Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, 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("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 | ||||||||
\(3\) | −1.94782 | −1.12458 | −0.562288 | − | 0.826942i | \(-0.690079\pi\) | ||||
−0.562288 | + | 0.826942i | \(0.690079\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.45647 | 1.54578 | 0.772891 | − | 0.634539i | \(-0.218810\pi\) | ||||
0.772891 | + | 0.634539i | \(0.218810\pi\) | |||||||
\(6\) | 1.94782 | 0.795195 | ||||||||
\(7\) | −2.39115 | −0.903771 | −0.451886 | − | 0.892076i | \(-0.649248\pi\) | ||||
−0.451886 | + | 0.892076i | \(0.649248\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.794011 | 0.264670 | ||||||||
\(10\) | −3.45647 | −1.09303 | ||||||||
\(11\) | 0.977749 | 0.294803 | 0.147401 | − | 0.989077i | \(-0.452909\pi\) | ||||
0.147401 | + | 0.989077i | \(0.452909\pi\) | |||||||
\(12\) | −1.94782 | −0.562288 | ||||||||
\(13\) | −5.92195 | −1.64245 | −0.821227 | − | 0.570602i | \(-0.806710\pi\) | ||||
−0.821227 | + | 0.570602i | \(0.806710\pi\) | |||||||
\(14\) | 2.39115 | 0.639063 | ||||||||
\(15\) | −6.73259 | −1.73835 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.06365 | −0.743045 | −0.371523 | − | 0.928424i | \(-0.621164\pi\) | ||||
−0.371523 | + | 0.928424i | \(0.621164\pi\) | |||||||
\(18\) | −0.794011 | −0.187150 | ||||||||
\(19\) | 5.80636 | 1.33207 | 0.666035 | − | 0.745921i | \(-0.267990\pi\) | ||||
0.666035 | + | 0.745921i | \(0.267990\pi\) | |||||||
\(20\) | 3.45647 | 0.772891 | ||||||||
\(21\) | 4.65754 | 1.01636 | ||||||||
\(22\) | −0.977749 | −0.208457 | ||||||||
\(23\) | −1.03892 | −0.216630 | −0.108315 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108315 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(24\) | 1.94782 | 0.397598 | ||||||||
\(25\) | 6.94720 | 1.38944 | ||||||||
\(26\) | 5.92195 | 1.16139 | ||||||||
\(27\) | 4.29687 | 0.826934 | ||||||||
\(28\) | −2.39115 | −0.451886 | ||||||||
\(29\) | 3.53785 | 0.656962 | 0.328481 | − | 0.944510i | \(-0.393463\pi\) | ||||
0.328481 | + | 0.944510i | \(0.393463\pi\) | |||||||
\(30\) | 6.73259 | 1.22920 | ||||||||
\(31\) | 3.73582 | 0.670973 | 0.335486 | − | 0.942045i | \(-0.391099\pi\) | ||||
0.335486 | + | 0.942045i | \(0.391099\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.90448 | −0.331528 | ||||||||
\(34\) | 3.06365 | 0.525412 | ||||||||
\(35\) | −8.26495 | −1.39703 | ||||||||
\(36\) | 0.794011 | 0.132335 | ||||||||
\(37\) | 0.629177 | 0.103436 | 0.0517180 | − | 0.998662i | \(-0.483530\pi\) | ||||
0.0517180 | + | 0.998662i | \(0.483530\pi\) | |||||||
\(38\) | −5.80636 | −0.941915 | ||||||||
\(39\) | 11.5349 | 1.84706 | ||||||||
\(40\) | −3.45647 | −0.546516 | ||||||||
\(41\) | 7.85266 | 1.22638 | 0.613190 | − | 0.789936i | \(-0.289886\pi\) | ||||
0.613190 | + | 0.789936i | \(0.289886\pi\) | |||||||
\(42\) | −4.65754 | −0.718674 | ||||||||
\(43\) | −9.12530 | −1.39160 | −0.695798 | − | 0.718238i | \(-0.744949\pi\) | ||||
−0.695798 | + | 0.718238i | \(0.744949\pi\) | |||||||
\(44\) | 0.977749 | 0.147401 | ||||||||
\(45\) | 2.74448 | 0.409123 | ||||||||
\(46\) | 1.03892 | 0.153180 | ||||||||
\(47\) | 6.49858 | 0.947916 | 0.473958 | − | 0.880547i | \(-0.342825\pi\) | ||||
0.473958 | + | 0.880547i | \(0.342825\pi\) | |||||||
\(48\) | −1.94782 | −0.281144 | ||||||||
\(49\) | −1.28239 | −0.183198 | ||||||||
\(50\) | −6.94720 | −0.982482 | ||||||||
\(51\) | 5.96745 | 0.835611 | ||||||||
\(52\) | −5.92195 | −0.821227 | ||||||||
\(53\) | −7.59890 | −1.04379 | −0.521894 | − | 0.853010i | \(-0.674774\pi\) | ||||
−0.521894 | + | 0.853010i | \(0.674774\pi\) | |||||||
\(54\) | −4.29687 | −0.584730 | ||||||||
\(55\) | 3.37956 | 0.455700 | ||||||||
\(56\) | 2.39115 | 0.319531 | ||||||||
\(57\) | −11.3097 | −1.49801 | ||||||||
\(58\) | −3.53785 | −0.464543 | ||||||||
\(59\) | −7.49169 | −0.975335 | −0.487667 | − | 0.873030i | \(-0.662152\pi\) | ||||
−0.487667 | + | 0.873030i | \(0.662152\pi\) | |||||||
\(60\) | −6.73259 | −0.869174 | ||||||||
\(61\) | 5.09242 | 0.652018 | 0.326009 | − | 0.945367i | \(-0.394296\pi\) | ||||
0.326009 | + | 0.945367i | \(0.394296\pi\) | |||||||
\(62\) | −3.73582 | −0.474449 | ||||||||
\(63\) | −1.89860 | −0.239201 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −20.4691 | −2.53887 | ||||||||
\(66\) | 1.90448 | 0.234426 | ||||||||
\(67\) | 2.93883 | 0.359035 | 0.179517 | − | 0.983755i | \(-0.442546\pi\) | ||||
0.179517 | + | 0.983755i | \(0.442546\pi\) | |||||||
\(68\) | −3.06365 | −0.371523 | ||||||||
\(69\) | 2.02363 | 0.243616 | ||||||||
\(70\) | 8.26495 | 0.987851 | ||||||||
\(71\) | −0.869517 | −0.103193 | −0.0515964 | − | 0.998668i | \(-0.516431\pi\) | ||||
−0.0515964 | + | 0.998668i | \(0.516431\pi\) | |||||||
\(72\) | −0.794011 | −0.0935751 | ||||||||
\(73\) | −7.50447 | −0.878331 | −0.439166 | − | 0.898406i | \(-0.644726\pi\) | ||||
−0.439166 | + | 0.898406i | \(0.644726\pi\) | |||||||
\(74\) | −0.629177 | −0.0731403 | ||||||||
\(75\) | −13.5319 | −1.56253 | ||||||||
\(76\) | 5.80636 | 0.666035 | ||||||||
\(77\) | −2.33795 | −0.266434 | ||||||||
\(78\) | −11.5349 | −1.30607 | ||||||||
\(79\) | 9.44928 | 1.06313 | 0.531563 | − | 0.847019i | \(-0.321605\pi\) | ||||
0.531563 | + | 0.847019i | \(0.321605\pi\) | |||||||
\(80\) | 3.45647 | 0.386445 | ||||||||
\(81\) | −10.7516 | −1.19462 | ||||||||
\(82\) | −7.85266 | −0.867181 | ||||||||
\(83\) | 8.38779 | 0.920680 | 0.460340 | − | 0.887743i | \(-0.347728\pi\) | ||||
0.460340 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(84\) | 4.65754 | 0.508179 | ||||||||
\(85\) | −10.5894 | −1.14859 | ||||||||
\(86\) | 9.12530 | 0.984007 | ||||||||
\(87\) | −6.89111 | −0.738804 | ||||||||
\(88\) | −0.977749 | −0.104228 | ||||||||
\(89\) | −14.6218 | −1.54991 | −0.774956 | − | 0.632015i | \(-0.782228\pi\) | ||||
−0.774956 | + | 0.632015i | \(0.782228\pi\) | |||||||
\(90\) | −2.74448 | −0.289293 | ||||||||
\(91\) | 14.1603 | 1.48440 | ||||||||
\(92\) | −1.03892 | −0.108315 | ||||||||
\(93\) | −7.27671 | −0.754559 | ||||||||
\(94\) | −6.49858 | −0.670278 | ||||||||
\(95\) | 20.0695 | 2.05909 | ||||||||
\(96\) | 1.94782 | 0.198799 | ||||||||
\(97\) | −13.1082 | −1.33094 | −0.665468 | − | 0.746426i | \(-0.731768\pi\) | ||||
−0.665468 | + | 0.746426i | \(0.731768\pi\) | |||||||
\(98\) | 1.28239 | 0.129540 | ||||||||
\(99\) | 0.776344 | 0.0780255 | ||||||||
\(100\) | 6.94720 | 0.694720 | ||||||||
\(101\) | −12.8622 | −1.27983 | −0.639917 | − | 0.768444i | \(-0.721031\pi\) | ||||
−0.639917 | + | 0.768444i | \(0.721031\pi\) | |||||||
\(102\) | −5.96745 | −0.590866 | ||||||||
\(103\) | 4.69253 | 0.462369 | 0.231184 | − | 0.972910i | \(-0.425740\pi\) | ||||
0.231184 | + | 0.972910i | \(0.425740\pi\) | |||||||
\(104\) | 5.92195 | 0.580695 | ||||||||
\(105\) | 16.0987 | 1.57107 | ||||||||
\(106\) | 7.59890 | 0.738070 | ||||||||
\(107\) | −11.1173 | −1.07475 | −0.537375 | − | 0.843343i | \(-0.680584\pi\) | ||||
−0.537375 | + | 0.843343i | \(0.680584\pi\) | |||||||
\(108\) | 4.29687 | 0.413467 | ||||||||
\(109\) | 6.23740 | 0.597435 | 0.298717 | − | 0.954342i | \(-0.403441\pi\) | ||||
0.298717 | + | 0.954342i | \(0.403441\pi\) | |||||||
\(110\) | −3.37956 | −0.322229 | ||||||||
\(111\) | −1.22553 | −0.116322 | ||||||||
\(112\) | −2.39115 | −0.225943 | ||||||||
\(113\) | −9.62327 | −0.905281 | −0.452640 | − | 0.891693i | \(-0.649518\pi\) | ||||
−0.452640 | + | 0.891693i | \(0.649518\pi\) | |||||||
\(114\) | 11.3097 | 1.05925 | ||||||||
\(115\) | −3.59100 | −0.334862 | ||||||||
\(116\) | 3.53785 | 0.328481 | ||||||||
\(117\) | −4.70210 | −0.434709 | ||||||||
\(118\) | 7.49169 | 0.689666 | ||||||||
\(119\) | 7.32567 | 0.671543 | ||||||||
\(120\) | 6.73259 | 0.614599 | ||||||||
\(121\) | −10.0440 | −0.913091 | ||||||||
\(122\) | −5.09242 | −0.461046 | ||||||||
\(123\) | −15.2956 | −1.37916 | ||||||||
\(124\) | 3.73582 | 0.335486 | ||||||||
\(125\) | 6.73043 | 0.601988 | ||||||||
\(126\) | 1.89860 | 0.169141 | ||||||||
\(127\) | 17.6938 | 1.57007 | 0.785037 | − | 0.619449i | \(-0.212644\pi\) | ||||
0.785037 | + | 0.619449i | \(0.212644\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 17.7745 | 1.56495 | ||||||||
\(130\) | 20.4691 | 1.79526 | ||||||||
\(131\) | −4.91795 | −0.429683 | −0.214842 | − | 0.976649i | \(-0.568924\pi\) | ||||
−0.214842 | + | 0.976649i | \(0.568924\pi\) | |||||||
\(132\) | −1.90448 | −0.165764 | ||||||||
\(133\) | −13.8839 | −1.20389 | ||||||||
\(134\) | −2.93883 | −0.253876 | ||||||||
\(135\) | 14.8520 | 1.27826 | ||||||||
\(136\) | 3.06365 | 0.262706 | ||||||||
\(137\) | −4.47013 | −0.381909 | −0.190954 | − | 0.981599i | \(-0.561158\pi\) | ||||
−0.190954 | + | 0.981599i | \(0.561158\pi\) | |||||||
\(138\) | −2.02363 | −0.172263 | ||||||||
\(139\) | 9.71261 | 0.823813 | 0.411906 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411906 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(140\) | −8.26495 | −0.698516 | ||||||||
\(141\) | −12.6581 | −1.06600 | ||||||||
\(142\) | 0.869517 | 0.0729683 | ||||||||
\(143\) | −5.79019 | −0.484200 | ||||||||
\(144\) | 0.794011 | 0.0661676 | ||||||||
\(145\) | 12.2285 | 1.01552 | ||||||||
\(146\) | 7.50447 | 0.621074 | ||||||||
\(147\) | 2.49786 | 0.206020 | ||||||||
\(148\) | 0.629177 | 0.0517180 | ||||||||
\(149\) | 7.33772 | 0.601129 | 0.300565 | − | 0.953761i | \(-0.402825\pi\) | ||||
0.300565 | + | 0.953761i | \(0.402825\pi\) | |||||||
\(150\) | 13.5319 | 1.10488 | ||||||||
\(151\) | −5.72157 | −0.465614 | −0.232807 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232807 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(152\) | −5.80636 | −0.470958 | ||||||||
\(153\) | −2.43258 | −0.196662 | ||||||||
\(154\) | 2.33795 | 0.188397 | ||||||||
\(155\) | 12.9127 | 1.03718 | ||||||||
\(156\) | 11.5349 | 0.923532 | ||||||||
\(157\) | 10.0393 | 0.801224 | 0.400612 | − | 0.916248i | \(-0.368798\pi\) | ||||
0.400612 | + | 0.916248i | \(0.368798\pi\) | |||||||
\(158\) | −9.44928 | −0.751744 | ||||||||
\(159\) | 14.8013 | 1.17382 | ||||||||
\(160\) | −3.45647 | −0.273258 | ||||||||
\(161\) | 2.48422 | 0.195784 | ||||||||
\(162\) | 10.7516 | 0.844724 | ||||||||
\(163\) | −20.7645 | −1.62640 | −0.813201 | − | 0.581983i | \(-0.802277\pi\) | ||||
−0.813201 | + | 0.581983i | \(0.802277\pi\) | |||||||
\(164\) | 7.85266 | 0.613190 | ||||||||
\(165\) | −6.58279 | −0.512469 | ||||||||
\(166\) | −8.38779 | −0.651019 | ||||||||
\(167\) | 11.8093 | 0.913831 | 0.456915 | − | 0.889510i | \(-0.348954\pi\) | ||||
0.456915 | + | 0.889510i | \(0.348954\pi\) | |||||||
\(168\) | −4.65754 | −0.359337 | ||||||||
\(169\) | 22.0695 | 1.69765 | ||||||||
\(170\) | 10.5894 | 0.812172 | ||||||||
\(171\) | 4.61031 | 0.352559 | ||||||||
\(172\) | −9.12530 | −0.695798 | ||||||||
\(173\) | −1.56209 | −0.118764 | −0.0593818 | − | 0.998235i | \(-0.518913\pi\) | ||||
−0.0593818 | + | 0.998235i | \(0.518913\pi\) | |||||||
\(174\) | 6.89111 | 0.522413 | ||||||||
\(175\) | −16.6118 | −1.25573 | ||||||||
\(176\) | 0.977749 | 0.0737006 | ||||||||
\(177\) | 14.5925 | 1.09684 | ||||||||
\(178\) | 14.6218 | 1.09595 | ||||||||
\(179\) | −11.1537 | −0.833666 | −0.416833 | − | 0.908983i | \(-0.636860\pi\) | ||||
−0.416833 | + | 0.908983i | \(0.636860\pi\) | |||||||
\(180\) | 2.74448 | 0.204561 | ||||||||
\(181\) | 16.5708 | 1.23169 | 0.615847 | − | 0.787865i | \(-0.288814\pi\) | ||||
0.615847 | + | 0.787865i | \(0.288814\pi\) | |||||||
\(182\) | −14.1603 | −1.04963 | ||||||||
\(183\) | −9.91914 | −0.733244 | ||||||||
\(184\) | 1.03892 | 0.0765902 | ||||||||
\(185\) | 2.17473 | 0.159890 | ||||||||
\(186\) | 7.27671 | 0.533554 | ||||||||
\(187\) | −2.99549 | −0.219052 | ||||||||
\(188\) | 6.49858 | 0.473958 | ||||||||
\(189\) | −10.2745 | −0.747359 | ||||||||
\(190\) | −20.0695 | −1.45599 | ||||||||
\(191\) | −17.7089 | −1.28137 | −0.640686 | − | 0.767803i | \(-0.721350\pi\) | ||||
−0.640686 | + | 0.767803i | \(0.721350\pi\) | |||||||
\(192\) | −1.94782 | −0.140572 | ||||||||
\(193\) | −13.2164 | −0.951335 | −0.475667 | − | 0.879625i | \(-0.657793\pi\) | ||||
−0.475667 | + | 0.879625i | \(0.657793\pi\) | |||||||
\(194\) | 13.1082 | 0.941114 | ||||||||
\(195\) | 39.8701 | 2.85516 | ||||||||
\(196\) | −1.28239 | −0.0915990 | ||||||||
\(197\) | 12.1174 | 0.863328 | 0.431664 | − | 0.902034i | \(-0.357927\pi\) | ||||
0.431664 | + | 0.902034i | \(0.357927\pi\) | |||||||
\(198\) | −0.776344 | −0.0551724 | ||||||||
\(199\) | −8.59925 | −0.609585 | −0.304792 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304792 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(200\) | −6.94720 | −0.491241 | ||||||||
\(201\) | −5.72431 | −0.403762 | ||||||||
\(202\) | 12.8622 | 0.904979 | ||||||||
\(203\) | −8.45954 | −0.593744 | ||||||||
\(204\) | 5.96745 | 0.417805 | ||||||||
\(205\) | 27.1425 | 1.89571 | ||||||||
\(206\) | −4.69253 | −0.326944 | ||||||||
\(207\) | −0.824914 | −0.0573355 | ||||||||
\(208\) | −5.92195 | −0.410613 | ||||||||
\(209\) | 5.67716 | 0.392697 | ||||||||
\(210\) | −16.0987 | −1.11091 | ||||||||
\(211\) | −15.1078 | −1.04006 | −0.520031 | − | 0.854147i | \(-0.674080\pi\) | ||||
−0.520031 | + | 0.854147i | \(0.674080\pi\) | |||||||
\(212\) | −7.59890 | −0.521894 | ||||||||
\(213\) | 1.69367 | 0.116048 | ||||||||
\(214\) | 11.1173 | 0.759963 | ||||||||
\(215\) | −31.5414 | −2.15110 | ||||||||
\(216\) | −4.29687 | −0.292365 | ||||||||
\(217\) | −8.93291 | −0.606406 | ||||||||
\(218\) | −6.23740 | −0.422450 | ||||||||
\(219\) | 14.6174 | 0.987750 | ||||||||
\(220\) | 3.37956 | 0.227850 | ||||||||
\(221\) | 18.1428 | 1.22042 | ||||||||
\(222\) | 1.22553 | 0.0822519 | ||||||||
\(223\) | 12.4181 | 0.831576 | 0.415788 | − | 0.909461i | \(-0.363506\pi\) | ||||
0.415788 | + | 0.909461i | \(0.363506\pi\) | |||||||
\(224\) | 2.39115 | 0.159766 | ||||||||
\(225\) | 5.51615 | 0.367743 | ||||||||
\(226\) | 9.62327 | 0.640130 | ||||||||
\(227\) | 4.51477 | 0.299656 | 0.149828 | − | 0.988712i | \(-0.452128\pi\) | ||||
0.149828 | + | 0.988712i | \(0.452128\pi\) | |||||||
\(228\) | −11.3097 | −0.749006 | ||||||||
\(229\) | −29.4052 | −1.94315 | −0.971576 | − | 0.236729i | \(-0.923925\pi\) | ||||
−0.971576 | + | 0.236729i | \(0.923925\pi\) | |||||||
\(230\) | 3.59100 | 0.236783 | ||||||||
\(231\) | 4.55391 | 0.299625 | ||||||||
\(232\) | −3.53785 | −0.232271 | ||||||||
\(233\) | −3.90158 | −0.255601 | −0.127800 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127800 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(234\) | 4.70210 | 0.307386 | ||||||||
\(235\) | 22.4622 | 1.46527 | ||||||||
\(236\) | −7.49169 | −0.487667 | ||||||||
\(237\) | −18.4055 | −1.19557 | ||||||||
\(238\) | −7.32567 | −0.474852 | ||||||||
\(239\) | −24.4116 | −1.57905 | −0.789526 | − | 0.613717i | \(-0.789674\pi\) | ||||
−0.789526 | + | 0.613717i | \(0.789674\pi\) | |||||||
\(240\) | −6.73259 | −0.434587 | ||||||||
\(241\) | −26.1321 | −1.68332 | −0.841660 | − | 0.540008i | \(-0.818421\pi\) | ||||
−0.841660 | + | 0.540008i | \(0.818421\pi\) | |||||||
\(242\) | 10.0440 | 0.645653 | ||||||||
\(243\) | 8.05154 | 0.516507 | ||||||||
\(244\) | 5.09242 | 0.326009 | ||||||||
\(245\) | −4.43253 | −0.283184 | ||||||||
\(246\) | 15.2956 | 0.975211 | ||||||||
\(247\) | −34.3850 | −2.18786 | ||||||||
\(248\) | −3.73582 | −0.237225 | ||||||||
\(249\) | −16.3379 | −1.03537 | ||||||||
\(250\) | −6.73043 | −0.425670 | ||||||||
\(251\) | 21.9976 | 1.38848 | 0.694238 | − | 0.719745i | \(-0.255741\pi\) | ||||
0.694238 | + | 0.719745i | \(0.255741\pi\) | |||||||
\(252\) | −1.89860 | −0.119601 | ||||||||
\(253\) | −1.01580 | −0.0638630 | ||||||||
\(254\) | −17.6938 | −1.11021 | ||||||||
\(255\) | 20.6263 | 1.29167 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0947 | −0.879206 | −0.439603 | − | 0.898192i | \(-0.644881\pi\) | ||||
−0.439603 | + | 0.898192i | \(0.644881\pi\) | |||||||
\(258\) | −17.7745 | −1.10659 | ||||||||
\(259\) | −1.50446 | −0.0934825 | ||||||||
\(260\) | −20.4691 | −1.26944 | ||||||||
\(261\) | 2.80909 | 0.173879 | ||||||||
\(262\) | 4.91795 | 0.303832 | ||||||||
\(263\) | −14.0607 | −0.867018 | −0.433509 | − | 0.901149i | \(-0.642725\pi\) | ||||
−0.433509 | + | 0.901149i | \(0.642725\pi\) | |||||||
\(264\) | 1.90448 | 0.117213 | ||||||||
\(265\) | −26.2654 | −1.61347 | ||||||||
\(266\) | 13.8839 | 0.851276 | ||||||||
\(267\) | 28.4808 | 1.74299 | ||||||||
\(268\) | 2.93883 | 0.179517 | ||||||||
\(269\) | −32.4136 | −1.97629 | −0.988145 | − | 0.153526i | \(-0.950937\pi\) | ||||
−0.988145 | + | 0.153526i | \(0.950937\pi\) | |||||||
\(270\) | −14.8520 | −0.903865 | ||||||||
\(271\) | −1.57480 | −0.0956621 | −0.0478310 | − | 0.998855i | \(-0.515231\pi\) | ||||
−0.0478310 | + | 0.998855i | \(0.515231\pi\) | |||||||
\(272\) | −3.06365 | −0.185761 | ||||||||
\(273\) | −27.5817 | −1.66932 | ||||||||
\(274\) | 4.47013 | 0.270050 | ||||||||
\(275\) | 6.79262 | 0.409610 | ||||||||
\(276\) | 2.02363 | 0.121808 | ||||||||
\(277\) | −0.196864 | −0.0118284 | −0.00591420 | − | 0.999983i | \(-0.501883\pi\) | ||||
−0.00591420 | + | 0.999983i | \(0.501883\pi\) | |||||||
\(278\) | −9.71261 | −0.582524 | ||||||||
\(279\) | 2.96628 | 0.177587 | ||||||||
\(280\) | 8.26495 | 0.493925 | ||||||||
\(281\) | −13.1151 | −0.782378 | −0.391189 | − | 0.920310i | \(-0.627936\pi\) | ||||
−0.391189 | + | 0.920310i | \(0.627936\pi\) | |||||||
\(282\) | 12.6581 | 0.753778 | ||||||||
\(283\) | 15.0768 | 0.896223 | 0.448111 | − | 0.893978i | \(-0.352097\pi\) | ||||
0.448111 | + | 0.893978i | \(0.352097\pi\) | |||||||
\(284\) | −0.869517 | −0.0515964 | ||||||||
\(285\) | −39.0918 | −2.31560 | ||||||||
\(286\) | 5.79019 | 0.342381 | ||||||||
\(287\) | −18.7769 | −1.10837 | ||||||||
\(288\) | −0.794011 | −0.0467876 | ||||||||
\(289\) | −7.61402 | −0.447884 | ||||||||
\(290\) | −12.2285 | −0.718081 | ||||||||
\(291\) | 25.5324 | 1.49674 | ||||||||
\(292\) | −7.50447 | −0.439166 | ||||||||
\(293\) | 23.4079 | 1.36751 | 0.683753 | − | 0.729714i | \(-0.260347\pi\) | ||||
0.683753 | + | 0.729714i | \(0.260347\pi\) | |||||||
\(294\) | −2.49786 | −0.145678 | ||||||||
\(295\) | −25.8948 | −1.50765 | ||||||||
\(296\) | −0.629177 | −0.0365702 | ||||||||
\(297\) | 4.20127 | 0.243782 | ||||||||
\(298\) | −7.33772 | −0.425062 | ||||||||
\(299\) | 6.15243 | 0.355804 | ||||||||
\(300\) | −13.5319 | −0.781265 | ||||||||
\(301\) | 21.8200 | 1.25768 | ||||||||
\(302\) | 5.72157 | 0.329239 | ||||||||
\(303\) | 25.0532 | 1.43927 | ||||||||
\(304\) | 5.80636 | 0.333017 | ||||||||
\(305\) | 17.6018 | 1.00788 | ||||||||
\(306\) | 2.43258 | 0.139061 | ||||||||
\(307\) | −21.3899 | −1.22078 | −0.610392 | − | 0.792100i | \(-0.708988\pi\) | ||||
−0.610392 | + | 0.792100i | \(0.708988\pi\) | |||||||
\(308\) | −2.33795 | −0.133217 | ||||||||
\(309\) | −9.14021 | −0.519969 | ||||||||
\(310\) | −12.9127 | −0.733395 | ||||||||
\(311\) | 3.11928 | 0.176878 | 0.0884391 | − | 0.996082i | \(-0.471812\pi\) | ||||
0.0884391 | + | 0.996082i | \(0.471812\pi\) | |||||||
\(312\) | −11.5349 | −0.653036 | ||||||||
\(313\) | −17.3323 | −0.979679 | −0.489840 | − | 0.871813i | \(-0.662945\pi\) | ||||
−0.489840 | + | 0.871813i | \(0.662945\pi\) | |||||||
\(314\) | −10.0393 | −0.566551 | ||||||||
\(315\) | −6.56247 | −0.369753 | ||||||||
\(316\) | 9.44928 | 0.531563 | ||||||||
\(317\) | −15.4248 | −0.866341 | −0.433171 | − | 0.901312i | \(-0.642605\pi\) | ||||
−0.433171 | + | 0.901312i | \(0.642605\pi\) | |||||||
\(318\) | −14.8013 | −0.830016 | ||||||||
\(319\) | 3.45913 | 0.193674 | ||||||||
\(320\) | 3.45647 | 0.193223 | ||||||||
\(321\) | 21.6545 | 1.20864 | ||||||||
\(322\) | −2.48422 | −0.138440 | ||||||||
\(323\) | −17.7887 | −0.989788 | ||||||||
\(324\) | −10.7516 | −0.597310 | ||||||||
\(325\) | −41.1410 | −2.28209 | ||||||||
\(326\) | 20.7645 | 1.15004 | ||||||||
\(327\) | −12.1494 | −0.671861 | ||||||||
\(328\) | −7.85266 | −0.433591 | ||||||||
\(329\) | −15.5391 | −0.856699 | ||||||||
\(330\) | 6.58279 | 0.362371 | ||||||||
\(331\) | 17.1044 | 0.940140 | 0.470070 | − | 0.882629i | \(-0.344229\pi\) | ||||
0.470070 | + | 0.882629i | \(0.344229\pi\) | |||||||
\(332\) | 8.38779 | 0.460340 | ||||||||
\(333\) | 0.499574 | 0.0273765 | ||||||||
\(334\) | −11.8093 | −0.646176 | ||||||||
\(335\) | 10.1580 | 0.554989 | ||||||||
\(336\) | 4.65754 | 0.254090 | ||||||||
\(337\) | 22.4924 | 1.22524 | 0.612621 | − | 0.790377i | \(-0.290115\pi\) | ||||
0.612621 | + | 0.790377i | \(0.290115\pi\) | |||||||
\(338\) | −22.0695 | −1.20042 | ||||||||
\(339\) | 18.7444 | 1.01806 | ||||||||
\(340\) | −10.5894 | −0.574293 | ||||||||
\(341\) | 3.65269 | 0.197804 | ||||||||
\(342\) | −4.61031 | −0.249297 | ||||||||
\(343\) | 19.8045 | 1.06934 | ||||||||
\(344\) | 9.12530 | 0.492003 | ||||||||
\(345\) | 6.99462 | 0.376578 | ||||||||
\(346\) | 1.56209 | 0.0839785 | ||||||||
\(347\) | 8.55698 | 0.459363 | 0.229681 | − | 0.973266i | \(-0.426232\pi\) | ||||
0.229681 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(348\) | −6.89111 | −0.369402 | ||||||||
\(349\) | 27.2249 | 1.45731 | 0.728657 | − | 0.684878i | \(-0.240145\pi\) | ||||
0.728657 | + | 0.684878i | \(0.240145\pi\) | |||||||
\(350\) | 16.6118 | 0.887939 | ||||||||
\(351\) | −25.4459 | −1.35820 | ||||||||
\(352\) | −0.977749 | −0.0521142 | ||||||||
\(353\) | 30.4965 | 1.62317 | 0.811584 | − | 0.584236i | \(-0.198606\pi\) | ||||
0.811584 | + | 0.584236i | \(0.198606\pi\) | |||||||
\(354\) | −14.5925 | −0.775581 | ||||||||
\(355\) | −3.00546 | −0.159513 | ||||||||
\(356\) | −14.6218 | −0.774956 | ||||||||
\(357\) | −14.2691 | −0.755201 | ||||||||
\(358\) | 11.1537 | 0.589491 | ||||||||
\(359\) | −12.0849 | −0.637814 | −0.318907 | − | 0.947786i | \(-0.603316\pi\) | ||||
−0.318907 | + | 0.947786i | \(0.603316\pi\) | |||||||
\(360\) | −2.74448 | −0.144647 | ||||||||
\(361\) | 14.7138 | 0.774409 | ||||||||
\(362\) | −16.5708 | −0.870940 | ||||||||
\(363\) | 19.5639 | 1.02684 | ||||||||
\(364\) | 14.1603 | 0.742201 | ||||||||
\(365\) | −25.9390 | −1.35771 | ||||||||
\(366\) | 9.91914 | 0.518482 | ||||||||
\(367\) | −23.9765 | −1.25157 | −0.625783 | − | 0.779997i | \(-0.715220\pi\) | ||||
−0.625783 | + | 0.779997i | \(0.715220\pi\) | |||||||
\(368\) | −1.03892 | −0.0541574 | ||||||||
\(369\) | 6.23510 | 0.324586 | ||||||||
\(370\) | −2.17473 | −0.113059 | ||||||||
\(371\) | 18.1701 | 0.943346 | ||||||||
\(372\) | −7.27671 | −0.377280 | ||||||||
\(373\) | −17.4513 | −0.903592 | −0.451796 | − | 0.892121i | \(-0.649217\pi\) | ||||
−0.451796 | + | 0.892121i | \(0.649217\pi\) | |||||||
\(374\) | 2.99549 | 0.154893 | ||||||||
\(375\) | −13.1097 | −0.676981 | ||||||||
\(376\) | −6.49858 | −0.335139 | ||||||||
\(377\) | −20.9510 | −1.07903 | ||||||||
\(378\) | 10.2745 | 0.528462 | ||||||||
\(379\) | −18.6880 | −0.959937 | −0.479969 | − | 0.877286i | \(-0.659352\pi\) | ||||
−0.479969 | + | 0.877286i | \(0.659352\pi\) | |||||||
\(380\) | 20.0695 | 1.02954 | ||||||||
\(381\) | −34.4644 | −1.76567 | ||||||||
\(382\) | 17.7089 | 0.906067 | ||||||||
\(383\) | −7.52543 | −0.384532 | −0.192266 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192266 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(384\) | 1.94782 | 0.0993994 | ||||||||
\(385\) | −8.08105 | −0.411849 | ||||||||
\(386\) | 13.2164 | 0.672695 | ||||||||
\(387\) | −7.24559 | −0.368314 | ||||||||
\(388\) | −13.1082 | −0.665468 | ||||||||
\(389\) | 7.36501 | 0.373421 | 0.186710 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186710 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(390\) | −39.8701 | −2.01890 | ||||||||
\(391\) | 3.18289 | 0.160966 | ||||||||
\(392\) | 1.28239 | 0.0647702 | ||||||||
\(393\) | 9.57929 | 0.483211 | ||||||||
\(394\) | −12.1174 | −0.610465 | ||||||||
\(395\) | 32.6612 | 1.64336 | ||||||||
\(396\) | 0.776344 | 0.0390128 | ||||||||
\(397\) | 21.1057 | 1.05926 | 0.529632 | − | 0.848228i | \(-0.322330\pi\) | ||||
0.529632 | + | 0.848228i | \(0.322330\pi\) | |||||||
\(398\) | 8.59925 | 0.431042 | ||||||||
\(399\) | 27.0433 | 1.35386 | ||||||||
\(400\) | 6.94720 | 0.347360 | ||||||||
\(401\) | 3.15705 | 0.157655 | 0.0788277 | − | 0.996888i | \(-0.474882\pi\) | ||||
0.0788277 | + | 0.996888i | \(0.474882\pi\) | |||||||
\(402\) | 5.72431 | 0.285503 | ||||||||
\(403\) | −22.1233 | −1.10204 | ||||||||
\(404\) | −12.8622 | −0.639917 | ||||||||
\(405\) | −37.1625 | −1.84662 | ||||||||
\(406\) | 8.45954 | 0.419840 | ||||||||
\(407\) | 0.615178 | 0.0304932 | ||||||||
\(408\) | −5.96745 | −0.295433 | ||||||||
\(409\) | −25.4041 | −1.25615 | −0.628077 | − | 0.778151i | \(-0.716158\pi\) | ||||
−0.628077 | + | 0.778151i | \(0.716158\pi\) | |||||||
\(410\) | −27.1425 | −1.34047 | ||||||||
\(411\) | 8.70701 | 0.429485 | ||||||||
\(412\) | 4.69253 | 0.231184 | ||||||||
\(413\) | 17.9138 | 0.881479 | ||||||||
\(414\) | 0.824914 | 0.0405423 | ||||||||
\(415\) | 28.9922 | 1.42317 | ||||||||
\(416\) | 5.92195 | 0.290348 | ||||||||
\(417\) | −18.9184 | −0.926440 | ||||||||
\(418\) | −5.67716 | −0.277679 | ||||||||
\(419\) | −25.8634 | −1.26351 | −0.631754 | − | 0.775169i | \(-0.717665\pi\) | ||||
−0.631754 | + | 0.775169i | \(0.717665\pi\) | |||||||
\(420\) | 16.0987 | 0.785534 | ||||||||
\(421\) | −18.3138 | −0.892559 | −0.446280 | − | 0.894894i | \(-0.647251\pi\) | ||||
−0.446280 | + | 0.894894i | \(0.647251\pi\) | |||||||
\(422\) | 15.1078 | 0.735435 | ||||||||
\(423\) | 5.15995 | 0.250885 | ||||||||
\(424\) | 7.59890 | 0.369035 | ||||||||
\(425\) | −21.2838 | −1.03242 | ||||||||
\(426\) | −1.69367 | −0.0820583 | ||||||||
\(427\) | −12.1768 | −0.589275 | ||||||||
\(428\) | −11.1173 | −0.537375 | ||||||||
\(429\) | 11.2783 | 0.544519 | ||||||||
\(430\) | 31.5414 | 1.52106 | ||||||||
\(431\) | −6.22975 | −0.300077 | −0.150038 | − | 0.988680i | \(-0.547940\pi\) | ||||
−0.150038 | + | 0.988680i | \(0.547940\pi\) | |||||||
\(432\) | 4.29687 | 0.206733 | ||||||||
\(433\) | −27.8348 | −1.33765 | −0.668827 | − | 0.743418i | \(-0.733203\pi\) | ||||
−0.668827 | + | 0.743418i | \(0.733203\pi\) | |||||||
\(434\) | 8.93291 | 0.428793 | ||||||||
\(435\) | −23.8189 | −1.14203 | ||||||||
\(436\) | 6.23740 | 0.298717 | ||||||||
\(437\) | −6.03234 | −0.288566 | ||||||||
\(438\) | −14.6174 | −0.698445 | ||||||||
\(439\) | −15.9019 | −0.758958 | −0.379479 | − | 0.925200i | \(-0.623897\pi\) | ||||
−0.379479 | + | 0.925200i | \(0.623897\pi\) | |||||||
\(440\) | −3.37956 | −0.161114 | ||||||||
\(441\) | −1.01823 | −0.0484871 | ||||||||
\(442\) | −18.1428 | −0.862966 | ||||||||
\(443\) | 0.277743 | 0.0131959 | 0.00659797 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659797 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(444\) | −1.22553 | −0.0581608 | ||||||||
\(445\) | −50.5400 | −2.39583 | ||||||||
\(446\) | −12.4181 | −0.588013 | ||||||||
\(447\) | −14.2926 | −0.676015 | ||||||||
\(448\) | −2.39115 | −0.112971 | ||||||||
\(449\) | 23.1883 | 1.09432 | 0.547162 | − | 0.837027i | \(-0.315708\pi\) | ||||
0.547162 | + | 0.837027i | \(0.315708\pi\) | |||||||
\(450\) | −5.51615 | −0.260034 | ||||||||
\(451\) | 7.67793 | 0.361540 | ||||||||
\(452\) | −9.62327 | −0.452640 | ||||||||
\(453\) | 11.1446 | 0.523619 | ||||||||
\(454\) | −4.51477 | −0.211888 | ||||||||
\(455\) | 48.9447 | 2.29456 | ||||||||
\(456\) | 11.3097 | 0.529627 | ||||||||
\(457\) | −10.6967 | −0.500368 | −0.250184 | − | 0.968198i | \(-0.580491\pi\) | ||||
−0.250184 | + | 0.968198i | \(0.580491\pi\) | |||||||
\(458\) | 29.4052 | 1.37402 | ||||||||
\(459\) | −13.1641 | −0.614449 | ||||||||
\(460\) | −3.59100 | −0.167431 | ||||||||
\(461\) | −26.2415 | −1.22219 | −0.611094 | − | 0.791558i | \(-0.709270\pi\) | ||||
−0.611094 | + | 0.791558i | \(0.709270\pi\) | |||||||
\(462\) | −4.55391 | −0.211867 | ||||||||
\(463\) | 8.58195 | 0.398837 | 0.199419 | − | 0.979914i | \(-0.436095\pi\) | ||||
0.199419 | + | 0.979914i | \(0.436095\pi\) | |||||||
\(464\) | 3.53785 | 0.164241 | ||||||||
\(465\) | −25.1517 | −1.16638 | ||||||||
\(466\) | 3.90158 | 0.180737 | ||||||||
\(467\) | −2.85203 | −0.131976 | −0.0659881 | − | 0.997820i | \(-0.521020\pi\) | ||||
−0.0659881 | + | 0.997820i | \(0.521020\pi\) | |||||||
\(468\) | −4.70210 | −0.217354 | ||||||||
\(469\) | −7.02718 | −0.324485 | ||||||||
\(470\) | −22.4622 | −1.03610 | ||||||||
\(471\) | −19.5548 | −0.901037 | ||||||||
\(472\) | 7.49169 | 0.344833 | ||||||||
\(473\) | −8.92226 | −0.410246 | ||||||||
\(474\) | 18.4055 | 0.845393 | ||||||||
\(475\) | 40.3379 | 1.85083 | ||||||||
\(476\) | 7.32567 | 0.335771 | ||||||||
\(477\) | −6.03361 | −0.276260 | ||||||||
\(478\) | 24.4116 | 1.11656 | ||||||||
\(479\) | 8.83196 | 0.403543 | 0.201771 | − | 0.979433i | \(-0.435330\pi\) | ||||
0.201771 | + | 0.979433i | \(0.435330\pi\) | |||||||
\(480\) | 6.73259 | 0.307299 | ||||||||
\(481\) | −3.72596 | −0.169889 | ||||||||
\(482\) | 26.1321 | 1.19029 | ||||||||
\(483\) | −4.83881 | −0.220174 | ||||||||
\(484\) | −10.0440 | −0.456546 | ||||||||
\(485\) | −45.3081 | −2.05734 | ||||||||
\(486\) | −8.05154 | −0.365225 | ||||||||
\(487\) | −6.17488 | −0.279811 | −0.139905 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139905 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(488\) | −5.09242 | −0.230523 | ||||||||
\(489\) | 40.4456 | 1.82901 | ||||||||
\(490\) | 4.43253 | 0.200241 | ||||||||
\(491\) | 16.0000 | 0.722070 | 0.361035 | − | 0.932552i | \(-0.382424\pi\) | ||||
0.361035 | + | 0.932552i | \(0.382424\pi\) | |||||||
\(492\) | −15.2956 | −0.689578 | ||||||||
\(493\) | −10.8388 | −0.488153 | ||||||||
\(494\) | 34.3850 | 1.54705 | ||||||||
\(495\) | 2.68341 | 0.120610 | ||||||||
\(496\) | 3.73582 | 0.167743 | ||||||||
\(497\) | 2.07915 | 0.0932626 | ||||||||
\(498\) | 16.3379 | 0.732120 | ||||||||
\(499\) | 33.0280 | 1.47853 | 0.739267 | − | 0.673412i | \(-0.235172\pi\) | ||||
0.739267 | + | 0.673412i | \(0.235172\pi\) | |||||||
\(500\) | 6.73043 | 0.300994 | ||||||||
\(501\) | −23.0024 | −1.02767 | ||||||||
\(502\) | −21.9976 | −0.981801 | ||||||||
\(503\) | 15.6359 | 0.697171 | 0.348586 | − | 0.937277i | \(-0.386662\pi\) | ||||
0.348586 | + | 0.937277i | \(0.386662\pi\) | |||||||
\(504\) | 1.89860 | 0.0845705 | ||||||||
\(505\) | −44.4577 | −1.97834 | ||||||||
\(506\) | 1.01580 | 0.0451580 | ||||||||
\(507\) | −42.9875 | −1.90914 | ||||||||
\(508\) | 17.6938 | 0.785037 | ||||||||
\(509\) | 12.7332 | 0.564391 | 0.282195 | − | 0.959357i | \(-0.408937\pi\) | ||||
0.282195 | + | 0.959357i | \(0.408937\pi\) | |||||||
\(510\) | −20.6263 | −0.913349 | ||||||||
\(511\) | 17.9443 | 0.793810 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 24.9492 | 1.10153 | ||||||||
\(514\) | 14.0947 | 0.621693 | ||||||||
\(515\) | 16.2196 | 0.714721 | ||||||||
\(516\) | 17.7745 | 0.782477 | ||||||||
\(517\) | 6.35399 | 0.279448 | ||||||||
\(518\) | 1.50446 | 0.0661021 | ||||||||
\(519\) | 3.04267 | 0.133559 | ||||||||
\(520\) | 20.4691 | 0.897628 | ||||||||
\(521\) | −14.2619 | −0.624825 | −0.312413 | − | 0.949947i | \(-0.601137\pi\) | ||||
−0.312413 | + | 0.949947i | \(0.601137\pi\) | |||||||
\(522\) | −2.80909 | −0.122951 | ||||||||
\(523\) | −19.6422 | −0.858894 | −0.429447 | − | 0.903092i | \(-0.641291\pi\) | ||||
−0.429447 | + | 0.903092i | \(0.641291\pi\) | |||||||
\(524\) | −4.91795 | −0.214842 | ||||||||
\(525\) | 32.3569 | 1.41217 | ||||||||
\(526\) | 14.0607 | 0.613074 | ||||||||
\(527\) | −11.4453 | −0.498563 | ||||||||
\(528\) | −1.90448 | −0.0828819 | ||||||||
\(529\) | −21.9206 | −0.953072 | ||||||||
\(530\) | 26.2654 | 1.14089 | ||||||||
\(531\) | −5.94848 | −0.258142 | ||||||||
\(532\) | −13.8839 | −0.601943 | ||||||||
\(533\) | −46.5031 | −2.01427 | ||||||||
\(534\) | −28.4808 | −1.23248 | ||||||||
\(535\) | −38.4266 | −1.66133 | ||||||||
\(536\) | −2.93883 | −0.126938 | ||||||||
\(537\) | 21.7254 | 0.937520 | ||||||||
\(538\) | 32.4136 | 1.39745 | ||||||||
\(539\) | −1.25385 | −0.0540072 | ||||||||
\(540\) | 14.8520 | 0.639129 | ||||||||
\(541\) | −34.0235 | −1.46278 | −0.731392 | − | 0.681957i | \(-0.761129\pi\) | ||||
−0.731392 | + | 0.681957i | \(0.761129\pi\) | |||||||
\(542\) | 1.57480 | 0.0676433 | ||||||||
\(543\) | −32.2769 | −1.38513 | ||||||||
\(544\) | 3.06365 | 0.131353 | ||||||||
\(545\) | 21.5594 | 0.923503 | ||||||||
\(546\) | 27.5817 | 1.18039 | ||||||||
\(547\) | 20.3929 | 0.871939 | 0.435970 | − | 0.899961i | \(-0.356405\pi\) | ||||
0.435970 | + | 0.899961i | \(0.356405\pi\) | |||||||
\(548\) | −4.47013 | −0.190954 | ||||||||
\(549\) | 4.04344 | 0.172570 | ||||||||
\(550\) | −6.79262 | −0.289638 | ||||||||
\(551\) | 20.5420 | 0.875120 | ||||||||
\(552\) | −2.02363 | −0.0861314 | ||||||||
\(553\) | −22.5947 | −0.960823 | ||||||||
\(554\) | 0.196864 | 0.00836394 | ||||||||
\(555\) | −4.23599 | −0.179808 | ||||||||
\(556\) | 9.71261 | 0.411906 | ||||||||
\(557\) | 10.1574 | 0.430383 | 0.215192 | − | 0.976572i | \(-0.430962\pi\) | ||||
0.215192 | + | 0.976572i | \(0.430962\pi\) | |||||||
\(558\) | −2.96628 | −0.125573 | ||||||||
\(559\) | 54.0396 | 2.28563 | ||||||||
\(560\) | −8.26495 | −0.349258 | ||||||||
\(561\) | 5.83467 | 0.246340 | ||||||||
\(562\) | 13.1151 | 0.553225 | ||||||||
\(563\) | −11.8407 | −0.499027 | −0.249514 | − | 0.968371i | \(-0.580271\pi\) | ||||
−0.249514 | + | 0.968371i | \(0.580271\pi\) | |||||||
\(564\) | −12.6581 | −0.533002 | ||||||||
\(565\) | −33.2625 | −1.39937 | ||||||||
\(566\) | −15.0768 | −0.633725 | ||||||||
\(567\) | 25.7087 | 1.07966 | ||||||||
\(568\) | 0.869517 | 0.0364841 | ||||||||
\(569\) | 1.10203 | 0.0461995 | 0.0230998 | − | 0.999733i | \(-0.492646\pi\) | ||||
0.0230998 | + | 0.999733i | \(0.492646\pi\) | |||||||
\(570\) | 39.0918 | 1.63738 | ||||||||
\(571\) | −13.9479 | −0.583703 | −0.291852 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291852 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(572\) | −5.79019 | −0.242100 | ||||||||
\(573\) | 34.4938 | 1.44100 | ||||||||
\(574\) | 18.7769 | 0.783733 | ||||||||
\(575\) | −7.21758 | −0.300994 | ||||||||
\(576\) | 0.794011 | 0.0330838 | ||||||||
\(577\) | −10.5434 | −0.438928 | −0.219464 | − | 0.975621i | \(-0.570431\pi\) | ||||
−0.219464 | + | 0.975621i | \(0.570431\pi\) | |||||||
\(578\) | 7.61402 | 0.316702 | ||||||||
\(579\) | 25.7431 | 1.06985 | ||||||||
\(580\) | 12.2285 | 0.507760 | ||||||||
\(581\) | −20.0565 | −0.832084 | ||||||||
\(582\) | −25.5324 | −1.05835 | ||||||||
\(583\) | −7.42982 | −0.307712 | ||||||||
\(584\) | 7.50447 | 0.310537 | ||||||||
\(585\) | −16.2527 | −0.671965 | ||||||||
\(586\) | −23.4079 | −0.966972 | ||||||||
\(587\) | −4.23027 | −0.174602 | −0.0873010 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0873010 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(588\) | 2.49786 | 0.103010 | ||||||||
\(589\) | 21.6915 | 0.893782 | ||||||||
\(590\) | 25.8948 | 1.06607 | ||||||||
\(591\) | −23.6025 | −0.970878 | ||||||||
\(592\) | 0.629177 | 0.0258590 | ||||||||
\(593\) | 11.4230 | 0.469087 | 0.234543 | − | 0.972106i | \(-0.424640\pi\) | ||||
0.234543 | + | 0.972106i | \(0.424640\pi\) | |||||||
\(594\) | −4.20127 | −0.172380 | ||||||||
\(595\) | 25.3210 | 1.03806 | ||||||||
\(596\) | 7.33772 | 0.300565 | ||||||||
\(597\) | 16.7498 | 0.685524 | ||||||||
\(598\) | −6.15243 | −0.251592 | ||||||||
\(599\) | −31.8719 | −1.30225 | −0.651125 | − | 0.758971i | \(-0.725702\pi\) | ||||
−0.651125 | + | 0.758971i | \(0.725702\pi\) | |||||||
\(600\) | 13.5319 | 0.552438 | ||||||||
\(601\) | 14.7214 | 0.600500 | 0.300250 | − | 0.953860i | \(-0.402930\pi\) | ||||
0.300250 | + | 0.953860i | \(0.402930\pi\) | |||||||
\(602\) | −21.8200 | −0.889317 | ||||||||
\(603\) | 2.33346 | 0.0950259 | ||||||||
\(604\) | −5.72157 | −0.232807 | ||||||||
\(605\) | −34.7168 | −1.41144 | ||||||||
\(606\) | −25.0532 | −1.01772 | ||||||||
\(607\) | 8.87986 | 0.360423 | 0.180211 | − | 0.983628i | \(-0.442322\pi\) | ||||
0.180211 | + | 0.983628i | \(0.442322\pi\) | |||||||
\(608\) | −5.80636 | −0.235479 | ||||||||
\(609\) | 16.4777 | 0.667710 | ||||||||
\(610\) | −17.6018 | −0.712677 | ||||||||
\(611\) | −38.4843 | −1.55691 | ||||||||
\(612\) | −2.43258 | −0.0983310 | ||||||||
\(613\) | −12.0865 | −0.488168 | −0.244084 | − | 0.969754i | \(-0.578487\pi\) | ||||
−0.244084 | + | 0.969754i | \(0.578487\pi\) | |||||||
\(614\) | 21.3899 | 0.863224 | ||||||||
\(615\) | −52.8688 | −2.13187 | ||||||||
\(616\) | 2.33795 | 0.0941986 | ||||||||
\(617\) | 45.3182 | 1.82444 | 0.912221 | − | 0.409699i | \(-0.134366\pi\) | ||||
0.912221 | + | 0.409699i | \(0.134366\pi\) | |||||||
\(618\) | 9.14021 | 0.367673 | ||||||||
\(619\) | 10.0733 | 0.404879 | 0.202439 | − | 0.979295i | \(-0.435113\pi\) | ||||
0.202439 | + | 0.979295i | \(0.435113\pi\) | |||||||
\(620\) | 12.9127 | 0.518588 | ||||||||
\(621\) | −4.46411 | −0.179138 | ||||||||
\(622\) | −3.11928 | −0.125072 | ||||||||
\(623\) | 34.9631 | 1.40077 | ||||||||
\(624\) | 11.5349 | 0.461766 | ||||||||
\(625\) | −11.4724 | −0.458898 | ||||||||
\(626\) | 17.3323 | 0.692738 | ||||||||
\(627\) | −11.0581 | −0.441618 | ||||||||
\(628\) | 10.0393 | 0.400612 | ||||||||
\(629\) | −1.92758 | −0.0768577 | ||||||||
\(630\) | 6.56247 | 0.261455 | ||||||||
\(631\) | −6.91807 | −0.275404 | −0.137702 | − | 0.990474i | \(-0.543972\pi\) | ||||
−0.137702 | + | 0.990474i | \(0.543972\pi\) | |||||||
\(632\) | −9.44928 | −0.375872 | ||||||||
\(633\) | 29.4273 | 1.16963 | ||||||||
\(634\) | 15.4248 | 0.612596 | ||||||||
\(635\) | 61.1582 | 2.42699 | ||||||||
\(636\) | 14.8013 | 0.586910 | ||||||||
\(637\) | 7.59423 | 0.300894 | ||||||||
\(638\) | −3.45913 | −0.136948 | ||||||||
\(639\) | −0.690407 | −0.0273121 | ||||||||
\(640\) | −3.45647 | −0.136629 | ||||||||
\(641\) | 24.8111 | 0.979979 | 0.489990 | − | 0.871728i | \(-0.337001\pi\) | ||||
0.489990 | + | 0.871728i | \(0.337001\pi\) | |||||||
\(642\) | −21.6545 | −0.854636 | ||||||||
\(643\) | −4.43907 | −0.175060 | −0.0875300 | − | 0.996162i | \(-0.527897\pi\) | ||||
−0.0875300 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(644\) | 2.48422 | 0.0978918 | ||||||||
\(645\) | 61.4370 | 2.41908 | ||||||||
\(646\) | 17.7887 | 0.699886 | ||||||||
\(647\) | −23.1463 | −0.909973 | −0.454987 | − | 0.890498i | \(-0.650356\pi\) | ||||
−0.454987 | + | 0.890498i | \(0.650356\pi\) | |||||||
\(648\) | 10.7516 | 0.422362 | ||||||||
\(649\) | −7.32499 | −0.287531 | ||||||||
\(650\) | 41.1410 | 1.61368 | ||||||||
\(651\) | 17.3997 | 0.681949 | ||||||||
\(652\) | −20.7645 | −0.813201 | ||||||||
\(653\) | −9.62947 | −0.376830 | −0.188415 | − | 0.982089i | \(-0.560335\pi\) | ||||
−0.188415 | + | 0.982089i | \(0.560335\pi\) | |||||||
\(654\) | 12.1494 | 0.475077 | ||||||||
\(655\) | −16.9988 | −0.664196 | ||||||||
\(656\) | 7.85266 | 0.306595 | ||||||||
\(657\) | −5.95863 | −0.232468 | ||||||||
\(658\) | 15.5391 | 0.605778 | ||||||||
\(659\) | −5.29072 | −0.206097 | −0.103048 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103048 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(660\) | −6.58279 | −0.256235 | ||||||||
\(661\) | −36.7220 | −1.42832 | −0.714159 | − | 0.699983i | \(-0.753191\pi\) | ||||
−0.714159 | + | 0.699983i | \(0.753191\pi\) | |||||||
\(662\) | −17.1044 | −0.664780 | ||||||||
\(663\) | −35.3390 | −1.37245 | ||||||||
\(664\) | −8.38779 | −0.325509 | ||||||||
\(665\) | −47.9893 | −1.86094 | ||||||||
\(666\) | −0.499574 | −0.0193581 | ||||||||
\(667\) | −3.67554 | −0.142318 | ||||||||
\(668\) | 11.8093 | 0.456915 | ||||||||
\(669\) | −24.1882 | −0.935171 | ||||||||
\(670\) | −10.1580 | −0.392437 | ||||||||
\(671\) | 4.97912 | 0.192217 | ||||||||
\(672\) | −4.65754 | −0.179669 | ||||||||
\(673\) | 38.3598 | 1.47866 | 0.739330 | − | 0.673343i | \(-0.235142\pi\) | ||||
0.739330 | + | 0.673343i | \(0.235142\pi\) | |||||||
\(674\) | −22.4924 | −0.866376 | ||||||||
\(675\) | 29.8512 | 1.14897 | ||||||||
\(676\) | 22.0695 | 0.848827 | ||||||||
\(677\) | 29.6043 | 1.13779 | 0.568894 | − | 0.822411i | \(-0.307372\pi\) | ||||
0.568894 | + | 0.822411i | \(0.307372\pi\) | |||||||
\(678\) | −18.7444 | −0.719875 | ||||||||
\(679\) | 31.3437 | 1.20286 | ||||||||
\(680\) | 10.5894 | 0.406086 | ||||||||
\(681\) | −8.79396 | −0.336985 | ||||||||
\(682\) | −3.65269 | −0.139869 | ||||||||
\(683\) | 27.8840 | 1.06695 | 0.533477 | − | 0.845815i | \(-0.320885\pi\) | ||||
0.533477 | + | 0.845815i | \(0.320885\pi\) | |||||||
\(684\) | 4.61031 | 0.176280 | ||||||||
\(685\) | −15.4509 | −0.590347 | ||||||||
\(686\) | −19.8045 | −0.756138 | ||||||||
\(687\) | 57.2761 | 2.18522 | ||||||||
\(688\) | −9.12530 | −0.347899 | ||||||||
\(689\) | 45.0003 | 1.71437 | ||||||||
\(690\) | −6.99462 | −0.266281 | ||||||||
\(691\) | −18.6111 | −0.708001 | −0.354001 | − | 0.935245i | \(-0.615179\pi\) | ||||
−0.354001 | + | 0.935245i | \(0.615179\pi\) | |||||||
\(692\) | −1.56209 | −0.0593818 | ||||||||
\(693\) | −1.85636 | −0.0705172 | ||||||||
\(694\) | −8.55698 | −0.324818 | ||||||||
\(695\) | 33.5714 | 1.27343 | ||||||||
\(696\) | 6.89111 | 0.261207 | ||||||||
\(697\) | −24.0578 | −0.911255 | ||||||||
\(698\) | −27.2249 | −1.03048 | ||||||||
\(699\) | 7.59958 | 0.287443 | ||||||||
\(700\) | −16.6118 | −0.627867 | ||||||||
\(701\) | −14.0763 | −0.531656 | −0.265828 | − | 0.964021i | \(-0.585645\pi\) | ||||
−0.265828 | + | 0.964021i | \(0.585645\pi\) | |||||||
\(702\) | 25.4459 | 0.960393 | ||||||||
\(703\) | 3.65323 | 0.137784 | ||||||||
\(704\) | 0.977749 | 0.0368503 | ||||||||
\(705\) | −43.7523 | −1.64781 | ||||||||
\(706\) | −30.4965 | −1.14775 | ||||||||
\(707\) | 30.7554 | 1.15668 | ||||||||
\(708\) | 14.5925 | 0.548419 | ||||||||
\(709\) | −1.87960 | −0.0705900 | −0.0352950 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352950 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(710\) | 3.00546 | 0.112793 | ||||||||
\(711\) | 7.50283 | 0.281378 | ||||||||
\(712\) | 14.6218 | 0.547977 | ||||||||
\(713\) | −3.88121 | −0.145353 | ||||||||
\(714\) | 14.2691 | 0.534007 | ||||||||
\(715\) | −20.0136 | −0.748467 | ||||||||
\(716\) | −11.1537 | −0.416833 | ||||||||
\(717\) | 47.5494 | 1.77576 | ||||||||
\(718\) | 12.0849 | 0.451003 | ||||||||
\(719\) | −33.8694 | −1.26312 | −0.631558 | − | 0.775329i | \(-0.717584\pi\) | ||||
−0.631558 | + | 0.775329i | \(0.717584\pi\) | |||||||
\(720\) | 2.74448 | 0.102281 | ||||||||
\(721\) | −11.2206 | −0.417875 | ||||||||
\(722\) | −14.7138 | −0.547590 | ||||||||
\(723\) | 50.9008 | 1.89302 | ||||||||
\(724\) | 16.5708 | 0.615847 | ||||||||
\(725\) | 24.5781 | 0.912809 | ||||||||
\(726\) | −19.5639 | −0.726086 | ||||||||
\(727\) | −25.7838 | −0.956266 | −0.478133 | − | 0.878287i | \(-0.658686\pi\) | ||||
−0.478133 | + | 0.878287i | \(0.658686\pi\) | |||||||
\(728\) | −14.1603 | −0.524815 | ||||||||
\(729\) | 16.5718 | 0.613769 | ||||||||
\(730\) | 25.9390 | 0.960044 | ||||||||
\(731\) | 27.9568 | 1.03402 | ||||||||
\(732\) | −9.91914 | −0.366622 | ||||||||
\(733\) | −12.3942 | −0.457788 | −0.228894 | − | 0.973451i | \(-0.573511\pi\) | ||||
−0.228894 | + | 0.973451i | \(0.573511\pi\) | |||||||
\(734\) | 23.9765 | 0.884990 | ||||||||
\(735\) | 8.63378 | 0.318462 | ||||||||
\(736\) | 1.03892 | 0.0382951 | ||||||||
\(737\) | 2.87344 | 0.105844 | ||||||||
\(738\) | −6.23510 | −0.229517 | ||||||||
\(739\) | 14.3947 | 0.529519 | 0.264760 | − | 0.964314i | \(-0.414707\pi\) | ||||
0.264760 | + | 0.964314i | \(0.414707\pi\) | |||||||
\(740\) | 2.17473 | 0.0799448 | ||||||||
\(741\) | 66.9758 | 2.46042 | ||||||||
\(742\) | −18.1701 | −0.667046 | ||||||||
\(743\) | 43.5855 | 1.59900 | 0.799498 | − | 0.600668i | \(-0.205099\pi\) | ||||
0.799498 | + | 0.600668i | \(0.205099\pi\) | |||||||
\(744\) | 7.27671 | 0.266777 | ||||||||
\(745\) | 25.3626 | 0.929214 | ||||||||
\(746\) | 17.4513 | 0.638936 | ||||||||
\(747\) | 6.66000 | 0.243677 | ||||||||
\(748\) | −2.99549 | −0.109526 | ||||||||
\(749\) | 26.5832 | 0.971328 | ||||||||
\(750\) | 13.1097 | 0.478698 | ||||||||
\(751\) | −34.7991 | −1.26984 | −0.634918 | − | 0.772579i | \(-0.718966\pi\) | ||||
−0.634918 | + | 0.772579i | \(0.718966\pi\) | |||||||
\(752\) | 6.49858 | 0.236979 | ||||||||
\(753\) | −42.8474 | −1.56145 | ||||||||
\(754\) | 20.9510 | 0.762990 | ||||||||
\(755\) | −19.7764 | −0.719738 | ||||||||
\(756\) | −10.2745 | −0.373679 | ||||||||
\(757\) | 28.3582 | 1.03070 | 0.515349 | − | 0.856981i | \(-0.327662\pi\) | ||||
0.515349 | + | 0.856981i | \(0.327662\pi\) | |||||||
\(758\) | 18.6880 | 0.678778 | ||||||||
\(759\) | 1.97860 | 0.0718188 | ||||||||
\(760\) | −20.0695 | −0.727997 | ||||||||
\(761\) | −5.87340 | −0.212911 | −0.106455 | − | 0.994317i | \(-0.533950\pi\) | ||||
−0.106455 | + | 0.994317i | \(0.533950\pi\) | |||||||
\(762\) | 34.4644 | 1.24851 | ||||||||
\(763\) | −14.9146 | −0.539944 | ||||||||
\(764\) | −17.7089 | −0.640686 | ||||||||
\(765\) | −8.40813 | −0.303997 | ||||||||
\(766\) | 7.52543 | 0.271905 | ||||||||
\(767\) | 44.3654 | 1.60194 | ||||||||
\(768\) | −1.94782 | −0.0702860 | ||||||||
\(769\) | −16.8641 | −0.608136 | −0.304068 | − | 0.952650i | \(-0.598345\pi\) | ||||
−0.304068 | + | 0.952650i | \(0.598345\pi\) | |||||||
\(770\) | 8.08105 | 0.291221 | ||||||||
\(771\) | 27.4541 | 0.988734 | ||||||||
\(772\) | −13.2164 | −0.475667 | ||||||||
\(773\) | 29.0197 | 1.04376 | 0.521882 | − | 0.853018i | \(-0.325230\pi\) | ||||
0.521882 | + | 0.853018i | \(0.325230\pi\) | |||||||
\(774\) | 7.24559 | 0.260438 | ||||||||
\(775\) | 25.9535 | 0.932275 | ||||||||
\(776\) | 13.1082 | 0.470557 | ||||||||
\(777\) | 2.93042 | 0.105128 | ||||||||
\(778\) | −7.36501 | −0.264048 | ||||||||
\(779\) | 45.5953 | 1.63362 | ||||||||
\(780\) | 39.8701 | 1.42758 | ||||||||
\(781\) | −0.850170 | −0.0304215 | ||||||||
\(782\) | −3.18289 | −0.113820 | ||||||||
\(783\) | 15.2017 | 0.543264 | ||||||||
\(784\) | −1.28239 | −0.0457995 | ||||||||
\(785\) | 34.7006 | 1.23852 | ||||||||
\(786\) | −9.57929 | −0.341682 | ||||||||
\(787\) | −52.5340 | −1.87263 | −0.936317 | − | 0.351156i | \(-0.885789\pi\) | ||||
−0.936317 | + | 0.351156i | \(0.885789\pi\) | |||||||
\(788\) | 12.1174 | 0.431664 | ||||||||
\(789\) | 27.3877 | 0.975027 | ||||||||
\(790\) | −32.6612 | −1.16203 | ||||||||
\(791\) | 23.0107 | 0.818166 | ||||||||
\(792\) | −0.776344 | −0.0275862 | ||||||||
\(793\) | −30.1571 | −1.07091 | ||||||||
\(794\) | −21.1057 | −0.749013 | ||||||||
\(795\) | 51.1603 | 1.81447 | ||||||||
\(796\) | −8.59925 | −0.304792 | ||||||||
\(797\) | −37.8357 | −1.34021 | −0.670105 | − | 0.742267i | \(-0.733751\pi\) | ||||
−0.670105 | + | 0.742267i | \(0.733751\pi\) | |||||||
\(798\) | −27.0433 | −0.957324 | ||||||||
\(799\) | −19.9094 | −0.704344 | ||||||||
\(800\) | −6.94720 | −0.245620 | ||||||||
\(801\) | −11.6099 | −0.410216 | ||||||||
\(802\) | −3.15705 | −0.111479 | ||||||||
\(803\) | −7.33749 | −0.258934 | ||||||||
\(804\) | −5.72431 | −0.201881 | ||||||||
\(805\) | 8.58662 | 0.302639 | ||||||||
\(806\) | 22.1233 | 0.779261 | ||||||||
\(807\) | 63.1358 | 2.22249 | ||||||||
\(808\) | 12.8622 | 0.452489 | ||||||||
\(809\) | 17.3244 | 0.609093 | 0.304547 | − | 0.952497i | \(-0.401495\pi\) | ||||
0.304547 | + | 0.952497i | \(0.401495\pi\) | |||||||
\(810\) | 37.1625 | 1.30576 | ||||||||
\(811\) | 52.0696 | 1.82841 | 0.914206 | − | 0.405249i | \(-0.132815\pi\) | ||||
0.914206 | + | 0.405249i | \(0.132815\pi\) | |||||||
\(812\) | −8.45954 | −0.296872 | ||||||||
\(813\) | 3.06742 | 0.107579 | ||||||||
\(814\) | −0.615178 | −0.0215620 | ||||||||
\(815\) | −71.7719 | −2.51406 | ||||||||
\(816\) | 5.96745 | 0.208903 | ||||||||
\(817\) | −52.9848 | −1.85370 | ||||||||
\(818\) | 25.4041 | 0.888235 | ||||||||
\(819\) | 11.2434 | 0.392877 | ||||||||
\(820\) | 27.1425 | 0.947857 | ||||||||
\(821\) | 21.2633 | 0.742094 | 0.371047 | − | 0.928614i | \(-0.378999\pi\) | ||||
0.371047 | + | 0.928614i | \(0.378999\pi\) | |||||||
\(822\) | −8.70701 | −0.303692 | ||||||||
\(823\) | −20.8761 | −0.727696 | −0.363848 | − | 0.931458i | \(-0.618537\pi\) | ||||
−0.363848 | + | 0.931458i | \(0.618537\pi\) | |||||||
\(824\) | −4.69253 | −0.163472 | ||||||||
\(825\) | −13.2308 | −0.460638 | ||||||||
\(826\) | −17.9138 | −0.623300 | ||||||||
\(827\) | 45.9878 | 1.59915 | 0.799577 | − | 0.600564i | \(-0.205057\pi\) | ||||
0.799577 | + | 0.600564i | \(0.205057\pi\) | |||||||
\(828\) | −0.824914 | −0.0286677 | ||||||||
\(829\) | −31.4132 | −1.09103 | −0.545513 | − | 0.838102i | \(-0.683665\pi\) | ||||
−0.545513 | + | 0.838102i | \(0.683665\pi\) | |||||||
\(830\) | −28.9922 | −1.00633 | ||||||||
\(831\) | 0.383455 | 0.0133019 | ||||||||
\(832\) | −5.92195 | −0.205307 | ||||||||
\(833\) | 3.92879 | 0.136124 | ||||||||
\(834\) | 18.9184 | 0.655092 | ||||||||
\(835\) | 40.8185 | 1.41258 | ||||||||
\(836\) | 5.67716 | 0.196349 | ||||||||
\(837\) | 16.0523 | 0.554850 | ||||||||
\(838\) | 25.8634 | 0.893435 | ||||||||
\(839\) | 46.5165 | 1.60593 | 0.802964 | − | 0.596027i | \(-0.203255\pi\) | ||||
0.802964 | + | 0.596027i | \(0.203255\pi\) | |||||||
\(840\) | −16.0987 | −0.555457 | ||||||||
\(841\) | −16.4836 | −0.568400 | ||||||||
\(842\) | 18.3138 | 0.631135 | ||||||||
\(843\) | 25.5458 | 0.879844 | ||||||||
\(844\) | −15.1078 | −0.520031 | ||||||||
\(845\) | 76.2826 | 2.62420 | ||||||||
\(846\) | −5.15995 | −0.177403 | ||||||||
\(847\) | 24.0168 | 0.825226 | ||||||||
\(848\) | −7.59890 | −0.260947 | ||||||||
\(849\) | −29.3669 | −1.00787 | ||||||||
\(850\) | 21.2838 | 0.730028 | ||||||||
\(851\) | −0.653664 | −0.0224073 | ||||||||
\(852\) | 1.69367 | 0.0580240 | ||||||||
\(853\) | 20.9271 | 0.716530 | 0.358265 | − | 0.933620i | \(-0.383368\pi\) | ||||
0.358265 | + | 0.933620i | \(0.383368\pi\) | |||||||
\(854\) | 12.1768 | 0.416680 | ||||||||
\(855\) | 15.9354 | 0.544980 | ||||||||
\(856\) | 11.1173 | 0.379982 | ||||||||
\(857\) | 34.5692 | 1.18086 | 0.590431 | − | 0.807088i | \(-0.298958\pi\) | ||||
0.590431 | + | 0.807088i | \(0.298958\pi\) | |||||||
\(858\) | −11.2783 | −0.385033 | ||||||||
\(859\) | −38.4860 | −1.31313 | −0.656563 | − | 0.754272i | \(-0.727990\pi\) | ||||
−0.656563 | + | 0.754272i | \(0.727990\pi\) | |||||||
\(860\) | −31.5414 | −1.07555 | ||||||||
\(861\) | 36.5741 | 1.24644 | ||||||||
\(862\) | 6.22975 | 0.212186 | ||||||||
\(863\) | −9.71330 | −0.330645 | −0.165322 | − | 0.986240i | \(-0.552866\pi\) | ||||
−0.165322 | + | 0.986240i | \(0.552866\pi\) | |||||||
\(864\) | −4.29687 | −0.146183 | ||||||||
\(865\) | −5.39932 | −0.183582 | ||||||||
\(866\) | 27.8348 | 0.945864 | ||||||||
\(867\) | 14.8308 | 0.503679 | ||||||||
\(868\) | −8.93291 | −0.303203 | ||||||||
\(869\) | 9.23903 | 0.313412 | ||||||||
\(870\) | 23.8189 | 0.807537 | ||||||||
\(871\) | −17.4036 | −0.589698 | ||||||||
\(872\) | −6.23740 | −0.211225 | ||||||||
\(873\) | −10.4081 | −0.352259 | ||||||||
\(874\) | 6.03234 | 0.204047 | ||||||||
\(875\) | −16.0935 | −0.544059 | ||||||||
\(876\) | 14.6174 | 0.493875 | ||||||||
\(877\) | −30.8135 | −1.04050 | −0.520248 | − | 0.854015i | \(-0.674161\pi\) | ||||
−0.520248 | + | 0.854015i | \(0.674161\pi\) | |||||||
\(878\) | 15.9019 | 0.536665 | ||||||||
\(879\) | −45.5945 | −1.53786 | ||||||||
\(880\) | 3.37956 | 0.113925 | ||||||||
\(881\) | −13.7664 | −0.463802 | −0.231901 | − | 0.972739i | \(-0.574495\pi\) | ||||
−0.231901 | + | 0.972739i | \(0.574495\pi\) | |||||||
\(882\) | 1.01823 | 0.0342855 | ||||||||
\(883\) | −36.2822 | −1.22099 | −0.610496 | − | 0.792019i | \(-0.709030\pi\) | ||||
−0.610496 | + | 0.792019i | \(0.709030\pi\) | |||||||
\(884\) | 18.1428 | 0.610209 | ||||||||
\(885\) | 50.4385 | 1.69547 | ||||||||
\(886\) | −0.277743 | −0.00933094 | ||||||||
\(887\) | −13.7336 | −0.461128 | −0.230564 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230564 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(888\) | 1.22553 | 0.0411259 | ||||||||
\(889\) | −42.3087 | −1.41899 | ||||||||
\(890\) | 50.5400 | 1.69410 | ||||||||
\(891\) | −10.5124 | −0.352177 | ||||||||
\(892\) | 12.4181 | 0.415788 | ||||||||
\(893\) | 37.7331 | 1.26269 | ||||||||
\(894\) | 14.2926 | 0.478015 | ||||||||
\(895\) | −38.5524 | −1.28867 | ||||||||
\(896\) | 2.39115 | 0.0798828 | ||||||||
\(897\) | −11.9838 | −0.400129 | ||||||||
\(898\) | −23.1883 | −0.773804 | ||||||||
\(899\) | 13.2168 | 0.440804 | ||||||||
\(900\) | 5.51615 | 0.183872 | ||||||||
\(901\) | 23.2804 | 0.775582 | ||||||||
\(902\) | −7.67793 | −0.255647 | ||||||||
\(903\) | −42.5015 | −1.41436 | ||||||||
\(904\) | 9.62327 | 0.320065 | ||||||||
\(905\) | 57.2764 | 1.90393 | ||||||||
\(906\) | −11.1446 | −0.370254 | ||||||||
\(907\) | 45.4762 | 1.51001 | 0.755006 | − | 0.655717i | \(-0.227634\pi\) | ||||
0.755006 | + | 0.655717i | \(0.227634\pi\) | |||||||
\(908\) | 4.51477 | 0.149828 | ||||||||
\(909\) | −10.2127 | −0.338734 | ||||||||
\(910\) | −48.9447 | −1.62250 | ||||||||
\(911\) | −18.1413 | −0.601048 | −0.300524 | − | 0.953774i | \(-0.597162\pi\) | ||||
−0.300524 | + | 0.953774i | \(0.597162\pi\) | |||||||
\(912\) | −11.3097 | −0.374503 | ||||||||
\(913\) | 8.20116 | 0.271419 | ||||||||
\(914\) | 10.6967 | 0.353814 | ||||||||
\(915\) | −34.2852 | −1.13343 | ||||||||
\(916\) | −29.4052 | −0.971576 | ||||||||
\(917\) | 11.7596 | 0.388335 | ||||||||
\(918\) | 13.1641 | 0.434481 | ||||||||
\(919\) | 54.6117 | 1.80147 | 0.900737 | − | 0.434365i | \(-0.143027\pi\) | ||||
0.900737 | + | 0.434365i | \(0.143027\pi\) | |||||||
\(920\) | 3.59100 | 0.118392 | ||||||||
\(921\) | 41.6636 | 1.37286 | ||||||||
\(922\) | 26.2415 | 0.864217 | ||||||||
\(923\) | 5.14924 | 0.169489 | ||||||||
\(924\) | 4.55391 | 0.149813 | ||||||||
\(925\) | 4.37102 | 0.143718 | ||||||||
\(926\) | −8.58195 | −0.282020 | ||||||||
\(927\) | 3.72592 | 0.122375 | ||||||||
\(928\) | −3.53785 | −0.116136 | ||||||||
\(929\) | 37.5139 | 1.23079 | 0.615396 | − | 0.788218i | \(-0.288996\pi\) | ||||
0.615396 | + | 0.788218i | \(0.288996\pi\) | |||||||
\(930\) | 25.1517 | 0.824758 | ||||||||
\(931\) | −7.44599 | −0.244032 | ||||||||
\(932\) | −3.90158 | −0.127800 | ||||||||
\(933\) | −6.07581 | −0.198913 | ||||||||
\(934\) | 2.85203 | 0.0933213 | ||||||||
\(935\) | −10.3538 | −0.338606 | ||||||||
\(936\) | 4.70210 | 0.153693 | ||||||||
\(937\) | −26.8071 | −0.875751 | −0.437876 | − | 0.899036i | \(-0.644269\pi\) | ||||
−0.437876 | + | 0.899036i | \(0.644269\pi\) | |||||||
\(938\) | 7.02718 | 0.229446 | ||||||||
\(939\) | 33.7602 | 1.10172 | ||||||||
\(940\) | 22.4622 | 0.732635 | ||||||||
\(941\) | 21.7970 | 0.710561 | 0.355281 | − | 0.934760i | \(-0.384385\pi\) | ||||
0.355281 | + | 0.934760i | \(0.384385\pi\) | |||||||
\(942\) | 19.5548 | 0.637129 | ||||||||
\(943\) | −8.15828 | −0.265670 | ||||||||
\(944\) | −7.49169 | −0.243834 | ||||||||
\(945\) | −35.5135 | −1.15525 | ||||||||
\(946\) | 8.92226 | 0.290088 | ||||||||
\(947\) | 27.3554 | 0.888932 | 0.444466 | − | 0.895796i | \(-0.353393\pi\) | ||||
0.444466 | + | 0.895796i | \(0.353393\pi\) | |||||||
\(948\) | −18.4055 | −0.597783 | ||||||||
\(949\) | 44.4411 | 1.44262 | ||||||||
\(950\) | −40.3379 | −1.30873 | ||||||||
\(951\) | 30.0447 | 0.974266 | ||||||||
\(952\) | −7.32567 | −0.237426 | ||||||||
\(953\) | −24.9250 | −0.807401 | −0.403701 | − | 0.914891i | \(-0.632276\pi\) | ||||
−0.403701 | + | 0.914891i | \(0.632276\pi\) | |||||||
\(954\) | 6.03361 | 0.195345 | ||||||||
\(955\) | −61.2104 | −1.98072 | ||||||||
\(956\) | −24.4116 | −0.789526 | ||||||||
\(957\) | −6.73777 | −0.217801 | ||||||||
\(958\) | −8.83196 | −0.285348 | ||||||||
\(959\) | 10.6888 | 0.345158 | ||||||||
\(960\) | −6.73259 | −0.217293 | ||||||||
\(961\) | −17.0437 | −0.549796 | ||||||||
\(962\) | 3.72596 | 0.120130 | ||||||||
\(963\) | −8.82726 | −0.284455 | ||||||||
\(964\) | −26.1321 | −0.841660 | ||||||||
\(965\) | −45.6820 | −1.47056 | ||||||||
\(966\) | 4.83881 | 0.155686 | ||||||||
\(967\) | 21.7212 | 0.698507 | 0.349253 | − | 0.937028i | \(-0.386435\pi\) | ||||
0.349253 | + | 0.937028i | \(0.386435\pi\) | |||||||
\(968\) | 10.0440 | 0.322827 | ||||||||
\(969\) | 34.6492 | 1.11309 | ||||||||
\(970\) | 45.3081 | 1.45476 | ||||||||
\(971\) | 44.0353 | 1.41316 | 0.706580 | − | 0.707633i | \(-0.250237\pi\) | ||||
0.706580 | + | 0.707633i | \(0.250237\pi\) | |||||||
\(972\) | 8.05154 | 0.258253 | ||||||||
\(973\) | −23.2243 | −0.744538 | ||||||||
\(974\) | 6.17488 | 0.197856 | ||||||||
\(975\) | 80.1353 | 2.56638 | ||||||||
\(976\) | 5.09242 | 0.163005 | ||||||||
\(977\) | 39.2032 | 1.25422 | 0.627111 | − | 0.778930i | \(-0.284237\pi\) | ||||
0.627111 | + | 0.778930i | \(0.284237\pi\) | |||||||
\(978\) | −40.4456 | −1.29331 | ||||||||
\(979\) | −14.2965 | −0.456918 | ||||||||
\(980\) | −4.43253 | −0.141592 | ||||||||
\(981\) | 4.95257 | 0.158123 | ||||||||
\(982\) | −16.0000 | −0.510580 | ||||||||
\(983\) | 24.5197 | 0.782056 | 0.391028 | − | 0.920379i | \(-0.372120\pi\) | ||||
0.391028 | + | 0.920379i | \(0.372120\pi\) | |||||||
\(984\) | 15.2956 | 0.487605 | ||||||||
\(985\) | 41.8834 | 1.33452 | ||||||||
\(986\) | 10.8388 | 0.345176 | ||||||||
\(987\) | 30.2674 | 0.963423 | ||||||||
\(988\) | −34.3850 | −1.09393 | ||||||||
\(989\) | 9.48046 | 0.301461 | ||||||||
\(990\) | −2.68341 | −0.0852844 | ||||||||
\(991\) | −19.3469 | −0.614575 | −0.307288 | − | 0.951617i | \(-0.599421\pi\) | ||||
−0.307288 | + | 0.951617i | \(0.599421\pi\) | |||||||
\(992\) | −3.73582 | −0.118612 | ||||||||
\(993\) | −33.3162 | −1.05726 | ||||||||
\(994\) | −2.07915 | −0.0659466 | ||||||||
\(995\) | −29.7231 | −0.942285 | ||||||||
\(996\) | −16.3379 | −0.517687 | ||||||||
\(997\) | −32.0044 | −1.01359 | −0.506794 | − | 0.862067i | \(-0.669170\pi\) | ||||
−0.506794 | + | 0.862067i | \(0.669170\pi\) | |||||||
\(998\) | −33.0280 | −1.04548 | ||||||||
\(999\) | 2.70349 | 0.0855348 |
(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 | 4022.2.a.d.1.9 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.9 | ✓ | 37 | 1.1 | even | 1 | trivial |