Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.639237 | −0.452009 | −0.226004 | − | 0.974126i | \(-0.572566\pi\) | ||||
−0.226004 | + | 0.974126i | \(0.572566\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.59138 | −0.795688 | ||||||||
\(5\) | −1.53158 | −0.684942 | −0.342471 | − | 0.939528i | \(-0.611264\pi\) | ||||
−0.342471 | + | 0.939528i | \(0.611264\pi\) | |||||||
\(6\) | −0.639237 | −0.260967 | ||||||||
\(7\) | −2.74819 | −1.03872 | −0.519360 | − | 0.854556i | \(-0.673829\pi\) | ||||
−0.519360 | + | 0.854556i | \(0.673829\pi\) | |||||||
\(8\) | 2.29574 | 0.811667 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.979040 | 0.309600 | ||||||||
\(11\) | 4.38312 | 1.32156 | 0.660780 | − | 0.750580i | \(-0.270226\pi\) | ||||
0.660780 | + | 0.750580i | \(0.270226\pi\) | |||||||
\(12\) | −1.59138 | −0.459391 | ||||||||
\(13\) | 2.19700 | 0.609337 | 0.304668 | − | 0.952458i | \(-0.401454\pi\) | ||||
0.304668 | + | 0.952458i | \(0.401454\pi\) | |||||||
\(14\) | 1.75675 | 0.469510 | ||||||||
\(15\) | −1.53158 | −0.395451 | ||||||||
\(16\) | 1.71523 | 0.428807 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.639237 | −0.150670 | ||||||||
\(19\) | 4.55900 | 1.04591 | 0.522953 | − | 0.852362i | \(-0.324830\pi\) | ||||
0.522953 | + | 0.852362i | \(0.324830\pi\) | |||||||
\(20\) | 2.43731 | 0.545000 | ||||||||
\(21\) | −2.74819 | −0.599705 | ||||||||
\(22\) | −2.80185 | −0.597357 | ||||||||
\(23\) | −7.35985 | −1.53463 | −0.767317 | − | 0.641267i | \(-0.778409\pi\) | ||||
−0.767317 | + | 0.641267i | \(0.778409\pi\) | |||||||
\(24\) | 2.29574 | 0.468616 | ||||||||
\(25\) | −2.65427 | −0.530855 | ||||||||
\(26\) | −1.40440 | −0.275426 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.37341 | 0.826496 | ||||||||
\(29\) | −1.31023 | −0.243304 | −0.121652 | − | 0.992573i | \(-0.538819\pi\) | ||||
−0.121652 | + | 0.992573i | \(0.538819\pi\) | |||||||
\(30\) | 0.979040 | 0.178748 | ||||||||
\(31\) | −5.83625 | −1.04822 | −0.524110 | − | 0.851650i | \(-0.675602\pi\) | ||||
−0.524110 | + | 0.851650i | \(0.675602\pi\) | |||||||
\(32\) | −5.68792 | −1.00549 | ||||||||
\(33\) | 4.38312 | 0.763003 | ||||||||
\(34\) | −0.639237 | −0.109628 | ||||||||
\(35\) | 4.20907 | 0.711462 | ||||||||
\(36\) | −1.59138 | −0.265229 | ||||||||
\(37\) | 4.21370 | 0.692727 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(38\) | −2.91428 | −0.472759 | ||||||||
\(39\) | 2.19700 | 0.351801 | ||||||||
\(40\) | −3.51610 | −0.555945 | ||||||||
\(41\) | 3.78873 | 0.591700 | 0.295850 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295850 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(42\) | 1.75675 | 0.271072 | ||||||||
\(43\) | 3.27995 | 0.500187 | 0.250094 | − | 0.968222i | \(-0.419539\pi\) | ||||
0.250094 | + | 0.968222i | \(0.419539\pi\) | |||||||
\(44\) | −6.97519 | −1.05155 | ||||||||
\(45\) | −1.53158 | −0.228314 | ||||||||
\(46\) | 4.70469 | 0.693669 | ||||||||
\(47\) | −5.56863 | −0.812268 | −0.406134 | − | 0.913814i | \(-0.633123\pi\) | ||||
−0.406134 | + | 0.913814i | \(0.633123\pi\) | |||||||
\(48\) | 1.71523 | 0.247572 | ||||||||
\(49\) | 0.552565 | 0.0789379 | ||||||||
\(50\) | 1.69671 | 0.239951 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.49625 | −0.484842 | ||||||||
\(53\) | −1.40021 | −0.192333 | −0.0961667 | − | 0.995365i | \(-0.530658\pi\) | ||||
−0.0961667 | + | 0.995365i | \(0.530658\pi\) | |||||||
\(54\) | −0.639237 | −0.0869892 | ||||||||
\(55\) | −6.71308 | −0.905191 | ||||||||
\(56\) | −6.30914 | −0.843094 | ||||||||
\(57\) | 4.55900 | 0.603854 | ||||||||
\(58\) | 0.837548 | 0.109975 | ||||||||
\(59\) | 14.2575 | 1.85616 | 0.928081 | − | 0.372378i | \(-0.121458\pi\) | ||||
0.928081 | + | 0.372378i | \(0.121458\pi\) | |||||||
\(60\) | 2.43731 | 0.314656 | ||||||||
\(61\) | −2.49345 | −0.319253 | −0.159626 | − | 0.987177i | \(-0.551029\pi\) | ||||
−0.159626 | + | 0.987177i | \(0.551029\pi\) | |||||||
\(62\) | 3.73075 | 0.473805 | ||||||||
\(63\) | −2.74819 | −0.346240 | ||||||||
\(64\) | 0.205472 | 0.0256840 | ||||||||
\(65\) | −3.36487 | −0.417360 | ||||||||
\(66\) | −2.80185 | −0.344884 | ||||||||
\(67\) | −0.208432 | −0.0254640 | −0.0127320 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127320 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(68\) | −1.59138 | −0.192983 | ||||||||
\(69\) | −7.35985 | −0.886022 | ||||||||
\(70\) | −2.69059 | −0.321587 | ||||||||
\(71\) | 5.71350 | 0.678068 | 0.339034 | − | 0.940774i | \(-0.389900\pi\) | ||||
0.339034 | + | 0.940774i | \(0.389900\pi\) | |||||||
\(72\) | 2.29574 | 0.270556 | ||||||||
\(73\) | −1.55512 | −0.182013 | −0.0910067 | − | 0.995850i | \(-0.529008\pi\) | ||||
−0.0910067 | + | 0.995850i | \(0.529008\pi\) | |||||||
\(74\) | −2.69355 | −0.313119 | ||||||||
\(75\) | −2.65427 | −0.306489 | ||||||||
\(76\) | −7.25508 | −0.832214 | ||||||||
\(77\) | −12.0457 | −1.37273 | ||||||||
\(78\) | −1.40440 | −0.159017 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −2.62700 | −0.293708 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.42190 | −0.267454 | ||||||||
\(83\) | −14.1845 | −1.55695 | −0.778476 | − | 0.627674i | \(-0.784007\pi\) | ||||
−0.778476 | + | 0.627674i | \(0.784007\pi\) | |||||||
\(84\) | 4.37341 | 0.477178 | ||||||||
\(85\) | −1.53158 | −0.166123 | ||||||||
\(86\) | −2.09666 | −0.226089 | ||||||||
\(87\) | −1.31023 | −0.140471 | ||||||||
\(88\) | 10.0625 | 1.07267 | ||||||||
\(89\) | 8.42513 | 0.893062 | 0.446531 | − | 0.894768i | \(-0.352659\pi\) | ||||
0.446531 | + | 0.894768i | \(0.352659\pi\) | |||||||
\(90\) | 0.979040 | 0.103200 | ||||||||
\(91\) | −6.03777 | −0.632930 | ||||||||
\(92\) | 11.7123 | 1.22109 | ||||||||
\(93\) | −5.83625 | −0.605191 | ||||||||
\(94\) | 3.55967 | 0.367152 | ||||||||
\(95\) | −6.98245 | −0.716384 | ||||||||
\(96\) | −5.68792 | −0.580521 | ||||||||
\(97\) | 1.90697 | 0.193623 | 0.0968116 | − | 0.995303i | \(-0.469136\pi\) | ||||
0.0968116 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(98\) | −0.353220 | −0.0356806 | ||||||||
\(99\) | 4.38312 | 0.440520 | ||||||||
\(100\) | 4.22395 | 0.422395 | ||||||||
\(101\) | −12.6867 | −1.26238 | −0.631188 | − | 0.775630i | \(-0.717432\pi\) | ||||
−0.631188 | + | 0.775630i | \(0.717432\pi\) | |||||||
\(102\) | −0.639237 | −0.0632939 | ||||||||
\(103\) | 18.8984 | 1.86211 | 0.931057 | − | 0.364873i | \(-0.118888\pi\) | ||||
0.931057 | + | 0.364873i | \(0.118888\pi\) | |||||||
\(104\) | 5.04373 | 0.494579 | ||||||||
\(105\) | 4.20907 | 0.410763 | ||||||||
\(106\) | 0.895065 | 0.0869364 | ||||||||
\(107\) | −1.99970 | −0.193318 | −0.0966590 | − | 0.995318i | \(-0.530816\pi\) | ||||
−0.0966590 | + | 0.995318i | \(0.530816\pi\) | |||||||
\(108\) | −1.59138 | −0.153130 | ||||||||
\(109\) | 18.5527 | 1.77702 | 0.888511 | − | 0.458856i | \(-0.151741\pi\) | ||||
0.888511 | + | 0.458856i | \(0.151741\pi\) | |||||||
\(110\) | 4.29125 | 0.409155 | ||||||||
\(111\) | 4.21370 | 0.399946 | ||||||||
\(112\) | −4.71378 | −0.445410 | ||||||||
\(113\) | −2.42445 | −0.228073 | −0.114037 | − | 0.993477i | \(-0.536378\pi\) | ||||
−0.114037 | + | 0.993477i | \(0.536378\pi\) | |||||||
\(114\) | −2.91428 | −0.272947 | ||||||||
\(115\) | 11.2722 | 1.05114 | ||||||||
\(116\) | 2.08507 | 0.193594 | ||||||||
\(117\) | 2.19700 | 0.203112 | ||||||||
\(118\) | −9.11389 | −0.839002 | ||||||||
\(119\) | −2.74819 | −0.251926 | ||||||||
\(120\) | −3.51610 | −0.320975 | ||||||||
\(121\) | 8.21172 | 0.746520 | ||||||||
\(122\) | 1.59390 | 0.144305 | ||||||||
\(123\) | 3.78873 | 0.341618 | ||||||||
\(124\) | 9.28766 | 0.834057 | ||||||||
\(125\) | 11.7231 | 1.04855 | ||||||||
\(126\) | 1.75675 | 0.156503 | ||||||||
\(127\) | −3.87578 | −0.343920 | −0.171960 | − | 0.985104i | \(-0.555010\pi\) | ||||
−0.171960 | + | 0.985104i | \(0.555010\pi\) | |||||||
\(128\) | 11.2445 | 0.993882 | ||||||||
\(129\) | 3.27995 | 0.288783 | ||||||||
\(130\) | 2.15095 | 0.188651 | ||||||||
\(131\) | −2.04395 | −0.178581 | −0.0892906 | − | 0.996006i | \(-0.528460\pi\) | ||||
−0.0892906 | + | 0.996006i | \(0.528460\pi\) | |||||||
\(132\) | −6.97519 | −0.607112 | ||||||||
\(133\) | −12.5290 | −1.08640 | ||||||||
\(134\) | 0.133237 | 0.0115099 | ||||||||
\(135\) | −1.53158 | −0.131817 | ||||||||
\(136\) | 2.29574 | 0.196858 | ||||||||
\(137\) | 11.9562 | 1.02149 | 0.510743 | − | 0.859733i | \(-0.329370\pi\) | ||||
0.510743 | + | 0.859733i | \(0.329370\pi\) | |||||||
\(138\) | 4.70469 | 0.400490 | ||||||||
\(139\) | 15.8345 | 1.34307 | 0.671533 | − | 0.740974i | \(-0.265636\pi\) | ||||
0.671533 | + | 0.740974i | \(0.265636\pi\) | |||||||
\(140\) | −6.69821 | −0.566102 | ||||||||
\(141\) | −5.56863 | −0.468963 | ||||||||
\(142\) | −3.65228 | −0.306493 | ||||||||
\(143\) | 9.62969 | 0.805275 | ||||||||
\(144\) | 1.71523 | 0.142936 | ||||||||
\(145\) | 2.00672 | 0.166649 | ||||||||
\(146\) | 0.994093 | 0.0822717 | ||||||||
\(147\) | 0.552565 | 0.0455748 | ||||||||
\(148\) | −6.70557 | −0.551195 | ||||||||
\(149\) | −2.92417 | −0.239557 | −0.119779 | − | 0.992801i | \(-0.538219\pi\) | ||||
−0.119779 | + | 0.992801i | \(0.538219\pi\) | |||||||
\(150\) | 1.69671 | 0.138536 | ||||||||
\(151\) | 5.51386 | 0.448712 | 0.224356 | − | 0.974507i | \(-0.427972\pi\) | ||||
0.224356 | + | 0.974507i | \(0.427972\pi\) | |||||||
\(152\) | 10.4663 | 0.848927 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 7.70003 | 0.620486 | ||||||||
\(155\) | 8.93866 | 0.717970 | ||||||||
\(156\) | −3.49625 | −0.279924 | ||||||||
\(157\) | −18.8903 | −1.50761 | −0.753803 | − | 0.657100i | \(-0.771783\pi\) | ||||
−0.753803 | + | 0.657100i | \(0.771783\pi\) | |||||||
\(158\) | −0.639237 | −0.0508550 | ||||||||
\(159\) | −1.40021 | −0.111044 | ||||||||
\(160\) | 8.71148 | 0.688703 | ||||||||
\(161\) | 20.2263 | 1.59406 | ||||||||
\(162\) | −0.639237 | −0.0502232 | ||||||||
\(163\) | −0.132491 | −0.0103775 | −0.00518875 | − | 0.999987i | \(-0.501652\pi\) | ||||
−0.00518875 | + | 0.999987i | \(0.501652\pi\) | |||||||
\(164\) | −6.02929 | −0.470809 | ||||||||
\(165\) | −6.71308 | −0.522612 | ||||||||
\(166\) | 9.06727 | 0.703756 | ||||||||
\(167\) | 15.4476 | 1.19537 | 0.597685 | − | 0.801731i | \(-0.296087\pi\) | ||||
0.597685 | + | 0.801731i | \(0.296087\pi\) | |||||||
\(168\) | −6.30914 | −0.486761 | ||||||||
\(169\) | −8.17321 | −0.628708 | ||||||||
\(170\) | 0.979040 | 0.0750890 | ||||||||
\(171\) | 4.55900 | 0.348635 | ||||||||
\(172\) | −5.21963 | −0.397993 | ||||||||
\(173\) | 23.8426 | 1.81272 | 0.906359 | − | 0.422508i | \(-0.138850\pi\) | ||||
0.906359 | + | 0.422508i | \(0.138850\pi\) | |||||||
\(174\) | 0.837548 | 0.0634943 | ||||||||
\(175\) | 7.29446 | 0.551409 | ||||||||
\(176\) | 7.51805 | 0.566694 | ||||||||
\(177\) | 14.2575 | 1.07166 | ||||||||
\(178\) | −5.38566 | −0.403672 | ||||||||
\(179\) | 11.4316 | 0.854436 | 0.427218 | − | 0.904149i | \(-0.359494\pi\) | ||||
0.427218 | + | 0.904149i | \(0.359494\pi\) | |||||||
\(180\) | 2.43731 | 0.181667 | ||||||||
\(181\) | 8.05109 | 0.598433 | 0.299216 | − | 0.954185i | \(-0.403275\pi\) | ||||
0.299216 | + | 0.954185i | \(0.403275\pi\) | |||||||
\(182\) | 3.85957 | 0.286090 | ||||||||
\(183\) | −2.49345 | −0.184321 | ||||||||
\(184\) | −16.8963 | −1.24561 | ||||||||
\(185\) | −6.45360 | −0.474478 | ||||||||
\(186\) | 3.73075 | 0.273552 | ||||||||
\(187\) | 4.38312 | 0.320525 | ||||||||
\(188\) | 8.86178 | 0.646312 | ||||||||
\(189\) | −2.74819 | −0.199902 | ||||||||
\(190\) | 4.46344 | 0.323812 | ||||||||
\(191\) | 9.52470 | 0.689183 | 0.344592 | − | 0.938753i | \(-0.388017\pi\) | ||||
0.344592 | + | 0.938753i | \(0.388017\pi\) | |||||||
\(192\) | 0.205472 | 0.0148287 | ||||||||
\(193\) | 6.09563 | 0.438773 | 0.219387 | − | 0.975638i | \(-0.429594\pi\) | ||||
0.219387 | + | 0.975638i | \(0.429594\pi\) | |||||||
\(194\) | −1.21900 | −0.0875195 | ||||||||
\(195\) | −3.36487 | −0.240963 | ||||||||
\(196\) | −0.879339 | −0.0628099 | ||||||||
\(197\) | 22.4157 | 1.59705 | 0.798527 | − | 0.601959i | \(-0.205613\pi\) | ||||
0.798527 | + | 0.601959i | \(0.205613\pi\) | |||||||
\(198\) | −2.80185 | −0.199119 | ||||||||
\(199\) | −1.68609 | −0.119524 | −0.0597620 | − | 0.998213i | \(-0.519034\pi\) | ||||
−0.0597620 | + | 0.998213i | \(0.519034\pi\) | |||||||
\(200\) | −6.09353 | −0.430877 | ||||||||
\(201\) | −0.208432 | −0.0147016 | ||||||||
\(202\) | 8.10983 | 0.570605 | ||||||||
\(203\) | 3.60077 | 0.252724 | ||||||||
\(204\) | −1.59138 | −0.111419 | ||||||||
\(205\) | −5.80273 | −0.405280 | ||||||||
\(206\) | −12.0806 | −0.841692 | ||||||||
\(207\) | −7.35985 | −0.511545 | ||||||||
\(208\) | 3.76835 | 0.261288 | ||||||||
\(209\) | 19.9826 | 1.38223 | ||||||||
\(210\) | −2.69059 | −0.185668 | ||||||||
\(211\) | −10.3572 | −0.713022 | −0.356511 | − | 0.934291i | \(-0.616034\pi\) | ||||
−0.356511 | + | 0.934291i | \(0.616034\pi\) | |||||||
\(212\) | 2.22826 | 0.153037 | ||||||||
\(213\) | 5.71350 | 0.391483 | ||||||||
\(214\) | 1.27828 | 0.0873814 | ||||||||
\(215\) | −5.02349 | −0.342599 | ||||||||
\(216\) | 2.29574 | 0.156205 | ||||||||
\(217\) | 16.0391 | 1.08881 | ||||||||
\(218\) | −11.8595 | −0.803230 | ||||||||
\(219\) | −1.55512 | −0.105086 | ||||||||
\(220\) | 10.6830 | 0.720250 | ||||||||
\(221\) | 2.19700 | 0.147786 | ||||||||
\(222\) | −2.69355 | −0.180779 | ||||||||
\(223\) | 2.90854 | 0.194771 | 0.0973853 | − | 0.995247i | \(-0.468952\pi\) | ||||
0.0973853 | + | 0.995247i | \(0.468952\pi\) | |||||||
\(224\) | 15.6315 | 1.04442 | ||||||||
\(225\) | −2.65427 | −0.176952 | ||||||||
\(226\) | 1.54980 | 0.103091 | ||||||||
\(227\) | 11.1090 | 0.737332 | 0.368666 | − | 0.929562i | \(-0.379815\pi\) | ||||
0.368666 | + | 0.929562i | \(0.379815\pi\) | |||||||
\(228\) | −7.25508 | −0.480479 | ||||||||
\(229\) | −10.3041 | −0.680916 | −0.340458 | − | 0.940260i | \(-0.610582\pi\) | ||||
−0.340458 | + | 0.940260i | \(0.610582\pi\) | |||||||
\(230\) | −7.20559 | −0.475123 | ||||||||
\(231\) | −12.0457 | −0.792546 | ||||||||
\(232\) | −3.00795 | −0.197482 | ||||||||
\(233\) | 6.98827 | 0.457817 | 0.228908 | − | 0.973448i | \(-0.426484\pi\) | ||||
0.228908 | + | 0.973448i | \(0.426484\pi\) | |||||||
\(234\) | −1.40440 | −0.0918086 | ||||||||
\(235\) | 8.52878 | 0.556356 | ||||||||
\(236\) | −22.6890 | −1.47693 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 1.75675 | 0.113873 | ||||||||
\(239\) | 15.5426 | 1.00537 | 0.502685 | − | 0.864470i | \(-0.332346\pi\) | ||||
0.502685 | + | 0.864470i | \(0.332346\pi\) | |||||||
\(240\) | −2.62700 | −0.169572 | ||||||||
\(241\) | −6.67896 | −0.430229 | −0.215115 | − | 0.976589i | \(-0.569013\pi\) | ||||
−0.215115 | + | 0.976589i | \(0.569013\pi\) | |||||||
\(242\) | −5.24923 | −0.337434 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.96801 | 0.254026 | ||||||||
\(245\) | −0.846296 | −0.0540678 | ||||||||
\(246\) | −2.42190 | −0.154415 | ||||||||
\(247\) | 10.0161 | 0.637309 | ||||||||
\(248\) | −13.3985 | −0.850806 | ||||||||
\(249\) | −14.1845 | −0.898907 | ||||||||
\(250\) | −7.49384 | −0.473952 | ||||||||
\(251\) | 28.7096 | 1.81213 | 0.906067 | − | 0.423135i | \(-0.139070\pi\) | ||||
0.906067 | + | 0.423135i | \(0.139070\pi\) | |||||||
\(252\) | 4.37341 | 0.275499 | ||||||||
\(253\) | −32.2591 | −2.02811 | ||||||||
\(254\) | 2.47755 | 0.155455 | ||||||||
\(255\) | −1.53158 | −0.0959110 | ||||||||
\(256\) | −7.59884 | −0.474928 | ||||||||
\(257\) | −3.46899 | −0.216389 | −0.108195 | − | 0.994130i | \(-0.534507\pi\) | ||||
−0.108195 | + | 0.994130i | \(0.534507\pi\) | |||||||
\(258\) | −2.09666 | −0.130533 | ||||||||
\(259\) | −11.5801 | −0.719549 | ||||||||
\(260\) | 5.35477 | 0.332089 | ||||||||
\(261\) | −1.31023 | −0.0811012 | ||||||||
\(262\) | 1.30657 | 0.0807203 | ||||||||
\(263\) | −26.4058 | −1.62825 | −0.814124 | − | 0.580690i | \(-0.802783\pi\) | ||||
−0.814124 | + | 0.580690i | \(0.802783\pi\) | |||||||
\(264\) | 10.0625 | 0.619304 | ||||||||
\(265\) | 2.14453 | 0.131737 | ||||||||
\(266\) | 8.00900 | 0.491064 | ||||||||
\(267\) | 8.42513 | 0.515610 | ||||||||
\(268\) | 0.331693 | 0.0202614 | ||||||||
\(269\) | 28.2967 | 1.72528 | 0.862639 | − | 0.505820i | \(-0.168810\pi\) | ||||
0.862639 | + | 0.505820i | \(0.168810\pi\) | |||||||
\(270\) | 0.979040 | 0.0595825 | ||||||||
\(271\) | −6.19456 | −0.376292 | −0.188146 | − | 0.982141i | \(-0.560248\pi\) | ||||
−0.188146 | + | 0.982141i | \(0.560248\pi\) | |||||||
\(272\) | 1.71523 | 0.104001 | ||||||||
\(273\) | −6.03777 | −0.365422 | ||||||||
\(274\) | −7.64284 | −0.461721 | ||||||||
\(275\) | −11.6340 | −0.701556 | ||||||||
\(276\) | 11.7123 | 0.704997 | ||||||||
\(277\) | −8.05092 | −0.483733 | −0.241866 | − | 0.970310i | \(-0.577760\pi\) | ||||
−0.241866 | + | 0.970310i | \(0.577760\pi\) | |||||||
\(278\) | −10.1220 | −0.607078 | ||||||||
\(279\) | −5.83625 | −0.349407 | ||||||||
\(280\) | 9.66293 | 0.577470 | ||||||||
\(281\) | 20.6325 | 1.23083 | 0.615415 | − | 0.788203i | \(-0.288988\pi\) | ||||
0.615415 | + | 0.788203i | \(0.288988\pi\) | |||||||
\(282\) | 3.55967 | 0.211975 | ||||||||
\(283\) | 29.1318 | 1.73170 | 0.865852 | − | 0.500301i | \(-0.166777\pi\) | ||||
0.865852 | + | 0.500301i | \(0.166777\pi\) | |||||||
\(284\) | −9.09233 | −0.539531 | ||||||||
\(285\) | −6.98245 | −0.413605 | ||||||||
\(286\) | −6.15566 | −0.363992 | ||||||||
\(287\) | −10.4122 | −0.614611 | ||||||||
\(288\) | −5.68792 | −0.335164 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.28277 | −0.0753268 | ||||||||
\(291\) | 1.90697 | 0.111788 | ||||||||
\(292\) | 2.47479 | 0.144826 | ||||||||
\(293\) | −13.6054 | −0.794833 | −0.397417 | − | 0.917638i | \(-0.630093\pi\) | ||||
−0.397417 | + | 0.917638i | \(0.630093\pi\) | |||||||
\(294\) | −0.353220 | −0.0206002 | ||||||||
\(295\) | −21.8364 | −1.27136 | ||||||||
\(296\) | 9.67356 | 0.562264 | ||||||||
\(297\) | 4.38312 | 0.254334 | ||||||||
\(298\) | 1.86924 | 0.108282 | ||||||||
\(299\) | −16.1696 | −0.935110 | ||||||||
\(300\) | 4.22395 | 0.243870 | ||||||||
\(301\) | −9.01392 | −0.519554 | ||||||||
\(302\) | −3.52466 | −0.202822 | ||||||||
\(303\) | −12.6867 | −0.728833 | ||||||||
\(304\) | 7.81972 | 0.448492 | ||||||||
\(305\) | 3.81890 | 0.218670 | ||||||||
\(306\) | −0.639237 | −0.0365428 | ||||||||
\(307\) | −2.41280 | −0.137706 | −0.0688530 | − | 0.997627i | \(-0.521934\pi\) | ||||
−0.0688530 | + | 0.997627i | \(0.521934\pi\) | |||||||
\(308\) | 19.1692 | 1.09226 | ||||||||
\(309\) | 18.8984 | 1.07509 | ||||||||
\(310\) | −5.71392 | −0.324529 | ||||||||
\(311\) | 9.07562 | 0.514631 | 0.257316 | − | 0.966327i | \(-0.417162\pi\) | ||||
0.257316 | + | 0.966327i | \(0.417162\pi\) | |||||||
\(312\) | 5.04373 | 0.285545 | ||||||||
\(313\) | −19.7211 | −1.11470 | −0.557351 | − | 0.830277i | \(-0.688182\pi\) | ||||
−0.557351 | + | 0.830277i | \(0.688182\pi\) | |||||||
\(314\) | 12.0754 | 0.681452 | ||||||||
\(315\) | 4.20907 | 0.237154 | ||||||||
\(316\) | −1.59138 | −0.0895219 | ||||||||
\(317\) | 5.46386 | 0.306881 | 0.153441 | − | 0.988158i | \(-0.450965\pi\) | ||||
0.153441 | + | 0.988158i | \(0.450965\pi\) | |||||||
\(318\) | 0.895065 | 0.0501928 | ||||||||
\(319\) | −5.74289 | −0.321540 | ||||||||
\(320\) | −0.314696 | −0.0175921 | ||||||||
\(321\) | −1.99970 | −0.111612 | ||||||||
\(322\) | −12.9294 | −0.720527 | ||||||||
\(323\) | 4.55900 | 0.253669 | ||||||||
\(324\) | −1.59138 | −0.0884098 | ||||||||
\(325\) | −5.83143 | −0.323470 | ||||||||
\(326\) | 0.0846933 | 0.00469073 | ||||||||
\(327\) | 18.5527 | 1.02596 | ||||||||
\(328\) | 8.69794 | 0.480264 | ||||||||
\(329\) | 15.3037 | 0.843718 | ||||||||
\(330\) | 4.29125 | 0.236225 | ||||||||
\(331\) | −6.21216 | −0.341451 | −0.170726 | − | 0.985319i | \(-0.554611\pi\) | ||||
−0.170726 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(332\) | 22.5729 | 1.23885 | ||||||||
\(333\) | 4.21370 | 0.230909 | ||||||||
\(334\) | −9.87467 | −0.540318 | ||||||||
\(335\) | 0.319229 | 0.0174413 | ||||||||
\(336\) | −4.71378 | −0.257158 | ||||||||
\(337\) | 28.9127 | 1.57498 | 0.787489 | − | 0.616329i | \(-0.211381\pi\) | ||||
0.787489 | + | 0.616329i | \(0.211381\pi\) | |||||||
\(338\) | 5.22462 | 0.284182 | ||||||||
\(339\) | −2.42445 | −0.131678 | ||||||||
\(340\) | 2.43731 | 0.132182 | ||||||||
\(341\) | −25.5810 | −1.38529 | ||||||||
\(342\) | −2.91428 | −0.157586 | ||||||||
\(343\) | 17.7188 | 0.956725 | ||||||||
\(344\) | 7.52991 | 0.405985 | ||||||||
\(345\) | 11.2722 | 0.606873 | ||||||||
\(346\) | −15.2411 | −0.819365 | ||||||||
\(347\) | −7.99135 | −0.428998 | −0.214499 | − | 0.976724i | \(-0.568812\pi\) | ||||
−0.214499 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(348\) | 2.08507 | 0.111771 | ||||||||
\(349\) | −6.34237 | −0.339499 | −0.169750 | − | 0.985487i | \(-0.554296\pi\) | ||||
−0.169750 | + | 0.985487i | \(0.554296\pi\) | |||||||
\(350\) | −4.66289 | −0.249242 | ||||||||
\(351\) | 2.19700 | 0.117267 | ||||||||
\(352\) | −24.9308 | −1.32882 | ||||||||
\(353\) | −10.2365 | −0.544836 | −0.272418 | − | 0.962179i | \(-0.587823\pi\) | ||||
−0.272418 | + | 0.962179i | \(0.587823\pi\) | |||||||
\(354\) | −9.11389 | −0.484398 | ||||||||
\(355\) | −8.75066 | −0.464437 | ||||||||
\(356\) | −13.4076 | −0.710599 | ||||||||
\(357\) | −2.74819 | −0.145450 | ||||||||
\(358\) | −7.30749 | −0.386213 | ||||||||
\(359\) | 21.7170 | 1.14618 | 0.573089 | − | 0.819493i | \(-0.305745\pi\) | ||||
0.573089 | + | 0.819493i | \(0.305745\pi\) | |||||||
\(360\) | −3.51610 | −0.185315 | ||||||||
\(361\) | 1.78445 | 0.0939183 | ||||||||
\(362\) | −5.14656 | −0.270497 | ||||||||
\(363\) | 8.21172 | 0.431003 | ||||||||
\(364\) | 9.60836 | 0.503615 | ||||||||
\(365\) | 2.38179 | 0.124669 | ||||||||
\(366\) | 1.59390 | 0.0833146 | ||||||||
\(367\) | −29.6223 | −1.54627 | −0.773135 | − | 0.634242i | \(-0.781312\pi\) | ||||
−0.773135 | + | 0.634242i | \(0.781312\pi\) | |||||||
\(368\) | −12.6238 | −0.658063 | ||||||||
\(369\) | 3.78873 | 0.197233 | ||||||||
\(370\) | 4.12538 | 0.214468 | ||||||||
\(371\) | 3.84804 | 0.199780 | ||||||||
\(372\) | 9.28766 | 0.481543 | ||||||||
\(373\) | −27.0448 | −1.40032 | −0.700162 | − | 0.713984i | \(-0.746889\pi\) | ||||
−0.700162 | + | 0.713984i | \(0.746889\pi\) | |||||||
\(374\) | −2.80185 | −0.144880 | ||||||||
\(375\) | 11.7231 | 0.605379 | ||||||||
\(376\) | −12.7841 | −0.659291 | ||||||||
\(377\) | −2.87857 | −0.148254 | ||||||||
\(378\) | 1.75675 | 0.0903573 | ||||||||
\(379\) | −3.69238 | −0.189665 | −0.0948325 | − | 0.995493i | \(-0.530232\pi\) | ||||
−0.0948325 | + | 0.995493i | \(0.530232\pi\) | |||||||
\(380\) | 11.1117 | 0.570018 | ||||||||
\(381\) | −3.87578 | −0.198562 | ||||||||
\(382\) | −6.08854 | −0.311517 | ||||||||
\(383\) | −38.5338 | −1.96899 | −0.984493 | − | 0.175425i | \(-0.943870\pi\) | ||||
−0.984493 | + | 0.175425i | \(0.943870\pi\) | |||||||
\(384\) | 11.2445 | 0.573818 | ||||||||
\(385\) | 18.4488 | 0.940240 | ||||||||
\(386\) | −3.89655 | −0.198329 | ||||||||
\(387\) | 3.27995 | 0.166729 | ||||||||
\(388\) | −3.03470 | −0.154064 | ||||||||
\(389\) | 14.4916 | 0.734755 | 0.367378 | − | 0.930072i | \(-0.380256\pi\) | ||||
0.367378 | + | 0.930072i | \(0.380256\pi\) | |||||||
\(390\) | 2.15095 | 0.108917 | ||||||||
\(391\) | −7.35985 | −0.372204 | ||||||||
\(392\) | 1.26855 | 0.0640713 | ||||||||
\(393\) | −2.04395 | −0.103104 | ||||||||
\(394\) | −14.3290 | −0.721883 | ||||||||
\(395\) | −1.53158 | −0.0770620 | ||||||||
\(396\) | −6.97519 | −0.350516 | ||||||||
\(397\) | −8.04317 | −0.403675 | −0.201837 | − | 0.979419i | \(-0.564691\pi\) | ||||
−0.201837 | + | 0.979419i | \(0.564691\pi\) | |||||||
\(398\) | 1.07781 | 0.0540260 | ||||||||
\(399\) | −12.5290 | −0.627235 | ||||||||
\(400\) | −4.55269 | −0.227634 | ||||||||
\(401\) | 33.2791 | 1.66188 | 0.830939 | − | 0.556363i | \(-0.187804\pi\) | ||||
0.830939 | + | 0.556363i | \(0.187804\pi\) | |||||||
\(402\) | 0.133237 | 0.00664527 | ||||||||
\(403\) | −12.8222 | −0.638720 | ||||||||
\(404\) | 20.1893 | 1.00446 | ||||||||
\(405\) | −1.53158 | −0.0761046 | ||||||||
\(406\) | −2.30174 | −0.114234 | ||||||||
\(407\) | 18.4691 | 0.915481 | ||||||||
\(408\) | 2.29574 | 0.113656 | ||||||||
\(409\) | 21.9818 | 1.08693 | 0.543466 | − | 0.839431i | \(-0.317112\pi\) | ||||
0.543466 | + | 0.839431i | \(0.317112\pi\) | |||||||
\(410\) | 3.70932 | 0.183190 | ||||||||
\(411\) | 11.9562 | 0.589755 | ||||||||
\(412\) | −30.0745 | −1.48166 | ||||||||
\(413\) | −39.1822 | −1.92803 | ||||||||
\(414\) | 4.70469 | 0.231223 | ||||||||
\(415\) | 21.7247 | 1.06642 | ||||||||
\(416\) | −12.4963 | −0.612683 | ||||||||
\(417\) | 15.8345 | 0.775420 | ||||||||
\(418\) | −12.7736 | −0.624779 | ||||||||
\(419\) | −0.856858 | −0.0418602 | −0.0209301 | − | 0.999781i | \(-0.506663\pi\) | ||||
−0.0209301 | + | 0.999781i | \(0.506663\pi\) | |||||||
\(420\) | −6.69821 | −0.326839 | ||||||||
\(421\) | −30.9844 | −1.51009 | −0.755043 | − | 0.655675i | \(-0.772384\pi\) | ||||
−0.755043 | + | 0.655675i | \(0.772384\pi\) | |||||||
\(422\) | 6.62074 | 0.322292 | ||||||||
\(423\) | −5.56863 | −0.270756 | ||||||||
\(424\) | −3.21451 | −0.156111 | ||||||||
\(425\) | −2.65427 | −0.128751 | ||||||||
\(426\) | −3.65228 | −0.176954 | ||||||||
\(427\) | 6.85247 | 0.331614 | ||||||||
\(428\) | 3.18227 | 0.153821 | ||||||||
\(429\) | 9.62969 | 0.464926 | ||||||||
\(430\) | 3.21120 | 0.154858 | ||||||||
\(431\) | 32.3595 | 1.55870 | 0.779351 | − | 0.626587i | \(-0.215549\pi\) | ||||
0.779351 | + | 0.626587i | \(0.215549\pi\) | |||||||
\(432\) | 1.71523 | 0.0825240 | ||||||||
\(433\) | 2.15428 | 0.103528 | 0.0517640 | − | 0.998659i | \(-0.483516\pi\) | ||||
0.0517640 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(434\) | −10.2528 | −0.492151 | ||||||||
\(435\) | 2.00672 | 0.0962147 | ||||||||
\(436\) | −29.5242 | −1.41395 | ||||||||
\(437\) | −33.5535 | −1.60508 | ||||||||
\(438\) | 0.994093 | 0.0474996 | ||||||||
\(439\) | −31.0399 | −1.48145 | −0.740727 | − | 0.671806i | \(-0.765519\pi\) | ||||
−0.740727 | + | 0.671806i | \(0.765519\pi\) | |||||||
\(440\) | −15.4115 | −0.734714 | ||||||||
\(441\) | 0.552565 | 0.0263126 | ||||||||
\(442\) | −1.40440 | −0.0668006 | ||||||||
\(443\) | −12.8171 | −0.608960 | −0.304480 | − | 0.952519i | \(-0.598483\pi\) | ||||
−0.304480 | + | 0.952519i | \(0.598483\pi\) | |||||||
\(444\) | −6.70557 | −0.318232 | ||||||||
\(445\) | −12.9037 | −0.611696 | ||||||||
\(446\) | −1.85925 | −0.0880380 | ||||||||
\(447\) | −2.92417 | −0.138309 | ||||||||
\(448\) | −0.564677 | −0.0266785 | ||||||||
\(449\) | 17.0630 | 0.805251 | 0.402626 | − | 0.915365i | \(-0.368098\pi\) | ||||
0.402626 | + | 0.915365i | \(0.368098\pi\) | |||||||
\(450\) | 1.69671 | 0.0799837 | ||||||||
\(451\) | 16.6064 | 0.781967 | ||||||||
\(452\) | 3.85821 | 0.181475 | ||||||||
\(453\) | 5.51386 | 0.259064 | ||||||||
\(454\) | −7.10130 | −0.333281 | ||||||||
\(455\) | 9.24730 | 0.433520 | ||||||||
\(456\) | 10.4663 | 0.490128 | ||||||||
\(457\) | 21.2560 | 0.994313 | 0.497157 | − | 0.867661i | \(-0.334377\pi\) | ||||
0.497157 | + | 0.867661i | \(0.334377\pi\) | |||||||
\(458\) | 6.58678 | 0.307780 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −17.9383 | −0.836376 | ||||||||
\(461\) | −3.89040 | −0.181194 | −0.0905970 | − | 0.995888i | \(-0.528878\pi\) | ||||
−0.0905970 | + | 0.995888i | \(0.528878\pi\) | |||||||
\(462\) | 7.70003 | 0.358238 | ||||||||
\(463\) | 21.5731 | 1.00259 | 0.501294 | − | 0.865277i | \(-0.332857\pi\) | ||||
0.501294 | + | 0.865277i | \(0.332857\pi\) | |||||||
\(464\) | −2.24734 | −0.104330 | ||||||||
\(465\) | 8.93866 | 0.414520 | ||||||||
\(466\) | −4.46716 | −0.206937 | ||||||||
\(467\) | −8.01654 | −0.370961 | −0.185481 | − | 0.982648i | \(-0.559384\pi\) | ||||
−0.185481 | + | 0.982648i | \(0.559384\pi\) | |||||||
\(468\) | −3.49625 | −0.161614 | ||||||||
\(469\) | 0.572810 | 0.0264499 | ||||||||
\(470\) | −5.45191 | −0.251478 | ||||||||
\(471\) | −18.8903 | −0.870417 | ||||||||
\(472\) | 32.7314 | 1.50659 | ||||||||
\(473\) | 14.3764 | 0.661027 | ||||||||
\(474\) | −0.639237 | −0.0293611 | ||||||||
\(475\) | −12.1008 | −0.555224 | ||||||||
\(476\) | 4.37341 | 0.200455 | ||||||||
\(477\) | −1.40021 | −0.0641111 | ||||||||
\(478\) | −9.93544 | −0.454436 | ||||||||
\(479\) | 12.0584 | 0.550963 | 0.275482 | − | 0.961306i | \(-0.411163\pi\) | ||||
0.275482 | + | 0.961306i | \(0.411163\pi\) | |||||||
\(480\) | 8.71148 | 0.397623 | ||||||||
\(481\) | 9.25747 | 0.422104 | ||||||||
\(482\) | 4.26944 | 0.194468 | ||||||||
\(483\) | 20.2263 | 0.920328 | ||||||||
\(484\) | −13.0679 | −0.593997 | ||||||||
\(485\) | −2.92067 | −0.132621 | ||||||||
\(486\) | −0.639237 | −0.0289964 | ||||||||
\(487\) | −8.21823 | −0.372404 | −0.186202 | − | 0.982512i | \(-0.559618\pi\) | ||||
−0.186202 | + | 0.982512i | \(0.559618\pi\) | |||||||
\(488\) | −5.72430 | −0.259127 | ||||||||
\(489\) | −0.132491 | −0.00599146 | ||||||||
\(490\) | 0.540984 | 0.0244391 | ||||||||
\(491\) | −11.6895 | −0.527539 | −0.263770 | − | 0.964586i | \(-0.584966\pi\) | ||||
−0.263770 | + | 0.964586i | \(0.584966\pi\) | |||||||
\(492\) | −6.02929 | −0.271822 | ||||||||
\(493\) | −1.31023 | −0.0590098 | ||||||||
\(494\) | −6.40266 | −0.288069 | ||||||||
\(495\) | −6.71308 | −0.301730 | ||||||||
\(496\) | −10.0105 | −0.449485 | ||||||||
\(497\) | −15.7018 | −0.704322 | ||||||||
\(498\) | 9.06727 | 0.406314 | ||||||||
\(499\) | 21.1973 | 0.948920 | 0.474460 | − | 0.880277i | \(-0.342643\pi\) | ||||
0.474460 | + | 0.880277i | \(0.342643\pi\) | |||||||
\(500\) | −18.6559 | −0.834316 | ||||||||
\(501\) | 15.4476 | 0.690147 | ||||||||
\(502\) | −18.3522 | −0.819100 | ||||||||
\(503\) | 14.8819 | 0.663553 | 0.331776 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331776 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(504\) | −6.30914 | −0.281031 | ||||||||
\(505\) | 19.4307 | 0.864654 | ||||||||
\(506\) | 20.6212 | 0.916725 | ||||||||
\(507\) | −8.17321 | −0.362985 | ||||||||
\(508\) | 6.16783 | 0.273653 | ||||||||
\(509\) | 25.5199 | 1.13115 | 0.565575 | − | 0.824697i | \(-0.308654\pi\) | ||||
0.565575 | + | 0.824697i | \(0.308654\pi\) | |||||||
\(510\) | 0.979040 | 0.0433526 | ||||||||
\(511\) | 4.27378 | 0.189061 | ||||||||
\(512\) | −17.6315 | −0.779211 | ||||||||
\(513\) | 4.55900 | 0.201285 | ||||||||
\(514\) | 2.21751 | 0.0978100 | ||||||||
\(515\) | −28.9443 | −1.27544 | ||||||||
\(516\) | −5.21963 | −0.229781 | ||||||||
\(517\) | −24.4079 | −1.07346 | ||||||||
\(518\) | 7.40240 | 0.325243 | ||||||||
\(519\) | 23.8426 | 1.04657 | ||||||||
\(520\) | −7.72486 | −0.338758 | ||||||||
\(521\) | −18.9658 | −0.830908 | −0.415454 | − | 0.909614i | \(-0.636377\pi\) | ||||
−0.415454 | + | 0.909614i | \(0.636377\pi\) | |||||||
\(522\) | 0.837548 | 0.0366585 | ||||||||
\(523\) | −29.6697 | −1.29736 | −0.648682 | − | 0.761060i | \(-0.724679\pi\) | ||||
−0.648682 | + | 0.761060i | \(0.724679\pi\) | |||||||
\(524\) | 3.25270 | 0.142095 | ||||||||
\(525\) | 7.29446 | 0.318356 | ||||||||
\(526\) | 16.8795 | 0.735983 | ||||||||
\(527\) | −5.83625 | −0.254231 | ||||||||
\(528\) | 7.51805 | 0.327181 | ||||||||
\(529\) | 31.1674 | 1.35510 | ||||||||
\(530\) | −1.37086 | −0.0595464 | ||||||||
\(531\) | 14.2575 | 0.618721 | ||||||||
\(532\) | 19.9384 | 0.864437 | ||||||||
\(533\) | 8.32382 | 0.360545 | ||||||||
\(534\) | −5.38566 | −0.233060 | ||||||||
\(535\) | 3.06269 | 0.132412 | ||||||||
\(536\) | −0.478505 | −0.0206683 | ||||||||
\(537\) | 11.4316 | 0.493309 | ||||||||
\(538\) | −18.0883 | −0.779841 | ||||||||
\(539\) | 2.42196 | 0.104321 | ||||||||
\(540\) | 2.43731 | 0.104885 | ||||||||
\(541\) | −11.5696 | −0.497418 | −0.248709 | − | 0.968578i | \(-0.580006\pi\) | ||||
−0.248709 | + | 0.968578i | \(0.580006\pi\) | |||||||
\(542\) | 3.95979 | 0.170088 | ||||||||
\(543\) | 8.05109 | 0.345505 | ||||||||
\(544\) | −5.68792 | −0.243868 | ||||||||
\(545\) | −28.4148 | −1.21716 | ||||||||
\(546\) | 3.85957 | 0.165174 | ||||||||
\(547\) | −0.0317545 | −0.00135772 | −0.000678862 | − | 1.00000i | \(-0.500216\pi\) | ||||
−0.000678862 | 1.00000i | \(0.500216\pi\) | ||||||||
\(548\) | −19.0268 | −0.812784 | ||||||||
\(549\) | −2.49345 | −0.106418 | ||||||||
\(550\) | 7.43688 | 0.317110 | ||||||||
\(551\) | −5.97334 | −0.254473 | ||||||||
\(552\) | −16.8963 | −0.719155 | ||||||||
\(553\) | −2.74819 | −0.116865 | ||||||||
\(554\) | 5.14645 | 0.218652 | ||||||||
\(555\) | −6.45360 | −0.273940 | ||||||||
\(556\) | −25.1987 | −1.06866 | ||||||||
\(557\) | −31.4076 | −1.33078 | −0.665391 | − | 0.746495i | \(-0.731735\pi\) | ||||
−0.665391 | + | 0.746495i | \(0.731735\pi\) | |||||||
\(558\) | 3.73075 | 0.157935 | ||||||||
\(559\) | 7.20603 | 0.304782 | ||||||||
\(560\) | 7.21951 | 0.305080 | ||||||||
\(561\) | 4.38312 | 0.185055 | ||||||||
\(562\) | −13.1890 | −0.556346 | ||||||||
\(563\) | −29.5588 | −1.24576 | −0.622878 | − | 0.782319i | \(-0.714037\pi\) | ||||
−0.622878 | + | 0.782319i | \(0.714037\pi\) | |||||||
\(564\) | 8.86178 | 0.373148 | ||||||||
\(565\) | 3.71323 | 0.156217 | ||||||||
\(566\) | −18.6221 | −0.782745 | ||||||||
\(567\) | −2.74819 | −0.115413 | ||||||||
\(568\) | 13.1167 | 0.550365 | ||||||||
\(569\) | 27.3442 | 1.14633 | 0.573163 | − | 0.819441i | \(-0.305716\pi\) | ||||
0.573163 | + | 0.819441i | \(0.305716\pi\) | |||||||
\(570\) | 4.46344 | 0.186953 | ||||||||
\(571\) | −31.5959 | −1.32225 | −0.661124 | − | 0.750277i | \(-0.729920\pi\) | ||||
−0.661124 | + | 0.750277i | \(0.729920\pi\) | |||||||
\(572\) | −15.3245 | −0.640748 | ||||||||
\(573\) | 9.52470 | 0.397900 | ||||||||
\(574\) | 6.65584 | 0.277809 | ||||||||
\(575\) | 19.5351 | 0.814668 | ||||||||
\(576\) | 0.205472 | 0.00856134 | ||||||||
\(577\) | 25.2670 | 1.05188 | 0.525940 | − | 0.850522i | \(-0.323714\pi\) | ||||
0.525940 | + | 0.850522i | \(0.323714\pi\) | |||||||
\(578\) | −0.639237 | −0.0265888 | ||||||||
\(579\) | 6.09563 | 0.253326 | ||||||||
\(580\) | −3.19344 | −0.132600 | ||||||||
\(581\) | 38.9818 | 1.61724 | ||||||||
\(582\) | −1.21900 | −0.0505294 | ||||||||
\(583\) | −6.13728 | −0.254180 | ||||||||
\(584\) | −3.57016 | −0.147734 | ||||||||
\(585\) | −3.36487 | −0.139120 | ||||||||
\(586\) | 8.69705 | 0.359272 | ||||||||
\(587\) | 44.1293 | 1.82141 | 0.910705 | − | 0.413057i | \(-0.135539\pi\) | ||||
0.910705 | + | 0.413057i | \(0.135539\pi\) | |||||||
\(588\) | −0.879339 | −0.0362633 | ||||||||
\(589\) | −26.6074 | −1.09634 | ||||||||
\(590\) | 13.9586 | 0.574667 | ||||||||
\(591\) | 22.4157 | 0.922060 | ||||||||
\(592\) | 7.22745 | 0.297047 | ||||||||
\(593\) | −0.859655 | −0.0353018 | −0.0176509 | − | 0.999844i | \(-0.505619\pi\) | ||||
−0.0176509 | + | 0.999844i | \(0.505619\pi\) | |||||||
\(594\) | −2.80185 | −0.114961 | ||||||||
\(595\) | 4.20907 | 0.172555 | ||||||||
\(596\) | 4.65346 | 0.190613 | ||||||||
\(597\) | −1.68609 | −0.0690073 | ||||||||
\(598\) | 10.3362 | 0.422678 | ||||||||
\(599\) | 8.77920 | 0.358708 | 0.179354 | − | 0.983785i | \(-0.442599\pi\) | ||||
0.179354 | + | 0.983785i | \(0.442599\pi\) | |||||||
\(600\) | −6.09353 | −0.248767 | ||||||||
\(601\) | −28.3246 | −1.15539 | −0.577693 | − | 0.816254i | \(-0.696047\pi\) | ||||
−0.577693 | + | 0.816254i | \(0.696047\pi\) | |||||||
\(602\) | 5.76204 | 0.234843 | ||||||||
\(603\) | −0.208432 | −0.00848799 | ||||||||
\(604\) | −8.77462 | −0.357034 | ||||||||
\(605\) | −12.5769 | −0.511322 | ||||||||
\(606\) | 8.10983 | 0.329439 | ||||||||
\(607\) | −0.208548 | −0.00846471 | −0.00423236 | − | 0.999991i | \(-0.501347\pi\) | ||||
−0.00423236 | + | 0.999991i | \(0.501347\pi\) | |||||||
\(608\) | −25.9312 | −1.05165 | ||||||||
\(609\) | 3.60077 | 0.145910 | ||||||||
\(610\) | −2.44118 | −0.0988406 | ||||||||
\(611\) | −12.2342 | −0.494945 | ||||||||
\(612\) | −1.59138 | −0.0643276 | ||||||||
\(613\) | −18.9206 | −0.764197 | −0.382098 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382098 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(614\) | 1.54235 | 0.0622443 | ||||||||
\(615\) | −5.80273 | −0.233989 | ||||||||
\(616\) | −27.6537 | −1.11420 | ||||||||
\(617\) | 1.74435 | 0.0702249 | 0.0351125 | − | 0.999383i | \(-0.488821\pi\) | ||||
0.0351125 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(618\) | −12.0806 | −0.485951 | ||||||||
\(619\) | 35.0971 | 1.41067 | 0.705335 | − | 0.708874i | \(-0.250796\pi\) | ||||
0.705335 | + | 0.708874i | \(0.250796\pi\) | |||||||
\(620\) | −14.2248 | −0.571280 | ||||||||
\(621\) | −7.35985 | −0.295341 | ||||||||
\(622\) | −5.80147 | −0.232618 | ||||||||
\(623\) | −23.1539 | −0.927641 | ||||||||
\(624\) | 3.76835 | 0.150855 | ||||||||
\(625\) | −4.68345 | −0.187338 | ||||||||
\(626\) | 12.6065 | 0.503855 | ||||||||
\(627\) | 19.9826 | 0.798029 | ||||||||
\(628\) | 30.0615 | 1.19958 | ||||||||
\(629\) | 4.21370 | 0.168011 | ||||||||
\(630\) | −2.69059 | −0.107196 | ||||||||
\(631\) | 13.6340 | 0.542762 | 0.271381 | − | 0.962472i | \(-0.412520\pi\) | ||||
0.271381 | + | 0.962472i | \(0.412520\pi\) | |||||||
\(632\) | 2.29574 | 0.0913197 | ||||||||
\(633\) | −10.3572 | −0.411664 | ||||||||
\(634\) | −3.49270 | −0.138713 | ||||||||
\(635\) | 5.93606 | 0.235565 | ||||||||
\(636\) | 2.22826 | 0.0883561 | ||||||||
\(637\) | 1.21398 | 0.0480998 | ||||||||
\(638\) | 3.67107 | 0.145339 | ||||||||
\(639\) | 5.71350 | 0.226023 | ||||||||
\(640\) | −17.2218 | −0.680751 | ||||||||
\(641\) | 38.0087 | 1.50125 | 0.750627 | − | 0.660726i | \(-0.229751\pi\) | ||||
0.750627 | + | 0.660726i | \(0.229751\pi\) | |||||||
\(642\) | 1.27828 | 0.0504497 | ||||||||
\(643\) | 34.8705 | 1.37516 | 0.687579 | − | 0.726110i | \(-0.258673\pi\) | ||||
0.687579 | + | 0.726110i | \(0.258673\pi\) | |||||||
\(644\) | −32.1876 | −1.26837 | ||||||||
\(645\) | −5.02349 | −0.197800 | ||||||||
\(646\) | −2.91428 | −0.114661 | ||||||||
\(647\) | 8.31044 | 0.326717 | 0.163359 | − | 0.986567i | \(-0.447767\pi\) | ||||
0.163359 | + | 0.986567i | \(0.447767\pi\) | |||||||
\(648\) | 2.29574 | 0.0901852 | ||||||||
\(649\) | 62.4921 | 2.45303 | ||||||||
\(650\) | 3.72767 | 0.146211 | ||||||||
\(651\) | 16.0391 | 0.628623 | ||||||||
\(652\) | 0.210843 | 0.00825726 | ||||||||
\(653\) | 34.1786 | 1.33751 | 0.668757 | − | 0.743481i | \(-0.266827\pi\) | ||||
0.668757 | + | 0.743481i | \(0.266827\pi\) | |||||||
\(654\) | −11.8595 | −0.463745 | ||||||||
\(655\) | 3.13047 | 0.122318 | ||||||||
\(656\) | 6.49854 | 0.253725 | ||||||||
\(657\) | −1.55512 | −0.0606712 | ||||||||
\(658\) | −9.78267 | −0.381368 | ||||||||
\(659\) | −35.6527 | −1.38883 | −0.694416 | − | 0.719574i | \(-0.744337\pi\) | ||||
−0.694416 | + | 0.719574i | \(0.744337\pi\) | |||||||
\(660\) | 10.6830 | 0.415836 | ||||||||
\(661\) | 15.7411 | 0.612256 | 0.306128 | − | 0.951990i | \(-0.400966\pi\) | ||||
0.306128 | + | 0.951990i | \(0.400966\pi\) | |||||||
\(662\) | 3.97104 | 0.154339 | ||||||||
\(663\) | 2.19700 | 0.0853242 | ||||||||
\(664\) | −32.5640 | −1.26373 | ||||||||
\(665\) | 19.1891 | 0.744122 | ||||||||
\(666\) | −2.69355 | −0.104373 | ||||||||
\(667\) | 9.64310 | 0.373382 | ||||||||
\(668\) | −24.5829 | −0.951141 | ||||||||
\(669\) | 2.90854 | 0.112451 | ||||||||
\(670\) | −0.204063 | −0.00788364 | ||||||||
\(671\) | −10.9291 | −0.421912 | ||||||||
\(672\) | 15.6315 | 0.602998 | ||||||||
\(673\) | 44.9580 | 1.73301 | 0.866503 | − | 0.499173i | \(-0.166363\pi\) | ||||
0.866503 | + | 0.499173i | \(0.166363\pi\) | |||||||
\(674\) | −18.4821 | −0.711904 | ||||||||
\(675\) | −2.65427 | −0.102163 | ||||||||
\(676\) | 13.0066 | 0.500256 | ||||||||
\(677\) | 11.5958 | 0.445662 | 0.222831 | − | 0.974857i | \(-0.428470\pi\) | ||||
0.222831 | + | 0.974857i | \(0.428470\pi\) | |||||||
\(678\) | 1.54980 | 0.0595197 | ||||||||
\(679\) | −5.24072 | −0.201120 | ||||||||
\(680\) | −3.51610 | −0.134836 | ||||||||
\(681\) | 11.1090 | 0.425699 | ||||||||
\(682\) | 16.3523 | 0.626162 | ||||||||
\(683\) | 12.6798 | 0.485177 | 0.242589 | − | 0.970129i | \(-0.422003\pi\) | ||||
0.242589 | + | 0.970129i | \(0.422003\pi\) | |||||||
\(684\) | −7.25508 | −0.277405 | ||||||||
\(685\) | −18.3118 | −0.699658 | ||||||||
\(686\) | −11.3265 | −0.432448 | ||||||||
\(687\) | −10.3041 | −0.393127 | ||||||||
\(688\) | 5.62586 | 0.214484 | ||||||||
\(689\) | −3.07625 | −0.117196 | ||||||||
\(690\) | −7.20559 | −0.274312 | ||||||||
\(691\) | −3.53616 | −0.134522 | −0.0672609 | − | 0.997735i | \(-0.521426\pi\) | ||||
−0.0672609 | + | 0.997735i | \(0.521426\pi\) | |||||||
\(692\) | −37.9425 | −1.44236 | ||||||||
\(693\) | −12.0457 | −0.457576 | ||||||||
\(694\) | 5.10837 | 0.193911 | ||||||||
\(695\) | −24.2518 | −0.919922 | ||||||||
\(696\) | −3.00795 | −0.114016 | ||||||||
\(697\) | 3.78873 | 0.143508 | ||||||||
\(698\) | 4.05428 | 0.153457 | ||||||||
\(699\) | 6.98827 | 0.264321 | ||||||||
\(700\) | −11.6082 | −0.438750 | ||||||||
\(701\) | −0.126135 | −0.00476404 | −0.00238202 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238202 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(702\) | −1.40440 | −0.0530057 | ||||||||
\(703\) | 19.2102 | 0.724527 | ||||||||
\(704\) | 0.900609 | 0.0339430 | ||||||||
\(705\) | 8.52878 | 0.321212 | ||||||||
\(706\) | 6.54358 | 0.246271 | ||||||||
\(707\) | 34.8656 | 1.31125 | ||||||||
\(708\) | −22.6890 | −0.852703 | ||||||||
\(709\) | −10.2108 | −0.383474 | −0.191737 | − | 0.981446i | \(-0.561412\pi\) | ||||
−0.191737 | + | 0.981446i | \(0.561412\pi\) | |||||||
\(710\) | 5.59375 | 0.209930 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 19.3419 | 0.724869 | ||||||||
\(713\) | 42.9539 | 1.60864 | ||||||||
\(714\) | 1.75675 | 0.0657446 | ||||||||
\(715\) | −14.7486 | −0.551566 | ||||||||
\(716\) | −18.1919 | −0.679864 | ||||||||
\(717\) | 15.5426 | 0.580451 | ||||||||
\(718\) | −13.8823 | −0.518083 | ||||||||
\(719\) | 43.3429 | 1.61642 | 0.808209 | − | 0.588896i | \(-0.200437\pi\) | ||||
0.808209 | + | 0.588896i | \(0.200437\pi\) | |||||||
\(720\) | −2.62700 | −0.0979026 | ||||||||
\(721\) | −51.9365 | −1.93421 | ||||||||
\(722\) | −1.14069 | −0.0424519 | ||||||||
\(723\) | −6.67896 | −0.248393 | ||||||||
\(724\) | −12.8123 | −0.476166 | ||||||||
\(725\) | 3.47771 | 0.129159 | ||||||||
\(726\) | −5.24923 | −0.194817 | ||||||||
\(727\) | 43.0937 | 1.59826 | 0.799129 | − | 0.601160i | \(-0.205295\pi\) | ||||
0.799129 | + | 0.601160i | \(0.205295\pi\) | |||||||
\(728\) | −13.8612 | −0.513728 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.52253 | −0.0563513 | ||||||||
\(731\) | 3.27995 | 0.121313 | ||||||||
\(732\) | 3.96801 | 0.146662 | ||||||||
\(733\) | −26.2300 | −0.968826 | −0.484413 | − | 0.874840i | \(-0.660967\pi\) | ||||
−0.484413 | + | 0.874840i | \(0.660967\pi\) | |||||||
\(734\) | 18.9356 | 0.698927 | ||||||||
\(735\) | −0.846296 | −0.0312161 | ||||||||
\(736\) | 41.8622 | 1.54306 | ||||||||
\(737\) | −0.913580 | −0.0336522 | ||||||||
\(738\) | −2.42190 | −0.0891513 | ||||||||
\(739\) | −13.9075 | −0.511595 | −0.255797 | − | 0.966730i | \(-0.582338\pi\) | ||||
−0.255797 | + | 0.966730i | \(0.582338\pi\) | |||||||
\(740\) | 10.2701 | 0.377536 | ||||||||
\(741\) | 10.0161 | 0.367950 | ||||||||
\(742\) | −2.45981 | −0.0903025 | ||||||||
\(743\) | 3.68086 | 0.135038 | 0.0675189 | − | 0.997718i | \(-0.478492\pi\) | ||||
0.0675189 | + | 0.997718i | \(0.478492\pi\) | |||||||
\(744\) | −13.3985 | −0.491213 | ||||||||
\(745\) | 4.47859 | 0.164083 | ||||||||
\(746\) | 17.2880 | 0.632959 | ||||||||
\(747\) | −14.1845 | −0.518984 | ||||||||
\(748\) | −6.97519 | −0.255038 | ||||||||
\(749\) | 5.49555 | 0.200803 | ||||||||
\(750\) | −7.49384 | −0.273636 | ||||||||
\(751\) | −9.88190 | −0.360596 | −0.180298 | − | 0.983612i | \(-0.557706\pi\) | ||||
−0.180298 | + | 0.983612i | \(0.557706\pi\) | |||||||
\(752\) | −9.55147 | −0.348306 | ||||||||
\(753\) | 28.7096 | 1.04624 | ||||||||
\(754\) | 1.84009 | 0.0670121 | ||||||||
\(755\) | −8.44490 | −0.307341 | ||||||||
\(756\) | 4.37341 | 0.159059 | ||||||||
\(757\) | −8.05261 | −0.292677 | −0.146339 | − | 0.989235i | \(-0.546749\pi\) | ||||
−0.146339 | + | 0.989235i | \(0.546749\pi\) | |||||||
\(758\) | 2.36031 | 0.0857303 | ||||||||
\(759\) | −32.2591 | −1.17093 | ||||||||
\(760\) | −16.0299 | −0.581465 | ||||||||
\(761\) | −33.5101 | −1.21474 | −0.607369 | − | 0.794420i | \(-0.707775\pi\) | ||||
−0.607369 | + | 0.794420i | \(0.707775\pi\) | |||||||
\(762\) | 2.47755 | 0.0897520 | ||||||||
\(763\) | −50.9863 | −1.84583 | ||||||||
\(764\) | −15.1574 | −0.548375 | ||||||||
\(765\) | −1.53158 | −0.0553743 | ||||||||
\(766\) | 24.6322 | 0.889999 | ||||||||
\(767\) | 31.3236 | 1.13103 | ||||||||
\(768\) | −7.59884 | −0.274200 | ||||||||
\(769\) | −3.96696 | −0.143052 | −0.0715261 | − | 0.997439i | \(-0.522787\pi\) | ||||
−0.0715261 | + | 0.997439i | \(0.522787\pi\) | |||||||
\(770\) | −11.7932 | −0.424997 | ||||||||
\(771\) | −3.46899 | −0.124933 | ||||||||
\(772\) | −9.70044 | −0.349127 | ||||||||
\(773\) | 7.08867 | 0.254962 | 0.127481 | − | 0.991841i | \(-0.459311\pi\) | ||||
0.127481 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(774\) | −2.09666 | −0.0753630 | ||||||||
\(775\) | 15.4910 | 0.556453 | ||||||||
\(776\) | 4.37790 | 0.157158 | ||||||||
\(777\) | −11.5801 | −0.415432 | ||||||||
\(778\) | −9.26359 | −0.332116 | ||||||||
\(779\) | 17.2728 | 0.618863 | ||||||||
\(780\) | 5.35477 | 0.191731 | ||||||||
\(781\) | 25.0430 | 0.896107 | ||||||||
\(782\) | 4.70469 | 0.168239 | ||||||||
\(783\) | −1.31023 | −0.0468238 | ||||||||
\(784\) | 0.947776 | 0.0338491 | ||||||||
\(785\) | 28.9319 | 1.03262 | ||||||||
\(786\) | 1.30657 | 0.0466039 | ||||||||
\(787\) | −10.1096 | −0.360369 | −0.180185 | − | 0.983633i | \(-0.557670\pi\) | ||||
−0.180185 | + | 0.983633i | \(0.557670\pi\) | |||||||
\(788\) | −35.6718 | −1.27076 | ||||||||
\(789\) | −26.4058 | −0.940070 | ||||||||
\(790\) | 0.979040 | 0.0348327 | ||||||||
\(791\) | 6.66286 | 0.236904 | ||||||||
\(792\) | 10.0625 | 0.357555 | ||||||||
\(793\) | −5.47809 | −0.194533 | ||||||||
\(794\) | 5.14149 | 0.182465 | ||||||||
\(795\) | 2.14453 | 0.0760585 | ||||||||
\(796\) | 2.68321 | 0.0951039 | ||||||||
\(797\) | −13.3690 | −0.473554 | −0.236777 | − | 0.971564i | \(-0.576091\pi\) | ||||
−0.236777 | + | 0.971564i | \(0.576091\pi\) | |||||||
\(798\) | 8.00900 | 0.283516 | ||||||||
\(799\) | −5.56863 | −0.197004 | ||||||||
\(800\) | 15.0973 | 0.533770 | ||||||||
\(801\) | 8.42513 | 0.297687 | ||||||||
\(802\) | −21.2732 | −0.751184 | ||||||||
\(803\) | −6.81629 | −0.240542 | ||||||||
\(804\) | 0.331693 | 0.0116979 | ||||||||
\(805\) | −30.9781 | −1.09183 | ||||||||
\(806\) | 8.19643 | 0.288707 | ||||||||
\(807\) | 28.2967 | 0.996090 | ||||||||
\(808\) | −29.1254 | −1.02463 | ||||||||
\(809\) | −23.4715 | −0.825213 | −0.412607 | − | 0.910909i | \(-0.635382\pi\) | ||||
−0.412607 | + | 0.910909i | \(0.635382\pi\) | |||||||
\(810\) | 0.979040 | 0.0344000 | ||||||||
\(811\) | −12.6488 | −0.444161 | −0.222081 | − | 0.975028i | \(-0.571285\pi\) | ||||
−0.222081 | + | 0.975028i | \(0.571285\pi\) | |||||||
\(812\) | −5.73017 | −0.201090 | ||||||||
\(813\) | −6.19456 | −0.217253 | ||||||||
\(814\) | −11.8062 | −0.413805 | ||||||||
\(815\) | 0.202920 | 0.00710799 | ||||||||
\(816\) | 1.71523 | 0.0600450 | ||||||||
\(817\) | 14.9533 | 0.523148 | ||||||||
\(818\) | −14.0516 | −0.491303 | ||||||||
\(819\) | −6.03777 | −0.210977 | ||||||||
\(820\) | 9.23432 | 0.322477 | ||||||||
\(821\) | −40.6010 | −1.41699 | −0.708493 | − | 0.705718i | \(-0.750624\pi\) | ||||
−0.708493 | + | 0.705718i | \(0.750624\pi\) | |||||||
\(822\) | −7.64284 | −0.266575 | ||||||||
\(823\) | 10.5219 | 0.366769 | 0.183385 | − | 0.983041i | \(-0.441295\pi\) | ||||
0.183385 | + | 0.983041i | \(0.441295\pi\) | |||||||
\(824\) | 43.3858 | 1.51142 | ||||||||
\(825\) | −11.6340 | −0.405044 | ||||||||
\(826\) | 25.0467 | 0.871487 | ||||||||
\(827\) | 48.7409 | 1.69489 | 0.847444 | − | 0.530885i | \(-0.178140\pi\) | ||||
0.847444 | + | 0.530885i | \(0.178140\pi\) | |||||||
\(828\) | 11.7123 | 0.407030 | ||||||||
\(829\) | −30.0911 | −1.04511 | −0.522554 | − | 0.852606i | \(-0.675021\pi\) | ||||
−0.522554 | + | 0.852606i | \(0.675021\pi\) | |||||||
\(830\) | −13.8872 | −0.482032 | ||||||||
\(831\) | −8.05092 | −0.279283 | ||||||||
\(832\) | 0.451422 | 0.0156502 | ||||||||
\(833\) | 0.552565 | 0.0191452 | ||||||||
\(834\) | −10.1220 | −0.350497 | ||||||||
\(835\) | −23.6591 | −0.818758 | ||||||||
\(836\) | −31.7999 | −1.09982 | ||||||||
\(837\) | −5.83625 | −0.201730 | ||||||||
\(838\) | 0.547735 | 0.0189212 | ||||||||
\(839\) | −26.6346 | −0.919529 | −0.459765 | − | 0.888041i | \(-0.652066\pi\) | ||||
−0.459765 | + | 0.888041i | \(0.652066\pi\) | |||||||
\(840\) | 9.66293 | 0.333403 | ||||||||
\(841\) | −27.2833 | −0.940803 | ||||||||
\(842\) | 19.8064 | 0.682572 | ||||||||
\(843\) | 20.6325 | 0.710620 | ||||||||
\(844\) | 16.4823 | 0.567343 | ||||||||
\(845\) | 12.5179 | 0.430629 | ||||||||
\(846\) | 3.55967 | 0.122384 | ||||||||
\(847\) | −22.5674 | −0.775424 | ||||||||
\(848\) | −2.40168 | −0.0824739 | ||||||||
\(849\) | 29.1318 | 0.999800 | ||||||||
\(850\) | 1.69671 | 0.0581967 | ||||||||
\(851\) | −31.0122 | −1.06308 | ||||||||
\(852\) | −9.09233 | −0.311498 | ||||||||
\(853\) | 8.27726 | 0.283408 | 0.141704 | − | 0.989909i | \(-0.454742\pi\) | ||||
0.141704 | + | 0.989909i | \(0.454742\pi\) | |||||||
\(854\) | −4.38035 | −0.149893 | ||||||||
\(855\) | −6.98245 | −0.238795 | ||||||||
\(856\) | −4.59078 | −0.156910 | ||||||||
\(857\) | −3.76957 | −0.128766 | −0.0643831 | − | 0.997925i | \(-0.520508\pi\) | ||||
−0.0643831 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(858\) | −6.15566 | −0.210151 | ||||||||
\(859\) | 17.1490 | 0.585115 | 0.292557 | − | 0.956248i | \(-0.405494\pi\) | ||||
0.292557 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(860\) | 7.99426 | 0.272602 | ||||||||
\(861\) | −10.4122 | −0.354846 | ||||||||
\(862\) | −20.6854 | −0.704547 | ||||||||
\(863\) | −18.0469 | −0.614323 | −0.307161 | − | 0.951657i | \(-0.599379\pi\) | ||||
−0.307161 | + | 0.951657i | \(0.599379\pi\) | |||||||
\(864\) | −5.68792 | −0.193507 | ||||||||
\(865\) | −36.5167 | −1.24161 | ||||||||
\(866\) | −1.37710 | −0.0467956 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −25.5243 | −0.866351 | ||||||||
\(869\) | 4.38312 | 0.148687 | ||||||||
\(870\) | −1.28277 | −0.0434899 | ||||||||
\(871\) | −0.457923 | −0.0155161 | ||||||||
\(872\) | 42.5921 | 1.44235 | ||||||||
\(873\) | 1.90697 | 0.0645411 | ||||||||
\(874\) | 21.4487 | 0.725512 | ||||||||
\(875\) | −32.2174 | −1.08915 | ||||||||
\(876\) | 2.47479 | 0.0836153 | ||||||||
\(877\) | 43.5591 | 1.47089 | 0.735443 | − | 0.677586i | \(-0.236974\pi\) | ||||
0.735443 | + | 0.677586i | \(0.236974\pi\) | |||||||
\(878\) | 19.8419 | 0.669631 | ||||||||
\(879\) | −13.6054 | −0.458897 | ||||||||
\(880\) | −11.5145 | −0.388153 | ||||||||
\(881\) | 1.71058 | 0.0576308 | 0.0288154 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288154 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(882\) | −0.353220 | −0.0118935 | ||||||||
\(883\) | 13.0727 | 0.439931 | 0.219966 | − | 0.975508i | \(-0.429405\pi\) | ||||
0.219966 | + | 0.975508i | \(0.429405\pi\) | |||||||
\(884\) | −3.49625 | −0.117591 | ||||||||
\(885\) | −21.8364 | −0.734022 | ||||||||
\(886\) | 8.19318 | 0.275255 | ||||||||
\(887\) | −31.7780 | −1.06700 | −0.533501 | − | 0.845800i | \(-0.679124\pi\) | ||||
−0.533501 | + | 0.845800i | \(0.679124\pi\) | |||||||
\(888\) | 9.67356 | 0.324623 | ||||||||
\(889\) | 10.6514 | 0.357237 | ||||||||
\(890\) | 8.24854 | 0.276492 | ||||||||
\(891\) | 4.38312 | 0.146840 | ||||||||
\(892\) | −4.62859 | −0.154977 | ||||||||
\(893\) | −25.3873 | −0.849555 | ||||||||
\(894\) | 1.86924 | 0.0625167 | ||||||||
\(895\) | −17.5083 | −0.585239 | ||||||||
\(896\) | −30.9020 | −1.03236 | ||||||||
\(897\) | −16.1696 | −0.539886 | ||||||||
\(898\) | −10.9073 | −0.363981 | ||||||||
\(899\) | 7.64683 | 0.255036 | ||||||||
\(900\) | 4.22395 | 0.140798 | ||||||||
\(901\) | −1.40021 | −0.0466477 | ||||||||
\(902\) | −10.6155 | −0.353456 | ||||||||
\(903\) | −9.01392 | −0.299965 | ||||||||
\(904\) | −5.56591 | −0.185119 | ||||||||
\(905\) | −12.3309 | −0.409892 | ||||||||
\(906\) | −3.52466 | −0.117099 | ||||||||
\(907\) | 20.7824 | 0.690069 | 0.345035 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345035 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(908\) | −17.6786 | −0.586686 | ||||||||
\(909\) | −12.6867 | −0.420792 | ||||||||
\(910\) | −5.91122 | −0.195955 | ||||||||
\(911\) | 13.0279 | 0.431633 | 0.215816 | − | 0.976434i | \(-0.430759\pi\) | ||||
0.215816 | + | 0.976434i | \(0.430759\pi\) | |||||||
\(912\) | 7.81972 | 0.258937 | ||||||||
\(913\) | −62.1724 | −2.05761 | ||||||||
\(914\) | −13.5876 | −0.449438 | ||||||||
\(915\) | 3.81890 | 0.126249 | ||||||||
\(916\) | 16.3977 | 0.541796 | ||||||||
\(917\) | 5.61718 | 0.185496 | ||||||||
\(918\) | −0.639237 | −0.0210980 | ||||||||
\(919\) | −20.8694 | −0.688417 | −0.344208 | − | 0.938893i | \(-0.611853\pi\) | ||||
−0.344208 | + | 0.938893i | \(0.611853\pi\) | |||||||
\(920\) | 25.8780 | 0.853172 | ||||||||
\(921\) | −2.41280 | −0.0795046 | ||||||||
\(922\) | 2.48689 | 0.0819013 | ||||||||
\(923\) | 12.5525 | 0.413172 | ||||||||
\(924\) | 19.1692 | 0.630619 | ||||||||
\(925\) | −11.1843 | −0.367738 | ||||||||
\(926\) | −13.7903 | −0.453179 | ||||||||
\(927\) | 18.8984 | 0.620705 | ||||||||
\(928\) | 7.45248 | 0.244640 | ||||||||
\(929\) | −32.2722 | −1.05882 | −0.529408 | − | 0.848367i | \(-0.677586\pi\) | ||||
−0.529408 | + | 0.848367i | \(0.677586\pi\) | |||||||
\(930\) | −5.71392 | −0.187367 | ||||||||
\(931\) | 2.51914 | 0.0825616 | ||||||||
\(932\) | −11.1210 | −0.364279 | ||||||||
\(933\) | 9.07562 | 0.297123 | ||||||||
\(934\) | 5.12447 | 0.167678 | ||||||||
\(935\) | −6.71308 | −0.219541 | ||||||||
\(936\) | 5.04373 | 0.164860 | ||||||||
\(937\) | −9.16845 | −0.299520 | −0.149760 | − | 0.988722i | \(-0.547850\pi\) | ||||
−0.149760 | + | 0.988722i | \(0.547850\pi\) | |||||||
\(938\) | −0.366162 | −0.0119556 | ||||||||
\(939\) | −19.7211 | −0.643574 | ||||||||
\(940\) | −13.5725 | −0.442686 | ||||||||
\(941\) | −34.3260 | −1.11900 | −0.559498 | − | 0.828832i | \(-0.689006\pi\) | ||||
−0.559498 | + | 0.828832i | \(0.689006\pi\) | |||||||
\(942\) | 12.0754 | 0.393436 | ||||||||
\(943\) | −27.8845 | −0.908044 | ||||||||
\(944\) | 24.4548 | 0.795936 | ||||||||
\(945\) | 4.20907 | 0.136921 | ||||||||
\(946\) | −9.18992 | −0.298790 | ||||||||
\(947\) | 53.4886 | 1.73815 | 0.869074 | − | 0.494683i | \(-0.164716\pi\) | ||||
0.869074 | + | 0.494683i | \(0.164716\pi\) | |||||||
\(948\) | −1.59138 | −0.0516855 | ||||||||
\(949\) | −3.41660 | −0.110908 | ||||||||
\(950\) | 7.73530 | 0.250966 | ||||||||
\(951\) | 5.46386 | 0.177178 | ||||||||
\(952\) | −6.30914 | −0.204480 | ||||||||
\(953\) | −31.6375 | −1.02484 | −0.512420 | − | 0.858735i | \(-0.671251\pi\) | ||||
−0.512420 | + | 0.858735i | \(0.671251\pi\) | |||||||
\(954\) | 0.895065 | 0.0289788 | ||||||||
\(955\) | −14.5878 | −0.472050 | ||||||||
\(956\) | −24.7342 | −0.799961 | ||||||||
\(957\) | −5.74289 | −0.185641 | ||||||||
\(958\) | −7.70819 | −0.249040 | ||||||||
\(959\) | −32.8579 | −1.06104 | ||||||||
\(960\) | −0.314696 | −0.0101568 | ||||||||
\(961\) | 3.06178 | 0.0987670 | ||||||||
\(962\) | −5.91772 | −0.190795 | ||||||||
\(963\) | −1.99970 | −0.0644393 | ||||||||
\(964\) | 10.6287 | 0.342328 | ||||||||
\(965\) | −9.33593 | −0.300534 | ||||||||
\(966\) | −12.9294 | −0.415997 | ||||||||
\(967\) | 47.3885 | 1.52391 | 0.761955 | − | 0.647630i | \(-0.224240\pi\) | ||||
0.761955 | + | 0.647630i | \(0.224240\pi\) | |||||||
\(968\) | 18.8520 | 0.605925 | ||||||||
\(969\) | 4.55900 | 0.146456 | ||||||||
\(970\) | 1.86700 | 0.0599457 | ||||||||
\(971\) | 5.60608 | 0.179908 | 0.0899538 | − | 0.995946i | \(-0.471328\pi\) | ||||
0.0899538 | + | 0.995946i | \(0.471328\pi\) | |||||||
\(972\) | −1.59138 | −0.0510434 | ||||||||
\(973\) | −43.5163 | −1.39507 | ||||||||
\(974\) | 5.25340 | 0.168330 | ||||||||
\(975\) | −5.83143 | −0.186755 | ||||||||
\(976\) | −4.27683 | −0.136898 | ||||||||
\(977\) | −28.3396 | −0.906663 | −0.453332 | − | 0.891342i | \(-0.649765\pi\) | ||||
−0.453332 | + | 0.891342i | \(0.649765\pi\) | |||||||
\(978\) | 0.0846933 | 0.00270819 | ||||||||
\(979\) | 36.9283 | 1.18023 | ||||||||
\(980\) | 1.34677 | 0.0430211 | ||||||||
\(981\) | 18.5527 | 0.592341 | ||||||||
\(982\) | 7.47236 | 0.238453 | ||||||||
\(983\) | −39.7618 | −1.26821 | −0.634103 | − | 0.773249i | \(-0.718630\pi\) | ||||
−0.634103 | + | 0.773249i | \(0.718630\pi\) | |||||||
\(984\) | 8.69794 | 0.277280 | ||||||||
\(985\) | −34.3314 | −1.09389 | ||||||||
\(986\) | 0.837548 | 0.0266730 | ||||||||
\(987\) | 15.3037 | 0.487121 | ||||||||
\(988\) | −15.9394 | −0.507099 | ||||||||
\(989\) | −24.1399 | −0.767604 | ||||||||
\(990\) | 4.29125 | 0.136385 | ||||||||
\(991\) | 10.0089 | 0.317943 | 0.158971 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158971 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(992\) | 33.1961 | 1.05398 | ||||||||
\(993\) | −6.21216 | −0.197137 | ||||||||
\(994\) | 10.0372 | 0.318360 | ||||||||
\(995\) | 2.58238 | 0.0818670 | ||||||||
\(996\) | 22.5729 | 0.715249 | ||||||||
\(997\) | −3.49583 | −0.110714 | −0.0553571 | − | 0.998467i | \(-0.517630\pi\) | ||||
−0.0553571 | + | 0.998467i | \(0.517630\pi\) | |||||||
\(998\) | −13.5501 | −0.428920 | ||||||||
\(999\) | 4.21370 | 0.133315 |
(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 | 4029.2.a.k.1.12 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.12 | ✓ | 31 | 1.1 | even | 1 | trivial |