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: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 | ||||||||
\(3\) | −1.75046 | −1.01063 | −0.505314 | − | 0.862936i | \(-0.668623\pi\) | ||||
−0.505314 | + | 0.862936i | \(0.668623\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.28935 | 0.576617 | 0.288308 | − | 0.957538i | \(-0.406907\pi\) | ||||
0.288308 | + | 0.957538i | \(0.406907\pi\) | |||||||
\(6\) | −1.75046 | −0.714622 | ||||||||
\(7\) | −0.876800 | −0.331399 | −0.165700 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165700 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0641056 | 0.0213685 | ||||||||
\(10\) | 1.28935 | 0.407730 | ||||||||
\(11\) | −1.28293 | −0.386818 | −0.193409 | − | 0.981118i | \(-0.561954\pi\) | ||||
−0.193409 | + | 0.981118i | \(0.561954\pi\) | |||||||
\(12\) | −1.75046 | −0.505314 | ||||||||
\(13\) | 0.225028 | 0.0624114 | 0.0312057 | − | 0.999513i | \(-0.490065\pi\) | ||||
0.0312057 | + | 0.999513i | \(0.490065\pi\) | |||||||
\(14\) | −0.876800 | −0.234335 | ||||||||
\(15\) | −2.25696 | −0.582745 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.98652 | 1.45194 | 0.725972 | − | 0.687724i | \(-0.241390\pi\) | ||||
0.725972 | + | 0.687724i | \(0.241390\pi\) | |||||||
\(18\) | 0.0641056 | 0.0151098 | ||||||||
\(19\) | −7.24448 | −1.66200 | −0.830999 | − | 0.556273i | \(-0.812231\pi\) | ||||
−0.830999 | + | 0.556273i | \(0.812231\pi\) | |||||||
\(20\) | 1.28935 | 0.288308 | ||||||||
\(21\) | 1.53480 | 0.334921 | ||||||||
\(22\) | −1.28293 | −0.273521 | ||||||||
\(23\) | 2.70981 | 0.565034 | 0.282517 | − | 0.959262i | \(-0.408831\pi\) | ||||
0.282517 | + | 0.959262i | \(0.408831\pi\) | |||||||
\(24\) | −1.75046 | −0.357311 | ||||||||
\(25\) | −3.33757 | −0.667513 | ||||||||
\(26\) | 0.225028 | 0.0441315 | ||||||||
\(27\) | 5.13916 | 0.989032 | ||||||||
\(28\) | −0.876800 | −0.165700 | ||||||||
\(29\) | −6.42309 | −1.19274 | −0.596369 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596369 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(30\) | −2.25696 | −0.412063 | ||||||||
\(31\) | 1.49008 | 0.267626 | 0.133813 | − | 0.991007i | \(-0.457278\pi\) | ||||
0.133813 | + | 0.991007i | \(0.457278\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.24571 | 0.390929 | ||||||||
\(34\) | 5.98652 | 1.02668 | ||||||||
\(35\) | −1.13051 | −0.191090 | ||||||||
\(36\) | 0.0641056 | 0.0106843 | ||||||||
\(37\) | −2.10289 | −0.345712 | −0.172856 | − | 0.984947i | \(-0.555300\pi\) | ||||
−0.172856 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(38\) | −7.24448 | −1.17521 | ||||||||
\(39\) | −0.393901 | −0.0630747 | ||||||||
\(40\) | 1.28935 | 0.203865 | ||||||||
\(41\) | 4.13514 | 0.645801 | 0.322901 | − | 0.946433i | \(-0.395342\pi\) | ||||
0.322901 | + | 0.946433i | \(0.395342\pi\) | |||||||
\(42\) | 1.53480 | 0.236825 | ||||||||
\(43\) | −4.91283 | −0.749200 | −0.374600 | − | 0.927187i | \(-0.622220\pi\) | ||||
−0.374600 | + | 0.927187i | \(0.622220\pi\) | |||||||
\(44\) | −1.28293 | −0.193409 | ||||||||
\(45\) | 0.0826548 | 0.0123214 | ||||||||
\(46\) | 2.70981 | 0.399539 | ||||||||
\(47\) | −1.88312 | −0.274681 | −0.137340 | − | 0.990524i | \(-0.543855\pi\) | ||||
−0.137340 | + | 0.990524i | \(0.543855\pi\) | |||||||
\(48\) | −1.75046 | −0.252657 | ||||||||
\(49\) | −6.23122 | −0.890175 | ||||||||
\(50\) | −3.33757 | −0.472003 | ||||||||
\(51\) | −10.4792 | −1.46738 | ||||||||
\(52\) | 0.225028 | 0.0312057 | ||||||||
\(53\) | 2.06927 | 0.284237 | 0.142118 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142118 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(54\) | 5.13916 | 0.699351 | ||||||||
\(55\) | −1.65415 | −0.223045 | ||||||||
\(56\) | −0.876800 | −0.117167 | ||||||||
\(57\) | 12.6812 | 1.67966 | ||||||||
\(58\) | −6.42309 | −0.843393 | ||||||||
\(59\) | −8.60286 | −1.12000 | −0.559999 | − | 0.828494i | \(-0.689198\pi\) | ||||
−0.559999 | + | 0.828494i | \(0.689198\pi\) | |||||||
\(60\) | −2.25696 | −0.291372 | ||||||||
\(61\) | 12.1418 | 1.55460 | 0.777301 | − | 0.629129i | \(-0.216588\pi\) | ||||
0.777301 | + | 0.629129i | \(0.216588\pi\) | |||||||
\(62\) | 1.49008 | 0.189240 | ||||||||
\(63\) | −0.0562077 | −0.00708151 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.290140 | 0.0359875 | ||||||||
\(66\) | 2.24571 | 0.276428 | ||||||||
\(67\) | 5.48626 | 0.670254 | 0.335127 | − | 0.942173i | \(-0.391221\pi\) | ||||
0.335127 | + | 0.942173i | \(0.391221\pi\) | |||||||
\(68\) | 5.98652 | 0.725972 | ||||||||
\(69\) | −4.74341 | −0.571039 | ||||||||
\(70\) | −1.13051 | −0.135121 | ||||||||
\(71\) | −16.2228 | −1.92530 | −0.962648 | − | 0.270756i | \(-0.912726\pi\) | ||||
−0.962648 | + | 0.270756i | \(0.912726\pi\) | |||||||
\(72\) | 0.0641056 | 0.00755491 | ||||||||
\(73\) | 2.50459 | 0.293140 | 0.146570 | − | 0.989200i | \(-0.453177\pi\) | ||||
0.146570 | + | 0.989200i | \(0.453177\pi\) | |||||||
\(74\) | −2.10289 | −0.244456 | ||||||||
\(75\) | 5.84227 | 0.674607 | ||||||||
\(76\) | −7.24448 | −0.830999 | ||||||||
\(77\) | 1.12487 | 0.128191 | ||||||||
\(78\) | −0.393901 | −0.0446006 | ||||||||
\(79\) | −10.0611 | −1.13196 | −0.565981 | − | 0.824418i | \(-0.691502\pi\) | ||||
−0.565981 | + | 0.824418i | \(0.691502\pi\) | |||||||
\(80\) | 1.28935 | 0.144154 | ||||||||
\(81\) | −9.18821 | −1.02091 | ||||||||
\(82\) | 4.13514 | 0.456650 | ||||||||
\(83\) | −6.40976 | −0.703562 | −0.351781 | − | 0.936082i | \(-0.614424\pi\) | ||||
−0.351781 | + | 0.936082i | \(0.614424\pi\) | |||||||
\(84\) | 1.53480 | 0.167461 | ||||||||
\(85\) | 7.71874 | 0.837215 | ||||||||
\(86\) | −4.91283 | −0.529764 | ||||||||
\(87\) | 11.2433 | 1.20541 | ||||||||
\(88\) | −1.28293 | −0.136761 | ||||||||
\(89\) | −14.1815 | −1.50324 | −0.751619 | − | 0.659597i | \(-0.770727\pi\) | ||||
−0.751619 | + | 0.659597i | \(0.770727\pi\) | |||||||
\(90\) | 0.0826548 | 0.00871258 | ||||||||
\(91\) | −0.197304 | −0.0206831 | ||||||||
\(92\) | 2.70981 | 0.282517 | ||||||||
\(93\) | −2.60832 | −0.270470 | ||||||||
\(94\) | −1.88312 | −0.194228 | ||||||||
\(95\) | −9.34071 | −0.958336 | ||||||||
\(96\) | −1.75046 | −0.178655 | ||||||||
\(97\) | 8.26993 | 0.839684 | 0.419842 | − | 0.907597i | \(-0.362086\pi\) | ||||
0.419842 | + | 0.907597i | \(0.362086\pi\) | |||||||
\(98\) | −6.23122 | −0.629449 | ||||||||
\(99\) | −0.0822429 | −0.00826572 | ||||||||
\(100\) | −3.33757 | −0.333757 | ||||||||
\(101\) | −14.5779 | −1.45055 | −0.725277 | − | 0.688458i | \(-0.758288\pi\) | ||||
−0.725277 | + | 0.688458i | \(0.758288\pi\) | |||||||
\(102\) | −10.4792 | −1.03759 | ||||||||
\(103\) | −0.271941 | −0.0267952 | −0.0133976 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133976 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(104\) | 0.225028 | 0.0220658 | ||||||||
\(105\) | 1.97890 | 0.193121 | ||||||||
\(106\) | 2.06927 | 0.200986 | ||||||||
\(107\) | 9.60580 | 0.928627 | 0.464314 | − | 0.885671i | \(-0.346301\pi\) | ||||
0.464314 | + | 0.885671i | \(0.346301\pi\) | |||||||
\(108\) | 5.13916 | 0.494516 | ||||||||
\(109\) | 15.7206 | 1.50576 | 0.752881 | − | 0.658157i | \(-0.228664\pi\) | ||||
0.752881 | + | 0.658157i | \(0.228664\pi\) | |||||||
\(110\) | −1.65415 | −0.157717 | ||||||||
\(111\) | 3.68102 | 0.349387 | ||||||||
\(112\) | −0.876800 | −0.0828498 | ||||||||
\(113\) | −10.0760 | −0.947866 | −0.473933 | − | 0.880561i | \(-0.657166\pi\) | ||||
−0.473933 | + | 0.880561i | \(0.657166\pi\) | |||||||
\(114\) | 12.6812 | 1.18770 | ||||||||
\(115\) | 3.49390 | 0.325808 | ||||||||
\(116\) | −6.42309 | −0.596369 | ||||||||
\(117\) | 0.0144255 | 0.00133364 | ||||||||
\(118\) | −8.60286 | −0.791958 | ||||||||
\(119\) | −5.24898 | −0.481173 | ||||||||
\(120\) | −2.25696 | −0.206031 | ||||||||
\(121\) | −9.35409 | −0.850372 | ||||||||
\(122\) | 12.1418 | 1.09927 | ||||||||
\(123\) | −7.23840 | −0.652665 | ||||||||
\(124\) | 1.49008 | 0.133813 | ||||||||
\(125\) | −10.7501 | −0.961516 | ||||||||
\(126\) | −0.0562077 | −0.00500738 | ||||||||
\(127\) | −9.12133 | −0.809387 | −0.404694 | − | 0.914452i | \(-0.632622\pi\) | ||||
−0.404694 | + | 0.914452i | \(0.632622\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.59971 | 0.757162 | ||||||||
\(130\) | 0.290140 | 0.0254470 | ||||||||
\(131\) | −6.00235 | −0.524428 | −0.262214 | − | 0.965010i | \(-0.584453\pi\) | ||||
−0.262214 | + | 0.965010i | \(0.584453\pi\) | |||||||
\(132\) | 2.24571 | 0.195464 | ||||||||
\(133\) | 6.35196 | 0.550785 | ||||||||
\(134\) | 5.48626 | 0.473941 | ||||||||
\(135\) | 6.62620 | 0.570292 | ||||||||
\(136\) | 5.98652 | 0.513340 | ||||||||
\(137\) | 8.40096 | 0.717742 | 0.358871 | − | 0.933387i | \(-0.383162\pi\) | ||||
0.358871 | + | 0.933387i | \(0.383162\pi\) | |||||||
\(138\) | −4.74341 | −0.403786 | ||||||||
\(139\) | 0.768712 | 0.0652013 | 0.0326007 | − | 0.999468i | \(-0.489621\pi\) | ||||
0.0326007 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(140\) | −1.13051 | −0.0955451 | ||||||||
\(141\) | 3.29632 | 0.277600 | ||||||||
\(142\) | −16.2228 | −1.36139 | ||||||||
\(143\) | −0.288694 | −0.0241418 | ||||||||
\(144\) | 0.0641056 | 0.00534213 | ||||||||
\(145\) | −8.28163 | −0.687752 | ||||||||
\(146\) | 2.50459 | 0.207281 | ||||||||
\(147\) | 10.9075 | 0.899635 | ||||||||
\(148\) | −2.10289 | −0.172856 | ||||||||
\(149\) | −11.1812 | −0.916001 | −0.458000 | − | 0.888952i | \(-0.651434\pi\) | ||||
−0.458000 | + | 0.888952i | \(0.651434\pi\) | |||||||
\(150\) | 5.84227 | 0.477019 | ||||||||
\(151\) | 2.38218 | 0.193859 | 0.0969296 | − | 0.995291i | \(-0.469098\pi\) | ||||
0.0969296 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(152\) | −7.24448 | −0.587605 | ||||||||
\(153\) | 0.383769 | 0.0310259 | ||||||||
\(154\) | 1.12487 | 0.0906447 | ||||||||
\(155\) | 1.92124 | 0.154317 | ||||||||
\(156\) | −0.393901 | −0.0315374 | ||||||||
\(157\) | −0.304865 | −0.0243309 | −0.0121654 | − | 0.999926i | \(-0.503872\pi\) | ||||
−0.0121654 | + | 0.999926i | \(0.503872\pi\) | |||||||
\(158\) | −10.0611 | −0.800418 | ||||||||
\(159\) | −3.62218 | −0.287257 | ||||||||
\(160\) | 1.28935 | 0.101932 | ||||||||
\(161\) | −2.37596 | −0.187252 | ||||||||
\(162\) | −9.18821 | −0.721894 | ||||||||
\(163\) | 8.38198 | 0.656528 | 0.328264 | − | 0.944586i | \(-0.393536\pi\) | ||||
0.328264 | + | 0.944586i | \(0.393536\pi\) | |||||||
\(164\) | 4.13514 | 0.322901 | ||||||||
\(165\) | 2.89552 | 0.225416 | ||||||||
\(166\) | −6.40976 | −0.497494 | ||||||||
\(167\) | −12.1234 | −0.938139 | −0.469069 | − | 0.883161i | \(-0.655411\pi\) | ||||
−0.469069 | + | 0.883161i | \(0.655411\pi\) | |||||||
\(168\) | 1.53480 | 0.118413 | ||||||||
\(169\) | −12.9494 | −0.996105 | ||||||||
\(170\) | 7.71874 | 0.592001 | ||||||||
\(171\) | −0.464412 | −0.0355145 | ||||||||
\(172\) | −4.91283 | −0.374600 | ||||||||
\(173\) | 24.9433 | 1.89641 | 0.948204 | − | 0.317663i | \(-0.102898\pi\) | ||||
0.948204 | + | 0.317663i | \(0.102898\pi\) | |||||||
\(174\) | 11.2433 | 0.852356 | ||||||||
\(175\) | 2.92638 | 0.221213 | ||||||||
\(176\) | −1.28293 | −0.0967044 | ||||||||
\(177\) | 15.0590 | 1.13190 | ||||||||
\(178\) | −14.1815 | −1.06295 | ||||||||
\(179\) | −14.3700 | −1.07406 | −0.537031 | − | 0.843563i | \(-0.680454\pi\) | ||||
−0.537031 | + | 0.843563i | \(0.680454\pi\) | |||||||
\(180\) | 0.0826548 | 0.00616072 | ||||||||
\(181\) | 11.7556 | 0.873787 | 0.436893 | − | 0.899513i | \(-0.356079\pi\) | ||||
0.436893 | + | 0.899513i | \(0.356079\pi\) | |||||||
\(182\) | −0.197304 | −0.0146252 | ||||||||
\(183\) | −21.2538 | −1.57112 | ||||||||
\(184\) | 2.70981 | 0.199770 | ||||||||
\(185\) | −2.71137 | −0.199344 | ||||||||
\(186\) | −2.60832 | −0.191251 | ||||||||
\(187\) | −7.68028 | −0.561637 | ||||||||
\(188\) | −1.88312 | −0.137340 | ||||||||
\(189\) | −4.50602 | −0.327764 | ||||||||
\(190\) | −9.34071 | −0.677646 | ||||||||
\(191\) | −17.9153 | −1.29631 | −0.648154 | − | 0.761509i | \(-0.724459\pi\) | ||||
−0.648154 | + | 0.761509i | \(0.724459\pi\) | |||||||
\(192\) | −1.75046 | −0.126328 | ||||||||
\(193\) | −22.0973 | −1.59060 | −0.795300 | − | 0.606216i | \(-0.792687\pi\) | ||||
−0.795300 | + | 0.606216i | \(0.792687\pi\) | |||||||
\(194\) | 8.26993 | 0.593746 | ||||||||
\(195\) | −0.507878 | −0.0363699 | ||||||||
\(196\) | −6.23122 | −0.445087 | ||||||||
\(197\) | −5.86785 | −0.418067 | −0.209034 | − | 0.977908i | \(-0.567032\pi\) | ||||
−0.209034 | + | 0.977908i | \(0.567032\pi\) | |||||||
\(198\) | −0.0822429 | −0.00584475 | ||||||||
\(199\) | −3.73945 | −0.265083 | −0.132541 | − | 0.991177i | \(-0.542314\pi\) | ||||
−0.132541 | + | 0.991177i | \(0.542314\pi\) | |||||||
\(200\) | −3.33757 | −0.236002 | ||||||||
\(201\) | −9.60347 | −0.677377 | ||||||||
\(202\) | −14.5779 | −1.02570 | ||||||||
\(203\) | 5.63176 | 0.395272 | ||||||||
\(204\) | −10.4792 | −0.733688 | ||||||||
\(205\) | 5.33167 | 0.372380 | ||||||||
\(206\) | −0.271941 | −0.0189471 | ||||||||
\(207\) | 0.173714 | 0.0120739 | ||||||||
\(208\) | 0.225028 | 0.0156029 | ||||||||
\(209\) | 9.29416 | 0.642890 | ||||||||
\(210\) | 1.97890 | 0.136557 | ||||||||
\(211\) | 27.7812 | 1.91254 | 0.956268 | − | 0.292493i | \(-0.0944849\pi\) | ||||
0.956268 | + | 0.292493i | \(0.0944849\pi\) | |||||||
\(212\) | 2.06927 | 0.142118 | ||||||||
\(213\) | 28.3974 | 1.94576 | ||||||||
\(214\) | 9.60580 | 0.656639 | ||||||||
\(215\) | −6.33438 | −0.432001 | ||||||||
\(216\) | 5.13916 | 0.349676 | ||||||||
\(217\) | −1.30650 | −0.0886909 | ||||||||
\(218\) | 15.7206 | 1.06473 | ||||||||
\(219\) | −4.38417 | −0.296255 | ||||||||
\(220\) | −1.65415 | −0.111523 | ||||||||
\(221\) | 1.34713 | 0.0906179 | ||||||||
\(222\) | 3.68102 | 0.247054 | ||||||||
\(223\) | −22.9164 | −1.53460 | −0.767299 | − | 0.641290i | \(-0.778400\pi\) | ||||
−0.767299 | + | 0.641290i | \(0.778400\pi\) | |||||||
\(224\) | −0.876800 | −0.0585836 | ||||||||
\(225\) | −0.213957 | −0.0142638 | ||||||||
\(226\) | −10.0760 | −0.670243 | ||||||||
\(227\) | −2.08411 | −0.138328 | −0.0691638 | − | 0.997605i | \(-0.522033\pi\) | ||||
−0.0691638 | + | 0.997605i | \(0.522033\pi\) | |||||||
\(228\) | 12.6812 | 0.839831 | ||||||||
\(229\) | 15.3090 | 1.01165 | 0.505823 | − | 0.862637i | \(-0.331189\pi\) | ||||
0.505823 | + | 0.862637i | \(0.331189\pi\) | |||||||
\(230\) | 3.49390 | 0.230381 | ||||||||
\(231\) | −1.96904 | −0.129553 | ||||||||
\(232\) | −6.42309 | −0.421696 | ||||||||
\(233\) | 19.1212 | 1.25267 | 0.626337 | − | 0.779553i | \(-0.284554\pi\) | ||||
0.626337 | + | 0.779553i | \(0.284554\pi\) | |||||||
\(234\) | 0.0144255 | 0.000943026 0 | ||||||||
\(235\) | −2.42800 | −0.158385 | ||||||||
\(236\) | −8.60286 | −0.559999 | ||||||||
\(237\) | 17.6115 | 1.14399 | ||||||||
\(238\) | −5.24898 | −0.340241 | ||||||||
\(239\) | −11.8207 | −0.764615 | −0.382307 | − | 0.924035i | \(-0.624870\pi\) | ||||
−0.382307 | + | 0.924035i | \(0.624870\pi\) | |||||||
\(240\) | −2.25696 | −0.145686 | ||||||||
\(241\) | −9.30234 | −0.599216 | −0.299608 | − | 0.954062i | \(-0.596856\pi\) | ||||
−0.299608 | + | 0.954062i | \(0.596856\pi\) | |||||||
\(242\) | −9.35409 | −0.601304 | ||||||||
\(243\) | 0.666091 | 0.0427298 | ||||||||
\(244\) | 12.1418 | 0.777301 | ||||||||
\(245\) | −8.03425 | −0.513290 | ||||||||
\(246\) | −7.23840 | −0.461504 | ||||||||
\(247\) | −1.63021 | −0.103728 | ||||||||
\(248\) | 1.49008 | 0.0946200 | ||||||||
\(249\) | 11.2200 | 0.711039 | ||||||||
\(250\) | −10.7501 | −0.679894 | ||||||||
\(251\) | −9.41531 | −0.594289 | −0.297145 | − | 0.954832i | \(-0.596034\pi\) | ||||
−0.297145 | + | 0.954832i | \(0.596034\pi\) | |||||||
\(252\) | −0.0562077 | −0.00354075 | ||||||||
\(253\) | −3.47649 | −0.218565 | ||||||||
\(254\) | −9.12133 | −0.572323 | ||||||||
\(255\) | −13.5113 | −0.846113 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.59526 | 0.598536 | 0.299268 | − | 0.954169i | \(-0.403258\pi\) | ||||
0.299268 | + | 0.954169i | \(0.403258\pi\) | |||||||
\(258\) | 8.59971 | 0.535394 | ||||||||
\(259\) | 1.84381 | 0.114569 | ||||||||
\(260\) | 0.290140 | 0.0179937 | ||||||||
\(261\) | −0.411756 | −0.0254870 | ||||||||
\(262\) | −6.00235 | −0.370826 | ||||||||
\(263\) | −10.3149 | −0.636042 | −0.318021 | − | 0.948084i | \(-0.603018\pi\) | ||||
−0.318021 | + | 0.948084i | \(0.603018\pi\) | |||||||
\(264\) | 2.24571 | 0.138214 | ||||||||
\(265\) | 2.66803 | 0.163896 | ||||||||
\(266\) | 6.35196 | 0.389464 | ||||||||
\(267\) | 24.8242 | 1.51921 | ||||||||
\(268\) | 5.48626 | 0.335127 | ||||||||
\(269\) | −6.15327 | −0.375171 | −0.187586 | − | 0.982248i | \(-0.560066\pi\) | ||||
−0.187586 | + | 0.982248i | \(0.560066\pi\) | |||||||
\(270\) | 6.62620 | 0.403258 | ||||||||
\(271\) | −14.6018 | −0.886998 | −0.443499 | − | 0.896275i | \(-0.646263\pi\) | ||||
−0.443499 | + | 0.896275i | \(0.646263\pi\) | |||||||
\(272\) | 5.98652 | 0.362986 | ||||||||
\(273\) | 0.345373 | 0.0209029 | ||||||||
\(274\) | 8.40096 | 0.507520 | ||||||||
\(275\) | 4.28186 | 0.258206 | ||||||||
\(276\) | −4.74341 | −0.285520 | ||||||||
\(277\) | 4.45111 | 0.267441 | 0.133721 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133721 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(278\) | 0.768712 | 0.0461043 | ||||||||
\(279\) | 0.0955222 | 0.00571877 | ||||||||
\(280\) | −1.13051 | −0.0675606 | ||||||||
\(281\) | 11.8982 | 0.709785 | 0.354892 | − | 0.934907i | \(-0.384517\pi\) | ||||
0.354892 | + | 0.934907i | \(0.384517\pi\) | |||||||
\(282\) | 3.29632 | 0.196293 | ||||||||
\(283\) | −26.8019 | −1.59321 | −0.796605 | − | 0.604500i | \(-0.793373\pi\) | ||||
−0.796605 | + | 0.604500i | \(0.793373\pi\) | |||||||
\(284\) | −16.2228 | −0.962648 | ||||||||
\(285\) | 16.3505 | 0.968521 | ||||||||
\(286\) | −0.288694 | −0.0170709 | ||||||||
\(287\) | −3.62569 | −0.214018 | ||||||||
\(288\) | 0.0641056 | 0.00377746 | ||||||||
\(289\) | 18.8384 | 1.10814 | ||||||||
\(290\) | −8.28163 | −0.486314 | ||||||||
\(291\) | −14.4762 | −0.848608 | ||||||||
\(292\) | 2.50459 | 0.146570 | ||||||||
\(293\) | −18.9677 | −1.10811 | −0.554053 | − | 0.832481i | \(-0.686920\pi\) | ||||
−0.554053 | + | 0.832481i | \(0.686920\pi\) | |||||||
\(294\) | 10.9075 | 0.636138 | ||||||||
\(295\) | −11.0921 | −0.645809 | ||||||||
\(296\) | −2.10289 | −0.122228 | ||||||||
\(297\) | −6.59318 | −0.382575 | ||||||||
\(298\) | −11.1812 | −0.647711 | ||||||||
\(299\) | 0.609782 | 0.0352646 | ||||||||
\(300\) | 5.84227 | 0.337304 | ||||||||
\(301\) | 4.30757 | 0.248284 | ||||||||
\(302\) | 2.38218 | 0.137079 | ||||||||
\(303\) | 25.5180 | 1.46597 | ||||||||
\(304\) | −7.24448 | −0.415500 | ||||||||
\(305\) | 15.6551 | 0.896409 | ||||||||
\(306\) | 0.383769 | 0.0219386 | ||||||||
\(307\) | −8.17486 | −0.466564 | −0.233282 | − | 0.972409i | \(-0.574947\pi\) | ||||
−0.233282 | + | 0.972409i | \(0.574947\pi\) | |||||||
\(308\) | 1.12487 | 0.0640955 | ||||||||
\(309\) | 0.476022 | 0.0270800 | ||||||||
\(310\) | 1.92124 | 0.109119 | ||||||||
\(311\) | 15.6131 | 0.885339 | 0.442669 | − | 0.896685i | \(-0.354032\pi\) | ||||
0.442669 | + | 0.896685i | \(0.354032\pi\) | |||||||
\(312\) | −0.393901 | −0.0223003 | ||||||||
\(313\) | −15.4596 | −0.873828 | −0.436914 | − | 0.899503i | \(-0.643929\pi\) | ||||
−0.436914 | + | 0.899503i | \(0.643929\pi\) | |||||||
\(314\) | −0.304865 | −0.0172045 | ||||||||
\(315\) | −0.0724717 | −0.00408332 | ||||||||
\(316\) | −10.0611 | −0.565981 | ||||||||
\(317\) | −3.65132 | −0.205079 | −0.102539 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102539 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(318\) | −3.62218 | −0.203122 | ||||||||
\(319\) | 8.24036 | 0.461372 | ||||||||
\(320\) | 1.28935 | 0.0720771 | ||||||||
\(321\) | −16.8146 | −0.938497 | ||||||||
\(322\) | −2.37596 | −0.132407 | ||||||||
\(323\) | −43.3692 | −2.41313 | ||||||||
\(324\) | −9.18821 | −0.510456 | ||||||||
\(325\) | −0.751044 | −0.0416604 | ||||||||
\(326\) | 8.38198 | 0.464235 | ||||||||
\(327\) | −27.5183 | −1.52177 | ||||||||
\(328\) | 4.13514 | 0.228325 | ||||||||
\(329\) | 1.65111 | 0.0910289 | ||||||||
\(330\) | 2.89552 | 0.159393 | ||||||||
\(331\) | −7.54768 | −0.414858 | −0.207429 | − | 0.978250i | \(-0.566510\pi\) | ||||
−0.207429 | + | 0.978250i | \(0.566510\pi\) | |||||||
\(332\) | −6.40976 | −0.351781 | ||||||||
\(333\) | −0.134807 | −0.00738736 | ||||||||
\(334\) | −12.1234 | −0.663364 | ||||||||
\(335\) | 7.07373 | 0.386479 | ||||||||
\(336\) | 1.53480 | 0.0837303 | ||||||||
\(337\) | −25.3131 | −1.37889 | −0.689447 | − | 0.724336i | \(-0.742146\pi\) | ||||
−0.689447 | + | 0.724336i | \(0.742146\pi\) | |||||||
\(338\) | −12.9494 | −0.704352 | ||||||||
\(339\) | 17.6375 | 0.957940 | ||||||||
\(340\) | 7.71874 | 0.418608 | ||||||||
\(341\) | −1.91166 | −0.103522 | ||||||||
\(342\) | −0.464412 | −0.0251125 | ||||||||
\(343\) | 11.6011 | 0.626402 | ||||||||
\(344\) | −4.91283 | −0.264882 | ||||||||
\(345\) | −6.11593 | −0.329271 | ||||||||
\(346\) | 24.9433 | 1.34096 | ||||||||
\(347\) | −17.3694 | −0.932441 | −0.466220 | − | 0.884669i | \(-0.654385\pi\) | ||||
−0.466220 | + | 0.884669i | \(0.654385\pi\) | |||||||
\(348\) | 11.2433 | 0.602707 | ||||||||
\(349\) | −0.264359 | −0.0141508 | −0.00707540 | − | 0.999975i | \(-0.502252\pi\) | ||||
−0.00707540 | + | 0.999975i | \(0.502252\pi\) | |||||||
\(350\) | 2.92638 | 0.156421 | ||||||||
\(351\) | 1.15645 | 0.0617269 | ||||||||
\(352\) | −1.28293 | −0.0683803 | ||||||||
\(353\) | 11.7868 | 0.627348 | 0.313674 | − | 0.949531i | \(-0.398440\pi\) | ||||
0.313674 | + | 0.949531i | \(0.398440\pi\) | |||||||
\(354\) | 15.0590 | 0.800374 | ||||||||
\(355\) | −20.9170 | −1.11016 | ||||||||
\(356\) | −14.1815 | −0.751619 | ||||||||
\(357\) | 9.18812 | 0.486287 | ||||||||
\(358\) | −14.3700 | −0.759476 | ||||||||
\(359\) | 24.0748 | 1.27062 | 0.635309 | − | 0.772258i | \(-0.280873\pi\) | ||||
0.635309 | + | 0.772258i | \(0.280873\pi\) | |||||||
\(360\) | 0.0826548 | 0.00435629 | ||||||||
\(361\) | 33.4826 | 1.76224 | ||||||||
\(362\) | 11.7556 | 0.617861 | ||||||||
\(363\) | 16.3740 | 0.859410 | ||||||||
\(364\) | −0.197304 | −0.0103415 | ||||||||
\(365\) | 3.22930 | 0.169029 | ||||||||
\(366\) | −21.2538 | −1.11095 | ||||||||
\(367\) | −20.4094 | −1.06536 | −0.532681 | − | 0.846316i | \(-0.678816\pi\) | ||||
−0.532681 | + | 0.846316i | \(0.678816\pi\) | |||||||
\(368\) | 2.70981 | 0.141259 | ||||||||
\(369\) | 0.265086 | 0.0137998 | ||||||||
\(370\) | −2.71137 | −0.140957 | ||||||||
\(371\) | −1.81434 | −0.0941958 | ||||||||
\(372\) | −2.60832 | −0.135235 | ||||||||
\(373\) | 5.72325 | 0.296339 | 0.148169 | − | 0.988962i | \(-0.452662\pi\) | ||||
0.148169 | + | 0.988962i | \(0.452662\pi\) | |||||||
\(374\) | −7.68028 | −0.397138 | ||||||||
\(375\) | 18.8176 | 0.971735 | ||||||||
\(376\) | −1.88312 | −0.0971142 | ||||||||
\(377\) | −1.44537 | −0.0744404 | ||||||||
\(378\) | −4.50602 | −0.231764 | ||||||||
\(379\) | 13.6464 | 0.700970 | 0.350485 | − | 0.936568i | \(-0.386017\pi\) | ||||
0.350485 | + | 0.936568i | \(0.386017\pi\) | |||||||
\(380\) | −9.34071 | −0.479168 | ||||||||
\(381\) | 15.9665 | 0.817989 | ||||||||
\(382\) | −17.9153 | −0.916629 | ||||||||
\(383\) | 26.0858 | 1.33292 | 0.666460 | − | 0.745541i | \(-0.267809\pi\) | ||||
0.666460 | + | 0.745541i | \(0.267809\pi\) | |||||||
\(384\) | −1.75046 | −0.0893277 | ||||||||
\(385\) | 1.45036 | 0.0739171 | ||||||||
\(386\) | −22.0973 | −1.12472 | ||||||||
\(387\) | −0.314940 | −0.0160093 | ||||||||
\(388\) | 8.26993 | 0.419842 | ||||||||
\(389\) | 1.01582 | 0.0515040 | 0.0257520 | − | 0.999668i | \(-0.491802\pi\) | ||||
0.0257520 | + | 0.999668i | \(0.491802\pi\) | |||||||
\(390\) | −0.507878 | −0.0257174 | ||||||||
\(391\) | 16.2223 | 0.820398 | ||||||||
\(392\) | −6.23122 | −0.314724 | ||||||||
\(393\) | 10.5069 | 0.530001 | ||||||||
\(394\) | −5.86785 | −0.295618 | ||||||||
\(395\) | −12.9723 | −0.652708 | ||||||||
\(396\) | −0.0822429 | −0.00413286 | ||||||||
\(397\) | 34.9079 | 1.75198 | 0.875988 | − | 0.482333i | \(-0.160210\pi\) | ||||
0.875988 | + | 0.482333i | \(0.160210\pi\) | |||||||
\(398\) | −3.73945 | −0.187442 | ||||||||
\(399\) | −11.1188 | −0.556639 | ||||||||
\(400\) | −3.33757 | −0.166878 | ||||||||
\(401\) | 22.3295 | 1.11508 | 0.557542 | − | 0.830149i | \(-0.311744\pi\) | ||||
0.557542 | + | 0.830149i | \(0.311744\pi\) | |||||||
\(402\) | −9.60347 | −0.478978 | ||||||||
\(403\) | 0.335308 | 0.0167029 | ||||||||
\(404\) | −14.5779 | −0.725277 | ||||||||
\(405\) | −11.8469 | −0.588675 | ||||||||
\(406\) | 5.63176 | 0.279500 | ||||||||
\(407\) | 2.69785 | 0.133728 | ||||||||
\(408\) | −10.4792 | −0.518795 | ||||||||
\(409\) | −21.9297 | −1.08435 | −0.542177 | − | 0.840264i | \(-0.682400\pi\) | ||||
−0.542177 | + | 0.840264i | \(0.682400\pi\) | |||||||
\(410\) | 5.33167 | 0.263312 | ||||||||
\(411\) | −14.7055 | −0.725370 | ||||||||
\(412\) | −0.271941 | −0.0133976 | ||||||||
\(413\) | 7.54299 | 0.371166 | ||||||||
\(414\) | 0.173714 | 0.00853757 | ||||||||
\(415\) | −8.26445 | −0.405686 | ||||||||
\(416\) | 0.225028 | 0.0110329 | ||||||||
\(417\) | −1.34560 | −0.0658943 | ||||||||
\(418\) | 9.29416 | 0.454592 | ||||||||
\(419\) | 26.0991 | 1.27502 | 0.637512 | − | 0.770440i | \(-0.279964\pi\) | ||||
0.637512 | + | 0.770440i | \(0.279964\pi\) | |||||||
\(420\) | 1.97890 | 0.0965606 | ||||||||
\(421\) | −13.5905 | −0.662360 | −0.331180 | − | 0.943568i | \(-0.607447\pi\) | ||||
−0.331180 | + | 0.943568i | \(0.607447\pi\) | |||||||
\(422\) | 27.7812 | 1.35237 | ||||||||
\(423\) | −0.120718 | −0.00586952 | ||||||||
\(424\) | 2.06927 | 0.100493 | ||||||||
\(425\) | −19.9804 | −0.969192 | ||||||||
\(426\) | 28.3974 | 1.37586 | ||||||||
\(427\) | −10.6459 | −0.515194 | ||||||||
\(428\) | 9.60580 | 0.464314 | ||||||||
\(429\) | 0.505347 | 0.0243984 | ||||||||
\(430\) | −6.33438 | −0.305471 | ||||||||
\(431\) | 6.09508 | 0.293590 | 0.146795 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146795 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(432\) | 5.13916 | 0.247258 | ||||||||
\(433\) | 8.05600 | 0.387147 | 0.193573 | − | 0.981086i | \(-0.437992\pi\) | ||||
0.193573 | + | 0.981086i | \(0.437992\pi\) | |||||||
\(434\) | −1.30650 | −0.0627140 | ||||||||
\(435\) | 14.4967 | 0.695062 | ||||||||
\(436\) | 15.7206 | 0.752881 | ||||||||
\(437\) | −19.6312 | −0.939086 | ||||||||
\(438\) | −4.38417 | −0.209484 | ||||||||
\(439\) | −30.2636 | −1.44440 | −0.722202 | − | 0.691682i | \(-0.756870\pi\) | ||||
−0.722202 | + | 0.691682i | \(0.756870\pi\) | |||||||
\(440\) | −1.65415 | −0.0788585 | ||||||||
\(441\) | −0.399456 | −0.0190217 | ||||||||
\(442\) | 1.34713 | 0.0640765 | ||||||||
\(443\) | 3.80455 | 0.180760 | 0.0903799 | − | 0.995907i | \(-0.471192\pi\) | ||||
0.0903799 | + | 0.995907i | \(0.471192\pi\) | |||||||
\(444\) | 3.68102 | 0.174693 | ||||||||
\(445\) | −18.2850 | −0.866792 | ||||||||
\(446\) | −22.9164 | −1.08512 | ||||||||
\(447\) | 19.5723 | 0.925736 | ||||||||
\(448\) | −0.876800 | −0.0414249 | ||||||||
\(449\) | 27.3357 | 1.29005 | 0.645026 | − | 0.764161i | \(-0.276847\pi\) | ||||
0.645026 | + | 0.764161i | \(0.276847\pi\) | |||||||
\(450\) | −0.213957 | −0.0100860 | ||||||||
\(451\) | −5.30510 | −0.249807 | ||||||||
\(452\) | −10.0760 | −0.473933 | ||||||||
\(453\) | −4.16991 | −0.195919 | ||||||||
\(454\) | −2.08411 | −0.0978123 | ||||||||
\(455\) | −0.254395 | −0.0119262 | ||||||||
\(456\) | 12.6812 | 0.593850 | ||||||||
\(457\) | −1.81388 | −0.0848496 | −0.0424248 | − | 0.999100i | \(-0.513508\pi\) | ||||
−0.0424248 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(458\) | 15.3090 | 0.715341 | ||||||||
\(459\) | 30.7657 | 1.43602 | ||||||||
\(460\) | 3.49390 | 0.162904 | ||||||||
\(461\) | 16.2086 | 0.754912 | 0.377456 | − | 0.926028i | \(-0.376799\pi\) | ||||
0.377456 | + | 0.926028i | \(0.376799\pi\) | |||||||
\(462\) | −1.96904 | −0.0916081 | ||||||||
\(463\) | 35.3990 | 1.64513 | 0.822567 | − | 0.568669i | \(-0.192541\pi\) | ||||
0.822567 | + | 0.568669i | \(0.192541\pi\) | |||||||
\(464\) | −6.42309 | −0.298184 | ||||||||
\(465\) | −3.36305 | −0.155958 | ||||||||
\(466\) | 19.1212 | 0.885774 | ||||||||
\(467\) | 29.3005 | 1.35586 | 0.677932 | − | 0.735125i | \(-0.262877\pi\) | ||||
0.677932 | + | 0.735125i | \(0.262877\pi\) | |||||||
\(468\) | 0.0144255 | 0.000666820 0 | ||||||||
\(469\) | −4.81035 | −0.222121 | ||||||||
\(470\) | −2.42800 | −0.111995 | ||||||||
\(471\) | 0.533653 | 0.0245894 | ||||||||
\(472\) | −8.60286 | −0.395979 | ||||||||
\(473\) | 6.30281 | 0.289804 | ||||||||
\(474\) | 17.6115 | 0.808924 | ||||||||
\(475\) | 24.1789 | 1.10941 | ||||||||
\(476\) | −5.24898 | −0.240587 | ||||||||
\(477\) | 0.132652 | 0.00607372 | ||||||||
\(478\) | −11.8207 | −0.540664 | ||||||||
\(479\) | −13.4423 | −0.614193 | −0.307096 | − | 0.951678i | \(-0.599357\pi\) | ||||
−0.307096 | + | 0.951678i | \(0.599357\pi\) | |||||||
\(480\) | −2.25696 | −0.103016 | ||||||||
\(481\) | −0.473207 | −0.0215764 | ||||||||
\(482\) | −9.30234 | −0.423710 | ||||||||
\(483\) | 4.15902 | 0.189242 | ||||||||
\(484\) | −9.35409 | −0.425186 | ||||||||
\(485\) | 10.6629 | 0.484176 | ||||||||
\(486\) | 0.666091 | 0.0302145 | ||||||||
\(487\) | −6.77727 | −0.307107 | −0.153554 | − | 0.988140i | \(-0.549072\pi\) | ||||
−0.153554 | + | 0.988140i | \(0.549072\pi\) | |||||||
\(488\) | 12.1418 | 0.549635 | ||||||||
\(489\) | −14.6723 | −0.663505 | ||||||||
\(490\) | −8.03425 | −0.362951 | ||||||||
\(491\) | 13.0202 | 0.587594 | 0.293797 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293797 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(492\) | −7.23840 | −0.326332 | ||||||||
\(493\) | −38.4519 | −1.73179 | ||||||||
\(494\) | −1.63021 | −0.0733466 | ||||||||
\(495\) | −0.106040 | −0.00476615 | ||||||||
\(496\) | 1.49008 | 0.0669064 | ||||||||
\(497\) | 14.2242 | 0.638041 | ||||||||
\(498\) | 11.2200 | 0.502781 | ||||||||
\(499\) | −31.9234 | −1.42909 | −0.714543 | − | 0.699591i | \(-0.753365\pi\) | ||||
−0.714543 | + | 0.699591i | \(0.753365\pi\) | |||||||
\(500\) | −10.7501 | −0.480758 | ||||||||
\(501\) | 21.2216 | 0.948109 | ||||||||
\(502\) | −9.41531 | −0.420226 | ||||||||
\(503\) | −34.3361 | −1.53097 | −0.765484 | − | 0.643454i | \(-0.777501\pi\) | ||||
−0.765484 | + | 0.643454i | \(0.777501\pi\) | |||||||
\(504\) | −0.0562077 | −0.00250369 | ||||||||
\(505\) | −18.7960 | −0.836413 | ||||||||
\(506\) | −3.47649 | −0.154549 | ||||||||
\(507\) | 22.6673 | 1.00669 | ||||||||
\(508\) | −9.12133 | −0.404694 | ||||||||
\(509\) | −12.2442 | −0.542715 | −0.271358 | − | 0.962479i | \(-0.587473\pi\) | ||||
−0.271358 | + | 0.962479i | \(0.587473\pi\) | |||||||
\(510\) | −13.5113 | −0.598292 | ||||||||
\(511\) | −2.19602 | −0.0971462 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −37.2306 | −1.64377 | ||||||||
\(514\) | 9.59526 | 0.423229 | ||||||||
\(515\) | −0.350629 | −0.0154506 | ||||||||
\(516\) | 8.59971 | 0.378581 | ||||||||
\(517\) | 2.41590 | 0.106251 | ||||||||
\(518\) | 1.84381 | 0.0810124 | ||||||||
\(519\) | −43.6623 | −1.91656 | ||||||||
\(520\) | 0.290140 | 0.0127235 | ||||||||
\(521\) | −5.21914 | −0.228654 | −0.114327 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114327 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(522\) | −0.411756 | −0.0180221 | ||||||||
\(523\) | 2.36493 | 0.103411 | 0.0517055 | − | 0.998662i | \(-0.483534\pi\) | ||||
0.0517055 | + | 0.998662i | \(0.483534\pi\) | |||||||
\(524\) | −6.00235 | −0.262214 | ||||||||
\(525\) | −5.12250 | −0.223564 | ||||||||
\(526\) | −10.3149 | −0.449749 | ||||||||
\(527\) | 8.92038 | 0.388578 | ||||||||
\(528\) | 2.24571 | 0.0977321 | ||||||||
\(529\) | −15.6569 | −0.680736 | ||||||||
\(530\) | 2.66803 | 0.115892 | ||||||||
\(531\) | −0.551491 | −0.0239327 | ||||||||
\(532\) | 6.35196 | 0.275392 | ||||||||
\(533\) | 0.930522 | 0.0403054 | ||||||||
\(534\) | 24.8242 | 1.07425 | ||||||||
\(535\) | 12.3853 | 0.535462 | ||||||||
\(536\) | 5.48626 | 0.236970 | ||||||||
\(537\) | 25.1540 | 1.08548 | ||||||||
\(538\) | −6.15327 | −0.265286 | ||||||||
\(539\) | 7.99421 | 0.344335 | ||||||||
\(540\) | 6.62620 | 0.285146 | ||||||||
\(541\) | 28.2125 | 1.21295 | 0.606474 | − | 0.795103i | \(-0.292583\pi\) | ||||
0.606474 | + | 0.795103i | \(0.292583\pi\) | |||||||
\(542\) | −14.6018 | −0.627202 | ||||||||
\(543\) | −20.5777 | −0.883073 | ||||||||
\(544\) | 5.98652 | 0.256670 | ||||||||
\(545\) | 20.2694 | 0.868248 | ||||||||
\(546\) | 0.345373 | 0.0147806 | ||||||||
\(547\) | 40.4922 | 1.73132 | 0.865660 | − | 0.500632i | \(-0.166899\pi\) | ||||
0.865660 | + | 0.500632i | \(0.166899\pi\) | |||||||
\(548\) | 8.40096 | 0.358871 | ||||||||
\(549\) | 0.778358 | 0.0332195 | ||||||||
\(550\) | 4.28186 | 0.182579 | ||||||||
\(551\) | 46.5320 | 1.98233 | ||||||||
\(552\) | −4.74341 | −0.201893 | ||||||||
\(553\) | 8.82156 | 0.375131 | ||||||||
\(554\) | 4.45111 | 0.189109 | ||||||||
\(555\) | 4.74613 | 0.201462 | ||||||||
\(556\) | 0.768712 | 0.0326007 | ||||||||
\(557\) | 2.23615 | 0.0947486 | 0.0473743 | − | 0.998877i | \(-0.484915\pi\) | ||||
0.0473743 | + | 0.998877i | \(0.484915\pi\) | |||||||
\(558\) | 0.0955222 | 0.00404378 | ||||||||
\(559\) | −1.10552 | −0.0467586 | ||||||||
\(560\) | −1.13051 | −0.0477726 | ||||||||
\(561\) | 13.4440 | 0.567606 | ||||||||
\(562\) | 11.8982 | 0.501894 | ||||||||
\(563\) | 15.4818 | 0.652482 | 0.326241 | − | 0.945287i | \(-0.394218\pi\) | ||||
0.326241 | + | 0.945287i | \(0.394218\pi\) | |||||||
\(564\) | 3.29632 | 0.138800 | ||||||||
\(565\) | −12.9915 | −0.546555 | ||||||||
\(566\) | −26.8019 | −1.12657 | ||||||||
\(567\) | 8.05622 | 0.338329 | ||||||||
\(568\) | −16.2228 | −0.680695 | ||||||||
\(569\) | −23.2083 | −0.972942 | −0.486471 | − | 0.873697i | \(-0.661716\pi\) | ||||
−0.486471 | + | 0.873697i | \(0.661716\pi\) | |||||||
\(570\) | 16.3505 | 0.684848 | ||||||||
\(571\) | 15.1595 | 0.634404 | 0.317202 | − | 0.948358i | \(-0.397257\pi\) | ||||
0.317202 | + | 0.948358i | \(0.397257\pi\) | |||||||
\(572\) | −0.288694 | −0.0120709 | ||||||||
\(573\) | 31.3601 | 1.31009 | ||||||||
\(574\) | −3.62569 | −0.151334 | ||||||||
\(575\) | −9.04416 | −0.377168 | ||||||||
\(576\) | 0.0641056 | 0.00267107 | ||||||||
\(577\) | −4.70253 | −0.195769 | −0.0978845 | − | 0.995198i | \(-0.531208\pi\) | ||||
−0.0978845 | + | 0.995198i | \(0.531208\pi\) | |||||||
\(578\) | 18.8384 | 0.783575 | ||||||||
\(579\) | 38.6804 | 1.60750 | ||||||||
\(580\) | −8.28163 | −0.343876 | ||||||||
\(581\) | 5.62007 | 0.233160 | ||||||||
\(582\) | −14.4762 | −0.600056 | ||||||||
\(583\) | −2.65473 | −0.109948 | ||||||||
\(584\) | 2.50459 | 0.103640 | ||||||||
\(585\) | 0.0185996 | 0.000768999 0 | ||||||||
\(586\) | −18.9677 | −0.783550 | ||||||||
\(587\) | 41.2810 | 1.70385 | 0.851925 | − | 0.523664i | \(-0.175435\pi\) | ||||
0.851925 | + | 0.523664i | \(0.175435\pi\) | |||||||
\(588\) | 10.9075 | 0.449818 | ||||||||
\(589\) | −10.7948 | −0.444794 | ||||||||
\(590\) | −11.0921 | −0.456656 | ||||||||
\(591\) | 10.2714 | 0.422510 | ||||||||
\(592\) | −2.10289 | −0.0864281 | ||||||||
\(593\) | 20.3271 | 0.834735 | 0.417367 | − | 0.908738i | \(-0.362953\pi\) | ||||
0.417367 | + | 0.908738i | \(0.362953\pi\) | |||||||
\(594\) | −6.59318 | −0.270521 | ||||||||
\(595\) | −6.76779 | −0.277452 | ||||||||
\(596\) | −11.1812 | −0.458000 | ||||||||
\(597\) | 6.54575 | 0.267900 | ||||||||
\(598\) | 0.609782 | 0.0249358 | ||||||||
\(599\) | −14.4756 | −0.591458 | −0.295729 | − | 0.955272i | \(-0.595563\pi\) | ||||
−0.295729 | + | 0.955272i | \(0.595563\pi\) | |||||||
\(600\) | 5.84227 | 0.238510 | ||||||||
\(601\) | −1.33792 | −0.0545748 | −0.0272874 | − | 0.999628i | \(-0.508687\pi\) | ||||
−0.0272874 | + | 0.999628i | \(0.508687\pi\) | |||||||
\(602\) | 4.30757 | 0.175563 | ||||||||
\(603\) | 0.351700 | 0.0143223 | ||||||||
\(604\) | 2.38218 | 0.0969296 | ||||||||
\(605\) | −12.0607 | −0.490339 | ||||||||
\(606\) | 25.5180 | 1.03660 | ||||||||
\(607\) | 29.3920 | 1.19298 | 0.596491 | − | 0.802620i | \(-0.296561\pi\) | ||||
0.596491 | + | 0.802620i | \(0.296561\pi\) | |||||||
\(608\) | −7.24448 | −0.293803 | ||||||||
\(609\) | −9.85816 | −0.399473 | ||||||||
\(610\) | 15.6551 | 0.633857 | ||||||||
\(611\) | −0.423753 | −0.0171432 | ||||||||
\(612\) | 0.383769 | 0.0155129 | ||||||||
\(613\) | 13.0862 | 0.528545 | 0.264272 | − | 0.964448i | \(-0.414868\pi\) | ||||
0.264272 | + | 0.964448i | \(0.414868\pi\) | |||||||
\(614\) | −8.17486 | −0.329911 | ||||||||
\(615\) | −9.33286 | −0.376337 | ||||||||
\(616\) | 1.12487 | 0.0453224 | ||||||||
\(617\) | −5.00707 | −0.201577 | −0.100789 | − | 0.994908i | \(-0.532137\pi\) | ||||
−0.100789 | + | 0.994908i | \(0.532137\pi\) | |||||||
\(618\) | 0.476022 | 0.0191484 | ||||||||
\(619\) | −26.7064 | −1.07342 | −0.536711 | − | 0.843766i | \(-0.680334\pi\) | ||||
−0.536711 | + | 0.843766i | \(0.680334\pi\) | |||||||
\(620\) | 1.92124 | 0.0771587 | ||||||||
\(621\) | 13.9261 | 0.558837 | ||||||||
\(622\) | 15.6131 | 0.626029 | ||||||||
\(623\) | 12.4344 | 0.498172 | ||||||||
\(624\) | −0.393901 | −0.0157687 | ||||||||
\(625\) | 2.82718 | 0.113087 | ||||||||
\(626\) | −15.4596 | −0.617890 | ||||||||
\(627\) | −16.2690 | −0.649723 | ||||||||
\(628\) | −0.304865 | −0.0121654 | ||||||||
\(629\) | −12.5890 | −0.501955 | ||||||||
\(630\) | −0.0724717 | −0.00288734 | ||||||||
\(631\) | −15.1426 | −0.602817 | −0.301408 | − | 0.953495i | \(-0.597457\pi\) | ||||
−0.301408 | + | 0.953495i | \(0.597457\pi\) | |||||||
\(632\) | −10.0611 | −0.400209 | ||||||||
\(633\) | −48.6298 | −1.93286 | ||||||||
\(634\) | −3.65132 | −0.145012 | ||||||||
\(635\) | −11.7606 | −0.466706 | ||||||||
\(636\) | −3.62218 | −0.143629 | ||||||||
\(637\) | −1.40220 | −0.0555571 | ||||||||
\(638\) | 8.24036 | 0.326239 | ||||||||
\(639\) | −1.03997 | −0.0411407 | ||||||||
\(640\) | 1.28935 | 0.0509662 | ||||||||
\(641\) | 31.8157 | 1.25664 | 0.628322 | − | 0.777954i | \(-0.283742\pi\) | ||||
0.628322 | + | 0.777954i | \(0.283742\pi\) | |||||||
\(642\) | −16.8146 | −0.663617 | ||||||||
\(643\) | −18.0477 | −0.711732 | −0.355866 | − | 0.934537i | \(-0.615814\pi\) | ||||
−0.355866 | + | 0.934537i | \(0.615814\pi\) | |||||||
\(644\) | −2.37596 | −0.0936259 | ||||||||
\(645\) | 11.0881 | 0.436592 | ||||||||
\(646\) | −43.3692 | −1.70634 | ||||||||
\(647\) | 36.5087 | 1.43531 | 0.717653 | − | 0.696400i | \(-0.245216\pi\) | ||||
0.717653 | + | 0.696400i | \(0.245216\pi\) | |||||||
\(648\) | −9.18821 | −0.360947 | ||||||||
\(649\) | 11.0369 | 0.433234 | ||||||||
\(650\) | −0.751044 | −0.0294584 | ||||||||
\(651\) | 2.28697 | 0.0896335 | ||||||||
\(652\) | 8.38198 | 0.328264 | ||||||||
\(653\) | 23.9062 | 0.935521 | 0.467761 | − | 0.883855i | \(-0.345061\pi\) | ||||
0.467761 | + | 0.883855i | \(0.345061\pi\) | |||||||
\(654\) | −27.5183 | −1.07605 | ||||||||
\(655\) | −7.73915 | −0.302394 | ||||||||
\(656\) | 4.13514 | 0.161450 | ||||||||
\(657\) | 0.160558 | 0.00626396 | ||||||||
\(658\) | 1.65111 | 0.0643672 | ||||||||
\(659\) | 4.05862 | 0.158101 | 0.0790507 | − | 0.996871i | \(-0.474811\pi\) | ||||
0.0790507 | + | 0.996871i | \(0.474811\pi\) | |||||||
\(660\) | 2.89552 | 0.112708 | ||||||||
\(661\) | 7.52174 | 0.292562 | 0.146281 | − | 0.989243i | \(-0.453270\pi\) | ||||
0.146281 | + | 0.989243i | \(0.453270\pi\) | |||||||
\(662\) | −7.54768 | −0.293349 | ||||||||
\(663\) | −2.35810 | −0.0915810 | ||||||||
\(664\) | −6.40976 | −0.248747 | ||||||||
\(665\) | 8.18993 | 0.317592 | ||||||||
\(666\) | −0.134807 | −0.00522365 | ||||||||
\(667\) | −17.4053 | −0.673937 | ||||||||
\(668\) | −12.1234 | −0.469069 | ||||||||
\(669\) | 40.1143 | 1.55091 | ||||||||
\(670\) | 7.07373 | 0.273282 | ||||||||
\(671\) | −15.5771 | −0.601347 | ||||||||
\(672\) | 1.53480 | 0.0592063 | ||||||||
\(673\) | 31.7023 | 1.22203 | 0.611017 | − | 0.791618i | \(-0.290761\pi\) | ||||
0.611017 | + | 0.791618i | \(0.290761\pi\) | |||||||
\(674\) | −25.3131 | −0.975026 | ||||||||
\(675\) | −17.1523 | −0.660192 | ||||||||
\(676\) | −12.9494 | −0.498052 | ||||||||
\(677\) | −34.8319 | −1.33870 | −0.669350 | − | 0.742947i | \(-0.733427\pi\) | ||||
−0.669350 | + | 0.742947i | \(0.733427\pi\) | |||||||
\(678\) | 17.6375 | 0.677366 | ||||||||
\(679\) | −7.25107 | −0.278270 | ||||||||
\(680\) | 7.71874 | 0.296000 | ||||||||
\(681\) | 3.64816 | 0.139798 | ||||||||
\(682\) | −1.91166 | −0.0732013 | ||||||||
\(683\) | 35.7552 | 1.36814 | 0.684068 | − | 0.729418i | \(-0.260209\pi\) | ||||
0.684068 | + | 0.729418i | \(0.260209\pi\) | |||||||
\(684\) | −0.464412 | −0.0177572 | ||||||||
\(685\) | 10.8318 | 0.413862 | ||||||||
\(686\) | 11.6011 | 0.442933 | ||||||||
\(687\) | −26.7977 | −1.02240 | ||||||||
\(688\) | −4.91283 | −0.187300 | ||||||||
\(689\) | 0.465644 | 0.0177396 | ||||||||
\(690\) | −6.11593 | −0.232830 | ||||||||
\(691\) | 1.28873 | 0.0490258 | 0.0245129 | − | 0.999700i | \(-0.492197\pi\) | ||||
0.0245129 | + | 0.999700i | \(0.492197\pi\) | |||||||
\(692\) | 24.9433 | 0.948204 | ||||||||
\(693\) | 0.0721105 | 0.00273925 | ||||||||
\(694\) | −17.3694 | −0.659335 | ||||||||
\(695\) | 0.991142 | 0.0375962 | ||||||||
\(696\) | 11.2433 | 0.426178 | ||||||||
\(697\) | 24.7551 | 0.937667 | ||||||||
\(698\) | −0.264359 | −0.0100061 | ||||||||
\(699\) | −33.4709 | −1.26599 | ||||||||
\(700\) | 2.92638 | 0.110607 | ||||||||
\(701\) | −32.9992 | −1.24636 | −0.623181 | − | 0.782078i | \(-0.714160\pi\) | ||||
−0.623181 | + | 0.782078i | \(0.714160\pi\) | |||||||
\(702\) | 1.15645 | 0.0436475 | ||||||||
\(703\) | 15.2343 | 0.574574 | ||||||||
\(704\) | −1.28293 | −0.0483522 | ||||||||
\(705\) | 4.25012 | 0.160069 | ||||||||
\(706\) | 11.7868 | 0.443602 | ||||||||
\(707\) | 12.7819 | 0.480712 | ||||||||
\(708\) | 15.0590 | 0.565950 | ||||||||
\(709\) | −15.3692 | −0.577203 | −0.288601 | − | 0.957449i | \(-0.593190\pi\) | ||||
−0.288601 | + | 0.957449i | \(0.593190\pi\) | |||||||
\(710\) | −20.9170 | −0.785000 | ||||||||
\(711\) | −0.644972 | −0.0241883 | ||||||||
\(712\) | −14.1815 | −0.531475 | ||||||||
\(713\) | 4.03782 | 0.151218 | ||||||||
\(714\) | 9.18812 | 0.343857 | ||||||||
\(715\) | −0.372229 | −0.0139206 | ||||||||
\(716\) | −14.3700 | −0.537031 | ||||||||
\(717\) | 20.6916 | 0.772741 | ||||||||
\(718\) | 24.0748 | 0.898463 | ||||||||
\(719\) | 33.2661 | 1.24061 | 0.620307 | − | 0.784359i | \(-0.287008\pi\) | ||||
0.620307 | + | 0.784359i | \(0.287008\pi\) | |||||||
\(720\) | 0.0826548 | 0.00308036 | ||||||||
\(721\) | 0.238438 | 0.00887990 | ||||||||
\(722\) | 33.4826 | 1.24609 | ||||||||
\(723\) | 16.2834 | 0.605585 | ||||||||
\(724\) | 11.7556 | 0.436893 | ||||||||
\(725\) | 21.4375 | 0.796168 | ||||||||
\(726\) | 16.3740 | 0.607694 | ||||||||
\(727\) | 6.03799 | 0.223937 | 0.111968 | − | 0.993712i | \(-0.464284\pi\) | ||||
0.111968 | + | 0.993712i | \(0.464284\pi\) | |||||||
\(728\) | −0.197304 | −0.00731258 | ||||||||
\(729\) | 26.3987 | 0.977728 | ||||||||
\(730\) | 3.22930 | 0.119522 | ||||||||
\(731\) | −29.4108 | −1.08780 | ||||||||
\(732\) | −21.2538 | −0.785562 | ||||||||
\(733\) | −8.66873 | −0.320187 | −0.160093 | − | 0.987102i | \(-0.551180\pi\) | ||||
−0.160093 | + | 0.987102i | \(0.551180\pi\) | |||||||
\(734\) | −20.4094 | −0.753325 | ||||||||
\(735\) | 14.0636 | 0.518745 | ||||||||
\(736\) | 2.70981 | 0.0998849 | ||||||||
\(737\) | −7.03848 | −0.259266 | ||||||||
\(738\) | 0.265086 | 0.00975794 | ||||||||
\(739\) | 45.1675 | 1.66151 | 0.830757 | − | 0.556636i | \(-0.187908\pi\) | ||||
0.830757 | + | 0.556636i | \(0.187908\pi\) | |||||||
\(740\) | −2.71137 | −0.0996718 | ||||||||
\(741\) | 2.85361 | 0.104830 | ||||||||
\(742\) | −1.81434 | −0.0666065 | ||||||||
\(743\) | 13.1991 | 0.484227 | 0.242113 | − | 0.970248i | \(-0.422159\pi\) | ||||
0.242113 | + | 0.970248i | \(0.422159\pi\) | |||||||
\(744\) | −2.60832 | −0.0956256 | ||||||||
\(745\) | −14.4165 | −0.528181 | ||||||||
\(746\) | 5.72325 | 0.209543 | ||||||||
\(747\) | −0.410901 | −0.0150341 | ||||||||
\(748\) | −7.68028 | −0.280819 | ||||||||
\(749\) | −8.42236 | −0.307746 | ||||||||
\(750\) | 18.8176 | 0.687120 | ||||||||
\(751\) | 34.0223 | 1.24149 | 0.620745 | − | 0.784012i | \(-0.286830\pi\) | ||||
0.620745 | + | 0.784012i | \(0.286830\pi\) | |||||||
\(752\) | −1.88312 | −0.0686701 | ||||||||
\(753\) | 16.4811 | 0.600605 | ||||||||
\(754\) | −1.44537 | −0.0526373 | ||||||||
\(755\) | 3.07147 | 0.111782 | ||||||||
\(756\) | −4.50602 | −0.163882 | ||||||||
\(757\) | −19.1666 | −0.696622 | −0.348311 | − | 0.937379i | \(-0.613245\pi\) | ||||
−0.348311 | + | 0.937379i | \(0.613245\pi\) | |||||||
\(758\) | 13.6464 | 0.495661 | ||||||||
\(759\) | 6.08545 | 0.220888 | ||||||||
\(760\) | −9.34071 | −0.338823 | ||||||||
\(761\) | −23.3773 | −0.847427 | −0.423713 | − | 0.905796i | \(-0.639274\pi\) | ||||
−0.423713 | + | 0.905796i | \(0.639274\pi\) | |||||||
\(762\) | 15.9665 | 0.578406 | ||||||||
\(763\) | −13.7838 | −0.499008 | ||||||||
\(764\) | −17.9153 | −0.648154 | ||||||||
\(765\) | 0.494814 | 0.0178901 | ||||||||
\(766\) | 26.0858 | 0.942516 | ||||||||
\(767\) | −1.93588 | −0.0699006 | ||||||||
\(768\) | −1.75046 | −0.0631642 | ||||||||
\(769\) | 32.0206 | 1.15469 | 0.577346 | − | 0.816500i | \(-0.304088\pi\) | ||||
0.577346 | + | 0.816500i | \(0.304088\pi\) | |||||||
\(770\) | 1.45036 | 0.0522673 | ||||||||
\(771\) | −16.7961 | −0.604897 | ||||||||
\(772\) | −22.0973 | −0.795300 | ||||||||
\(773\) | 35.7581 | 1.28613 | 0.643065 | − | 0.765811i | \(-0.277662\pi\) | ||||
0.643065 | + | 0.765811i | \(0.277662\pi\) | |||||||
\(774\) | −0.314940 | −0.0113203 | ||||||||
\(775\) | −4.97323 | −0.178644 | ||||||||
\(776\) | 8.26993 | 0.296873 | ||||||||
\(777\) | −3.22751 | −0.115786 | ||||||||
\(778\) | 1.01582 | 0.0364188 | ||||||||
\(779\) | −29.9570 | −1.07332 | ||||||||
\(780\) | −0.507878 | −0.0181850 | ||||||||
\(781\) | 20.8127 | 0.744738 | ||||||||
\(782\) | 16.2223 | 0.580109 | ||||||||
\(783\) | −33.0093 | −1.17966 | ||||||||
\(784\) | −6.23122 | −0.222544 | ||||||||
\(785\) | −0.393079 | −0.0140296 | ||||||||
\(786\) | 10.5069 | 0.374767 | ||||||||
\(787\) | −35.0827 | −1.25056 | −0.625282 | − | 0.780399i | \(-0.715016\pi\) | ||||
−0.625282 | + | 0.780399i | \(0.715016\pi\) | |||||||
\(788\) | −5.86785 | −0.209034 | ||||||||
\(789\) | 18.0557 | 0.642801 | ||||||||
\(790\) | −12.9723 | −0.461534 | ||||||||
\(791\) | 8.83459 | 0.314122 | ||||||||
\(792\) | −0.0822429 | −0.00292237 | ||||||||
\(793\) | 2.73225 | 0.0970249 | ||||||||
\(794\) | 34.9079 | 1.23883 | ||||||||
\(795\) | −4.67027 | −0.165637 | ||||||||
\(796\) | −3.73945 | −0.132541 | ||||||||
\(797\) | 0.567616 | 0.0201060 | 0.0100530 | − | 0.999949i | \(-0.496800\pi\) | ||||
0.0100530 | + | 0.999949i | \(0.496800\pi\) | |||||||
\(798\) | −11.1188 | −0.393603 | ||||||||
\(799\) | −11.2733 | −0.398821 | ||||||||
\(800\) | −3.33757 | −0.118001 | ||||||||
\(801\) | −0.909114 | −0.0321220 | ||||||||
\(802\) | 22.3295 | 0.788484 | ||||||||
\(803\) | −3.21320 | −0.113392 | ||||||||
\(804\) | −9.60347 | −0.338688 | ||||||||
\(805\) | −3.06345 | −0.107973 | ||||||||
\(806\) | 0.335308 | 0.0118107 | ||||||||
\(807\) | 10.7710 | 0.379158 | ||||||||
\(808\) | −14.5779 | −0.512848 | ||||||||
\(809\) | 50.5102 | 1.77584 | 0.887922 | − | 0.459994i | \(-0.152148\pi\) | ||||
0.887922 | + | 0.459994i | \(0.152148\pi\) | |||||||
\(810\) | −11.8469 | −0.416256 | ||||||||
\(811\) | 1.99742 | 0.0701391 | 0.0350695 | − | 0.999385i | \(-0.488835\pi\) | ||||
0.0350695 | + | 0.999385i | \(0.488835\pi\) | |||||||
\(812\) | 5.63176 | 0.197636 | ||||||||
\(813\) | 25.5599 | 0.896425 | ||||||||
\(814\) | 2.69785 | 0.0945597 | ||||||||
\(815\) | 10.8073 | 0.378565 | ||||||||
\(816\) | −10.4792 | −0.366844 | ||||||||
\(817\) | 35.5909 | 1.24517 | ||||||||
\(818\) | −21.9297 | −0.766754 | ||||||||
\(819\) | −0.0126483 | −0.000441967 0 | ||||||||
\(820\) | 5.33167 | 0.186190 | ||||||||
\(821\) | −38.2673 | −1.33554 | −0.667768 | − | 0.744369i | \(-0.732750\pi\) | ||||
−0.667768 | + | 0.744369i | \(0.732750\pi\) | |||||||
\(822\) | −14.7055 | −0.512914 | ||||||||
\(823\) | 45.7897 | 1.59613 | 0.798065 | − | 0.602571i | \(-0.205857\pi\) | ||||
0.798065 | + | 0.602571i | \(0.205857\pi\) | |||||||
\(824\) | −0.271941 | −0.00947353 | ||||||||
\(825\) | −7.49522 | −0.260950 | ||||||||
\(826\) | 7.54299 | 0.262454 | ||||||||
\(827\) | 12.3187 | 0.428363 | 0.214181 | − | 0.976794i | \(-0.431292\pi\) | ||||
0.214181 | + | 0.976794i | \(0.431292\pi\) | |||||||
\(828\) | 0.173714 | 0.00603697 | ||||||||
\(829\) | 45.5199 | 1.58097 | 0.790485 | − | 0.612481i | \(-0.209828\pi\) | ||||
0.790485 | + | 0.612481i | \(0.209828\pi\) | |||||||
\(830\) | −8.26445 | −0.286863 | ||||||||
\(831\) | −7.79148 | −0.270283 | ||||||||
\(832\) | 0.225028 | 0.00780143 | ||||||||
\(833\) | −37.3033 | −1.29248 | ||||||||
\(834\) | −1.34560 | −0.0465943 | ||||||||
\(835\) | −15.6314 | −0.540946 | ||||||||
\(836\) | 9.29416 | 0.321445 | ||||||||
\(837\) | 7.65775 | 0.264690 | ||||||||
\(838\) | 26.0991 | 0.901578 | ||||||||
\(839\) | −35.8346 | −1.23715 | −0.618575 | − | 0.785726i | \(-0.712290\pi\) | ||||
−0.618575 | + | 0.785726i | \(0.712290\pi\) | |||||||
\(840\) | 1.97890 | 0.0682786 | ||||||||
\(841\) | 12.2560 | 0.422622 | ||||||||
\(842\) | −13.5905 | −0.468359 | ||||||||
\(843\) | −20.8272 | −0.717328 | ||||||||
\(844\) | 27.7812 | 0.956268 | ||||||||
\(845\) | −16.6963 | −0.574371 | ||||||||
\(846\) | −0.120718 | −0.00415038 | ||||||||
\(847\) | 8.20167 | 0.281813 | ||||||||
\(848\) | 2.06927 | 0.0710592 | ||||||||
\(849\) | 46.9157 | 1.61014 | ||||||||
\(850\) | −19.9804 | −0.685322 | ||||||||
\(851\) | −5.69842 | −0.195339 | ||||||||
\(852\) | 28.3974 | 0.972879 | ||||||||
\(853\) | 31.3074 | 1.07195 | 0.535973 | − | 0.844235i | \(-0.319945\pi\) | ||||
0.535973 | + | 0.844235i | \(0.319945\pi\) | |||||||
\(854\) | −10.6459 | −0.364297 | ||||||||
\(855\) | −0.598791 | −0.0204782 | ||||||||
\(856\) | 9.60580 | 0.328319 | ||||||||
\(857\) | −35.2234 | −1.20321 | −0.601604 | − | 0.798794i | \(-0.705472\pi\) | ||||
−0.601604 | + | 0.798794i | \(0.705472\pi\) | |||||||
\(858\) | 0.505347 | 0.0172523 | ||||||||
\(859\) | −37.7463 | −1.28789 | −0.643943 | − | 0.765074i | \(-0.722703\pi\) | ||||
−0.643943 | + | 0.765074i | \(0.722703\pi\) | |||||||
\(860\) | −6.33438 | −0.216001 | ||||||||
\(861\) | 6.34663 | 0.216292 | ||||||||
\(862\) | 6.09508 | 0.207599 | ||||||||
\(863\) | −8.56516 | −0.291561 | −0.145781 | − | 0.989317i | \(-0.546569\pi\) | ||||
−0.145781 | + | 0.989317i | \(0.546569\pi\) | |||||||
\(864\) | 5.13916 | 0.174838 | ||||||||
\(865\) | 32.1608 | 1.09350 | ||||||||
\(866\) | 8.05600 | 0.273754 | ||||||||
\(867\) | −32.9759 | −1.11992 | ||||||||
\(868\) | −1.30650 | −0.0443455 | ||||||||
\(869\) | 12.9077 | 0.437863 | ||||||||
\(870\) | 14.4967 | 0.491483 | ||||||||
\(871\) | 1.23456 | 0.0418315 | ||||||||
\(872\) | 15.7206 | 0.532367 | ||||||||
\(873\) | 0.530148 | 0.0179428 | ||||||||
\(874\) | −19.6312 | −0.664034 | ||||||||
\(875\) | 9.42566 | 0.318646 | ||||||||
\(876\) | −4.38417 | −0.148127 | ||||||||
\(877\) | −1.10800 | −0.0374146 | −0.0187073 | − | 0.999825i | \(-0.505955\pi\) | ||||
−0.0187073 | + | 0.999825i | \(0.505955\pi\) | |||||||
\(878\) | −30.2636 | −1.02135 | ||||||||
\(879\) | 33.2022 | 1.11988 | ||||||||
\(880\) | −1.65415 | −0.0557614 | ||||||||
\(881\) | 23.9405 | 0.806575 | 0.403288 | − | 0.915073i | \(-0.367867\pi\) | ||||
0.403288 | + | 0.915073i | \(0.367867\pi\) | |||||||
\(882\) | −0.399456 | −0.0134504 | ||||||||
\(883\) | −42.1192 | −1.41742 | −0.708712 | − | 0.705497i | \(-0.750724\pi\) | ||||
−0.708712 | + | 0.705497i | \(0.750724\pi\) | |||||||
\(884\) | 1.34713 | 0.0453089 | ||||||||
\(885\) | 19.4163 | 0.652672 | ||||||||
\(886\) | 3.80455 | 0.127817 | ||||||||
\(887\) | −14.0197 | −0.470735 | −0.235367 | − | 0.971906i | \(-0.575629\pi\) | ||||
−0.235367 | + | 0.971906i | \(0.575629\pi\) | |||||||
\(888\) | 3.68102 | 0.123527 | ||||||||
\(889\) | 7.99758 | 0.268230 | ||||||||
\(890\) | −18.2850 | −0.612915 | ||||||||
\(891\) | 11.7878 | 0.394907 | ||||||||
\(892\) | −22.9164 | −0.767299 | ||||||||
\(893\) | 13.6422 | 0.456519 | ||||||||
\(894\) | 19.5723 | 0.654594 | ||||||||
\(895\) | −18.5280 | −0.619321 | ||||||||
\(896\) | −0.876800 | −0.0292918 | ||||||||
\(897\) | −1.06740 | −0.0356394 | ||||||||
\(898\) | 27.3357 | 0.912204 | ||||||||
\(899\) | −9.57089 | −0.319207 | ||||||||
\(900\) | −0.213957 | −0.00713189 | ||||||||
\(901\) | 12.3877 | 0.412696 | ||||||||
\(902\) | −5.30510 | −0.176640 | ||||||||
\(903\) | −7.54022 | −0.250923 | ||||||||
\(904\) | −10.0760 | −0.335121 | ||||||||
\(905\) | 15.1571 | 0.503840 | ||||||||
\(906\) | −4.16991 | −0.138536 | ||||||||
\(907\) | 0.401987 | 0.0133478 | 0.00667388 | − | 0.999978i | \(-0.497876\pi\) | ||||
0.00667388 | + | 0.999978i | \(0.497876\pi\) | |||||||
\(908\) | −2.08411 | −0.0691638 | ||||||||
\(909\) | −0.934523 | −0.0309962 | ||||||||
\(910\) | −0.254395 | −0.00843311 | ||||||||
\(911\) | 15.8456 | 0.524987 | 0.262494 | − | 0.964934i | \(-0.415455\pi\) | ||||
0.262494 | + | 0.964934i | \(0.415455\pi\) | |||||||
\(912\) | 12.6812 | 0.419916 | ||||||||
\(913\) | 8.22326 | 0.272150 | ||||||||
\(914\) | −1.81388 | −0.0599977 | ||||||||
\(915\) | −27.4036 | −0.905936 | ||||||||
\(916\) | 15.3090 | 0.505823 | ||||||||
\(917\) | 5.26286 | 0.173795 | ||||||||
\(918\) | 30.7657 | 1.01542 | ||||||||
\(919\) | −35.3236 | −1.16522 | −0.582610 | − | 0.812752i | \(-0.697968\pi\) | ||||
−0.582610 | + | 0.812752i | \(0.697968\pi\) | |||||||
\(920\) | 3.49390 | 0.115191 | ||||||||
\(921\) | 14.3098 | 0.471523 | ||||||||
\(922\) | 16.2086 | 0.533803 | ||||||||
\(923\) | −3.65058 | −0.120160 | ||||||||
\(924\) | −1.96904 | −0.0647767 | ||||||||
\(925\) | 7.01852 | 0.230768 | ||||||||
\(926\) | 35.3990 | 1.16328 | ||||||||
\(927\) | −0.0174330 | −0.000572573 0 | ||||||||
\(928\) | −6.42309 | −0.210848 | ||||||||
\(929\) | 48.9587 | 1.60628 | 0.803141 | − | 0.595788i | \(-0.203160\pi\) | ||||
0.803141 | + | 0.595788i | \(0.203160\pi\) | |||||||
\(930\) | −3.36305 | −0.110279 | ||||||||
\(931\) | 45.1420 | 1.47947 | ||||||||
\(932\) | 19.1212 | 0.626337 | ||||||||
\(933\) | −27.3301 | −0.894748 | ||||||||
\(934\) | 29.3005 | 0.958740 | ||||||||
\(935\) | −9.90260 | −0.323850 | ||||||||
\(936\) | 0.0144255 | 0.000471513 0 | ||||||||
\(937\) | 31.6916 | 1.03532 | 0.517660 | − | 0.855586i | \(-0.326803\pi\) | ||||
0.517660 | + | 0.855586i | \(0.326803\pi\) | |||||||
\(938\) | −4.81035 | −0.157064 | ||||||||
\(939\) | 27.0614 | 0.883115 | ||||||||
\(940\) | −2.42800 | −0.0791927 | ||||||||
\(941\) | 40.5097 | 1.32058 | 0.660289 | − | 0.751011i | \(-0.270434\pi\) | ||||
0.660289 | + | 0.751011i | \(0.270434\pi\) | |||||||
\(942\) | 0.533653 | 0.0173874 | ||||||||
\(943\) | 11.2054 | 0.364900 | ||||||||
\(944\) | −8.60286 | −0.279999 | ||||||||
\(945\) | −5.80985 | −0.188994 | ||||||||
\(946\) | 6.30281 | 0.204922 | ||||||||
\(947\) | 2.08600 | 0.0677860 | 0.0338930 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338930 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(948\) | 17.6115 | 0.571996 | ||||||||
\(949\) | 0.563601 | 0.0182953 | ||||||||
\(950\) | 24.1789 | 0.784469 | ||||||||
\(951\) | 6.39149 | 0.207258 | ||||||||
\(952\) | −5.24898 | −0.170120 | ||||||||
\(953\) | −2.86376 | −0.0927664 | −0.0463832 | − | 0.998924i | \(-0.514770\pi\) | ||||
−0.0463832 | + | 0.998924i | \(0.514770\pi\) | |||||||
\(954\) | 0.132652 | 0.00429477 | ||||||||
\(955\) | −23.0992 | −0.747473 | ||||||||
\(956\) | −11.8207 | −0.382307 | ||||||||
\(957\) | −14.4244 | −0.466275 | ||||||||
\(958\) | −13.4423 | −0.434300 | ||||||||
\(959\) | −7.36596 | −0.237859 | ||||||||
\(960\) | −2.25696 | −0.0728431 | ||||||||
\(961\) | −28.7797 | −0.928376 | ||||||||
\(962\) | −0.473207 | −0.0152568 | ||||||||
\(963\) | 0.615785 | 0.0198434 | ||||||||
\(964\) | −9.30234 | −0.299608 | ||||||||
\(965\) | −28.4913 | −0.917166 | ||||||||
\(966\) | 4.15902 | 0.133814 | ||||||||
\(967\) | 40.7329 | 1.30988 | 0.654941 | − | 0.755680i | \(-0.272693\pi\) | ||||
0.654941 | + | 0.755680i | \(0.272693\pi\) | |||||||
\(968\) | −9.35409 | −0.300652 | ||||||||
\(969\) | 75.9161 | 2.43878 | ||||||||
\(970\) | 10.6629 | 0.342364 | ||||||||
\(971\) | 58.1185 | 1.86511 | 0.932556 | − | 0.361024i | \(-0.117573\pi\) | ||||
0.932556 | + | 0.361024i | \(0.117573\pi\) | |||||||
\(972\) | 0.666091 | 0.0213649 | ||||||||
\(973\) | −0.674007 | −0.0216077 | ||||||||
\(974\) | −6.77727 | −0.217158 | ||||||||
\(975\) | 1.31467 | 0.0421032 | ||||||||
\(976\) | 12.1418 | 0.388650 | ||||||||
\(977\) | −50.9658 | −1.63054 | −0.815270 | − | 0.579080i | \(-0.803412\pi\) | ||||
−0.815270 | + | 0.579080i | \(0.803412\pi\) | |||||||
\(978\) | −14.6723 | −0.469169 | ||||||||
\(979\) | 18.1939 | 0.581479 | ||||||||
\(980\) | −8.03425 | −0.256645 | ||||||||
\(981\) | 1.00778 | 0.0321759 | ||||||||
\(982\) | 13.0202 | 0.415492 | ||||||||
\(983\) | −57.8220 | −1.84423 | −0.922117 | − | 0.386911i | \(-0.873542\pi\) | ||||
−0.922117 | + | 0.386911i | \(0.873542\pi\) | |||||||
\(984\) | −7.23840 | −0.230752 | ||||||||
\(985\) | −7.56574 | −0.241065 | ||||||||
\(986\) | −38.4519 | −1.22456 | ||||||||
\(987\) | −2.89021 | −0.0919963 | ||||||||
\(988\) | −1.63021 | −0.0518638 | ||||||||
\(989\) | −13.3128 | −0.423323 | ||||||||
\(990\) | −0.106040 | −0.00337018 | ||||||||
\(991\) | −26.5421 | −0.843138 | −0.421569 | − | 0.906796i | \(-0.638520\pi\) | ||||
−0.421569 | + | 0.906796i | \(0.638520\pi\) | |||||||
\(992\) | 1.49008 | 0.0473100 | ||||||||
\(993\) | 13.2119 | 0.419267 | ||||||||
\(994\) | 14.2242 | 0.451163 | ||||||||
\(995\) | −4.82147 | −0.152851 | ||||||||
\(996\) | 11.2200 | 0.355520 | ||||||||
\(997\) | −53.3927 | −1.69097 | −0.845483 | − | 0.534003i | \(-0.820687\pi\) | ||||
−0.845483 | + | 0.534003i | \(0.820687\pi\) | |||||||
\(998\) | −31.9234 | −1.01052 | ||||||||
\(999\) | −10.8071 | −0.341921 |
(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.c.1.11 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.c.1.11 | ✓ | 31 | 1.1 | even | 1 | trivial |