Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −1.86236 | −1.07523 | −0.537616 | − | 0.843190i | \(-0.680675\pi\) | ||||
−0.537616 | + | 0.843190i | \(0.680675\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.878383 | −0.392825 | −0.196412 | − | 0.980521i | \(-0.562929\pi\) | ||||
−0.196412 | + | 0.980521i | \(0.562929\pi\) | |||||||
\(6\) | −1.86236 | −0.760303 | ||||||||
\(7\) | 0.141603 | 0.0535210 | 0.0267605 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267605 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.468368 | 0.156123 | ||||||||
\(10\) | −0.878383 | −0.277769 | ||||||||
\(11\) | −3.52538 | −1.06294 | −0.531471 | − | 0.847076i | \(-0.678361\pi\) | ||||
−0.531471 | + | 0.847076i | \(0.678361\pi\) | |||||||
\(12\) | −1.86236 | −0.537616 | ||||||||
\(13\) | 0.284387 | 0.0788747 | 0.0394373 | − | 0.999222i | \(-0.487443\pi\) | ||||
0.0394373 | + | 0.999222i | \(0.487443\pi\) | |||||||
\(14\) | 0.141603 | 0.0378450 | ||||||||
\(15\) | 1.63586 | 0.422378 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.97859 | 1.20749 | 0.603743 | − | 0.797179i | \(-0.293675\pi\) | ||||
0.603743 | + | 0.797179i | \(0.293675\pi\) | |||||||
\(18\) | 0.468368 | 0.110395 | ||||||||
\(19\) | −5.84511 | −1.34096 | −0.670480 | − | 0.741927i | \(-0.733912\pi\) | ||||
−0.670480 | + | 0.741927i | \(0.733912\pi\) | |||||||
\(20\) | −0.878383 | −0.196412 | ||||||||
\(21\) | −0.263716 | −0.0575474 | ||||||||
\(22\) | −3.52538 | −0.751614 | ||||||||
\(23\) | 2.56520 | 0.534882 | 0.267441 | − | 0.963574i | \(-0.413822\pi\) | ||||
0.267441 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(24\) | −1.86236 | −0.380152 | ||||||||
\(25\) | −4.22844 | −0.845689 | ||||||||
\(26\) | 0.284387 | 0.0557728 | ||||||||
\(27\) | 4.71480 | 0.907363 | ||||||||
\(28\) | 0.141603 | 0.0267605 | ||||||||
\(29\) | 7.07784 | 1.31432 | 0.657161 | − | 0.753750i | \(-0.271757\pi\) | ||||
0.657161 | + | 0.753750i | \(0.271757\pi\) | |||||||
\(30\) | 1.63586 | 0.298666 | ||||||||
\(31\) | 9.16073 | 1.64532 | 0.822658 | − | 0.568536i | \(-0.192490\pi\) | ||||
0.822658 | + | 0.568536i | \(0.192490\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.56551 | 1.14291 | ||||||||
\(34\) | 4.97859 | 0.853822 | ||||||||
\(35\) | −0.124382 | −0.0210244 | ||||||||
\(36\) | 0.468368 | 0.0780614 | ||||||||
\(37\) | −3.98793 | −0.655611 | −0.327805 | − | 0.944745i | \(-0.606309\pi\) | ||||
−0.327805 | + | 0.944745i | \(0.606309\pi\) | |||||||
\(38\) | −5.84511 | −0.948202 | ||||||||
\(39\) | −0.529629 | −0.0848085 | ||||||||
\(40\) | −0.878383 | −0.138885 | ||||||||
\(41\) | −3.25631 | −0.508550 | −0.254275 | − | 0.967132i | \(-0.581837\pi\) | ||||
−0.254275 | + | 0.967132i | \(0.581837\pi\) | |||||||
\(42\) | −0.263716 | −0.0406922 | ||||||||
\(43\) | −0.968504 | −0.147696 | −0.0738478 | − | 0.997270i | \(-0.523528\pi\) | ||||
−0.0738478 | + | 0.997270i | \(0.523528\pi\) | |||||||
\(44\) | −3.52538 | −0.531471 | ||||||||
\(45\) | −0.411407 | −0.0613289 | ||||||||
\(46\) | 2.56520 | 0.378218 | ||||||||
\(47\) | 4.49473 | 0.655623 | 0.327812 | − | 0.944743i | \(-0.393689\pi\) | ||||
0.327812 | + | 0.944743i | \(0.393689\pi\) | |||||||
\(48\) | −1.86236 | −0.268808 | ||||||||
\(49\) | −6.97995 | −0.997136 | ||||||||
\(50\) | −4.22844 | −0.597992 | ||||||||
\(51\) | −9.27191 | −1.29833 | ||||||||
\(52\) | 0.284387 | 0.0394373 | ||||||||
\(53\) | 2.63159 | 0.361477 | 0.180739 | − | 0.983531i | \(-0.442151\pi\) | ||||
0.180739 | + | 0.983531i | \(0.442151\pi\) | |||||||
\(54\) | 4.71480 | 0.641603 | ||||||||
\(55\) | 3.09664 | 0.417550 | ||||||||
\(56\) | 0.141603 | 0.0189225 | ||||||||
\(57\) | 10.8857 | 1.44184 | ||||||||
\(58\) | 7.07784 | 0.929366 | ||||||||
\(59\) | −11.8218 | −1.53906 | −0.769531 | − | 0.638609i | \(-0.779510\pi\) | ||||
−0.769531 | + | 0.638609i | \(0.779510\pi\) | |||||||
\(60\) | 1.63586 | 0.211189 | ||||||||
\(61\) | 0.646205 | 0.0827380 | 0.0413690 | − | 0.999144i | \(-0.486828\pi\) | ||||
0.0413690 | + | 0.999144i | \(0.486828\pi\) | |||||||
\(62\) | 9.16073 | 1.16341 | ||||||||
\(63\) | 0.0663224 | 0.00835584 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.249801 | −0.0309839 | ||||||||
\(66\) | 6.56551 | 0.808159 | ||||||||
\(67\) | 13.2199 | 1.61507 | 0.807533 | − | 0.589822i | \(-0.200802\pi\) | ||||
0.807533 | + | 0.589822i | \(0.200802\pi\) | |||||||
\(68\) | 4.97859 | 0.603743 | ||||||||
\(69\) | −4.77732 | −0.575122 | ||||||||
\(70\) | −0.124382 | −0.0148665 | ||||||||
\(71\) | 11.0119 | 1.30687 | 0.653436 | − | 0.756981i | \(-0.273327\pi\) | ||||
0.653436 | + | 0.756981i | \(0.273327\pi\) | |||||||
\(72\) | 0.468368 | 0.0551977 | ||||||||
\(73\) | 5.90064 | 0.690618 | 0.345309 | − | 0.938489i | \(-0.387774\pi\) | ||||
0.345309 | + | 0.938489i | \(0.387774\pi\) | |||||||
\(74\) | −3.98793 | −0.463587 | ||||||||
\(75\) | 7.87486 | 0.909311 | ||||||||
\(76\) | −5.84511 | −0.670480 | ||||||||
\(77\) | −0.499205 | −0.0568897 | ||||||||
\(78\) | −0.529629 | −0.0599687 | ||||||||
\(79\) | −4.49078 | −0.505252 | −0.252626 | − | 0.967564i | \(-0.581294\pi\) | ||||
−0.252626 | + | 0.967564i | \(0.581294\pi\) | |||||||
\(80\) | −0.878383 | −0.0982062 | ||||||||
\(81\) | −10.1857 | −1.13175 | ||||||||
\(82\) | −3.25631 | −0.359599 | ||||||||
\(83\) | −14.8597 | −1.63107 | −0.815533 | − | 0.578710i | \(-0.803556\pi\) | ||||
−0.815533 | + | 0.578710i | \(0.803556\pi\) | |||||||
\(84\) | −0.263716 | −0.0287737 | ||||||||
\(85\) | −4.37311 | −0.474331 | ||||||||
\(86\) | −0.968504 | −0.104437 | ||||||||
\(87\) | −13.1815 | −1.41320 | ||||||||
\(88\) | −3.52538 | −0.375807 | ||||||||
\(89\) | −11.9727 | −1.26910 | −0.634550 | − | 0.772882i | \(-0.718814\pi\) | ||||
−0.634550 | + | 0.772882i | \(0.718814\pi\) | |||||||
\(90\) | −0.411407 | −0.0433661 | ||||||||
\(91\) | 0.0402701 | 0.00422145 | ||||||||
\(92\) | 2.56520 | 0.267441 | ||||||||
\(93\) | −17.0605 | −1.76910 | ||||||||
\(94\) | 4.49473 | 0.463596 | ||||||||
\(95\) | 5.13425 | 0.526763 | ||||||||
\(96\) | −1.86236 | −0.190076 | ||||||||
\(97\) | 7.98287 | 0.810538 | 0.405269 | − | 0.914198i | \(-0.367178\pi\) | ||||
0.405269 | + | 0.914198i | \(0.367178\pi\) | |||||||
\(98\) | −6.97995 | −0.705081 | ||||||||
\(99\) | −1.65118 | −0.165950 | ||||||||
\(100\) | −4.22844 | −0.422844 | ||||||||
\(101\) | −11.6296 | −1.15719 | −0.578595 | − | 0.815615i | \(-0.696399\pi\) | ||||
−0.578595 | + | 0.815615i | \(0.696399\pi\) | |||||||
\(102\) | −9.27191 | −0.918056 | ||||||||
\(103\) | 5.86002 | 0.577405 | 0.288702 | − | 0.957419i | \(-0.406776\pi\) | ||||
0.288702 | + | 0.957419i | \(0.406776\pi\) | |||||||
\(104\) | 0.284387 | 0.0278864 | ||||||||
\(105\) | 0.231643 | 0.0226061 | ||||||||
\(106\) | 2.63159 | 0.255603 | ||||||||
\(107\) | −0.654070 | −0.0632313 | −0.0316157 | − | 0.999500i | \(-0.510065\pi\) | ||||
−0.0316157 | + | 0.999500i | \(0.510065\pi\) | |||||||
\(108\) | 4.71480 | 0.453682 | ||||||||
\(109\) | 1.24286 | 0.119044 | 0.0595220 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595220 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(110\) | 3.09664 | 0.295253 | ||||||||
\(111\) | 7.42694 | 0.704934 | ||||||||
\(112\) | 0.141603 | 0.0133802 | ||||||||
\(113\) | −6.47849 | −0.609445 | −0.304723 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304723 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(114\) | 10.8857 | 1.01954 | ||||||||
\(115\) | −2.25323 | −0.210115 | ||||||||
\(116\) | 7.07784 | 0.657161 | ||||||||
\(117\) | 0.133198 | 0.0123141 | ||||||||
\(118\) | −11.8218 | −1.08828 | ||||||||
\(119\) | 0.704985 | 0.0646258 | ||||||||
\(120\) | 1.63586 | 0.149333 | ||||||||
\(121\) | 1.42831 | 0.129847 | ||||||||
\(122\) | 0.646205 | 0.0585046 | ||||||||
\(123\) | 6.06441 | 0.546809 | ||||||||
\(124\) | 9.16073 | 0.822658 | ||||||||
\(125\) | 8.10611 | 0.725033 | ||||||||
\(126\) | 0.0663224 | 0.00590847 | ||||||||
\(127\) | −5.90292 | −0.523799 | −0.261900 | − | 0.965095i | \(-0.584349\pi\) | ||||
−0.261900 | + | 0.965095i | \(0.584349\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.80370 | 0.158807 | ||||||||
\(130\) | −0.249801 | −0.0219090 | ||||||||
\(131\) | 13.4225 | 1.17273 | 0.586366 | − | 0.810046i | \(-0.300558\pi\) | ||||
0.586366 | + | 0.810046i | \(0.300558\pi\) | |||||||
\(132\) | 6.56551 | 0.571455 | ||||||||
\(133\) | −0.827686 | −0.0717695 | ||||||||
\(134\) | 13.2199 | 1.14202 | ||||||||
\(135\) | −4.14140 | −0.356435 | ||||||||
\(136\) | 4.97859 | 0.426911 | ||||||||
\(137\) | 4.17159 | 0.356403 | 0.178201 | − | 0.983994i | \(-0.442972\pi\) | ||||
0.178201 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(138\) | −4.77732 | −0.406672 | ||||||||
\(139\) | −12.2987 | −1.04316 | −0.521581 | − | 0.853202i | \(-0.674658\pi\) | ||||
−0.521581 | + | 0.853202i | \(0.674658\pi\) | |||||||
\(140\) | −0.124382 | −0.0105122 | ||||||||
\(141\) | −8.37078 | −0.704947 | ||||||||
\(142\) | 11.0119 | 0.924099 | ||||||||
\(143\) | −1.00257 | −0.0838392 | ||||||||
\(144\) | 0.468368 | 0.0390307 | ||||||||
\(145\) | −6.21706 | −0.516299 | ||||||||
\(146\) | 5.90064 | 0.488341 | ||||||||
\(147\) | 12.9991 | 1.07215 | ||||||||
\(148\) | −3.98793 | −0.327805 | ||||||||
\(149\) | −15.4457 | −1.26536 | −0.632682 | − | 0.774412i | \(-0.718046\pi\) | ||||
−0.632682 | + | 0.774412i | \(0.718046\pi\) | |||||||
\(150\) | 7.87486 | 0.642980 | ||||||||
\(151\) | −9.89714 | −0.805418 | −0.402709 | − | 0.915328i | \(-0.631931\pi\) | ||||
−0.402709 | + | 0.915328i | \(0.631931\pi\) | |||||||
\(152\) | −5.84511 | −0.474101 | ||||||||
\(153\) | 2.33181 | 0.188516 | ||||||||
\(154\) | −0.499205 | −0.0402271 | ||||||||
\(155\) | −8.04664 | −0.646321 | ||||||||
\(156\) | −0.529629 | −0.0424043 | ||||||||
\(157\) | −18.7245 | −1.49437 | −0.747187 | − | 0.664614i | \(-0.768596\pi\) | ||||
−0.747187 | + | 0.664614i | \(0.768596\pi\) | |||||||
\(158\) | −4.49078 | −0.357267 | ||||||||
\(159\) | −4.90096 | −0.388672 | ||||||||
\(160\) | −0.878383 | −0.0694423 | ||||||||
\(161\) | 0.363241 | 0.0286274 | ||||||||
\(162\) | −10.1857 | −0.800267 | ||||||||
\(163\) | 8.96605 | 0.702275 | 0.351138 | − | 0.936324i | \(-0.385795\pi\) | ||||
0.351138 | + | 0.936324i | \(0.385795\pi\) | |||||||
\(164\) | −3.25631 | −0.254275 | ||||||||
\(165\) | −5.76704 | −0.448963 | ||||||||
\(166\) | −14.8597 | −1.15334 | ||||||||
\(167\) | −12.1450 | −0.939807 | −0.469904 | − | 0.882718i | \(-0.655711\pi\) | ||||
−0.469904 | + | 0.882718i | \(0.655711\pi\) | |||||||
\(168\) | −0.263716 | −0.0203461 | ||||||||
\(169\) | −12.9191 | −0.993779 | ||||||||
\(170\) | −4.37311 | −0.335402 | ||||||||
\(171\) | −2.73766 | −0.209354 | ||||||||
\(172\) | −0.968504 | −0.0738478 | ||||||||
\(173\) | −1.44330 | −0.109732 | −0.0548662 | − | 0.998494i | \(-0.517473\pi\) | ||||
−0.0548662 | + | 0.998494i | \(0.517473\pi\) | |||||||
\(174\) | −13.1815 | −0.999284 | ||||||||
\(175\) | −0.598761 | −0.0452621 | ||||||||
\(176\) | −3.52538 | −0.265736 | ||||||||
\(177\) | 22.0163 | 1.65485 | ||||||||
\(178\) | −11.9727 | −0.897389 | ||||||||
\(179\) | −4.37680 | −0.327137 | −0.163569 | − | 0.986532i | \(-0.552301\pi\) | ||||
−0.163569 | + | 0.986532i | \(0.552301\pi\) | |||||||
\(180\) | −0.411407 | −0.0306645 | ||||||||
\(181\) | −23.9988 | −1.78382 | −0.891910 | − | 0.452214i | \(-0.850634\pi\) | ||||
−0.891910 | + | 0.452214i | \(0.850634\pi\) | |||||||
\(182\) | 0.0402701 | 0.00298502 | ||||||||
\(183\) | −1.20346 | −0.0889626 | ||||||||
\(184\) | 2.56520 | 0.189109 | ||||||||
\(185\) | 3.50293 | 0.257540 | ||||||||
\(186\) | −17.0605 | −1.25094 | ||||||||
\(187\) | −17.5514 | −1.28349 | ||||||||
\(188\) | 4.49473 | 0.327812 | ||||||||
\(189\) | 0.667631 | 0.0485630 | ||||||||
\(190\) | 5.13425 | 0.372478 | ||||||||
\(191\) | 10.5894 | 0.766221 | 0.383110 | − | 0.923703i | \(-0.374853\pi\) | ||||
0.383110 | + | 0.923703i | \(0.374853\pi\) | |||||||
\(192\) | −1.86236 | −0.134404 | ||||||||
\(193\) | −8.01743 | −0.577108 | −0.288554 | − | 0.957464i | \(-0.593174\pi\) | ||||
−0.288554 | + | 0.957464i | \(0.593174\pi\) | |||||||
\(194\) | 7.98287 | 0.573137 | ||||||||
\(195\) | 0.465217 | 0.0333149 | ||||||||
\(196\) | −6.97995 | −0.498568 | ||||||||
\(197\) | −16.6672 | −1.18749 | −0.593744 | − | 0.804654i | \(-0.702351\pi\) | ||||
−0.593744 | + | 0.804654i | \(0.702351\pi\) | |||||||
\(198\) | −1.65118 | −0.117344 | ||||||||
\(199\) | 26.9698 | 1.91184 | 0.955919 | − | 0.293631i | \(-0.0948636\pi\) | ||||
0.955919 | + | 0.293631i | \(0.0948636\pi\) | |||||||
\(200\) | −4.22844 | −0.298996 | ||||||||
\(201\) | −24.6201 | −1.73657 | ||||||||
\(202\) | −11.6296 | −0.818257 | ||||||||
\(203\) | 1.00225 | 0.0703438 | ||||||||
\(204\) | −9.27191 | −0.649164 | ||||||||
\(205\) | 2.86029 | 0.199771 | ||||||||
\(206\) | 5.86002 | 0.408287 | ||||||||
\(207\) | 1.20146 | 0.0835072 | ||||||||
\(208\) | 0.284387 | 0.0197187 | ||||||||
\(209\) | 20.6062 | 1.42536 | ||||||||
\(210\) | 0.231643 | 0.0159849 | ||||||||
\(211\) | −22.0766 | −1.51982 | −0.759910 | − | 0.650029i | \(-0.774757\pi\) | ||||
−0.759910 | + | 0.650029i | \(0.774757\pi\) | |||||||
\(212\) | 2.63159 | 0.180739 | ||||||||
\(213\) | −20.5081 | −1.40519 | ||||||||
\(214\) | −0.654070 | −0.0447113 | ||||||||
\(215\) | 0.850718 | 0.0580185 | ||||||||
\(216\) | 4.71480 | 0.320801 | ||||||||
\(217\) | 1.29719 | 0.0880589 | ||||||||
\(218\) | 1.24286 | 0.0841768 | ||||||||
\(219\) | −10.9891 | −0.742574 | ||||||||
\(220\) | 3.09664 | 0.208775 | ||||||||
\(221\) | 1.41585 | 0.0952401 | ||||||||
\(222\) | 7.42694 | 0.498463 | ||||||||
\(223\) | −9.63646 | −0.645305 | −0.322653 | − | 0.946517i | \(-0.604575\pi\) | ||||
−0.322653 | + | 0.946517i | \(0.604575\pi\) | |||||||
\(224\) | 0.141603 | 0.00946126 | ||||||||
\(225\) | −1.98047 | −0.132031 | ||||||||
\(226\) | −6.47849 | −0.430943 | ||||||||
\(227\) | 17.6804 | 1.17349 | 0.586744 | − | 0.809773i | \(-0.300410\pi\) | ||||
0.586744 | + | 0.809773i | \(0.300410\pi\) | |||||||
\(228\) | 10.8857 | 0.720921 | ||||||||
\(229\) | −0.450830 | −0.0297917 | −0.0148958 | − | 0.999889i | \(-0.504742\pi\) | ||||
−0.0148958 | + | 0.999889i | \(0.504742\pi\) | |||||||
\(230\) | −2.25323 | −0.148574 | ||||||||
\(231\) | 0.929698 | 0.0611696 | ||||||||
\(232\) | 7.07784 | 0.464683 | ||||||||
\(233\) | −0.302059 | −0.0197886 | −0.00989428 | − | 0.999951i | \(-0.503149\pi\) | ||||
−0.00989428 | + | 0.999951i | \(0.503149\pi\) | |||||||
\(234\) | 0.133198 | 0.00870741 | ||||||||
\(235\) | −3.94809 | −0.257545 | ||||||||
\(236\) | −11.8218 | −0.769531 | ||||||||
\(237\) | 8.36343 | 0.543263 | ||||||||
\(238\) | 0.704985 | 0.0456974 | ||||||||
\(239\) | 3.38848 | 0.219183 | 0.109591 | − | 0.993977i | \(-0.465046\pi\) | ||||
0.109591 | + | 0.993977i | \(0.465046\pi\) | |||||||
\(240\) | 1.63586 | 0.105594 | ||||||||
\(241\) | 18.1980 | 1.17224 | 0.586118 | − | 0.810226i | \(-0.300656\pi\) | ||||
0.586118 | + | 0.810226i | \(0.300656\pi\) | |||||||
\(242\) | 1.42831 | 0.0918155 | ||||||||
\(243\) | 4.82507 | 0.309528 | ||||||||
\(244\) | 0.646205 | 0.0413690 | ||||||||
\(245\) | 6.13107 | 0.391700 | ||||||||
\(246\) | 6.06441 | 0.386652 | ||||||||
\(247\) | −1.66227 | −0.105768 | ||||||||
\(248\) | 9.16073 | 0.581707 | ||||||||
\(249\) | 27.6741 | 1.75377 | ||||||||
\(250\) | 8.10611 | 0.512675 | ||||||||
\(251\) | 23.2298 | 1.46625 | 0.733127 | − | 0.680092i | \(-0.238060\pi\) | ||||
0.733127 | + | 0.680092i | \(0.238060\pi\) | |||||||
\(252\) | 0.0663224 | 0.00417792 | ||||||||
\(253\) | −9.04332 | −0.568548 | ||||||||
\(254\) | −5.90292 | −0.370382 | ||||||||
\(255\) | 8.14429 | 0.510015 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.8328 | 1.29952 | 0.649758 | − | 0.760141i | \(-0.274870\pi\) | ||||
0.649758 | + | 0.760141i | \(0.274870\pi\) | |||||||
\(258\) | 1.80370 | 0.112293 | ||||||||
\(259\) | −0.564703 | −0.0350889 | ||||||||
\(260\) | −0.249801 | −0.0154920 | ||||||||
\(261\) | 3.31504 | 0.205196 | ||||||||
\(262\) | 13.4225 | 0.829247 | ||||||||
\(263\) | 0.718720 | 0.0443182 | 0.0221591 | − | 0.999754i | \(-0.492946\pi\) | ||||
0.0221591 | + | 0.999754i | \(0.492946\pi\) | |||||||
\(264\) | 6.56551 | 0.404079 | ||||||||
\(265\) | −2.31155 | −0.141997 | ||||||||
\(266\) | −0.827686 | −0.0507487 | ||||||||
\(267\) | 22.2974 | 1.36458 | ||||||||
\(268\) | 13.2199 | 0.807533 | ||||||||
\(269\) | −20.3809 | −1.24264 | −0.621322 | − | 0.783555i | \(-0.713404\pi\) | ||||
−0.621322 | + | 0.783555i | \(0.713404\pi\) | |||||||
\(270\) | −4.14140 | −0.252038 | ||||||||
\(271\) | −28.1812 | −1.71189 | −0.855943 | − | 0.517070i | \(-0.827023\pi\) | ||||
−0.855943 | + | 0.517070i | \(0.827023\pi\) | |||||||
\(272\) | 4.97859 | 0.301872 | ||||||||
\(273\) | −0.0749972 | −0.00453904 | ||||||||
\(274\) | 4.17159 | 0.252015 | ||||||||
\(275\) | 14.9069 | 0.898918 | ||||||||
\(276\) | −4.77732 | −0.287561 | ||||||||
\(277\) | 12.0953 | 0.726734 | 0.363367 | − | 0.931646i | \(-0.381627\pi\) | ||||
0.363367 | + | 0.931646i | \(0.381627\pi\) | |||||||
\(278\) | −12.2987 | −0.737627 | ||||||||
\(279\) | 4.29060 | 0.256871 | ||||||||
\(280\) | −0.124382 | −0.00743324 | ||||||||
\(281\) | −30.1348 | −1.79769 | −0.898846 | − | 0.438265i | \(-0.855593\pi\) | ||||
−0.898846 | + | 0.438265i | \(0.855593\pi\) | |||||||
\(282\) | −8.37078 | −0.498473 | ||||||||
\(283\) | 15.1822 | 0.902490 | 0.451245 | − | 0.892400i | \(-0.350980\pi\) | ||||
0.451245 | + | 0.892400i | \(0.350980\pi\) | |||||||
\(284\) | 11.0119 | 0.653436 | ||||||||
\(285\) | −9.56180 | −0.566392 | ||||||||
\(286\) | −1.00257 | −0.0592833 | ||||||||
\(287\) | −0.461104 | −0.0272181 | ||||||||
\(288\) | 0.468368 | 0.0275989 | ||||||||
\(289\) | 7.78638 | 0.458023 | ||||||||
\(290\) | −6.21706 | −0.365078 | ||||||||
\(291\) | −14.8669 | −0.871515 | ||||||||
\(292\) | 5.90064 | 0.345309 | ||||||||
\(293\) | 20.7875 | 1.21442 | 0.607209 | − | 0.794542i | \(-0.292289\pi\) | ||||
0.607209 | + | 0.794542i | \(0.292289\pi\) | |||||||
\(294\) | 12.9991 | 0.758126 | ||||||||
\(295\) | 10.3840 | 0.604582 | ||||||||
\(296\) | −3.98793 | −0.231793 | ||||||||
\(297\) | −16.6215 | −0.964475 | ||||||||
\(298\) | −15.4457 | −0.894747 | ||||||||
\(299\) | 0.729509 | 0.0421886 | ||||||||
\(300\) | 7.87486 | 0.454655 | ||||||||
\(301\) | −0.137143 | −0.00790481 | ||||||||
\(302\) | −9.89714 | −0.569517 | ||||||||
\(303\) | 21.6585 | 1.24425 | ||||||||
\(304\) | −5.84511 | −0.335240 | ||||||||
\(305\) | −0.567616 | −0.0325016 | ||||||||
\(306\) | 2.33181 | 0.133301 | ||||||||
\(307\) | 6.97316 | 0.397979 | 0.198990 | − | 0.980002i | \(-0.436234\pi\) | ||||
0.198990 | + | 0.980002i | \(0.436234\pi\) | |||||||
\(308\) | −0.499205 | −0.0284449 | ||||||||
\(309\) | −10.9134 | −0.620844 | ||||||||
\(310\) | −8.04664 | −0.457018 | ||||||||
\(311\) | −8.73597 | −0.495371 | −0.247686 | − | 0.968840i | \(-0.579670\pi\) | ||||
−0.247686 | + | 0.968840i | \(0.579670\pi\) | |||||||
\(312\) | −0.529629 | −0.0299843 | ||||||||
\(313\) | 10.0540 | 0.568284 | 0.284142 | − | 0.958782i | \(-0.408291\pi\) | ||||
0.284142 | + | 0.958782i | \(0.408291\pi\) | |||||||
\(314\) | −18.7245 | −1.05668 | ||||||||
\(315\) | −0.0582565 | −0.00328238 | ||||||||
\(316\) | −4.49078 | −0.252626 | ||||||||
\(317\) | −17.8156 | −1.00062 | −0.500311 | − | 0.865845i | \(-0.666781\pi\) | ||||
−0.500311 | + | 0.865845i | \(0.666781\pi\) | |||||||
\(318\) | −4.90096 | −0.274832 | ||||||||
\(319\) | −24.9521 | −1.39705 | ||||||||
\(320\) | −0.878383 | −0.0491031 | ||||||||
\(321\) | 1.21811 | 0.0679883 | ||||||||
\(322\) | 0.363241 | 0.0202426 | ||||||||
\(323\) | −29.1004 | −1.61919 | ||||||||
\(324\) | −10.1857 | −0.565874 | ||||||||
\(325\) | −1.20251 | −0.0667034 | ||||||||
\(326\) | 8.96605 | 0.496584 | ||||||||
\(327\) | −2.31464 | −0.128000 | ||||||||
\(328\) | −3.25631 | −0.179800 | ||||||||
\(329\) | 0.636468 | 0.0350896 | ||||||||
\(330\) | −5.76704 | −0.317465 | ||||||||
\(331\) | −0.772988 | −0.0424872 | −0.0212436 | − | 0.999774i | \(-0.506763\pi\) | ||||
−0.0212436 | + | 0.999774i | \(0.506763\pi\) | |||||||
\(332\) | −14.8597 | −0.815533 | ||||||||
\(333\) | −1.86782 | −0.102356 | ||||||||
\(334\) | −12.1450 | −0.664544 | ||||||||
\(335\) | −11.6121 | −0.634438 | ||||||||
\(336\) | −0.263716 | −0.0143869 | ||||||||
\(337\) | −11.7517 | −0.640154 | −0.320077 | − | 0.947391i | \(-0.603709\pi\) | ||||
−0.320077 | + | 0.947391i | \(0.603709\pi\) | |||||||
\(338\) | −12.9191 | −0.702708 | ||||||||
\(339\) | 12.0653 | 0.655295 | ||||||||
\(340\) | −4.37311 | −0.237165 | ||||||||
\(341\) | −32.2951 | −1.74888 | ||||||||
\(342\) | −2.73766 | −0.148036 | ||||||||
\(343\) | −1.97961 | −0.106889 | ||||||||
\(344\) | −0.968504 | −0.0522183 | ||||||||
\(345\) | 4.19632 | 0.225922 | ||||||||
\(346\) | −1.44330 | −0.0775925 | ||||||||
\(347\) | 36.6012 | 1.96486 | 0.982428 | − | 0.186644i | \(-0.0597610\pi\) | ||||
0.982428 | + | 0.186644i | \(0.0597610\pi\) | |||||||
\(348\) | −13.1815 | −0.706600 | ||||||||
\(349\) | −34.0850 | −1.82453 | −0.912265 | − | 0.409602i | \(-0.865668\pi\) | ||||
−0.912265 | + | 0.409602i | \(0.865668\pi\) | |||||||
\(350\) | −0.598761 | −0.0320051 | ||||||||
\(351\) | 1.34083 | 0.0715680 | ||||||||
\(352\) | −3.52538 | −0.187903 | ||||||||
\(353\) | −3.87943 | −0.206481 | −0.103241 | − | 0.994656i | \(-0.532921\pi\) | ||||
−0.103241 | + | 0.994656i | \(0.532921\pi\) | |||||||
\(354\) | 22.0163 | 1.17015 | ||||||||
\(355\) | −9.67268 | −0.513372 | ||||||||
\(356\) | −11.9727 | −0.634550 | ||||||||
\(357\) | −1.31293 | −0.0694877 | ||||||||
\(358\) | −4.37680 | −0.231321 | ||||||||
\(359\) | −1.45585 | −0.0768366 | −0.0384183 | − | 0.999262i | \(-0.512232\pi\) | ||||
−0.0384183 | + | 0.999262i | \(0.512232\pi\) | |||||||
\(360\) | −0.411407 | −0.0216830 | ||||||||
\(361\) | 15.1653 | 0.798175 | ||||||||
\(362\) | −23.9988 | −1.26135 | ||||||||
\(363\) | −2.66003 | −0.139615 | ||||||||
\(364\) | 0.0402701 | 0.00211072 | ||||||||
\(365\) | −5.18303 | −0.271292 | ||||||||
\(366\) | −1.20346 | −0.0629060 | ||||||||
\(367\) | −33.4927 | −1.74831 | −0.874153 | − | 0.485652i | \(-0.838582\pi\) | ||||
−0.874153 | + | 0.485652i | \(0.838582\pi\) | |||||||
\(368\) | 2.56520 | 0.133720 | ||||||||
\(369\) | −1.52515 | −0.0793962 | ||||||||
\(370\) | 3.50293 | 0.182109 | ||||||||
\(371\) | 0.372642 | 0.0193466 | ||||||||
\(372\) | −17.0605 | −0.884548 | ||||||||
\(373\) | 7.64489 | 0.395837 | 0.197919 | − | 0.980218i | \(-0.436582\pi\) | ||||
0.197919 | + | 0.980218i | \(0.436582\pi\) | |||||||
\(374\) | −17.5514 | −0.907563 | ||||||||
\(375\) | −15.0965 | −0.779578 | ||||||||
\(376\) | 4.49473 | 0.231798 | ||||||||
\(377\) | 2.01284 | 0.103667 | ||||||||
\(378\) | 0.667631 | 0.0343392 | ||||||||
\(379\) | −38.0059 | −1.95223 | −0.976117 | − | 0.217246i | \(-0.930293\pi\) | ||||
−0.976117 | + | 0.217246i | \(0.930293\pi\) | |||||||
\(380\) | 5.13425 | 0.263381 | ||||||||
\(381\) | 10.9933 | 0.563205 | ||||||||
\(382\) | 10.5894 | 0.541800 | ||||||||
\(383\) | 16.3762 | 0.836784 | 0.418392 | − | 0.908267i | \(-0.362594\pi\) | ||||
0.418392 | + | 0.908267i | \(0.362594\pi\) | |||||||
\(384\) | −1.86236 | −0.0950379 | ||||||||
\(385\) | 0.438494 | 0.0223477 | ||||||||
\(386\) | −8.01743 | −0.408077 | ||||||||
\(387\) | −0.453617 | −0.0230586 | ||||||||
\(388\) | 7.98287 | 0.405269 | ||||||||
\(389\) | −26.7429 | −1.35592 | −0.677960 | − | 0.735099i | \(-0.737136\pi\) | ||||
−0.677960 | + | 0.735099i | \(0.737136\pi\) | |||||||
\(390\) | 0.465217 | 0.0235572 | ||||||||
\(391\) | 12.7711 | 0.645862 | ||||||||
\(392\) | −6.97995 | −0.352541 | ||||||||
\(393\) | −24.9975 | −1.26096 | ||||||||
\(394\) | −16.6672 | −0.839680 | ||||||||
\(395\) | 3.94463 | 0.198476 | ||||||||
\(396\) | −1.65118 | −0.0829748 | ||||||||
\(397\) | −27.2404 | −1.36715 | −0.683577 | − | 0.729878i | \(-0.739577\pi\) | ||||
−0.683577 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(398\) | 26.9698 | 1.35187 | ||||||||
\(399\) | 1.54145 | 0.0771688 | ||||||||
\(400\) | −4.22844 | −0.211422 | ||||||||
\(401\) | 34.3241 | 1.71406 | 0.857031 | − | 0.515264i | \(-0.172306\pi\) | ||||
0.857031 | + | 0.515264i | \(0.172306\pi\) | |||||||
\(402\) | −24.6201 | −1.22794 | ||||||||
\(403\) | 2.60519 | 0.129774 | ||||||||
\(404\) | −11.6296 | −0.578595 | ||||||||
\(405\) | 8.94698 | 0.444579 | ||||||||
\(406\) | 1.00225 | 0.0497406 | ||||||||
\(407\) | 14.0590 | 0.696877 | ||||||||
\(408\) | −9.27191 | −0.459028 | ||||||||
\(409\) | −4.95539 | −0.245028 | −0.122514 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122514 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(410\) | 2.86029 | 0.141260 | ||||||||
\(411\) | −7.76898 | −0.383215 | ||||||||
\(412\) | 5.86002 | 0.288702 | ||||||||
\(413\) | −1.67400 | −0.0823721 | ||||||||
\(414\) | 1.20146 | 0.0590485 | ||||||||
\(415\) | 13.0525 | 0.640724 | ||||||||
\(416\) | 0.284387 | 0.0139432 | ||||||||
\(417\) | 22.9045 | 1.12164 | ||||||||
\(418\) | 20.6062 | 1.00788 | ||||||||
\(419\) | −26.0862 | −1.27440 | −0.637198 | − | 0.770700i | \(-0.719907\pi\) | ||||
−0.637198 | + | 0.770700i | \(0.719907\pi\) | |||||||
\(420\) | 0.231643 | 0.0113030 | ||||||||
\(421\) | 28.2421 | 1.37644 | 0.688218 | − | 0.725504i | \(-0.258393\pi\) | ||||
0.688218 | + | 0.725504i | \(0.258393\pi\) | |||||||
\(422\) | −22.0766 | −1.07467 | ||||||||
\(423\) | 2.10519 | 0.102358 | ||||||||
\(424\) | 2.63159 | 0.127801 | ||||||||
\(425\) | −21.0517 | −1.02116 | ||||||||
\(426\) | −20.5081 | −0.993620 | ||||||||
\(427\) | 0.0915047 | 0.00442822 | ||||||||
\(428\) | −0.654070 | −0.0316157 | ||||||||
\(429\) | 1.86714 | 0.0901466 | ||||||||
\(430\) | 0.850718 | 0.0410253 | ||||||||
\(431\) | −10.9748 | −0.528639 | −0.264320 | − | 0.964435i | \(-0.585147\pi\) | ||||
−0.264320 | + | 0.964435i | \(0.585147\pi\) | |||||||
\(432\) | 4.71480 | 0.226841 | ||||||||
\(433\) | 5.53798 | 0.266138 | 0.133069 | − | 0.991107i | \(-0.457517\pi\) | ||||
0.133069 | + | 0.991107i | \(0.457517\pi\) | |||||||
\(434\) | 1.29719 | 0.0622671 | ||||||||
\(435\) | 11.5784 | 0.555141 | ||||||||
\(436\) | 1.24286 | 0.0595220 | ||||||||
\(437\) | −14.9939 | −0.717255 | ||||||||
\(438\) | −10.9891 | −0.525079 | ||||||||
\(439\) | −28.8937 | −1.37902 | −0.689511 | − | 0.724276i | \(-0.742174\pi\) | ||||
−0.689511 | + | 0.724276i | \(0.742174\pi\) | |||||||
\(440\) | 3.09664 | 0.147626 | ||||||||
\(441\) | −3.26919 | −0.155676 | ||||||||
\(442\) | 1.41585 | 0.0673449 | ||||||||
\(443\) | −20.1205 | −0.955953 | −0.477976 | − | 0.878373i | \(-0.658630\pi\) | ||||
−0.477976 | + | 0.878373i | \(0.658630\pi\) | |||||||
\(444\) | 7.42694 | 0.352467 | ||||||||
\(445\) | 10.5166 | 0.498534 | ||||||||
\(446\) | −9.63646 | −0.456300 | ||||||||
\(447\) | 28.7654 | 1.36056 | ||||||||
\(448\) | 0.141603 | 0.00669012 | ||||||||
\(449\) | −30.1798 | −1.42427 | −0.712137 | − | 0.702041i | \(-0.752272\pi\) | ||||
−0.712137 | + | 0.702041i | \(0.752272\pi\) | |||||||
\(450\) | −1.98047 | −0.0933602 | ||||||||
\(451\) | 11.4797 | 0.540559 | ||||||||
\(452\) | −6.47849 | −0.304723 | ||||||||
\(453\) | 18.4320 | 0.866011 | ||||||||
\(454\) | 17.6804 | 0.829781 | ||||||||
\(455\) | −0.0353726 | −0.00165829 | ||||||||
\(456\) | 10.8857 | 0.509768 | ||||||||
\(457\) | −36.6265 | −1.71332 | −0.856659 | − | 0.515884i | \(-0.827464\pi\) | ||||
−0.856659 | + | 0.515884i | \(0.827464\pi\) | |||||||
\(458\) | −0.450830 | −0.0210659 | ||||||||
\(459\) | 23.4731 | 1.09563 | ||||||||
\(460\) | −2.25323 | −0.105057 | ||||||||
\(461\) | −31.4929 | −1.46677 | −0.733385 | − | 0.679814i | \(-0.762061\pi\) | ||||
−0.733385 | + | 0.679814i | \(0.762061\pi\) | |||||||
\(462\) | 0.929698 | 0.0432535 | ||||||||
\(463\) | 13.9316 | 0.647457 | 0.323728 | − | 0.946150i | \(-0.395064\pi\) | ||||
0.323728 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(464\) | 7.07784 | 0.328581 | ||||||||
\(465\) | 14.9857 | 0.694945 | ||||||||
\(466\) | −0.302059 | −0.0139926 | ||||||||
\(467\) | 30.7439 | 1.42266 | 0.711330 | − | 0.702858i | \(-0.248093\pi\) | ||||
0.711330 | + | 0.702858i | \(0.248093\pi\) | |||||||
\(468\) | 0.133198 | 0.00615707 | ||||||||
\(469\) | 1.87198 | 0.0864399 | ||||||||
\(470\) | −3.94809 | −0.182112 | ||||||||
\(471\) | 34.8716 | 1.60680 | ||||||||
\(472\) | −11.8218 | −0.544141 | ||||||||
\(473\) | 3.41435 | 0.156992 | ||||||||
\(474\) | 8.36343 | 0.384145 | ||||||||
\(475\) | 24.7157 | 1.13403 | ||||||||
\(476\) | 0.704985 | 0.0323129 | ||||||||
\(477\) | 1.23255 | 0.0564348 | ||||||||
\(478\) | 3.38848 | 0.154986 | ||||||||
\(479\) | −25.8778 | −1.18238 | −0.591192 | − | 0.806531i | \(-0.701343\pi\) | ||||
−0.591192 | + | 0.806531i | \(0.701343\pi\) | |||||||
\(480\) | 1.63586 | 0.0746665 | ||||||||
\(481\) | −1.13411 | −0.0517111 | ||||||||
\(482\) | 18.1980 | 0.828896 | ||||||||
\(483\) | −0.676484 | −0.0307811 | ||||||||
\(484\) | 1.42831 | 0.0649234 | ||||||||
\(485\) | −7.01202 | −0.318399 | ||||||||
\(486\) | 4.82507 | 0.218869 | ||||||||
\(487\) | −19.7582 | −0.895329 | −0.447664 | − | 0.894202i | \(-0.647744\pi\) | ||||
−0.447664 | + | 0.894202i | \(0.647744\pi\) | |||||||
\(488\) | 0.646205 | 0.0292523 | ||||||||
\(489\) | −16.6980 | −0.755108 | ||||||||
\(490\) | 6.13107 | 0.276974 | ||||||||
\(491\) | −7.90154 | −0.356592 | −0.178296 | − | 0.983977i | \(-0.557058\pi\) | ||||
−0.178296 | + | 0.983977i | \(0.557058\pi\) | |||||||
\(492\) | 6.06441 | 0.273405 | ||||||||
\(493\) | 35.2377 | 1.58703 | ||||||||
\(494\) | −1.66227 | −0.0747891 | ||||||||
\(495\) | 1.45037 | 0.0651891 | ||||||||
\(496\) | 9.16073 | 0.411329 | ||||||||
\(497\) | 1.55932 | 0.0699451 | ||||||||
\(498\) | 27.6741 | 1.24011 | ||||||||
\(499\) | 10.9025 | 0.488062 | 0.244031 | − | 0.969767i | \(-0.421530\pi\) | ||||
0.244031 | + | 0.969767i | \(0.421530\pi\) | |||||||
\(500\) | 8.10611 | 0.362516 | ||||||||
\(501\) | 22.6183 | 1.01051 | ||||||||
\(502\) | 23.2298 | 1.03680 | ||||||||
\(503\) | −33.3057 | −1.48503 | −0.742514 | − | 0.669831i | \(-0.766367\pi\) | ||||
−0.742514 | + | 0.669831i | \(0.766367\pi\) | |||||||
\(504\) | 0.0663224 | 0.00295424 | ||||||||
\(505\) | 10.2153 | 0.454573 | ||||||||
\(506\) | −9.04332 | −0.402024 | ||||||||
\(507\) | 24.0600 | 1.06854 | ||||||||
\(508\) | −5.90292 | −0.261900 | ||||||||
\(509\) | −14.2511 | −0.631670 | −0.315835 | − | 0.948814i | \(-0.602285\pi\) | ||||
−0.315835 | + | 0.948814i | \(0.602285\pi\) | |||||||
\(510\) | 8.14429 | 0.360635 | ||||||||
\(511\) | 0.835550 | 0.0369625 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −27.5585 | −1.21674 | ||||||||
\(514\) | 20.8328 | 0.918896 | ||||||||
\(515\) | −5.14734 | −0.226819 | ||||||||
\(516\) | 1.80370 | 0.0794034 | ||||||||
\(517\) | −15.8456 | −0.696890 | ||||||||
\(518\) | −0.564703 | −0.0248116 | ||||||||
\(519\) | 2.68795 | 0.117988 | ||||||||
\(520\) | −0.249801 | −0.0109545 | ||||||||
\(521\) | 24.6385 | 1.07943 | 0.539717 | − | 0.841847i | \(-0.318531\pi\) | ||||
0.539717 | + | 0.841847i | \(0.318531\pi\) | |||||||
\(522\) | 3.31504 | 0.145095 | ||||||||
\(523\) | −27.7214 | −1.21217 | −0.606085 | − | 0.795400i | \(-0.707261\pi\) | ||||
−0.606085 | + | 0.795400i | \(0.707261\pi\) | |||||||
\(524\) | 13.4225 | 0.586366 | ||||||||
\(525\) | 1.11511 | 0.0486672 | ||||||||
\(526\) | 0.718720 | 0.0313377 | ||||||||
\(527\) | 45.6076 | 1.98670 | ||||||||
\(528\) | 6.56551 | 0.285727 | ||||||||
\(529\) | −16.4197 | −0.713902 | ||||||||
\(530\) | −2.31155 | −0.100407 | ||||||||
\(531\) | −5.53694 | −0.240283 | ||||||||
\(532\) | −0.827686 | −0.0358848 | ||||||||
\(533\) | −0.926051 | −0.0401117 | ||||||||
\(534\) | 22.2974 | 0.964901 | ||||||||
\(535\) | 0.574524 | 0.0248388 | ||||||||
\(536\) | 13.2199 | 0.571012 | ||||||||
\(537\) | 8.15116 | 0.351749 | ||||||||
\(538\) | −20.3809 | −0.878682 | ||||||||
\(539\) | 24.6070 | 1.05990 | ||||||||
\(540\) | −4.14140 | −0.178218 | ||||||||
\(541\) | −6.27573 | −0.269815 | −0.134907 | − | 0.990858i | \(-0.543074\pi\) | ||||
−0.134907 | + | 0.990858i | \(0.543074\pi\) | |||||||
\(542\) | −28.1812 | −1.21049 | ||||||||
\(543\) | 44.6944 | 1.91802 | ||||||||
\(544\) | 4.97859 | 0.213455 | ||||||||
\(545\) | −1.09170 | −0.0467635 | ||||||||
\(546\) | −0.0749972 | −0.00320958 | ||||||||
\(547\) | 29.2716 | 1.25156 | 0.625781 | − | 0.779998i | \(-0.284780\pi\) | ||||
0.625781 | + | 0.779998i | \(0.284780\pi\) | |||||||
\(548\) | 4.17159 | 0.178201 | ||||||||
\(549\) | 0.302662 | 0.0129173 | ||||||||
\(550\) | 14.9069 | 0.635631 | ||||||||
\(551\) | −41.3708 | −1.76245 | ||||||||
\(552\) | −4.77732 | −0.203336 | ||||||||
\(553\) | −0.635909 | −0.0270416 | ||||||||
\(554\) | 12.0953 | 0.513879 | ||||||||
\(555\) | −6.52370 | −0.276915 | ||||||||
\(556\) | −12.2987 | −0.521581 | ||||||||
\(557\) | −31.5199 | −1.33554 | −0.667771 | − | 0.744367i | \(-0.732751\pi\) | ||||
−0.667771 | + | 0.744367i | \(0.732751\pi\) | |||||||
\(558\) | 4.29060 | 0.181635 | ||||||||
\(559\) | −0.275430 | −0.0116494 | ||||||||
\(560\) | −0.124382 | −0.00525609 | ||||||||
\(561\) | 32.6870 | 1.38005 | ||||||||
\(562\) | −30.1348 | −1.27116 | ||||||||
\(563\) | −27.1655 | −1.14489 | −0.572444 | − | 0.819943i | \(-0.694005\pi\) | ||||
−0.572444 | + | 0.819943i | \(0.694005\pi\) | |||||||
\(564\) | −8.37078 | −0.352473 | ||||||||
\(565\) | 5.69060 | 0.239405 | ||||||||
\(566\) | 15.1822 | 0.638157 | ||||||||
\(567\) | −1.44233 | −0.0605723 | ||||||||
\(568\) | 11.0119 | 0.462049 | ||||||||
\(569\) | 15.7815 | 0.661593 | 0.330796 | − | 0.943702i | \(-0.392683\pi\) | ||||
0.330796 | + | 0.943702i | \(0.392683\pi\) | |||||||
\(570\) | −9.56180 | −0.400500 | ||||||||
\(571\) | −25.6775 | −1.07457 | −0.537285 | − | 0.843401i | \(-0.680550\pi\) | ||||
−0.537285 | + | 0.843401i | \(0.680550\pi\) | |||||||
\(572\) | −1.00257 | −0.0419196 | ||||||||
\(573\) | −19.7212 | −0.823865 | ||||||||
\(574\) | −0.461104 | −0.0192461 | ||||||||
\(575\) | −10.8468 | −0.452343 | ||||||||
\(576\) | 0.468368 | 0.0195153 | ||||||||
\(577\) | 8.05862 | 0.335485 | 0.167742 | − | 0.985831i | \(-0.446352\pi\) | ||||
0.167742 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(578\) | 7.78638 | 0.323871 | ||||||||
\(579\) | 14.9313 | 0.620524 | ||||||||
\(580\) | −6.21706 | −0.258149 | ||||||||
\(581\) | −2.10418 | −0.0872963 | ||||||||
\(582\) | −14.8669 | −0.616255 | ||||||||
\(583\) | −9.27737 | −0.384229 | ||||||||
\(584\) | 5.90064 | 0.244170 | ||||||||
\(585\) | −0.116999 | −0.00483730 | ||||||||
\(586\) | 20.7875 | 0.858723 | ||||||||
\(587\) | −27.6986 | −1.14324 | −0.571622 | − | 0.820517i | \(-0.693686\pi\) | ||||
−0.571622 | + | 0.820517i | \(0.693686\pi\) | |||||||
\(588\) | 12.9991 | 0.536076 | ||||||||
\(589\) | −53.5455 | −2.20630 | ||||||||
\(590\) | 10.3840 | 0.427504 | ||||||||
\(591\) | 31.0402 | 1.27682 | ||||||||
\(592\) | −3.98793 | −0.163903 | ||||||||
\(593\) | −5.66975 | −0.232829 | −0.116414 | − | 0.993201i | \(-0.537140\pi\) | ||||
−0.116414 | + | 0.993201i | \(0.537140\pi\) | |||||||
\(594\) | −16.6215 | −0.681987 | ||||||||
\(595\) | −0.619247 | −0.0253866 | ||||||||
\(596\) | −15.4457 | −0.632682 | ||||||||
\(597\) | −50.2273 | −2.05567 | ||||||||
\(598\) | 0.729509 | 0.0298319 | ||||||||
\(599\) | 45.5563 | 1.86138 | 0.930690 | − | 0.365808i | \(-0.119207\pi\) | ||||
0.930690 | + | 0.365808i | \(0.119207\pi\) | |||||||
\(600\) | 7.87486 | 0.321490 | ||||||||
\(601\) | 16.2865 | 0.664340 | 0.332170 | − | 0.943220i | \(-0.392219\pi\) | ||||
0.332170 | + | 0.943220i | \(0.392219\pi\) | |||||||
\(602\) | −0.137143 | −0.00558954 | ||||||||
\(603\) | 6.19178 | 0.252149 | ||||||||
\(604\) | −9.89714 | −0.402709 | ||||||||
\(605\) | −1.25461 | −0.0510071 | ||||||||
\(606\) | 21.6585 | 0.879815 | ||||||||
\(607\) | −11.6060 | −0.471074 | −0.235537 | − | 0.971865i | \(-0.575685\pi\) | ||||
−0.235537 | + | 0.971865i | \(0.575685\pi\) | |||||||
\(608\) | −5.84511 | −0.237051 | ||||||||
\(609\) | −1.86654 | −0.0756359 | ||||||||
\(610\) | −0.567616 | −0.0229821 | ||||||||
\(611\) | 1.27824 | 0.0517121 | ||||||||
\(612\) | 2.33181 | 0.0942580 | ||||||||
\(613\) | 17.9087 | 0.723324 | 0.361662 | − | 0.932309i | \(-0.382209\pi\) | ||||
0.361662 | + | 0.932309i | \(0.382209\pi\) | |||||||
\(614\) | 6.97316 | 0.281414 | ||||||||
\(615\) | −5.32687 | −0.214800 | ||||||||
\(616\) | −0.499205 | −0.0201136 | ||||||||
\(617\) | −3.41505 | −0.137485 | −0.0687423 | − | 0.997634i | \(-0.521899\pi\) | ||||
−0.0687423 | + | 0.997634i | \(0.521899\pi\) | |||||||
\(618\) | −10.9134 | −0.439003 | ||||||||
\(619\) | −32.7170 | −1.31501 | −0.657504 | − | 0.753451i | \(-0.728388\pi\) | ||||
−0.657504 | + | 0.753451i | \(0.728388\pi\) | |||||||
\(620\) | −8.04664 | −0.323161 | ||||||||
\(621\) | 12.0944 | 0.485332 | ||||||||
\(622\) | −8.73597 | −0.350280 | ||||||||
\(623\) | −1.69537 | −0.0679234 | ||||||||
\(624\) | −0.529629 | −0.0212021 | ||||||||
\(625\) | 14.0219 | 0.560878 | ||||||||
\(626\) | 10.0540 | 0.401837 | ||||||||
\(627\) | −38.3762 | −1.53260 | ||||||||
\(628\) | −18.7245 | −0.747187 | ||||||||
\(629\) | −19.8543 | −0.791641 | ||||||||
\(630\) | −0.0582565 | −0.00232100 | ||||||||
\(631\) | 39.3751 | 1.56750 | 0.783748 | − | 0.621079i | \(-0.213305\pi\) | ||||
0.783748 | + | 0.621079i | \(0.213305\pi\) | |||||||
\(632\) | −4.49078 | −0.178634 | ||||||||
\(633\) | 41.1146 | 1.63416 | ||||||||
\(634\) | −17.8156 | −0.707547 | ||||||||
\(635\) | 5.18502 | 0.205761 | ||||||||
\(636\) | −4.90096 | −0.194336 | ||||||||
\(637\) | −1.98500 | −0.0786487 | ||||||||
\(638\) | −24.9521 | −0.987863 | ||||||||
\(639\) | 5.15763 | 0.204033 | ||||||||
\(640\) | −0.878383 | −0.0347212 | ||||||||
\(641\) | 6.77066 | 0.267425 | 0.133713 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133713 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(642\) | 1.21811 | 0.0480750 | ||||||||
\(643\) | 0.281208 | 0.0110897 | 0.00554487 | − | 0.999985i | \(-0.498235\pi\) | ||||
0.00554487 | + | 0.999985i | \(0.498235\pi\) | |||||||
\(644\) | 0.363241 | 0.0143137 | ||||||||
\(645\) | −1.58434 | −0.0623833 | ||||||||
\(646\) | −29.1004 | −1.14494 | ||||||||
\(647\) | 48.9842 | 1.92577 | 0.962883 | − | 0.269918i | \(-0.0869967\pi\) | ||||
0.962883 | + | 0.269918i | \(0.0869967\pi\) | |||||||
\(648\) | −10.1857 | −0.400133 | ||||||||
\(649\) | 41.6762 | 1.63594 | ||||||||
\(650\) | −1.20251 | −0.0471664 | ||||||||
\(651\) | −2.41583 | −0.0946837 | ||||||||
\(652\) | 8.96605 | 0.351138 | ||||||||
\(653\) | 23.4517 | 0.917734 | 0.458867 | − | 0.888505i | \(-0.348255\pi\) | ||||
0.458867 | + | 0.888505i | \(0.348255\pi\) | |||||||
\(654\) | −2.31464 | −0.0905096 | ||||||||
\(655\) | −11.7901 | −0.460678 | ||||||||
\(656\) | −3.25631 | −0.127138 | ||||||||
\(657\) | 2.76367 | 0.107821 | ||||||||
\(658\) | 0.636468 | 0.0248121 | ||||||||
\(659\) | −29.5520 | −1.15118 | −0.575591 | − | 0.817738i | \(-0.695228\pi\) | ||||
−0.575591 | + | 0.817738i | \(0.695228\pi\) | |||||||
\(660\) | −5.76704 | −0.224482 | ||||||||
\(661\) | 3.84627 | 0.149603 | 0.0748014 | − | 0.997198i | \(-0.476168\pi\) | ||||
0.0748014 | + | 0.997198i | \(0.476168\pi\) | |||||||
\(662\) | −0.772988 | −0.0300430 | ||||||||
\(663\) | −2.63681 | −0.102405 | ||||||||
\(664\) | −14.8597 | −0.576669 | ||||||||
\(665\) | 0.727026 | 0.0281929 | ||||||||
\(666\) | −1.86782 | −0.0723765 | ||||||||
\(667\) | 18.1561 | 0.703007 | ||||||||
\(668\) | −12.1450 | −0.469904 | ||||||||
\(669\) | 17.9465 | 0.693853 | ||||||||
\(670\) | −11.6121 | −0.448616 | ||||||||
\(671\) | −2.27812 | −0.0879458 | ||||||||
\(672\) | −0.263716 | −0.0101730 | ||||||||
\(673\) | 48.1622 | 1.85652 | 0.928259 | − | 0.371935i | \(-0.121306\pi\) | ||||
0.928259 | + | 0.371935i | \(0.121306\pi\) | |||||||
\(674\) | −11.7517 | −0.452657 | ||||||||
\(675\) | −19.9363 | −0.767347 | ||||||||
\(676\) | −12.9191 | −0.496889 | ||||||||
\(677\) | −15.9300 | −0.612238 | −0.306119 | − | 0.951993i | \(-0.599031\pi\) | ||||
−0.306119 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(678\) | 12.0653 | 0.463363 | ||||||||
\(679\) | 1.13040 | 0.0433808 | ||||||||
\(680\) | −4.37311 | −0.167701 | ||||||||
\(681\) | −32.9272 | −1.26177 | ||||||||
\(682\) | −32.2951 | −1.23664 | ||||||||
\(683\) | 32.6067 | 1.24766 | 0.623830 | − | 0.781560i | \(-0.285576\pi\) | ||||
0.623830 | + | 0.781560i | \(0.285576\pi\) | |||||||
\(684\) | −2.73766 | −0.104677 | ||||||||
\(685\) | −3.66425 | −0.140004 | ||||||||
\(686\) | −1.97961 | −0.0755817 | ||||||||
\(687\) | 0.839605 | 0.0320329 | ||||||||
\(688\) | −0.968504 | −0.0369239 | ||||||||
\(689\) | 0.748390 | 0.0285114 | ||||||||
\(690\) | 4.19632 | 0.159751 | ||||||||
\(691\) | 45.3110 | 1.72371 | 0.861856 | − | 0.507154i | \(-0.169302\pi\) | ||||
0.861856 | + | 0.507154i | \(0.169302\pi\) | |||||||
\(692\) | −1.44330 | −0.0548662 | ||||||||
\(693\) | −0.233812 | −0.00888178 | ||||||||
\(694\) | 36.6012 | 1.38936 | ||||||||
\(695\) | 10.8030 | 0.409780 | ||||||||
\(696\) | −13.1815 | −0.499642 | ||||||||
\(697\) | −16.2118 | −0.614067 | ||||||||
\(698\) | −34.0850 | −1.29014 | ||||||||
\(699\) | 0.562541 | 0.0212773 | ||||||||
\(700\) | −0.598761 | −0.0226310 | ||||||||
\(701\) | −39.7274 | −1.50048 | −0.750241 | − | 0.661164i | \(-0.770063\pi\) | ||||
−0.750241 | + | 0.661164i | \(0.770063\pi\) | |||||||
\(702\) | 1.34083 | 0.0506062 | ||||||||
\(703\) | 23.3099 | 0.879148 | ||||||||
\(704\) | −3.52538 | −0.132868 | ||||||||
\(705\) | 7.35275 | 0.276921 | ||||||||
\(706\) | −3.87943 | −0.146004 | ||||||||
\(707\) | −1.64679 | −0.0619339 | ||||||||
\(708\) | 22.0163 | 0.827424 | ||||||||
\(709\) | 24.4279 | 0.917408 | 0.458704 | − | 0.888589i | \(-0.348314\pi\) | ||||
0.458704 | + | 0.888589i | \(0.348314\pi\) | |||||||
\(710\) | −9.67268 | −0.363009 | ||||||||
\(711\) | −2.10334 | −0.0788814 | ||||||||
\(712\) | −11.9727 | −0.448694 | ||||||||
\(713\) | 23.4991 | 0.880049 | ||||||||
\(714\) | −1.31293 | −0.0491352 | ||||||||
\(715\) | 0.880642 | 0.0329341 | ||||||||
\(716\) | −4.37680 | −0.163569 | ||||||||
\(717\) | −6.31056 | −0.235672 | ||||||||
\(718\) | −1.45585 | −0.0543317 | ||||||||
\(719\) | 13.0240 | 0.485713 | 0.242856 | − | 0.970062i | \(-0.421916\pi\) | ||||
0.242856 | + | 0.970062i | \(0.421916\pi\) | |||||||
\(720\) | −0.411407 | −0.0153322 | ||||||||
\(721\) | 0.829798 | 0.0309033 | ||||||||
\(722\) | 15.1653 | 0.564395 | ||||||||
\(723\) | −33.8911 | −1.26042 | ||||||||
\(724\) | −23.9988 | −0.891910 | ||||||||
\(725\) | −29.9282 | −1.11151 | ||||||||
\(726\) | −2.66003 | −0.0987229 | ||||||||
\(727\) | 30.5655 | 1.13361 | 0.566806 | − | 0.823852i | \(-0.308179\pi\) | ||||
0.566806 | + | 0.823852i | \(0.308179\pi\) | |||||||
\(728\) | 0.0402701 | 0.00149251 | ||||||||
\(729\) | 21.5712 | 0.798934 | ||||||||
\(730\) | −5.18303 | −0.191832 | ||||||||
\(731\) | −4.82179 | −0.178340 | ||||||||
\(732\) | −1.20346 | −0.0444813 | ||||||||
\(733\) | −14.8471 | −0.548391 | −0.274195 | − | 0.961674i | \(-0.588411\pi\) | ||||
−0.274195 | + | 0.961674i | \(0.588411\pi\) | |||||||
\(734\) | −33.4927 | −1.23624 | ||||||||
\(735\) | −11.4182 | −0.421168 | ||||||||
\(736\) | 2.56520 | 0.0945546 | ||||||||
\(737\) | −46.6051 | −1.71672 | ||||||||
\(738\) | −1.52515 | −0.0561416 | ||||||||
\(739\) | 34.8636 | 1.28248 | 0.641239 | − | 0.767341i | \(-0.278421\pi\) | ||||
0.641239 | + | 0.767341i | \(0.278421\pi\) | |||||||
\(740\) | 3.50293 | 0.128770 | ||||||||
\(741\) | 3.09574 | 0.113725 | ||||||||
\(742\) | 0.372642 | 0.0136801 | ||||||||
\(743\) | −50.8248 | −1.86458 | −0.932291 | − | 0.361708i | \(-0.882194\pi\) | ||||
−0.932291 | + | 0.361708i | \(0.882194\pi\) | |||||||
\(744\) | −17.0605 | −0.625470 | ||||||||
\(745\) | 13.5673 | 0.497066 | ||||||||
\(746\) | 7.64489 | 0.279899 | ||||||||
\(747\) | −6.95982 | −0.254647 | ||||||||
\(748\) | −17.5514 | −0.641744 | ||||||||
\(749\) | −0.0926184 | −0.00338420 | ||||||||
\(750\) | −15.0965 | −0.551245 | ||||||||
\(751\) | 32.0136 | 1.16819 | 0.584097 | − | 0.811684i | \(-0.301449\pi\) | ||||
0.584097 | + | 0.811684i | \(0.301449\pi\) | |||||||
\(752\) | 4.49473 | 0.163906 | ||||||||
\(753\) | −43.2622 | −1.57656 | ||||||||
\(754\) | 2.01284 | 0.0733035 | ||||||||
\(755\) | 8.69349 | 0.316388 | ||||||||
\(756\) | 0.667631 | 0.0242815 | ||||||||
\(757\) | 15.1634 | 0.551125 | 0.275562 | − | 0.961283i | \(-0.411136\pi\) | ||||
0.275562 | + | 0.961283i | \(0.411136\pi\) | |||||||
\(758\) | −38.0059 | −1.38044 | ||||||||
\(759\) | 16.8419 | 0.611321 | ||||||||
\(760\) | 5.13425 | 0.186239 | ||||||||
\(761\) | −31.5300 | −1.14296 | −0.571481 | − | 0.820615i | \(-0.693631\pi\) | ||||
−0.571481 | + | 0.820615i | \(0.693631\pi\) | |||||||
\(762\) | 10.9933 | 0.398246 | ||||||||
\(763\) | 0.175992 | 0.00637135 | ||||||||
\(764\) | 10.5894 | 0.383110 | ||||||||
\(765\) | −2.04823 | −0.0740538 | ||||||||
\(766\) | 16.3762 | 0.591696 | ||||||||
\(767\) | −3.36195 | −0.121393 | ||||||||
\(768\) | −1.86236 | −0.0672020 | ||||||||
\(769\) | 12.5218 | 0.451548 | 0.225774 | − | 0.974180i | \(-0.427509\pi\) | ||||
0.225774 | + | 0.974180i | \(0.427509\pi\) | |||||||
\(770\) | 0.438494 | 0.0158022 | ||||||||
\(771\) | −38.7981 | −1.39728 | ||||||||
\(772\) | −8.01743 | −0.288554 | ||||||||
\(773\) | −1.82043 | −0.0654763 | −0.0327382 | − | 0.999464i | \(-0.510423\pi\) | ||||
−0.0327382 | + | 0.999464i | \(0.510423\pi\) | |||||||
\(774\) | −0.453617 | −0.0163049 | ||||||||
\(775\) | −38.7356 | −1.39143 | ||||||||
\(776\) | 7.98287 | 0.286568 | ||||||||
\(777\) | 1.05168 | 0.0377287 | ||||||||
\(778\) | −26.7429 | −0.958780 | ||||||||
\(779\) | 19.0335 | 0.681946 | ||||||||
\(780\) | 0.465217 | 0.0166575 | ||||||||
\(781\) | −38.8212 | −1.38913 | ||||||||
\(782\) | 12.7711 | 0.456693 | ||||||||
\(783\) | 33.3706 | 1.19257 | ||||||||
\(784\) | −6.97995 | −0.249284 | ||||||||
\(785\) | 16.4472 | 0.587027 | ||||||||
\(786\) | −24.9975 | −0.891632 | ||||||||
\(787\) | 35.1032 | 1.25129 | 0.625646 | − | 0.780107i | \(-0.284835\pi\) | ||||
0.625646 | + | 0.780107i | \(0.284835\pi\) | |||||||
\(788\) | −16.6672 | −0.593744 | ||||||||
\(789\) | −1.33851 | −0.0476523 | ||||||||
\(790\) | 3.94463 | 0.140343 | ||||||||
\(791\) | −0.917375 | −0.0326181 | ||||||||
\(792\) | −1.65118 | −0.0586720 | ||||||||
\(793\) | 0.183772 | 0.00652594 | ||||||||
\(794\) | −27.2404 | −0.966724 | ||||||||
\(795\) | 4.30492 | 0.152680 | ||||||||
\(796\) | 26.9698 | 0.955919 | ||||||||
\(797\) | −45.3458 | −1.60623 | −0.803116 | − | 0.595823i | \(-0.796826\pi\) | ||||
−0.803116 | + | 0.595823i | \(0.796826\pi\) | |||||||
\(798\) | 1.54145 | 0.0545666 | ||||||||
\(799\) | 22.3774 | 0.791656 | ||||||||
\(800\) | −4.22844 | −0.149498 | ||||||||
\(801\) | −5.60761 | −0.198135 | ||||||||
\(802\) | 34.3241 | 1.21203 | ||||||||
\(803\) | −20.8020 | −0.734087 | ||||||||
\(804\) | −24.6201 | −0.868285 | ||||||||
\(805\) | −0.319065 | −0.0112456 | ||||||||
\(806\) | 2.60519 | 0.0917639 | ||||||||
\(807\) | 37.9564 | 1.33613 | ||||||||
\(808\) | −11.6296 | −0.409128 | ||||||||
\(809\) | 17.5703 | 0.617738 | 0.308869 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308869 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(810\) | 8.94698 | 0.314365 | ||||||||
\(811\) | −45.4995 | −1.59770 | −0.798851 | − | 0.601528i | \(-0.794559\pi\) | ||||
−0.798851 | + | 0.601528i | \(0.794559\pi\) | |||||||
\(812\) | 1.00225 | 0.0351719 | ||||||||
\(813\) | 52.4834 | 1.84067 | ||||||||
\(814\) | 14.0590 | 0.492766 | ||||||||
\(815\) | −7.87563 | −0.275871 | ||||||||
\(816\) | −9.27191 | −0.324582 | ||||||||
\(817\) | 5.66102 | 0.198054 | ||||||||
\(818\) | −4.95539 | −0.173261 | ||||||||
\(819\) | 0.0188612 | 0.000659064 0 | ||||||||
\(820\) | 2.86029 | 0.0998856 | ||||||||
\(821\) | 48.5889 | 1.69576 | 0.847881 | − | 0.530186i | \(-0.177878\pi\) | ||||
0.847881 | + | 0.530186i | \(0.177878\pi\) | |||||||
\(822\) | −7.76898 | −0.270974 | ||||||||
\(823\) | −27.7645 | −0.967809 | −0.483905 | − | 0.875121i | \(-0.660782\pi\) | ||||
−0.483905 | + | 0.875121i | \(0.660782\pi\) | |||||||
\(824\) | 5.86002 | 0.204143 | ||||||||
\(825\) | −27.7619 | −0.966545 | ||||||||
\(826\) | −1.67400 | −0.0582459 | ||||||||
\(827\) | −27.9723 | −0.972693 | −0.486347 | − | 0.873766i | \(-0.661671\pi\) | ||||
−0.486347 | + | 0.873766i | \(0.661671\pi\) | |||||||
\(828\) | 1.20146 | 0.0417536 | ||||||||
\(829\) | −24.2882 | −0.843563 | −0.421782 | − | 0.906697i | \(-0.638595\pi\) | ||||
−0.421782 | + | 0.906697i | \(0.638595\pi\) | |||||||
\(830\) | 13.0525 | 0.453060 | ||||||||
\(831\) | −22.5257 | −0.781407 | ||||||||
\(832\) | 0.284387 | 0.00985933 | ||||||||
\(833\) | −34.7503 | −1.20403 | ||||||||
\(834\) | 22.9045 | 0.793120 | ||||||||
\(835\) | 10.6680 | 0.369180 | ||||||||
\(836\) | 20.6062 | 0.712682 | ||||||||
\(837\) | 43.1910 | 1.49290 | ||||||||
\(838\) | −26.0862 | −0.901134 | ||||||||
\(839\) | −27.7153 | −0.956837 | −0.478419 | − | 0.878132i | \(-0.658790\pi\) | ||||
−0.478419 | + | 0.878132i | \(0.658790\pi\) | |||||||
\(840\) | 0.231643 | 0.00799245 | ||||||||
\(841\) | 21.0958 | 0.727443 | ||||||||
\(842\) | 28.2421 | 0.973287 | ||||||||
\(843\) | 56.1217 | 1.93293 | ||||||||
\(844\) | −22.0766 | −0.759910 | ||||||||
\(845\) | 11.3479 | 0.390381 | ||||||||
\(846\) | 2.10519 | 0.0723778 | ||||||||
\(847\) | 0.202254 | 0.00694953 | ||||||||
\(848\) | 2.63159 | 0.0903693 | ||||||||
\(849\) | −28.2747 | −0.970386 | ||||||||
\(850\) | −21.0517 | −0.722067 | ||||||||
\(851\) | −10.2298 | −0.350674 | ||||||||
\(852\) | −20.5081 | −0.702595 | ||||||||
\(853\) | 0.857427 | 0.0293577 | 0.0146789 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146789 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(854\) | 0.0915047 | 0.00313123 | ||||||||
\(855\) | 2.40472 | 0.0822397 | ||||||||
\(856\) | −0.654070 | −0.0223556 | ||||||||
\(857\) | −51.9181 | −1.77349 | −0.886745 | − | 0.462259i | \(-0.847039\pi\) | ||||
−0.886745 | + | 0.462259i | \(0.847039\pi\) | |||||||
\(858\) | 1.86714 | 0.0637433 | ||||||||
\(859\) | 9.01728 | 0.307666 | 0.153833 | − | 0.988097i | \(-0.450838\pi\) | ||||
0.153833 | + | 0.988097i | \(0.450838\pi\) | |||||||
\(860\) | 0.850718 | 0.0290092 | ||||||||
\(861\) | 0.858739 | 0.0292658 | ||||||||
\(862\) | −10.9748 | −0.373804 | ||||||||
\(863\) | −5.87738 | −0.200068 | −0.100034 | − | 0.994984i | \(-0.531895\pi\) | ||||
−0.100034 | + | 0.994984i | \(0.531895\pi\) | |||||||
\(864\) | 4.71480 | 0.160401 | ||||||||
\(865\) | 1.26777 | 0.0431056 | ||||||||
\(866\) | 5.53798 | 0.188188 | ||||||||
\(867\) | −14.5010 | −0.492480 | ||||||||
\(868\) | 1.29719 | 0.0440295 | ||||||||
\(869\) | 15.8317 | 0.537054 | ||||||||
\(870\) | 11.5784 | 0.392544 | ||||||||
\(871\) | 3.75956 | 0.127388 | ||||||||
\(872\) | 1.24286 | 0.0420884 | ||||||||
\(873\) | 3.73892 | 0.126543 | ||||||||
\(874\) | −14.9939 | −0.507176 | ||||||||
\(875\) | 1.14785 | 0.0388045 | ||||||||
\(876\) | −10.9891 | −0.371287 | ||||||||
\(877\) | −12.2548 | −0.413816 | −0.206908 | − | 0.978360i | \(-0.566340\pi\) | ||||
−0.206908 | + | 0.978360i | \(0.566340\pi\) | |||||||
\(878\) | −28.8937 | −0.975115 | ||||||||
\(879\) | −38.7137 | −1.30578 | ||||||||
\(880\) | 3.09664 | 0.104388 | ||||||||
\(881\) | −0.837034 | −0.0282004 | −0.0141002 | − | 0.999901i | \(-0.504488\pi\) | ||||
−0.0141002 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(882\) | −3.26919 | −0.110079 | ||||||||
\(883\) | 44.6016 | 1.50096 | 0.750482 | − | 0.660891i | \(-0.229821\pi\) | ||||
0.750482 | + | 0.660891i | \(0.229821\pi\) | |||||||
\(884\) | 1.41585 | 0.0476200 | ||||||||
\(885\) | −19.3388 | −0.650066 | ||||||||
\(886\) | −20.1205 | −0.675961 | ||||||||
\(887\) | −17.3231 | −0.581652 | −0.290826 | − | 0.956776i | \(-0.593930\pi\) | ||||
−0.290826 | + | 0.956776i | \(0.593930\pi\) | |||||||
\(888\) | 7.42694 | 0.249232 | ||||||||
\(889\) | −0.835872 | −0.0280342 | ||||||||
\(890\) | 10.5166 | 0.352517 | ||||||||
\(891\) | 35.9086 | 1.20298 | ||||||||
\(892\) | −9.63646 | −0.322653 | ||||||||
\(893\) | −26.2722 | −0.879165 | ||||||||
\(894\) | 28.7654 | 0.962060 | ||||||||
\(895\) | 3.84451 | 0.128508 | ||||||||
\(896\) | 0.141603 | 0.00473063 | ||||||||
\(897\) | −1.35861 | −0.0453625 | ||||||||
\(898\) | −30.1798 | −1.00711 | ||||||||
\(899\) | 64.8382 | 2.16248 | ||||||||
\(900\) | −1.98047 | −0.0660156 | ||||||||
\(901\) | 13.1016 | 0.436479 | ||||||||
\(902\) | 11.4797 | 0.382233 | ||||||||
\(903\) | 0.255410 | 0.00849950 | ||||||||
\(904\) | −6.47849 | −0.215471 | ||||||||
\(905\) | 21.0802 | 0.700729 | ||||||||
\(906\) | 18.4320 | 0.612362 | ||||||||
\(907\) | −28.6392 | −0.950950 | −0.475475 | − | 0.879729i | \(-0.657724\pi\) | ||||
−0.475475 | + | 0.879729i | \(0.657724\pi\) | |||||||
\(908\) | 17.6804 | 0.586744 | ||||||||
\(909\) | −5.44694 | −0.180664 | ||||||||
\(910\) | −0.0353726 | −0.00117259 | ||||||||
\(911\) | −49.9955 | −1.65642 | −0.828212 | − | 0.560415i | \(-0.810641\pi\) | ||||
−0.828212 | + | 0.560415i | \(0.810641\pi\) | |||||||
\(912\) | 10.8857 | 0.360461 | ||||||||
\(913\) | 52.3862 | 1.73373 | ||||||||
\(914\) | −36.6265 | −1.21150 | ||||||||
\(915\) | 1.05710 | 0.0349467 | ||||||||
\(916\) | −0.450830 | −0.0148958 | ||||||||
\(917\) | 1.90067 | 0.0627657 | ||||||||
\(918\) | 23.4731 | 0.774726 | ||||||||
\(919\) | −23.8951 | −0.788226 | −0.394113 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394113 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(920\) | −2.25323 | −0.0742868 | ||||||||
\(921\) | −12.9865 | −0.427920 | ||||||||
\(922\) | −31.4929 | −1.03716 | ||||||||
\(923\) | 3.13164 | 0.103079 | ||||||||
\(924\) | 0.929698 | 0.0305848 | ||||||||
\(925\) | 16.8627 | 0.554443 | ||||||||
\(926\) | 13.9316 | 0.457821 | ||||||||
\(927\) | 2.74465 | 0.0901460 | ||||||||
\(928\) | 7.07784 | 0.232342 | ||||||||
\(929\) | 45.1902 | 1.48264 | 0.741321 | − | 0.671151i | \(-0.234200\pi\) | ||||
0.741321 | + | 0.671151i | \(0.234200\pi\) | |||||||
\(930\) | 14.9857 | 0.491400 | ||||||||
\(931\) | 40.7986 | 1.33712 | ||||||||
\(932\) | −0.302059 | −0.00989428 | ||||||||
\(933\) | 16.2695 | 0.532639 | ||||||||
\(934\) | 30.7439 | 1.00597 | ||||||||
\(935\) | 15.4169 | 0.504186 | ||||||||
\(936\) | 0.133198 | 0.00435370 | ||||||||
\(937\) | −36.3889 | −1.18877 | −0.594387 | − | 0.804179i | \(-0.702605\pi\) | ||||
−0.594387 | + | 0.804179i | \(0.702605\pi\) | |||||||
\(938\) | 1.87198 | 0.0611223 | ||||||||
\(939\) | −18.7241 | −0.611036 | ||||||||
\(940\) | −3.94809 | −0.128773 | ||||||||
\(941\) | 56.3622 | 1.83736 | 0.918678 | − | 0.395008i | \(-0.129258\pi\) | ||||
0.918678 | + | 0.395008i | \(0.129258\pi\) | |||||||
\(942\) | 34.8716 | 1.13618 | ||||||||
\(943\) | −8.35309 | −0.272014 | ||||||||
\(944\) | −11.8218 | −0.384766 | ||||||||
\(945\) | −0.586436 | −0.0190768 | ||||||||
\(946\) | 3.41435 | 0.111010 | ||||||||
\(947\) | 50.0176 | 1.62535 | 0.812676 | − | 0.582715i | \(-0.198010\pi\) | ||||
0.812676 | + | 0.582715i | \(0.198010\pi\) | |||||||
\(948\) | 8.36343 | 0.271632 | ||||||||
\(949\) | 1.67806 | 0.0544723 | ||||||||
\(950\) | 24.7157 | 0.801884 | ||||||||
\(951\) | 33.1790 | 1.07590 | ||||||||
\(952\) | 0.704985 | 0.0228487 | ||||||||
\(953\) | 0.128291 | 0.00415575 | 0.00207788 | − | 0.999998i | \(-0.499339\pi\) | ||||
0.00207788 | + | 0.999998i | \(0.499339\pi\) | |||||||
\(954\) | 1.23255 | 0.0399054 | ||||||||
\(955\) | −9.30154 | −0.300991 | ||||||||
\(956\) | 3.38848 | 0.109591 | ||||||||
\(957\) | 46.4697 | 1.50215 | ||||||||
\(958\) | −25.8778 | −0.836072 | ||||||||
\(959\) | 0.590710 | 0.0190750 | ||||||||
\(960\) | 1.63586 | 0.0527972 | ||||||||
\(961\) | 52.9190 | 1.70707 | ||||||||
\(962\) | −1.13411 | −0.0365653 | ||||||||
\(963\) | −0.306346 | −0.00987185 | ||||||||
\(964\) | 18.1980 | 0.586118 | ||||||||
\(965\) | 7.04238 | 0.226702 | ||||||||
\(966\) | −0.676484 | −0.0217655 | ||||||||
\(967\) | −3.43643 | −0.110508 | −0.0552541 | − | 0.998472i | \(-0.517597\pi\) | ||||
−0.0552541 | + | 0.998472i | \(0.517597\pi\) | |||||||
\(968\) | 1.42831 | 0.0459078 | ||||||||
\(969\) | 54.1953 | 1.74101 | ||||||||
\(970\) | −7.01202 | −0.225142 | ||||||||
\(971\) | −29.3235 | −0.941035 | −0.470517 | − | 0.882391i | \(-0.655933\pi\) | ||||
−0.470517 | + | 0.882391i | \(0.655933\pi\) | |||||||
\(972\) | 4.82507 | 0.154764 | ||||||||
\(973\) | −1.74153 | −0.0558310 | ||||||||
\(974\) | −19.7582 | −0.633093 | ||||||||
\(975\) | 2.23951 | 0.0717216 | ||||||||
\(976\) | 0.646205 | 0.0206845 | ||||||||
\(977\) | −54.4195 | −1.74104 | −0.870518 | − | 0.492137i | \(-0.836216\pi\) | ||||
−0.870518 | + | 0.492137i | \(0.836216\pi\) | |||||||
\(978\) | −16.6980 | −0.533942 | ||||||||
\(979\) | 42.2082 | 1.34898 | ||||||||
\(980\) | 6.13107 | 0.195850 | ||||||||
\(981\) | 0.582114 | 0.0185855 | ||||||||
\(982\) | −7.90154 | −0.252148 | ||||||||
\(983\) | 50.5793 | 1.61323 | 0.806614 | − | 0.591078i | \(-0.201298\pi\) | ||||
0.806614 | + | 0.591078i | \(0.201298\pi\) | |||||||
\(984\) | 6.06441 | 0.193326 | ||||||||
\(985\) | 14.6402 | 0.466475 | ||||||||
\(986\) | 35.2377 | 1.12220 | ||||||||
\(987\) | −1.18533 | −0.0377294 | ||||||||
\(988\) | −1.66227 | −0.0528839 | ||||||||
\(989\) | −2.48441 | −0.0789996 | ||||||||
\(990\) | 1.45037 | 0.0460957 | ||||||||
\(991\) | 58.8726 | 1.87015 | 0.935074 | − | 0.354452i | \(-0.115332\pi\) | ||||
0.935074 | + | 0.354452i | \(0.115332\pi\) | |||||||
\(992\) | 9.16073 | 0.290854 | ||||||||
\(993\) | 1.43958 | 0.0456836 | ||||||||
\(994\) | 1.55932 | 0.0494587 | ||||||||
\(995\) | −23.6898 | −0.751018 | ||||||||
\(996\) | 27.6741 | 0.876887 | ||||||||
\(997\) | 17.3078 | 0.548143 | 0.274071 | − | 0.961709i | \(-0.411630\pi\) | ||||
0.274071 | + | 0.961709i | \(0.411630\pi\) | |||||||
\(998\) | 10.9025 | 0.345112 | ||||||||
\(999\) | −18.8023 | −0.594877 |
(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 | 8002.2.a.d.1.21 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.21 | ✓ | 69 | 1.1 | even | 1 | trivial |