||||||||
\(391\) | 4.61181 | 0.233229 | ||||||||
\(392\) | 15.2934 | 0.772434 | ||||||||
\(393\) | −2.56266 | −0.129269 | ||||||||
\(394\) | −27.6435 | −1.39266 | ||||||||
\(395\) | 31.3791 | 1.57885 | ||||||||
\(396\) | −40.7569 | −2.04811 | ||||||||
\(397\) | 0.149511 | 0.00750373 | 0.00375186 | − | 0.999993i | \(-0.498806\pi\) | ||||
0.00375186 | + | 0.999993i | \(0.498806\pi\) | |||||||
\(398\) | −3.78811 | −0.189881 | ||||||||
\(399\) | −11.9559 | −0.598543 | ||||||||
\(400\) | 19.6016 | 0.980080 | ||||||||
\(401\) | 18.1305 | 0.905396 | 0.452698 | − | 0.891664i | \(-0.350462\pi\) | ||||
0.452698 | + | 0.891664i | \(0.350462\pi\) | |||||||
\(402\) | −0.891919 | −0.0444849 | ||||||||
\(403\) | −19.0094 | −0.946926 | ||||||||
\(404\) | −36.4645 | −1.81418 | ||||||||
\(405\) | 8.40247 | 0.417522 | ||||||||
\(406\) | 5.28885 | 0.262481 | ||||||||
\(407\) | 3.92300 | 0.194456 | ||||||||
\(408\) | 14.9477 | 0.740019 | ||||||||
\(409\) | 7.38380 | 0.365105 | 0.182553 | − | 0.983196i | \(-0.441564\pi\) | ||||
0.182553 | + | 0.983196i | \(0.441564\pi\) | |||||||
\(410\) | 15.7037 | 0.775550 | ||||||||
\(411\) | −1.18871 | −0.0586346 | ||||||||
\(412\) | 57.8888 | 2.85197 | ||||||||
\(413\) | 17.2346 | 0.848061 | ||||||||
\(414\) | −8.90397 | −0.437606 | ||||||||
\(415\) | 4.84021 | 0.237597 | ||||||||
\(416\) | 13.2622 | 0.650231 | ||||||||
\(417\) | 14.0636 | 0.688697 | ||||||||
\(418\) | −69.3244 | −3.39077 | ||||||||
\(419\) | −11.7518 | −0.574113 | −0.287057 | − | 0.957914i | \(-0.592677\pi\) | ||||
−0.287057 | + | 0.957914i | \(0.592677\pi\) | |||||||
\(420\) | −22.3248 | −1.08934 | ||||||||
\(421\) | 22.3489 | 1.08922 | 0.544609 | − | 0.838690i | \(-0.316678\pi\) | ||||
0.544609 | + | 0.838690i | \(0.316678\pi\) | |||||||
\(422\) | −21.1515 | −1.02964 | ||||||||
\(423\) | −12.2168 | −0.594003 | ||||||||
\(424\) | 58.7248 | 2.85193 | ||||||||
\(425\) | −9.37835 | −0.454917 | ||||||||
\(426\) | 18.4348 | 0.893171 | ||||||||
\(427\) | −7.02389 | −0.339910 | ||||||||
\(428\) | 51.4610 | 2.48746 | ||||||||
\(429\) | −12.4956 | −0.603292 | ||||||||
\(430\) | 75.3595 | 3.63416 | ||||||||
\(431\) | −1.09141 | −0.0525712 | −0.0262856 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262856 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(432\) | −27.8739 | −1.34108 | ||||||||
\(433\) | −34.2048 | −1.64378 | −0.821889 | − | 0.569647i | \(-0.807080\pi\) | ||||
−0.821889 | + | 0.569647i | \(0.807080\pi\) | |||||||
\(434\) | 28.5143 | 1.36873 | ||||||||
\(435\) | 2.44755 | 0.117351 | ||||||||
\(436\) | −50.5223 | −2.41958 | ||||||||
\(437\) | −10.3702 | −0.496075 | ||||||||
\(438\) | 6.47829 | 0.309545 | ||||||||
\(439\) | 18.9437 | 0.904131 | 0.452066 | − | 0.891985i | \(-0.350687\pi\) | ||||
0.452066 | + | 0.891985i | \(0.350687\pi\) | |||||||
\(440\) | −69.8461 | −3.32978 | ||||||||
\(441\) | 5.87272 | 0.279653 | ||||||||
\(442\) | −26.2624 | −1.24918 | ||||||||
\(443\) | 38.4274 | 1.82574 | 0.912870 | − | 0.408251i | \(-0.133861\pi\) | ||||
0.912870 | + | 0.408251i | \(0.133861\pi\) | |||||||
\(444\) | 3.52510 | 0.167294 | ||||||||
\(445\) | 1.58710 | 0.0752359 | ||||||||
\(446\) | −3.28017 | −0.155320 | ||||||||
\(447\) | −3.66903 | −0.173539 | ||||||||
\(448\) | 6.06482 | 0.286536 | ||||||||
\(449\) | −4.75483 | −0.224394 | −0.112197 | − | 0.993686i | \(-0.535789\pi\) | ||||
−0.112197 | + | 0.993686i | \(0.535789\pi\) | |||||||
\(450\) | 18.1067 | 0.853556 | ||||||||
\(451\) | −9.02786 | −0.425105 | ||||||||
\(452\) | 33.2569 | 1.56427 | ||||||||
\(453\) | 7.58108 | 0.356190 | ||||||||
\(454\) | 65.0628 | 3.05355 | ||||||||
\(455\) | 21.1641 | 0.992187 | ||||||||
\(456\) | −33.6116 | −1.57401 | ||||||||
\(457\) | 3.86701 | 0.180891 | 0.0904454 | − | 0.995901i | \(-0.471171\pi\) | ||||
0.0904454 | + | 0.995901i | \(0.471171\pi\) | |||||||
\(458\) | −35.9710 | −1.68081 | ||||||||
\(459\) | 13.3362 | 0.622481 | ||||||||
\(460\) | −19.3639 | −0.902849 | ||||||||
\(461\) | −38.5274 | −1.79440 | −0.897201 | − | 0.441623i | \(-0.854403\pi\) | ||||
−0.897201 | + | 0.441623i | \(0.854403\pi\) | |||||||
\(462\) | 18.7435 | 0.872026 | ||||||||
\(463\) | −21.8997 | −1.01777 | −0.508883 | − | 0.860835i | \(-0.669942\pi\) | ||||
−0.508883 | + | 0.860835i | \(0.669942\pi\) | |||||||
\(464\) | 6.18098 | 0.286945 | ||||||||
\(465\) | 13.1957 | 0.611936 | ||||||||
\(466\) | 40.4624 | 1.87438 | ||||||||
\(467\) | 1.83733 | 0.0850216 | 0.0425108 | − | 0.999096i | \(-0.486464\pi\) | ||||
0.0425108 | + | 0.999096i | \(0.486464\pi\) | |||||||
\(468\) | 34.7189 | 1.60488 | ||||||||
\(469\) | −0.868463 | −0.0401019 | ||||||||
\(470\) | −38.8015 | −1.78978 | ||||||||
\(471\) | 0.133129 | 0.00613426 | ||||||||
\(472\) | 48.4518 | 2.23018 | ||||||||
\(473\) | −43.3233 | −1.99201 | ||||||||
\(474\) | −23.6732 | −1.08734 | ||||||||
\(475\) | 21.0884 | 0.967600 | ||||||||
\(476\) | 26.9742 | 1.23636 | ||||||||
\(477\) | 22.5505 | 1.03252 | ||||||||
\(478\) | 25.3456 | 1.15928 | ||||||||
\(479\) | −39.8237 | −1.81959 | −0.909796 | − | 0.415056i | \(-0.863762\pi\) | ||||
−0.909796 | + | 0.415056i | \(0.863762\pi\) | |||||||
\(480\) | −9.20614 | −0.420201 | ||||||||
\(481\) | −3.34182 | −0.152374 | ||||||||
\(482\) | 62.4020 | 2.84233 | ||||||||
\(483\) | 2.80383 | 0.127579 | ||||||||
\(484\) | 26.6357 | 1.21071 | ||||||||
\(485\) | −32.9123 | −1.49447 | ||||||||
\(486\) | −40.4140 | −1.83322 | ||||||||
\(487\) | −8.23037 | −0.372954 | −0.186477 | − | 0.982459i | \(-0.559707\pi\) | ||||
−0.186477 | + | 0.982459i | \(0.559707\pi\) | |||||||
\(488\) | −19.7463 | −0.893872 | ||||||||
\(489\) | 1.75255 | 0.0792529 | ||||||||
\(490\) | 18.6522 | 0.842619 | ||||||||
\(491\) | −40.8957 | −1.84560 | −0.922798 | − | 0.385285i | \(-0.874103\pi\) | ||||
−0.922798 | + | 0.385285i | \(0.874103\pi\) | |||||||
\(492\) | −8.11218 | −0.365726 | ||||||||
\(493\) | −2.95728 | −0.133189 | ||||||||
\(494\) | 59.0542 | 2.65697 | ||||||||
\(495\) | −26.8211 | −1.20552 | ||||||||
\(496\) | 33.3241 | 1.49630 | ||||||||
\(497\) | 17.9500 | 0.805170 | ||||||||
\(498\) | −3.65158 | −0.163631 | ||||||||
\(499\) | 40.8679 | 1.82950 | 0.914750 | − | 0.404020i | \(-0.132387\pi\) | ||||
0.914750 | + | 0.404020i | \(0.132387\pi\) | |||||||
\(500\) | −22.7072 | −1.01549 | ||||||||
\(501\) | −14.5030 | −0.647947 | ||||||||
\(502\) | −21.7663 | −0.971478 | ||||||||
\(503\) | 38.1445 | 1.70078 | 0.850389 | − | 0.526154i | \(-0.176366\pi\) | ||||
0.850389 | + | 0.526154i | \(0.176366\pi\) | |||||||
\(504\) | −28.1003 | −1.25169 | ||||||||
\(505\) | −23.9964 | −1.06782 | ||||||||
\(506\) | 16.2576 | 0.722739 | ||||||||
\(507\) | −0.486485 | −0.0216056 | ||||||||
\(508\) | −35.4092 | −1.57103 | ||||||||
\(509\) | −13.5944 | −0.602561 | −0.301280 | − | 0.953536i | \(-0.597414\pi\) | ||||
−0.301280 | + | 0.953536i | \(0.597414\pi\) | |||||||
\(510\) | 18.2305 | 0.807259 | ||||||||
\(511\) | 6.30793 | 0.279046 | ||||||||
\(512\) | 49.7274 | 2.19766 | ||||||||
\(513\) | −29.9881 | −1.32401 | ||||||||
\(514\) | 9.21443 | 0.406431 | ||||||||
\(515\) | 38.0951 | 1.67867 | ||||||||
\(516\) | −38.9291 | −1.71376 | ||||||||
\(517\) | 22.3065 | 0.981040 | ||||||||
\(518\) | 5.01276 | 0.220248 | ||||||||
\(519\) | −18.8839 | −0.828910 | ||||||||
\(520\) | 59.4986 | 2.60919 | ||||||||
\(521\) | 27.4885 | 1.20429 | 0.602146 | − | 0.798386i | \(-0.294313\pi\) | ||||
0.602146 | + | 0.798386i | \(0.294313\pi\) | |||||||
\(522\) | 5.70958 | 0.249902 | ||||||||
\(523\) | 3.52604 | 0.154183 | 0.0770914 | − | 0.997024i | \(-0.475437\pi\) | ||||
0.0770914 | + | 0.997024i | \(0.475437\pi\) | |||||||
\(524\) | −13.0009 | −0.567947 | ||||||||
\(525\) | −5.70174 | −0.248844 | ||||||||
\(526\) | −0.671712 | −0.0292880 | ||||||||
\(527\) | −15.9439 | −0.694526 | ||||||||
\(528\) | 21.9051 | 0.953299 | ||||||||
\(529\) | −20.5680 | −0.894262 | ||||||||
\(530\) | 71.6220 | 3.11106 | ||||||||
\(531\) | 18.6056 | 0.807416 | ||||||||
\(532\) | −60.6548 | −2.62972 | ||||||||
\(533\) | 7.69041 | 0.333109 | ||||||||
\(534\) | −1.19735 | −0.0518144 | ||||||||
\(535\) | 33.8652 | 1.46412 | ||||||||
\(536\) | −2.44151 | −0.105457 | ||||||||
\(537\) | 12.3010 | 0.530829 | ||||||||
\(538\) | −31.8833 | −1.37458 | ||||||||
\(539\) | −10.7229 | −0.461868 | ||||||||
\(540\) | −55.9957 | −2.40967 | ||||||||
\(541\) | −22.4310 | −0.964383 | −0.482191 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482191 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(542\) | 71.1890 | 3.05783 | ||||||||
\(543\) | −3.58848 | −0.153996 | ||||||||
\(544\) | 11.1234 | 0.476914 | ||||||||
\(545\) | −33.2475 | −1.42417 | ||||||||
\(546\) | −15.9667 | −0.683312 | ||||||||
\(547\) | 1.30938 | 0.0559851 | 0.0279925 | − | 0.999608i | \(-0.491089\pi\) | ||||
0.0279925 | + | 0.999608i | \(0.491089\pi\) | |||||||
\(548\) | −6.03057 | −0.257613 | ||||||||
\(549\) | −7.58263 | −0.323619 | ||||||||
\(550\) | −33.0606 | −1.40971 | ||||||||
\(551\) | 6.64980 | 0.283291 | ||||||||
\(552\) | 7.88243 | 0.335498 | ||||||||
\(553\) | −23.0506 | −0.980212 | ||||||||
\(554\) | −2.51869 | −0.107009 | ||||||||
\(555\) | 2.31978 | 0.0984691 | ||||||||
\(556\) | 71.3476 | 3.02581 | ||||||||
\(557\) | 35.1849 | 1.49083 | 0.745416 | − | 0.666600i | \(-0.232251\pi\) | ||||
0.745416 | + | 0.666600i | \(0.232251\pi\) | |||||||
\(558\) | 30.7826 | 1.30313 | ||||||||
\(559\) | 36.9051 | 1.56092 | ||||||||
\(560\) | −37.1013 | −1.56782 | ||||||||
\(561\) | −10.4805 | −0.442486 | ||||||||
\(562\) | 32.2853 | 1.36187 | ||||||||
\(563\) | −6.09706 | −0.256960 | −0.128480 | − | 0.991712i | \(-0.541010\pi\) | ||||
−0.128480 | + | 0.991712i | \(0.541010\pi\) | |||||||
\(564\) | 20.0440 | 0.844006 | ||||||||
\(565\) | 21.8855 | 0.920732 | ||||||||
\(566\) | 61.7323 | 2.59480 | ||||||||
\(567\) | −6.17233 | −0.259213 | ||||||||
\(568\) | 50.4630 | 2.11738 | ||||||||
\(569\) | −35.0861 | −1.47088 | −0.735442 | − | 0.677588i | \(-0.763026\pi\) | ||||
−0.735442 | + | 0.677588i | \(0.763026\pi\) | |||||||
\(570\) | −40.9935 | −1.71703 | ||||||||
\(571\) | −6.63598 | −0.277707 | −0.138854 | − | 0.990313i | \(-0.544342\pi\) | ||||
−0.138854 | + | 0.990313i | \(0.544342\pi\) | |||||||
\(572\) | −63.3927 | −2.65058 | ||||||||
\(573\) | −1.38541 | −0.0578765 | ||||||||
\(574\) | −11.5357 | −0.481491 | ||||||||
\(575\) | −4.94554 | −0.206243 | ||||||||
\(576\) | 6.54727 | 0.272803 | ||||||||
\(577\) | 13.7613 | 0.572892 | 0.286446 | − | 0.958096i | \(-0.407526\pi\) | ||||
0.286446 | + | 0.958096i | \(0.407526\pi\) | |||||||
\(578\) | 20.7905 | 0.864771 | ||||||||
\(579\) | −23.0206 | −0.956705 | ||||||||
\(580\) | 12.4169 | 0.515585 | ||||||||
\(581\) | −3.55555 | −0.147509 | ||||||||
\(582\) | 24.8298 | 1.02923 | ||||||||
\(583\) | −41.1746 | −1.70528 | ||||||||
\(584\) | 17.7335 | 0.733817 | ||||||||
\(585\) | 22.8477 | 0.944635 | ||||||||
\(586\) | −76.1415 | −3.14538 | ||||||||
\(587\) | 32.1541 | 1.32714 | 0.663571 | − | 0.748114i | \(-0.269040\pi\) | ||||
0.663571 | + | 0.748114i | \(0.269040\pi\) | |||||||
\(588\) | −9.63530 | −0.397353 | ||||||||
\(589\) | 35.8517 | 1.47724 | ||||||||
\(590\) | 59.0928 | 2.43281 | ||||||||
\(591\) | 9.39732 | 0.386554 | ||||||||
\(592\) | 5.85832 | 0.240775 | ||||||||
\(593\) | 40.0677 | 1.64538 | 0.822691 | − | 0.568488i | \(-0.192471\pi\) | ||||
0.822691 | + | 0.568488i | \(0.192471\pi\) | |||||||
\(594\) | 47.0129 | 1.92896 | ||||||||
\(595\) | 17.7511 | 0.727723 | ||||||||
\(596\) | −18.6138 | −0.762450 | ||||||||
\(597\) | 1.28776 | 0.0527044 | ||||||||
\(598\) | −13.8491 | −0.566332 | ||||||||
\(599\) | −46.4938 | −1.89969 | −0.949843 | − | 0.312727i | \(-0.898757\pi\) | ||||
−0.949843 | + | 0.312727i | \(0.898757\pi\) | |||||||
\(600\) | −16.0293 | −0.654394 | ||||||||
\(601\) | −14.0866 | −0.574603 | −0.287301 | − | 0.957840i | \(-0.592758\pi\) | ||||
−0.287301 | + | 0.957840i | \(0.592758\pi\) | |||||||
\(602\) | −55.3580 | −2.25622 | ||||||||
\(603\) | −0.937549 | −0.0381800 | ||||||||
\(604\) | 38.4604 | 1.56493 | ||||||||
\(605\) | 17.5283 | 0.712625 | ||||||||
\(606\) | 18.1035 | 0.735403 | ||||||||
\(607\) | −11.2435 | −0.456358 | −0.228179 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228179 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(608\) | −25.0124 | −1.01439 | ||||||||
\(609\) | −1.79793 | −0.0728558 | ||||||||
\(610\) | −24.0830 | −0.975091 | ||||||||
\(611\) | −19.0019 | −0.768734 | ||||||||
\(612\) | 29.1200 | 1.17711 | ||||||||
\(613\) | −16.1613 | −0.652747 | −0.326374 | − | 0.945241i | \(-0.605827\pi\) | ||||
−0.326374 | + | 0.945241i | \(0.605827\pi\) | |||||||
\(614\) | 52.5062 | 2.11898 | ||||||||
\(615\) | −5.33843 | −0.215266 | ||||||||
\(616\) | 51.3079 | 2.06725 | ||||||||
\(617\) | 10.8028 | 0.434903 | 0.217451 | − | 0.976071i | \(-0.430226\pi\) | ||||
0.217451 | + | 0.976071i | \(0.430226\pi\) | |||||||
\(618\) | −28.7399 | −1.15609 | ||||||||
\(619\) | −27.4689 | −1.10407 | −0.552035 | − | 0.833821i | \(-0.686149\pi\) | ||||
−0.552035 | + | 0.833821i | \(0.686149\pi\) | |||||||
\(620\) | 66.9446 | 2.68856 | ||||||||
\(621\) | 7.03265 | 0.282211 | ||||||||
\(622\) | −1.99165 | −0.0798578 | ||||||||
\(623\) | −1.16586 | −0.0467093 | ||||||||
\(624\) | −18.6600 | −0.746996 | ||||||||
\(625\) | −30.7994 | −1.23198 | ||||||||
\(626\) | 7.43604 | 0.297204 | ||||||||
\(627\) | 23.5666 | 0.941161 | ||||||||
\(628\) | 0.675393 | 0.0269511 | ||||||||
\(629\) | −2.80290 | −0.111759 | ||||||||
\(630\) | −34.2717 | −1.36542 | ||||||||
\(631\) | −34.7367 | −1.38285 | −0.691424 | − | 0.722450i | \(-0.743016\pi\) | ||||
−0.691424 | + | 0.722450i | \(0.743016\pi\) | |||||||
\(632\) | −64.8023 | −2.57770 | ||||||||
\(633\) | 7.19040 | 0.285793 | ||||||||
\(634\) | −47.7844 | −1.89776 | ||||||||
\(635\) | −23.3019 | −0.924709 | ||||||||
\(636\) | −36.9983 | −1.46708 | ||||||||
\(637\) | 9.13434 | 0.361916 | ||||||||
\(638\) | −10.4250 | −0.412731 | ||||||||
\(639\) | 19.3780 | 0.766580 | ||||||||
\(640\) | 42.2987 | 1.67200 | ||||||||
\(641\) | 27.3510 | 1.08030 | 0.540150 | − | 0.841569i | \(-0.318368\pi\) | ||||
0.540150 | + | 0.841569i | \(0.318368\pi\) | |||||||
\(642\) | −25.5487 | −1.00833 | ||||||||
\(643\) | 5.86751 | 0.231392 | 0.115696 | − | 0.993285i | \(-0.463090\pi\) | ||||
0.115696 | + | 0.993285i | \(0.463090\pi\) | |||||||
\(644\) | 14.2245 | 0.560522 | ||||||||
\(645\) | −25.6183 | −1.00872 | ||||||||
\(646\) | 49.5309 | 1.94877 | ||||||||
\(647\) | 40.8789 | 1.60712 | 0.803558 | − | 0.595226i | \(-0.202937\pi\) | ||||
0.803558 | + | 0.595226i | \(0.202937\pi\) | |||||||
\(648\) | −17.3523 | −0.681662 | ||||||||
\(649\) | −33.9717 | −1.33351 | ||||||||
\(650\) | 28.1628 | 1.10464 | ||||||||
\(651\) | −9.69336 | −0.379913 | ||||||||
\(652\) | 8.89105 | 0.348200 | ||||||||
\(653\) | 30.4819 | 1.19285 | 0.596425 | − | 0.802669i | \(-0.296587\pi\) | ||||
0.596425 | + | 0.802669i | \(0.296587\pi\) | |||||||
\(654\) | 25.0827 | 0.980812 | ||||||||
\(655\) | −8.55557 | −0.334294 | ||||||||
\(656\) | −13.4815 | −0.526366 | ||||||||
\(657\) | 6.80972 | 0.265672 | ||||||||
\(658\) | 28.5030 | 1.11116 | ||||||||
\(659\) | 3.54622 | 0.138141 | 0.0690706 | − | 0.997612i | \(-0.477997\pi\) | ||||
0.0690706 | + | 0.997612i | \(0.477997\pi\) | |||||||
\(660\) | 44.0051 | 1.71290 | ||||||||
\(661\) | −44.6989 | −1.73859 | −0.869293 | − | 0.494298i | \(-0.835425\pi\) | ||||
−0.869293 | + | 0.494298i | \(0.835425\pi\) | |||||||
\(662\) | −65.4234 | −2.54275 | ||||||||
\(663\) | 8.92783 | 0.346728 | ||||||||
\(664\) | −9.99573 | −0.387909 | ||||||||
\(665\) | −39.9154 | −1.54785 | ||||||||
\(666\) | 5.41152 | 0.209692 | ||||||||
\(667\) | −1.55948 | −0.0603832 | ||||||||
\(668\) | −73.5769 | −2.84678 | ||||||||
\(669\) | 1.11508 | 0.0431116 | ||||||||
\(670\) | −2.97772 | −0.115039 | ||||||||
\(671\) | 13.8450 | 0.534481 | ||||||||
\(672\) | 6.76269 | 0.260877 | ||||||||
\(673\) | 37.0770 | 1.42922 | 0.714608 | − | 0.699526i | \(-0.246605\pi\) | ||||
0.714608 | + | 0.699526i | \(0.246605\pi\) | |||||||
\(674\) | 50.0115 | 1.92637 | ||||||||
\(675\) | −14.3012 | −0.550455 | ||||||||
\(676\) | −2.46805 | −0.0949248 | ||||||||
\(677\) | −7.53102 | −0.289441 | −0.144720 | − | 0.989473i | \(-0.546228\pi\) | ||||
−0.144720 | + | 0.989473i | \(0.546228\pi\) | |||||||
\(678\) | −16.5110 | −0.634101 | ||||||||
\(679\) | 24.1769 | 0.927823 | ||||||||
\(680\) | 49.9036 | 1.91372 | ||||||||
\(681\) | −22.1179 | −0.847560 | ||||||||
\(682\) | −56.2055 | −2.15222 | ||||||||
\(683\) | −1.80706 | −0.0691454 | −0.0345727 | − | 0.999402i | \(-0.511007\pi\) | ||||
−0.0345727 | + | 0.999402i | \(0.511007\pi\) | |||||||
\(684\) | −65.4799 | −2.50369 | ||||||||
\(685\) | −3.96857 | −0.151631 | ||||||||
\(686\) | −50.7236 | −1.93664 | ||||||||
\(687\) | 12.2282 | 0.466536 | ||||||||
\(688\) | −64.6958 | −2.46650 | ||||||||
\(689\) | 35.0747 | 1.33624 | ||||||||
\(690\) | 9.61358 | 0.365983 | ||||||||
\(691\) | −34.5983 | −1.31618 | −0.658091 | − | 0.752939i | \(-0.728636\pi\) | ||||
−0.658091 | + | 0.752939i | \(0.728636\pi\) | |||||||
\(692\) | −95.8020 | −3.64185 | ||||||||
\(693\) | 19.7024 | 0.748432 | ||||||||
\(694\) | 25.5790 | 0.970965 | ||||||||
\(695\) | 46.9521 | 1.78099 | ||||||||
\(696\) | −5.05453 | −0.191591 | ||||||||
\(697\) | 6.45022 | 0.244320 | ||||||||
\(698\) | 65.4850 | 2.47864 | ||||||||
\(699\) | −13.7551 | −0.520264 | ||||||||
\(700\) | −28.9261 | −1.09331 | ||||||||
\(701\) | 17.6387 | 0.666206 | 0.333103 | − | 0.942890i | \(-0.391904\pi\) | ||||
0.333103 | + | 0.942890i | \(0.391904\pi\) | |||||||
\(702\) | −40.0481 | −1.51152 | ||||||||
\(703\) | 6.30267 | 0.237710 | ||||||||
\(704\) | −11.9546 | −0.450554 | ||||||||
\(705\) | 13.1905 | 0.496782 | ||||||||
\(706\) | −7.29764 | −0.274650 | ||||||||
\(707\) | 17.6274 | 0.662946 | ||||||||
\(708\) | −30.5261 | −1.14724 | ||||||||
\(709\) | −0.708073 | −0.0265923 | −0.0132961 | − | 0.999912i | \(-0.504232\pi\) | ||||
−0.0132961 | + | 0.999912i | \(0.504232\pi\) | |||||||
\(710\) | 61.5458 | 2.30977 | ||||||||
\(711\) | −24.8843 | −0.933234 | ||||||||
\(712\) | −3.27759 | −0.122833 | ||||||||
\(713\) | −8.40777 | −0.314873 | ||||||||
\(714\) | −13.3918 | −0.501177 | ||||||||
\(715\) | −41.7172 | −1.56013 | ||||||||
\(716\) | 62.4058 | 2.33221 | ||||||||
\(717\) | −8.61616 | −0.321776 | ||||||||
\(718\) | −35.5778 | −1.32775 | ||||||||
\(719\) | 20.3321 | 0.758258 | 0.379129 | − | 0.925344i | \(-0.376224\pi\) | ||||
0.379129 | + | 0.925344i | \(0.376224\pi\) | |||||||
\(720\) | −40.0527 | −1.49268 | ||||||||
\(721\) | −27.9841 | −1.04218 | ||||||||
\(722\) | −63.5211 | −2.36401 | ||||||||
\(723\) | −21.2134 | −0.788934 | ||||||||
\(724\) | −18.2051 | −0.676589 | ||||||||
\(725\) | 3.17128 | 0.117778 | ||||||||
\(726\) | −13.2237 | −0.490779 | ||||||||
\(727\) | 46.3373 | 1.71855 | 0.859277 | − | 0.511510i | \(-0.170914\pi\) | ||||
0.859277 | + | 0.511510i | \(0.170914\pi\) | |||||||
\(728\) | −43.7068 | −1.61988 | ||||||||
\(729\) | 4.92036 | 0.182236 | ||||||||
\(730\) | 21.6281 | 0.800494 | ||||||||
\(731\) | 30.9536 | 1.14486 | ||||||||
\(732\) | 12.4407 | 0.459823 | ||||||||
\(733\) | −30.3974 | −1.12275 | −0.561377 | − | 0.827560i | \(-0.689728\pi\) | ||||
−0.561377 | + | 0.827560i | \(0.689728\pi\) | |||||||
\(734\) | 48.3884 | 1.78605 | ||||||||
\(735\) | −6.34075 | −0.233882 | ||||||||
\(736\) | 5.86578 | 0.216216 | ||||||||
\(737\) | 1.71186 | 0.0630570 | ||||||||
\(738\) | −12.4534 | −0.458414 | ||||||||
\(739\) | −36.1793 | −1.33088 | −0.665439 | − | 0.746452i | \(-0.731756\pi\) | ||||
−0.665439 | + | 0.746452i | \(0.731756\pi\) | |||||||
\(740\) | 11.7687 | 0.432627 | ||||||||
\(741\) | −20.0753 | −0.737485 | ||||||||
\(742\) | −52.6124 | −1.93146 | ||||||||
\(743\) | −18.0751 | −0.663110 | −0.331555 | − | 0.943436i | \(-0.607573\pi\) | ||||
−0.331555 | + | 0.943436i | \(0.607573\pi\) | |||||||
\(744\) | −27.2510 | −0.999069 | ||||||||
\(745\) | −12.2493 | −0.448778 | ||||||||
\(746\) | −4.52282 | −0.165592 | ||||||||
\(747\) | −3.83839 | −0.140439 | ||||||||
\(748\) | −53.1697 | −1.94408 | ||||||||
\(749\) | −24.8769 | −0.908981 | ||||||||
\(750\) | 11.2734 | 0.411645 | ||||||||
\(751\) | −25.7349 | −0.939081 | −0.469540 | − | 0.882911i | \(-0.655580\pi\) | ||||
−0.469540 | + | 0.882911i | \(0.655580\pi\) | |||||||
\(752\) | 33.3109 | 1.21472 | ||||||||
\(753\) | 7.39939 | 0.269649 | ||||||||
\(754\) | 8.88059 | 0.323412 | ||||||||
\(755\) | 25.3099 | 0.921120 | ||||||||
\(756\) | 41.1336 | 1.49601 | ||||||||
\(757\) | −42.3861 | −1.54055 | −0.770275 | − | 0.637712i | \(-0.779881\pi\) | ||||
−0.770275 | + | 0.637712i | \(0.779881\pi\) | |||||||
\(758\) | 8.47352 | 0.307772 | ||||||||
\(759\) | −5.52673 | −0.200607 | ||||||||
\(760\) | −112.214 | −4.07044 | ||||||||
\(761\) | −43.3464 | −1.57131 | −0.785654 | − | 0.618666i | \(-0.787673\pi\) | ||||
−0.785654 | + | 0.618666i | \(0.787673\pi\) | |||||||
\(762\) | 17.5795 | 0.636840 | ||||||||
\(763\) | 24.4231 | 0.884176 | ||||||||
\(764\) | −7.02850 | −0.254282 | ||||||||
\(765\) | 19.1631 | 0.692845 | ||||||||
\(766\) | 2.64449 | 0.0955494 | ||||||||
\(767\) | 28.9389 | 1.04492 | ||||||||
\(768\) | −26.9653 | −0.973025 | ||||||||
\(769\) | −37.7656 | −1.36186 | −0.680931 | − | 0.732347i | \(-0.738425\pi\) | ||||
−0.680931 | + | 0.732347i | \(0.738425\pi\) | |||||||
\(770\) | 62.5762 | 2.25509 | ||||||||
\(771\) | −3.13242 | −0.112811 | ||||||||
\(772\) | −116.789 | −4.20332 | ||||||||
\(773\) | −41.6732 | −1.49888 | −0.749440 | − | 0.662073i | \(-0.769677\pi\) | ||||
−0.749440 | + | 0.662073i | \(0.769677\pi\) | |||||||
\(774\) | −59.7617 | −2.14809 | ||||||||
\(775\) | 17.0976 | 0.614164 | ||||||||
\(776\) | 67.9685 | 2.43993 | ||||||||
\(777\) | −1.70407 | −0.0611333 | ||||||||
\(778\) | −43.6804 | −1.56602 | ||||||||
\(779\) | −14.5041 | −0.519664 | ||||||||
\(780\) | −37.4859 | −1.34221 | ||||||||
\(781\) | −35.3819 | −1.26606 | ||||||||
\(782\) | −11.6157 | −0.415378 | ||||||||
\(783\) | −4.50962 | −0.161161 | ||||||||
\(784\) | −16.0128 | −0.571885 | ||||||||
\(785\) | 0.444459 | 0.0158634 | ||||||||
\(786\) | 6.45453 | 0.230226 | ||||||||
\(787\) | 12.3528 | 0.440329 | 0.220165 | − | 0.975463i | \(-0.429341\pi\) | ||||
0.220165 | + | 0.975463i | \(0.429341\pi\) | |||||||
\(788\) | 47.6746 | 1.69834 | ||||||||
\(789\) | 0.228347 | 0.00812935 | ||||||||
\(790\) | −79.0342 | −2.81191 | ||||||||
\(791\) | −16.0768 | −0.571625 | ||||||||
\(792\) | 55.3894 | 1.96818 | ||||||||
\(793\) | −11.7939 | −0.418814 | ||||||||
\(794\) | −0.376571 | −0.0133640 | ||||||||
\(795\) | −24.3477 | −0.863523 | ||||||||
\(796\) | 6.53307 | 0.231559 | ||||||||
\(797\) | −39.2510 | −1.39034 | −0.695171 | − | 0.718845i | \(-0.744671\pi\) | ||||
−0.695171 | + | 0.718845i | \(0.744671\pi\) | |||||||
\(798\) | 30.1132 | 1.06599 | ||||||||
\(799\) | −15.9376 | −0.563830 | ||||||||
\(800\) | −11.9284 | −0.421731 | ||||||||
\(801\) | −1.25861 | −0.0444706 | ||||||||
\(802\) | −45.6652 | −1.61249 | ||||||||
\(803\) | −12.4338 | −0.438778 | ||||||||
\(804\) | 1.53823 | 0.0542491 | ||||||||
\(805\) | 9.36076 | 0.329924 | ||||||||
\(806\) | 47.8788 | 1.68646 | ||||||||
\(807\) | 10.8386 | 0.381538 | ||||||||
\(808\) | 49.5559 | 1.74337 | ||||||||
\(809\) | −24.5108 | −0.861753 | −0.430877 | − | 0.902411i | \(-0.641796\pi\) | ||||
−0.430877 | + | 0.902411i | \(0.641796\pi\) | |||||||
\(810\) | −21.1632 | −0.743599 | ||||||||
\(811\) | 16.9152 | 0.593972 | 0.296986 | − | 0.954882i | \(-0.404018\pi\) | ||||
0.296986 | + | 0.954882i | \(0.404018\pi\) | |||||||
\(812\) | −9.12130 | −0.320095 | ||||||||
\(813\) | −24.2005 | −0.848749 | ||||||||
\(814\) | −9.88081 | −0.346322 | ||||||||
\(815\) | 5.85098 | 0.204951 | ||||||||
\(816\) | −15.6508 | −0.547887 | ||||||||
\(817\) | −69.6029 | −2.43510 | ||||||||
\(818\) | −18.5975 | −0.650246 | ||||||||
\(819\) | −16.7836 | −0.586465 | ||||||||
\(820\) | −27.0830 | −0.945779 | ||||||||
\(821\) | −4.19836 | −0.146524 | −0.0732620 | − | 0.997313i | \(-0.523341\pi\) | ||||
−0.0732620 | + | 0.997313i | \(0.523341\pi\) | |||||||
\(822\) | 2.99399 | 0.104427 | ||||||||
\(823\) | −43.1022 | −1.50245 | −0.751225 | − | 0.660046i | \(-0.770537\pi\) | ||||
−0.751225 | + | 0.660046i | \(0.770537\pi\) | |||||||
\(824\) | −78.6719 | −2.74066 | ||||||||
\(825\) | 11.2389 | 0.391287 | ||||||||
\(826\) | −43.4087 | −1.51038 | ||||||||
\(827\) | 22.2369 | 0.773253 | 0.386626 | − | 0.922236i | \(-0.373640\pi\) | ||||
0.386626 | + | 0.922236i | \(0.373640\pi\) | |||||||
\(828\) | 15.3560 | 0.533658 | ||||||||
\(829\) | −6.67857 | −0.231956 | −0.115978 | − | 0.993252i | \(-0.537000\pi\) | ||||
−0.115978 | + | 0.993252i | \(0.537000\pi\) | |||||||
\(830\) | −12.1910 | −0.423156 | ||||||||
\(831\) | 0.856221 | 0.0297020 | ||||||||
\(832\) | 10.1835 | 0.353050 | ||||||||
\(833\) | 7.66129 | 0.265448 | ||||||||
\(834\) | −35.4218 | −1.22656 | ||||||||
\(835\) | −48.4191 | −1.67561 | ||||||||
\(836\) | 119.559 | 4.13502 | ||||||||
\(837\) | −24.3131 | −0.840385 | ||||||||
\(838\) | 29.5991 | 1.02249 | ||||||||
\(839\) | 30.3710 | 1.04852 | 0.524261 | − | 0.851558i | \(-0.324342\pi\) | ||||
0.524261 | + | 0.851558i | \(0.324342\pi\) | |||||||
\(840\) | 30.3398 | 1.04682 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −56.2899 | −1.93988 | ||||||||
\(843\) | −10.9753 | −0.378009 | ||||||||
\(844\) | 36.4785 | 1.25564 | ||||||||
\(845\) | −1.62416 | −0.0558728 | ||||||||
\(846\) | 30.7704 | 1.05791 | ||||||||
\(847\) | −12.8760 | −0.442425 | ||||||||
\(848\) | −61.4871 | −2.11148 | ||||||||
\(849\) | −20.9857 | −0.720228 | ||||||||
\(850\) | 23.6212 | 0.810199 | ||||||||
\(851\) | −1.47807 | −0.0506676 | ||||||||
\(852\) | −31.7932 | −1.08922 | ||||||||
\(853\) | −18.6118 | −0.637256 | −0.318628 | − | 0.947880i | \(-0.603222\pi\) | ||||
−0.318628 | + | 0.947880i | \(0.603222\pi\) | |||||||
\(854\) | 17.6910 | 0.605373 | ||||||||
\(855\) | −43.0907 | −1.47367 | ||||||||
\(856\) | −69.9364 | −2.39038 | ||||||||
\(857\) | 24.0912 | 0.822939 | 0.411469 | − | 0.911424i | \(-0.365016\pi\) | ||||
0.411469 | + | 0.911424i | \(0.365016\pi\) | |||||||
\(858\) | 31.4725 | 1.07445 | ||||||||
\(859\) | −25.8870 | −0.883252 | −0.441626 | − | 0.897199i | \(-0.645598\pi\) | ||||
−0.441626 | + | 0.897199i | \(0.645598\pi\) | |||||||
\(860\) | −129.967 | −4.43184 | ||||||||
\(861\) | 3.92153 | 0.133645 | ||||||||
\(862\) | 2.74891 | 0.0936284 | ||||||||
\(863\) | 21.8572 | 0.744029 | 0.372015 | − | 0.928227i | \(-0.378667\pi\) | ||||
0.372015 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(864\) | 16.9624 | 0.577072 | ||||||||
\(865\) | −63.0449 | −2.14359 | ||||||||
\(866\) | 86.1513 | 2.92754 | ||||||||
\(867\) | −7.06768 | −0.240031 | ||||||||
\(868\) | −49.1765 | −1.66916 | ||||||||
\(869\) | 45.4358 | 1.54130 | ||||||||
\(870\) | −6.16461 | −0.209000 | ||||||||
\(871\) | −1.45825 | −0.0494109 | ||||||||
\(872\) | 68.6607 | 2.32515 | ||||||||
\(873\) | 26.1001 | 0.883355 | ||||||||
\(874\) | 26.1194 | 0.883501 | ||||||||
\(875\) | 10.9769 | 0.371087 | ||||||||
\(876\) | −11.1726 | −0.377488 | ||||||||
\(877\) | −17.7222 | −0.598436 | −0.299218 | − | 0.954185i | \(-0.596726\pi\) | ||||
−0.299218 | + | 0.954185i | \(0.596726\pi\) | |||||||
\(878\) | −47.7132 | −1.61024 | ||||||||
\(879\) | 25.8841 | 0.873049 | ||||||||
\(880\) | 73.1316 | 2.46526 | ||||||||
\(881\) | 14.7145 | 0.495744 | 0.247872 | − | 0.968793i | \(-0.420269\pi\) | ||||
0.247872 | + | 0.968793i | \(0.420269\pi\) | |||||||
\(882\) | −14.7916 | −0.498058 | ||||||||
\(883\) | −6.99333 | −0.235344 | −0.117672 | − | 0.993053i | \(-0.537543\pi\) | ||||
−0.117672 | + | 0.993053i | \(0.537543\pi\) | |||||||
\(884\) | 45.2928 | 1.52336 | ||||||||
\(885\) | −20.0884 | −0.675266 | ||||||||
\(886\) | −96.7866 | −3.25161 | ||||||||
\(887\) | −26.5254 | −0.890636 | −0.445318 | − | 0.895372i | \(-0.646909\pi\) | ||||
−0.445318 | + | 0.895372i | \(0.646909\pi\) | |||||||
\(888\) | −4.79067 | −0.160764 | ||||||||
\(889\) | 17.1172 | 0.574094 | ||||||||
\(890\) | −3.99742 | −0.133994 | ||||||||
\(891\) | 12.1665 | 0.407592 | ||||||||
\(892\) | 5.65706 | 0.189412 | ||||||||
\(893\) | 35.8375 | 1.19926 | ||||||||
\(894\) | 9.24114 | 0.309070 | ||||||||
\(895\) | 41.0677 | 1.37274 | ||||||||
\(896\) | −31.0720 | −1.03804 | ||||||||
\(897\) | 4.70796 | 0.157194 | ||||||||
\(898\) | 11.9759 | 0.399642 | ||||||||
\(899\) | 5.39140 | 0.179813 | ||||||||
\(900\) | −31.2272 | −1.04091 | ||||||||
\(901\) | 29.4184 | 0.980069 | ||||||||
\(902\) | 22.7384 | 0.757105 | ||||||||
\(903\) | 18.8188 | 0.626250 | ||||||||
\(904\) | −45.1967 | −1.50322 | ||||||||
\(905\) | −11.9803 | −0.398240 | ||||||||
\(906\) | −19.0944 | −0.634368 | ||||||||
\(907\) | 2.13682 | 0.0709519 | 0.0354760 | − | 0.999371i | \(-0.488705\pi\) | ||||
0.0354760 | + | 0.999371i | \(0.488705\pi\) | |||||||
\(908\) | −112.209 | −3.72379 | ||||||||
\(909\) | 19.0296 | 0.631173 | ||||||||
\(910\) | −53.3057 | −1.76707 | ||||||||
\(911\) | −16.5092 | −0.546974 | −0.273487 | − | 0.961876i | \(-0.588177\pi\) | ||||
−0.273487 | + | 0.961876i | \(0.588177\pi\) | |||||||
\(912\) | 35.1927 | 1.16535 | ||||||||
\(913\) | 7.00845 | 0.231946 | ||||||||
\(914\) | −9.73979 | −0.322164 | ||||||||
\(915\) | 8.18694 | 0.270652 | ||||||||
\(916\) | 62.0364 | 2.04974 | ||||||||
\(917\) | 6.28480 | 0.207542 | ||||||||
\(918\) | −33.5898 | −1.10863 | ||||||||
\(919\) | 27.9190 | 0.920962 | 0.460481 | − | 0.887670i | \(-0.347677\pi\) | ||||
0.460481 | + | 0.887670i | \(0.347677\pi\) | |||||||
\(920\) | 26.3159 | 0.867611 | ||||||||
\(921\) | −17.8493 | −0.588155 | ||||||||
\(922\) | 97.0387 | 3.19580 | ||||||||
\(923\) | 30.1402 | 0.992076 | ||||||||
\(924\) | −32.3255 | −1.06343 | ||||||||
\(925\) | 3.00573 | 0.0988277 | ||||||||
\(926\) | 55.1586 | 1.81262 | ||||||||
\(927\) | −30.2102 | −0.992235 | ||||||||
\(928\) | −3.76138 | −0.123473 | ||||||||
\(929\) | 32.6952 | 1.07270 | 0.536348 | − | 0.843997i | \(-0.319804\pi\) | ||||
0.536348 | + | 0.843997i | \(0.319804\pi\) | |||||||
\(930\) | −33.2359 | −1.08985 | ||||||||
\(931\) | −17.2274 | −0.564604 | ||||||||
\(932\) | −69.7824 | −2.28580 | ||||||||
\(933\) | 0.677055 | 0.0221658 | ||||||||
\(934\) | −4.62767 | −0.151422 | ||||||||
\(935\) | −34.9897 | −1.14428 | ||||||||
\(936\) | −47.1837 | −1.54225 | ||||||||
\(937\) | 59.0521 | 1.92915 | 0.964575 | − | 0.263810i | \(-0.0849792\pi\) | ||||
0.964575 | + | 0.263810i | \(0.0849792\pi\) | |||||||
\(938\) | 2.18739 | 0.0714208 | ||||||||
\(939\) | −2.52786 | −0.0824936 | ||||||||
\(940\) | 66.9181 | 2.18263 | ||||||||
\(941\) | −0.410091 | −0.0133686 | −0.00668429 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668429 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(942\) | −0.335311 | −0.0109250 | ||||||||
\(943\) | 3.40143 | 0.110766 | ||||||||
\(944\) | −50.7309 | −1.65115 | ||||||||
\(945\) | 27.0690 | 0.880554 | ||||||||
\(946\) | 109.118 | 3.54773 | ||||||||
\(947\) | −39.8359 | −1.29449 | −0.647246 | − | 0.762281i | \(-0.724079\pi\) | ||||
−0.647246 | + | 0.762281i | \(0.724079\pi\) | |||||||
\(948\) | 40.8274 | 1.32601 | ||||||||
\(949\) | 10.5917 | 0.343822 | ||||||||
\(950\) | −53.1150 | −1.72328 | ||||||||
\(951\) | 16.2442 | 0.526753 | ||||||||
\(952\) | −36.6585 | −1.18811 | ||||||||
\(953\) | −45.9080 | −1.48711 | −0.743553 | − | 0.668677i | \(-0.766861\pi\) | ||||
−0.743553 | + | 0.668677i | \(0.766861\pi\) | |||||||
\(954\) | −56.7977 | −1.83889 | ||||||||
\(955\) | −4.62528 | −0.149671 | ||||||||
\(956\) | −43.7117 | −1.41374 | ||||||||
\(957\) | 3.54396 | 0.114560 | ||||||||
\(958\) | 100.304 | 3.24066 | ||||||||
\(959\) | 2.91525 | 0.0941384 | ||||||||
\(960\) | −7.06906 | −0.228153 | ||||||||
\(961\) | −1.93284 | −0.0623496 | ||||||||
\(962\) | 8.41700 | 0.271375 | ||||||||
\(963\) | −26.8558 | −0.865416 | ||||||||
\(964\) | −107.620 | −3.46621 | ||||||||
\(965\) | −76.8558 | −2.47407 | ||||||||
\(966\) | −7.06199 | −0.227216 | ||||||||
\(967\) | 7.39389 | 0.237772 | 0.118886 | − | 0.992908i | \(-0.462068\pi\) | ||||
0.118886 | + | 0.992908i | \(0.462068\pi\) | |||||||
\(968\) | −36.1983 | −1.16346 | ||||||||
\(969\) | −16.8379 | −0.540911 | ||||||||
\(970\) | 82.8958 | 2.66162 | ||||||||
\(971\) | 27.1226 | 0.870405 | 0.435203 | − | 0.900332i | \(-0.356677\pi\) | ||||
0.435203 | + | 0.900332i | \(0.356677\pi\) | |||||||
\(972\) | 69.6991 | 2.23560 | ||||||||
\(973\) | −34.4903 | −1.10571 | ||||||||
\(974\) | 20.7297 | 0.664224 | ||||||||
\(975\) | −9.57387 | −0.306609 | ||||||||
\(976\) | 20.6751 | 0.661794 | ||||||||
\(977\) | 11.5374 | 0.369113 | 0.184556 | − | 0.982822i | \(-0.440915\pi\) | ||||
0.184556 | + | 0.982822i | \(0.440915\pi\) | |||||||
\(978\) | −4.41412 | −0.141148 | ||||||||
\(979\) | 2.29807 | 0.0734465 | ||||||||
\(980\) | −32.1680 | −1.02757 | ||||||||
\(981\) | 26.3659 | 0.841800 | ||||||||
\(982\) | 103.003 | 3.28697 | ||||||||
\(983\) | 35.8124 | 1.14224 | 0.571120 | − | 0.820867i | \(-0.306509\pi\) | ||||
0.571120 | + | 0.820867i | \(0.306509\pi\) | |||||||
\(984\) | 11.0246 | 0.351452 | ||||||||
\(985\) | 31.3735 | 0.999643 | ||||||||
\(986\) | 7.44847 | 0.237208 | ||||||||
\(987\) | −9.68953 | −0.308421 | ||||||||
\(988\) | −101.846 | −3.24017 | ||||||||
\(989\) | 16.3229 | 0.519039 | ||||||||
\(990\) | 67.5541 | 2.14701 | ||||||||
\(991\) | 51.0094 | 1.62037 | 0.810184 | − | 0.586176i | \(-0.199367\pi\) | ||||
0.810184 | + | 0.586176i | \(0.199367\pi\) | |||||||
\(992\) | −20.2791 | −0.643861 | ||||||||
\(993\) | 22.2405 | 0.705781 | ||||||||
\(994\) | −45.2106 | −1.43399 | ||||||||
\(995\) | 4.29925 | 0.136295 | ||||||||
\(996\) | 6.29760 | 0.199547 | ||||||||
\(997\) | −23.0628 | −0.730406 | −0.365203 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365203 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(998\) | −102.934 | −3.25831 | ||||||||
\(999\) | −4.27421 | −0.135230 |
(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 | 8033.2.a.c.1.10 | ✓ | 154 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8033.2.a.c.1.10 | ✓ | 154 | 1.1 | even | 1 | trivial |