Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(95\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.68330 | −1.54920 | −0.774602 | − | 0.632448i | \(-0.782050\pi\) | ||||
−0.774602 | + | 0.632448i | \(0.782050\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.68032 | −0.751461 | −0.375730 | − | 0.926729i | \(-0.622608\pi\) | ||||
−0.375730 | + | 0.926729i | \(0.622608\pi\) | |||||||
\(6\) | −2.68330 | −1.09545 | ||||||||
\(7\) | 0.225636 | 0.0852824 | 0.0426412 | − | 0.999090i | \(-0.486423\pi\) | ||||
0.0426412 | + | 0.999090i | \(0.486423\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.20011 | 1.40004 | ||||||||
\(10\) | −1.68032 | −0.531363 | ||||||||
\(11\) | 3.84702 | 1.15992 | 0.579960 | − | 0.814645i | \(-0.303068\pi\) | ||||
0.579960 | + | 0.814645i | \(0.303068\pi\) | |||||||
\(12\) | −2.68330 | −0.774602 | ||||||||
\(13\) | −2.95410 | −0.819320 | −0.409660 | − | 0.912238i | \(-0.634353\pi\) | ||||
−0.409660 | + | 0.912238i | \(0.634353\pi\) | |||||||
\(14\) | 0.225636 | 0.0603037 | ||||||||
\(15\) | 4.50880 | 1.16417 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.77287 | 1.15759 | 0.578795 | − | 0.815473i | \(-0.303523\pi\) | ||||
0.578795 | + | 0.815473i | \(0.303523\pi\) | |||||||
\(18\) | 4.20011 | 0.989975 | ||||||||
\(19\) | −1.36548 | −0.313262 | −0.156631 | − | 0.987657i | \(-0.550063\pi\) | ||||
−0.156631 | + | 0.987657i | \(0.550063\pi\) | |||||||
\(20\) | −1.68032 | −0.375730 | ||||||||
\(21\) | −0.605449 | −0.132120 | ||||||||
\(22\) | 3.84702 | 0.820187 | ||||||||
\(23\) | −8.06646 | −1.68197 | −0.840986 | − | 0.541056i | \(-0.818025\pi\) | ||||
−0.840986 | + | 0.541056i | \(0.818025\pi\) | |||||||
\(24\) | −2.68330 | −0.547727 | ||||||||
\(25\) | −2.17654 | −0.435307 | ||||||||
\(26\) | −2.95410 | −0.579347 | ||||||||
\(27\) | −3.22025 | −0.619737 | ||||||||
\(28\) | 0.225636 | 0.0426412 | ||||||||
\(29\) | 5.05096 | 0.937940 | 0.468970 | − | 0.883214i | \(-0.344625\pi\) | ||||
0.468970 | + | 0.883214i | \(0.344625\pi\) | |||||||
\(30\) | 4.50880 | 0.823190 | ||||||||
\(31\) | 6.01553 | 1.08042 | 0.540210 | − | 0.841530i | \(-0.318345\pi\) | ||||
0.540210 | + | 0.841530i | \(0.318345\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.3227 | −1.79695 | ||||||||
\(34\) | 4.77287 | 0.818540 | ||||||||
\(35\) | −0.379140 | −0.0640863 | ||||||||
\(36\) | 4.20011 | 0.700018 | ||||||||
\(37\) | 11.6724 | 1.91893 | 0.959463 | − | 0.281835i | \(-0.0909432\pi\) | ||||
0.959463 | + | 0.281835i | \(0.0909432\pi\) | |||||||
\(38\) | −1.36548 | −0.221510 | ||||||||
\(39\) | 7.92675 | 1.26930 | ||||||||
\(40\) | −1.68032 | −0.265681 | ||||||||
\(41\) | 5.20726 | 0.813237 | 0.406619 | − | 0.913598i | \(-0.366708\pi\) | ||||
0.406619 | + | 0.913598i | \(0.366708\pi\) | |||||||
\(42\) | −0.605449 | −0.0934229 | ||||||||
\(43\) | −10.7804 | −1.64399 | −0.821997 | − | 0.569492i | \(-0.807140\pi\) | ||||
−0.821997 | + | 0.569492i | \(0.807140\pi\) | |||||||
\(44\) | 3.84702 | 0.579960 | ||||||||
\(45\) | −7.05751 | −1.05207 | ||||||||
\(46\) | −8.06646 | −1.18933 | ||||||||
\(47\) | 6.78382 | 0.989522 | 0.494761 | − | 0.869029i | \(-0.335256\pi\) | ||||
0.494761 | + | 0.869029i | \(0.335256\pi\) | |||||||
\(48\) | −2.68330 | −0.387301 | ||||||||
\(49\) | −6.94909 | −0.992727 | ||||||||
\(50\) | −2.17654 | −0.307809 | ||||||||
\(51\) | −12.8070 | −1.79334 | ||||||||
\(52\) | −2.95410 | −0.409660 | ||||||||
\(53\) | 0.601041 | 0.0825594 | 0.0412797 | − | 0.999148i | \(-0.486857\pi\) | ||||
0.0412797 | + | 0.999148i | \(0.486857\pi\) | |||||||
\(54\) | −3.22025 | −0.438220 | ||||||||
\(55\) | −6.46421 | −0.871634 | ||||||||
\(56\) | 0.225636 | 0.0301519 | ||||||||
\(57\) | 3.66399 | 0.485307 | ||||||||
\(58\) | 5.05096 | 0.663224 | ||||||||
\(59\) | −3.91123 | −0.509199 | −0.254600 | − | 0.967047i | \(-0.581944\pi\) | ||||
−0.254600 | + | 0.967047i | \(0.581944\pi\) | |||||||
\(60\) | 4.50880 | 0.582083 | ||||||||
\(61\) | −10.8515 | −1.38939 | −0.694694 | − | 0.719306i | \(-0.744460\pi\) | ||||
−0.694694 | + | 0.719306i | \(0.744460\pi\) | |||||||
\(62\) | 6.01553 | 0.763973 | ||||||||
\(63\) | 0.947695 | 0.119398 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.96383 | 0.615687 | ||||||||
\(66\) | −10.3227 | −1.27064 | ||||||||
\(67\) | 10.2729 | 1.25503 | 0.627514 | − | 0.778605i | \(-0.284072\pi\) | ||||
0.627514 | + | 0.778605i | \(0.284072\pi\) | |||||||
\(68\) | 4.77287 | 0.578795 | ||||||||
\(69\) | 21.6447 | 2.60572 | ||||||||
\(70\) | −0.379140 | −0.0453159 | ||||||||
\(71\) | −15.4875 | −1.83803 | −0.919014 | − | 0.394225i | \(-0.871013\pi\) | ||||
−0.919014 | + | 0.394225i | \(0.871013\pi\) | |||||||
\(72\) | 4.20011 | 0.494987 | ||||||||
\(73\) | 2.03264 | 0.237902 | 0.118951 | − | 0.992900i | \(-0.462047\pi\) | ||||
0.118951 | + | 0.992900i | \(0.462047\pi\) | |||||||
\(74\) | 11.6724 | 1.35689 | ||||||||
\(75\) | 5.84030 | 0.674380 | ||||||||
\(76\) | −1.36548 | −0.156631 | ||||||||
\(77\) | 0.868026 | 0.0989207 | ||||||||
\(78\) | 7.92675 | 0.897527 | ||||||||
\(79\) | −4.20596 | −0.473208 | −0.236604 | − | 0.971606i | \(-0.576034\pi\) | ||||
−0.236604 | + | 0.971606i | \(0.576034\pi\) | |||||||
\(80\) | −1.68032 | −0.187865 | ||||||||
\(81\) | −3.95942 | −0.439936 | ||||||||
\(82\) | 5.20726 | 0.575045 | ||||||||
\(83\) | −0.353279 | −0.0387774 | −0.0193887 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193887 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(84\) | −0.605449 | −0.0660599 | ||||||||
\(85\) | −8.01993 | −0.869883 | ||||||||
\(86\) | −10.7804 | −1.16248 | ||||||||
\(87\) | −13.5533 | −1.45306 | ||||||||
\(88\) | 3.84702 | 0.410094 | ||||||||
\(89\) | 4.55562 | 0.482895 | 0.241447 | − | 0.970414i | \(-0.422378\pi\) | ||||
0.241447 | + | 0.970414i | \(0.422378\pi\) | |||||||
\(90\) | −7.05751 | −0.743927 | ||||||||
\(91\) | −0.666552 | −0.0698736 | ||||||||
\(92\) | −8.06646 | −0.840986 | ||||||||
\(93\) | −16.1415 | −1.67379 | ||||||||
\(94\) | 6.78382 | 0.699697 | ||||||||
\(95\) | 2.29443 | 0.235404 | ||||||||
\(96\) | −2.68330 | −0.273863 | ||||||||
\(97\) | 15.7585 | 1.60004 | 0.800018 | − | 0.599976i | \(-0.204823\pi\) | ||||
0.800018 | + | 0.599976i | \(0.204823\pi\) | |||||||
\(98\) | −6.94909 | −0.701964 | ||||||||
\(99\) | 16.1579 | 1.62393 | ||||||||
\(100\) | −2.17654 | −0.217654 | ||||||||
\(101\) | 7.95815 | 0.791866 | 0.395933 | − | 0.918279i | \(-0.370421\pi\) | ||||
0.395933 | + | 0.918279i | \(0.370421\pi\) | |||||||
\(102\) | −12.8070 | −1.26809 | ||||||||
\(103\) | 14.9934 | 1.47734 | 0.738671 | − | 0.674066i | \(-0.235454\pi\) | ||||
0.738671 | + | 0.674066i | \(0.235454\pi\) | |||||||
\(104\) | −2.95410 | −0.289673 | ||||||||
\(105\) | 1.01735 | 0.0992829 | ||||||||
\(106\) | 0.601041 | 0.0583783 | ||||||||
\(107\) | −12.5165 | −1.21001 | −0.605007 | − | 0.796220i | \(-0.706830\pi\) | ||||
−0.605007 | + | 0.796220i | \(0.706830\pi\) | |||||||
\(108\) | −3.22025 | −0.309869 | ||||||||
\(109\) | −10.6058 | −1.01585 | −0.507924 | − | 0.861402i | \(-0.669587\pi\) | ||||
−0.507924 | + | 0.861402i | \(0.669587\pi\) | |||||||
\(110\) | −6.46421 | −0.616338 | ||||||||
\(111\) | −31.3205 | −2.97281 | ||||||||
\(112\) | 0.225636 | 0.0213206 | ||||||||
\(113\) | −19.5772 | −1.84167 | −0.920834 | − | 0.389955i | \(-0.872491\pi\) | ||||
−0.920834 | + | 0.389955i | \(0.872491\pi\) | |||||||
\(114\) | 3.66399 | 0.343164 | ||||||||
\(115\) | 13.5542 | 1.26394 | ||||||||
\(116\) | 5.05096 | 0.468970 | ||||||||
\(117\) | −12.4075 | −1.14708 | ||||||||
\(118\) | −3.91123 | −0.360058 | ||||||||
\(119\) | 1.07693 | 0.0987221 | ||||||||
\(120\) | 4.50880 | 0.411595 | ||||||||
\(121\) | 3.79956 | 0.345415 | ||||||||
\(122\) | −10.8515 | −0.982445 | ||||||||
\(123\) | −13.9726 | −1.25987 | ||||||||
\(124\) | 6.01553 | 0.540210 | ||||||||
\(125\) | 12.0589 | 1.07858 | ||||||||
\(126\) | 0.947695 | 0.0844274 | ||||||||
\(127\) | 16.5915 | 1.47225 | 0.736127 | − | 0.676844i | \(-0.236653\pi\) | ||||
0.736127 | + | 0.676844i | \(0.236653\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 28.9270 | 2.54688 | ||||||||
\(130\) | 4.96383 | 0.435356 | ||||||||
\(131\) | −16.5521 | −1.44617 | −0.723083 | − | 0.690762i | \(-0.757275\pi\) | ||||
−0.723083 | + | 0.690762i | \(0.757275\pi\) | |||||||
\(132\) | −10.3227 | −0.898477 | ||||||||
\(133\) | −0.308101 | −0.0267157 | ||||||||
\(134\) | 10.2729 | 0.887439 | ||||||||
\(135\) | 5.41104 | 0.465708 | ||||||||
\(136\) | 4.77287 | 0.409270 | ||||||||
\(137\) | −21.3183 | −1.82134 | −0.910672 | − | 0.413131i | \(-0.864435\pi\) | ||||
−0.910672 | + | 0.413131i | \(0.864435\pi\) | |||||||
\(138\) | 21.6447 | 1.84252 | ||||||||
\(139\) | 9.91975 | 0.841382 | 0.420691 | − | 0.907204i | \(-0.361788\pi\) | ||||
0.420691 | + | 0.907204i | \(0.361788\pi\) | |||||||
\(140\) | −0.379140 | −0.0320432 | ||||||||
\(141\) | −18.2030 | −1.53297 | ||||||||
\(142\) | −15.4875 | −1.29968 | ||||||||
\(143\) | −11.3645 | −0.950346 | ||||||||
\(144\) | 4.20011 | 0.350009 | ||||||||
\(145\) | −8.48722 | −0.704825 | ||||||||
\(146\) | 2.03264 | 0.168222 | ||||||||
\(147\) | 18.6465 | 1.53794 | ||||||||
\(148\) | 11.6724 | 0.959463 | ||||||||
\(149\) | 17.4631 | 1.43063 | 0.715317 | − | 0.698800i | \(-0.246282\pi\) | ||||
0.715317 | + | 0.698800i | \(0.246282\pi\) | |||||||
\(150\) | 5.84030 | 0.476859 | ||||||||
\(151\) | 0.506723 | 0.0412365 | 0.0206183 | − | 0.999787i | \(-0.493437\pi\) | ||||
0.0206183 | + | 0.999787i | \(0.493437\pi\) | |||||||
\(152\) | −1.36548 | −0.110755 | ||||||||
\(153\) | 20.0466 | 1.62067 | ||||||||
\(154\) | 0.868026 | 0.0699475 | ||||||||
\(155\) | −10.1080 | −0.811893 | ||||||||
\(156\) | 7.92675 | 0.634648 | ||||||||
\(157\) | 7.32806 | 0.584843 | 0.292422 | − | 0.956290i | \(-0.405539\pi\) | ||||
0.292422 | + | 0.956290i | \(0.405539\pi\) | |||||||
\(158\) | −4.20596 | −0.334608 | ||||||||
\(159\) | −1.61278 | −0.127901 | ||||||||
\(160\) | −1.68032 | −0.132841 | ||||||||
\(161\) | −1.82008 | −0.143443 | ||||||||
\(162\) | −3.95942 | −0.311081 | ||||||||
\(163\) | 22.7737 | 1.78377 | 0.891886 | − | 0.452261i | \(-0.149382\pi\) | ||||
0.891886 | + | 0.452261i | \(0.149382\pi\) | |||||||
\(164\) | 5.20726 | 0.406619 | ||||||||
\(165\) | 17.3454 | 1.35034 | ||||||||
\(166\) | −0.353279 | −0.0274197 | ||||||||
\(167\) | 2.42920 | 0.187977 | 0.0939885 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939885 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(168\) | −0.605449 | −0.0467114 | ||||||||
\(169\) | −4.27328 | −0.328714 | ||||||||
\(170\) | −8.01993 | −0.615101 | ||||||||
\(171\) | −5.73515 | −0.438578 | ||||||||
\(172\) | −10.7804 | −0.821997 | ||||||||
\(173\) | 3.84593 | 0.292401 | 0.146200 | − | 0.989255i | \(-0.453296\pi\) | ||||
0.146200 | + | 0.989255i | \(0.453296\pi\) | |||||||
\(174\) | −13.5533 | −1.02747 | ||||||||
\(175\) | −0.491105 | −0.0371240 | ||||||||
\(176\) | 3.84702 | 0.289980 | ||||||||
\(177\) | 10.4950 | 0.788854 | ||||||||
\(178\) | 4.55562 | 0.341458 | ||||||||
\(179\) | 17.5869 | 1.31451 | 0.657254 | − | 0.753670i | \(-0.271718\pi\) | ||||
0.657254 | + | 0.753670i | \(0.271718\pi\) | |||||||
\(180\) | −7.05751 | −0.526036 | ||||||||
\(181\) | −6.37852 | −0.474112 | −0.237056 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237056 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(182\) | −0.666552 | −0.0494081 | ||||||||
\(183\) | 29.1178 | 2.15245 | ||||||||
\(184\) | −8.06646 | −0.594667 | ||||||||
\(185\) | −19.6133 | −1.44200 | ||||||||
\(186\) | −16.1415 | −1.18355 | ||||||||
\(187\) | 18.3613 | 1.34271 | ||||||||
\(188\) | 6.78382 | 0.494761 | ||||||||
\(189\) | −0.726604 | −0.0528527 | ||||||||
\(190\) | 2.29443 | 0.166456 | ||||||||
\(191\) | −6.42409 | −0.464831 | −0.232415 | − | 0.972617i | \(-0.574663\pi\) | ||||
−0.232415 | + | 0.972617i | \(0.574663\pi\) | |||||||
\(192\) | −2.68330 | −0.193651 | ||||||||
\(193\) | 3.71798 | 0.267626 | 0.133813 | − | 0.991007i | \(-0.457278\pi\) | ||||
0.133813 | + | 0.991007i | \(0.457278\pi\) | |||||||
\(194\) | 15.7585 | 1.13140 | ||||||||
\(195\) | −13.3194 | −0.953825 | ||||||||
\(196\) | −6.94909 | −0.496363 | ||||||||
\(197\) | −0.678498 | −0.0483410 | −0.0241705 | − | 0.999708i | \(-0.507694\pi\) | ||||
−0.0241705 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(198\) | 16.1579 | 1.14829 | ||||||||
\(199\) | −20.9925 | −1.48812 | −0.744059 | − | 0.668114i | \(-0.767102\pi\) | ||||
−0.744059 | + | 0.668114i | \(0.767102\pi\) | |||||||
\(200\) | −2.17654 | −0.153904 | ||||||||
\(201\) | −27.5652 | −1.94430 | ||||||||
\(202\) | 7.95815 | 0.559934 | ||||||||
\(203\) | 1.13968 | 0.0799898 | ||||||||
\(204\) | −12.8070 | −0.896672 | ||||||||
\(205\) | −8.74984 | −0.611116 | ||||||||
\(206\) | 14.9934 | 1.04464 | ||||||||
\(207\) | −33.8800 | −2.35482 | ||||||||
\(208\) | −2.95410 | −0.204830 | ||||||||
\(209\) | −5.25302 | −0.363359 | ||||||||
\(210\) | 1.01735 | 0.0702036 | ||||||||
\(211\) | 21.8374 | 1.50335 | 0.751674 | − | 0.659535i | \(-0.229247\pi\) | ||||
0.751674 | + | 0.659535i | \(0.229247\pi\) | |||||||
\(212\) | 0.601041 | 0.0412797 | ||||||||
\(213\) | 41.5576 | 2.84748 | ||||||||
\(214\) | −12.5165 | −0.855609 | ||||||||
\(215\) | 18.1145 | 1.23540 | ||||||||
\(216\) | −3.22025 | −0.219110 | ||||||||
\(217\) | 1.35732 | 0.0921408 | ||||||||
\(218\) | −10.6058 | −0.718313 | ||||||||
\(219\) | −5.45417 | −0.368559 | ||||||||
\(220\) | −6.46421 | −0.435817 | ||||||||
\(221\) | −14.0995 | −0.948437 | ||||||||
\(222\) | −31.3205 | −2.10209 | ||||||||
\(223\) | 7.19054 | 0.481514 | 0.240757 | − | 0.970585i | \(-0.422604\pi\) | ||||
0.240757 | + | 0.970585i | \(0.422604\pi\) | |||||||
\(224\) | 0.225636 | 0.0150759 | ||||||||
\(225\) | −9.14168 | −0.609445 | ||||||||
\(226\) | −19.5772 | −1.30226 | ||||||||
\(227\) | −10.6488 | −0.706784 | −0.353392 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353392 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(228\) | 3.66399 | 0.242653 | ||||||||
\(229\) | 8.32483 | 0.550120 | 0.275060 | − | 0.961427i | \(-0.411302\pi\) | ||||
0.275060 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(230\) | 13.5542 | 0.893738 | ||||||||
\(231\) | −2.32918 | −0.153248 | ||||||||
\(232\) | 5.05096 | 0.331612 | ||||||||
\(233\) | 8.86125 | 0.580520 | 0.290260 | − | 0.956948i | \(-0.406258\pi\) | ||||
0.290260 | + | 0.956948i | \(0.406258\pi\) | |||||||
\(234\) | −12.4075 | −0.811107 | ||||||||
\(235\) | −11.3990 | −0.743586 | ||||||||
\(236\) | −3.91123 | −0.254600 | ||||||||
\(237\) | 11.2859 | 0.733096 | ||||||||
\(238\) | 1.07693 | 0.0698070 | ||||||||
\(239\) | −9.42805 | −0.609850 | −0.304925 | − | 0.952376i | \(-0.598631\pi\) | ||||
−0.304925 | + | 0.952376i | \(0.598631\pi\) | |||||||
\(240\) | 4.50880 | 0.291042 | ||||||||
\(241\) | −17.5918 | −1.13319 | −0.566593 | − | 0.823998i | \(-0.691739\pi\) | ||||
−0.566593 | + | 0.823998i | \(0.691739\pi\) | |||||||
\(242\) | 3.79956 | 0.244245 | ||||||||
\(243\) | 20.2851 | 1.30129 | ||||||||
\(244\) | −10.8515 | −0.694694 | ||||||||
\(245\) | 11.6767 | 0.745995 | ||||||||
\(246\) | −13.9726 | −0.890863 | ||||||||
\(247\) | 4.03376 | 0.256662 | ||||||||
\(248\) | 6.01553 | 0.381986 | ||||||||
\(249\) | 0.947953 | 0.0600741 | ||||||||
\(250\) | 12.0589 | 0.762669 | ||||||||
\(251\) | 10.8159 | 0.682692 | 0.341346 | − | 0.939938i | \(-0.389117\pi\) | ||||
0.341346 | + | 0.939938i | \(0.389117\pi\) | |||||||
\(252\) | 0.947695 | 0.0596992 | ||||||||
\(253\) | −31.0318 | −1.95095 | ||||||||
\(254\) | 16.5915 | 1.04104 | ||||||||
\(255\) | 21.5199 | 1.34763 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0486 | 1.06346 | 0.531730 | − | 0.846914i | \(-0.321542\pi\) | ||||
0.531730 | + | 0.846914i | \(0.321542\pi\) | |||||||
\(258\) | 28.9270 | 1.80092 | ||||||||
\(259\) | 2.63371 | 0.163651 | ||||||||
\(260\) | 4.96383 | 0.307843 | ||||||||
\(261\) | 21.2146 | 1.31315 | ||||||||
\(262\) | −16.5521 | −1.02259 | ||||||||
\(263\) | −7.59101 | −0.468082 | −0.234041 | − | 0.972227i | \(-0.575195\pi\) | ||||
−0.234041 | + | 0.972227i | \(0.575195\pi\) | |||||||
\(264\) | −10.3227 | −0.635319 | ||||||||
\(265\) | −1.00994 | −0.0620401 | ||||||||
\(266\) | −0.308101 | −0.0188909 | ||||||||
\(267\) | −12.2241 | −0.748103 | ||||||||
\(268\) | 10.2729 | 0.627514 | ||||||||
\(269\) | 19.8977 | 1.21318 | 0.606592 | − | 0.795013i | \(-0.292536\pi\) | ||||
0.606592 | + | 0.795013i | \(0.292536\pi\) | |||||||
\(270\) | 5.41104 | 0.329305 | ||||||||
\(271\) | 7.67959 | 0.466502 | 0.233251 | − | 0.972417i | \(-0.425064\pi\) | ||||
0.233251 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(272\) | 4.77287 | 0.289398 | ||||||||
\(273\) | 1.78856 | 0.108249 | ||||||||
\(274\) | −21.3183 | −1.28788 | ||||||||
\(275\) | −8.37318 | −0.504921 | ||||||||
\(276\) | 21.6447 | 1.30286 | ||||||||
\(277\) | −4.56678 | −0.274392 | −0.137196 | − | 0.990544i | \(-0.543809\pi\) | ||||
−0.137196 | + | 0.990544i | \(0.543809\pi\) | |||||||
\(278\) | 9.91975 | 0.594947 | ||||||||
\(279\) | 25.2659 | 1.51263 | ||||||||
\(280\) | −0.379140 | −0.0226579 | ||||||||
\(281\) | 0.119233 | 0.00711283 | 0.00355641 | − | 0.999994i | \(-0.498868\pi\) | ||||
0.00355641 | + | 0.999994i | \(0.498868\pi\) | |||||||
\(282\) | −18.2030 | −1.08397 | ||||||||
\(283\) | 0.672403 | 0.0399702 | 0.0199851 | − | 0.999800i | \(-0.493638\pi\) | ||||
0.0199851 | + | 0.999800i | \(0.493638\pi\) | |||||||
\(284\) | −15.4875 | −0.919014 | ||||||||
\(285\) | −6.15666 | −0.364689 | ||||||||
\(286\) | −11.3645 | −0.671996 | ||||||||
\(287\) | 1.17494 | 0.0693548 | ||||||||
\(288\) | 4.20011 | 0.247494 | ||||||||
\(289\) | 5.78026 | 0.340016 | ||||||||
\(290\) | −8.48722 | −0.498387 | ||||||||
\(291\) | −42.2849 | −2.47878 | ||||||||
\(292\) | 2.03264 | 0.118951 | ||||||||
\(293\) | 29.1055 | 1.70036 | 0.850181 | − | 0.526490i | \(-0.176492\pi\) | ||||
0.850181 | + | 0.526490i | \(0.176492\pi\) | |||||||
\(294\) | 18.6465 | 1.08749 | ||||||||
\(295\) | 6.57211 | 0.382643 | ||||||||
\(296\) | 11.6724 | 0.678443 | ||||||||
\(297\) | −12.3884 | −0.718846 | ||||||||
\(298\) | 17.4631 | 1.01161 | ||||||||
\(299\) | 23.8291 | 1.37807 | ||||||||
\(300\) | 5.84030 | 0.337190 | ||||||||
\(301\) | −2.43244 | −0.140204 | ||||||||
\(302\) | 0.506723 | 0.0291586 | ||||||||
\(303\) | −21.3541 | −1.22676 | ||||||||
\(304\) | −1.36548 | −0.0783155 | ||||||||
\(305\) | 18.2339 | 1.04407 | ||||||||
\(306\) | 20.0466 | 1.14599 | ||||||||
\(307\) | 23.7691 | 1.35657 | 0.678287 | − | 0.734797i | \(-0.262723\pi\) | ||||
0.678287 | + | 0.734797i | \(0.262723\pi\) | |||||||
\(308\) | 0.868026 | 0.0494604 | ||||||||
\(309\) | −40.2318 | −2.28871 | ||||||||
\(310\) | −10.1080 | −0.574095 | ||||||||
\(311\) | 9.28733 | 0.526636 | 0.263318 | − | 0.964709i | \(-0.415183\pi\) | ||||
0.263318 | + | 0.964709i | \(0.415183\pi\) | |||||||
\(312\) | 7.92675 | 0.448764 | ||||||||
\(313\) | 21.5581 | 1.21854 | 0.609269 | − | 0.792964i | \(-0.291463\pi\) | ||||
0.609269 | + | 0.792964i | \(0.291463\pi\) | |||||||
\(314\) | 7.32806 | 0.413547 | ||||||||
\(315\) | −1.59243 | −0.0897232 | ||||||||
\(316\) | −4.20596 | −0.236604 | ||||||||
\(317\) | 24.7069 | 1.38768 | 0.693840 | − | 0.720129i | \(-0.255918\pi\) | ||||
0.693840 | + | 0.720129i | \(0.255918\pi\) | |||||||
\(318\) | −1.61278 | −0.0904399 | ||||||||
\(319\) | 19.4312 | 1.08794 | ||||||||
\(320\) | −1.68032 | −0.0939326 | ||||||||
\(321\) | 33.5855 | 1.87456 | ||||||||
\(322\) | −1.82008 | −0.101429 | ||||||||
\(323\) | −6.51724 | −0.362629 | ||||||||
\(324\) | −3.95942 | −0.219968 | ||||||||
\(325\) | 6.42971 | 0.356656 | ||||||||
\(326\) | 22.7737 | 1.26132 | ||||||||
\(327\) | 28.4585 | 1.57376 | ||||||||
\(328\) | 5.20726 | 0.287523 | ||||||||
\(329\) | 1.53067 | 0.0843888 | ||||||||
\(330\) | 17.3454 | 0.954835 | ||||||||
\(331\) | 20.0324 | 1.10108 | 0.550541 | − | 0.834808i | \(-0.314422\pi\) | ||||
0.550541 | + | 0.834808i | \(0.314422\pi\) | |||||||
\(332\) | −0.353279 | −0.0193887 | ||||||||
\(333\) | 49.0252 | 2.68656 | ||||||||
\(334\) | 2.42920 | 0.132920 | ||||||||
\(335\) | −17.2616 | −0.943104 | ||||||||
\(336\) | −0.605449 | −0.0330300 | ||||||||
\(337\) | 12.1012 | 0.659193 | 0.329597 | − | 0.944122i | \(-0.393087\pi\) | ||||
0.329597 | + | 0.944122i | \(0.393087\pi\) | |||||||
\(338\) | −4.27328 | −0.232436 | ||||||||
\(339\) | 52.5315 | 2.85312 | ||||||||
\(340\) | −8.01993 | −0.434942 | ||||||||
\(341\) | 23.1419 | 1.25320 | ||||||||
\(342\) | −5.73515 | −0.310121 | ||||||||
\(343\) | −3.14742 | −0.169944 | ||||||||
\(344\) | −10.7804 | −0.581240 | ||||||||
\(345\) | −36.3700 | −1.95810 | ||||||||
\(346\) | 3.84593 | 0.206758 | ||||||||
\(347\) | 12.1759 | 0.653634 | 0.326817 | − | 0.945088i | \(-0.394024\pi\) | ||||
0.326817 | + | 0.945088i | \(0.394024\pi\) | |||||||
\(348\) | −13.5533 | −0.726531 | ||||||||
\(349\) | 6.28232 | 0.336285 | 0.168142 | − | 0.985763i | \(-0.446223\pi\) | ||||
0.168142 | + | 0.985763i | \(0.446223\pi\) | |||||||
\(350\) | −0.491105 | −0.0262506 | ||||||||
\(351\) | 9.51294 | 0.507763 | ||||||||
\(352\) | 3.84702 | 0.205047 | ||||||||
\(353\) | 16.3024 | 0.867690 | 0.433845 | − | 0.900987i | \(-0.357156\pi\) | ||||
0.433845 | + | 0.900987i | \(0.357156\pi\) | |||||||
\(354\) | 10.4950 | 0.557804 | ||||||||
\(355\) | 26.0239 | 1.38121 | ||||||||
\(356\) | 4.55562 | 0.241447 | ||||||||
\(357\) | −2.88973 | −0.152941 | ||||||||
\(358\) | 17.5869 | 0.929497 | ||||||||
\(359\) | 26.2461 | 1.38522 | 0.692609 | − | 0.721313i | \(-0.256461\pi\) | ||||
0.692609 | + | 0.721313i | \(0.256461\pi\) | |||||||
\(360\) | −7.05751 | −0.371963 | ||||||||
\(361\) | −17.1355 | −0.901867 | ||||||||
\(362\) | −6.37852 | −0.335248 | ||||||||
\(363\) | −10.1954 | −0.535118 | ||||||||
\(364\) | −0.666552 | −0.0349368 | ||||||||
\(365\) | −3.41547 | −0.178774 | ||||||||
\(366\) | 29.1178 | 1.52201 | ||||||||
\(367\) | 26.2518 | 1.37033 | 0.685166 | − | 0.728387i | \(-0.259730\pi\) | ||||
0.685166 | + | 0.728387i | \(0.259730\pi\) | |||||||
\(368\) | −8.06646 | −0.420493 | ||||||||
\(369\) | 21.8710 | 1.13856 | ||||||||
\(370\) | −19.6133 | −1.01965 | ||||||||
\(371\) | 0.135617 | 0.00704086 | ||||||||
\(372\) | −16.1415 | −0.836896 | ||||||||
\(373\) | 36.8164 | 1.90628 | 0.953141 | − | 0.302525i | \(-0.0978297\pi\) | ||||
0.953141 | + | 0.302525i | \(0.0978297\pi\) | |||||||
\(374\) | 18.3613 | 0.949441 | ||||||||
\(375\) | −32.3575 | −1.67094 | ||||||||
\(376\) | 6.78382 | 0.349849 | ||||||||
\(377\) | −14.9211 | −0.768474 | ||||||||
\(378\) | −0.726604 | −0.0373725 | ||||||||
\(379\) | −33.7663 | −1.73446 | −0.867230 | − | 0.497908i | \(-0.834102\pi\) | ||||
−0.867230 | + | 0.497908i | \(0.834102\pi\) | |||||||
\(380\) | 2.29443 | 0.117702 | ||||||||
\(381\) | −44.5199 | −2.28082 | ||||||||
\(382\) | −6.42409 | −0.328685 | ||||||||
\(383\) | 22.2087 | 1.13481 | 0.567407 | − | 0.823438i | \(-0.307947\pi\) | ||||
0.567407 | + | 0.823438i | \(0.307947\pi\) | |||||||
\(384\) | −2.68330 | −0.136932 | ||||||||
\(385\) | −1.45856 | −0.0743350 | ||||||||
\(386\) | 3.71798 | 0.189240 | ||||||||
\(387\) | −45.2788 | −2.30165 | ||||||||
\(388\) | 15.7585 | 0.800018 | ||||||||
\(389\) | 14.1829 | 0.719103 | 0.359552 | − | 0.933125i | \(-0.382930\pi\) | ||||
0.359552 | + | 0.933125i | \(0.382930\pi\) | |||||||
\(390\) | −13.3194 | −0.674456 | ||||||||
\(391\) | −38.5001 | −1.94704 | ||||||||
\(392\) | −6.94909 | −0.350982 | ||||||||
\(393\) | 44.4143 | 2.24041 | ||||||||
\(394\) | −0.678498 | −0.0341822 | ||||||||
\(395\) | 7.06735 | 0.355597 | ||||||||
\(396\) | 16.1579 | 0.811965 | ||||||||
\(397\) | 17.4555 | 0.876067 | 0.438034 | − | 0.898959i | \(-0.355675\pi\) | ||||
0.438034 | + | 0.898959i | \(0.355675\pi\) | |||||||
\(398\) | −20.9925 | −1.05226 | ||||||||
\(399\) | 0.826727 | 0.0413881 | ||||||||
\(400\) | −2.17654 | −0.108827 | ||||||||
\(401\) | 4.63869 | 0.231645 | 0.115823 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115823 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(402\) | −27.5652 | −1.37483 | ||||||||
\(403\) | −17.7705 | −0.885211 | ||||||||
\(404\) | 7.95815 | 0.395933 | ||||||||
\(405\) | 6.65308 | 0.330594 | ||||||||
\(406\) | 1.13968 | 0.0565613 | ||||||||
\(407\) | 44.9038 | 2.22580 | ||||||||
\(408\) | −12.8070 | −0.634043 | ||||||||
\(409\) | −13.1906 | −0.652231 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(410\) | −8.74984 | −0.432124 | ||||||||
\(411\) | 57.2034 | 2.82163 | ||||||||
\(412\) | 14.9934 | 0.738671 | ||||||||
\(413\) | −0.882515 | −0.0434257 | ||||||||
\(414\) | −33.8800 | −1.66511 | ||||||||
\(415\) | 0.593620 | 0.0291397 | ||||||||
\(416\) | −2.95410 | −0.144837 | ||||||||
\(417\) | −26.6177 | −1.30347 | ||||||||
\(418\) | −5.25302 | −0.256933 | ||||||||
\(419\) | 10.9101 | 0.532995 | 0.266498 | − | 0.963836i | \(-0.414134\pi\) | ||||
0.266498 | + | 0.963836i | \(0.414134\pi\) | |||||||
\(420\) | 1.01735 | 0.0496414 | ||||||||
\(421\) | 20.0882 | 0.979038 | 0.489519 | − | 0.871993i | \(-0.337172\pi\) | ||||
0.489519 | + | 0.871993i | \(0.337172\pi\) | |||||||
\(422\) | 21.8374 | 1.06303 | ||||||||
\(423\) | 28.4928 | 1.38537 | ||||||||
\(424\) | 0.601041 | 0.0291891 | ||||||||
\(425\) | −10.3883 | −0.503907 | ||||||||
\(426\) | 41.5576 | 2.01347 | ||||||||
\(427\) | −2.44848 | −0.118490 | ||||||||
\(428\) | −12.5165 | −0.605007 | ||||||||
\(429\) | 30.4943 | 1.47228 | ||||||||
\(430\) | 18.1145 | 0.873557 | ||||||||
\(431\) | −16.7089 | −0.804837 | −0.402419 | − | 0.915456i | \(-0.631830\pi\) | ||||
−0.402419 | + | 0.915456i | \(0.631830\pi\) | |||||||
\(432\) | −3.22025 | −0.154934 | ||||||||
\(433\) | 19.2394 | 0.924588 | 0.462294 | − | 0.886727i | \(-0.347027\pi\) | ||||
0.462294 | + | 0.886727i | \(0.347027\pi\) | |||||||
\(434\) | 1.35732 | 0.0651534 | ||||||||
\(435\) | 22.7738 | 1.09192 | ||||||||
\(436\) | −10.6058 | −0.507924 | ||||||||
\(437\) | 11.0146 | 0.526898 | ||||||||
\(438\) | −5.45417 | −0.260610 | ||||||||
\(439\) | −30.8022 | −1.47011 | −0.735055 | − | 0.678008i | \(-0.762844\pi\) | ||||
−0.735055 | + | 0.678008i | \(0.762844\pi\) | |||||||
\(440\) | −6.46421 | −0.308169 | ||||||||
\(441\) | −29.1869 | −1.38985 | ||||||||
\(442\) | −14.0995 | −0.670647 | ||||||||
\(443\) | −23.3912 | −1.11135 | −0.555675 | − | 0.831400i | \(-0.687540\pi\) | ||||
−0.555675 | + | 0.831400i | \(0.687540\pi\) | |||||||
\(444\) | −31.3205 | −1.48640 | ||||||||
\(445\) | −7.65489 | −0.362876 | ||||||||
\(446\) | 7.19054 | 0.340482 | ||||||||
\(447\) | −46.8588 | −2.21635 | ||||||||
\(448\) | 0.225636 | 0.0106603 | ||||||||
\(449\) | 38.3699 | 1.81079 | 0.905393 | − | 0.424575i | \(-0.139576\pi\) | ||||
0.905393 | + | 0.424575i | \(0.139576\pi\) | |||||||
\(450\) | −9.14168 | −0.430943 | ||||||||
\(451\) | 20.0324 | 0.943290 | ||||||||
\(452\) | −19.5772 | −0.920834 | ||||||||
\(453\) | −1.35969 | −0.0638839 | ||||||||
\(454\) | −10.6488 | −0.499772 | ||||||||
\(455\) | 1.12002 | 0.0525072 | ||||||||
\(456\) | 3.66399 | 0.171582 | ||||||||
\(457\) | −6.02517 | −0.281846 | −0.140923 | − | 0.990021i | \(-0.545007\pi\) | ||||
−0.140923 | + | 0.990021i | \(0.545007\pi\) | |||||||
\(458\) | 8.32483 | 0.388994 | ||||||||
\(459\) | −15.3698 | −0.717402 | ||||||||
\(460\) | 13.5542 | 0.631968 | ||||||||
\(461\) | 10.2411 | 0.476974 | 0.238487 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238487 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(462\) | −2.32918 | −0.108363 | ||||||||
\(463\) | −21.3465 | −0.992054 | −0.496027 | − | 0.868307i | \(-0.665208\pi\) | ||||
−0.496027 | + | 0.868307i | \(0.665208\pi\) | |||||||
\(464\) | 5.05096 | 0.234485 | ||||||||
\(465\) | 27.1228 | 1.25779 | ||||||||
\(466\) | 8.86125 | 0.410490 | ||||||||
\(467\) | −19.0455 | −0.881321 | −0.440661 | − | 0.897674i | \(-0.645256\pi\) | ||||
−0.440661 | + | 0.897674i | \(0.645256\pi\) | |||||||
\(468\) | −12.4075 | −0.573539 | ||||||||
\(469\) | 2.31792 | 0.107032 | ||||||||
\(470\) | −11.3990 | −0.525795 | ||||||||
\(471\) | −19.6634 | −0.906042 | ||||||||
\(472\) | −3.91123 | −0.180029 | ||||||||
\(473\) | −41.4724 | −1.90690 | ||||||||
\(474\) | 11.2859 | 0.518377 | ||||||||
\(475\) | 2.97201 | 0.136365 | ||||||||
\(476\) | 1.07693 | 0.0493610 | ||||||||
\(477\) | 2.52444 | 0.115586 | ||||||||
\(478\) | −9.42805 | −0.431229 | ||||||||
\(479\) | −30.5336 | −1.39512 | −0.697559 | − | 0.716528i | \(-0.745730\pi\) | ||||
−0.697559 | + | 0.716528i | \(0.745730\pi\) | |||||||
\(480\) | 4.50880 | 0.205797 | ||||||||
\(481\) | −34.4814 | −1.57221 | ||||||||
\(482\) | −17.5918 | −0.801284 | ||||||||
\(483\) | 4.88383 | 0.222222 | ||||||||
\(484\) | 3.79956 | 0.172707 | ||||||||
\(485\) | −26.4793 | −1.20236 | ||||||||
\(486\) | 20.2851 | 0.920149 | ||||||||
\(487\) | −13.0500 | −0.591353 | −0.295677 | − | 0.955288i | \(-0.595545\pi\) | ||||
−0.295677 | + | 0.955288i | \(0.595545\pi\) | |||||||
\(488\) | −10.8515 | −0.491223 | ||||||||
\(489\) | −61.1086 | −2.76343 | ||||||||
\(490\) | 11.6767 | 0.527498 | ||||||||
\(491\) | −15.2680 | −0.689034 | −0.344517 | − | 0.938780i | \(-0.611957\pi\) | ||||
−0.344517 | + | 0.938780i | \(0.611957\pi\) | |||||||
\(492\) | −13.9726 | −0.629935 | ||||||||
\(493\) | 24.1076 | 1.08575 | ||||||||
\(494\) | 4.03376 | 0.181487 | ||||||||
\(495\) | −27.1504 | −1.22032 | ||||||||
\(496\) | 6.01553 | 0.270105 | ||||||||
\(497\) | −3.49454 | −0.156751 | ||||||||
\(498\) | 0.947953 | 0.0424788 | ||||||||
\(499\) | 14.3339 | 0.641674 | 0.320837 | − | 0.947134i | \(-0.396036\pi\) | ||||
0.320837 | + | 0.947134i | \(0.396036\pi\) | |||||||
\(500\) | 12.0589 | 0.539288 | ||||||||
\(501\) | −6.51827 | −0.291215 | ||||||||
\(502\) | 10.8159 | 0.482736 | ||||||||
\(503\) | 4.41655 | 0.196924 | 0.0984622 | − | 0.995141i | \(-0.468608\pi\) | ||||
0.0984622 | + | 0.995141i | \(0.468608\pi\) | |||||||
\(504\) | 0.947695 | 0.0422137 | ||||||||
\(505\) | −13.3722 | −0.595056 | ||||||||
\(506\) | −31.0318 | −1.37953 | ||||||||
\(507\) | 11.4665 | 0.509246 | ||||||||
\(508\) | 16.5915 | 0.736127 | ||||||||
\(509\) | −14.0675 | −0.623531 | −0.311766 | − | 0.950159i | \(-0.600920\pi\) | ||||
−0.311766 | + | 0.950159i | \(0.600920\pi\) | |||||||
\(510\) | 21.5199 | 0.952917 | ||||||||
\(511\) | 0.458636 | 0.0202888 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.39718 | 0.194140 | ||||||||
\(514\) | 17.0486 | 0.751980 | ||||||||
\(515\) | −25.1936 | −1.11016 | ||||||||
\(516\) | 28.9270 | 1.27344 | ||||||||
\(517\) | 26.0975 | 1.14777 | ||||||||
\(518\) | 2.63371 | 0.115718 | ||||||||
\(519\) | −10.3198 | −0.452988 | ||||||||
\(520\) | 4.96383 | 0.217678 | ||||||||
\(521\) | 31.8288 | 1.39445 | 0.697223 | − | 0.716854i | \(-0.254419\pi\) | ||||
0.697223 | + | 0.716854i | \(0.254419\pi\) | |||||||
\(522\) | 21.2146 | 0.928537 | ||||||||
\(523\) | −6.34236 | −0.277332 | −0.138666 | − | 0.990339i | \(-0.544281\pi\) | ||||
−0.138666 | + | 0.990339i | \(0.544281\pi\) | |||||||
\(524\) | −16.5521 | −0.723083 | ||||||||
\(525\) | 1.31778 | 0.0575127 | ||||||||
\(526\) | −7.59101 | −0.330984 | ||||||||
\(527\) | 28.7113 | 1.25068 | ||||||||
\(528\) | −10.3227 | −0.449238 | ||||||||
\(529\) | 42.0677 | 1.82903 | ||||||||
\(530\) | −1.00994 | −0.0438690 | ||||||||
\(531\) | −16.4276 | −0.712897 | ||||||||
\(532\) | −0.308101 | −0.0133579 | ||||||||
\(533\) | −15.3828 | −0.666302 | ||||||||
\(534\) | −12.2241 | −0.528989 | ||||||||
\(535\) | 21.0317 | 0.909278 | ||||||||
\(536\) | 10.2729 | 0.443720 | ||||||||
\(537\) | −47.1910 | −2.03644 | ||||||||
\(538\) | 19.8977 | 0.857851 | ||||||||
\(539\) | −26.7333 | −1.15148 | ||||||||
\(540\) | 5.41104 | 0.232854 | ||||||||
\(541\) | 34.2015 | 1.47044 | 0.735220 | − | 0.677829i | \(-0.237079\pi\) | ||||
0.735220 | + | 0.677829i | \(0.237079\pi\) | |||||||
\(542\) | 7.67959 | 0.329867 | ||||||||
\(543\) | 17.1155 | 0.734496 | ||||||||
\(544\) | 4.77287 | 0.204635 | ||||||||
\(545\) | 17.8211 | 0.763370 | ||||||||
\(546\) | 1.78856 | 0.0765432 | ||||||||
\(547\) | −42.1308 | −1.80138 | −0.900692 | − | 0.434458i | \(-0.856940\pi\) | ||||
−0.900692 | + | 0.434458i | \(0.856940\pi\) | |||||||
\(548\) | −21.3183 | −0.910672 | ||||||||
\(549\) | −45.5773 | −1.94519 | ||||||||
\(550\) | −8.37318 | −0.357033 | ||||||||
\(551\) | −6.89697 | −0.293821 | ||||||||
\(552\) | 21.6447 | 0.921261 | ||||||||
\(553\) | −0.949016 | −0.0403563 | ||||||||
\(554\) | −4.56678 | −0.194024 | ||||||||
\(555\) | 52.6283 | 2.23395 | ||||||||
\(556\) | 9.91975 | 0.420691 | ||||||||
\(557\) | −27.1023 | −1.14836 | −0.574181 | − | 0.818728i | \(-0.694679\pi\) | ||||
−0.574181 | + | 0.818728i | \(0.694679\pi\) | |||||||
\(558\) | 25.2659 | 1.06959 | ||||||||
\(559\) | 31.8464 | 1.34696 | ||||||||
\(560\) | −0.379140 | −0.0160216 | ||||||||
\(561\) | −49.2689 | −2.08014 | ||||||||
\(562\) | 0.119233 | 0.00502953 | ||||||||
\(563\) | 7.97741 | 0.336208 | 0.168104 | − | 0.985769i | \(-0.446236\pi\) | ||||
0.168104 | + | 0.985769i | \(0.446236\pi\) | |||||||
\(564\) | −18.2030 | −0.766486 | ||||||||
\(565\) | 32.8959 | 1.38394 | ||||||||
\(566\) | 0.672403 | 0.0282632 | ||||||||
\(567\) | −0.893388 | −0.0375188 | ||||||||
\(568\) | −15.4875 | −0.649841 | ||||||||
\(569\) | 5.05963 | 0.212111 | 0.106055 | − | 0.994360i | \(-0.466178\pi\) | ||||
0.106055 | + | 0.994360i | \(0.466178\pi\) | |||||||
\(570\) | −6.15666 | −0.257874 | ||||||||
\(571\) | 9.67371 | 0.404832 | 0.202416 | − | 0.979300i | \(-0.435121\pi\) | ||||
0.202416 | + | 0.979300i | \(0.435121\pi\) | |||||||
\(572\) | −11.3645 | −0.475173 | ||||||||
\(573\) | 17.2378 | 0.720118 | ||||||||
\(574\) | 1.17494 | 0.0490412 | ||||||||
\(575\) | 17.5569 | 0.732175 | ||||||||
\(576\) | 4.20011 | 0.175004 | ||||||||
\(577\) | 11.5695 | 0.481645 | 0.240823 | − | 0.970569i | \(-0.422583\pi\) | ||||
0.240823 | + | 0.970569i | \(0.422583\pi\) | |||||||
\(578\) | 5.78026 | 0.240427 | ||||||||
\(579\) | −9.97646 | −0.414607 | ||||||||
\(580\) | −8.48722 | −0.352413 | ||||||||
\(581\) | −0.0797124 | −0.00330703 | ||||||||
\(582\) | −42.2849 | −1.75276 | ||||||||
\(583\) | 2.31222 | 0.0957623 | ||||||||
\(584\) | 2.03264 | 0.0841110 | ||||||||
\(585\) | 20.8486 | 0.861984 | ||||||||
\(586\) | 29.1055 | 1.20234 | ||||||||
\(587\) | 10.5560 | 0.435694 | 0.217847 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217847 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(588\) | 18.6465 | 0.768969 | ||||||||
\(589\) | −8.21406 | −0.338455 | ||||||||
\(590\) | 6.57211 | 0.270569 | ||||||||
\(591\) | 1.82062 | 0.0748901 | ||||||||
\(592\) | 11.6724 | 0.479731 | ||||||||
\(593\) | −8.82954 | −0.362586 | −0.181293 | − | 0.983429i | \(-0.558028\pi\) | ||||
−0.181293 | + | 0.983429i | \(0.558028\pi\) | |||||||
\(594\) | −12.3884 | −0.508301 | ||||||||
\(595\) | −1.80958 | −0.0741857 | ||||||||
\(596\) | 17.4631 | 0.715317 | ||||||||
\(597\) | 56.3292 | 2.30540 | ||||||||
\(598\) | 23.8291 | 0.974446 | ||||||||
\(599\) | −1.97107 | −0.0805355 | −0.0402678 | − | 0.999189i | \(-0.512821\pi\) | ||||
−0.0402678 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(600\) | 5.84030 | 0.238429 | ||||||||
\(601\) | 25.5369 | 1.04167 | 0.520837 | − | 0.853656i | \(-0.325620\pi\) | ||||
0.520837 | + | 0.853656i | \(0.325620\pi\) | |||||||
\(602\) | −2.43244 | −0.0991390 | ||||||||
\(603\) | 43.1471 | 1.75708 | ||||||||
\(604\) | 0.506723 | 0.0206183 | ||||||||
\(605\) | −6.38447 | −0.259566 | ||||||||
\(606\) | −21.3541 | −0.867452 | ||||||||
\(607\) | 12.1428 | 0.492860 | 0.246430 | − | 0.969161i | \(-0.420742\pi\) | ||||
0.246430 | + | 0.969161i | \(0.420742\pi\) | |||||||
\(608\) | −1.36548 | −0.0553774 | ||||||||
\(609\) | −3.05810 | −0.123921 | ||||||||
\(610\) | 18.2339 | 0.738269 | ||||||||
\(611\) | −20.0401 | −0.810735 | ||||||||
\(612\) | 20.0466 | 0.810334 | ||||||||
\(613\) | −18.0253 | −0.728033 | −0.364017 | − | 0.931392i | \(-0.618595\pi\) | ||||
−0.364017 | + | 0.931392i | \(0.618595\pi\) | |||||||
\(614\) | 23.7691 | 0.959243 | ||||||||
\(615\) | 23.4785 | 0.946743 | ||||||||
\(616\) | 0.868026 | 0.0349738 | ||||||||
\(617\) | 16.1230 | 0.649086 | 0.324543 | − | 0.945871i | \(-0.394790\pi\) | ||||
0.324543 | + | 0.945871i | \(0.394790\pi\) | |||||||
\(618\) | −40.2318 | −1.61836 | ||||||||
\(619\) | −25.3181 | −1.01762 | −0.508811 | − | 0.860879i | \(-0.669915\pi\) | ||||
−0.508811 | + | 0.860879i | \(0.669915\pi\) | |||||||
\(620\) | −10.1080 | −0.405947 | ||||||||
\(621\) | 25.9760 | 1.04238 | ||||||||
\(622\) | 9.28733 | 0.372388 | ||||||||
\(623\) | 1.02791 | 0.0411824 | ||||||||
\(624\) | 7.92675 | 0.317324 | ||||||||
\(625\) | −9.38002 | −0.375201 | ||||||||
\(626\) | 21.5581 | 0.861636 | ||||||||
\(627\) | 14.0954 | 0.562917 | ||||||||
\(628\) | 7.32806 | 0.292422 | ||||||||
\(629\) | 55.7107 | 2.22133 | ||||||||
\(630\) | −1.59243 | −0.0634439 | ||||||||
\(631\) | −21.7155 | −0.864479 | −0.432239 | − | 0.901759i | \(-0.642276\pi\) | ||||
−0.432239 | + | 0.901759i | \(0.642276\pi\) | |||||||
\(632\) | −4.20596 | −0.167304 | ||||||||
\(633\) | −58.5963 | −2.32899 | ||||||||
\(634\) | 24.7069 | 0.981238 | ||||||||
\(635\) | −27.8789 | −1.10634 | ||||||||
\(636\) | −1.61278 | −0.0639507 | ||||||||
\(637\) | 20.5283 | 0.813361 | ||||||||
\(638\) | 19.4312 | 0.769287 | ||||||||
\(639\) | −65.0492 | −2.57330 | ||||||||
\(640\) | −1.68032 | −0.0664204 | ||||||||
\(641\) | 13.4720 | 0.532112 | 0.266056 | − | 0.963958i | \(-0.414279\pi\) | ||||
0.266056 | + | 0.963958i | \(0.414279\pi\) | |||||||
\(642\) | 33.5855 | 1.32551 | ||||||||
\(643\) | −2.58080 | −0.101777 | −0.0508884 | − | 0.998704i | \(-0.516205\pi\) | ||||
−0.0508884 | + | 0.998704i | \(0.516205\pi\) | |||||||
\(644\) | −1.82008 | −0.0717213 | ||||||||
\(645\) | −48.6066 | −1.91388 | ||||||||
\(646\) | −6.51724 | −0.256417 | ||||||||
\(647\) | 21.5142 | 0.845811 | 0.422905 | − | 0.906174i | \(-0.361010\pi\) | ||||
0.422905 | + | 0.906174i | \(0.361010\pi\) | |||||||
\(648\) | −3.95942 | −0.155541 | ||||||||
\(649\) | −15.0466 | −0.590630 | ||||||||
\(650\) | 6.42971 | 0.252194 | ||||||||
\(651\) | −3.64210 | −0.142745 | ||||||||
\(652\) | 22.7737 | 0.891886 | ||||||||
\(653\) | 11.5442 | 0.451758 | 0.225879 | − | 0.974155i | \(-0.427475\pi\) | ||||
0.225879 | + | 0.974155i | \(0.427475\pi\) | |||||||
\(654\) | 28.4585 | 1.11281 | ||||||||
\(655\) | 27.8128 | 1.08674 | ||||||||
\(656\) | 5.20726 | 0.203309 | ||||||||
\(657\) | 8.53729 | 0.333071 | ||||||||
\(658\) | 1.53067 | 0.0596719 | ||||||||
\(659\) | −2.96362 | −0.115446 | −0.0577231 | − | 0.998333i | \(-0.518384\pi\) | ||||
−0.0577231 | + | 0.998333i | \(0.518384\pi\) | |||||||
\(660\) | 17.3454 | 0.675170 | ||||||||
\(661\) | −43.1303 | −1.67757 | −0.838787 | − | 0.544459i | \(-0.816735\pi\) | ||||
−0.838787 | + | 0.544459i | \(0.816735\pi\) | |||||||
\(662\) | 20.0324 | 0.778582 | ||||||||
\(663\) | 37.8333 | 1.46932 | ||||||||
\(664\) | −0.353279 | −0.0137099 | ||||||||
\(665\) | 0.517707 | 0.0200758 | ||||||||
\(666\) | 49.0252 | 1.89969 | ||||||||
\(667\) | −40.7434 | −1.57759 | ||||||||
\(668\) | 2.42920 | 0.0939885 | ||||||||
\(669\) | −19.2944 | −0.745964 | ||||||||
\(670\) | −17.2616 | −0.666875 | ||||||||
\(671\) | −41.7458 | −1.61158 | ||||||||
\(672\) | −0.605449 | −0.0233557 | ||||||||
\(673\) | −9.68284 | −0.373246 | −0.186623 | − | 0.982432i | \(-0.559754\pi\) | ||||
−0.186623 | + | 0.982432i | \(0.559754\pi\) | |||||||
\(674\) | 12.1012 | 0.466120 | ||||||||
\(675\) | 7.00899 | 0.269776 | ||||||||
\(676\) | −4.27328 | −0.164357 | ||||||||
\(677\) | 20.7483 | 0.797424 | 0.398712 | − | 0.917076i | \(-0.369457\pi\) | ||||
0.398712 | + | 0.917076i | \(0.369457\pi\) | |||||||
\(678\) | 52.5315 | 2.01746 | ||||||||
\(679\) | 3.55569 | 0.136455 | ||||||||
\(680\) | −8.01993 | −0.307550 | ||||||||
\(681\) | 28.5739 | 1.09495 | ||||||||
\(682\) | 23.1419 | 0.886147 | ||||||||
\(683\) | −1.94790 | −0.0745344 | −0.0372672 | − | 0.999305i | \(-0.511865\pi\) | ||||
−0.0372672 | + | 0.999305i | \(0.511865\pi\) | |||||||
\(684\) | −5.73515 | −0.219289 | ||||||||
\(685\) | 35.8215 | 1.36867 | ||||||||
\(686\) | −3.14742 | −0.120169 | ||||||||
\(687\) | −22.3380 | −0.852249 | ||||||||
\(688\) | −10.7804 | −0.410999 | ||||||||
\(689\) | −1.77554 | −0.0676426 | ||||||||
\(690\) | −36.3700 | −1.38458 | ||||||||
\(691\) | −33.2622 | −1.26535 | −0.632677 | − | 0.774416i | \(-0.718044\pi\) | ||||
−0.632677 | + | 0.774416i | \(0.718044\pi\) | |||||||
\(692\) | 3.84593 | 0.146200 | ||||||||
\(693\) | 3.64580 | 0.138493 | ||||||||
\(694\) | 12.1759 | 0.462189 | ||||||||
\(695\) | −16.6683 | −0.632266 | ||||||||
\(696\) | −13.5533 | −0.513735 | ||||||||
\(697\) | 24.8536 | 0.941395 | ||||||||
\(698\) | 6.28232 | 0.237789 | ||||||||
\(699\) | −23.7774 | −0.899344 | ||||||||
\(700\) | −0.491105 | −0.0185620 | ||||||||
\(701\) | 12.6612 | 0.478209 | 0.239104 | − | 0.970994i | \(-0.423146\pi\) | ||||
0.239104 | + | 0.970994i | \(0.423146\pi\) | |||||||
\(702\) | 9.51294 | 0.359043 | ||||||||
\(703\) | −15.9383 | −0.601126 | ||||||||
\(704\) | 3.84702 | 0.144990 | ||||||||
\(705\) | 30.5869 | 1.15197 | ||||||||
\(706\) | 16.3024 | 0.613550 | ||||||||
\(707\) | 1.79565 | 0.0675322 | ||||||||
\(708\) | 10.4950 | 0.394427 | ||||||||
\(709\) | −35.6941 | −1.34052 | −0.670260 | − | 0.742126i | \(-0.733818\pi\) | ||||
−0.670260 | + | 0.742126i | \(0.733818\pi\) | |||||||
\(710\) | 26.0239 | 0.976660 | ||||||||
\(711\) | −17.6655 | −0.662508 | ||||||||
\(712\) | 4.55562 | 0.170729 | ||||||||
\(713\) | −48.5240 | −1.81724 | ||||||||
\(714\) | −2.88973 | −0.108145 | ||||||||
\(715\) | 19.0959 | 0.714148 | ||||||||
\(716\) | 17.5869 | 0.657254 | ||||||||
\(717\) | 25.2983 | 0.944783 | ||||||||
\(718\) | 26.2461 | 0.979497 | ||||||||
\(719\) | −46.8750 | −1.74814 | −0.874071 | − | 0.485798i | \(-0.838529\pi\) | ||||
−0.874071 | + | 0.485798i | \(0.838529\pi\) | |||||||
\(720\) | −7.05751 | −0.263018 | ||||||||
\(721\) | 3.38305 | 0.125991 | ||||||||
\(722\) | −17.1355 | −0.637716 | ||||||||
\(723\) | 47.2041 | 1.75554 | ||||||||
\(724\) | −6.37852 | −0.237056 | ||||||||
\(725\) | −10.9936 | −0.408292 | ||||||||
\(726\) | −10.1954 | −0.378386 | ||||||||
\(727\) | −46.0093 | −1.70639 | −0.853195 | − | 0.521591i | \(-0.825339\pi\) | ||||
−0.853195 | + | 0.521591i | \(0.825339\pi\) | |||||||
\(728\) | −0.666552 | −0.0247040 | ||||||||
\(729\) | −42.5527 | −1.57603 | ||||||||
\(730\) | −3.41547 | −0.126412 | ||||||||
\(731\) | −51.4534 | −1.90307 | ||||||||
\(732\) | 29.1178 | 1.07622 | ||||||||
\(733\) | 30.8570 | 1.13973 | 0.569866 | − | 0.821738i | \(-0.306995\pi\) | ||||
0.569866 | + | 0.821738i | \(0.306995\pi\) | |||||||
\(734\) | 26.2518 | 0.968972 | ||||||||
\(735\) | −31.3320 | −1.15570 | ||||||||
\(736\) | −8.06646 | −0.297334 | ||||||||
\(737\) | 39.5199 | 1.45573 | ||||||||
\(738\) | 21.8710 | 0.805084 | ||||||||
\(739\) | 5.59810 | 0.205929 | 0.102965 | − | 0.994685i | \(-0.467167\pi\) | ||||
0.102965 | + | 0.994685i | \(0.467167\pi\) | |||||||
\(740\) | −19.6133 | −0.720998 | ||||||||
\(741\) | −10.8238 | −0.397622 | ||||||||
\(742\) | 0.135617 | 0.00497864 | ||||||||
\(743\) | 33.9157 | 1.24425 | 0.622123 | − | 0.782920i | \(-0.286270\pi\) | ||||
0.622123 | + | 0.782920i | \(0.286270\pi\) | |||||||
\(744\) | −16.1415 | −0.591775 | ||||||||
\(745\) | −29.3436 | −1.07507 | ||||||||
\(746\) | 36.8164 | 1.34795 | ||||||||
\(747\) | −1.48381 | −0.0542897 | ||||||||
\(748\) | 18.3613 | 0.671356 | ||||||||
\(749\) | −2.82417 | −0.103193 | ||||||||
\(750\) | −32.3575 | −1.18153 | ||||||||
\(751\) | −44.6549 | −1.62948 | −0.814741 | − | 0.579825i | \(-0.803121\pi\) | ||||
−0.814741 | + | 0.579825i | \(0.803121\pi\) | |||||||
\(752\) | 6.78382 | 0.247380 | ||||||||
\(753\) | −29.0222 | −1.05763 | ||||||||
\(754\) | −14.9211 | −0.543393 | ||||||||
\(755\) | −0.851455 | −0.0309876 | ||||||||
\(756\) | −0.726604 | −0.0264263 | ||||||||
\(757\) | 23.6763 | 0.860528 | 0.430264 | − | 0.902703i | \(-0.358420\pi\) | ||||
0.430264 | + | 0.902703i | \(0.358420\pi\) | |||||||
\(758\) | −33.7663 | −1.22645 | ||||||||
\(759\) | 83.2677 | 3.02243 | ||||||||
\(760\) | 2.29443 | 0.0832279 | ||||||||
\(761\) | 0.431496 | 0.0156417 | 0.00782086 | − | 0.999969i | \(-0.497511\pi\) | ||||
0.00782086 | + | 0.999969i | \(0.497511\pi\) | |||||||
\(762\) | −44.5199 | −1.61278 | ||||||||
\(763\) | −2.39304 | −0.0866340 | ||||||||
\(764\) | −6.42409 | −0.232415 | ||||||||
\(765\) | −33.6846 | −1.21787 | ||||||||
\(766\) | 22.2087 | 0.802434 | ||||||||
\(767\) | 11.5542 | 0.417197 | ||||||||
\(768\) | −2.68330 | −0.0968253 | ||||||||
\(769\) | 1.91917 | 0.0692069 | 0.0346035 | − | 0.999401i | \(-0.488983\pi\) | ||||
0.0346035 | + | 0.999401i | \(0.488983\pi\) | |||||||
\(770\) | −1.45856 | −0.0525628 | ||||||||
\(771\) | −45.7464 | −1.64752 | ||||||||
\(772\) | 3.71798 | 0.133813 | ||||||||
\(773\) | −52.3153 | −1.88165 | −0.940825 | − | 0.338893i | \(-0.889948\pi\) | ||||
−0.940825 | + | 0.338893i | \(0.889948\pi\) | |||||||
\(774\) | −45.2788 | −1.62751 | ||||||||
\(775\) | −13.0930 | −0.470315 | ||||||||
\(776\) | 15.7585 | 0.565698 | ||||||||
\(777\) | −7.06703 | −0.253528 | ||||||||
\(778\) | 14.1829 | 0.508483 | ||||||||
\(779\) | −7.11039 | −0.254756 | ||||||||
\(780\) | −13.3194 | −0.476913 | ||||||||
\(781\) | −59.5807 | −2.13197 | ||||||||
\(782\) | −38.5001 | −1.37676 | ||||||||
\(783\) | −16.2654 | −0.581277 | ||||||||
\(784\) | −6.94909 | −0.248182 | ||||||||
\(785\) | −12.3135 | −0.439487 | ||||||||
\(786\) | 44.4143 | 1.58421 | ||||||||
\(787\) | −4.64276 | −0.165496 | −0.0827482 | − | 0.996570i | \(-0.526370\pi\) | ||||
−0.0827482 | + | 0.996570i | \(0.526370\pi\) | |||||||
\(788\) | −0.678498 | −0.0241705 | ||||||||
\(789\) | 20.3690 | 0.725155 | ||||||||
\(790\) | 7.06735 | 0.251445 | ||||||||
\(791\) | −4.41732 | −0.157062 | ||||||||
\(792\) | 16.1579 | 0.574146 | ||||||||
\(793\) | 32.0563 | 1.13835 | ||||||||
\(794\) | 17.4555 | 0.619473 | ||||||||
\(795\) | 2.70997 | 0.0961128 | ||||||||
\(796\) | −20.9925 | −0.744059 | ||||||||
\(797\) | 17.0240 | 0.603022 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(798\) | 0.826727 | 0.0292658 | ||||||||
\(799\) | 32.3783 | 1.14546 | ||||||||
\(800\) | −2.17654 | −0.0769521 | ||||||||
\(801\) | 19.1341 | 0.676070 | ||||||||
\(802\) | 4.63869 | 0.163798 | ||||||||
\(803\) | 7.81959 | 0.275947 | ||||||||
\(804\) | −27.5652 | −0.972148 | ||||||||
\(805\) | 3.05832 | 0.107791 | ||||||||
\(806\) | −17.7705 | −0.625938 | ||||||||
\(807\) | −53.3916 | −1.87947 | ||||||||
\(808\) | 7.95815 | 0.279967 | ||||||||
\(809\) | 36.0486 | 1.26740 | 0.633701 | − | 0.773578i | \(-0.281535\pi\) | ||||
0.633701 | + | 0.773578i | \(0.281535\pi\) | |||||||
\(810\) | 6.65308 | 0.233765 | ||||||||
\(811\) | 54.7598 | 1.92288 | 0.961438 | − | 0.275023i | \(-0.0886855\pi\) | ||||
0.961438 | + | 0.275023i | \(0.0886855\pi\) | |||||||
\(812\) | 1.13968 | 0.0399949 | ||||||||
\(813\) | −20.6067 | −0.722707 | ||||||||
\(814\) | 44.9038 | 1.57388 | ||||||||
\(815\) | −38.2670 | −1.34043 | ||||||||
\(816\) | −12.8070 | −0.448336 | ||||||||
\(817\) | 14.7204 | 0.515001 | ||||||||
\(818\) | −13.1906 | −0.461197 | ||||||||
\(819\) | −2.79959 | −0.0978255 | ||||||||
\(820\) | −8.74984 | −0.305558 | ||||||||
\(821\) | −42.5798 | −1.48605 | −0.743023 | − | 0.669266i | \(-0.766609\pi\) | ||||
−0.743023 | + | 0.669266i | \(0.766609\pi\) | |||||||
\(822\) | 57.2034 | 1.99520 | ||||||||
\(823\) | 10.9712 | 0.382431 | 0.191215 | − | 0.981548i | \(-0.438757\pi\) | ||||
0.191215 | + | 0.981548i | \(0.438757\pi\) | |||||||
\(824\) | 14.9934 | 0.522319 | ||||||||
\(825\) | 22.4678 | 0.782227 | ||||||||
\(826\) | −0.882515 | −0.0307066 | ||||||||
\(827\) | 28.0809 | 0.976469 | 0.488235 | − | 0.872712i | \(-0.337641\pi\) | ||||
0.488235 | + | 0.872712i | \(0.337641\pi\) | |||||||
\(828\) | −33.8800 | −1.17741 | ||||||||
\(829\) | −38.7257 | −1.34500 | −0.672500 | − | 0.740097i | \(-0.734779\pi\) | ||||
−0.672500 | + | 0.740097i | \(0.734779\pi\) | |||||||
\(830\) | 0.593620 | 0.0206048 | ||||||||
\(831\) | 12.2541 | 0.425089 | ||||||||
\(832\) | −2.95410 | −0.102415 | ||||||||
\(833\) | −33.1671 | −1.14917 | ||||||||
\(834\) | −26.6177 | −0.921695 | ||||||||
\(835\) | −4.08182 | −0.141257 | ||||||||
\(836\) | −5.25302 | −0.181679 | ||||||||
\(837\) | −19.3715 | −0.669577 | ||||||||
\(838\) | 10.9101 | 0.376885 | ||||||||
\(839\) | 11.2050 | 0.386839 | 0.193419 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193419 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(840\) | 1.01735 | 0.0351018 | ||||||||
\(841\) | −3.48777 | −0.120268 | ||||||||
\(842\) | 20.0882 | 0.692285 | ||||||||
\(843\) | −0.319937 | −0.0110192 | ||||||||
\(844\) | 21.8374 | 0.751674 | ||||||||
\(845\) | 7.18047 | 0.247016 | ||||||||
\(846\) | 28.4928 | 0.979602 | ||||||||
\(847\) | 0.857318 | 0.0294578 | ||||||||
\(848\) | 0.601041 | 0.0206398 | ||||||||
\(849\) | −1.80426 | −0.0619220 | ||||||||
\(850\) | −10.3883 | −0.356316 | ||||||||
\(851\) | −94.1547 | −3.22758 | ||||||||
\(852\) | 41.5576 | 1.42374 | ||||||||
\(853\) | 32.1920 | 1.10223 | 0.551116 | − | 0.834428i | \(-0.314202\pi\) | ||||
0.551116 | + | 0.834428i | \(0.314202\pi\) | |||||||
\(854\) | −2.44848 | −0.0837853 | ||||||||
\(855\) | 9.63687 | 0.329574 | ||||||||
\(856\) | −12.5165 | −0.427805 | ||||||||
\(857\) | −5.88904 | −0.201166 | −0.100583 | − | 0.994929i | \(-0.532071\pi\) | ||||
−0.100583 | + | 0.994929i | \(0.532071\pi\) | |||||||
\(858\) | 30.4943 | 1.04106 | ||||||||
\(859\) | −24.1026 | −0.822371 | −0.411185 | − | 0.911552i | \(-0.634885\pi\) | ||||
−0.411185 | + | 0.911552i | \(0.634885\pi\) | |||||||
\(860\) | 18.1145 | 0.617698 | ||||||||
\(861\) | −3.15273 | −0.107445 | ||||||||
\(862\) | −16.7089 | −0.569106 | ||||||||
\(863\) | 44.4893 | 1.51443 | 0.757217 | − | 0.653163i | \(-0.226558\pi\) | ||||
0.757217 | + | 0.653163i | \(0.226558\pi\) | |||||||
\(864\) | −3.22025 | −0.109555 | ||||||||
\(865\) | −6.46238 | −0.219728 | ||||||||
\(866\) | 19.2394 | 0.653782 | ||||||||
\(867\) | −15.5102 | −0.526754 | ||||||||
\(868\) | 1.35732 | 0.0460704 | ||||||||
\(869\) | −16.1804 | −0.548883 | ||||||||
\(870\) | 22.7738 | 0.772103 | ||||||||
\(871\) | −30.3470 | −1.02827 | ||||||||
\(872\) | −10.6058 | −0.359157 | ||||||||
\(873\) | 66.1875 | 2.24011 | ||||||||
\(874\) | 11.0146 | 0.372573 | ||||||||
\(875\) | 2.72091 | 0.0919836 | ||||||||
\(876\) | −5.45417 | −0.184279 | ||||||||
\(877\) | 18.1579 | 0.613147 | 0.306574 | − | 0.951847i | \(-0.400817\pi\) | ||||
0.306574 | + | 0.951847i | \(0.400817\pi\) | |||||||
\(878\) | −30.8022 | −1.03952 | ||||||||
\(879\) | −78.0989 | −2.63421 | ||||||||
\(880\) | −6.46421 | −0.217909 | ||||||||
\(881\) | 3.90672 | 0.131621 | 0.0658103 | − | 0.997832i | \(-0.479037\pi\) | ||||
0.0658103 | + | 0.997832i | \(0.479037\pi\) | |||||||
\(882\) | −29.1869 | −0.982775 | ||||||||
\(883\) | 46.5102 | 1.56519 | 0.782596 | − | 0.622530i | \(-0.213895\pi\) | ||||
0.782596 | + | 0.622530i | \(0.213895\pi\) | |||||||
\(884\) | −14.0995 | −0.474219 | ||||||||
\(885\) | −17.6350 | −0.592792 | ||||||||
\(886\) | −23.3912 | −0.785843 | ||||||||
\(887\) | 43.7691 | 1.46962 | 0.734811 | − | 0.678271i | \(-0.237271\pi\) | ||||
0.734811 | + | 0.678271i | \(0.237271\pi\) | |||||||
\(888\) | −31.3205 | −1.05105 | ||||||||
\(889\) | 3.74363 | 0.125557 | ||||||||
\(890\) | −7.65489 | −0.256592 | ||||||||
\(891\) | −15.2320 | −0.510290 | ||||||||
\(892\) | 7.19054 | 0.240757 | ||||||||
\(893\) | −9.26315 | −0.309979 | ||||||||
\(894\) | −46.8588 | −1.56719 | ||||||||
\(895\) | −29.5516 | −0.987800 | ||||||||
\(896\) | 0.225636 | 0.00753797 | ||||||||
\(897\) | −63.9408 | −2.13492 | ||||||||
\(898\) | 38.3699 | 1.28042 | ||||||||
\(899\) | 30.3842 | 1.01337 | ||||||||
\(900\) | −9.14168 | −0.304723 | ||||||||
\(901\) | 2.86869 | 0.0955699 | ||||||||
\(902\) | 20.0324 | 0.667007 | ||||||||
\(903\) | 6.52698 | 0.217204 | ||||||||
\(904\) | −19.5772 | −0.651128 | ||||||||
\(905\) | 10.7179 | 0.356276 | ||||||||
\(906\) | −1.35969 | −0.0451727 | ||||||||
\(907\) | 36.4271 | 1.20954 | 0.604771 | − | 0.796399i | \(-0.293265\pi\) | ||||
0.604771 | + | 0.796399i | \(0.293265\pi\) | |||||||
\(908\) | −10.6488 | −0.353392 | ||||||||
\(909\) | 33.4251 | 1.10864 | ||||||||
\(910\) | 1.12002 | 0.0371282 | ||||||||
\(911\) | 53.6734 | 1.77828 | 0.889139 | − | 0.457637i | \(-0.151304\pi\) | ||||
0.889139 | + | 0.457637i | \(0.151304\pi\) | |||||||
\(912\) | 3.66399 | 0.121327 | ||||||||
\(913\) | −1.35907 | −0.0449786 | ||||||||
\(914\) | −6.02517 | −0.199295 | ||||||||
\(915\) | −48.9270 | −1.61748 | ||||||||
\(916\) | 8.32483 | 0.275060 | ||||||||
\(917\) | −3.73475 | −0.123332 | ||||||||
\(918\) | −15.3698 | −0.507280 | ||||||||
\(919\) | −49.3526 | −1.62799 | −0.813996 | − | 0.580870i | \(-0.802712\pi\) | ||||
−0.813996 | + | 0.580870i | \(0.802712\pi\) | |||||||
\(920\) | 13.5542 | 0.446869 | ||||||||
\(921\) | −63.7797 | −2.10161 | ||||||||
\(922\) | 10.2411 | 0.337272 | ||||||||
\(923\) | 45.7516 | 1.50593 | ||||||||
\(924\) | −2.32918 | −0.0766242 | ||||||||
\(925\) | −25.4053 | −0.835322 | ||||||||
\(926\) | −21.3465 | −0.701488 | ||||||||
\(927\) | 62.9738 | 2.06833 | ||||||||
\(928\) | 5.05096 | 0.165806 | ||||||||
\(929\) | 10.9159 | 0.358140 | 0.179070 | − | 0.983836i | \(-0.442691\pi\) | ||||
0.179070 | + | 0.983836i | \(0.442691\pi\) | |||||||
\(930\) | 27.1228 | 0.889391 | ||||||||
\(931\) | 9.48882 | 0.310984 | ||||||||
\(932\) | 8.86125 | 0.290260 | ||||||||
\(933\) | −24.9207 | −0.815868 | ||||||||
\(934\) | −19.0455 | −0.623188 | ||||||||
\(935\) | −30.8528 | −1.00900 | ||||||||
\(936\) | −12.4075 | −0.405553 | ||||||||
\(937\) | 13.4346 | 0.438890 | 0.219445 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219445 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(938\) | 2.31792 | 0.0756829 | ||||||||
\(939\) | −57.8470 | −1.88776 | ||||||||
\(940\) | −11.3990 | −0.371793 | ||||||||
\(941\) | −1.16986 | −0.0381363 | −0.0190682 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190682 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(942\) | −19.6634 | −0.640668 | ||||||||
\(943\) | −42.0041 | −1.36784 | ||||||||
\(944\) | −3.91123 | −0.127300 | ||||||||
\(945\) | 1.22093 | 0.0397167 | ||||||||
\(946\) | −41.4724 | −1.34838 | ||||||||
\(947\) | 28.3277 | 0.920526 | 0.460263 | − | 0.887783i | \(-0.347755\pi\) | ||||
0.460263 | + | 0.887783i | \(0.347755\pi\) | |||||||
\(948\) | 11.2859 | 0.366548 | ||||||||
\(949\) | −6.00461 | −0.194918 | ||||||||
\(950\) | 2.97201 | 0.0964247 | ||||||||
\(951\) | −66.2962 | −2.14980 | ||||||||
\(952\) | 1.07693 | 0.0349035 | ||||||||
\(953\) | −0.229724 | −0.00744150 | −0.00372075 | − | 0.999993i | \(-0.501184\pi\) | ||||
−0.00372075 | + | 0.999993i | \(0.501184\pi\) | |||||||
\(954\) | 2.52444 | 0.0817317 | ||||||||
\(955\) | 10.7945 | 0.349302 | ||||||||
\(956\) | −9.42805 | −0.304925 | ||||||||
\(957\) | −52.1396 | −1.68544 | ||||||||
\(958\) | −30.5336 | −0.986497 | ||||||||
\(959\) | −4.81017 | −0.155328 | ||||||||
\(960\) | 4.50880 | 0.145521 | ||||||||
\(961\) | 5.18656 | 0.167308 | ||||||||
\(962\) | −34.4814 | −1.11172 | ||||||||
\(963\) | −52.5706 | −1.69406 | ||||||||
\(964\) | −17.5918 | −0.566593 | ||||||||
\(965\) | −6.24738 | −0.201110 | ||||||||
\(966\) | 4.88383 | 0.157135 | ||||||||
\(967\) | −49.2093 | −1.58247 | −0.791233 | − | 0.611515i | \(-0.790560\pi\) | ||||
−0.791233 | + | 0.611515i | \(0.790560\pi\) | |||||||
\(968\) | 3.79956 | 0.122123 | ||||||||
\(969\) | 17.4877 | 0.561787 | ||||||||
\(970\) | −26.4793 | −0.850199 | ||||||||
\(971\) | 18.0725 | 0.579974 | 0.289987 | − | 0.957031i | \(-0.406349\pi\) | ||||
0.289987 | + | 0.957031i | \(0.406349\pi\) | |||||||
\(972\) | 20.2851 | 0.650644 | ||||||||
\(973\) | 2.23825 | 0.0717551 | ||||||||
\(974\) | −13.0500 | −0.418150 | ||||||||
\(975\) | −17.2528 | −0.552533 | ||||||||
\(976\) | −10.8515 | −0.347347 | ||||||||
\(977\) | −1.98541 | −0.0635189 | −0.0317595 | − | 0.999496i | \(-0.510111\pi\) | ||||
−0.0317595 | + | 0.999496i | \(0.510111\pi\) | |||||||
\(978\) | −61.1086 | −1.95404 | ||||||||
\(979\) | 17.5256 | 0.560119 | ||||||||
\(980\) | 11.6767 | 0.372998 | ||||||||
\(981\) | −44.5454 | −1.42222 | ||||||||
\(982\) | −15.2680 | −0.487220 | ||||||||
\(983\) | 34.3541 | 1.09573 | 0.547863 | − | 0.836568i | \(-0.315442\pi\) | ||||
0.547863 | + | 0.836568i | \(0.315442\pi\) | |||||||
\(984\) | −13.9726 | −0.445432 | ||||||||
\(985\) | 1.14009 | 0.0363263 | ||||||||
\(986\) | 24.1076 | 0.767742 | ||||||||
\(987\) | −4.10726 | −0.130735 | ||||||||
\(988\) | 4.03376 | 0.128331 | ||||||||
\(989\) | 86.9596 | 2.76515 | ||||||||
\(990\) | −27.1504 | −0.862896 | ||||||||
\(991\) | −3.79368 | −0.120510 | −0.0602551 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602551 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(992\) | 6.01553 | 0.190993 | ||||||||
\(993\) | −53.7530 | −1.70580 | ||||||||
\(994\) | −3.49454 | −0.110840 | ||||||||
\(995\) | 35.2740 | 1.11826 | ||||||||
\(996\) | 0.947953 | 0.0300370 | ||||||||
\(997\) | −29.5813 | −0.936850 | −0.468425 | − | 0.883503i | \(-0.655178\pi\) | ||||
−0.468425 | + | 0.883503i | \(0.655178\pi\) | |||||||
\(998\) | 14.3339 | 0.453732 | ||||||||
\(999\) | −37.5879 | −1.18923 |
(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 | 8002.2.a.g.1.11 | ✓ | 95 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.g.1.11 | ✓ | 95 | 1.1 | even | 1 | trivial |