Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2005,2,Mod(1,2005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.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: | \(16.0100056053\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 2005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33194 | −0.941821 | −0.470911 | − | 0.882181i | \(-0.656075\pi\) | ||||
−0.470911 | + | 0.882181i | \(0.656075\pi\) | |||||||
\(3\) | −3.14709 | −1.81697 | −0.908486 | − | 0.417916i | \(-0.862761\pi\) | ||||
−0.908486 | + | 0.417916i | \(0.862761\pi\) | |||||||
\(4\) | −0.225946 | −0.112973 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 4.19172 | 1.71126 | ||||||||
\(7\) | −4.67738 | −1.76788 | −0.883942 | − | 0.467597i | \(-0.845120\pi\) | ||||
−0.883942 | + | 0.467597i | \(0.845120\pi\) | |||||||
\(8\) | 2.96482 | 1.04822 | ||||||||
\(9\) | 6.90415 | 2.30138 | ||||||||
\(10\) | 1.33194 | 0.421195 | ||||||||
\(11\) | 5.05534 | 1.52424 | 0.762121 | − | 0.647434i | \(-0.224158\pi\) | ||||
0.762121 | + | 0.647434i | \(0.224158\pi\) | |||||||
\(12\) | 0.711072 | 0.205269 | ||||||||
\(13\) | 1.63013 | 0.452118 | 0.226059 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226059 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(14\) | 6.22997 | 1.66503 | ||||||||
\(15\) | 3.14709 | 0.812574 | ||||||||
\(16\) | −3.49706 | −0.874264 | ||||||||
\(17\) | −4.32572 | −1.04914 | −0.524570 | − | 0.851367i | \(-0.675774\pi\) | ||||
−0.524570 | + | 0.851367i | \(0.675774\pi\) | |||||||
\(18\) | −9.19589 | −2.16749 | ||||||||
\(19\) | 2.37172 | 0.544110 | 0.272055 | − | 0.962282i | \(-0.412297\pi\) | ||||
0.272055 | + | 0.962282i | \(0.412297\pi\) | |||||||
\(20\) | 0.225946 | 0.0505231 | ||||||||
\(21\) | 14.7201 | 3.21219 | ||||||||
\(22\) | −6.73339 | −1.43556 | ||||||||
\(23\) | −1.08473 | −0.226181 | −0.113091 | − | 0.993585i | \(-0.536075\pi\) | ||||
−0.113091 | + | 0.993585i | \(0.536075\pi\) | |||||||
\(24\) | −9.33054 | −1.90459 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.17123 | −0.425814 | ||||||||
\(27\) | −12.2867 | −2.36458 | ||||||||
\(28\) | 1.05684 | 0.199723 | ||||||||
\(29\) | −7.88273 | −1.46379 | −0.731893 | − | 0.681419i | \(-0.761363\pi\) | ||||
−0.731893 | + | 0.681419i | \(0.761363\pi\) | |||||||
\(30\) | −4.19172 | −0.765300 | ||||||||
\(31\) | 2.44114 | 0.438441 | 0.219221 | − | 0.975675i | \(-0.429649\pi\) | ||||
0.219221 | + | 0.975675i | \(0.429649\pi\) | |||||||
\(32\) | −1.27178 | −0.224821 | ||||||||
\(33\) | −15.9096 | −2.76950 | ||||||||
\(34\) | 5.76158 | 0.988103 | ||||||||
\(35\) | 4.67738 | 0.790621 | ||||||||
\(36\) | −1.55997 | −0.259994 | ||||||||
\(37\) | −6.13003 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668097\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668097\pi\) | |||||||
\(38\) | −3.15898 | −0.512454 | ||||||||
\(39\) | −5.13017 | −0.821485 | ||||||||
\(40\) | −2.96482 | −0.468779 | ||||||||
\(41\) | −8.57579 | −1.33931 | −0.669657 | − | 0.742671i | \(-0.733559\pi\) | ||||
−0.669657 | + | 0.742671i | \(0.733559\pi\) | |||||||
\(42\) | −19.6063 | −3.02531 | ||||||||
\(43\) | −2.55480 | −0.389603 | −0.194801 | − | 0.980843i | \(-0.562406\pi\) | ||||
−0.194801 | + | 0.980843i | \(0.562406\pi\) | |||||||
\(44\) | −1.14223 | −0.172198 | ||||||||
\(45\) | −6.90415 | −1.02921 | ||||||||
\(46\) | 1.44479 | 0.213022 | ||||||||
\(47\) | 7.47452 | 1.09027 | 0.545135 | − | 0.838348i | \(-0.316478\pi\) | ||||
0.545135 | + | 0.838348i | \(0.316478\pi\) | |||||||
\(48\) | 11.0055 | 1.58851 | ||||||||
\(49\) | 14.8779 | 2.12541 | ||||||||
\(50\) | −1.33194 | −0.188364 | ||||||||
\(51\) | 13.6134 | 1.90626 | ||||||||
\(52\) | −0.368322 | −0.0510771 | ||||||||
\(53\) | 2.08798 | 0.286807 | 0.143403 | − | 0.989664i | \(-0.454195\pi\) | ||||
0.143403 | + | 0.989664i | \(0.454195\pi\) | |||||||
\(54\) | 16.3651 | 2.22701 | ||||||||
\(55\) | −5.05534 | −0.681662 | ||||||||
\(56\) | −13.8676 | −1.85313 | ||||||||
\(57\) | −7.46400 | −0.988631 | ||||||||
\(58\) | 10.4993 | 1.37862 | ||||||||
\(59\) | −13.3507 | −1.73812 | −0.869059 | − | 0.494709i | \(-0.835275\pi\) | ||||
−0.869059 | + | 0.494709i | \(0.835275\pi\) | |||||||
\(60\) | −0.711072 | −0.0917990 | ||||||||
\(61\) | −11.4901 | −1.47116 | −0.735578 | − | 0.677440i | \(-0.763089\pi\) | ||||
−0.735578 | + | 0.677440i | \(0.763089\pi\) | |||||||
\(62\) | −3.25144 | −0.412933 | ||||||||
\(63\) | −32.2933 | −4.06858 | ||||||||
\(64\) | 8.68804 | 1.08601 | ||||||||
\(65\) | −1.63013 | −0.202193 | ||||||||
\(66\) | 21.1906 | 2.60838 | ||||||||
\(67\) | 14.2309 | 1.73858 | 0.869288 | − | 0.494306i | \(-0.164578\pi\) | ||||
0.869288 | + | 0.494306i | \(0.164578\pi\) | |||||||
\(68\) | 0.977379 | 0.118525 | ||||||||
\(69\) | 3.41373 | 0.410965 | ||||||||
\(70\) | −6.22997 | −0.744624 | ||||||||
\(71\) | 8.47954 | 1.00634 | 0.503168 | − | 0.864189i | \(-0.332168\pi\) | ||||
0.503168 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(72\) | 20.4696 | 2.41236 | ||||||||
\(73\) | 4.82319 | 0.564511 | 0.282256 | − | 0.959339i | \(-0.408917\pi\) | ||||
0.282256 | + | 0.959339i | \(0.408917\pi\) | |||||||
\(74\) | 8.16480 | 0.949139 | ||||||||
\(75\) | −3.14709 | −0.363394 | ||||||||
\(76\) | −0.535880 | −0.0614697 | ||||||||
\(77\) | −23.6457 | −2.69468 | ||||||||
\(78\) | 6.83306 | 0.773692 | ||||||||
\(79\) | −4.38807 | −0.493697 | −0.246848 | − | 0.969054i | \(-0.579395\pi\) | ||||
−0.246848 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(80\) | 3.49706 | 0.390983 | ||||||||
\(81\) | 17.9549 | 1.99499 | ||||||||
\(82\) | 11.4224 | 1.26139 | ||||||||
\(83\) | 9.81209 | 1.07702 | 0.538508 | − | 0.842620i | \(-0.318988\pi\) | ||||
0.538508 | + | 0.842620i | \(0.318988\pi\) | |||||||
\(84\) | −3.32595 | −0.362891 | ||||||||
\(85\) | 4.32572 | 0.469190 | ||||||||
\(86\) | 3.40283 | 0.366936 | ||||||||
\(87\) | 24.8076 | 2.65966 | ||||||||
\(88\) | 14.9882 | 1.59774 | ||||||||
\(89\) | −13.1613 | −1.39510 | −0.697549 | − | 0.716537i | \(-0.745726\pi\) | ||||
−0.697549 | + | 0.716537i | \(0.745726\pi\) | |||||||
\(90\) | 9.19589 | 0.969332 | ||||||||
\(91\) | −7.62476 | −0.799292 | ||||||||
\(92\) | 0.245090 | 0.0255524 | ||||||||
\(93\) | −7.68247 | −0.796636 | ||||||||
\(94\) | −9.95558 | −1.02684 | ||||||||
\(95\) | −2.37172 | −0.243333 | ||||||||
\(96\) | 4.00240 | 0.408494 | ||||||||
\(97\) | −17.4022 | −1.76692 | −0.883462 | − | 0.468503i | \(-0.844793\pi\) | ||||
−0.883462 | + | 0.468503i | \(0.844793\pi\) | |||||||
\(98\) | −19.8164 | −2.00176 | ||||||||
\(99\) | 34.9028 | 3.50787 | ||||||||
\(100\) | −0.225946 | −0.0225946 | ||||||||
\(101\) | −8.96048 | −0.891601 | −0.445801 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445801 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(102\) | −18.1322 | −1.79535 | ||||||||
\(103\) | −6.55858 | −0.646236 | −0.323118 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323118 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(104\) | 4.83305 | 0.473920 | ||||||||
\(105\) | −14.7201 | −1.43654 | ||||||||
\(106\) | −2.78106 | −0.270121 | ||||||||
\(107\) | 0.962257 | 0.0930249 | 0.0465124 | − | 0.998918i | \(-0.485189\pi\) | ||||
0.0465124 | + | 0.998918i | \(0.485189\pi\) | |||||||
\(108\) | 2.77613 | 0.267134 | ||||||||
\(109\) | −0.925856 | −0.0886809 | −0.0443405 | − | 0.999016i | \(-0.514119\pi\) | ||||
−0.0443405 | + | 0.999016i | \(0.514119\pi\) | |||||||
\(110\) | 6.73339 | 0.642004 | ||||||||
\(111\) | 19.2917 | 1.83109 | ||||||||
\(112\) | 16.3571 | 1.54560 | ||||||||
\(113\) | 7.44701 | 0.700555 | 0.350278 | − | 0.936646i | \(-0.386087\pi\) | ||||
0.350278 | + | 0.936646i | \(0.386087\pi\) | |||||||
\(114\) | 9.94158 | 0.931114 | ||||||||
\(115\) | 1.08473 | 0.101151 | ||||||||
\(116\) | 1.78107 | 0.165368 | ||||||||
\(117\) | 11.2547 | 1.04050 | ||||||||
\(118\) | 17.7823 | 1.63700 | ||||||||
\(119\) | 20.2330 | 1.85476 | ||||||||
\(120\) | 9.33054 | 0.851758 | ||||||||
\(121\) | 14.5565 | 1.32331 | ||||||||
\(122\) | 15.3041 | 1.38557 | ||||||||
\(123\) | 26.9888 | 2.43349 | ||||||||
\(124\) | −0.551566 | −0.0495321 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 43.0127 | 3.83187 | ||||||||
\(127\) | −15.0404 | −1.33462 | −0.667309 | − | 0.744781i | \(-0.732554\pi\) | ||||
−0.667309 | + | 0.744781i | \(0.732554\pi\) | |||||||
\(128\) | −9.02836 | −0.798002 | ||||||||
\(129\) | 8.04017 | 0.707897 | ||||||||
\(130\) | 2.17123 | 0.190430 | ||||||||
\(131\) | −5.04718 | −0.440974 | −0.220487 | − | 0.975390i | \(-0.570765\pi\) | ||||
−0.220487 | + | 0.975390i | \(0.570765\pi\) | |||||||
\(132\) | 3.59471 | 0.312879 | ||||||||
\(133\) | −11.0934 | −0.961922 | ||||||||
\(134\) | −18.9546 | −1.63743 | ||||||||
\(135\) | 12.2867 | 1.05747 | ||||||||
\(136\) | −12.8250 | −1.09973 | ||||||||
\(137\) | 17.8652 | 1.52633 | 0.763164 | − | 0.646204i | \(-0.223645\pi\) | ||||
0.763164 | + | 0.646204i | \(0.223645\pi\) | |||||||
\(138\) | −4.54687 | −0.387055 | ||||||||
\(139\) | 13.0736 | 1.10889 | 0.554443 | − | 0.832221i | \(-0.312931\pi\) | ||||
0.554443 | + | 0.832221i | \(0.312931\pi\) | |||||||
\(140\) | −1.05684 | −0.0893189 | ||||||||
\(141\) | −23.5230 | −1.98099 | ||||||||
\(142\) | −11.2942 | −0.947788 | ||||||||
\(143\) | 8.24088 | 0.689137 | ||||||||
\(144\) | −24.1442 | −2.01202 | ||||||||
\(145\) | 7.88273 | 0.654625 | ||||||||
\(146\) | −6.42418 | −0.531669 | ||||||||
\(147\) | −46.8220 | −3.86181 | ||||||||
\(148\) | 1.38506 | 0.113851 | ||||||||
\(149\) | 4.76000 | 0.389954 | 0.194977 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194977 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(150\) | 4.19172 | 0.342252 | ||||||||
\(151\) | 7.59676 | 0.618216 | 0.309108 | − | 0.951027i | \(-0.399970\pi\) | ||||
0.309108 | + | 0.951027i | \(0.399970\pi\) | |||||||
\(152\) | 7.03171 | 0.570347 | ||||||||
\(153\) | −29.8654 | −2.41448 | ||||||||
\(154\) | 31.4946 | 2.53791 | ||||||||
\(155\) | −2.44114 | −0.196077 | ||||||||
\(156\) | 1.15914 | 0.0928057 | ||||||||
\(157\) | −8.34378 | −0.665906 | −0.332953 | − | 0.942943i | \(-0.608045\pi\) | ||||
−0.332953 | + | 0.942943i | \(0.608045\pi\) | |||||||
\(158\) | 5.84463 | 0.464974 | ||||||||
\(159\) | −6.57106 | −0.521119 | ||||||||
\(160\) | 1.27178 | 0.100543 | ||||||||
\(161\) | 5.07368 | 0.399862 | ||||||||
\(162\) | −23.9147 | −1.87892 | ||||||||
\(163\) | −22.7894 | −1.78500 | −0.892501 | − | 0.451044i | \(-0.851052\pi\) | ||||
−0.892501 | + | 0.451044i | \(0.851052\pi\) | |||||||
\(164\) | 1.93767 | 0.151306 | ||||||||
\(165\) | 15.9096 | 1.23856 | ||||||||
\(166\) | −13.0691 | −1.01436 | ||||||||
\(167\) | −4.11836 | −0.318688 | −0.159344 | − | 0.987223i | \(-0.550938\pi\) | ||||
−0.159344 | + | 0.987223i | \(0.550938\pi\) | |||||||
\(168\) | 43.6425 | 3.36709 | ||||||||
\(169\) | −10.3427 | −0.795589 | ||||||||
\(170\) | −5.76158 | −0.441893 | ||||||||
\(171\) | 16.3747 | 1.25221 | ||||||||
\(172\) | 0.577246 | 0.0440146 | ||||||||
\(173\) | 6.33232 | 0.481438 | 0.240719 | − | 0.970595i | \(-0.422617\pi\) | ||||
0.240719 | + | 0.970595i | \(0.422617\pi\) | |||||||
\(174\) | −33.0422 | −2.50492 | ||||||||
\(175\) | −4.67738 | −0.353577 | ||||||||
\(176\) | −17.6788 | −1.33259 | ||||||||
\(177\) | 42.0159 | 3.15811 | ||||||||
\(178\) | 17.5300 | 1.31393 | ||||||||
\(179\) | 6.18122 | 0.462006 | 0.231003 | − | 0.972953i | \(-0.425799\pi\) | ||||
0.231003 | + | 0.972953i | \(0.425799\pi\) | |||||||
\(180\) | 1.55997 | 0.116273 | ||||||||
\(181\) | −21.3322 | −1.58561 | −0.792807 | − | 0.609473i | \(-0.791381\pi\) | ||||
−0.792807 | + | 0.609473i | \(0.791381\pi\) | |||||||
\(182\) | 10.1557 | 0.752790 | ||||||||
\(183\) | 36.1603 | 2.67305 | ||||||||
\(184\) | −3.21602 | −0.237088 | ||||||||
\(185\) | 6.13003 | 0.450689 | ||||||||
\(186\) | 10.2326 | 0.750288 | ||||||||
\(187\) | −21.8680 | −1.59914 | ||||||||
\(188\) | −1.68884 | −0.123171 | ||||||||
\(189\) | 57.4696 | 4.18030 | ||||||||
\(190\) | 3.15898 | 0.229176 | ||||||||
\(191\) | −16.8463 | −1.21896 | −0.609478 | − | 0.792803i | \(-0.708621\pi\) | ||||
−0.609478 | + | 0.792803i | \(0.708621\pi\) | |||||||
\(192\) | −27.3420 | −1.97324 | ||||||||
\(193\) | 18.0433 | 1.29879 | 0.649394 | − | 0.760452i | \(-0.275023\pi\) | ||||
0.649394 | + | 0.760452i | \(0.275023\pi\) | |||||||
\(194\) | 23.1786 | 1.66413 | ||||||||
\(195\) | 5.13017 | 0.367379 | ||||||||
\(196\) | −3.36160 | −0.240114 | ||||||||
\(197\) | −24.1481 | −1.72048 | −0.860240 | − | 0.509889i | \(-0.829687\pi\) | ||||
−0.860240 | + | 0.509889i | \(0.829687\pi\) | |||||||
\(198\) | −46.4884 | −3.30378 | ||||||||
\(199\) | 18.5154 | 1.31252 | 0.656260 | − | 0.754535i | \(-0.272138\pi\) | ||||
0.656260 | + | 0.754535i | \(0.272138\pi\) | |||||||
\(200\) | 2.96482 | 0.209644 | ||||||||
\(201\) | −44.7857 | −3.15894 | ||||||||
\(202\) | 11.9348 | 0.839729 | ||||||||
\(203\) | 36.8705 | 2.58780 | ||||||||
\(204\) | −3.07590 | −0.215356 | ||||||||
\(205\) | 8.57579 | 0.598959 | ||||||||
\(206\) | 8.73561 | 0.608638 | ||||||||
\(207\) | −7.48912 | −0.520530 | ||||||||
\(208\) | −5.70067 | −0.395270 | ||||||||
\(209\) | 11.9898 | 0.829355 | ||||||||
\(210\) | 19.6063 | 1.35296 | ||||||||
\(211\) | 2.42963 | 0.167262 | 0.0836312 | − | 0.996497i | \(-0.473348\pi\) | ||||
0.0836312 | + | 0.996497i | \(0.473348\pi\) | |||||||
\(212\) | −0.471772 | −0.0324014 | ||||||||
\(213\) | −26.6858 | −1.82848 | ||||||||
\(214\) | −1.28166 | −0.0876128 | ||||||||
\(215\) | 2.55480 | 0.174236 | ||||||||
\(216\) | −36.4279 | −2.47860 | ||||||||
\(217\) | −11.4181 | −0.775113 | ||||||||
\(218\) | 1.23318 | 0.0835216 | ||||||||
\(219\) | −15.1790 | −1.02570 | ||||||||
\(220\) | 1.14223 | 0.0770094 | ||||||||
\(221\) | −7.05150 | −0.474335 | ||||||||
\(222\) | −25.6953 | −1.72456 | ||||||||
\(223\) | 11.4006 | 0.763444 | 0.381722 | − | 0.924277i | \(-0.375331\pi\) | ||||
0.381722 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(224\) | 5.94860 | 0.397457 | ||||||||
\(225\) | 6.90415 | 0.460277 | ||||||||
\(226\) | −9.91894 | −0.659798 | ||||||||
\(227\) | −2.39704 | −0.159097 | −0.0795486 | − | 0.996831i | \(-0.525348\pi\) | ||||
−0.0795486 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(228\) | 1.68646 | 0.111689 | ||||||||
\(229\) | 27.3071 | 1.80451 | 0.902253 | − | 0.431208i | \(-0.141912\pi\) | ||||
0.902253 | + | 0.431208i | \(0.141912\pi\) | |||||||
\(230\) | −1.44479 | −0.0952664 | ||||||||
\(231\) | 74.4152 | 4.89616 | ||||||||
\(232\) | −23.3709 | −1.53437 | ||||||||
\(233\) | 23.3595 | 1.53033 | 0.765165 | − | 0.643834i | \(-0.222657\pi\) | ||||
0.765165 | + | 0.643834i | \(0.222657\pi\) | |||||||
\(234\) | −14.9905 | −0.979962 | ||||||||
\(235\) | −7.47452 | −0.487584 | ||||||||
\(236\) | 3.01654 | 0.196360 | ||||||||
\(237\) | 13.8096 | 0.897033 | ||||||||
\(238\) | −26.9491 | −1.74685 | ||||||||
\(239\) | 27.2516 | 1.76276 | 0.881379 | − | 0.472409i | \(-0.156616\pi\) | ||||
0.881379 | + | 0.472409i | \(0.156616\pi\) | |||||||
\(240\) | −11.0055 | −0.710404 | ||||||||
\(241\) | 14.0351 | 0.904081 | 0.452041 | − | 0.891997i | \(-0.350696\pi\) | ||||
0.452041 | + | 0.891997i | \(0.350696\pi\) | |||||||
\(242\) | −19.3883 | −1.24633 | ||||||||
\(243\) | −19.6454 | −1.26025 | ||||||||
\(244\) | 2.59614 | 0.166201 | ||||||||
\(245\) | −14.8779 | −0.950513 | ||||||||
\(246\) | −35.9473 | −2.29192 | ||||||||
\(247\) | 3.86622 | 0.246002 | ||||||||
\(248\) | 7.23753 | 0.459584 | ||||||||
\(249\) | −30.8795 | −1.95691 | ||||||||
\(250\) | 1.33194 | 0.0842390 | ||||||||
\(251\) | 18.7805 | 1.18541 | 0.592706 | − | 0.805419i | \(-0.298060\pi\) | ||||
0.592706 | + | 0.805419i | \(0.298060\pi\) | |||||||
\(252\) | 7.29655 | 0.459640 | ||||||||
\(253\) | −5.48366 | −0.344755 | ||||||||
\(254\) | 20.0328 | 1.25697 | ||||||||
\(255\) | −13.6134 | −0.852505 | ||||||||
\(256\) | −5.35089 | −0.334431 | ||||||||
\(257\) | −17.5562 | −1.09513 | −0.547564 | − | 0.836764i | \(-0.684445\pi\) | ||||
−0.547564 | + | 0.836764i | \(0.684445\pi\) | |||||||
\(258\) | −10.7090 | −0.666713 | ||||||||
\(259\) | 28.6725 | 1.78162 | ||||||||
\(260\) | 0.368322 | 0.0228424 | ||||||||
\(261\) | −54.4236 | −3.36873 | ||||||||
\(262\) | 6.72253 | 0.415319 | ||||||||
\(263\) | −9.79893 | −0.604228 | −0.302114 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302114 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(264\) | −47.1690 | −2.90305 | ||||||||
\(265\) | −2.08798 | −0.128264 | ||||||||
\(266\) | 14.7757 | 0.905959 | ||||||||
\(267\) | 41.4198 | 2.53485 | ||||||||
\(268\) | −3.21541 | −0.196412 | ||||||||
\(269\) | 4.89910 | 0.298704 | 0.149352 | − | 0.988784i | \(-0.452281\pi\) | ||||
0.149352 | + | 0.988784i | \(0.452281\pi\) | |||||||
\(270\) | −16.3651 | −0.995949 | ||||||||
\(271\) | −7.83632 | −0.476022 | −0.238011 | − | 0.971262i | \(-0.576495\pi\) | ||||
−0.238011 | + | 0.971262i | \(0.576495\pi\) | |||||||
\(272\) | 15.1273 | 0.917226 | ||||||||
\(273\) | 23.9958 | 1.45229 | ||||||||
\(274\) | −23.7953 | −1.43753 | ||||||||
\(275\) | 5.05534 | 0.304848 | ||||||||
\(276\) | −0.771319 | −0.0464279 | ||||||||
\(277\) | 14.4895 | 0.870592 | 0.435296 | − | 0.900287i | \(-0.356644\pi\) | ||||
0.435296 | + | 0.900287i | \(0.356644\pi\) | |||||||
\(278\) | −17.4132 | −1.04437 | ||||||||
\(279\) | 16.8540 | 1.00902 | ||||||||
\(280\) | 13.8676 | 0.828746 | ||||||||
\(281\) | 11.9755 | 0.714399 | 0.357200 | − | 0.934028i | \(-0.383732\pi\) | ||||
0.357200 | + | 0.934028i | \(0.383732\pi\) | |||||||
\(282\) | 31.3311 | 1.86574 | ||||||||
\(283\) | −0.00720674 | −0.000428396 0 | −0.000214198 | − | 1.00000i | \(-0.500068\pi\) | ||||
−0.000214198 | 1.00000i | \(0.500068\pi\) | ||||||||
\(284\) | −1.91592 | −0.113689 | ||||||||
\(285\) | 7.46400 | 0.442129 | ||||||||
\(286\) | −10.9763 | −0.649044 | ||||||||
\(287\) | 40.1122 | 2.36775 | ||||||||
\(288\) | −8.78057 | −0.517400 | ||||||||
\(289\) | 1.71184 | 0.100696 | ||||||||
\(290\) | −10.4993 | −0.616540 | ||||||||
\(291\) | 54.7662 | 3.21045 | ||||||||
\(292\) | −1.08978 | −0.0637746 | ||||||||
\(293\) | 9.55771 | 0.558368 | 0.279184 | − | 0.960238i | \(-0.409936\pi\) | ||||
0.279184 | + | 0.960238i | \(0.409936\pi\) | |||||||
\(294\) | 62.3639 | 3.63713 | ||||||||
\(295\) | 13.3507 | 0.777310 | ||||||||
\(296\) | −18.1744 | −1.05637 | ||||||||
\(297\) | −62.1135 | −3.60419 | ||||||||
\(298\) | −6.34001 | −0.367267 | ||||||||
\(299\) | −1.76825 | −0.102261 | ||||||||
\(300\) | 0.711072 | 0.0410537 | ||||||||
\(301\) | 11.9498 | 0.688773 | ||||||||
\(302\) | −10.1184 | −0.582248 | ||||||||
\(303\) | 28.1994 | 1.62001 | ||||||||
\(304\) | −8.29403 | −0.475695 | ||||||||
\(305\) | 11.4901 | 0.657921 | ||||||||
\(306\) | 39.7788 | 2.27400 | ||||||||
\(307\) | 6.17788 | 0.352590 | 0.176295 | − | 0.984337i | \(-0.443589\pi\) | ||||
0.176295 | + | 0.984337i | \(0.443589\pi\) | |||||||
\(308\) | 5.34266 | 0.304426 | ||||||||
\(309\) | 20.6404 | 1.17419 | ||||||||
\(310\) | 3.25144 | 0.184669 | ||||||||
\(311\) | 1.90916 | 0.108259 | 0.0541294 | − | 0.998534i | \(-0.482762\pi\) | ||||
0.0541294 | + | 0.998534i | \(0.482762\pi\) | |||||||
\(312\) | −15.2100 | −0.861098 | ||||||||
\(313\) | −7.32354 | −0.413951 | −0.206975 | − | 0.978346i | \(-0.566362\pi\) | ||||
−0.206975 | + | 0.978346i | \(0.566362\pi\) | |||||||
\(314\) | 11.1134 | 0.627164 | ||||||||
\(315\) | 32.2933 | 1.81952 | ||||||||
\(316\) | 0.991467 | 0.0557744 | ||||||||
\(317\) | 1.56878 | 0.0881116 | 0.0440558 | − | 0.999029i | \(-0.485972\pi\) | ||||
0.0440558 | + | 0.999029i | \(0.485972\pi\) | |||||||
\(318\) | 8.75224 | 0.490801 | ||||||||
\(319\) | −39.8499 | −2.23117 | ||||||||
\(320\) | −8.68804 | −0.485676 | ||||||||
\(321\) | −3.02831 | −0.169024 | ||||||||
\(322\) | −6.75782 | −0.376598 | ||||||||
\(323\) | −10.2594 | −0.570848 | ||||||||
\(324\) | −4.05683 | −0.225380 | ||||||||
\(325\) | 1.63013 | 0.0904236 | ||||||||
\(326\) | 30.3540 | 1.68115 | ||||||||
\(327\) | 2.91375 | 0.161131 | ||||||||
\(328\) | −25.4257 | −1.40390 | ||||||||
\(329\) | −34.9612 | −1.92747 | ||||||||
\(330\) | −21.1906 | −1.16650 | ||||||||
\(331\) | −34.2692 | −1.88360 | −0.941802 | − | 0.336168i | \(-0.890869\pi\) | ||||
−0.941802 | + | 0.336168i | \(0.890869\pi\) | |||||||
\(332\) | −2.21700 | −0.121674 | ||||||||
\(333\) | −42.3226 | −2.31927 | ||||||||
\(334\) | 5.48539 | 0.300147 | ||||||||
\(335\) | −14.2309 | −0.777515 | ||||||||
\(336\) | −51.4771 | −2.80830 | ||||||||
\(337\) | −10.3283 | −0.562617 | −0.281308 | − | 0.959617i | \(-0.590768\pi\) | ||||
−0.281308 | + | 0.959617i | \(0.590768\pi\) | |||||||
\(338\) | 13.7758 | 0.749303 | ||||||||
\(339\) | −23.4364 | −1.27289 | ||||||||
\(340\) | −0.977379 | −0.0530058 | ||||||||
\(341\) | 12.3408 | 0.668291 | ||||||||
\(342\) | −21.8101 | −1.17935 | ||||||||
\(343\) | −36.8478 | −1.98960 | ||||||||
\(344\) | −7.57451 | −0.408390 | ||||||||
\(345\) | −3.41373 | −0.183789 | ||||||||
\(346\) | −8.43425 | −0.453428 | ||||||||
\(347\) | 36.2019 | 1.94342 | 0.971711 | − | 0.236175i | \(-0.0758939\pi\) | ||||
0.971711 | + | 0.236175i | \(0.0758939\pi\) | |||||||
\(348\) | −5.60519 | −0.300470 | ||||||||
\(349\) | 12.0418 | 0.644580 | 0.322290 | − | 0.946641i | \(-0.395547\pi\) | ||||
0.322290 | + | 0.946641i | \(0.395547\pi\) | |||||||
\(350\) | 6.22997 | 0.333006 | ||||||||
\(351\) | −20.0290 | −1.06907 | ||||||||
\(352\) | −6.42928 | −0.342682 | ||||||||
\(353\) | 8.81876 | 0.469375 | 0.234688 | − | 0.972071i | \(-0.424593\pi\) | ||||
0.234688 | + | 0.972071i | \(0.424593\pi\) | |||||||
\(354\) | −55.9625 | −2.97437 | ||||||||
\(355\) | −8.47954 | −0.450047 | ||||||||
\(356\) | 2.97375 | 0.157608 | ||||||||
\(357\) | −63.6751 | −3.37004 | ||||||||
\(358\) | −8.23299 | −0.435127 | ||||||||
\(359\) | −7.74389 | −0.408707 | −0.204354 | − | 0.978897i | \(-0.565509\pi\) | ||||
−0.204354 | + | 0.978897i | \(0.565509\pi\) | |||||||
\(360\) | −20.4696 | −1.07884 | ||||||||
\(361\) | −13.3750 | −0.703945 | ||||||||
\(362\) | 28.4132 | 1.49336 | ||||||||
\(363\) | −45.8104 | −2.40442 | ||||||||
\(364\) | 1.72278 | 0.0902984 | ||||||||
\(365\) | −4.82319 | −0.252457 | ||||||||
\(366\) | −48.1632 | −2.51753 | ||||||||
\(367\) | −28.7516 | −1.50082 | −0.750411 | − | 0.660972i | \(-0.770144\pi\) | ||||
−0.750411 | + | 0.660972i | \(0.770144\pi\) | |||||||
\(368\) | 3.79335 | 0.197742 | ||||||||
\(369\) | −59.2086 | −3.08228 | ||||||||
\(370\) | −8.16480 | −0.424468 | ||||||||
\(371\) | −9.76629 | −0.507041 | ||||||||
\(372\) | 1.73582 | 0.0899983 | ||||||||
\(373\) | 10.5310 | 0.545277 | 0.272638 | − | 0.962117i | \(-0.412104\pi\) | ||||
0.272638 | + | 0.962117i | \(0.412104\pi\) | |||||||
\(374\) | 29.1267 | 1.50611 | ||||||||
\(375\) | 3.14709 | 0.162515 | ||||||||
\(376\) | 22.1606 | 1.14284 | ||||||||
\(377\) | −12.8499 | −0.661804 | ||||||||
\(378\) | −76.5458 | −3.93709 | ||||||||
\(379\) | −27.1783 | −1.39605 | −0.698027 | − | 0.716072i | \(-0.745938\pi\) | ||||
−0.698027 | + | 0.716072i | \(0.745938\pi\) | |||||||
\(380\) | 0.535880 | 0.0274901 | ||||||||
\(381\) | 47.3334 | 2.42496 | ||||||||
\(382\) | 22.4382 | 1.14804 | ||||||||
\(383\) | 12.5973 | 0.643692 | 0.321846 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321846 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(384\) | 28.4130 | 1.44995 | ||||||||
\(385\) | 23.6457 | 1.20510 | ||||||||
\(386\) | −24.0326 | −1.22323 | ||||||||
\(387\) | −17.6387 | −0.896626 | ||||||||
\(388\) | 3.93195 | 0.199615 | ||||||||
\(389\) | −7.28219 | −0.369222 | −0.184611 | − | 0.982812i | \(-0.559103\pi\) | ||||
−0.184611 | + | 0.982812i | \(0.559103\pi\) | |||||||
\(390\) | −6.83306 | −0.346006 | ||||||||
\(391\) | 4.69222 | 0.237296 | ||||||||
\(392\) | 44.1102 | 2.22790 | ||||||||
\(393\) | 15.8839 | 0.801238 | ||||||||
\(394\) | 32.1637 | 1.62039 | ||||||||
\(395\) | 4.38807 | 0.220788 | ||||||||
\(396\) | −7.88616 | −0.396294 | ||||||||
\(397\) | 15.0633 | 0.756004 | 0.378002 | − | 0.925805i | \(-0.376611\pi\) | ||||
0.378002 | + | 0.925805i | \(0.376611\pi\) | |||||||
\(398\) | −24.6613 | −1.23616 | ||||||||
\(399\) | 34.9120 | 1.74778 | ||||||||
\(400\) | −3.49706 | −0.174853 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 59.6518 | 2.97516 | ||||||||
\(403\) | 3.97938 | 0.198227 | ||||||||
\(404\) | 2.02459 | 0.100727 | ||||||||
\(405\) | −17.9549 | −0.892185 | ||||||||
\(406\) | −49.1092 | −2.43725 | ||||||||
\(407\) | −30.9894 | −1.53609 | ||||||||
\(408\) | 40.3613 | 1.99818 | ||||||||
\(409\) | −23.6374 | −1.16879 | −0.584396 | − | 0.811468i | \(-0.698669\pi\) | ||||
−0.584396 | + | 0.811468i | \(0.698669\pi\) | |||||||
\(410\) | −11.4224 | −0.564112 | ||||||||
\(411\) | −56.2234 | −2.77330 | ||||||||
\(412\) | 1.48188 | 0.0730072 | ||||||||
\(413\) | 62.4464 | 3.07279 | ||||||||
\(414\) | 9.97503 | 0.490246 | ||||||||
\(415\) | −9.81209 | −0.481657 | ||||||||
\(416\) | −2.07317 | −0.101646 | ||||||||
\(417\) | −41.1437 | −2.01482 | ||||||||
\(418\) | −15.9697 | −0.781104 | ||||||||
\(419\) | 9.64766 | 0.471319 | 0.235660 | − | 0.971836i | \(-0.424275\pi\) | ||||
0.235660 | + | 0.971836i | \(0.424275\pi\) | |||||||
\(420\) | 3.32595 | 0.162290 | ||||||||
\(421\) | 11.2023 | 0.545968 | 0.272984 | − | 0.962019i | \(-0.411989\pi\) | ||||
0.272984 | + | 0.962019i | \(0.411989\pi\) | |||||||
\(422\) | −3.23611 | −0.157531 | ||||||||
\(423\) | 51.6052 | 2.50913 | ||||||||
\(424\) | 6.19049 | 0.300637 | ||||||||
\(425\) | −4.32572 | −0.209828 | ||||||||
\(426\) | 35.5438 | 1.72210 | ||||||||
\(427\) | 53.7435 | 2.60083 | ||||||||
\(428\) | −0.217418 | −0.0105093 | ||||||||
\(429\) | −25.9348 | −1.25214 | ||||||||
\(430\) | −3.40283 | −0.164099 | ||||||||
\(431\) | 19.8437 | 0.955838 | 0.477919 | − | 0.878404i | \(-0.341391\pi\) | ||||
0.477919 | + | 0.878404i | \(0.341391\pi\) | |||||||
\(432\) | 42.9673 | 2.06727 | ||||||||
\(433\) | −6.53186 | −0.313901 | −0.156951 | − | 0.987606i | \(-0.550166\pi\) | ||||
−0.156951 | + | 0.987606i | \(0.550166\pi\) | |||||||
\(434\) | 15.2082 | 0.730018 | ||||||||
\(435\) | −24.8076 | −1.18944 | ||||||||
\(436\) | 0.209194 | 0.0100186 | ||||||||
\(437\) | −2.57267 | −0.123067 | ||||||||
\(438\) | 20.2174 | 0.966027 | ||||||||
\(439\) | −19.2152 | −0.917093 | −0.458547 | − | 0.888670i | \(-0.651630\pi\) | ||||
−0.458547 | + | 0.888670i | \(0.651630\pi\) | |||||||
\(440\) | −14.9882 | −0.714533 | ||||||||
\(441\) | 102.719 | 4.89139 | ||||||||
\(442\) | 9.39215 | 0.446739 | ||||||||
\(443\) | −1.76374 | −0.0837980 | −0.0418990 | − | 0.999122i | \(-0.513341\pi\) | ||||
−0.0418990 | + | 0.999122i | \(0.513341\pi\) | |||||||
\(444\) | −4.35889 | −0.206864 | ||||||||
\(445\) | 13.1613 | 0.623907 | ||||||||
\(446\) | −15.1849 | −0.719027 | ||||||||
\(447\) | −14.9801 | −0.708535 | ||||||||
\(448\) | −40.6373 | −1.91993 | ||||||||
\(449\) | 11.0092 | 0.519559 | 0.259779 | − | 0.965668i | \(-0.416350\pi\) | ||||
0.259779 | + | 0.965668i | \(0.416350\pi\) | |||||||
\(450\) | −9.19589 | −0.433498 | ||||||||
\(451\) | −43.3535 | −2.04144 | ||||||||
\(452\) | −1.68262 | −0.0791439 | ||||||||
\(453\) | −23.9077 | −1.12328 | ||||||||
\(454\) | 3.19271 | 0.149841 | ||||||||
\(455\) | 7.62476 | 0.357454 | ||||||||
\(456\) | −22.1294 | −1.03630 | ||||||||
\(457\) | −19.3983 | −0.907417 | −0.453708 | − | 0.891150i | \(-0.649899\pi\) | ||||
−0.453708 | + | 0.891150i | \(0.649899\pi\) | |||||||
\(458\) | −36.3713 | −1.69952 | ||||||||
\(459\) | 53.1488 | 2.48078 | ||||||||
\(460\) | −0.245090 | −0.0114274 | ||||||||
\(461\) | 23.7034 | 1.10398 | 0.551988 | − | 0.833852i | \(-0.313869\pi\) | ||||
0.551988 | + | 0.833852i | \(0.313869\pi\) | |||||||
\(462\) | −99.1163 | −4.61131 | ||||||||
\(463\) | −19.7966 | −0.920026 | −0.460013 | − | 0.887912i | \(-0.652155\pi\) | ||||
−0.460013 | + | 0.887912i | \(0.652155\pi\) | |||||||
\(464\) | 27.5664 | 1.27974 | ||||||||
\(465\) | 7.68247 | 0.356266 | ||||||||
\(466\) | −31.1133 | −1.44130 | ||||||||
\(467\) | 24.7579 | 1.14566 | 0.572829 | − | 0.819675i | \(-0.305846\pi\) | ||||
0.572829 | + | 0.819675i | \(0.305846\pi\) | |||||||
\(468\) | −2.54295 | −0.117548 | ||||||||
\(469\) | −66.5631 | −3.07360 | ||||||||
\(470\) | 9.95558 | 0.459217 | ||||||||
\(471\) | 26.2586 | 1.20993 | ||||||||
\(472\) | −39.5825 | −1.82193 | ||||||||
\(473\) | −12.9154 | −0.593849 | ||||||||
\(474\) | −18.3936 | −0.844844 | ||||||||
\(475\) | 2.37172 | 0.108822 | ||||||||
\(476\) | −4.57157 | −0.209538 | ||||||||
\(477\) | 14.4158 | 0.660052 | ||||||||
\(478\) | −36.2974 | −1.66020 | ||||||||
\(479\) | 14.5018 | 0.662603 | 0.331302 | − | 0.943525i | \(-0.392512\pi\) | ||||
0.331302 | + | 0.943525i | \(0.392512\pi\) | |||||||
\(480\) | −4.00240 | −0.182684 | ||||||||
\(481\) | −9.99277 | −0.455631 | ||||||||
\(482\) | −18.6939 | −0.851483 | ||||||||
\(483\) | −15.9673 | −0.726538 | ||||||||
\(484\) | −3.28897 | −0.149499 | ||||||||
\(485\) | 17.4022 | 0.790192 | ||||||||
\(486\) | 26.1664 | 1.18693 | ||||||||
\(487\) | 33.3055 | 1.50922 | 0.754609 | − | 0.656174i | \(-0.227826\pi\) | ||||
0.754609 | + | 0.656174i | \(0.227826\pi\) | |||||||
\(488\) | −34.0660 | −1.54210 | ||||||||
\(489\) | 71.7202 | 3.24330 | ||||||||
\(490\) | 19.8164 | 0.895213 | ||||||||
\(491\) | 19.5046 | 0.880232 | 0.440116 | − | 0.897941i | \(-0.354937\pi\) | ||||
0.440116 | + | 0.897941i | \(0.354937\pi\) | |||||||
\(492\) | −6.09800 | −0.274919 | ||||||||
\(493\) | 34.0985 | 1.53572 | ||||||||
\(494\) | −5.14956 | −0.231690 | ||||||||
\(495\) | −34.9028 | −1.56877 | ||||||||
\(496\) | −8.53680 | −0.383314 | ||||||||
\(497\) | −39.6620 | −1.77908 | ||||||||
\(498\) | 41.1295 | 1.84306 | ||||||||
\(499\) | −21.8187 | −0.976741 | −0.488370 | − | 0.872637i | \(-0.662408\pi\) | ||||
−0.488370 | + | 0.872637i | \(0.662408\pi\) | |||||||
\(500\) | 0.225946 | 0.0101046 | ||||||||
\(501\) | 12.9608 | 0.579047 | ||||||||
\(502\) | −25.0144 | −1.11645 | ||||||||
\(503\) | −32.2929 | −1.43987 | −0.719935 | − | 0.694041i | \(-0.755829\pi\) | ||||
−0.719935 | + | 0.694041i | \(0.755829\pi\) | |||||||
\(504\) | −95.7439 | −4.26477 | ||||||||
\(505\) | 8.96048 | 0.398736 | ||||||||
\(506\) | 7.30389 | 0.324697 | ||||||||
\(507\) | 32.5493 | 1.44556 | ||||||||
\(508\) | 3.39831 | 0.150776 | ||||||||
\(509\) | 14.0154 | 0.621220 | 0.310610 | − | 0.950537i | \(-0.399467\pi\) | ||||
0.310610 | + | 0.950537i | \(0.399467\pi\) | |||||||
\(510\) | 18.1322 | 0.802907 | ||||||||
\(511\) | −22.5599 | −0.997990 | ||||||||
\(512\) | 25.1838 | 1.11298 | ||||||||
\(513\) | −29.1406 | −1.28659 | ||||||||
\(514\) | 23.3838 | 1.03141 | ||||||||
\(515\) | 6.55858 | 0.289005 | ||||||||
\(516\) | −1.81664 | −0.0799733 | ||||||||
\(517\) | 37.7862 | 1.66184 | ||||||||
\(518\) | −38.1899 | −1.67797 | ||||||||
\(519\) | −19.9284 | −0.874758 | ||||||||
\(520\) | −4.83305 | −0.211943 | ||||||||
\(521\) | 7.64852 | 0.335088 | 0.167544 | − | 0.985865i | \(-0.446416\pi\) | ||||
0.167544 | + | 0.985865i | \(0.446416\pi\) | |||||||
\(522\) | 72.4887 | 3.17275 | ||||||||
\(523\) | 19.7800 | 0.864919 | 0.432459 | − | 0.901653i | \(-0.357646\pi\) | ||||
0.432459 | + | 0.901653i | \(0.357646\pi\) | |||||||
\(524\) | 1.14039 | 0.0498182 | ||||||||
\(525\) | 14.7201 | 0.642439 | ||||||||
\(526\) | 13.0516 | 0.569075 | ||||||||
\(527\) | −10.5597 | −0.459987 | ||||||||
\(528\) | 55.6367 | 2.42128 | ||||||||
\(529\) | −21.8234 | −0.948842 | ||||||||
\(530\) | 2.78106 | 0.120802 | ||||||||
\(531\) | −92.1755 | −4.00008 | ||||||||
\(532\) | 2.50652 | 0.108671 | ||||||||
\(533\) | −13.9797 | −0.605528 | ||||||||
\(534\) | −55.1686 | −2.38738 | ||||||||
\(535\) | −0.962257 | −0.0416020 | ||||||||
\(536\) | 42.1919 | 1.82241 | ||||||||
\(537\) | −19.4528 | −0.839451 | ||||||||
\(538\) | −6.52529 | −0.281325 | ||||||||
\(539\) | 75.2127 | 3.23964 | ||||||||
\(540\) | −2.77613 | −0.119466 | ||||||||
\(541\) | 32.0621 | 1.37846 | 0.689229 | − | 0.724544i | \(-0.257950\pi\) | ||||
0.689229 | + | 0.724544i | \(0.257950\pi\) | |||||||
\(542\) | 10.4375 | 0.448328 | ||||||||
\(543\) | 67.1344 | 2.88101 | ||||||||
\(544\) | 5.50136 | 0.235869 | ||||||||
\(545\) | 0.925856 | 0.0396593 | ||||||||
\(546\) | −31.9608 | −1.36780 | ||||||||
\(547\) | 39.9796 | 1.70940 | 0.854702 | − | 0.519118i | \(-0.173740\pi\) | ||||
0.854702 | + | 0.519118i | \(0.173740\pi\) | |||||||
\(548\) | −4.03658 | −0.172434 | ||||||||
\(549\) | −79.3293 | −3.38569 | ||||||||
\(550\) | −6.73339 | −0.287113 | ||||||||
\(551\) | −18.6956 | −0.796460 | ||||||||
\(552\) | 10.1211 | 0.430782 | ||||||||
\(553\) | 20.5247 | 0.872798 | ||||||||
\(554\) | −19.2991 | −0.819942 | ||||||||
\(555\) | −19.2917 | −0.818888 | ||||||||
\(556\) | −2.95392 | −0.125274 | ||||||||
\(557\) | −6.03776 | −0.255828 | −0.127914 | − | 0.991785i | \(-0.540828\pi\) | ||||
−0.127914 | + | 0.991785i | \(0.540828\pi\) | |||||||
\(558\) | −22.4484 | −0.950319 | ||||||||
\(559\) | −4.16466 | −0.176146 | ||||||||
\(560\) | −16.3571 | −0.691212 | ||||||||
\(561\) | 68.8204 | 2.90560 | ||||||||
\(562\) | −15.9506 | −0.672836 | ||||||||
\(563\) | 6.16676 | 0.259898 | 0.129949 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129949 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(564\) | 5.31492 | 0.223798 | ||||||||
\(565\) | −7.44701 | −0.313298 | ||||||||
\(566\) | 0.00959891 | 0.000403472 0 | ||||||||
\(567\) | −83.9817 | −3.52690 | ||||||||
\(568\) | 25.1403 | 1.05486 | ||||||||
\(569\) | 6.94361 | 0.291091 | 0.145546 | − | 0.989352i | \(-0.453506\pi\) | ||||
0.145546 | + | 0.989352i | \(0.453506\pi\) | |||||||
\(570\) | −9.94158 | −0.416407 | ||||||||
\(571\) | 25.3313 | 1.06008 | 0.530040 | − | 0.847972i | \(-0.322177\pi\) | ||||
0.530040 | + | 0.847972i | \(0.322177\pi\) | |||||||
\(572\) | −1.86199 | −0.0778539 | ||||||||
\(573\) | 53.0167 | 2.21481 | ||||||||
\(574\) | −53.4269 | −2.23000 | ||||||||
\(575\) | −1.08473 | −0.0452362 | ||||||||
\(576\) | 59.9836 | 2.49932 | ||||||||
\(577\) | −5.04835 | −0.210165 | −0.105083 | − | 0.994463i | \(-0.533511\pi\) | ||||
−0.105083 | + | 0.994463i | \(0.533511\pi\) | |||||||
\(578\) | −2.28006 | −0.0948380 | ||||||||
\(579\) | −56.7839 | −2.35986 | ||||||||
\(580\) | −1.78107 | −0.0739550 | ||||||||
\(581\) | −45.8949 | −1.90404 | ||||||||
\(582\) | −72.9450 | −3.02367 | ||||||||
\(583\) | 10.5555 | 0.437163 | ||||||||
\(584\) | 14.2999 | 0.591733 | ||||||||
\(585\) | −11.2547 | −0.465324 | ||||||||
\(586\) | −12.7303 | −0.525882 | ||||||||
\(587\) | 1.41615 | 0.0584509 | 0.0292255 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292255 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(588\) | 10.5792 | 0.436280 | ||||||||
\(589\) | 5.78969 | 0.238560 | ||||||||
\(590\) | −17.7823 | −0.732087 | ||||||||
\(591\) | 75.9962 | 3.12606 | ||||||||
\(592\) | 21.4370 | 0.881057 | ||||||||
\(593\) | 37.5146 | 1.54054 | 0.770270 | − | 0.637718i | \(-0.220122\pi\) | ||||
0.770270 | + | 0.637718i | \(0.220122\pi\) | |||||||
\(594\) | 82.7312 | 3.39450 | ||||||||
\(595\) | −20.2330 | −0.829473 | ||||||||
\(596\) | −1.07550 | −0.0440543 | ||||||||
\(597\) | −58.2694 | −2.38481 | ||||||||
\(598\) | 2.35520 | 0.0963111 | ||||||||
\(599\) | 26.8331 | 1.09637 | 0.548185 | − | 0.836357i | \(-0.315319\pi\) | ||||
0.548185 | + | 0.836357i | \(0.315319\pi\) | |||||||
\(600\) | −9.33054 | −0.380918 | ||||||||
\(601\) | 9.40978 | 0.383833 | 0.191916 | − | 0.981411i | \(-0.438530\pi\) | ||||
0.191916 | + | 0.981411i | \(0.438530\pi\) | |||||||
\(602\) | −15.9163 | −0.648700 | ||||||||
\(603\) | 98.2520 | 4.00113 | ||||||||
\(604\) | −1.71646 | −0.0698417 | ||||||||
\(605\) | −14.5565 | −0.591804 | ||||||||
\(606\) | −37.5598 | −1.52576 | ||||||||
\(607\) | −36.4057 | −1.47766 | −0.738830 | − | 0.673892i | \(-0.764621\pi\) | ||||
−0.738830 | + | 0.673892i | \(0.764621\pi\) | |||||||
\(608\) | −3.01630 | −0.122327 | ||||||||
\(609\) | −116.035 | −4.70196 | ||||||||
\(610\) | −15.3041 | −0.619644 | ||||||||
\(611\) | 12.1845 | 0.492931 | ||||||||
\(612\) | 6.74797 | 0.272771 | ||||||||
\(613\) | 40.1766 | 1.62272 | 0.811358 | − | 0.584549i | \(-0.198729\pi\) | ||||
0.811358 | + | 0.584549i | \(0.198729\pi\) | |||||||
\(614\) | −8.22854 | −0.332077 | ||||||||
\(615\) | −26.9888 | −1.08829 | ||||||||
\(616\) | −70.1053 | −2.82462 | ||||||||
\(617\) | 19.8434 | 0.798866 | 0.399433 | − | 0.916762i | \(-0.369207\pi\) | ||||
0.399433 | + | 0.916762i | \(0.369207\pi\) | |||||||
\(618\) | −27.4917 | −1.10588 | ||||||||
\(619\) | −15.0648 | −0.605505 | −0.302752 | − | 0.953069i | \(-0.597905\pi\) | ||||
−0.302752 | + | 0.953069i | \(0.597905\pi\) | |||||||
\(620\) | 0.551566 | 0.0221514 | ||||||||
\(621\) | 13.3277 | 0.534823 | ||||||||
\(622\) | −2.54288 | −0.101960 | ||||||||
\(623\) | 61.5605 | 2.46637 | ||||||||
\(624\) | 17.9405 | 0.718195 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.75448 | 0.389868 | ||||||||
\(627\) | −37.7331 | −1.50691 | ||||||||
\(628\) | 1.88524 | 0.0752294 | ||||||||
\(629\) | 26.5168 | 1.05729 | ||||||||
\(630\) | −43.0127 | −1.71367 | ||||||||
\(631\) | 17.0579 | 0.679062 | 0.339531 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339531 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(632\) | −13.0098 | −0.517503 | ||||||||
\(633\) | −7.64624 | −0.303911 | ||||||||
\(634\) | −2.08952 | −0.0829853 | ||||||||
\(635\) | 15.0404 | 0.596859 | ||||||||
\(636\) | 1.48471 | 0.0588724 | ||||||||
\(637\) | 24.2529 | 0.960936 | ||||||||
\(638\) | 53.0775 | 2.10136 | ||||||||
\(639\) | 58.5440 | 2.31597 | ||||||||
\(640\) | 9.02836 | 0.356877 | ||||||||
\(641\) | −30.5408 | −1.20629 | −0.603145 | − | 0.797631i | \(-0.706086\pi\) | ||||
−0.603145 | + | 0.797631i | \(0.706086\pi\) | |||||||
\(642\) | 4.03351 | 0.159190 | ||||||||
\(643\) | 2.11400 | 0.0833680 | 0.0416840 | − | 0.999131i | \(-0.486728\pi\) | ||||
0.0416840 | + | 0.999131i | \(0.486728\pi\) | |||||||
\(644\) | −1.14638 | −0.0451736 | ||||||||
\(645\) | −8.04017 | −0.316581 | ||||||||
\(646\) | 13.6648 | 0.537636 | ||||||||
\(647\) | −9.90786 | −0.389518 | −0.194759 | − | 0.980851i | \(-0.562393\pi\) | ||||
−0.194759 | + | 0.980851i | \(0.562393\pi\) | |||||||
\(648\) | 53.2329 | 2.09119 | ||||||||
\(649\) | −67.4925 | −2.64931 | ||||||||
\(650\) | −2.17123 | −0.0851628 | ||||||||
\(651\) | 35.9338 | 1.40836 | ||||||||
\(652\) | 5.14917 | 0.201657 | ||||||||
\(653\) | −36.5645 | −1.43088 | −0.715439 | − | 0.698675i | \(-0.753773\pi\) | ||||
−0.715439 | + | 0.698675i | \(0.753773\pi\) | |||||||
\(654\) | −3.88093 | −0.151756 | ||||||||
\(655\) | 5.04718 | 0.197210 | ||||||||
\(656\) | 29.9900 | 1.17091 | ||||||||
\(657\) | 33.3000 | 1.29916 | ||||||||
\(658\) | 46.5660 | 1.81533 | ||||||||
\(659\) | 29.4584 | 1.14754 | 0.573768 | − | 0.819018i | \(-0.305481\pi\) | ||||
0.573768 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(660\) | −3.59471 | −0.139924 | ||||||||
\(661\) | 32.9103 | 1.28006 | 0.640030 | − | 0.768350i | \(-0.278922\pi\) | ||||
0.640030 | + | 0.768350i | \(0.278922\pi\) | |||||||
\(662\) | 45.6443 | 1.77402 | ||||||||
\(663\) | 22.1917 | 0.861854 | ||||||||
\(664\) | 29.0911 | 1.12895 | ||||||||
\(665\) | 11.0934 | 0.430185 | ||||||||
\(666\) | 56.3711 | 2.18433 | ||||||||
\(667\) | 8.55061 | 0.331081 | ||||||||
\(668\) | 0.930526 | 0.0360031 | ||||||||
\(669\) | −35.8788 | −1.38716 | ||||||||
\(670\) | 18.9546 | 0.732280 | ||||||||
\(671\) | −58.0863 | −2.24240 | ||||||||
\(672\) | −18.7208 | −0.722169 | ||||||||
\(673\) | 21.2481 | 0.819055 | 0.409528 | − | 0.912298i | \(-0.365693\pi\) | ||||
0.409528 | + | 0.912298i | \(0.365693\pi\) | |||||||
\(674\) | 13.7566 | 0.529884 | ||||||||
\(675\) | −12.2867 | −0.472916 | ||||||||
\(676\) | 2.33688 | 0.0898801 | ||||||||
\(677\) | −31.1394 | −1.19678 | −0.598392 | − | 0.801203i | \(-0.704194\pi\) | ||||
−0.598392 | + | 0.801203i | \(0.704194\pi\) | |||||||
\(678\) | 31.2158 | 1.19883 | ||||||||
\(679\) | 81.3966 | 3.12371 | ||||||||
\(680\) | 12.8250 | 0.491815 | ||||||||
\(681\) | 7.54369 | 0.289075 | ||||||||
\(682\) | −16.4371 | −0.629411 | ||||||||
\(683\) | 7.31863 | 0.280040 | 0.140020 | − | 0.990149i | \(-0.455283\pi\) | ||||
0.140020 | + | 0.990149i | \(0.455283\pi\) | |||||||
\(684\) | −3.69980 | −0.141465 | ||||||||
\(685\) | −17.8652 | −0.682595 | ||||||||
\(686\) | 49.0789 | 1.87384 | ||||||||
\(687\) | −85.9379 | −3.27873 | ||||||||
\(688\) | 8.93427 | 0.340616 | ||||||||
\(689\) | 3.40369 | 0.129670 | ||||||||
\(690\) | 4.54687 | 0.173096 | ||||||||
\(691\) | 37.7841 | 1.43738 | 0.718688 | − | 0.695332i | \(-0.244743\pi\) | ||||
0.718688 | + | 0.695332i | \(0.244743\pi\) | |||||||
\(692\) | −1.43076 | −0.0543895 | ||||||||
\(693\) | −163.254 | −6.20150 | ||||||||
\(694\) | −48.2186 | −1.83035 | ||||||||
\(695\) | −13.0736 | −0.495909 | ||||||||
\(696\) | 73.5501 | 2.78791 | ||||||||
\(697\) | 37.0965 | 1.40513 | ||||||||
\(698\) | −16.0388 | −0.607079 | ||||||||
\(699\) | −73.5143 | −2.78057 | ||||||||
\(700\) | 1.05684 | 0.0399446 | ||||||||
\(701\) | −21.4200 | −0.809024 | −0.404512 | − | 0.914533i | \(-0.632559\pi\) | ||||
−0.404512 | + | 0.914533i | \(0.632559\pi\) | |||||||
\(702\) | 26.6773 | 1.00687 | ||||||||
\(703\) | −14.5387 | −0.548337 | ||||||||
\(704\) | 43.9210 | 1.65534 | ||||||||
\(705\) | 23.5230 | 0.885926 | ||||||||
\(706\) | −11.7460 | −0.442068 | ||||||||
\(707\) | 41.9116 | 1.57625 | ||||||||
\(708\) | −9.49333 | −0.356781 | ||||||||
\(709\) | 30.4194 | 1.14242 | 0.571212 | − | 0.820803i | \(-0.306474\pi\) | ||||
0.571212 | + | 0.820803i | \(0.306474\pi\) | |||||||
\(710\) | 11.2942 | 0.423864 | ||||||||
\(711\) | −30.2959 | −1.13619 | ||||||||
\(712\) | −39.0209 | −1.46237 | ||||||||
\(713\) | −2.64797 | −0.0991672 | ||||||||
\(714\) | 84.8111 | 3.17398 | ||||||||
\(715\) | −8.24088 | −0.308192 | ||||||||
\(716\) | −1.39662 | −0.0521942 | ||||||||
\(717\) | −85.7631 | −3.20288 | ||||||||
\(718\) | 10.3144 | 0.384929 | ||||||||
\(719\) | −37.7154 | −1.40655 | −0.703274 | − | 0.710919i | \(-0.748279\pi\) | ||||
−0.703274 | + | 0.710919i | \(0.748279\pi\) | |||||||
\(720\) | 24.1442 | 0.899802 | ||||||||
\(721\) | 30.6770 | 1.14247 | ||||||||
\(722\) | 17.8146 | 0.662990 | ||||||||
\(723\) | −44.1697 | −1.64269 | ||||||||
\(724\) | 4.81994 | 0.179132 | ||||||||
\(725\) | −7.88273 | −0.292757 | ||||||||
\(726\) | 61.0166 | 2.26454 | ||||||||
\(727\) | 4.05298 | 0.150317 | 0.0751583 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751583 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(728\) | −22.6060 | −0.837835 | ||||||||
\(729\) | 7.96118 | 0.294859 | ||||||||
\(730\) | 6.42418 | 0.237769 | ||||||||
\(731\) | 11.0513 | 0.408748 | ||||||||
\(732\) | −8.17028 | −0.301982 | ||||||||
\(733\) | −12.0939 | −0.446699 | −0.223350 | − | 0.974738i | \(-0.571699\pi\) | ||||
−0.223350 | + | 0.974738i | \(0.571699\pi\) | |||||||
\(734\) | 38.2953 | 1.41351 | ||||||||
\(735\) | 46.8220 | 1.72705 | ||||||||
\(736\) | 1.37953 | 0.0508503 | ||||||||
\(737\) | 71.9418 | 2.65001 | ||||||||
\(738\) | 78.8620 | 2.90295 | ||||||||
\(739\) | 52.6129 | 1.93540 | 0.967699 | − | 0.252110i | \(-0.0811243\pi\) | ||||
0.967699 | + | 0.252110i | \(0.0811243\pi\) | |||||||
\(740\) | −1.38506 | −0.0509156 | ||||||||
\(741\) | −12.1673 | −0.446978 | ||||||||
\(742\) | 13.0081 | 0.477542 | ||||||||
\(743\) | −26.3937 | −0.968289 | −0.484145 | − | 0.874988i | \(-0.660869\pi\) | ||||
−0.484145 | + | 0.874988i | \(0.660869\pi\) | |||||||
\(744\) | −22.7771 | −0.835050 | ||||||||
\(745\) | −4.76000 | −0.174393 | ||||||||
\(746\) | −14.0267 | −0.513553 | ||||||||
\(747\) | 67.7442 | 2.47863 | ||||||||
\(748\) | 4.94098 | 0.180660 | ||||||||
\(749\) | −4.50084 | −0.164457 | ||||||||
\(750\) | −4.19172 | −0.153060 | ||||||||
\(751\) | 23.5431 | 0.859099 | 0.429549 | − | 0.903043i | \(-0.358672\pi\) | ||||
0.429549 | + | 0.903043i | \(0.358672\pi\) | |||||||
\(752\) | −26.1388 | −0.953184 | ||||||||
\(753\) | −59.1037 | −2.15386 | ||||||||
\(754\) | 17.1153 | 0.623301 | ||||||||
\(755\) | −7.59676 | −0.276474 | ||||||||
\(756\) | −12.9850 | −0.472261 | ||||||||
\(757\) | −38.4230 | −1.39651 | −0.698255 | − | 0.715849i | \(-0.746040\pi\) | ||||
−0.698255 | + | 0.715849i | \(0.746040\pi\) | |||||||
\(758\) | 36.1997 | 1.31483 | ||||||||
\(759\) | 17.2576 | 0.626410 | ||||||||
\(760\) | −7.03171 | −0.255067 | ||||||||
\(761\) | 48.1681 | 1.74609 | 0.873046 | − | 0.487637i | \(-0.162141\pi\) | ||||
0.873046 | + | 0.487637i | \(0.162141\pi\) | |||||||
\(762\) | −63.0450 | −2.28388 | ||||||||
\(763\) | 4.33058 | 0.156778 | ||||||||
\(764\) | 3.80635 | 0.137709 | ||||||||
\(765\) | 29.8654 | 1.07979 | ||||||||
\(766\) | −16.7788 | −0.606243 | ||||||||
\(767\) | −21.7635 | −0.785834 | ||||||||
\(768\) | 16.8397 | 0.607651 | ||||||||
\(769\) | 21.7647 | 0.784857 | 0.392428 | − | 0.919783i | \(-0.371635\pi\) | ||||
0.392428 | + | 0.919783i | \(0.371635\pi\) | |||||||
\(770\) | −31.4946 | −1.13499 | ||||||||
\(771\) | 55.2510 | 1.98982 | ||||||||
\(772\) | −4.07682 | −0.146728 | ||||||||
\(773\) | 14.7284 | 0.529743 | 0.264872 | − | 0.964284i | \(-0.414670\pi\) | ||||
0.264872 | + | 0.964284i | \(0.414670\pi\) | |||||||
\(774\) | 23.4936 | 0.844461 | ||||||||
\(775\) | 2.44114 | 0.0876883 | ||||||||
\(776\) | −51.5943 | −1.85213 | ||||||||
\(777\) | −90.2347 | −3.23715 | ||||||||
\(778\) | 9.69942 | 0.347741 | ||||||||
\(779\) | −20.3394 | −0.728733 | ||||||||
\(780\) | −1.15914 | −0.0415040 | ||||||||
\(781\) | 42.8669 | 1.53390 | ||||||||
\(782\) | −6.24974 | −0.223490 | ||||||||
\(783\) | 96.8528 | 3.46124 | ||||||||
\(784\) | −52.0288 | −1.85817 | ||||||||
\(785\) | 8.34378 | 0.297802 | ||||||||
\(786\) | −21.1564 | −0.754623 | ||||||||
\(787\) | 0.908663 | 0.0323903 | 0.0161952 | − | 0.999869i | \(-0.494845\pi\) | ||||
0.0161952 | + | 0.999869i | \(0.494845\pi\) | |||||||
\(788\) | 5.45617 | 0.194368 | ||||||||
\(789\) | 30.8381 | 1.09786 | ||||||||
\(790\) | −5.84463 | −0.207943 | ||||||||
\(791\) | −34.8325 | −1.23850 | ||||||||
\(792\) | 103.481 | 3.67702 | ||||||||
\(793\) | −18.7304 | −0.665136 | ||||||||
\(794\) | −20.0633 | −0.712021 | ||||||||
\(795\) | 6.57106 | 0.233052 | ||||||||
\(796\) | −4.18347 | −0.148279 | ||||||||
\(797\) | 0.320200 | 0.0113421 | 0.00567104 | − | 0.999984i | \(-0.498195\pi\) | ||||
0.00567104 | + | 0.999984i | \(0.498195\pi\) | |||||||
\(798\) | −46.5005 | −1.64610 | ||||||||
\(799\) | −32.3327 | −1.14385 | ||||||||
\(800\) | −1.27178 | −0.0449642 | ||||||||
\(801\) | −90.8678 | −3.21066 | ||||||||
\(802\) | −1.33194 | −0.0470323 | ||||||||
\(803\) | 24.3828 | 0.860452 | ||||||||
\(804\) | 10.1192 | 0.356875 | ||||||||
\(805\) | −5.07368 | −0.178824 | ||||||||
\(806\) | −5.30029 | −0.186695 | ||||||||
\(807\) | −15.4179 | −0.542736 | ||||||||
\(808\) | −26.5662 | −0.934596 | ||||||||
\(809\) | 5.59585 | 0.196740 | 0.0983699 | − | 0.995150i | \(-0.468637\pi\) | ||||
0.0983699 | + | 0.995150i | \(0.468637\pi\) | |||||||
\(810\) | 23.9147 | 0.840278 | ||||||||
\(811\) | 0.469348 | 0.0164810 | 0.00824051 | − | 0.999966i | \(-0.497377\pi\) | ||||
0.00824051 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(812\) | −8.33075 | −0.292352 | ||||||||
\(813\) | 24.6616 | 0.864919 | ||||||||
\(814\) | 41.2759 | 1.44672 | ||||||||
\(815\) | 22.7894 | 0.798278 | ||||||||
\(816\) | −47.6069 | −1.66657 | ||||||||
\(817\) | −6.05926 | −0.211987 | ||||||||
\(818\) | 31.4835 | 1.10079 | ||||||||
\(819\) | −52.6425 | −1.83948 | ||||||||
\(820\) | −1.93767 | −0.0676662 | ||||||||
\(821\) | 6.52091 | 0.227581 | 0.113791 | − | 0.993505i | \(-0.463701\pi\) | ||||
0.113791 | + | 0.993505i | \(0.463701\pi\) | |||||||
\(822\) | 74.8860 | 2.61195 | ||||||||
\(823\) | −23.7373 | −0.827430 | −0.413715 | − | 0.910406i | \(-0.635769\pi\) | ||||
−0.413715 | + | 0.910406i | \(0.635769\pi\) | |||||||
\(824\) | −19.4450 | −0.677398 | ||||||||
\(825\) | −15.9096 | −0.553901 | ||||||||
\(826\) | −83.1747 | −2.89402 | ||||||||
\(827\) | 47.1198 | 1.63852 | 0.819259 | − | 0.573424i | \(-0.194385\pi\) | ||||
0.819259 | + | 0.573424i | \(0.194385\pi\) | |||||||
\(828\) | 1.69214 | 0.0588058 | ||||||||
\(829\) | −4.22231 | −0.146647 | −0.0733234 | − | 0.997308i | \(-0.523361\pi\) | ||||
−0.0733234 | + | 0.997308i | \(0.523361\pi\) | |||||||
\(830\) | 13.0691 | 0.453634 | ||||||||
\(831\) | −45.5998 | −1.58184 | ||||||||
\(832\) | 14.1627 | 0.491002 | ||||||||
\(833\) | −64.3575 | −2.22986 | ||||||||
\(834\) | 54.8008 | 1.89760 | ||||||||
\(835\) | 4.11836 | 0.142522 | ||||||||
\(836\) | −2.70906 | −0.0936947 | ||||||||
\(837\) | −29.9936 | −1.03673 | ||||||||
\(838\) | −12.8501 | −0.443898 | ||||||||
\(839\) | 1.91583 | 0.0661419 | 0.0330710 | − | 0.999453i | \(-0.489471\pi\) | ||||
0.0330710 | + | 0.999453i | \(0.489471\pi\) | |||||||
\(840\) | −43.6425 | −1.50581 | ||||||||
\(841\) | 33.1374 | 1.14267 | ||||||||
\(842\) | −14.9208 | −0.514205 | ||||||||
\(843\) | −37.6880 | −1.29804 | ||||||||
\(844\) | −0.548964 | −0.0188961 | ||||||||
\(845\) | 10.3427 | 0.355798 | ||||||||
\(846\) | −68.7349 | −2.36315 | ||||||||
\(847\) | −68.0861 | −2.33947 | ||||||||
\(848\) | −7.30180 | −0.250745 | ||||||||
\(849\) | 0.0226802 | 0.000778383 0 | ||||||||
\(850\) | 5.76158 | 0.197621 | ||||||||
\(851\) | 6.64940 | 0.227939 | ||||||||
\(852\) | 6.02956 | 0.206569 | ||||||||
\(853\) | −0.367949 | −0.0125983 | −0.00629916 | − | 0.999980i | \(-0.502005\pi\) | ||||
−0.00629916 | + | 0.999980i | \(0.502005\pi\) | |||||||
\(854\) | −71.5829 | −2.44952 | ||||||||
\(855\) | −16.3747 | −0.560003 | ||||||||
\(856\) | 2.85292 | 0.0975107 | ||||||||
\(857\) | −1.29518 | −0.0442424 | −0.0221212 | − | 0.999755i | \(-0.507042\pi\) | ||||
−0.0221212 | + | 0.999755i | \(0.507042\pi\) | |||||||
\(858\) | 34.5435 | 1.17929 | ||||||||
\(859\) | −39.6041 | −1.35127 | −0.675637 | − | 0.737235i | \(-0.736131\pi\) | ||||
−0.675637 | + | 0.737235i | \(0.736131\pi\) | |||||||
\(860\) | −0.577246 | −0.0196839 | ||||||||
\(861\) | −126.237 | −4.30213 | ||||||||
\(862\) | −26.4306 | −0.900229 | ||||||||
\(863\) | 3.56282 | 0.121280 | 0.0606398 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606398 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(864\) | 15.6260 | 0.531607 | ||||||||
\(865\) | −6.33232 | −0.215305 | ||||||||
\(866\) | 8.70002 | 0.295639 | ||||||||
\(867\) | −5.38731 | −0.182963 | ||||||||
\(868\) | 2.57988 | 0.0875669 | ||||||||
\(869\) | −22.1832 | −0.752513 | ||||||||
\(870\) | 33.0422 | 1.12024 | ||||||||
\(871\) | 23.1982 | 0.786041 | ||||||||
\(872\) | −2.74499 | −0.0929572 | ||||||||
\(873\) | −120.147 | −4.06637 | ||||||||
\(874\) | 3.42663 | 0.115907 | ||||||||
\(875\) | 4.67738 | 0.158124 | ||||||||
\(876\) | 3.42963 | 0.115877 | ||||||||
\(877\) | 49.2908 | 1.66443 | 0.832216 | − | 0.554451i | \(-0.187072\pi\) | ||||
0.832216 | + | 0.554451i | \(0.187072\pi\) | |||||||
\(878\) | 25.5935 | 0.863738 | ||||||||
\(879\) | −30.0790 | −1.01454 | ||||||||
\(880\) | 17.6788 | 0.595952 | ||||||||
\(881\) | −0.118580 | −0.00399505 | −0.00199753 | − | 0.999998i | \(-0.500636\pi\) | ||||
−0.00199753 | + | 0.999998i | \(0.500636\pi\) | |||||||
\(882\) | −136.815 | −4.60681 | ||||||||
\(883\) | −10.4373 | −0.351242 | −0.175621 | − | 0.984458i | \(-0.556193\pi\) | ||||
−0.175621 | + | 0.984458i | \(0.556193\pi\) | |||||||
\(884\) | 1.59326 | 0.0535871 | ||||||||
\(885\) | −42.0159 | −1.41235 | ||||||||
\(886\) | 2.34919 | 0.0789227 | ||||||||
\(887\) | −23.4582 | −0.787648 | −0.393824 | − | 0.919186i | \(-0.628848\pi\) | ||||
−0.393824 | + | 0.919186i | \(0.628848\pi\) | |||||||
\(888\) | 57.1965 | 1.91939 | ||||||||
\(889\) | 70.3496 | 2.35945 | ||||||||
\(890\) | −17.5300 | −0.587609 | ||||||||
\(891\) | 90.7680 | 3.04084 | ||||||||
\(892\) | −2.57593 | −0.0862485 | ||||||||
\(893\) | 17.7275 | 0.593227 | ||||||||
\(894\) | 19.9526 | 0.667314 | ||||||||
\(895\) | −6.18122 | −0.206615 | ||||||||
\(896\) | 42.2291 | 1.41077 | ||||||||
\(897\) | 5.56484 | 0.185804 | ||||||||
\(898\) | −14.6636 | −0.489331 | ||||||||
\(899\) | −19.2428 | −0.641785 | ||||||||
\(900\) | −1.55997 | −0.0519989 | ||||||||
\(901\) | −9.03203 | −0.300901 | ||||||||
\(902\) | 57.7441 | 1.92267 | ||||||||
\(903\) | −37.6069 | −1.25148 | ||||||||
\(904\) | 22.0790 | 0.734337 | ||||||||
\(905\) | 21.3322 | 0.709108 | ||||||||
\(906\) | 31.8435 | 1.05793 | ||||||||
\(907\) | 27.9135 | 0.926854 | 0.463427 | − | 0.886135i | \(-0.346620\pi\) | ||||
0.463427 | + | 0.886135i | \(0.346620\pi\) | |||||||
\(908\) | 0.541602 | 0.0179737 | ||||||||
\(909\) | −61.8645 | −2.05192 | ||||||||
\(910\) | −10.1557 | −0.336658 | ||||||||
\(911\) | 5.66976 | 0.187847 | 0.0939237 | − | 0.995579i | \(-0.470059\pi\) | ||||
0.0939237 | + | 0.995579i | \(0.470059\pi\) | |||||||
\(912\) | 26.1020 | 0.864325 | ||||||||
\(913\) | 49.6034 | 1.64163 | ||||||||
\(914\) | 25.8374 | 0.854624 | ||||||||
\(915\) | −36.1603 | −1.19542 | ||||||||
\(916\) | −6.16994 | −0.203860 | ||||||||
\(917\) | 23.6076 | 0.779591 | ||||||||
\(918\) | −70.7909 | −2.33645 | ||||||||
\(919\) | 11.4842 | 0.378828 | 0.189414 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189414 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(920\) | 3.21602 | 0.106029 | ||||||||
\(921\) | −19.4423 | −0.640647 | ||||||||
\(922\) | −31.5714 | −1.03975 | ||||||||
\(923\) | 13.8228 | 0.454982 | ||||||||
\(924\) | −16.8138 | −0.553134 | ||||||||
\(925\) | −6.13003 | −0.201554 | ||||||||
\(926\) | 26.3678 | 0.866500 | ||||||||
\(927\) | −45.2814 | −1.48724 | ||||||||
\(928\) | 10.0251 | 0.329090 | ||||||||
\(929\) | 8.31839 | 0.272918 | 0.136459 | − | 0.990646i | \(-0.456428\pi\) | ||||
0.136459 | + | 0.990646i | \(0.456428\pi\) | |||||||
\(930\) | −10.2326 | −0.335539 | ||||||||
\(931\) | 35.2861 | 1.15646 | ||||||||
\(932\) | −5.27798 | −0.172886 | ||||||||
\(933\) | −6.00830 | −0.196703 | ||||||||
\(934\) | −32.9759 | −1.07900 | ||||||||
\(935\) | 21.8680 | 0.715159 | ||||||||
\(936\) | 33.3681 | 1.09067 | ||||||||
\(937\) | 28.1015 | 0.918037 | 0.459019 | − | 0.888427i | \(-0.348201\pi\) | ||||
0.459019 | + | 0.888427i | \(0.348201\pi\) | |||||||
\(938\) | 88.6578 | 2.89478 | ||||||||
\(939\) | 23.0478 | 0.752137 | ||||||||
\(940\) | 1.68884 | 0.0550838 | ||||||||
\(941\) | 46.5808 | 1.51849 | 0.759245 | − | 0.650805i | \(-0.225568\pi\) | ||||
0.759245 | + | 0.650805i | \(0.225568\pi\) | |||||||
\(942\) | −34.9748 | −1.13954 | ||||||||
\(943\) | 9.30239 | 0.302928 | ||||||||
\(944\) | 46.6883 | 1.51957 | ||||||||
\(945\) | −57.4696 | −1.86949 | ||||||||
\(946\) | 17.2024 | 0.559300 | ||||||||
\(947\) | 32.9615 | 1.07111 | 0.535553 | − | 0.844502i | \(-0.320103\pi\) | ||||
0.535553 | + | 0.844502i | \(0.320103\pi\) | |||||||
\(948\) | −3.12023 | −0.101340 | ||||||||
\(949\) | 7.86244 | 0.255226 | ||||||||
\(950\) | −3.15898 | −0.102491 | ||||||||
\(951\) | −4.93709 | −0.160096 | ||||||||
\(952\) | 59.9872 | 1.94420 | ||||||||
\(953\) | −29.7819 | −0.964729 | −0.482365 | − | 0.875971i | \(-0.660222\pi\) | ||||
−0.482365 | + | 0.875971i | \(0.660222\pi\) | |||||||
\(954\) | −19.2009 | −0.621651 | ||||||||
\(955\) | 16.8463 | 0.545133 | ||||||||
\(956\) | −6.15739 | −0.199144 | ||||||||
\(957\) | 125.411 | 4.05396 | ||||||||
\(958\) | −19.3154 | −0.624054 | ||||||||
\(959\) | −83.5624 | −2.69837 | ||||||||
\(960\) | 27.3420 | 0.882460 | ||||||||
\(961\) | −25.0408 | −0.807769 | ||||||||
\(962\) | 13.3097 | 0.429123 | ||||||||
\(963\) | 6.64357 | 0.214086 | ||||||||
\(964\) | −3.17118 | −0.102137 | ||||||||
\(965\) | −18.0433 | −0.580836 | ||||||||
\(966\) | 21.2674 | 0.684268 | ||||||||
\(967\) | −7.62327 | −0.245148 | −0.122574 | − | 0.992459i | \(-0.539115\pi\) | ||||
−0.122574 | + | 0.992459i | \(0.539115\pi\) | |||||||
\(968\) | 43.1573 | 1.38713 | ||||||||
\(969\) | 32.2872 | 1.03721 | ||||||||
\(970\) | −23.1786 | −0.744220 | ||||||||
\(971\) | 19.5160 | 0.626298 | 0.313149 | − | 0.949704i | \(-0.398616\pi\) | ||||
0.313149 | + | 0.949704i | \(0.398616\pi\) | |||||||
\(972\) | 4.43880 | 0.142375 | ||||||||
\(973\) | −61.1501 | −1.96038 | ||||||||
\(974\) | −44.3609 | −1.42141 | ||||||||
\(975\) | −5.13017 | −0.164297 | ||||||||
\(976\) | 40.1815 | 1.28618 | ||||||||
\(977\) | 27.4804 | 0.879176 | 0.439588 | − | 0.898200i | \(-0.355125\pi\) | ||||
0.439588 | + | 0.898200i | \(0.355125\pi\) | |||||||
\(978\) | −95.5267 | −3.05461 | ||||||||
\(979\) | −66.5350 | −2.12647 | ||||||||
\(980\) | 3.36160 | 0.107382 | ||||||||
\(981\) | −6.39225 | −0.204089 | ||||||||
\(982\) | −25.9789 | −0.829021 | ||||||||
\(983\) | −17.4876 | −0.557769 | −0.278884 | − | 0.960325i | \(-0.589965\pi\) | ||||
−0.278884 | + | 0.960325i | \(0.589965\pi\) | |||||||
\(984\) | 80.0167 | 2.55084 | ||||||||
\(985\) | 24.1481 | 0.769422 | ||||||||
\(986\) | −45.4170 | −1.44637 | ||||||||
\(987\) | 110.026 | 3.50216 | ||||||||
\(988\) | −0.873557 | −0.0277915 | ||||||||
\(989\) | 2.77126 | 0.0881209 | ||||||||
\(990\) | 46.4884 | 1.47750 | ||||||||
\(991\) | −3.09511 | −0.0983195 | −0.0491598 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491598 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(992\) | −3.10459 | −0.0985709 | ||||||||
\(993\) | 107.848 | 3.42245 | ||||||||
\(994\) | 52.8273 | 1.67558 | ||||||||
\(995\) | −18.5154 | −0.586976 | ||||||||
\(996\) | 6.97710 | 0.221078 | ||||||||
\(997\) | −18.9149 | −0.599041 | −0.299521 | − | 0.954090i | \(-0.596827\pi\) | ||||
−0.299521 | + | 0.954090i | \(0.596827\pi\) | |||||||
\(998\) | 29.0612 | 0.919915 | ||||||||
\(999\) | 75.3178 | 2.38295 |
(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 | 2005.2.a.f.1.9 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2005.2.a.f.1.9 | ✓ | 37 | 1.1 | even | 1 | trivial |