Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.22639 | −0.708057 | −0.354028 | − | 0.935235i | \(-0.615188\pi\) | ||||
−0.354028 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.99280 | −0.891208 | −0.445604 | − | 0.895230i | \(-0.647011\pi\) | ||||
−0.445604 | + | 0.895230i | \(0.647011\pi\) | |||||||
\(6\) | −1.22639 | −0.500672 | ||||||||
\(7\) | −0.468701 | −0.177152 | −0.0885761 | − | 0.996069i | \(-0.528232\pi\) | ||||
−0.0885761 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.49597 | −0.498656 | ||||||||
\(10\) | −1.99280 | −0.630179 | ||||||||
\(11\) | −3.45486 | −1.04168 | −0.520840 | − | 0.853654i | \(-0.674381\pi\) | ||||
−0.520840 | + | 0.853654i | \(0.674381\pi\) | |||||||
\(12\) | −1.22639 | −0.354028 | ||||||||
\(13\) | −1.26776 | −0.351614 | −0.175807 | − | 0.984425i | \(-0.556253\pi\) | ||||
−0.175807 | + | 0.984425i | \(0.556253\pi\) | |||||||
\(14\) | −0.468701 | −0.125266 | ||||||||
\(15\) | 2.44395 | 0.631026 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.46010 | −0.596661 | −0.298331 | − | 0.954463i | \(-0.596430\pi\) | ||||
−0.298331 | + | 0.954463i | \(0.596430\pi\) | |||||||
\(18\) | −1.49597 | −0.352603 | ||||||||
\(19\) | −5.31368 | −1.21904 | −0.609521 | − | 0.792770i | \(-0.708638\pi\) | ||||
−0.609521 | + | 0.792770i | \(0.708638\pi\) | |||||||
\(20\) | −1.99280 | −0.445604 | ||||||||
\(21\) | 0.574810 | 0.125434 | ||||||||
\(22\) | −3.45486 | −0.736579 | ||||||||
\(23\) | 5.20667 | 1.08567 | 0.542833 | − | 0.839841i | \(-0.317352\pi\) | ||||
0.542833 | + | 0.839841i | \(0.317352\pi\) | |||||||
\(24\) | −1.22639 | −0.250336 | ||||||||
\(25\) | −1.02874 | −0.205748 | ||||||||
\(26\) | −1.26776 | −0.248629 | ||||||||
\(27\) | 5.51381 | 1.06113 | ||||||||
\(28\) | −0.468701 | −0.0885761 | ||||||||
\(29\) | −7.19591 | −1.33625 | −0.668124 | − | 0.744050i | \(-0.732902\pi\) | ||||
−0.668124 | + | 0.744050i | \(0.732902\pi\) | |||||||
\(30\) | 2.44395 | 0.446203 | ||||||||
\(31\) | 2.21935 | 0.398607 | 0.199303 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199303 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.23701 | 0.737569 | ||||||||
\(34\) | −2.46010 | −0.421903 | ||||||||
\(35\) | 0.934028 | 0.157880 | ||||||||
\(36\) | −1.49597 | −0.249328 | ||||||||
\(37\) | 2.86218 | 0.470539 | 0.235269 | − | 0.971930i | \(-0.424403\pi\) | ||||
0.235269 | + | 0.971930i | \(0.424403\pi\) | |||||||
\(38\) | −5.31368 | −0.861993 | ||||||||
\(39\) | 1.55477 | 0.248963 | ||||||||
\(40\) | −1.99280 | −0.315090 | ||||||||
\(41\) | 1.05732 | 0.165125 | 0.0825624 | − | 0.996586i | \(-0.473690\pi\) | ||||
0.0825624 | + | 0.996586i | \(0.473690\pi\) | |||||||
\(42\) | 0.574810 | 0.0886951 | ||||||||
\(43\) | 9.41639 | 1.43599 | 0.717993 | − | 0.696050i | \(-0.245061\pi\) | ||||
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(44\) | −3.45486 | −0.520840 | ||||||||
\(45\) | 2.98117 | 0.444406 | ||||||||
\(46\) | 5.20667 | 0.767682 | ||||||||
\(47\) | 10.8071 | 1.57637 | 0.788187 | − | 0.615436i | \(-0.211020\pi\) | ||||
0.788187 | + | 0.615436i | \(0.211020\pi\) | |||||||
\(48\) | −1.22639 | −0.177014 | ||||||||
\(49\) | −6.78032 | −0.968617 | ||||||||
\(50\) | −1.02874 | −0.145486 | ||||||||
\(51\) | 3.01704 | 0.422470 | ||||||||
\(52\) | −1.26776 | −0.175807 | ||||||||
\(53\) | 13.2163 | 1.81540 | 0.907699 | − | 0.419621i | \(-0.137837\pi\) | ||||
0.907699 | + | 0.419621i | \(0.137837\pi\) | |||||||
\(54\) | 5.51381 | 0.750334 | ||||||||
\(55\) | 6.88486 | 0.928354 | ||||||||
\(56\) | −0.468701 | −0.0626328 | ||||||||
\(57\) | 6.51664 | 0.863151 | ||||||||
\(58\) | −7.19591 | −0.944870 | ||||||||
\(59\) | 9.17618 | 1.19464 | 0.597319 | − | 0.802004i | \(-0.296233\pi\) | ||||
0.597319 | + | 0.802004i | \(0.296233\pi\) | |||||||
\(60\) | 2.44395 | 0.315513 | ||||||||
\(61\) | 11.1857 | 1.43219 | 0.716094 | − | 0.698004i | \(-0.245928\pi\) | ||||
0.716094 | + | 0.698004i | \(0.245928\pi\) | |||||||
\(62\) | 2.21935 | 0.281858 | ||||||||
\(63\) | 0.701161 | 0.0883380 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.52640 | 0.313362 | ||||||||
\(66\) | 4.23701 | 0.521540 | ||||||||
\(67\) | −14.5904 | −1.78250 | −0.891251 | − | 0.453510i | \(-0.850172\pi\) | ||||
−0.891251 | + | 0.453510i | \(0.850172\pi\) | |||||||
\(68\) | −2.46010 | −0.298331 | ||||||||
\(69\) | −6.38541 | −0.768713 | ||||||||
\(70\) | 0.934028 | 0.111638 | ||||||||
\(71\) | −9.48130 | −1.12522 | −0.562612 | − | 0.826721i | \(-0.690203\pi\) | ||||
−0.562612 | + | 0.826721i | \(0.690203\pi\) | |||||||
\(72\) | −1.49597 | −0.176301 | ||||||||
\(73\) | −8.28665 | −0.969879 | −0.484940 | − | 0.874548i | \(-0.661158\pi\) | ||||
−0.484940 | + | 0.874548i | \(0.661158\pi\) | |||||||
\(74\) | 2.86218 | 0.332721 | ||||||||
\(75\) | 1.26163 | 0.145681 | ||||||||
\(76\) | −5.31368 | −0.609521 | ||||||||
\(77\) | 1.61930 | 0.184536 | ||||||||
\(78\) | 1.55477 | 0.176043 | ||||||||
\(79\) | −7.53123 | −0.847330 | −0.423665 | − | 0.905819i | \(-0.639257\pi\) | ||||
−0.423665 | + | 0.905819i | \(0.639257\pi\) | |||||||
\(80\) | −1.99280 | −0.222802 | ||||||||
\(81\) | −2.27418 | −0.252686 | ||||||||
\(82\) | 1.05732 | 0.116761 | ||||||||
\(83\) | −12.5561 | −1.37821 | −0.689104 | − | 0.724662i | \(-0.741996\pi\) | ||||
−0.689104 | + | 0.724662i | \(0.741996\pi\) | |||||||
\(84\) | 0.574810 | 0.0627169 | ||||||||
\(85\) | 4.90249 | 0.531750 | ||||||||
\(86\) | 9.41639 | 1.01540 | ||||||||
\(87\) | 8.82499 | 0.946139 | ||||||||
\(88\) | −3.45486 | −0.368290 | ||||||||
\(89\) | −11.0345 | −1.16965 | −0.584827 | − | 0.811158i | \(-0.698838\pi\) | ||||
−0.584827 | + | 0.811158i | \(0.698838\pi\) | |||||||
\(90\) | 2.98117 | 0.314243 | ||||||||
\(91\) | 0.594201 | 0.0622892 | ||||||||
\(92\) | 5.20667 | 0.542833 | ||||||||
\(93\) | −2.72179 | −0.282236 | ||||||||
\(94\) | 10.8071 | 1.11466 | ||||||||
\(95\) | 10.5891 | 1.08642 | ||||||||
\(96\) | −1.22639 | −0.125168 | ||||||||
\(97\) | 1.02710 | 0.104286 | 0.0521431 | − | 0.998640i | \(-0.483395\pi\) | ||||
0.0521431 | + | 0.998640i | \(0.483395\pi\) | |||||||
\(98\) | −6.78032 | −0.684916 | ||||||||
\(99\) | 5.16836 | 0.519440 | ||||||||
\(100\) | −1.02874 | −0.102874 | ||||||||
\(101\) | 5.56064 | 0.553305 | 0.276652 | − | 0.960970i | \(-0.410775\pi\) | ||||
0.276652 | + | 0.960970i | \(0.410775\pi\) | |||||||
\(102\) | 3.01704 | 0.298731 | ||||||||
\(103\) | 17.3209 | 1.70668 | 0.853341 | − | 0.521354i | \(-0.174573\pi\) | ||||
0.853341 | + | 0.521354i | \(0.174573\pi\) | |||||||
\(104\) | −1.26776 | −0.124314 | ||||||||
\(105\) | −1.14548 | −0.111788 | ||||||||
\(106\) | 13.2163 | 1.28368 | ||||||||
\(107\) | 4.27354 | 0.413139 | 0.206570 | − | 0.978432i | \(-0.433770\pi\) | ||||
0.206570 | + | 0.978432i | \(0.433770\pi\) | |||||||
\(108\) | 5.51381 | 0.530567 | ||||||||
\(109\) | 9.01216 | 0.863209 | 0.431604 | − | 0.902063i | \(-0.357948\pi\) | ||||
0.431604 | + | 0.902063i | \(0.357948\pi\) | |||||||
\(110\) | 6.88486 | 0.656446 | ||||||||
\(111\) | −3.51014 | −0.333168 | ||||||||
\(112\) | −0.468701 | −0.0442881 | ||||||||
\(113\) | 1.97136 | 0.185450 | 0.0927252 | − | 0.995692i | \(-0.470442\pi\) | ||||
0.0927252 | + | 0.995692i | \(0.470442\pi\) | |||||||
\(114\) | 6.51664 | 0.610340 | ||||||||
\(115\) | −10.3759 | −0.967555 | ||||||||
\(116\) | −7.19591 | −0.668124 | ||||||||
\(117\) | 1.89653 | 0.175335 | ||||||||
\(118\) | 9.17618 | 0.844736 | ||||||||
\(119\) | 1.15305 | 0.105700 | ||||||||
\(120\) | 2.44395 | 0.223101 | ||||||||
\(121\) | 0.936076 | 0.0850978 | ||||||||
\(122\) | 11.1857 | 1.01271 | ||||||||
\(123\) | −1.29668 | −0.116918 | ||||||||
\(124\) | 2.21935 | 0.199303 | ||||||||
\(125\) | 12.0141 | 1.07457 | ||||||||
\(126\) | 0.701161 | 0.0624644 | ||||||||
\(127\) | 18.0401 | 1.60080 | 0.800402 | − | 0.599464i | \(-0.204620\pi\) | ||||
0.800402 | + | 0.599464i | \(0.204620\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.5482 | −1.01676 | ||||||||
\(130\) | 2.52640 | 0.221580 | ||||||||
\(131\) | −10.7284 | −0.937346 | −0.468673 | − | 0.883372i | \(-0.655268\pi\) | ||||
−0.468673 | + | 0.883372i | \(0.655268\pi\) | |||||||
\(132\) | 4.23701 | 0.368784 | ||||||||
\(133\) | 2.49053 | 0.215956 | ||||||||
\(134\) | −14.5904 | −1.26042 | ||||||||
\(135\) | −10.9879 | −0.945691 | ||||||||
\(136\) | −2.46010 | −0.210952 | ||||||||
\(137\) | −0.261550 | −0.0223458 | −0.0111729 | − | 0.999938i | \(-0.503557\pi\) | ||||
−0.0111729 | + | 0.999938i | \(0.503557\pi\) | |||||||
\(138\) | −6.38541 | −0.543562 | ||||||||
\(139\) | 20.8819 | 1.77118 | 0.885591 | − | 0.464466i | \(-0.153754\pi\) | ||||
0.885591 | + | 0.464466i | \(0.153754\pi\) | |||||||
\(140\) | 0.934028 | 0.0789398 | ||||||||
\(141\) | −13.2537 | −1.11616 | ||||||||
\(142\) | −9.48130 | −0.795653 | ||||||||
\(143\) | 4.37995 | 0.366270 | ||||||||
\(144\) | −1.49597 | −0.124664 | ||||||||
\(145\) | 14.3400 | 1.19087 | ||||||||
\(146\) | −8.28665 | −0.685808 | ||||||||
\(147\) | 8.31532 | 0.685836 | ||||||||
\(148\) | 2.86218 | 0.235269 | ||||||||
\(149\) | 5.09400 | 0.417317 | 0.208658 | − | 0.977989i | \(-0.433090\pi\) | ||||
0.208658 | + | 0.977989i | \(0.433090\pi\) | |||||||
\(150\) | 1.26163 | 0.103012 | ||||||||
\(151\) | −12.1959 | −0.992489 | −0.496244 | − | 0.868183i | \(-0.665288\pi\) | ||||
−0.496244 | + | 0.868183i | \(0.665288\pi\) | |||||||
\(152\) | −5.31368 | −0.430996 | ||||||||
\(153\) | 3.68023 | 0.297529 | ||||||||
\(154\) | 1.61930 | 0.130487 | ||||||||
\(155\) | −4.42272 | −0.355242 | ||||||||
\(156\) | 1.55477 | 0.124481 | ||||||||
\(157\) | 22.6683 | 1.80913 | 0.904564 | − | 0.426337i | \(-0.140196\pi\) | ||||
0.904564 | + | 0.426337i | \(0.140196\pi\) | |||||||
\(158\) | −7.53123 | −0.599153 | ||||||||
\(159\) | −16.2083 | −1.28540 | ||||||||
\(160\) | −1.99280 | −0.157545 | ||||||||
\(161\) | −2.44037 | −0.192328 | ||||||||
\(162\) | −2.27418 | −0.178676 | ||||||||
\(163\) | 3.49835 | 0.274012 | 0.137006 | − | 0.990570i | \(-0.456252\pi\) | ||||
0.137006 | + | 0.990570i | \(0.456252\pi\) | |||||||
\(164\) | 1.05732 | 0.0825624 | ||||||||
\(165\) | −8.44352 | −0.657327 | ||||||||
\(166\) | −12.5561 | −0.974541 | ||||||||
\(167\) | 1.11061 | 0.0859412 | 0.0429706 | − | 0.999076i | \(-0.486318\pi\) | ||||
0.0429706 | + | 0.999076i | \(0.486318\pi\) | |||||||
\(168\) | 0.574810 | 0.0443475 | ||||||||
\(169\) | −11.3928 | −0.876367 | ||||||||
\(170\) | 4.90249 | 0.376004 | ||||||||
\(171\) | 7.94909 | 0.607882 | ||||||||
\(172\) | 9.41639 | 0.717993 | ||||||||
\(173\) | −4.81367 | −0.365977 | −0.182988 | − | 0.983115i | \(-0.558577\pi\) | ||||
−0.182988 | + | 0.983115i | \(0.558577\pi\) | |||||||
\(174\) | 8.82499 | 0.669021 | ||||||||
\(175\) | 0.482170 | 0.0364486 | ||||||||
\(176\) | −3.45486 | −0.260420 | ||||||||
\(177\) | −11.2536 | −0.845871 | ||||||||
\(178\) | −11.0345 | −0.827071 | ||||||||
\(179\) | −0.366851 | −0.0274198 | −0.0137099 | − | 0.999906i | \(-0.504364\pi\) | ||||
−0.0137099 | + | 0.999906i | \(0.504364\pi\) | |||||||
\(180\) | 2.98117 | 0.222203 | ||||||||
\(181\) | 16.7553 | 1.24541 | 0.622706 | − | 0.782456i | \(-0.286033\pi\) | ||||
0.622706 | + | 0.782456i | \(0.286033\pi\) | |||||||
\(182\) | 0.594201 | 0.0440451 | ||||||||
\(183\) | −13.7181 | −1.01407 | ||||||||
\(184\) | 5.20667 | 0.383841 | ||||||||
\(185\) | −5.70375 | −0.419348 | ||||||||
\(186\) | −2.72179 | −0.199571 | ||||||||
\(187\) | 8.49930 | 0.621530 | ||||||||
\(188\) | 10.8071 | 0.788187 | ||||||||
\(189\) | −2.58433 | −0.187982 | ||||||||
\(190\) | 10.5891 | 0.768215 | ||||||||
\(191\) | 14.6870 | 1.06271 | 0.531357 | − | 0.847148i | \(-0.321682\pi\) | ||||
0.531357 | + | 0.847148i | \(0.321682\pi\) | |||||||
\(192\) | −1.22639 | −0.0885071 | ||||||||
\(193\) | −1.48909 | −0.107187 | −0.0535935 | − | 0.998563i | \(-0.517068\pi\) | ||||
−0.0535935 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(194\) | 1.02710 | 0.0737415 | ||||||||
\(195\) | −3.09835 | −0.221878 | ||||||||
\(196\) | −6.78032 | −0.484309 | ||||||||
\(197\) | 11.1774 | 0.796358 | 0.398179 | − | 0.917308i | \(-0.369642\pi\) | ||||
0.398179 | + | 0.917308i | \(0.369642\pi\) | |||||||
\(198\) | 5.16836 | 0.367300 | ||||||||
\(199\) | −5.08108 | −0.360188 | −0.180094 | − | 0.983649i | \(-0.557640\pi\) | ||||
−0.180094 | + | 0.983649i | \(0.557640\pi\) | |||||||
\(200\) | −1.02874 | −0.0727428 | ||||||||
\(201\) | 17.8935 | 1.26211 | ||||||||
\(202\) | 5.56064 | 0.391245 | ||||||||
\(203\) | 3.37273 | 0.236719 | ||||||||
\(204\) | 3.01704 | 0.211235 | ||||||||
\(205\) | −2.10702 | −0.147161 | ||||||||
\(206\) | 17.3209 | 1.20681 | ||||||||
\(207\) | −7.78902 | −0.541374 | ||||||||
\(208\) | −1.26776 | −0.0879035 | ||||||||
\(209\) | 18.3580 | 1.26985 | ||||||||
\(210\) | −1.14548 | −0.0790458 | ||||||||
\(211\) | 16.1157 | 1.10945 | 0.554727 | − | 0.832033i | \(-0.312823\pi\) | ||||
0.554727 | + | 0.832033i | \(0.312823\pi\) | |||||||
\(212\) | 13.2163 | 0.907699 | ||||||||
\(213\) | 11.6278 | 0.796722 | ||||||||
\(214\) | 4.27354 | 0.292133 | ||||||||
\(215\) | −18.7650 | −1.27976 | ||||||||
\(216\) | 5.51381 | 0.375167 | ||||||||
\(217\) | −1.04021 | −0.0706141 | ||||||||
\(218\) | 9.01216 | 0.610381 | ||||||||
\(219\) | 10.1627 | 0.686729 | ||||||||
\(220\) | 6.88486 | 0.464177 | ||||||||
\(221\) | 3.11882 | 0.209795 | ||||||||
\(222\) | −3.51014 | −0.235585 | ||||||||
\(223\) | −14.0246 | −0.939158 | −0.469579 | − | 0.882890i | \(-0.655594\pi\) | ||||
−0.469579 | + | 0.882890i | \(0.655594\pi\) | |||||||
\(224\) | −0.468701 | −0.0313164 | ||||||||
\(225\) | 1.53896 | 0.102597 | ||||||||
\(226\) | 1.97136 | 0.131133 | ||||||||
\(227\) | −11.6235 | −0.771478 | −0.385739 | − | 0.922608i | \(-0.626054\pi\) | ||||
−0.385739 | + | 0.922608i | \(0.626054\pi\) | |||||||
\(228\) | 6.51664 | 0.431575 | ||||||||
\(229\) | −7.63220 | −0.504350 | −0.252175 | − | 0.967682i | \(-0.581146\pi\) | ||||
−0.252175 | + | 0.967682i | \(0.581146\pi\) | |||||||
\(230\) | −10.3759 | −0.684165 | ||||||||
\(231\) | −1.98589 | −0.130662 | ||||||||
\(232\) | −7.19591 | −0.472435 | ||||||||
\(233\) | 3.48540 | 0.228336 | 0.114168 | − | 0.993461i | \(-0.463580\pi\) | ||||
0.114168 | + | 0.993461i | \(0.463580\pi\) | |||||||
\(234\) | 1.89653 | 0.123980 | ||||||||
\(235\) | −21.5364 | −1.40488 | ||||||||
\(236\) | 9.17618 | 0.597319 | ||||||||
\(237\) | 9.23623 | 0.599957 | ||||||||
\(238\) | 1.15305 | 0.0747411 | ||||||||
\(239\) | −20.7109 | −1.33967 | −0.669837 | − | 0.742508i | \(-0.733636\pi\) | ||||
−0.669837 | + | 0.742508i | \(0.733636\pi\) | |||||||
\(240\) | 2.44395 | 0.157756 | ||||||||
\(241\) | −2.17768 | −0.140276 | −0.0701382 | − | 0.997537i | \(-0.522344\pi\) | ||||
−0.0701382 | + | 0.997537i | \(0.522344\pi\) | |||||||
\(242\) | 0.936076 | 0.0601732 | ||||||||
\(243\) | −13.7524 | −0.882217 | ||||||||
\(244\) | 11.1857 | 0.716094 | ||||||||
\(245\) | 13.5118 | 0.863240 | ||||||||
\(246\) | −1.29668 | −0.0826733 | ||||||||
\(247\) | 6.73649 | 0.428632 | ||||||||
\(248\) | 2.21935 | 0.140929 | ||||||||
\(249\) | 15.3986 | 0.975850 | ||||||||
\(250\) | 12.0141 | 0.759837 | ||||||||
\(251\) | −26.2146 | −1.65465 | −0.827324 | − | 0.561724i | \(-0.810138\pi\) | ||||
−0.827324 | + | 0.561724i | \(0.810138\pi\) | |||||||
\(252\) | 0.701161 | 0.0441690 | ||||||||
\(253\) | −17.9883 | −1.13092 | ||||||||
\(254\) | 18.0401 | 1.13194 | ||||||||
\(255\) | −6.01236 | −0.376509 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8492 | 0.676754 | 0.338377 | − | 0.941011i | \(-0.390122\pi\) | ||||
0.338377 | + | 0.941011i | \(0.390122\pi\) | |||||||
\(258\) | −11.5482 | −0.718958 | ||||||||
\(259\) | −1.34150 | −0.0833570 | ||||||||
\(260\) | 2.52640 | 0.156681 | ||||||||
\(261\) | 10.7649 | 0.666328 | ||||||||
\(262\) | −10.7284 | −0.662804 | ||||||||
\(263\) | −11.5792 | −0.714003 | −0.357001 | − | 0.934104i | \(-0.616201\pi\) | ||||
−0.357001 | + | 0.934104i | \(0.616201\pi\) | |||||||
\(264\) | 4.23701 | 0.260770 | ||||||||
\(265\) | −26.3375 | −1.61790 | ||||||||
\(266\) | 2.49053 | 0.152704 | ||||||||
\(267\) | 13.5326 | 0.828182 | ||||||||
\(268\) | −14.5904 | −0.891251 | ||||||||
\(269\) | −7.95732 | −0.485166 | −0.242583 | − | 0.970131i | \(-0.577995\pi\) | ||||
−0.242583 | + | 0.970131i | \(0.577995\pi\) | |||||||
\(270\) | −10.9879 | −0.668704 | ||||||||
\(271\) | 15.3230 | 0.930806 | 0.465403 | − | 0.885099i | \(-0.345909\pi\) | ||||
0.465403 | + | 0.885099i | \(0.345909\pi\) | |||||||
\(272\) | −2.46010 | −0.149165 | ||||||||
\(273\) | −0.728723 | −0.0441043 | ||||||||
\(274\) | −0.261550 | −0.0158008 | ||||||||
\(275\) | 3.55415 | 0.214323 | ||||||||
\(276\) | −6.38541 | −0.384357 | ||||||||
\(277\) | 23.9857 | 1.44116 | 0.720581 | − | 0.693371i | \(-0.243875\pi\) | ||||
0.720581 | + | 0.693371i | \(0.243875\pi\) | |||||||
\(278\) | 20.8819 | 1.25241 | ||||||||
\(279\) | −3.32007 | −0.198768 | ||||||||
\(280\) | 0.934028 | 0.0558188 | ||||||||
\(281\) | −0.496586 | −0.0296238 | −0.0148119 | − | 0.999890i | \(-0.504715\pi\) | ||||
−0.0148119 | + | 0.999890i | \(0.504715\pi\) | |||||||
\(282\) | −13.2537 | −0.789245 | ||||||||
\(283\) | 18.5242 | 1.10115 | 0.550575 | − | 0.834786i | \(-0.314408\pi\) | ||||
0.550575 | + | 0.834786i | \(0.314408\pi\) | |||||||
\(284\) | −9.48130 | −0.562612 | ||||||||
\(285\) | −12.9864 | −0.769247 | ||||||||
\(286\) | 4.37995 | 0.258992 | ||||||||
\(287\) | −0.495564 | −0.0292522 | ||||||||
\(288\) | −1.49597 | −0.0881507 | ||||||||
\(289\) | −10.9479 | −0.643995 | ||||||||
\(290\) | 14.3400 | 0.842076 | ||||||||
\(291\) | −1.25962 | −0.0738405 | ||||||||
\(292\) | −8.28665 | −0.484940 | ||||||||
\(293\) | 9.03198 | 0.527654 | 0.263827 | − | 0.964570i | \(-0.415015\pi\) | ||||
0.263827 | + | 0.964570i | \(0.415015\pi\) | |||||||
\(294\) | 8.31532 | 0.484959 | ||||||||
\(295\) | −18.2863 | −1.06467 | ||||||||
\(296\) | 2.86218 | 0.166361 | ||||||||
\(297\) | −19.0495 | −1.10536 | ||||||||
\(298\) | 5.09400 | 0.295088 | ||||||||
\(299\) | −6.60083 | −0.381736 | ||||||||
\(300\) | 1.26163 | 0.0728405 | ||||||||
\(301\) | −4.41347 | −0.254388 | ||||||||
\(302\) | −12.1959 | −0.701796 | ||||||||
\(303\) | −6.81952 | −0.391771 | ||||||||
\(304\) | −5.31368 | −0.304760 | ||||||||
\(305\) | −22.2910 | −1.27638 | ||||||||
\(306\) | 3.68023 | 0.210385 | ||||||||
\(307\) | 18.3884 | 1.04948 | 0.524741 | − | 0.851262i | \(-0.324162\pi\) | ||||
0.524741 | + | 0.851262i | \(0.324162\pi\) | |||||||
\(308\) | 1.61930 | 0.0922680 | ||||||||
\(309\) | −21.2422 | −1.20843 | ||||||||
\(310\) | −4.42272 | −0.251194 | ||||||||
\(311\) | −0.472049 | −0.0267674 | −0.0133837 | − | 0.999910i | \(-0.504260\pi\) | ||||
−0.0133837 | + | 0.999910i | \(0.504260\pi\) | |||||||
\(312\) | 1.55477 | 0.0880216 | ||||||||
\(313\) | 26.2113 | 1.48155 | 0.740775 | − | 0.671753i | \(-0.234459\pi\) | ||||
0.740775 | + | 0.671753i | \(0.234459\pi\) | |||||||
\(314\) | 22.6683 | 1.27925 | ||||||||
\(315\) | −1.39728 | −0.0787276 | ||||||||
\(316\) | −7.53123 | −0.423665 | ||||||||
\(317\) | 15.1408 | 0.850391 | 0.425195 | − | 0.905102i | \(-0.360205\pi\) | ||||
0.425195 | + | 0.905102i | \(0.360205\pi\) | |||||||
\(318\) | −16.2083 | −0.908918 | ||||||||
\(319\) | 24.8609 | 1.39194 | ||||||||
\(320\) | −1.99280 | −0.111401 | ||||||||
\(321\) | −5.24103 | −0.292526 | ||||||||
\(322\) | −2.44037 | −0.135997 | ||||||||
\(323\) | 13.0722 | 0.727355 | ||||||||
\(324\) | −2.27418 | −0.126343 | ||||||||
\(325\) | 1.30420 | 0.0723438 | ||||||||
\(326\) | 3.49835 | 0.193756 | ||||||||
\(327\) | −11.0524 | −0.611201 | ||||||||
\(328\) | 1.05732 | 0.0583805 | ||||||||
\(329\) | −5.06528 | −0.279258 | ||||||||
\(330\) | −8.44352 | −0.464801 | ||||||||
\(331\) | −27.5801 | −1.51594 | −0.757970 | − | 0.652290i | \(-0.773809\pi\) | ||||
−0.757970 | + | 0.652290i | \(0.773809\pi\) | |||||||
\(332\) | −12.5561 | −0.689104 | ||||||||
\(333\) | −4.28172 | −0.234637 | ||||||||
\(334\) | 1.11061 | 0.0607696 | ||||||||
\(335\) | 29.0758 | 1.58858 | ||||||||
\(336\) | 0.574810 | 0.0313584 | ||||||||
\(337\) | 16.0622 | 0.874962 | 0.437481 | − | 0.899228i | \(-0.355871\pi\) | ||||
0.437481 | + | 0.899228i | \(0.355871\pi\) | |||||||
\(338\) | −11.3928 | −0.619685 | ||||||||
\(339\) | −2.41766 | −0.131309 | ||||||||
\(340\) | 4.90249 | 0.265875 | ||||||||
\(341\) | −7.66755 | −0.415221 | ||||||||
\(342\) | 7.94909 | 0.429838 | ||||||||
\(343\) | 6.45885 | 0.348745 | ||||||||
\(344\) | 9.41639 | 0.507698 | ||||||||
\(345\) | 12.7249 | 0.685084 | ||||||||
\(346\) | −4.81367 | −0.258785 | ||||||||
\(347\) | −2.01697 | −0.108277 | −0.0541383 | − | 0.998533i | \(-0.517241\pi\) | ||||
−0.0541383 | + | 0.998533i | \(0.517241\pi\) | |||||||
\(348\) | 8.82499 | 0.473069 | ||||||||
\(349\) | 17.0248 | 0.911317 | 0.455658 | − | 0.890155i | \(-0.349404\pi\) | ||||
0.455658 | + | 0.890155i | \(0.349404\pi\) | |||||||
\(350\) | 0.482170 | 0.0257731 | ||||||||
\(351\) | −6.99020 | −0.373109 | ||||||||
\(352\) | −3.45486 | −0.184145 | ||||||||
\(353\) | 27.5866 | 1.46829 | 0.734143 | − | 0.678995i | \(-0.237584\pi\) | ||||
0.734143 | + | 0.678995i | \(0.237584\pi\) | |||||||
\(354\) | −11.2536 | −0.598121 | ||||||||
\(355\) | 18.8944 | 1.00281 | ||||||||
\(356\) | −11.0345 | −0.584827 | ||||||||
\(357\) | −1.41409 | −0.0748415 | ||||||||
\(358\) | −0.366851 | −0.0193887 | ||||||||
\(359\) | −33.2045 | −1.75247 | −0.876233 | − | 0.481888i | \(-0.839951\pi\) | ||||
−0.876233 | + | 0.481888i | \(0.839951\pi\) | |||||||
\(360\) | 2.98117 | 0.157121 | ||||||||
\(361\) | 9.23520 | 0.486063 | ||||||||
\(362\) | 16.7553 | 0.880640 | ||||||||
\(363\) | −1.14799 | −0.0602540 | ||||||||
\(364\) | 0.594201 | 0.0311446 | ||||||||
\(365\) | 16.5137 | 0.864364 | ||||||||
\(366\) | −13.7181 | −0.717056 | ||||||||
\(367\) | −2.21268 | −0.115501 | −0.0577505 | − | 0.998331i | \(-0.518393\pi\) | ||||
−0.0577505 | + | 0.998331i | \(0.518393\pi\) | |||||||
\(368\) | 5.20667 | 0.271417 | ||||||||
\(369\) | −1.58171 | −0.0823405 | ||||||||
\(370\) | −5.70375 | −0.296524 | ||||||||
\(371\) | −6.19449 | −0.321602 | ||||||||
\(372\) | −2.72179 | −0.141118 | ||||||||
\(373\) | 0.285462 | 0.0147807 | 0.00739034 | − | 0.999973i | \(-0.497648\pi\) | ||||
0.00739034 | + | 0.999973i | \(0.497648\pi\) | |||||||
\(374\) | 8.49930 | 0.439488 | ||||||||
\(375\) | −14.7340 | −0.760858 | ||||||||
\(376\) | 10.8071 | 0.557332 | ||||||||
\(377\) | 9.12271 | 0.469844 | ||||||||
\(378\) | −2.58433 | −0.132923 | ||||||||
\(379\) | 14.7529 | 0.757804 | 0.378902 | − | 0.925437i | \(-0.376302\pi\) | ||||
0.378902 | + | 0.925437i | \(0.376302\pi\) | |||||||
\(380\) | 10.5891 | 0.543210 | ||||||||
\(381\) | −22.1242 | −1.13346 | ||||||||
\(382\) | 14.6870 | 0.751453 | ||||||||
\(383\) | 5.84673 | 0.298754 | 0.149377 | − | 0.988780i | \(-0.452273\pi\) | ||||
0.149377 | + | 0.988780i | \(0.452273\pi\) | |||||||
\(384\) | −1.22639 | −0.0625839 | ||||||||
\(385\) | −3.22694 | −0.164460 | ||||||||
\(386\) | −1.48909 | −0.0757926 | ||||||||
\(387\) | −14.0866 | −0.716063 | ||||||||
\(388\) | 1.02710 | 0.0521431 | ||||||||
\(389\) | −22.9421 | −1.16321 | −0.581606 | − | 0.813471i | \(-0.697575\pi\) | ||||
−0.581606 | + | 0.813471i | \(0.697575\pi\) | |||||||
\(390\) | −3.09835 | −0.156891 | ||||||||
\(391\) | −12.8089 | −0.647775 | ||||||||
\(392\) | −6.78032 | −0.342458 | ||||||||
\(393\) | 13.1572 | 0.663694 | ||||||||
\(394\) | 11.1774 | 0.563110 | ||||||||
\(395\) | 15.0083 | 0.755147 | ||||||||
\(396\) | 5.16836 | 0.259720 | ||||||||
\(397\) | −27.6353 | −1.38698 | −0.693489 | − | 0.720467i | \(-0.743927\pi\) | ||||
−0.693489 | + | 0.720467i | \(0.743927\pi\) | |||||||
\(398\) | −5.08108 | −0.254691 | ||||||||
\(399\) | −3.05436 | −0.152909 | ||||||||
\(400\) | −1.02874 | −0.0514369 | ||||||||
\(401\) | −23.4743 | −1.17225 | −0.586125 | − | 0.810221i | \(-0.699347\pi\) | ||||
−0.586125 | + | 0.810221i | \(0.699347\pi\) | |||||||
\(402\) | 17.8935 | 0.892448 | ||||||||
\(403\) | −2.81361 | −0.140156 | ||||||||
\(404\) | 5.56064 | 0.276652 | ||||||||
\(405\) | 4.53199 | 0.225196 | ||||||||
\(406\) | 3.37273 | 0.167386 | ||||||||
\(407\) | −9.88843 | −0.490151 | ||||||||
\(408\) | 3.01704 | 0.149366 | ||||||||
\(409\) | −19.5672 | −0.967538 | −0.483769 | − | 0.875196i | \(-0.660733\pi\) | ||||
−0.483769 | + | 0.875196i | \(0.660733\pi\) | |||||||
\(410\) | −2.10702 | −0.104058 | ||||||||
\(411\) | 0.320763 | 0.0158221 | ||||||||
\(412\) | 17.3209 | 0.853341 | ||||||||
\(413\) | −4.30088 | −0.211633 | ||||||||
\(414\) | −7.78902 | −0.382809 | ||||||||
\(415\) | 25.0218 | 1.22827 | ||||||||
\(416\) | −1.26776 | −0.0621572 | ||||||||
\(417\) | −25.6094 | −1.25410 | ||||||||
\(418\) | 18.3580 | 0.897921 | ||||||||
\(419\) | −37.7940 | −1.84636 | −0.923179 | − | 0.384370i | \(-0.874419\pi\) | ||||
−0.923179 | + | 0.384370i | \(0.874419\pi\) | |||||||
\(420\) | −1.14548 | −0.0558938 | ||||||||
\(421\) | 5.94735 | 0.289856 | 0.144928 | − | 0.989442i | \(-0.453705\pi\) | ||||
0.144928 | + | 0.989442i | \(0.453705\pi\) | |||||||
\(422\) | 16.1157 | 0.784502 | ||||||||
\(423\) | −16.1670 | −0.786068 | ||||||||
\(424\) | 13.2163 | 0.641840 | ||||||||
\(425\) | 2.53080 | 0.122762 | ||||||||
\(426\) | 11.6278 | 0.563367 | ||||||||
\(427\) | −5.24277 | −0.253715 | ||||||||
\(428\) | 4.27354 | 0.206570 | ||||||||
\(429\) | −5.37152 | −0.259340 | ||||||||
\(430\) | −18.7650 | −0.904929 | ||||||||
\(431\) | −18.5632 | −0.894157 | −0.447078 | − | 0.894495i | \(-0.647535\pi\) | ||||
−0.447078 | + | 0.894495i | \(0.647535\pi\) | |||||||
\(432\) | 5.51381 | 0.265283 | ||||||||
\(433\) | 29.0746 | 1.39724 | 0.698618 | − | 0.715495i | \(-0.253799\pi\) | ||||
0.698618 | + | 0.715495i | \(0.253799\pi\) | |||||||
\(434\) | −1.04021 | −0.0499317 | ||||||||
\(435\) | −17.5865 | −0.843207 | ||||||||
\(436\) | 9.01216 | 0.431604 | ||||||||
\(437\) | −27.6666 | −1.32347 | ||||||||
\(438\) | 10.1627 | 0.485591 | ||||||||
\(439\) | 12.4853 | 0.595890 | 0.297945 | − | 0.954583i | \(-0.403699\pi\) | ||||
0.297945 | + | 0.954583i | \(0.403699\pi\) | |||||||
\(440\) | 6.88486 | 0.328223 | ||||||||
\(441\) | 10.1431 | 0.483007 | ||||||||
\(442\) | 3.11882 | 0.148347 | ||||||||
\(443\) | 10.6334 | 0.505210 | 0.252605 | − | 0.967570i | \(-0.418713\pi\) | ||||
0.252605 | + | 0.967570i | \(0.418713\pi\) | |||||||
\(444\) | −3.51014 | −0.166584 | ||||||||
\(445\) | 21.9896 | 1.04241 | ||||||||
\(446\) | −14.0246 | −0.664085 | ||||||||
\(447\) | −6.24723 | −0.295484 | ||||||||
\(448\) | −0.468701 | −0.0221440 | ||||||||
\(449\) | −13.8383 | −0.653068 | −0.326534 | − | 0.945186i | \(-0.605881\pi\) | ||||
−0.326534 | + | 0.945186i | \(0.605881\pi\) | |||||||
\(450\) | 1.53896 | 0.0725472 | ||||||||
\(451\) | −3.65288 | −0.172007 | ||||||||
\(452\) | 1.97136 | 0.0927252 | ||||||||
\(453\) | 14.9569 | 0.702738 | ||||||||
\(454\) | −11.6235 | −0.545517 | ||||||||
\(455\) | −1.18413 | −0.0555127 | ||||||||
\(456\) | 6.51664 | 0.305170 | ||||||||
\(457\) | −19.8523 | −0.928652 | −0.464326 | − | 0.885664i | \(-0.653703\pi\) | ||||
−0.464326 | + | 0.885664i | \(0.653703\pi\) | |||||||
\(458\) | −7.63220 | −0.356629 | ||||||||
\(459\) | −13.5645 | −0.633137 | ||||||||
\(460\) | −10.3759 | −0.483778 | ||||||||
\(461\) | 28.4002 | 1.32273 | 0.661366 | − | 0.750064i | \(-0.269977\pi\) | ||||
0.661366 | + | 0.750064i | \(0.269977\pi\) | |||||||
\(462\) | −1.98589 | −0.0923919 | ||||||||
\(463\) | 10.2596 | 0.476806 | 0.238403 | − | 0.971166i | \(-0.423376\pi\) | ||||
0.238403 | + | 0.971166i | \(0.423376\pi\) | |||||||
\(464\) | −7.19591 | −0.334062 | ||||||||
\(465\) | 5.42398 | 0.251531 | ||||||||
\(466\) | 3.48540 | 0.161458 | ||||||||
\(467\) | 36.2596 | 1.67789 | 0.838947 | − | 0.544214i | \(-0.183172\pi\) | ||||
0.838947 | + | 0.544214i | \(0.183172\pi\) | |||||||
\(468\) | 1.89653 | 0.0876673 | ||||||||
\(469\) | 6.83853 | 0.315774 | ||||||||
\(470\) | −21.5364 | −0.993398 | ||||||||
\(471\) | −27.8002 | −1.28097 | ||||||||
\(472\) | 9.17618 | 0.422368 | ||||||||
\(473\) | −32.5323 | −1.49584 | ||||||||
\(474\) | 9.23623 | 0.424234 | ||||||||
\(475\) | 5.46639 | 0.250815 | ||||||||
\(476\) | 1.15305 | 0.0528499 | ||||||||
\(477\) | −19.7712 | −0.905259 | ||||||||
\(478\) | −20.7109 | −0.947293 | ||||||||
\(479\) | 19.3438 | 0.883842 | 0.441921 | − | 0.897054i | \(-0.354297\pi\) | ||||
0.441921 | + | 0.897054i | \(0.354297\pi\) | |||||||
\(480\) | 2.44395 | 0.111551 | ||||||||
\(481\) | −3.62856 | −0.165448 | ||||||||
\(482\) | −2.17768 | −0.0991904 | ||||||||
\(483\) | 2.99285 | 0.136179 | ||||||||
\(484\) | 0.936076 | 0.0425489 | ||||||||
\(485\) | −2.04681 | −0.0929407 | ||||||||
\(486\) | −13.7524 | −0.623822 | ||||||||
\(487\) | −10.6202 | −0.481248 | −0.240624 | − | 0.970618i | \(-0.577352\pi\) | ||||
−0.240624 | + | 0.970618i | \(0.577352\pi\) | |||||||
\(488\) | 11.1857 | 0.506355 | ||||||||
\(489\) | −4.29034 | −0.194016 | ||||||||
\(490\) | 13.5118 | 0.610403 | ||||||||
\(491\) | 26.9304 | 1.21535 | 0.607676 | − | 0.794185i | \(-0.292102\pi\) | ||||
0.607676 | + | 0.794185i | \(0.292102\pi\) | |||||||
\(492\) | −1.29668 | −0.0584589 | ||||||||
\(493\) | 17.7026 | 0.797287 | ||||||||
\(494\) | 6.73649 | 0.303089 | ||||||||
\(495\) | −10.2995 | −0.462929 | ||||||||
\(496\) | 2.21935 | 0.0996517 | ||||||||
\(497\) | 4.44389 | 0.199336 | ||||||||
\(498\) | 15.3986 | 0.690030 | ||||||||
\(499\) | 8.48031 | 0.379631 | 0.189815 | − | 0.981820i | \(-0.439211\pi\) | ||||
0.189815 | + | 0.981820i | \(0.439211\pi\) | |||||||
\(500\) | 12.0141 | 0.537286 | ||||||||
\(501\) | −1.36204 | −0.0608513 | ||||||||
\(502\) | −26.2146 | −1.17001 | ||||||||
\(503\) | −28.6508 | −1.27748 | −0.638739 | − | 0.769424i | \(-0.720544\pi\) | ||||
−0.638739 | + | 0.769424i | \(0.720544\pi\) | |||||||
\(504\) | 0.701161 | 0.0312322 | ||||||||
\(505\) | −11.0813 | −0.493110 | ||||||||
\(506\) | −17.9883 | −0.799679 | ||||||||
\(507\) | 13.9720 | 0.620518 | ||||||||
\(508\) | 18.0401 | 0.800402 | ||||||||
\(509\) | 41.4837 | 1.83873 | 0.919366 | − | 0.393404i | \(-0.128703\pi\) | ||||
0.919366 | + | 0.393404i | \(0.128703\pi\) | |||||||
\(510\) | −6.01236 | −0.266232 | ||||||||
\(511\) | 3.88396 | 0.171816 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −29.2986 | −1.29357 | ||||||||
\(514\) | 10.8492 | 0.478537 | ||||||||
\(515\) | −34.5172 | −1.52101 | ||||||||
\(516\) | −11.5482 | −0.508380 | ||||||||
\(517\) | −37.3369 | −1.64208 | ||||||||
\(518\) | −1.34150 | −0.0589423 | ||||||||
\(519\) | 5.90344 | 0.259132 | ||||||||
\(520\) | 2.52640 | 0.110790 | ||||||||
\(521\) | −21.7332 | −0.952149 | −0.476075 | − | 0.879405i | \(-0.657941\pi\) | ||||
−0.476075 | + | 0.879405i | \(0.657941\pi\) | |||||||
\(522\) | 10.7649 | 0.471165 | ||||||||
\(523\) | 42.3559 | 1.85210 | 0.926048 | − | 0.377406i | \(-0.123184\pi\) | ||||
0.926048 | + | 0.377406i | \(0.123184\pi\) | |||||||
\(524\) | −10.7284 | −0.468673 | ||||||||
\(525\) | −0.591329 | −0.0258077 | ||||||||
\(526\) | −11.5792 | −0.504876 | ||||||||
\(527\) | −5.45982 | −0.237833 | ||||||||
\(528\) | 4.23701 | 0.184392 | ||||||||
\(529\) | 4.10945 | 0.178672 | ||||||||
\(530\) | −26.3375 | −1.14403 | ||||||||
\(531\) | −13.7273 | −0.595713 | ||||||||
\(532\) | 2.49053 | 0.107978 | ||||||||
\(533\) | −1.34043 | −0.0580603 | ||||||||
\(534\) | 13.5326 | 0.585613 | ||||||||
\(535\) | −8.51633 | −0.368193 | ||||||||
\(536\) | −14.5904 | −0.630210 | ||||||||
\(537\) | 0.449903 | 0.0194147 | ||||||||
\(538\) | −7.95732 | −0.343064 | ||||||||
\(539\) | 23.4251 | 1.00899 | ||||||||
\(540\) | −10.9879 | −0.472845 | ||||||||
\(541\) | 14.9391 | 0.642282 | 0.321141 | − | 0.947031i | \(-0.395934\pi\) | ||||
0.321141 | + | 0.947031i | \(0.395934\pi\) | |||||||
\(542\) | 15.3230 | 0.658179 | ||||||||
\(543\) | −20.5486 | −0.881823 | ||||||||
\(544\) | −2.46010 | −0.105476 | ||||||||
\(545\) | −17.9595 | −0.769299 | ||||||||
\(546\) | −0.728723 | −0.0311864 | ||||||||
\(547\) | −23.8414 | −1.01938 | −0.509692 | − | 0.860357i | \(-0.670241\pi\) | ||||
−0.509692 | + | 0.860357i | \(0.670241\pi\) | |||||||
\(548\) | −0.261550 | −0.0111729 | ||||||||
\(549\) | −16.7335 | −0.714169 | ||||||||
\(550\) | 3.55415 | 0.151549 | ||||||||
\(551\) | 38.2368 | 1.62894 | ||||||||
\(552\) | −6.38541 | −0.271781 | ||||||||
\(553\) | 3.52989 | 0.150106 | ||||||||
\(554\) | 23.9857 | 1.01906 | ||||||||
\(555\) | 6.99502 | 0.296922 | ||||||||
\(556\) | 20.8819 | 0.885591 | ||||||||
\(557\) | −25.4238 | −1.07724 | −0.538621 | − | 0.842548i | \(-0.681055\pi\) | ||||
−0.538621 | + | 0.842548i | \(0.681055\pi\) | |||||||
\(558\) | −3.32007 | −0.140550 | ||||||||
\(559\) | −11.9378 | −0.504913 | ||||||||
\(560\) | 0.934028 | 0.0394699 | ||||||||
\(561\) | −10.4235 | −0.440079 | ||||||||
\(562\) | −0.496586 | −0.0209472 | ||||||||
\(563\) | −31.7593 | −1.33849 | −0.669247 | − | 0.743040i | \(-0.733383\pi\) | ||||
−0.669247 | + | 0.743040i | \(0.733383\pi\) | |||||||
\(564\) | −13.2537 | −0.558081 | ||||||||
\(565\) | −3.92854 | −0.165275 | ||||||||
\(566\) | 18.5242 | 0.778631 | ||||||||
\(567\) | 1.06591 | 0.0447639 | ||||||||
\(568\) | −9.48130 | −0.397826 | ||||||||
\(569\) | 1.91690 | 0.0803607 | 0.0401803 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401803 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(570\) | −12.9864 | −0.543940 | ||||||||
\(571\) | 43.9925 | 1.84103 | 0.920514 | − | 0.390709i | \(-0.127770\pi\) | ||||
0.920514 | + | 0.390709i | \(0.127770\pi\) | |||||||
\(572\) | 4.37995 | 0.183135 | ||||||||
\(573\) | −18.0120 | −0.752462 | ||||||||
\(574\) | −0.495564 | −0.0206845 | ||||||||
\(575\) | −5.35630 | −0.223373 | ||||||||
\(576\) | −1.49597 | −0.0623320 | ||||||||
\(577\) | −40.7671 | −1.69716 | −0.848578 | − | 0.529070i | \(-0.822541\pi\) | ||||
−0.848578 | + | 0.529070i | \(0.822541\pi\) | |||||||
\(578\) | −10.9479 | −0.455373 | ||||||||
\(579\) | 1.82620 | 0.0758944 | ||||||||
\(580\) | 14.3400 | 0.595437 | ||||||||
\(581\) | 5.88504 | 0.244153 | ||||||||
\(582\) | −1.25962 | −0.0522131 | ||||||||
\(583\) | −45.6605 | −1.89106 | ||||||||
\(584\) | −8.28665 | −0.342904 | ||||||||
\(585\) | −3.77942 | −0.156260 | ||||||||
\(586\) | 9.03198 | 0.373107 | ||||||||
\(587\) | −34.9801 | −1.44378 | −0.721891 | − | 0.692007i | \(-0.756727\pi\) | ||||
−0.721891 | + | 0.692007i | \(0.756727\pi\) | |||||||
\(588\) | 8.31532 | 0.342918 | ||||||||
\(589\) | −11.7929 | −0.485918 | ||||||||
\(590\) | −18.2863 | −0.752836 | ||||||||
\(591\) | −13.7079 | −0.563867 | ||||||||
\(592\) | 2.86218 | 0.117635 | ||||||||
\(593\) | −12.4676 | −0.511983 | −0.255992 | − | 0.966679i | \(-0.582402\pi\) | ||||
−0.255992 | + | 0.966679i | \(0.582402\pi\) | |||||||
\(594\) | −19.0495 | −0.781609 | ||||||||
\(595\) | −2.29780 | −0.0942006 | ||||||||
\(596\) | 5.09400 | 0.208658 | ||||||||
\(597\) | 6.23138 | 0.255033 | ||||||||
\(598\) | −6.60083 | −0.269928 | ||||||||
\(599\) | 0.735309 | 0.0300439 | 0.0150220 | − | 0.999887i | \(-0.495218\pi\) | ||||
0.0150220 | + | 0.999887i | \(0.495218\pi\) | |||||||
\(600\) | 1.26163 | 0.0515060 | ||||||||
\(601\) | 37.9668 | 1.54870 | 0.774350 | − | 0.632758i | \(-0.218077\pi\) | ||||
0.774350 | + | 0.632758i | \(0.218077\pi\) | |||||||
\(602\) | −4.41347 | −0.179880 | ||||||||
\(603\) | 21.8268 | 0.888855 | ||||||||
\(604\) | −12.1959 | −0.496244 | ||||||||
\(605\) | −1.86541 | −0.0758399 | ||||||||
\(606\) | −6.81952 | −0.277024 | ||||||||
\(607\) | −6.91276 | −0.280580 | −0.140290 | − | 0.990110i | \(-0.544804\pi\) | ||||
−0.140290 | + | 0.990110i | \(0.544804\pi\) | |||||||
\(608\) | −5.31368 | −0.215498 | ||||||||
\(609\) | −4.13628 | −0.167611 | ||||||||
\(610\) | −22.2910 | −0.902535 | ||||||||
\(611\) | −13.7008 | −0.554275 | ||||||||
\(612\) | 3.68023 | 0.148764 | ||||||||
\(613\) | 42.0624 | 1.69888 | 0.849441 | − | 0.527683i | \(-0.176939\pi\) | ||||
0.849441 | + | 0.527683i | \(0.176939\pi\) | |||||||
\(614\) | 18.3884 | 0.742096 | ||||||||
\(615\) | 2.58403 | 0.104198 | ||||||||
\(616\) | 1.61930 | 0.0652433 | ||||||||
\(617\) | −38.5018 | −1.55003 | −0.775013 | − | 0.631946i | \(-0.782257\pi\) | ||||
−0.775013 | + | 0.631946i | \(0.782257\pi\) | |||||||
\(618\) | −21.2422 | −0.854487 | ||||||||
\(619\) | 21.7947 | 0.876003 | 0.438001 | − | 0.898974i | \(-0.355686\pi\) | ||||
0.438001 | + | 0.898974i | \(0.355686\pi\) | |||||||
\(620\) | −4.42272 | −0.177621 | ||||||||
\(621\) | 28.7086 | 1.15204 | ||||||||
\(622\) | −0.472049 | −0.0189274 | ||||||||
\(623\) | 5.17188 | 0.207207 | ||||||||
\(624\) | 1.55477 | 0.0622407 | ||||||||
\(625\) | −18.7980 | −0.751920 | ||||||||
\(626\) | 26.2113 | 1.04761 | ||||||||
\(627\) | −22.5141 | −0.899127 | ||||||||
\(628\) | 22.6683 | 0.904564 | ||||||||
\(629\) | −7.04123 | −0.280752 | ||||||||
\(630\) | −1.39728 | −0.0556688 | ||||||||
\(631\) | −27.9156 | −1.11130 | −0.555651 | − | 0.831416i | \(-0.687531\pi\) | ||||
−0.555651 | + | 0.831416i | \(0.687531\pi\) | |||||||
\(632\) | −7.53123 | −0.299576 | ||||||||
\(633\) | −19.7642 | −0.785556 | ||||||||
\(634\) | 15.1408 | 0.601317 | ||||||||
\(635\) | −35.9504 | −1.42665 | ||||||||
\(636\) | −16.2083 | −0.642702 | ||||||||
\(637\) | 8.59584 | 0.340580 | ||||||||
\(638\) | 24.8609 | 0.984252 | ||||||||
\(639\) | 14.1837 | 0.561099 | ||||||||
\(640\) | −1.99280 | −0.0787724 | ||||||||
\(641\) | −0.211616 | −0.00835835 | −0.00417917 | − | 0.999991i | \(-0.501330\pi\) | ||||
−0.00417917 | + | 0.999991i | \(0.501330\pi\) | |||||||
\(642\) | −5.24103 | −0.206847 | ||||||||
\(643\) | −36.7885 | −1.45080 | −0.725398 | − | 0.688330i | \(-0.758344\pi\) | ||||
−0.725398 | + | 0.688330i | \(0.758344\pi\) | |||||||
\(644\) | −2.44037 | −0.0961641 | ||||||||
\(645\) | 23.0132 | 0.906145 | ||||||||
\(646\) | 13.0722 | 0.514318 | ||||||||
\(647\) | 25.0198 | 0.983631 | 0.491815 | − | 0.870700i | \(-0.336334\pi\) | ||||
0.491815 | + | 0.870700i | \(0.336334\pi\) | |||||||
\(648\) | −2.27418 | −0.0893381 | ||||||||
\(649\) | −31.7024 | −1.24443 | ||||||||
\(650\) | 1.30420 | 0.0511548 | ||||||||
\(651\) | 1.27570 | 0.0499988 | ||||||||
\(652\) | 3.49835 | 0.137006 | ||||||||
\(653\) | −0.663535 | −0.0259661 | −0.0129831 | − | 0.999916i | \(-0.504133\pi\) | ||||
−0.0129831 | + | 0.999916i | \(0.504133\pi\) | |||||||
\(654\) | −11.0524 | −0.432184 | ||||||||
\(655\) | 21.3796 | 0.835371 | ||||||||
\(656\) | 1.05732 | 0.0412812 | ||||||||
\(657\) | 12.3966 | 0.483636 | ||||||||
\(658\) | −5.06528 | −0.197465 | ||||||||
\(659\) | −20.3893 | −0.794254 | −0.397127 | − | 0.917764i | \(-0.629993\pi\) | ||||
−0.397127 | + | 0.917764i | \(0.629993\pi\) | |||||||
\(660\) | −8.44352 | −0.328664 | ||||||||
\(661\) | 25.3599 | 0.986386 | 0.493193 | − | 0.869920i | \(-0.335830\pi\) | ||||
0.493193 | + | 0.869920i | \(0.335830\pi\) | |||||||
\(662\) | −27.5801 | −1.07193 | ||||||||
\(663\) | −3.82489 | −0.148546 | ||||||||
\(664\) | −12.5561 | −0.487270 | ||||||||
\(665\) | −4.96313 | −0.192462 | ||||||||
\(666\) | −4.28172 | −0.165913 | ||||||||
\(667\) | −37.4668 | −1.45072 | ||||||||
\(668\) | 1.11061 | 0.0429706 | ||||||||
\(669\) | 17.1997 | 0.664977 | ||||||||
\(670\) | 29.0758 | 1.12330 | ||||||||
\(671\) | −38.6452 | −1.49188 | ||||||||
\(672\) | 0.574810 | 0.0221738 | ||||||||
\(673\) | 22.6291 | 0.872288 | 0.436144 | − | 0.899877i | \(-0.356344\pi\) | ||||
0.436144 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(674\) | 16.0622 | 0.618692 | ||||||||
\(675\) | −5.67227 | −0.218326 | ||||||||
\(676\) | −11.3928 | −0.438184 | ||||||||
\(677\) | 38.5144 | 1.48023 | 0.740114 | − | 0.672481i | \(-0.234772\pi\) | ||||
0.740114 | + | 0.672481i | \(0.234772\pi\) | |||||||
\(678\) | −2.41766 | −0.0928498 | ||||||||
\(679\) | −0.481402 | −0.0184745 | ||||||||
\(680\) | 4.90249 | 0.188002 | ||||||||
\(681\) | 14.2549 | 0.546250 | ||||||||
\(682\) | −7.66755 | −0.293606 | ||||||||
\(683\) | −29.6764 | −1.13554 | −0.567768 | − | 0.823189i | \(-0.692193\pi\) | ||||
−0.567768 | + | 0.823189i | \(0.692193\pi\) | |||||||
\(684\) | 7.94909 | 0.303941 | ||||||||
\(685\) | 0.521218 | 0.0199147 | ||||||||
\(686\) | 6.45885 | 0.246600 | ||||||||
\(687\) | 9.36005 | 0.357108 | ||||||||
\(688\) | 9.41639 | 0.358997 | ||||||||
\(689\) | −16.7551 | −0.638320 | ||||||||
\(690\) | 12.7249 | 0.484427 | ||||||||
\(691\) | 17.2758 | 0.657204 | 0.328602 | − | 0.944469i | \(-0.393423\pi\) | ||||
0.328602 | + | 0.944469i | \(0.393423\pi\) | |||||||
\(692\) | −4.81367 | −0.182988 | ||||||||
\(693\) | −2.42242 | −0.0920200 | ||||||||
\(694\) | −2.01697 | −0.0765631 | ||||||||
\(695\) | −41.6136 | −1.57849 | ||||||||
\(696\) | 8.82499 | 0.334511 | ||||||||
\(697\) | −2.60110 | −0.0985236 | ||||||||
\(698\) | 17.0248 | 0.644398 | ||||||||
\(699\) | −4.27446 | −0.161675 | ||||||||
\(700\) | 0.482170 | 0.0182243 | ||||||||
\(701\) | 7.14664 | 0.269925 | 0.134962 | − | 0.990851i | \(-0.456909\pi\) | ||||
0.134962 | + | 0.990851i | \(0.456909\pi\) | |||||||
\(702\) | −6.99020 | −0.263828 | ||||||||
\(703\) | −15.2087 | −0.573607 | ||||||||
\(704\) | −3.45486 | −0.130210 | ||||||||
\(705\) | 26.4120 | 0.994732 | ||||||||
\(706\) | 27.5866 | 1.03823 | ||||||||
\(707\) | −2.60628 | −0.0980191 | ||||||||
\(708\) | −11.2536 | −0.422935 | ||||||||
\(709\) | 3.34637 | 0.125676 | 0.0628378 | − | 0.998024i | \(-0.479985\pi\) | ||||
0.0628378 | + | 0.998024i | \(0.479985\pi\) | |||||||
\(710\) | 18.8944 | 0.709093 | ||||||||
\(711\) | 11.2665 | 0.422526 | ||||||||
\(712\) | −11.0345 | −0.413535 | ||||||||
\(713\) | 11.5554 | 0.432754 | ||||||||
\(714\) | −1.41409 | −0.0529209 | ||||||||
\(715\) | −8.72837 | −0.326423 | ||||||||
\(716\) | −0.366851 | −0.0137099 | ||||||||
\(717\) | 25.3996 | 0.948565 | ||||||||
\(718\) | −33.2045 | −1.23918 | ||||||||
\(719\) | 30.2300 | 1.12739 | 0.563693 | − | 0.825984i | \(-0.309380\pi\) | ||||
0.563693 | + | 0.825984i | \(0.309380\pi\) | |||||||
\(720\) | 2.98117 | 0.111102 | ||||||||
\(721\) | −8.11833 | −0.302342 | ||||||||
\(722\) | 9.23520 | 0.343699 | ||||||||
\(723\) | 2.67068 | 0.0993236 | ||||||||
\(724\) | 16.7553 | 0.622706 | ||||||||
\(725\) | 7.40271 | 0.274930 | ||||||||
\(726\) | −1.14799 | −0.0426060 | ||||||||
\(727\) | −24.9277 | −0.924515 | −0.462258 | − | 0.886746i | \(-0.652960\pi\) | ||||
−0.462258 | + | 0.886746i | \(0.652960\pi\) | |||||||
\(728\) | 0.594201 | 0.0220226 | ||||||||
\(729\) | 23.6883 | 0.877346 | ||||||||
\(730\) | 16.5137 | 0.611198 | ||||||||
\(731\) | −23.1652 | −0.856798 | ||||||||
\(732\) | −13.7181 | −0.507035 | ||||||||
\(733\) | −34.7321 | −1.28286 | −0.641430 | − | 0.767182i | \(-0.721658\pi\) | ||||
−0.641430 | + | 0.767182i | \(0.721658\pi\) | |||||||
\(734\) | −2.21268 | −0.0816715 | ||||||||
\(735\) | −16.5708 | −0.611222 | ||||||||
\(736\) | 5.20667 | 0.191921 | ||||||||
\(737\) | 50.4079 | 1.85680 | ||||||||
\(738\) | −1.58171 | −0.0582235 | ||||||||
\(739\) | 32.8629 | 1.20888 | 0.604441 | − | 0.796650i | \(-0.293396\pi\) | ||||
0.604441 | + | 0.796650i | \(0.293396\pi\) | |||||||
\(740\) | −5.70375 | −0.209674 | ||||||||
\(741\) | −8.26156 | −0.303496 | ||||||||
\(742\) | −6.19449 | −0.227407 | ||||||||
\(743\) | −19.9724 | −0.732717 | −0.366358 | − | 0.930474i | \(-0.619396\pi\) | ||||
−0.366358 | + | 0.930474i | \(0.619396\pi\) | |||||||
\(744\) | −2.72179 | −0.0997856 | ||||||||
\(745\) | −10.1513 | −0.371916 | ||||||||
\(746\) | 0.285462 | 0.0104515 | ||||||||
\(747\) | 18.7835 | 0.687252 | ||||||||
\(748\) | 8.49930 | 0.310765 | ||||||||
\(749\) | −2.00301 | −0.0731885 | ||||||||
\(750\) | −14.7340 | −0.538008 | ||||||||
\(751\) | 38.3818 | 1.40057 | 0.700286 | − | 0.713862i | \(-0.253056\pi\) | ||||
0.700286 | + | 0.713862i | \(0.253056\pi\) | |||||||
\(752\) | 10.8071 | 0.394093 | ||||||||
\(753\) | 32.1493 | 1.17158 | ||||||||
\(754\) | 9.12271 | 0.332230 | ||||||||
\(755\) | 24.3040 | 0.884514 | ||||||||
\(756\) | −2.58433 | −0.0939910 | ||||||||
\(757\) | 4.98078 | 0.181030 | 0.0905148 | − | 0.995895i | \(-0.471149\pi\) | ||||
0.0905148 | + | 0.995895i | \(0.471149\pi\) | |||||||
\(758\) | 14.7529 | 0.535849 | ||||||||
\(759\) | 22.0607 | 0.800753 | ||||||||
\(760\) | 10.5891 | 0.384108 | ||||||||
\(761\) | 29.1946 | 1.05830 | 0.529152 | − | 0.848527i | \(-0.322510\pi\) | ||||
0.529152 | + | 0.848527i | \(0.322510\pi\) | |||||||
\(762\) | −22.1242 | −0.801477 | ||||||||
\(763\) | −4.22401 | −0.152919 | ||||||||
\(764\) | 14.6870 | 0.531357 | ||||||||
\(765\) | −7.33397 | −0.265160 | ||||||||
\(766\) | 5.84673 | 0.211251 | ||||||||
\(767\) | −11.6332 | −0.420051 | ||||||||
\(768\) | −1.22639 | −0.0442535 | ||||||||
\(769\) | −23.1290 | −0.834052 | −0.417026 | − | 0.908895i | \(-0.636928\pi\) | ||||
−0.417026 | + | 0.908895i | \(0.636928\pi\) | |||||||
\(770\) | −3.22694 | −0.116291 | ||||||||
\(771\) | −13.3053 | −0.479180 | ||||||||
\(772\) | −1.48909 | −0.0535935 | ||||||||
\(773\) | −5.18341 | −0.186434 | −0.0932171 | − | 0.995646i | \(-0.529715\pi\) | ||||
−0.0932171 | + | 0.995646i | \(0.529715\pi\) | |||||||
\(774\) | −14.0866 | −0.506333 | ||||||||
\(775\) | −2.28313 | −0.0820124 | ||||||||
\(776\) | 1.02710 | 0.0368707 | ||||||||
\(777\) | 1.64521 | 0.0590215 | ||||||||
\(778\) | −22.9421 | −0.822514 | ||||||||
\(779\) | −5.61823 | −0.201294 | ||||||||
\(780\) | −3.09835 | −0.110939 | ||||||||
\(781\) | 32.7566 | 1.17212 | ||||||||
\(782\) | −12.8089 | −0.458046 | ||||||||
\(783\) | −39.6769 | −1.41794 | ||||||||
\(784\) | −6.78032 | −0.242154 | ||||||||
\(785\) | −45.1735 | −1.61231 | ||||||||
\(786\) | 13.1572 | 0.469303 | ||||||||
\(787\) | −38.5988 | −1.37590 | −0.687949 | − | 0.725759i | \(-0.741489\pi\) | ||||
−0.687949 | + | 0.725759i | \(0.741489\pi\) | |||||||
\(788\) | 11.1774 | 0.398179 | ||||||||
\(789\) | 14.2006 | 0.505554 | ||||||||
\(790\) | 15.0083 | 0.533970 | ||||||||
\(791\) | −0.923980 | −0.0328530 | ||||||||
\(792\) | 5.16836 | 0.183650 | ||||||||
\(793\) | −14.1809 | −0.503577 | ||||||||
\(794\) | −27.6353 | −0.980742 | ||||||||
\(795\) | 32.3000 | 1.14556 | ||||||||
\(796\) | −5.08108 | −0.180094 | ||||||||
\(797\) | −17.2442 | −0.610820 | −0.305410 | − | 0.952221i | \(-0.598793\pi\) | ||||
−0.305410 | + | 0.952221i | \(0.598793\pi\) | |||||||
\(798\) | −3.05436 | −0.108123 | ||||||||
\(799\) | −26.5864 | −0.940561 | ||||||||
\(800\) | −1.02874 | −0.0363714 | ||||||||
\(801\) | 16.5073 | 0.583255 | ||||||||
\(802\) | −23.4743 | −0.828906 | ||||||||
\(803\) | 28.6292 | 1.01030 | ||||||||
\(804\) | 17.8935 | 0.631056 | ||||||||
\(805\) | 4.86318 | 0.171405 | ||||||||
\(806\) | −2.81361 | −0.0991051 | ||||||||
\(807\) | 9.75877 | 0.343525 | ||||||||
\(808\) | 5.56064 | 0.195623 | ||||||||
\(809\) | −39.6251 | −1.39314 | −0.696571 | − | 0.717488i | \(-0.745292\pi\) | ||||
−0.696571 | + | 0.717488i | \(0.745292\pi\) | |||||||
\(810\) | 4.53199 | 0.159238 | ||||||||
\(811\) | −15.3270 | −0.538202 | −0.269101 | − | 0.963112i | \(-0.586727\pi\) | ||||
−0.269101 | + | 0.963112i | \(0.586727\pi\) | |||||||
\(812\) | 3.37273 | 0.118360 | ||||||||
\(813\) | −18.7920 | −0.659063 | ||||||||
\(814\) | −9.88843 | −0.346589 | ||||||||
\(815\) | −6.97152 | −0.244202 | ||||||||
\(816\) | 3.01704 | 0.105617 | ||||||||
\(817\) | −50.0357 | −1.75053 | ||||||||
\(818\) | −19.5672 | −0.684153 | ||||||||
\(819\) | −0.888906 | −0.0310609 | ||||||||
\(820\) | −2.10702 | −0.0735803 | ||||||||
\(821\) | −31.4855 | −1.09885 | −0.549425 | − | 0.835543i | \(-0.685153\pi\) | ||||
−0.549425 | + | 0.835543i | \(0.685153\pi\) | |||||||
\(822\) | 0.320763 | 0.0111879 | ||||||||
\(823\) | 50.9733 | 1.77682 | 0.888409 | − | 0.459052i | \(-0.151811\pi\) | ||||
0.888409 | + | 0.459052i | \(0.151811\pi\) | |||||||
\(824\) | 17.3209 | 0.603403 | ||||||||
\(825\) | −4.35877 | −0.151753 | ||||||||
\(826\) | −4.30088 | −0.149647 | ||||||||
\(827\) | −14.6151 | −0.508218 | −0.254109 | − | 0.967176i | \(-0.581782\pi\) | ||||
−0.254109 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(828\) | −7.78902 | −0.270687 | ||||||||
\(829\) | 35.5328 | 1.23411 | 0.617053 | − | 0.786922i | \(-0.288326\pi\) | ||||
0.617053 | + | 0.786922i | \(0.288326\pi\) | |||||||
\(830\) | 25.0218 | 0.868519 | ||||||||
\(831\) | −29.4158 | −1.02042 | ||||||||
\(832\) | −1.26776 | −0.0439518 | ||||||||
\(833\) | 16.6802 | 0.577936 | ||||||||
\(834\) | −25.6094 | −0.886781 | ||||||||
\(835\) | −2.21322 | −0.0765916 | ||||||||
\(836\) | 18.3580 | 0.634926 | ||||||||
\(837\) | 12.2371 | 0.422975 | ||||||||
\(838\) | −37.7940 | −1.30557 | ||||||||
\(839\) | 48.5533 | 1.67625 | 0.838124 | − | 0.545480i | \(-0.183653\pi\) | ||||
0.838124 | + | 0.545480i | \(0.183653\pi\) | |||||||
\(840\) | −1.14548 | −0.0395229 | ||||||||
\(841\) | 22.7812 | 0.785557 | ||||||||
\(842\) | 5.94735 | 0.204959 | ||||||||
\(843\) | 0.609008 | 0.0209753 | ||||||||
\(844\) | 16.1157 | 0.554727 | ||||||||
\(845\) | 22.7036 | 0.781026 | ||||||||
\(846\) | −16.1670 | −0.555834 | ||||||||
\(847\) | −0.438739 | −0.0150753 | ||||||||
\(848\) | 13.2163 | 0.453850 | ||||||||
\(849\) | −22.7179 | −0.779677 | ||||||||
\(850\) | 2.53080 | 0.0868056 | ||||||||
\(851\) | 14.9024 | 0.510848 | ||||||||
\(852\) | 11.6278 | 0.398361 | ||||||||
\(853\) | 25.2425 | 0.864288 | 0.432144 | − | 0.901805i | \(-0.357757\pi\) | ||||
0.432144 | + | 0.901805i | \(0.357757\pi\) | |||||||
\(854\) | −5.24277 | −0.179404 | ||||||||
\(855\) | −15.8410 | −0.541750 | ||||||||
\(856\) | 4.27354 | 0.146067 | ||||||||
\(857\) | 34.5179 | 1.17911 | 0.589554 | − | 0.807729i | \(-0.299303\pi\) | ||||
0.589554 | + | 0.807729i | \(0.299303\pi\) | |||||||
\(858\) | −5.37152 | −0.183381 | ||||||||
\(859\) | −17.7314 | −0.604989 | −0.302495 | − | 0.953151i | \(-0.597819\pi\) | ||||
−0.302495 | + | 0.953151i | \(0.597819\pi\) | |||||||
\(860\) | −18.7650 | −0.639882 | ||||||||
\(861\) | 0.607755 | 0.0207122 | ||||||||
\(862\) | −18.5632 | −0.632264 | ||||||||
\(863\) | 24.6702 | 0.839785 | 0.419892 | − | 0.907574i | \(-0.362068\pi\) | ||||
0.419892 | + | 0.907574i | \(0.362068\pi\) | |||||||
\(864\) | 5.51381 | 0.187584 | ||||||||
\(865\) | 9.59270 | 0.326162 | ||||||||
\(866\) | 29.0746 | 0.987995 | ||||||||
\(867\) | 13.4264 | 0.455985 | ||||||||
\(868\) | −1.04021 | −0.0353070 | ||||||||
\(869\) | 26.0194 | 0.882647 | ||||||||
\(870\) | −17.5865 | −0.596237 | ||||||||
\(871\) | 18.4972 | 0.626753 | ||||||||
\(872\) | 9.01216 | 0.305190 | ||||||||
\(873\) | −1.53651 | −0.0520029 | ||||||||
\(874\) | −27.6666 | −0.935837 | ||||||||
\(875\) | −5.63101 | −0.190363 | ||||||||
\(876\) | 10.1627 | 0.343365 | ||||||||
\(877\) | 11.8329 | 0.399567 | 0.199784 | − | 0.979840i | \(-0.435976\pi\) | ||||
0.199784 | + | 0.979840i | \(0.435976\pi\) | |||||||
\(878\) | 12.4853 | 0.421358 | ||||||||
\(879\) | −11.0767 | −0.373609 | ||||||||
\(880\) | 6.88486 | 0.232089 | ||||||||
\(881\) | 5.19631 | 0.175068 | 0.0875340 | − | 0.996162i | \(-0.472101\pi\) | ||||
0.0875340 | + | 0.996162i | \(0.472101\pi\) | |||||||
\(882\) | 10.1431 | 0.341537 | ||||||||
\(883\) | 41.1552 | 1.38498 | 0.692492 | − | 0.721426i | \(-0.256513\pi\) | ||||
0.692492 | + | 0.721426i | \(0.256513\pi\) | |||||||
\(884\) | 3.11882 | 0.104897 | ||||||||
\(885\) | 22.4262 | 0.753847 | ||||||||
\(886\) | 10.6334 | 0.357237 | ||||||||
\(887\) | 49.2283 | 1.65293 | 0.826463 | − | 0.562992i | \(-0.190350\pi\) | ||||
0.826463 | + | 0.562992i | \(0.190350\pi\) | |||||||
\(888\) | −3.51014 | −0.117793 | ||||||||
\(889\) | −8.45543 | −0.283586 | ||||||||
\(890\) | 21.9896 | 0.737092 | ||||||||
\(891\) | 7.85697 | 0.263218 | ||||||||
\(892\) | −14.0246 | −0.469579 | ||||||||
\(893\) | −57.4253 | −1.92166 | ||||||||
\(894\) | −6.24723 | −0.208939 | ||||||||
\(895\) | 0.731062 | 0.0244367 | ||||||||
\(896\) | −0.468701 | −0.0156582 | ||||||||
\(897\) | 8.09519 | 0.270290 | ||||||||
\(898\) | −13.8383 | −0.461789 | ||||||||
\(899\) | −15.9702 | −0.532637 | ||||||||
\(900\) | 1.53896 | 0.0512986 | ||||||||
\(901\) | −32.5134 | −1.08318 | ||||||||
\(902\) | −3.65288 | −0.121628 | ||||||||
\(903\) | 5.41264 | 0.180121 | ||||||||
\(904\) | 1.97136 | 0.0655666 | ||||||||
\(905\) | −33.3900 | −1.10992 | ||||||||
\(906\) | 14.9569 | 0.496911 | ||||||||
\(907\) | −31.0853 | −1.03217 | −0.516085 | − | 0.856538i | \(-0.672611\pi\) | ||||
−0.516085 | + | 0.856538i | \(0.672611\pi\) | |||||||
\(908\) | −11.6235 | −0.385739 | ||||||||
\(909\) | −8.31854 | −0.275909 | ||||||||
\(910\) | −1.18413 | −0.0392534 | ||||||||
\(911\) | −55.7799 | −1.84807 | −0.924035 | − | 0.382309i | \(-0.875129\pi\) | ||||
−0.924035 | + | 0.382309i | \(0.875129\pi\) | |||||||
\(912\) | 6.51664 | 0.215788 | ||||||||
\(913\) | 43.3795 | 1.43565 | ||||||||
\(914\) | −19.8523 | −0.656656 | ||||||||
\(915\) | 27.3374 | 0.903747 | ||||||||
\(916\) | −7.63220 | −0.252175 | ||||||||
\(917\) | 5.02842 | 0.166053 | ||||||||
\(918\) | −13.5645 | −0.447696 | ||||||||
\(919\) | 22.9204 | 0.756073 | 0.378037 | − | 0.925791i | \(-0.376599\pi\) | ||||
0.378037 | + | 0.925791i | \(0.376599\pi\) | |||||||
\(920\) | −10.3759 | −0.342082 | ||||||||
\(921\) | −22.5514 | −0.743093 | ||||||||
\(922\) | 28.4002 | 0.935312 | ||||||||
\(923\) | 12.0200 | 0.395644 | ||||||||
\(924\) | −1.98589 | −0.0653309 | ||||||||
\(925\) | −2.94443 | −0.0968123 | ||||||||
\(926\) | 10.2596 | 0.337153 | ||||||||
\(927\) | −25.9115 | −0.851047 | ||||||||
\(928\) | −7.19591 | −0.236217 | ||||||||
\(929\) | 13.5354 | 0.444084 | 0.222042 | − | 0.975037i | \(-0.428728\pi\) | ||||
0.222042 | + | 0.975037i | \(0.428728\pi\) | |||||||
\(930\) | 5.42398 | 0.177859 | ||||||||
\(931\) | 36.0285 | 1.18078 | ||||||||
\(932\) | 3.48540 | 0.114168 | ||||||||
\(933\) | 0.578916 | 0.0189529 | ||||||||
\(934\) | 36.2596 | 1.18645 | ||||||||
\(935\) | −16.9374 | −0.553913 | ||||||||
\(936\) | 1.89653 | 0.0619901 | ||||||||
\(937\) | −16.2354 | −0.530389 | −0.265194 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265194 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(938\) | 6.83853 | 0.223286 | ||||||||
\(939\) | −32.1453 | −1.04902 | ||||||||
\(940\) | −21.5364 | −0.702438 | ||||||||
\(941\) | 57.8556 | 1.88604 | 0.943020 | − | 0.332737i | \(-0.107972\pi\) | ||||
0.943020 | + | 0.332737i | \(0.107972\pi\) | |||||||
\(942\) | −27.8002 | −0.905779 | ||||||||
\(943\) | 5.50509 | 0.179271 | ||||||||
\(944\) | 9.17618 | 0.298659 | ||||||||
\(945\) | 5.15005 | 0.167531 | ||||||||
\(946\) | −32.5323 | −1.05772 | ||||||||
\(947\) | 7.41463 | 0.240943 | 0.120472 | − | 0.992717i | \(-0.461559\pi\) | ||||
0.120472 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(948\) | 9.23623 | 0.299979 | ||||||||
\(949\) | 10.5055 | 0.341023 | ||||||||
\(950\) | 5.46639 | 0.177353 | ||||||||
\(951\) | −18.5685 | −0.602125 | ||||||||
\(952\) | 1.15305 | 0.0373705 | ||||||||
\(953\) | 28.1055 | 0.910426 | 0.455213 | − | 0.890382i | \(-0.349563\pi\) | ||||
0.455213 | + | 0.890382i | \(0.349563\pi\) | |||||||
\(954\) | −19.7712 | −0.640115 | ||||||||
\(955\) | −29.2683 | −0.947100 | ||||||||
\(956\) | −20.7109 | −0.669837 | ||||||||
\(957\) | −30.4891 | −0.985574 | ||||||||
\(958\) | 19.3438 | 0.624970 | ||||||||
\(959\) | 0.122589 | 0.00395860 | ||||||||
\(960\) | 2.44395 | 0.0788782 | ||||||||
\(961\) | −26.0745 | −0.841113 | ||||||||
\(962\) | −3.62856 | −0.116990 | ||||||||
\(963\) | −6.39308 | −0.206014 | ||||||||
\(964\) | −2.17768 | −0.0701382 | ||||||||
\(965\) | 2.96746 | 0.0955259 | ||||||||
\(966\) | 2.99285 | 0.0962933 | ||||||||
\(967\) | −54.4429 | −1.75077 | −0.875383 | − | 0.483430i | \(-0.839391\pi\) | ||||
−0.875383 | + | 0.483430i | \(0.839391\pi\) | |||||||
\(968\) | 0.936076 | 0.0300866 | ||||||||
\(969\) | −16.0316 | −0.515009 | ||||||||
\(970\) | −2.04681 | −0.0657190 | ||||||||
\(971\) | −26.5135 | −0.850860 | −0.425430 | − | 0.904991i | \(-0.639877\pi\) | ||||
−0.425430 | + | 0.904991i | \(0.639877\pi\) | |||||||
\(972\) | −13.7524 | −0.441108 | ||||||||
\(973\) | −9.78738 | −0.313769 | ||||||||
\(974\) | −10.6202 | −0.340293 | ||||||||
\(975\) | −1.59945 | −0.0512235 | ||||||||
\(976\) | 11.1857 | 0.358047 | ||||||||
\(977\) | 55.0904 | 1.76250 | 0.881250 | − | 0.472651i | \(-0.156703\pi\) | ||||
0.881250 | + | 0.472651i | \(0.156703\pi\) | |||||||
\(978\) | −4.29034 | −0.137190 | ||||||||
\(979\) | 38.1227 | 1.21841 | ||||||||
\(980\) | 13.5118 | 0.431620 | ||||||||
\(981\) | −13.4819 | −0.430444 | ||||||||
\(982\) | 26.9304 | 0.859384 | ||||||||
\(983\) | −15.8480 | −0.505472 | −0.252736 | − | 0.967535i | \(-0.581330\pi\) | ||||
−0.252736 | + | 0.967535i | \(0.581330\pi\) | |||||||
\(984\) | −1.29668 | −0.0413367 | ||||||||
\(985\) | −22.2744 | −0.709721 | ||||||||
\(986\) | 17.7026 | 0.563767 | ||||||||
\(987\) | 6.21201 | 0.197730 | ||||||||
\(988\) | 6.73649 | 0.214316 | ||||||||
\(989\) | 49.0281 | 1.55900 | ||||||||
\(990\) | −10.2995 | −0.327340 | ||||||||
\(991\) | −0.00674818 | −0.000214363 0 | −0.000107182 | − | 1.00000i | \(-0.500034\pi\) | ||||
−0.000107182 | 1.00000i | \(0.500034\pi\) | ||||||||
\(992\) | 2.21935 | 0.0704644 | ||||||||
\(993\) | 33.8240 | 1.07337 | ||||||||
\(994\) | 4.44389 | 0.140952 | ||||||||
\(995\) | 10.1256 | 0.321002 | ||||||||
\(996\) | 15.3986 | 0.487925 | ||||||||
\(997\) | −42.5804 | −1.34854 | −0.674268 | − | 0.738487i | \(-0.735541\pi\) | ||||
−0.674268 | + | 0.738487i | \(0.735541\pi\) | |||||||
\(998\) | 8.48031 | 0.268439 | ||||||||
\(999\) | 15.7815 | 0.499304 |
(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 | 4034.2.a.d.1.15 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.15 | ✓ | 52 | 1.1 | even | 1 | trivial |