Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.817573 | 0.578111 | 0.289056 | − | 0.957312i | \(-0.406659\pi\) | ||||
0.289056 | + | 0.957312i | \(0.406659\pi\) | |||||||
\(3\) | 1.89500 | 1.09408 | 0.547039 | − | 0.837107i | \(-0.315755\pi\) | ||||
0.547039 | + | 0.837107i | \(0.315755\pi\) | |||||||
\(4\) | −1.33157 | −0.665787 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.54930 | 0.632498 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.72381 | −0.963011 | ||||||||
\(9\) | 0.591014 | 0.197005 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12866 | 0.641814 | 0.320907 | − | 0.947111i | \(-0.396012\pi\) | ||||
0.320907 | + | 0.947111i | \(0.396012\pi\) | |||||||
\(12\) | −2.52333 | −0.728423 | ||||||||
\(13\) | 5.55212 | 1.53988 | 0.769940 | − | 0.638116i | \(-0.220286\pi\) | ||||
0.769940 | + | 0.638116i | \(0.220286\pi\) | |||||||
\(14\) | 0.817573 | 0.218506 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.436240 | 0.109060 | ||||||||
\(17\) | −0.145218 | −0.0352206 | −0.0176103 | − | 0.999845i | \(-0.505606\pi\) | ||||
−0.0176103 | + | 0.999845i | \(0.505606\pi\) | |||||||
\(18\) | 0.483197 | 0.113891 | ||||||||
\(19\) | −3.23410 | −0.741953 | −0.370976 | − | 0.928642i | \(-0.620977\pi\) | ||||
−0.370976 | + | 0.928642i | \(0.620977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.89500 | 0.413522 | ||||||||
\(22\) | 1.74033 | 0.371040 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −5.16160 | −1.05361 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.53926 | 0.890223 | ||||||||
\(27\) | −4.56502 | −0.878539 | ||||||||
\(28\) | −1.33157 | −0.251644 | ||||||||
\(29\) | 3.26934 | 0.607101 | 0.303551 | − | 0.952815i | \(-0.401828\pi\) | ||||
0.303551 | + | 0.952815i | \(0.401828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.223549 | 0.0401506 | 0.0200753 | − | 0.999798i | \(-0.493609\pi\) | ||||
0.0200753 | + | 0.999798i | \(0.493609\pi\) | |||||||
\(32\) | 5.80427 | 1.02606 | ||||||||
\(33\) | 4.03380 | 0.702194 | ||||||||
\(34\) | −0.118727 | −0.0203614 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.786979 | −0.131163 | ||||||||
\(37\) | −1.16019 | −0.190734 | −0.0953672 | − | 0.995442i | \(-0.530403\pi\) | ||||
−0.0953672 | + | 0.995442i | \(0.530403\pi\) | |||||||
\(38\) | −2.64411 | −0.428931 | ||||||||
\(39\) | 10.5213 | 1.68475 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.79850 | −0.437052 | −0.218526 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218526 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(42\) | 1.54930 | 0.239062 | ||||||||
\(43\) | 11.5742 | 1.76504 | 0.882522 | − | 0.470271i | \(-0.155844\pi\) | ||||
0.882522 | + | 0.470271i | \(0.155844\pi\) | |||||||
\(44\) | −2.83447 | −0.427312 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.817573 | 0.120545 | ||||||||
\(47\) | 2.13898 | 0.312002 | 0.156001 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.156001 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(48\) | 0.826674 | 0.119320 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.275188 | −0.0385341 | ||||||||
\(52\) | −7.39306 | −1.02523 | ||||||||
\(53\) | 7.28007 | 0.999995 | 0.499998 | − | 0.866027i | \(-0.333334\pi\) | ||||
0.499998 | + | 0.866027i | \(0.333334\pi\) | |||||||
\(54\) | −3.73224 | −0.507893 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.72381 | −0.363984 | ||||||||
\(57\) | −6.12860 | −0.811753 | ||||||||
\(58\) | 2.67292 | 0.350972 | ||||||||
\(59\) | 4.72568 | 0.615232 | 0.307616 | − | 0.951511i | \(-0.400469\pi\) | ||||
0.307616 | + | 0.951511i | \(0.400469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.99427 | 0.383377 | 0.191688 | − | 0.981456i | \(-0.438604\pi\) | ||||
0.191688 | + | 0.981456i | \(0.438604\pi\) | |||||||
\(62\) | 0.182767 | 0.0232115 | ||||||||
\(63\) | 0.591014 | 0.0744608 | ||||||||
\(64\) | 3.87293 | 0.484117 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.29793 | 0.405947 | ||||||||
\(67\) | 12.8063 | 1.56454 | 0.782269 | − | 0.622941i | \(-0.214062\pi\) | ||||
0.782269 | + | 0.622941i | \(0.214062\pi\) | |||||||
\(68\) | 0.193369 | 0.0234494 | ||||||||
\(69\) | 1.89500 | 0.228131 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.35757 | 0.161113 | 0.0805567 | − | 0.996750i | \(-0.474330\pi\) | ||||
0.0805567 | + | 0.996750i | \(0.474330\pi\) | |||||||
\(72\) | −1.60981 | −0.189718 | ||||||||
\(73\) | 5.64692 | 0.660922 | 0.330461 | − | 0.943820i | \(-0.392796\pi\) | ||||
0.330461 | + | 0.943820i | \(0.392796\pi\) | |||||||
\(74\) | −0.948542 | −0.110266 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.30644 | 0.493983 | ||||||||
\(77\) | 2.12866 | 0.242583 | ||||||||
\(78\) | 8.60189 | 0.973972 | ||||||||
\(79\) | −15.8310 | −1.78113 | −0.890564 | − | 0.454858i | \(-0.849690\pi\) | ||||
−0.890564 | + | 0.454858i | \(0.849690\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4237 | −1.15819 | ||||||||
\(82\) | −2.28798 | −0.252665 | ||||||||
\(83\) | −16.1543 | −1.77317 | −0.886584 | − | 0.462568i | \(-0.846928\pi\) | ||||
−0.886584 | + | 0.462568i | \(0.846928\pi\) | |||||||
\(84\) | −2.52333 | −0.275318 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.46273 | 1.02039 | ||||||||
\(87\) | 6.19539 | 0.664216 | ||||||||
\(88\) | −5.79805 | −0.618074 | ||||||||
\(89\) | 5.37869 | 0.570140 | 0.285070 | − | 0.958507i | \(-0.407983\pi\) | ||||
0.285070 | + | 0.958507i | \(0.407983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.55212 | 0.582020 | ||||||||
\(92\) | −1.33157 | −0.138826 | ||||||||
\(93\) | 0.423624 | 0.0439278 | ||||||||
\(94\) | 1.74877 | 0.180372 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.9991 | 1.12259 | ||||||||
\(97\) | 10.2405 | 1.03977 | 0.519884 | − | 0.854237i | \(-0.325975\pi\) | ||||
0.519884 | + | 0.854237i | \(0.325975\pi\) | |||||||
\(98\) | 0.817573 | 0.0825873 | ||||||||
\(99\) | 1.25807 | 0.126440 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.36317 | 0.931671 | 0.465835 | − | 0.884871i | \(-0.345754\pi\) | ||||
0.465835 | + | 0.884871i | \(0.345754\pi\) | |||||||
\(102\) | −0.224986 | −0.0222770 | ||||||||
\(103\) | 6.45952 | 0.636475 | 0.318238 | − | 0.948011i | \(-0.396909\pi\) | ||||
0.318238 | + | 0.948011i | \(0.396909\pi\) | |||||||
\(104\) | −15.1229 | −1.48292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.95199 | 0.578109 | ||||||||
\(107\) | 13.6196 | 1.31665 | 0.658326 | − | 0.752733i | \(-0.271265\pi\) | ||||
0.658326 | + | 0.752733i | \(0.271265\pi\) | |||||||
\(108\) | 6.07867 | 0.584920 | ||||||||
\(109\) | −19.7751 | −1.89411 | −0.947055 | − | 0.321073i | \(-0.895957\pi\) | ||||
−0.947055 | + | 0.321073i | \(0.895957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.19856 | −0.208678 | ||||||||
\(112\) | 0.436240 | 0.0412208 | ||||||||
\(113\) | −6.01223 | −0.565583 | −0.282792 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282792 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(114\) | −5.01058 | −0.469284 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.35337 | −0.404200 | ||||||||
\(117\) | 3.28138 | 0.303364 | ||||||||
\(118\) | 3.86359 | 0.355672 | ||||||||
\(119\) | −0.145218 | −0.0133121 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.46882 | −0.588074 | ||||||||
\(122\) | 2.44803 | 0.221634 | ||||||||
\(123\) | −5.30315 | −0.478169 | ||||||||
\(124\) | −0.297672 | −0.0267317 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.483197 | 0.0430466 | ||||||||
\(127\) | −4.25574 | −0.377636 | −0.188818 | − | 0.982012i | \(-0.560466\pi\) | ||||
−0.188818 | + | 0.982012i | \(0.560466\pi\) | |||||||
\(128\) | −8.44213 | −0.746186 | ||||||||
\(129\) | 21.9330 | 1.93109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.53859 | 0.483909 | 0.241955 | − | 0.970288i | \(-0.422212\pi\) | ||||
0.241955 | + | 0.970288i | \(0.422212\pi\) | |||||||
\(132\) | −5.37131 | −0.467512 | ||||||||
\(133\) | −3.23410 | −0.280432 | ||||||||
\(134\) | 10.4701 | 0.904477 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.395546 | 0.0339178 | ||||||||
\(137\) | 17.7030 | 1.51247 | 0.756236 | − | 0.654299i | \(-0.227036\pi\) | ||||
0.756236 | + | 0.654299i | \(0.227036\pi\) | |||||||
\(138\) | 1.54930 | 0.131885 | ||||||||
\(139\) | 9.23566 | 0.783358 | 0.391679 | − | 0.920102i | \(-0.371894\pi\) | ||||
0.391679 | + | 0.920102i | \(0.371894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.05335 | 0.341354 | ||||||||
\(142\) | 1.10991 | 0.0931414 | ||||||||
\(143\) | 11.8186 | 0.988318 | ||||||||
\(144\) | 0.257824 | 0.0214853 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.61677 | 0.382086 | ||||||||
\(147\) | 1.89500 | 0.156297 | ||||||||
\(148\) | 1.54488 | 0.126989 | ||||||||
\(149\) | 4.06403 | 0.332939 | 0.166469 | − | 0.986047i | \(-0.446763\pi\) | ||||
0.166469 | + | 0.986047i | \(0.446763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.18853 | −0.259479 | −0.129739 | − | 0.991548i | \(-0.541414\pi\) | ||||
−0.129739 | + | 0.991548i | \(0.541414\pi\) | |||||||
\(152\) | 8.80905 | 0.714508 | ||||||||
\(153\) | −0.0858260 | −0.00693862 | ||||||||
\(154\) | 1.74033 | 0.140240 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.0098 | −1.12168 | ||||||||
\(157\) | 17.1593 | 1.36946 | 0.684732 | − | 0.728795i | \(-0.259919\pi\) | ||||
0.684732 | + | 0.728795i | \(0.259919\pi\) | |||||||
\(158\) | −12.9430 | −1.02969 | ||||||||
\(159\) | 13.7957 | 1.09407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −8.52217 | −0.669565 | ||||||||
\(163\) | 10.8914 | 0.853078 | 0.426539 | − | 0.904469i | \(-0.359733\pi\) | ||||
0.426539 | + | 0.904469i | \(0.359733\pi\) | |||||||
\(164\) | 3.72641 | 0.290984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.2073 | −1.02509 | ||||||||
\(167\) | −5.62878 | −0.435568 | −0.217784 | − | 0.975997i | \(-0.569883\pi\) | ||||
−0.217784 | + | 0.975997i | \(0.569883\pi\) | |||||||
\(168\) | −5.16160 | −0.398226 | ||||||||
\(169\) | 17.8260 | 1.37123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.91140 | −0.146168 | ||||||||
\(172\) | −15.4119 | −1.17514 | ||||||||
\(173\) | −20.1921 | −1.53518 | −0.767590 | − | 0.640941i | \(-0.778544\pi\) | ||||
−0.767590 | + | 0.640941i | \(0.778544\pi\) | |||||||
\(174\) | 5.06518 | 0.383991 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.928606 | 0.0699963 | ||||||||
\(177\) | 8.95516 | 0.673111 | ||||||||
\(178\) | 4.39747 | 0.329605 | ||||||||
\(179\) | −0.0487966 | −0.00364723 | −0.00182361 | − | 0.999998i | \(-0.500580\pi\) | ||||
−0.00182361 | + | 0.999998i | \(0.500580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0147 | 0.818717 | 0.409358 | − | 0.912374i | \(-0.365753\pi\) | ||||
0.409358 | + | 0.912374i | \(0.365753\pi\) | |||||||
\(182\) | 4.53926 | 0.336473 | ||||||||
\(183\) | 5.67413 | 0.419444 | ||||||||
\(184\) | −2.72381 | −0.200802 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.346344 | 0.0253952 | ||||||||
\(187\) | −0.309120 | −0.0226051 | ||||||||
\(188\) | −2.84821 | −0.207727 | ||||||||
\(189\) | −4.56502 | −0.332056 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6292 | 0.986177 | 0.493088 | − | 0.869979i | \(-0.335868\pi\) | ||||
0.493088 | + | 0.869979i | \(0.335868\pi\) | |||||||
\(192\) | 7.33920 | 0.529661 | ||||||||
\(193\) | −8.24539 | −0.593516 | −0.296758 | − | 0.954953i | \(-0.595905\pi\) | ||||
−0.296758 | + | 0.954953i | \(0.595905\pi\) | |||||||
\(194\) | 8.37238 | 0.601102 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.33157 | −0.0951125 | ||||||||
\(197\) | −6.23251 | −0.444048 | −0.222024 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222024 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(198\) | 1.02856 | 0.0730967 | ||||||||
\(199\) | 7.76075 | 0.550145 | 0.275073 | − | 0.961423i | \(-0.411298\pi\) | ||||
0.275073 | + | 0.961423i | \(0.411298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.2679 | 1.71173 | ||||||||
\(202\) | 7.65508 | 0.538609 | ||||||||
\(203\) | 3.26934 | 0.229463 | ||||||||
\(204\) | 0.366434 | 0.0256555 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.28113 | 0.367954 | ||||||||
\(207\) | 0.591014 | 0.0410783 | ||||||||
\(208\) | 2.42206 | 0.167939 | ||||||||
\(209\) | −6.88428 | −0.476196 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0472 | 0.691678 | 0.345839 | − | 0.938294i | \(-0.387594\pi\) | ||||
0.345839 | + | 0.938294i | \(0.387594\pi\) | |||||||
\(212\) | −9.69396 | −0.665784 | ||||||||
\(213\) | 2.57258 | 0.176270 | ||||||||
\(214\) | 11.1350 | 0.761172 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.4342 | 0.846042 | ||||||||
\(217\) | 0.223549 | 0.0151755 | ||||||||
\(218\) | −16.1676 | −1.09501 | ||||||||
\(219\) | 10.7009 | 0.723100 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.806269 | −0.0542355 | ||||||||
\(222\) | −1.79748 | −0.120639 | ||||||||
\(223\) | −16.1886 | −1.08407 | −0.542034 | − | 0.840356i | \(-0.682346\pi\) | ||||
−0.542034 | + | 0.840356i | \(0.682346\pi\) | |||||||
\(224\) | 5.80427 | 0.387814 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.91544 | −0.326970 | ||||||||
\(227\) | −19.1412 | −1.27044 | −0.635222 | − | 0.772329i | \(-0.719092\pi\) | ||||
−0.635222 | + | 0.772329i | \(0.719092\pi\) | |||||||
\(228\) | 8.16069 | 0.540455 | ||||||||
\(229\) | −8.64191 | −0.571074 | −0.285537 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285537 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.03380 | 0.265405 | ||||||||
\(232\) | −8.90505 | −0.584645 | ||||||||
\(233\) | −25.5478 | −1.67369 | −0.836846 | − | 0.547439i | \(-0.815603\pi\) | ||||
−0.836846 | + | 0.547439i | \(0.815603\pi\) | |||||||
\(234\) | 2.68277 | 0.175378 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.29260 | −0.409613 | ||||||||
\(237\) | −29.9997 | −1.94869 | ||||||||
\(238\) | −0.118727 | −0.00769590 | ||||||||
\(239\) | 29.9879 | 1.93976 | 0.969879 | − | 0.243587i | \(-0.0783243\pi\) | ||||
0.969879 | + | 0.243587i | \(0.0783243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.47944 | 0.0952994 | 0.0476497 | − | 0.998864i | \(-0.484827\pi\) | ||||
0.0476497 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(242\) | −5.28873 | −0.339972 | ||||||||
\(243\) | −6.05790 | −0.388615 | ||||||||
\(244\) | −3.98709 | −0.255247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.33571 | −0.276435 | ||||||||
\(247\) | −17.9561 | −1.14252 | ||||||||
\(248\) | −0.608903 | −0.0386654 | ||||||||
\(249\) | −30.6124 | −1.93998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5809 | −1.23593 | −0.617967 | − | 0.786204i | \(-0.712043\pi\) | ||||
−0.617967 | + | 0.786204i | \(0.712043\pi\) | |||||||
\(252\) | −0.786979 | −0.0495750 | ||||||||
\(253\) | 2.12866 | 0.133828 | ||||||||
\(254\) | −3.47938 | −0.218316 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.6479 | −0.915495 | ||||||||
\(257\) | −9.42026 | −0.587620 | −0.293810 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293810 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(258\) | 17.9318 | 1.11639 | ||||||||
\(259\) | −1.16019 | −0.0720908 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.93223 | 0.119602 | ||||||||
\(262\) | 4.52820 | 0.279753 | ||||||||
\(263\) | −2.39107 | −0.147440 | −0.0737200 | − | 0.997279i | \(-0.523487\pi\) | ||||
−0.0737200 | + | 0.997279i | \(0.523487\pi\) | |||||||
\(264\) | −10.9873 | −0.676221 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.64411 | −0.162121 | ||||||||
\(267\) | 10.1926 | 0.623778 | ||||||||
\(268\) | −17.0525 | −1.04165 | ||||||||
\(269\) | 17.8491 | 1.08828 | 0.544141 | − | 0.838994i | \(-0.316856\pi\) | ||||
0.544141 | + | 0.838994i | \(0.316856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6951 | 1.01415 | 0.507077 | − | 0.861901i | \(-0.330726\pi\) | ||||
0.507077 | + | 0.861901i | \(0.330726\pi\) | |||||||
\(272\) | −0.0633500 | −0.00384116 | ||||||||
\(273\) | 10.5213 | 0.636775 | ||||||||
\(274\) | 14.4735 | 0.874378 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.52333 | −0.151887 | ||||||||
\(277\) | 28.0654 | 1.68628 | 0.843142 | − | 0.537691i | \(-0.180703\pi\) | ||||
0.843142 | + | 0.537691i | \(0.180703\pi\) | |||||||
\(278\) | 7.55082 | 0.452868 | ||||||||
\(279\) | 0.132121 | 0.00790985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2279 | −1.32601 | −0.663004 | − | 0.748616i | \(-0.730719\pi\) | ||||
−0.663004 | + | 0.748616i | \(0.730719\pi\) | |||||||
\(282\) | 3.31391 | 0.197341 | ||||||||
\(283\) | 11.0420 | 0.656379 | 0.328190 | − | 0.944612i | \(-0.393561\pi\) | ||||
0.328190 | + | 0.944612i | \(0.393561\pi\) | |||||||
\(284\) | −1.80770 | −0.107267 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.66254 | 0.571358 | ||||||||
\(287\) | −2.79850 | −0.165190 | ||||||||
\(288\) | 3.43040 | 0.202139 | ||||||||
\(289\) | −16.9789 | −0.998760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.4058 | 1.13759 | ||||||||
\(292\) | −7.51930 | −0.440033 | ||||||||
\(293\) | −8.90419 | −0.520188 | −0.260094 | − | 0.965583i | \(-0.583754\pi\) | ||||
−0.260094 | + | 0.965583i | \(0.583754\pi\) | |||||||
\(294\) | 1.54930 | 0.0903569 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.16014 | 0.183679 | ||||||||
\(297\) | −9.71737 | −0.563859 | ||||||||
\(298\) | 3.32264 | 0.192476 | ||||||||
\(299\) | 5.55212 | 0.321087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5742 | 0.667124 | ||||||||
\(302\) | −2.60685 | −0.150008 | ||||||||
\(303\) | 17.7432 | 1.01932 | ||||||||
\(304\) | −1.41084 | −0.0809174 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0701690 | −0.00401130 | ||||||||
\(307\) | 3.40251 | 0.194192 | 0.0970958 | − | 0.995275i | \(-0.469045\pi\) | ||||
0.0970958 | + | 0.995275i | \(0.469045\pi\) | |||||||
\(308\) | −2.83447 | −0.161509 | ||||||||
\(309\) | 12.2408 | 0.696353 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5337 | −1.22107 | −0.610533 | − | 0.791991i | \(-0.709045\pi\) | ||||
−0.610533 | + | 0.791991i | \(0.709045\pi\) | |||||||
\(312\) | −28.6578 | −1.62243 | ||||||||
\(313\) | −24.4624 | −1.38270 | −0.691348 | − | 0.722522i | \(-0.742983\pi\) | ||||
−0.691348 | + | 0.722522i | \(0.742983\pi\) | |||||||
\(314\) | 14.0290 | 0.791703 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.0802 | 1.18585 | ||||||||
\(317\) | −10.9401 | −0.614457 | −0.307228 | − | 0.951636i | \(-0.599402\pi\) | ||||
−0.307228 | + | 0.951636i | \(0.599402\pi\) | |||||||
\(318\) | 11.2790 | 0.632495 | ||||||||
\(319\) | 6.95931 | 0.389646 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.8090 | 1.44052 | ||||||||
\(322\) | 0.817573 | 0.0455616 | ||||||||
\(323\) | 0.469650 | 0.0261320 | ||||||||
\(324\) | 13.8800 | 0.771111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.90449 | 0.493174 | ||||||||
\(327\) | −37.4737 | −2.07230 | ||||||||
\(328\) | 7.62257 | 0.420886 | ||||||||
\(329\) | 2.13898 | 0.117926 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.4654 | 1.72949 | 0.864747 | − | 0.502207i | \(-0.167478\pi\) | ||||
0.864747 | + | 0.502207i | \(0.167478\pi\) | |||||||
\(332\) | 21.5107 | 1.18055 | ||||||||
\(333\) | −0.685690 | −0.0375756 | ||||||||
\(334\) | −4.60194 | −0.251807 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.826674 | 0.0450987 | ||||||||
\(337\) | −35.5298 | −1.93543 | −0.967717 | − | 0.252040i | \(-0.918899\pi\) | ||||
−0.967717 | + | 0.252040i | \(0.918899\pi\) | |||||||
\(338\) | 14.5741 | 0.792726 | ||||||||
\(339\) | −11.3932 | −0.618792 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.475859 | 0.0257692 | ||||||||
\(342\) | −1.56271 | −0.0845015 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −31.5258 | −1.69976 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.5085 | −0.887505 | ||||||||
\(347\) | −29.9862 | −1.60974 | −0.804870 | − | 0.593451i | \(-0.797765\pi\) | ||||
−0.804870 | + | 0.593451i | \(0.797765\pi\) | |||||||
\(348\) | −8.24963 | −0.442226 | ||||||||
\(349\) | 9.56989 | 0.512264 | 0.256132 | − | 0.966642i | \(-0.417552\pi\) | ||||
0.256132 | + | 0.966642i | \(0.417552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.3455 | −1.35285 | ||||||||
\(352\) | 12.3553 | 0.658540 | ||||||||
\(353\) | −1.92987 | −0.102717 | −0.0513584 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513584 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(354\) | 7.32149 | 0.389133 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.16213 | −0.379592 | ||||||||
\(357\) | −0.275188 | −0.0145645 | ||||||||
\(358\) | −0.0398947 | −0.00210850 | ||||||||
\(359\) | −27.4206 | −1.44720 | −0.723602 | − | 0.690217i | \(-0.757515\pi\) | ||||
−0.723602 | + | 0.690217i | \(0.757515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.54062 | −0.449506 | ||||||||
\(362\) | 9.00532 | 0.473309 | ||||||||
\(363\) | −12.2584 | −0.643399 | ||||||||
\(364\) | −7.39306 | −0.387502 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.63901 | 0.242485 | ||||||||
\(367\) | −28.8264 | −1.50472 | −0.752362 | − | 0.658750i | \(-0.771085\pi\) | ||||
−0.752362 | + | 0.658750i | \(0.771085\pi\) | |||||||
\(368\) | 0.436240 | 0.0227406 | ||||||||
\(369\) | −1.65395 | −0.0861013 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.28007 | 0.377963 | ||||||||
\(372\) | −0.564087 | −0.0292466 | ||||||||
\(373\) | 5.41771 | 0.280518 | 0.140259 | − | 0.990115i | \(-0.455206\pi\) | ||||
0.140259 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(374\) | −0.252728 | −0.0130683 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.82615 | −0.300461 | ||||||||
\(377\) | 18.1518 | 0.934864 | ||||||||
\(378\) | −3.73224 | −0.191966 | ||||||||
\(379\) | 6.96741 | 0.357892 | 0.178946 | − | 0.983859i | \(-0.442731\pi\) | ||||
0.178946 | + | 0.983859i | \(0.442731\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.06462 | −0.413163 | ||||||||
\(382\) | 11.1429 | 0.570120 | ||||||||
\(383\) | 11.7539 | 0.600598 | 0.300299 | − | 0.953845i | \(-0.402914\pi\) | ||||
0.300299 | + | 0.953845i | \(0.402914\pi\) | |||||||
\(384\) | −15.9978 | −0.816385 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.74120 | −0.343118 | ||||||||
\(387\) | 6.84050 | 0.347722 | ||||||||
\(388\) | −13.6360 | −0.692265 | ||||||||
\(389\) | −37.4964 | −1.90114 | −0.950572 | − | 0.310506i | \(-0.899502\pi\) | ||||
−0.950572 | + | 0.310506i | \(0.899502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.145218 | −0.00734400 | ||||||||
\(392\) | −2.72381 | −0.137573 | ||||||||
\(393\) | 10.4956 | 0.529434 | ||||||||
\(394\) | −5.09553 | −0.256709 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.67521 | −0.0841824 | ||||||||
\(397\) | 7.47066 | 0.374941 | 0.187471 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187471 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(398\) | 6.34498 | 0.318045 | ||||||||
\(399\) | −6.12860 | −0.306814 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9575 | 0.946695 | 0.473347 | − | 0.880876i | \(-0.343046\pi\) | ||||
0.473347 | + | 0.880876i | \(0.343046\pi\) | |||||||
\(402\) | 19.8408 | 0.989568 | ||||||||
\(403\) | 1.24117 | 0.0618271 | ||||||||
\(404\) | −12.4678 | −0.620294 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.67292 | 0.132655 | ||||||||
\(407\) | −2.46965 | −0.122416 | ||||||||
\(408\) | 0.749559 | 0.0371087 | ||||||||
\(409\) | 12.6697 | 0.626478 | 0.313239 | − | 0.949674i | \(-0.398586\pi\) | ||||
0.313239 | + | 0.949674i | \(0.398586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.5472 | 1.65476 | ||||||||
\(412\) | −8.60133 | −0.423757 | ||||||||
\(413\) | 4.72568 | 0.232536 | ||||||||
\(414\) | 0.483197 | 0.0237478 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.2260 | 1.58001 | ||||||||
\(417\) | 17.5015 | 0.857054 | ||||||||
\(418\) | −5.62840 | −0.275294 | ||||||||
\(419\) | 9.45883 | 0.462094 | 0.231047 | − | 0.972943i | \(-0.425785\pi\) | ||||
0.231047 | + | 0.972943i | \(0.425785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.83766 | 0.187036 | 0.0935180 | − | 0.995618i | \(-0.470189\pi\) | ||||
0.0935180 | + | 0.995618i | \(0.470189\pi\) | |||||||
\(422\) | 8.21433 | 0.399867 | ||||||||
\(423\) | 1.26416 | 0.0614658 | ||||||||
\(424\) | −19.8295 | −0.963006 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.10327 | 0.101904 | ||||||||
\(427\) | 2.99427 | 0.144903 | ||||||||
\(428\) | −18.1355 | −0.876610 | ||||||||
\(429\) | 22.3961 | 1.08130 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.26552 | −0.398136 | −0.199068 | − | 0.979986i | \(-0.563791\pi\) | ||||
−0.199068 | + | 0.979986i | \(0.563791\pi\) | |||||||
\(432\) | −1.99144 | −0.0958134 | ||||||||
\(433\) | −19.8987 | −0.956271 | −0.478136 | − | 0.878286i | \(-0.658687\pi\) | ||||
−0.478136 | + | 0.878286i | \(0.658687\pi\) | |||||||
\(434\) | 0.182767 | 0.00877312 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.3320 | 1.26107 | ||||||||
\(437\) | −3.23410 | −0.154708 | ||||||||
\(438\) | 8.74876 | 0.418032 | ||||||||
\(439\) | −6.12702 | −0.292427 | −0.146213 | − | 0.989253i | \(-0.546709\pi\) | ||||
−0.146213 | + | 0.989253i | \(0.546709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.591014 | 0.0281435 | ||||||||
\(442\) | −0.659184 | −0.0313542 | ||||||||
\(443\) | 6.22440 | 0.295730 | 0.147865 | − | 0.989008i | \(-0.452760\pi\) | ||||
0.147865 | + | 0.989008i | \(0.452760\pi\) | |||||||
\(444\) | 2.92755 | 0.138935 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.2354 | −0.626713 | ||||||||
\(447\) | 7.70133 | 0.364260 | ||||||||
\(448\) | 3.87293 | 0.182979 | ||||||||
\(449\) | 12.0155 | 0.567045 | 0.283523 | − | 0.958966i | \(-0.408497\pi\) | ||||
0.283523 | + | 0.958966i | \(0.408497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.95705 | −0.280506 | ||||||||
\(452\) | 8.00574 | 0.376558 | ||||||||
\(453\) | −6.04225 | −0.283890 | ||||||||
\(454\) | −15.6493 | −0.734459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.6931 | 0.781727 | ||||||||
\(457\) | 3.26533 | 0.152746 | 0.0763728 | − | 0.997079i | \(-0.475666\pi\) | ||||
0.0763728 | + | 0.997079i | \(0.475666\pi\) | |||||||
\(458\) | −7.06539 | −0.330144 | ||||||||
\(459\) | 0.662924 | 0.0309427 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.7704 | −0.734502 | −0.367251 | − | 0.930122i | \(-0.619701\pi\) | ||||
−0.367251 | + | 0.930122i | \(0.619701\pi\) | |||||||
\(462\) | 3.29793 | 0.153433 | ||||||||
\(463\) | −36.2016 | −1.68243 | −0.841215 | − | 0.540700i | \(-0.818159\pi\) | ||||
−0.841215 | + | 0.540700i | \(0.818159\pi\) | |||||||
\(464\) | 1.42622 | 0.0662105 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.8872 | −0.967580 | ||||||||
\(467\) | 27.2801 | 1.26237 | 0.631187 | − | 0.775631i | \(-0.282568\pi\) | ||||
0.631187 | + | 0.775631i | \(0.282568\pi\) | |||||||
\(468\) | −4.36940 | −0.201976 | ||||||||
\(469\) | 12.8063 | 0.591340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.5169 | 1.49830 | ||||||||
\(472\) | −12.8718 | −0.592475 | ||||||||
\(473\) | 24.6374 | 1.13283 | ||||||||
\(474\) | −24.5270 | −1.12656 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.193369 | 0.00886305 | ||||||||
\(477\) | 4.30263 | 0.197004 | ||||||||
\(478\) | 24.5173 | 1.12140 | ||||||||
\(479\) | −2.24978 | −0.102795 | −0.0513976 | − | 0.998678i | \(-0.516368\pi\) | ||||
−0.0513976 | + | 0.998678i | \(0.516368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.44153 | −0.293708 | ||||||||
\(482\) | 1.20955 | 0.0550937 | ||||||||
\(483\) | 1.89500 | 0.0862254 | ||||||||
\(484\) | 8.61371 | 0.391532 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.95278 | −0.224662 | ||||||||
\(487\) | −29.1879 | −1.32263 | −0.661314 | − | 0.750109i | \(-0.730001\pi\) | ||||
−0.661314 | + | 0.750109i | \(0.730001\pi\) | |||||||
\(488\) | −8.15580 | −0.369196 | ||||||||
\(489\) | 20.6391 | 0.933333 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.72378 | −0.393698 | −0.196849 | − | 0.980434i | \(-0.563071\pi\) | ||||
−0.196849 | + | 0.980434i | \(0.563071\pi\) | |||||||
\(492\) | 7.06154 | 0.318359 | ||||||||
\(493\) | −0.474768 | −0.0213825 | ||||||||
\(494\) | −14.6804 | −0.660503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0975209 | 0.00437882 | ||||||||
\(497\) | 1.35757 | 0.0608951 | ||||||||
\(498\) | −25.0279 | −1.12153 | ||||||||
\(499\) | 15.1622 | 0.678752 | 0.339376 | − | 0.940651i | \(-0.389784\pi\) | ||||
0.339376 | + | 0.940651i | \(0.389784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6665 | −0.476545 | ||||||||
\(502\) | −16.0088 | −0.714507 | ||||||||
\(503\) | −21.9258 | −0.977622 | −0.488811 | − | 0.872390i | \(-0.662569\pi\) | ||||
−0.488811 | + | 0.872390i | \(0.662569\pi\) | |||||||
\(504\) | −1.60981 | −0.0717065 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.74033 | 0.0773672 | ||||||||
\(507\) | 33.7803 | 1.50024 | ||||||||
\(508\) | 5.66684 | 0.251425 | ||||||||
\(509\) | −35.3864 | −1.56848 | −0.784238 | − | 0.620461i | \(-0.786946\pi\) | ||||
−0.784238 | + | 0.620461i | \(0.786946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.64692 | 0.249805 | ||||||||
\(512\) | 4.90852 | 0.216928 | ||||||||
\(513\) | 14.7637 | 0.651834 | ||||||||
\(514\) | −7.70175 | −0.339710 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −29.2054 | −1.28570 | ||||||||
\(517\) | 4.55315 | 0.200247 | ||||||||
\(518\) | −0.948542 | −0.0416765 | ||||||||
\(519\) | −38.2640 | −1.67960 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.41956 | −0.106003 | −0.0530015 | − | 0.998594i | \(-0.516879\pi\) | ||||
−0.0530015 | + | 0.998594i | \(0.516879\pi\) | |||||||
\(522\) | 1.57974 | 0.0691432 | ||||||||
\(523\) | −8.41047 | −0.367764 | −0.183882 | − | 0.982948i | \(-0.558866\pi\) | ||||
−0.183882 | + | 0.982948i | \(0.558866\pi\) | |||||||
\(524\) | −7.37505 | −0.322180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.95488 | −0.0852367 | ||||||||
\(527\) | −0.0324634 | −0.00141413 | ||||||||
\(528\) | 1.75970 | 0.0765813 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.79295 | 0.121204 | ||||||||
\(532\) | 4.30644 | 0.186708 | ||||||||
\(533\) | −15.5376 | −0.673008 | ||||||||
\(534\) | 8.33320 | 0.360613 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.8819 | −1.50667 | ||||||||
\(537\) | −0.0924693 | −0.00399035 | ||||||||
\(538\) | 14.5930 | 0.629148 | ||||||||
\(539\) | 2.12866 | 0.0916878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.1387 | −1.81168 | −0.905842 | − | 0.423617i | \(-0.860760\pi\) | ||||
−0.905842 | + | 0.423617i | \(0.860760\pi\) | |||||||
\(542\) | 13.6495 | 0.586294 | ||||||||
\(543\) | 20.8728 | 0.895739 | ||||||||
\(544\) | −0.842886 | −0.0361384 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.60189 | 0.368127 | ||||||||
\(547\) | −39.6226 | −1.69414 | −0.847069 | − | 0.531482i | \(-0.821635\pi\) | ||||
−0.847069 | + | 0.531482i | \(0.821635\pi\) | |||||||
\(548\) | −23.5729 | −1.00698 | ||||||||
\(549\) | 1.76965 | 0.0755270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.5734 | −0.450441 | ||||||||
\(552\) | −5.16160 | −0.219692 | ||||||||
\(553\) | −15.8310 | −0.673203 | ||||||||
\(554\) | 22.9455 | 0.974860 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.2980 | −0.521550 | ||||||||
\(557\) | 17.2373 | 0.730368 | 0.365184 | − | 0.930935i | \(-0.381006\pi\) | ||||
0.365184 | + | 0.930935i | \(0.381006\pi\) | |||||||
\(558\) | 0.108018 | 0.00457277 | ||||||||
\(559\) | 64.2612 | 2.71796 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.585781 | −0.0247317 | ||||||||
\(562\) | −18.1730 | −0.766580 | ||||||||
\(563\) | 40.4377 | 1.70425 | 0.852123 | − | 0.523341i | \(-0.175315\pi\) | ||||
0.852123 | + | 0.523341i | \(0.175315\pi\) | |||||||
\(564\) | −5.39734 | −0.227269 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.02765 | 0.379460 | ||||||||
\(567\) | −10.4237 | −0.437756 | ||||||||
\(568\) | −3.69774 | −0.155154 | ||||||||
\(569\) | 23.0934 | 0.968126 | 0.484063 | − | 0.875033i | \(-0.339161\pi\) | ||||
0.484063 | + | 0.875033i | \(0.339161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.95672 | −0.207432 | −0.103716 | − | 0.994607i | \(-0.533073\pi\) | ||||
−0.103716 | + | 0.994607i | \(0.533073\pi\) | |||||||
\(572\) | −15.7373 | −0.658009 | ||||||||
\(573\) | 25.8274 | 1.07895 | ||||||||
\(574\) | −2.28798 | −0.0954983 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.28896 | 0.0953732 | ||||||||
\(577\) | 21.6383 | 0.900815 | 0.450408 | − | 0.892823i | \(-0.351279\pi\) | ||||
0.450408 | + | 0.892823i | \(0.351279\pi\) | |||||||
\(578\) | −13.8815 | −0.577394 | ||||||||
\(579\) | −15.6250 | −0.649352 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.1543 | −0.670194 | ||||||||
\(582\) | 15.8656 | 0.657652 | ||||||||
\(583\) | 15.4968 | 0.641811 | ||||||||
\(584\) | −15.3811 | −0.636475 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.27982 | −0.300727 | ||||||||
\(587\) | −22.8051 | −0.941268 | −0.470634 | − | 0.882329i | \(-0.655975\pi\) | ||||
−0.470634 | + | 0.882329i | \(0.655975\pi\) | |||||||
\(588\) | −2.52333 | −0.104060 | ||||||||
\(589\) | −0.722979 | −0.0297898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8106 | −0.485823 | ||||||||
\(592\) | −0.506122 | −0.0208015 | ||||||||
\(593\) | 15.9010 | 0.652976 | 0.326488 | − | 0.945201i | \(-0.394135\pi\) | ||||
0.326488 | + | 0.945201i | \(0.394135\pi\) | |||||||
\(594\) | −7.94466 | −0.325973 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.41156 | −0.221666 | ||||||||
\(597\) | 14.7066 | 0.601901 | ||||||||
\(598\) | 4.53926 | 0.185624 | ||||||||
\(599\) | −20.5273 | −0.838725 | −0.419362 | − | 0.907819i | \(-0.637746\pi\) | ||||
−0.419362 | + | 0.907819i | \(0.637746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.6529 | −1.29115 | −0.645575 | − | 0.763697i | \(-0.723382\pi\) | ||||
−0.645575 | + | 0.763697i | \(0.723382\pi\) | |||||||
\(602\) | 9.46273 | 0.385672 | ||||||||
\(603\) | 7.56870 | 0.308221 | ||||||||
\(604\) | 4.24576 | 0.172758 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.5063 | 0.589280 | ||||||||
\(607\) | −15.7128 | −0.637762 | −0.318881 | − | 0.947795i | \(-0.603307\pi\) | ||||
−0.318881 | + | 0.947795i | \(0.603307\pi\) | |||||||
\(608\) | −18.7716 | −0.761287 | ||||||||
\(609\) | 6.19539 | 0.251050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.8759 | 0.480445 | ||||||||
\(612\) | 0.114284 | 0.00461965 | ||||||||
\(613\) | 35.5774 | 1.43696 | 0.718479 | − | 0.695549i | \(-0.244839\pi\) | ||||
0.718479 | + | 0.695549i | \(0.244839\pi\) | |||||||
\(614\) | 2.78180 | 0.112264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.79805 | −0.233610 | ||||||||
\(617\) | 6.23170 | 0.250879 | 0.125439 | − | 0.992101i | \(-0.459966\pi\) | ||||
0.125439 | + | 0.992101i | \(0.459966\pi\) | |||||||
\(618\) | 10.0077 | 0.402570 | ||||||||
\(619\) | −33.4737 | −1.34542 | −0.672712 | − | 0.739905i | \(-0.734870\pi\) | ||||
−0.672712 | + | 0.739905i | \(0.734870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.56502 | −0.183188 | ||||||||
\(622\) | −17.6054 | −0.705912 | ||||||||
\(623\) | 5.37869 | 0.215493 | ||||||||
\(624\) | 4.58979 | 0.183739 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.9998 | −0.799353 | ||||||||
\(627\) | −13.0457 | −0.520995 | ||||||||
\(628\) | −22.8489 | −0.911772 | ||||||||
\(629\) | 0.168481 | 0.00671778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.34219 | 0.172860 | 0.0864299 | − | 0.996258i | \(-0.472454\pi\) | ||||
0.0864299 | + | 0.996258i | \(0.472454\pi\) | |||||||
\(632\) | 43.1206 | 1.71525 | ||||||||
\(633\) | 19.0394 | 0.756749 | ||||||||
\(634\) | −8.94432 | −0.355224 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.3700 | −0.728419 | ||||||||
\(637\) | 5.55212 | 0.219983 | ||||||||
\(638\) | 5.68974 | 0.225259 | ||||||||
\(639\) | 0.802340 | 0.0317401 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5873 | 0.536667 | 0.268334 | − | 0.963326i | \(-0.413527\pi\) | ||||
0.268334 | + | 0.963326i | \(0.413527\pi\) | |||||||
\(642\) | 21.1008 | 0.832780 | ||||||||
\(643\) | −27.3763 | −1.07962 | −0.539808 | − | 0.841788i | \(-0.681503\pi\) | ||||
−0.539808 | + | 0.841788i | \(0.681503\pi\) | |||||||
\(644\) | −1.33157 | −0.0524714 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.383973 | 0.0151072 | ||||||||
\(647\) | −40.8194 | −1.60478 | −0.802389 | − | 0.596802i | \(-0.796438\pi\) | ||||
−0.802389 | + | 0.596802i | \(0.796438\pi\) | |||||||
\(648\) | 28.3922 | 1.11535 | ||||||||
\(649\) | 10.0594 | 0.394865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.423624 | 0.0166031 | ||||||||
\(652\) | −14.5027 | −0.567969 | ||||||||
\(653\) | −18.3223 | −0.717007 | −0.358504 | − | 0.933528i | \(-0.616713\pi\) | ||||
−0.358504 | + | 0.933528i | \(0.616713\pi\) | |||||||
\(654\) | −30.6375 | −1.19802 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.22082 | −0.0476649 | ||||||||
\(657\) | 3.33741 | 0.130205 | ||||||||
\(658\) | 1.74877 | 0.0681741 | ||||||||
\(659\) | 38.4961 | 1.49960 | 0.749798 | − | 0.661667i | \(-0.230151\pi\) | ||||
0.749798 | + | 0.661667i | \(0.230151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0492 | 0.818720 | 0.409360 | − | 0.912373i | \(-0.365752\pi\) | ||||
0.409360 | + | 0.912373i | \(0.365752\pi\) | |||||||
\(662\) | 25.7253 | 0.999841 | ||||||||
\(663\) | −1.52788 | −0.0593379 | ||||||||
\(664\) | 44.0012 | 1.70758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.560602 | −0.0217229 | ||||||||
\(667\) | 3.26934 | 0.126589 | ||||||||
\(668\) | 7.49514 | 0.289996 | ||||||||
\(669\) | −30.6774 | −1.18606 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.37377 | 0.246057 | ||||||||
\(672\) | 10.9991 | 0.424298 | ||||||||
\(673\) | −0.230881 | −0.00889982 | −0.00444991 | − | 0.999990i | \(-0.501416\pi\) | ||||
−0.00444991 | + | 0.999990i | \(0.501416\pi\) | |||||||
\(674\) | −29.0482 | −1.11890 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.7367 | −0.912950 | ||||||||
\(677\) | −33.4150 | −1.28424 | −0.642121 | − | 0.766603i | \(-0.721945\pi\) | ||||
−0.642121 | + | 0.766603i | \(0.721945\pi\) | |||||||
\(678\) | −9.31474 | −0.357731 | ||||||||
\(679\) | 10.2405 | 0.392995 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.2725 | −1.38996 | ||||||||
\(682\) | 0.389049 | 0.0148975 | ||||||||
\(683\) | −27.2707 | −1.04348 | −0.521742 | − | 0.853103i | \(-0.674718\pi\) | ||||
−0.521742 | + | 0.853103i | \(0.674718\pi\) | |||||||
\(684\) | 2.54517 | 0.0973169 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.817573 | 0.0312151 | ||||||||
\(687\) | −16.3764 | −0.624799 | ||||||||
\(688\) | 5.04912 | 0.192496 | ||||||||
\(689\) | 40.4198 | 1.53987 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1761 | −0.805576 | −0.402788 | − | 0.915293i | \(-0.631959\pi\) | ||||
−0.402788 | + | 0.915293i | \(0.631959\pi\) | |||||||
\(692\) | 26.8873 | 1.02210 | ||||||||
\(693\) | 1.25807 | 0.0477900 | ||||||||
\(694\) | −24.5159 | −0.930609 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −16.8750 | −0.639647 | ||||||||
\(697\) | 0.406393 | 0.0153932 | ||||||||
\(698\) | 7.82408 | 0.296146 | ||||||||
\(699\) | −48.4130 | −1.83115 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.6727 | −0.440873 | −0.220436 | − | 0.975401i | \(-0.570748\pi\) | ||||
−0.220436 | + | 0.975401i | \(0.570748\pi\) | |||||||
\(702\) | −20.7218 | −0.782095 | ||||||||
\(703\) | 3.75217 | 0.141516 | ||||||||
\(704\) | 8.24415 | 0.310713 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.57781 | −0.0593818 | ||||||||
\(707\) | 9.36317 | 0.352138 | ||||||||
\(708\) | −11.9245 | −0.448149 | ||||||||
\(709\) | 5.69291 | 0.213802 | 0.106901 | − | 0.994270i | \(-0.465907\pi\) | ||||
0.106901 | + | 0.994270i | \(0.465907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.35635 | −0.350891 | ||||||||
\(712\) | −14.6505 | −0.549051 | ||||||||
\(713\) | 0.223549 | 0.00837197 | ||||||||
\(714\) | −0.224986 | −0.00841990 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0649763 | 0.00242828 | ||||||||
\(717\) | 56.8270 | 2.12224 | ||||||||
\(718\) | −22.4183 | −0.836645 | ||||||||
\(719\) | 2.96662 | 0.110636 | 0.0553181 | − | 0.998469i | \(-0.482383\pi\) | ||||
0.0553181 | + | 0.998469i | \(0.482383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.45952 | 0.240565 | ||||||||
\(722\) | −6.98258 | −0.259865 | ||||||||
\(723\) | 2.80354 | 0.104265 | ||||||||
\(724\) | −14.6669 | −0.545091 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.0221 | −0.371956 | ||||||||
\(727\) | 18.3570 | 0.680822 | 0.340411 | − | 0.940277i | \(-0.389434\pi\) | ||||
0.340411 | + | 0.940277i | \(0.389434\pi\) | |||||||
\(728\) | −15.1229 | −0.560492 | ||||||||
\(729\) | 19.7915 | 0.733020 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.68078 | −0.0621659 | ||||||||
\(732\) | −7.55553 | −0.279260 | ||||||||
\(733\) | −9.59697 | −0.354472 | −0.177236 | − | 0.984168i | \(-0.556716\pi\) | ||||
−0.177236 | + | 0.984168i | \(0.556716\pi\) | |||||||
\(734\) | −23.5676 | −0.869898 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.80427 | 0.213948 | ||||||||
\(737\) | 27.2602 | 1.00414 | ||||||||
\(738\) | −1.35223 | −0.0497762 | ||||||||
\(739\) | 36.6324 | 1.34754 | 0.673772 | − | 0.738939i | \(-0.264673\pi\) | ||||
0.673772 | + | 0.738939i | \(0.264673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.0267 | −1.25000 | ||||||||
\(742\) | 5.95199 | 0.218504 | ||||||||
\(743\) | 11.6543 | 0.427554 | 0.213777 | − | 0.976882i | \(-0.431423\pi\) | ||||
0.213777 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(744\) | −1.15387 | −0.0423029 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.42937 | 0.162171 | ||||||||
\(747\) | −9.54743 | −0.349322 | ||||||||
\(748\) | 0.411616 | 0.0150502 | ||||||||
\(749\) | 13.6196 | 0.497648 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9424 | −0.691216 | −0.345608 | − | 0.938379i | \(-0.612327\pi\) | ||||
−0.345608 | + | 0.938379i | \(0.612327\pi\) | |||||||
\(752\) | 0.933107 | 0.0340269 | ||||||||
\(753\) | −37.1057 | −1.35221 | ||||||||
\(754\) | 14.8404 | 0.540455 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.07867 | 0.221079 | ||||||||
\(757\) | 17.4475 | 0.634139 | 0.317070 | − | 0.948402i | \(-0.397301\pi\) | ||||
0.317070 | + | 0.948402i | \(0.397301\pi\) | |||||||
\(758\) | 5.69636 | 0.206901 | ||||||||
\(759\) | 4.03380 | 0.146418 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.5646 | 1.47046 | 0.735232 | − | 0.677816i | \(-0.237073\pi\) | ||||
0.735232 | + | 0.677816i | \(0.237073\pi\) | |||||||
\(762\) | −6.59341 | −0.238854 | ||||||||
\(763\) | −19.7751 | −0.715906 | ||||||||
\(764\) | −18.1483 | −0.656584 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.60969 | 0.347212 | ||||||||
\(767\) | 26.2376 | 0.947383 | ||||||||
\(768\) | −27.7578 | −1.00162 | ||||||||
\(769\) | 24.6548 | 0.889076 | 0.444538 | − | 0.895760i | \(-0.353368\pi\) | ||||
0.444538 | + | 0.895760i | \(0.353368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.8514 | −0.642902 | ||||||||
\(772\) | 10.9793 | 0.395155 | ||||||||
\(773\) | 13.7942 | 0.496144 | 0.248072 | − | 0.968742i | \(-0.420203\pi\) | ||||
0.248072 | + | 0.968742i | \(0.420203\pi\) | |||||||
\(774\) | 5.59260 | 0.201022 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27.8932 | −1.00131 | ||||||||
\(777\) | −2.19856 | −0.0788729 | ||||||||
\(778\) | −30.6560 | −1.09907 | ||||||||
\(779\) | 9.05062 | 0.324272 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.88979 | 0.103405 | ||||||||
\(782\) | −0.118727 | −0.00424565 | ||||||||
\(783\) | −14.9246 | −0.533362 | ||||||||
\(784\) | 0.436240 | 0.0155800 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.58093 | 0.306072 | ||||||||
\(787\) | −27.0967 | −0.965892 | −0.482946 | − | 0.875650i | \(-0.660433\pi\) | ||||
−0.482946 | + | 0.875650i | \(0.660433\pi\) | |||||||
\(788\) | 8.29905 | 0.295641 | ||||||||
\(789\) | −4.53108 | −0.161311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.01223 | −0.213770 | ||||||||
\(792\) | −3.42673 | −0.121763 | ||||||||
\(793\) | 16.6245 | 0.590355 | ||||||||
\(794\) | 6.10781 | 0.216758 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.3340 | −0.366280 | ||||||||
\(797\) | −0.804834 | −0.0285087 | −0.0142543 | − | 0.999898i | \(-0.504537\pi\) | ||||
−0.0142543 | + | 0.999898i | \(0.504537\pi\) | |||||||
\(798\) | −5.01058 | −0.177373 | ||||||||
\(799\) | −0.310618 | −0.0109889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.17888 | 0.112320 | ||||||||
\(802\) | 15.4992 | 0.547295 | ||||||||
\(803\) | 12.0204 | 0.424189 | ||||||||
\(804\) | −32.3145 | −1.13964 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.01475 | 0.0357429 | ||||||||
\(807\) | 33.8241 | 1.19066 | ||||||||
\(808\) | −25.5035 | −0.897209 | ||||||||
\(809\) | −15.2092 | −0.534725 | −0.267363 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267363 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.1011 | −1.65394 | −0.826972 | − | 0.562243i | \(-0.809939\pi\) | ||||
−0.826972 | + | 0.562243i | \(0.809939\pi\) | |||||||
\(812\) | −4.35337 | −0.152773 | ||||||||
\(813\) | 31.6372 | 1.10956 | ||||||||
\(814\) | −2.01912 | −0.0707701 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.120048 | −0.00420252 | ||||||||
\(817\) | −37.4320 | −1.30958 | ||||||||
\(818\) | 10.3584 | 0.362174 | ||||||||
\(819\) | 3.28138 | 0.114661 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4688 | 1.23787 | 0.618935 | − | 0.785442i | \(-0.287565\pi\) | ||||
0.618935 | + | 0.785442i | \(0.287565\pi\) | |||||||
\(822\) | 27.4273 | 0.956636 | ||||||||
\(823\) | −21.9442 | −0.764928 | −0.382464 | − | 0.923970i | \(-0.624924\pi\) | ||||
−0.382464 | + | 0.923970i | \(0.624924\pi\) | |||||||
\(824\) | −17.5945 | −0.612932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.86359 | 0.134432 | ||||||||
\(827\) | 24.1922 | 0.841244 | 0.420622 | − | 0.907236i | \(-0.361812\pi\) | ||||
0.420622 | + | 0.907236i | \(0.361812\pi\) | |||||||
\(828\) | −0.786979 | −0.0273494 | ||||||||
\(829\) | 33.2183 | 1.15372 | 0.576860 | − | 0.816843i | \(-0.304278\pi\) | ||||
0.576860 | + | 0.816843i | \(0.304278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.1838 | 1.84493 | ||||||||
\(832\) | 21.5030 | 0.745482 | ||||||||
\(833\) | −0.145218 | −0.00503151 | ||||||||
\(834\) | 14.3088 | 0.495473 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.16694 | 0.317045 | ||||||||
\(837\) | −1.02051 | −0.0352738 | ||||||||
\(838\) | 7.73328 | 0.267142 | ||||||||
\(839\) | −25.8544 | −0.892592 | −0.446296 | − | 0.894885i | \(-0.647257\pi\) | ||||
−0.446296 | + | 0.894885i | \(0.647257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3114 | −0.631428 | ||||||||
\(842\) | 3.13757 | 0.108128 | ||||||||
\(843\) | −42.1219 | −1.45075 | ||||||||
\(844\) | −13.3786 | −0.460511 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.03355 | 0.0355341 | ||||||||
\(847\) | −6.46882 | −0.222271 | ||||||||
\(848\) | 3.17586 | 0.109059 | ||||||||
\(849\) | 20.9246 | 0.718130 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.16019 | −0.0397709 | ||||||||
\(852\) | −3.42558 | −0.117359 | ||||||||
\(853\) | −10.3145 | −0.353162 | −0.176581 | − | 0.984286i | \(-0.556504\pi\) | ||||
−0.176581 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(854\) | 2.44803 | 0.0837700 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −37.0970 | −1.26795 | ||||||||
\(857\) | 47.4897 | 1.62222 | 0.811109 | − | 0.584896i | \(-0.198865\pi\) | ||||
0.811109 | + | 0.584896i | \(0.198865\pi\) | |||||||
\(858\) | 18.3105 | 0.625109 | ||||||||
\(859\) | −37.5321 | −1.28058 | −0.640289 | − | 0.768134i | \(-0.721185\pi\) | ||||
−0.640289 | + | 0.768134i | \(0.721185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.30315 | −0.180731 | ||||||||
\(862\) | −6.75767 | −0.230167 | ||||||||
\(863\) | 29.7998 | 1.01440 | 0.507199 | − | 0.861829i | \(-0.330681\pi\) | ||||
0.507199 | + | 0.861829i | \(0.330681\pi\) | |||||||
\(864\) | −26.4966 | −0.901433 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.2686 | −0.552831 | ||||||||
\(867\) | −32.1750 | −1.09272 | ||||||||
\(868\) | −0.297672 | −0.0101036 | ||||||||
\(869\) | −33.6988 | −1.14315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.1021 | 2.40920 | ||||||||
\(872\) | 53.8635 | 1.82405 | ||||||||
\(873\) | 6.05230 | 0.204839 | ||||||||
\(874\) | −2.64411 | −0.0894383 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.2490 | −0.481431 | ||||||||
\(877\) | 36.3203 | 1.22645 | 0.613225 | − | 0.789908i | \(-0.289872\pi\) | ||||
0.613225 | + | 0.789908i | \(0.289872\pi\) | |||||||
\(878\) | −5.00929 | −0.169055 | ||||||||
\(879\) | −16.8734 | −0.569126 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.1876 | −0.376920 | −0.188460 | − | 0.982081i | \(-0.560350\pi\) | ||||
−0.188460 | + | 0.982081i | \(0.560350\pi\) | |||||||
\(882\) | 0.483197 | 0.0162701 | ||||||||
\(883\) | 36.6756 | 1.23423 | 0.617116 | − | 0.786872i | \(-0.288301\pi\) | ||||
0.617116 | + | 0.786872i | \(0.288301\pi\) | |||||||
\(884\) | 1.07361 | 0.0361093 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.08890 | 0.170965 | ||||||||
\(887\) | −52.6936 | −1.76928 | −0.884639 | − | 0.466276i | \(-0.845595\pi\) | ||||
−0.884639 | + | 0.466276i | \(0.845595\pi\) | |||||||
\(888\) | 5.98845 | 0.200959 | ||||||||
\(889\) | −4.25574 | −0.142733 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.1886 | −0.743346 | ||||||||
\(892\) | 21.5563 | 0.721759 | ||||||||
\(893\) | −6.91765 | −0.231490 | ||||||||
\(894\) | 6.29640 | 0.210583 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.44213 | −0.282032 | ||||||||
\(897\) | 10.5213 | 0.351294 | ||||||||
\(898\) | 9.82352 | 0.327815 | ||||||||
\(899\) | 0.730857 | 0.0243755 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.05720 | −0.0352204 | ||||||||
\(902\) | −4.87032 | −0.162164 | ||||||||
\(903\) | 21.9330 | 0.729885 | ||||||||
\(904\) | 16.3762 | 0.544663 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.93998 | −0.164120 | ||||||||
\(907\) | 25.9227 | 0.860750 | 0.430375 | − | 0.902650i | \(-0.358381\pi\) | ||||
0.430375 | + | 0.902650i | \(0.358381\pi\) | |||||||
\(908\) | 25.4879 | 0.845846 | ||||||||
\(909\) | 5.53377 | 0.183543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5021 | 1.37503 | 0.687513 | − | 0.726172i | \(-0.258703\pi\) | ||||
0.687513 | + | 0.726172i | \(0.258703\pi\) | |||||||
\(912\) | −2.67354 | −0.0885298 | ||||||||
\(913\) | −34.3870 | −1.13804 | ||||||||
\(914\) | 2.66965 | 0.0883040 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.5073 | 0.380214 | ||||||||
\(917\) | 5.53859 | 0.182900 | ||||||||
\(918\) | 0.541989 | 0.0178883 | ||||||||
\(919\) | 12.7219 | 0.419656 | 0.209828 | − | 0.977738i | \(-0.432710\pi\) | ||||
0.209828 | + | 0.977738i | \(0.432710\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.44775 | 0.212461 | ||||||||
\(922\) | −12.8935 | −0.424624 | ||||||||
\(923\) | 7.53736 | 0.248095 | ||||||||
\(924\) | −5.37131 | −0.176703 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.5974 | −0.972632 | ||||||||
\(927\) | 3.81767 | 0.125389 | ||||||||
\(928\) | 18.9761 | 0.622922 | ||||||||
\(929\) | −16.7846 | −0.550686 | −0.275343 | − | 0.961346i | \(-0.588791\pi\) | ||||
−0.275343 | + | 0.961346i | \(0.588791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.23410 | −0.105993 | ||||||||
\(932\) | 34.0188 | 1.11432 | ||||||||
\(933\) | −40.8063 | −1.33594 | ||||||||
\(934\) | 22.3035 | 0.729793 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.93784 | −0.292143 | ||||||||
\(937\) | 36.2327 | 1.18367 | 0.591835 | − | 0.806059i | \(-0.298404\pi\) | ||||
0.591835 | + | 0.806059i | \(0.298404\pi\) | |||||||
\(938\) | 10.4701 | 0.341860 | ||||||||
\(939\) | −46.3562 | −1.51278 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.57666 | −0.116596 | −0.0582979 | − | 0.998299i | \(-0.518567\pi\) | ||||
−0.0582979 | + | 0.998299i | \(0.518567\pi\) | |||||||
\(942\) | 26.5849 | 0.866184 | ||||||||
\(943\) | −2.79850 | −0.0911317 | ||||||||
\(944\) | 2.06153 | 0.0670972 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.1429 | 0.654902 | ||||||||
\(947\) | 1.14066 | 0.0370664 | 0.0185332 | − | 0.999828i | \(-0.494100\pi\) | ||||
0.0185332 | + | 0.999828i | \(0.494100\pi\) | |||||||
\(948\) | 39.9469 | 1.29741 | ||||||||
\(949\) | 31.3524 | 1.01774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.7314 | −0.672263 | ||||||||
\(952\) | 0.395546 | 0.0128197 | ||||||||
\(953\) | 26.0443 | 0.843659 | 0.421830 | − | 0.906675i | \(-0.361388\pi\) | ||||
0.421830 | + | 0.906675i | \(0.361388\pi\) | |||||||
\(954\) | 3.51771 | 0.113890 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −39.9312 | −1.29147 | ||||||||
\(957\) | 13.1879 | 0.426303 | ||||||||
\(958\) | −1.83936 | −0.0594271 | ||||||||
\(959\) | 17.7030 | 0.571661 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9500 | −0.998388 | ||||||||
\(962\) | −5.26642 | −0.169796 | ||||||||
\(963\) | 8.04935 | 0.259387 | ||||||||
\(964\) | −1.96999 | −0.0634491 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.54930 | 0.0498479 | ||||||||
\(967\) | −40.4020 | −1.29924 | −0.649620 | − | 0.760259i | \(-0.725072\pi\) | ||||
−0.649620 | + | 0.760259i | \(0.725072\pi\) | |||||||
\(968\) | 17.6198 | 0.566322 | ||||||||
\(969\) | 0.889985 | 0.0285904 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.75233 | −0.312967 | −0.156484 | − | 0.987681i | \(-0.550016\pi\) | ||||
−0.156484 | + | 0.987681i | \(0.550016\pi\) | |||||||
\(972\) | 8.06655 | 0.258735 | ||||||||
\(973\) | 9.23566 | 0.296082 | ||||||||
\(974\) | −23.8632 | −0.764626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.30622 | 0.0418111 | ||||||||
\(977\) | −18.1309 | −0.580060 | −0.290030 | − | 0.957018i | \(-0.593665\pi\) | ||||
−0.290030 | + | 0.957018i | \(0.593665\pi\) | |||||||
\(978\) | 16.8740 | 0.539571 | ||||||||
\(979\) | 11.4494 | 0.365924 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6874 | −0.373148 | ||||||||
\(982\) | −7.13232 | −0.227602 | ||||||||
\(983\) | −13.1228 | −0.418552 | −0.209276 | − | 0.977857i | \(-0.567111\pi\) | ||||
−0.209276 | + | 0.977857i | \(0.567111\pi\) | |||||||
\(984\) | 14.4447 | 0.460482 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.388158 | −0.0123615 | ||||||||
\(987\) | 4.05335 | 0.129020 | ||||||||
\(988\) | 23.9099 | 0.760674 | ||||||||
\(989\) | 11.5742 | 0.368037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.3779 | 1.40971 | 0.704855 | − | 0.709351i | \(-0.251012\pi\) | ||||
0.704855 | + | 0.709351i | \(0.251012\pi\) | |||||||
\(992\) | 1.29754 | 0.0411969 | ||||||||
\(993\) | 59.6268 | 1.89220 | ||||||||
\(994\) | 1.10991 | 0.0352042 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 40.7627 | 1.29162 | ||||||||
\(997\) | 10.0458 | 0.318152 | 0.159076 | − | 0.987266i | \(-0.449148\pi\) | ||||
0.159076 | + | 0.987266i | \(0.449148\pi\) | |||||||
\(998\) | 12.3962 | 0.392394 | ||||||||
\(999\) | 5.29630 | 0.167568 |
(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 | 4025.2.a.be.1.13 | 21 | ||
5.2 | odd | 4 | 805.2.c.c.484.27 | yes | 42 | ||
5.3 | odd | 4 | 805.2.c.c.484.16 | ✓ | 42 | ||
5.4 | even | 2 | 4025.2.a.bd.1.9 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.c.484.16 | ✓ | 42 | 5.3 | odd | 4 | ||
805.2.c.c.484.27 | yes | 42 | 5.2 | odd | 4 | ||
4025.2.a.bd.1.9 | 21 | 5.4 | even | 2 | |||
4025.2.a.be.1.13 | 21 | 1.1 | even | 1 | trivial |