Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42203 | −1.71264 | −0.856318 | − | 0.516449i | \(-0.827254\pi\) | ||||
−0.856318 | + | 0.516449i | \(0.827254\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.86625 | 1.93312 | ||||||||
\(5\) | 1.50568 | 0.673361 | 0.336681 | − | 0.941619i | \(-0.390696\pi\) | ||||
0.336681 | + | 0.941619i | \(0.390696\pi\) | |||||||
\(6\) | −2.42203 | −0.988791 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.52011 | −1.59810 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.64681 | −1.15322 | ||||||||
\(11\) | −2.29749 | −0.692720 | −0.346360 | − | 0.938102i | \(-0.612582\pi\) | ||||
−0.346360 | + | 0.938102i | \(0.612582\pi\) | |||||||
\(12\) | 3.86625 | 1.11609 | ||||||||
\(13\) | −3.95871 | −1.09795 | −0.548975 | − | 0.835839i | \(-0.684982\pi\) | ||||
−0.548975 | + | 0.835839i | \(0.684982\pi\) | |||||||
\(14\) | −2.42203 | −0.647316 | ||||||||
\(15\) | 1.50568 | 0.388765 | ||||||||
\(16\) | 3.21537 | 0.803844 | ||||||||
\(17\) | 6.76598 | 1.64099 | 0.820496 | − | 0.571652i | \(-0.193697\pi\) | ||||
0.820496 | + | 0.571652i | \(0.193697\pi\) | |||||||
\(18\) | −2.42203 | −0.570879 | ||||||||
\(19\) | 6.60199 | 1.51460 | 0.757300 | − | 0.653067i | \(-0.226518\pi\) | ||||
0.757300 | + | 0.653067i | \(0.226518\pi\) | |||||||
\(20\) | 5.82134 | 1.30169 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 5.56460 | 1.18638 | ||||||||
\(23\) | 8.27590 | 1.72565 | 0.862823 | − | 0.505507i | \(-0.168694\pi\) | ||||
0.862823 | + | 0.505507i | \(0.168694\pi\) | |||||||
\(24\) | −4.52011 | −0.922664 | ||||||||
\(25\) | −2.73292 | −0.546584 | ||||||||
\(26\) | 9.58814 | 1.88039 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.86625 | 0.730652 | ||||||||
\(29\) | −0.934325 | −0.173500 | −0.0867499 | − | 0.996230i | \(-0.527648\pi\) | ||||
−0.0867499 | + | 0.996230i | \(0.527648\pi\) | |||||||
\(30\) | −3.64681 | −0.665814 | ||||||||
\(31\) | 4.90812 | 0.881525 | 0.440762 | − | 0.897624i | \(-0.354708\pi\) | ||||
0.440762 | + | 0.897624i | \(0.354708\pi\) | |||||||
\(32\) | 1.25248 | 0.221410 | ||||||||
\(33\) | −2.29749 | −0.399942 | ||||||||
\(34\) | −16.3874 | −2.81042 | ||||||||
\(35\) | 1.50568 | 0.254507 | ||||||||
\(36\) | 3.86625 | 0.644375 | ||||||||
\(37\) | 0.901092 | 0.148139 | 0.0740693 | − | 0.997253i | \(-0.476401\pi\) | ||||
0.0740693 | + | 0.997253i | \(0.476401\pi\) | |||||||
\(38\) | −15.9902 | −2.59396 | ||||||||
\(39\) | −3.95871 | −0.633901 | ||||||||
\(40\) | −6.80585 | −1.07610 | ||||||||
\(41\) | −7.22158 | −1.12782 | −0.563910 | − | 0.825836i | \(-0.690704\pi\) | ||||
−0.563910 | + | 0.825836i | \(0.690704\pi\) | |||||||
\(42\) | −2.42203 | −0.373728 | ||||||||
\(43\) | −11.5710 | −1.76456 | −0.882279 | − | 0.470728i | \(-0.843991\pi\) | ||||
−0.882279 | + | 0.470728i | \(0.843991\pi\) | |||||||
\(44\) | −8.88267 | −1.33911 | ||||||||
\(45\) | 1.50568 | 0.224454 | ||||||||
\(46\) | −20.0445 | −2.95540 | ||||||||
\(47\) | −4.21712 | −0.615131 | −0.307565 | − | 0.951527i | \(-0.599514\pi\) | ||||
−0.307565 | + | 0.951527i | \(0.599514\pi\) | |||||||
\(48\) | 3.21537 | 0.464099 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.61923 | 0.936100 | ||||||||
\(51\) | 6.76598 | 0.947427 | ||||||||
\(52\) | −15.3054 | −2.12247 | ||||||||
\(53\) | 10.0585 | 1.38164 | 0.690818 | − | 0.723029i | \(-0.257251\pi\) | ||||
0.690818 | + | 0.723029i | \(0.257251\pi\) | |||||||
\(54\) | −2.42203 | −0.329597 | ||||||||
\(55\) | −3.45929 | −0.466451 | ||||||||
\(56\) | −4.52011 | −0.604026 | ||||||||
\(57\) | 6.60199 | 0.874455 | ||||||||
\(58\) | 2.26297 | 0.297142 | ||||||||
\(59\) | 7.86728 | 1.02423 | 0.512116 | − | 0.858916i | \(-0.328862\pi\) | ||||
0.512116 | + | 0.858916i | \(0.328862\pi\) | |||||||
\(60\) | 5.82134 | 0.751532 | ||||||||
\(61\) | 0.887307 | 0.113608 | 0.0568040 | − | 0.998385i | \(-0.481909\pi\) | ||||
0.0568040 | + | 0.998385i | \(0.481909\pi\) | |||||||
\(62\) | −11.8876 | −1.50973 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −9.46431 | −1.18304 | ||||||||
\(65\) | −5.96056 | −0.739317 | ||||||||
\(66\) | 5.56460 | 0.684955 | ||||||||
\(67\) | −7.42719 | −0.907375 | −0.453688 | − | 0.891161i | \(-0.649892\pi\) | ||||
−0.453688 | + | 0.891161i | \(0.649892\pi\) | |||||||
\(68\) | 26.1590 | 3.17224 | ||||||||
\(69\) | 8.27590 | 0.996302 | ||||||||
\(70\) | −3.64681 | −0.435877 | ||||||||
\(71\) | 2.31105 | 0.274271 | 0.137136 | − | 0.990552i | \(-0.456210\pi\) | ||||
0.137136 | + | 0.990552i | \(0.456210\pi\) | |||||||
\(72\) | −4.52011 | −0.532701 | ||||||||
\(73\) | 4.70238 | 0.550372 | 0.275186 | − | 0.961391i | \(-0.411261\pi\) | ||||
0.275186 | + | 0.961391i | \(0.411261\pi\) | |||||||
\(74\) | −2.18247 | −0.253707 | ||||||||
\(75\) | −2.73292 | −0.315571 | ||||||||
\(76\) | 25.5249 | 2.92791 | ||||||||
\(77\) | −2.29749 | −0.261823 | ||||||||
\(78\) | 9.58814 | 1.08564 | ||||||||
\(79\) | 11.8751 | 1.33606 | 0.668028 | − | 0.744136i | \(-0.267139\pi\) | ||||
0.668028 | + | 0.744136i | \(0.267139\pi\) | |||||||
\(80\) | 4.84133 | 0.541277 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.4909 | 1.93155 | ||||||||
\(83\) | 12.8321 | 1.40851 | 0.704254 | − | 0.709948i | \(-0.251282\pi\) | ||||
0.704254 | + | 0.709948i | \(0.251282\pi\) | |||||||
\(84\) | 3.86625 | 0.421842 | ||||||||
\(85\) | 10.1874 | 1.10498 | ||||||||
\(86\) | 28.0253 | 3.02205 | ||||||||
\(87\) | −0.934325 | −0.100170 | ||||||||
\(88\) | 10.3849 | 1.10704 | ||||||||
\(89\) | 2.55646 | 0.270984 | 0.135492 | − | 0.990778i | \(-0.456738\pi\) | ||||
0.135492 | + | 0.990778i | \(0.456738\pi\) | |||||||
\(90\) | −3.64681 | −0.384408 | ||||||||
\(91\) | −3.95871 | −0.414986 | ||||||||
\(92\) | 31.9967 | 3.33589 | ||||||||
\(93\) | 4.90812 | 0.508948 | ||||||||
\(94\) | 10.2140 | 1.05350 | ||||||||
\(95\) | 9.94050 | 1.01987 | ||||||||
\(96\) | 1.25248 | 0.127831 | ||||||||
\(97\) | −9.78138 | −0.993149 | −0.496575 | − | 0.867994i | \(-0.665409\pi\) | ||||
−0.496575 | + | 0.867994i | \(0.665409\pi\) | |||||||
\(98\) | −2.42203 | −0.244662 | ||||||||
\(99\) | −2.29749 | −0.230907 | ||||||||
\(100\) | −10.5662 | −1.05662 | ||||||||
\(101\) | −5.55675 | −0.552917 | −0.276458 | − | 0.961026i | \(-0.589161\pi\) | ||||
−0.276458 | + | 0.961026i | \(0.589161\pi\) | |||||||
\(102\) | −16.3874 | −1.62260 | ||||||||
\(103\) | −10.0408 | −0.989347 | −0.494674 | − | 0.869079i | \(-0.664712\pi\) | ||||
−0.494674 | + | 0.869079i | \(0.664712\pi\) | |||||||
\(104\) | 17.8938 | 1.75463 | ||||||||
\(105\) | 1.50568 | 0.146940 | ||||||||
\(106\) | −24.3619 | −2.36624 | ||||||||
\(107\) | −7.81185 | −0.755200 | −0.377600 | − | 0.925969i | \(-0.623251\pi\) | ||||
−0.377600 | + | 0.925969i | \(0.623251\pi\) | |||||||
\(108\) | 3.86625 | 0.372030 | ||||||||
\(109\) | −9.18047 | −0.879329 | −0.439665 | − | 0.898162i | \(-0.644903\pi\) | ||||
−0.439665 | + | 0.898162i | \(0.644903\pi\) | |||||||
\(110\) | 8.37852 | 0.798860 | ||||||||
\(111\) | 0.901092 | 0.0855278 | ||||||||
\(112\) | 3.21537 | 0.303824 | ||||||||
\(113\) | 15.2271 | 1.43245 | 0.716224 | − | 0.697870i | \(-0.245869\pi\) | ||||
0.716224 | + | 0.697870i | \(0.245869\pi\) | |||||||
\(114\) | −15.9902 | −1.49762 | ||||||||
\(115\) | 12.4609 | 1.16198 | ||||||||
\(116\) | −3.61233 | −0.335397 | ||||||||
\(117\) | −3.95871 | −0.365983 | ||||||||
\(118\) | −19.0548 | −1.75414 | ||||||||
\(119\) | 6.76598 | 0.620237 | ||||||||
\(120\) | −6.80585 | −0.621287 | ||||||||
\(121\) | −5.72154 | −0.520140 | ||||||||
\(122\) | −2.14909 | −0.194569 | ||||||||
\(123\) | −7.22158 | −0.651148 | ||||||||
\(124\) | 18.9760 | 1.70410 | ||||||||
\(125\) | −11.6433 | −1.04141 | ||||||||
\(126\) | −2.42203 | −0.215772 | ||||||||
\(127\) | 0.248562 | 0.0220563 | 0.0110281 | − | 0.999939i | \(-0.496490\pi\) | ||||
0.0110281 | + | 0.999939i | \(0.496490\pi\) | |||||||
\(128\) | 20.4179 | 1.80470 | ||||||||
\(129\) | −11.5710 | −1.01877 | ||||||||
\(130\) | 14.4367 | 1.26618 | ||||||||
\(131\) | −2.53084 | −0.221121 | −0.110560 | − | 0.993869i | \(-0.535265\pi\) | ||||
−0.110560 | + | 0.993869i | \(0.535265\pi\) | |||||||
\(132\) | −8.88267 | −0.773137 | ||||||||
\(133\) | 6.60199 | 0.572465 | ||||||||
\(134\) | 17.9889 | 1.55400 | ||||||||
\(135\) | 1.50568 | 0.129588 | ||||||||
\(136\) | −30.5830 | −2.62247 | ||||||||
\(137\) | 17.0146 | 1.45365 | 0.726826 | − | 0.686821i | \(-0.240995\pi\) | ||||
0.726826 | + | 0.686821i | \(0.240995\pi\) | |||||||
\(138\) | −20.0445 | −1.70630 | ||||||||
\(139\) | 18.6591 | 1.58264 | 0.791322 | − | 0.611399i | \(-0.209393\pi\) | ||||
0.791322 | + | 0.611399i | \(0.209393\pi\) | |||||||
\(140\) | 5.82134 | 0.491993 | ||||||||
\(141\) | −4.21712 | −0.355146 | ||||||||
\(142\) | −5.59745 | −0.469727 | ||||||||
\(143\) | 9.09511 | 0.760571 | ||||||||
\(144\) | 3.21537 | 0.267948 | ||||||||
\(145\) | −1.40680 | −0.116828 | ||||||||
\(146\) | −11.3893 | −0.942587 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 3.48384 | 0.286370 | ||||||||
\(149\) | 17.9376 | 1.46951 | 0.734753 | − | 0.678335i | \(-0.237298\pi\) | ||||
0.734753 | + | 0.678335i | \(0.237298\pi\) | |||||||
\(150\) | 6.61923 | 0.540458 | ||||||||
\(151\) | −6.02937 | −0.490663 | −0.245332 | − | 0.969439i | \(-0.578897\pi\) | ||||
−0.245332 | + | 0.969439i | \(0.578897\pi\) | |||||||
\(152\) | −29.8418 | −2.42049 | ||||||||
\(153\) | 6.76598 | 0.546997 | ||||||||
\(154\) | 5.56460 | 0.448408 | ||||||||
\(155\) | 7.39007 | 0.593585 | ||||||||
\(156\) | −15.3054 | −1.22541 | ||||||||
\(157\) | 6.84302 | 0.546133 | 0.273066 | − | 0.961995i | \(-0.411962\pi\) | ||||
0.273066 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(158\) | −28.7620 | −2.28818 | ||||||||
\(159\) | 10.0585 | 0.797688 | ||||||||
\(160\) | 1.88584 | 0.149089 | ||||||||
\(161\) | 8.27590 | 0.652233 | ||||||||
\(162\) | −2.42203 | −0.190293 | ||||||||
\(163\) | 22.4360 | 1.75733 | 0.878663 | − | 0.477443i | \(-0.158436\pi\) | ||||
0.878663 | + | 0.477443i | \(0.158436\pi\) | |||||||
\(164\) | −27.9204 | −2.18022 | ||||||||
\(165\) | −3.45929 | −0.269305 | ||||||||
\(166\) | −31.0798 | −2.41226 | ||||||||
\(167\) | −13.3217 | −1.03086 | −0.515431 | − | 0.856931i | \(-0.672368\pi\) | ||||
−0.515431 | + | 0.856931i | \(0.672368\pi\) | |||||||
\(168\) | −4.52011 | −0.348734 | ||||||||
\(169\) | 2.67141 | 0.205493 | ||||||||
\(170\) | −24.6743 | −1.89243 | ||||||||
\(171\) | 6.60199 | 0.504867 | ||||||||
\(172\) | −44.7363 | −3.41111 | ||||||||
\(173\) | −21.8313 | −1.65980 | −0.829901 | − | 0.557911i | \(-0.811603\pi\) | ||||
−0.829901 | + | 0.557911i | \(0.811603\pi\) | |||||||
\(174\) | 2.26297 | 0.171555 | ||||||||
\(175\) | −2.73292 | −0.206589 | ||||||||
\(176\) | −7.38729 | −0.556838 | ||||||||
\(177\) | 7.86728 | 0.591341 | ||||||||
\(178\) | −6.19183 | −0.464097 | ||||||||
\(179\) | −5.30716 | −0.396676 | −0.198338 | − | 0.980134i | \(-0.563554\pi\) | ||||
−0.198338 | + | 0.980134i | \(0.563554\pi\) | |||||||
\(180\) | 5.82134 | 0.433897 | ||||||||
\(181\) | −11.0696 | −0.822795 | −0.411397 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411397 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(182\) | 9.58814 | 0.710720 | ||||||||
\(183\) | 0.887307 | 0.0655916 | ||||||||
\(184\) | −37.4080 | −2.75776 | ||||||||
\(185\) | 1.35676 | 0.0997508 | ||||||||
\(186\) | −11.8876 | −0.871644 | ||||||||
\(187\) | −15.5448 | −1.13675 | ||||||||
\(188\) | −16.3044 | −1.18912 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −24.0762 | −1.74667 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | −9.46431 | −0.683027 | ||||||||
\(193\) | −6.75705 | −0.486383 | −0.243192 | − | 0.969978i | \(-0.578194\pi\) | ||||
−0.243192 | + | 0.969978i | \(0.578194\pi\) | |||||||
\(194\) | 23.6908 | 1.70090 | ||||||||
\(195\) | −5.96056 | −0.426845 | ||||||||
\(196\) | 3.86625 | 0.276161 | ||||||||
\(197\) | 22.5867 | 1.60924 | 0.804620 | − | 0.593791i | \(-0.202369\pi\) | ||||
0.804620 | + | 0.593791i | \(0.202369\pi\) | |||||||
\(198\) | 5.56460 | 0.395459 | ||||||||
\(199\) | 8.40653 | 0.595923 | 0.297961 | − | 0.954578i | \(-0.403693\pi\) | ||||
0.297961 | + | 0.954578i | \(0.403693\pi\) | |||||||
\(200\) | 12.3531 | 0.873497 | ||||||||
\(201\) | −7.42719 | −0.523873 | ||||||||
\(202\) | 13.4586 | 0.946946 | ||||||||
\(203\) | −0.934325 | −0.0655768 | ||||||||
\(204\) | 26.1590 | 1.83149 | ||||||||
\(205\) | −10.8734 | −0.759431 | ||||||||
\(206\) | 24.3191 | 1.69439 | ||||||||
\(207\) | 8.27590 | 0.575215 | ||||||||
\(208\) | −12.7287 | −0.882579 | ||||||||
\(209\) | −15.1680 | −1.04919 | ||||||||
\(210\) | −3.64681 | −0.251654 | ||||||||
\(211\) | 17.4880 | 1.20393 | 0.601963 | − | 0.798524i | \(-0.294386\pi\) | ||||
0.601963 | + | 0.798524i | \(0.294386\pi\) | |||||||
\(212\) | 38.8885 | 2.67087 | ||||||||
\(213\) | 2.31105 | 0.158351 | ||||||||
\(214\) | 18.9206 | 1.29338 | ||||||||
\(215\) | −17.4222 | −1.18818 | ||||||||
\(216\) | −4.52011 | −0.307555 | ||||||||
\(217\) | 4.90812 | 0.333185 | ||||||||
\(218\) | 22.2354 | 1.50597 | ||||||||
\(219\) | 4.70238 | 0.317757 | ||||||||
\(220\) | −13.3745 | −0.901707 | ||||||||
\(221\) | −26.7846 | −1.80173 | ||||||||
\(222\) | −2.18247 | −0.146478 | ||||||||
\(223\) | 9.19635 | 0.615833 | 0.307917 | − | 0.951413i | \(-0.400368\pi\) | ||||
0.307917 | + | 0.951413i | \(0.400368\pi\) | |||||||
\(224\) | 1.25248 | 0.0836851 | ||||||||
\(225\) | −2.73292 | −0.182195 | ||||||||
\(226\) | −36.8806 | −2.45326 | ||||||||
\(227\) | 9.49722 | 0.630352 | 0.315176 | − | 0.949033i | \(-0.397936\pi\) | ||||
0.315176 | + | 0.949033i | \(0.397936\pi\) | |||||||
\(228\) | 25.5249 | 1.69043 | ||||||||
\(229\) | −1.97384 | −0.130435 | −0.0652174 | − | 0.997871i | \(-0.520774\pi\) | ||||
−0.0652174 | + | 0.997871i | \(0.520774\pi\) | |||||||
\(230\) | −30.1807 | −1.99005 | ||||||||
\(231\) | −2.29749 | −0.151164 | ||||||||
\(232\) | 4.22326 | 0.277270 | ||||||||
\(233\) | −8.23215 | −0.539306 | −0.269653 | − | 0.962958i | \(-0.586909\pi\) | ||||
−0.269653 | + | 0.962958i | \(0.586909\pi\) | |||||||
\(234\) | 9.58814 | 0.626796 | ||||||||
\(235\) | −6.34965 | −0.414205 | ||||||||
\(236\) | 30.4169 | 1.97997 | ||||||||
\(237\) | 11.8751 | 0.771372 | ||||||||
\(238\) | −16.3874 | −1.06224 | ||||||||
\(239\) | 1.35691 | 0.0877709 | 0.0438855 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438855 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(240\) | 4.84133 | 0.312507 | ||||||||
\(241\) | −11.2200 | −0.722746 | −0.361373 | − | 0.932421i | \(-0.617692\pi\) | ||||
−0.361373 | + | 0.932421i | \(0.617692\pi\) | |||||||
\(242\) | 13.8578 | 0.890810 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.43055 | 0.219618 | ||||||||
\(245\) | 1.50568 | 0.0961945 | ||||||||
\(246\) | 17.4909 | 1.11518 | ||||||||
\(247\) | −26.1354 | −1.66295 | ||||||||
\(248\) | −22.1853 | −1.40877 | ||||||||
\(249\) | 12.8321 | 0.813203 | ||||||||
\(250\) | 28.2005 | 1.78356 | ||||||||
\(251\) | 29.7190 | 1.87585 | 0.937923 | − | 0.346844i | \(-0.112747\pi\) | ||||
0.937923 | + | 0.346844i | \(0.112747\pi\) | |||||||
\(252\) | 3.86625 | 0.243551 | ||||||||
\(253\) | −19.0138 | −1.19539 | ||||||||
\(254\) | −0.602025 | −0.0377744 | ||||||||
\(255\) | 10.1874 | 0.637961 | ||||||||
\(256\) | −30.5242 | −1.90776 | ||||||||
\(257\) | −7.27439 | −0.453764 | −0.226882 | − | 0.973922i | \(-0.572853\pi\) | ||||
−0.226882 | + | 0.973922i | \(0.572853\pi\) | |||||||
\(258\) | 28.0253 | 1.74478 | ||||||||
\(259\) | 0.901092 | 0.0559911 | ||||||||
\(260\) | −23.0450 | −1.42919 | ||||||||
\(261\) | −0.934325 | −0.0578333 | ||||||||
\(262\) | 6.12978 | 0.378699 | ||||||||
\(263\) | −1.90403 | −0.117408 | −0.0587039 | − | 0.998275i | \(-0.518697\pi\) | ||||
−0.0587039 | + | 0.998275i | \(0.518697\pi\) | |||||||
\(264\) | 10.3849 | 0.639148 | ||||||||
\(265\) | 15.1448 | 0.930340 | ||||||||
\(266\) | −15.9902 | −0.980425 | ||||||||
\(267\) | 2.55646 | 0.156453 | ||||||||
\(268\) | −28.7153 | −1.75407 | ||||||||
\(269\) | 8.88210 | 0.541551 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(270\) | −3.64681 | −0.221938 | ||||||||
\(271\) | −21.8086 | −1.32478 | −0.662389 | − | 0.749160i | \(-0.730457\pi\) | ||||
−0.662389 | + | 0.749160i | \(0.730457\pi\) | |||||||
\(272\) | 21.7552 | 1.31910 | ||||||||
\(273\) | −3.95871 | −0.239592 | ||||||||
\(274\) | −41.2098 | −2.48958 | ||||||||
\(275\) | 6.27886 | 0.378630 | ||||||||
\(276\) | 31.9967 | 1.92597 | ||||||||
\(277\) | 6.28833 | 0.377829 | 0.188915 | − | 0.981994i | \(-0.439503\pi\) | ||||
0.188915 | + | 0.981994i | \(0.439503\pi\) | |||||||
\(278\) | −45.1930 | −2.71049 | ||||||||
\(279\) | 4.90812 | 0.293842 | ||||||||
\(280\) | −6.80585 | −0.406728 | ||||||||
\(281\) | −0.227607 | −0.0135779 | −0.00678895 | − | 0.999977i | \(-0.502161\pi\) | ||||
−0.00678895 | + | 0.999977i | \(0.502161\pi\) | |||||||
\(282\) | 10.2140 | 0.608236 | ||||||||
\(283\) | −2.79415 | −0.166095 | −0.0830474 | − | 0.996546i | \(-0.526465\pi\) | ||||
−0.0830474 | + | 0.996546i | \(0.526465\pi\) | |||||||
\(284\) | 8.93510 | 0.530201 | ||||||||
\(285\) | 9.94050 | 0.588824 | ||||||||
\(286\) | −22.0287 | −1.30258 | ||||||||
\(287\) | −7.22158 | −0.426276 | ||||||||
\(288\) | 1.25248 | 0.0738033 | ||||||||
\(289\) | 28.7785 | 1.69285 | ||||||||
\(290\) | 3.40731 | 0.200084 | ||||||||
\(291\) | −9.78138 | −0.573395 | ||||||||
\(292\) | 18.1806 | 1.06394 | ||||||||
\(293\) | 17.6269 | 1.02978 | 0.514888 | − | 0.857258i | \(-0.327834\pi\) | ||||
0.514888 | + | 0.857258i | \(0.327834\pi\) | |||||||
\(294\) | −2.42203 | −0.141256 | ||||||||
\(295\) | 11.8456 | 0.689679 | ||||||||
\(296\) | −4.07304 | −0.236740 | ||||||||
\(297\) | −2.29749 | −0.133314 | ||||||||
\(298\) | −43.4455 | −2.51673 | ||||||||
\(299\) | −32.7619 | −1.89467 | ||||||||
\(300\) | −10.5662 | −0.610037 | ||||||||
\(301\) | −11.5710 | −0.666940 | ||||||||
\(302\) | 14.6033 | 0.840328 | ||||||||
\(303\) | −5.55675 | −0.319227 | ||||||||
\(304\) | 21.2279 | 1.21750 | ||||||||
\(305\) | 1.33600 | 0.0764993 | ||||||||
\(306\) | −16.3874 | −0.936807 | ||||||||
\(307\) | 15.4572 | 0.882191 | 0.441096 | − | 0.897460i | \(-0.354590\pi\) | ||||
0.441096 | + | 0.897460i | \(0.354590\pi\) | |||||||
\(308\) | −8.88267 | −0.506137 | ||||||||
\(309\) | −10.0408 | −0.571200 | ||||||||
\(310\) | −17.8990 | −1.01659 | ||||||||
\(311\) | −6.88320 | −0.390310 | −0.195155 | − | 0.980772i | \(-0.562521\pi\) | ||||
−0.195155 | + | 0.980772i | \(0.562521\pi\) | |||||||
\(312\) | 17.8938 | 1.01304 | ||||||||
\(313\) | 2.10273 | 0.118853 | 0.0594265 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594265 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(314\) | −16.5740 | −0.935326 | ||||||||
\(315\) | 1.50568 | 0.0848356 | ||||||||
\(316\) | 45.9122 | 2.58276 | ||||||||
\(317\) | −18.4185 | −1.03449 | −0.517243 | − | 0.855839i | \(-0.673042\pi\) | ||||
−0.517243 | + | 0.855839i | \(0.673042\pi\) | |||||||
\(318\) | −24.3619 | −1.36615 | ||||||||
\(319\) | 2.14660 | 0.120187 | ||||||||
\(320\) | −14.2502 | −0.796612 | ||||||||
\(321\) | −7.81185 | −0.436015 | ||||||||
\(322\) | −20.0445 | −1.11704 | ||||||||
\(323\) | 44.6690 | 2.48545 | ||||||||
\(324\) | 3.86625 | 0.214792 | ||||||||
\(325\) | 10.8189 | 0.600122 | ||||||||
\(326\) | −54.3408 | −3.00966 | ||||||||
\(327\) | −9.18047 | −0.507681 | ||||||||
\(328\) | 32.6423 | 1.80237 | ||||||||
\(329\) | −4.21712 | −0.232498 | ||||||||
\(330\) | 8.37852 | 0.461222 | ||||||||
\(331\) | 2.63914 | 0.145060 | 0.0725300 | − | 0.997366i | \(-0.476893\pi\) | ||||
0.0725300 | + | 0.997366i | \(0.476893\pi\) | |||||||
\(332\) | 49.6122 | 2.72282 | ||||||||
\(333\) | 0.901092 | 0.0493795 | ||||||||
\(334\) | 32.2655 | 1.76549 | ||||||||
\(335\) | −11.1830 | −0.610992 | ||||||||
\(336\) | 3.21537 | 0.175413 | ||||||||
\(337\) | 16.4792 | 0.897678 | 0.448839 | − | 0.893613i | \(-0.351838\pi\) | ||||
0.448839 | + | 0.893613i | \(0.351838\pi\) | |||||||
\(338\) | −6.47024 | −0.351934 | ||||||||
\(339\) | 15.2271 | 0.827025 | ||||||||
\(340\) | 39.3871 | 2.13606 | ||||||||
\(341\) | −11.2764 | −0.610649 | ||||||||
\(342\) | −15.9902 | −0.864653 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 52.3021 | 2.81994 | ||||||||
\(345\) | 12.4609 | 0.670871 | ||||||||
\(346\) | 52.8761 | 2.84264 | ||||||||
\(347\) | −30.0569 | −1.61354 | −0.806769 | − | 0.590867i | \(-0.798786\pi\) | ||||
−0.806769 | + | 0.590867i | \(0.798786\pi\) | |||||||
\(348\) | −3.61233 | −0.193641 | ||||||||
\(349\) | 26.5298 | 1.42011 | 0.710054 | − | 0.704148i | \(-0.248671\pi\) | ||||
0.710054 | + | 0.704148i | \(0.248671\pi\) | |||||||
\(350\) | 6.61923 | 0.353813 | ||||||||
\(351\) | −3.95871 | −0.211300 | ||||||||
\(352\) | −2.87757 | −0.153375 | ||||||||
\(353\) | −2.00123 | −0.106515 | −0.0532574 | − | 0.998581i | \(-0.516960\pi\) | ||||
−0.0532574 | + | 0.998581i | \(0.516960\pi\) | |||||||
\(354\) | −19.0548 | −1.01275 | ||||||||
\(355\) | 3.47971 | 0.184684 | ||||||||
\(356\) | 9.88391 | 0.523846 | ||||||||
\(357\) | 6.76598 | 0.358094 | ||||||||
\(358\) | 12.8541 | 0.679361 | ||||||||
\(359\) | 24.2465 | 1.27968 | 0.639840 | − | 0.768508i | \(-0.279000\pi\) | ||||
0.639840 | + | 0.768508i | \(0.279000\pi\) | |||||||
\(360\) | −6.80585 | −0.358700 | ||||||||
\(361\) | 24.5863 | 1.29402 | ||||||||
\(362\) | 26.8109 | 1.40915 | ||||||||
\(363\) | −5.72154 | −0.300303 | ||||||||
\(364\) | −15.3054 | −0.802219 | ||||||||
\(365\) | 7.08029 | 0.370599 | ||||||||
\(366\) | −2.14909 | −0.112335 | ||||||||
\(367\) | −14.0732 | −0.734614 | −0.367307 | − | 0.930100i | \(-0.619720\pi\) | ||||
−0.367307 | + | 0.930100i | \(0.619720\pi\) | |||||||
\(368\) | 26.6101 | 1.38715 | ||||||||
\(369\) | −7.22158 | −0.375940 | ||||||||
\(370\) | −3.28611 | −0.170837 | ||||||||
\(371\) | 10.0585 | 0.522209 | ||||||||
\(372\) | 18.9760 | 0.983860 | ||||||||
\(373\) | −30.9525 | −1.60266 | −0.801329 | − | 0.598224i | \(-0.795873\pi\) | ||||
−0.801329 | + | 0.598224i | \(0.795873\pi\) | |||||||
\(374\) | 37.6500 | 1.94683 | ||||||||
\(375\) | −11.6433 | −0.601259 | ||||||||
\(376\) | 19.0619 | 0.983042 | ||||||||
\(377\) | 3.69873 | 0.190494 | ||||||||
\(378\) | −2.42203 | −0.124576 | ||||||||
\(379\) | −20.6331 | −1.05985 | −0.529925 | − | 0.848044i | \(-0.677780\pi\) | ||||
−0.529925 | + | 0.848044i | \(0.677780\pi\) | |||||||
\(380\) | 38.4324 | 1.97154 | ||||||||
\(381\) | 0.248562 | 0.0127342 | ||||||||
\(382\) | −2.42203 | −0.123922 | ||||||||
\(383\) | 5.14345 | 0.262818 | 0.131409 | − | 0.991328i | \(-0.458050\pi\) | ||||
0.131409 | + | 0.991328i | \(0.458050\pi\) | |||||||
\(384\) | 20.4179 | 1.04195 | ||||||||
\(385\) | −3.45929 | −0.176302 | ||||||||
\(386\) | 16.3658 | 0.832998 | ||||||||
\(387\) | −11.5710 | −0.588186 | ||||||||
\(388\) | −37.8172 | −1.91988 | ||||||||
\(389\) | 20.9418 | 1.06179 | 0.530895 | − | 0.847438i | \(-0.321856\pi\) | ||||
0.530895 | + | 0.847438i | \(0.321856\pi\) | |||||||
\(390\) | 14.4367 | 0.731030 | ||||||||
\(391\) | 55.9946 | 2.83177 | ||||||||
\(392\) | −4.52011 | −0.228300 | ||||||||
\(393\) | −2.53084 | −0.127664 | ||||||||
\(394\) | −54.7059 | −2.75604 | ||||||||
\(395\) | 17.8802 | 0.899649 | ||||||||
\(396\) | −8.88267 | −0.446371 | ||||||||
\(397\) | −1.66874 | −0.0837518 | −0.0418759 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418759 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(398\) | −20.3609 | −1.02060 | ||||||||
\(399\) | 6.60199 | 0.330513 | ||||||||
\(400\) | −8.78737 | −0.439368 | ||||||||
\(401\) | 1.95998 | 0.0978766 | 0.0489383 | − | 0.998802i | \(-0.484416\pi\) | ||||
0.0489383 | + | 0.998802i | \(0.484416\pi\) | |||||||
\(402\) | 17.9889 | 0.897205 | ||||||||
\(403\) | −19.4298 | −0.967869 | ||||||||
\(404\) | −21.4838 | −1.06886 | ||||||||
\(405\) | 1.50568 | 0.0748179 | ||||||||
\(406\) | 2.26297 | 0.112309 | ||||||||
\(407\) | −2.07025 | −0.102618 | ||||||||
\(408\) | −30.5830 | −1.51408 | ||||||||
\(409\) | −11.5137 | −0.569316 | −0.284658 | − | 0.958629i | \(-0.591880\pi\) | ||||
−0.284658 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(410\) | 26.3357 | 1.30063 | ||||||||
\(411\) | 17.0146 | 0.839267 | ||||||||
\(412\) | −38.8201 | −1.91253 | ||||||||
\(413\) | 7.86728 | 0.387124 | ||||||||
\(414\) | −20.0445 | −0.985134 | ||||||||
\(415\) | 19.3211 | 0.948435 | ||||||||
\(416\) | −4.95822 | −0.243097 | ||||||||
\(417\) | 18.6591 | 0.913740 | ||||||||
\(418\) | 36.7374 | 1.79689 | ||||||||
\(419\) | 10.4582 | 0.510917 | 0.255458 | − | 0.966820i | \(-0.417774\pi\) | ||||
0.255458 | + | 0.966820i | \(0.417774\pi\) | |||||||
\(420\) | 5.82134 | 0.284052 | ||||||||
\(421\) | 37.3335 | 1.81952 | 0.909762 | − | 0.415131i | \(-0.136264\pi\) | ||||
0.909762 | + | 0.415131i | \(0.136264\pi\) | |||||||
\(422\) | −42.3566 | −2.06189 | ||||||||
\(423\) | −4.21712 | −0.205044 | ||||||||
\(424\) | −45.4654 | −2.20799 | ||||||||
\(425\) | −18.4909 | −0.896940 | ||||||||
\(426\) | −5.59745 | −0.271197 | ||||||||
\(427\) | 0.887307 | 0.0429398 | ||||||||
\(428\) | −30.2025 | −1.45989 | ||||||||
\(429\) | 9.09511 | 0.439116 | ||||||||
\(430\) | 42.1972 | 2.03493 | ||||||||
\(431\) | −18.3822 | −0.885440 | −0.442720 | − | 0.896660i | \(-0.645986\pi\) | ||||
−0.442720 | + | 0.896660i | \(0.645986\pi\) | |||||||
\(432\) | 3.21537 | 0.154700 | ||||||||
\(433\) | −9.21975 | −0.443073 | −0.221537 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221537 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(434\) | −11.8876 | −0.570625 | ||||||||
\(435\) | −1.40680 | −0.0674507 | ||||||||
\(436\) | −35.4940 | −1.69985 | ||||||||
\(437\) | 54.6374 | 2.61366 | ||||||||
\(438\) | −11.3893 | −0.544203 | ||||||||
\(439\) | 17.0972 | 0.816003 | 0.408002 | − | 0.912981i | \(-0.366226\pi\) | ||||
0.408002 | + | 0.912981i | \(0.366226\pi\) | |||||||
\(440\) | 15.6364 | 0.745436 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 64.8732 | 3.08570 | ||||||||
\(443\) | −25.3695 | −1.20534 | −0.602671 | − | 0.797990i | \(-0.705897\pi\) | ||||
−0.602671 | + | 0.797990i | \(0.705897\pi\) | |||||||
\(444\) | 3.48384 | 0.165336 | ||||||||
\(445\) | 3.84922 | 0.182470 | ||||||||
\(446\) | −22.2739 | −1.05470 | ||||||||
\(447\) | 17.9376 | 0.848420 | ||||||||
\(448\) | −9.46431 | −0.447146 | ||||||||
\(449\) | 34.7753 | 1.64115 | 0.820573 | − | 0.571542i | \(-0.193654\pi\) | ||||
0.820573 | + | 0.571542i | \(0.193654\pi\) | |||||||
\(450\) | 6.61923 | 0.312033 | ||||||||
\(451\) | 16.5915 | 0.781263 | ||||||||
\(452\) | 58.8719 | 2.76910 | ||||||||
\(453\) | −6.02937 | −0.283285 | ||||||||
\(454\) | −23.0026 | −1.07956 | ||||||||
\(455\) | −5.96056 | −0.279435 | ||||||||
\(456\) | −29.8418 | −1.39747 | ||||||||
\(457\) | −23.6669 | −1.10709 | −0.553546 | − | 0.832819i | \(-0.686726\pi\) | ||||
−0.553546 | + | 0.832819i | \(0.686726\pi\) | |||||||
\(458\) | 4.78070 | 0.223387 | ||||||||
\(459\) | 6.76598 | 0.315809 | ||||||||
\(460\) | 48.1768 | 2.24626 | ||||||||
\(461\) | −6.05063 | −0.281806 | −0.140903 | − | 0.990023i | \(-0.545001\pi\) | ||||
−0.140903 | + | 0.990023i | \(0.545001\pi\) | |||||||
\(462\) | 5.56460 | 0.258889 | ||||||||
\(463\) | 4.54394 | 0.211175 | 0.105587 | − | 0.994410i | \(-0.466328\pi\) | ||||
0.105587 | + | 0.994410i | \(0.466328\pi\) | |||||||
\(464\) | −3.00421 | −0.139467 | ||||||||
\(465\) | 7.39007 | 0.342706 | ||||||||
\(466\) | 19.9385 | 0.923635 | ||||||||
\(467\) | −6.39115 | −0.295747 | −0.147874 | − | 0.989006i | \(-0.547243\pi\) | ||||
−0.147874 | + | 0.989006i | \(0.547243\pi\) | |||||||
\(468\) | −15.3054 | −0.707491 | ||||||||
\(469\) | −7.42719 | −0.342956 | ||||||||
\(470\) | 15.3791 | 0.709383 | ||||||||
\(471\) | 6.84302 | 0.315310 | ||||||||
\(472\) | −35.5610 | −1.63683 | ||||||||
\(473\) | 26.5842 | 1.22234 | ||||||||
\(474\) | −28.7620 | −1.32108 | ||||||||
\(475\) | −18.0427 | −0.827857 | ||||||||
\(476\) | 26.1590 | 1.19899 | ||||||||
\(477\) | 10.0585 | 0.460545 | ||||||||
\(478\) | −3.28647 | −0.150320 | ||||||||
\(479\) | −24.8783 | −1.13672 | −0.568360 | − | 0.822780i | \(-0.692422\pi\) | ||||
−0.568360 | + | 0.822780i | \(0.692422\pi\) | |||||||
\(480\) | 1.88584 | 0.0860765 | ||||||||
\(481\) | −3.56716 | −0.162649 | ||||||||
\(482\) | 27.1753 | 1.23780 | ||||||||
\(483\) | 8.27590 | 0.376567 | ||||||||
\(484\) | −22.1209 | −1.00549 | ||||||||
\(485\) | −14.7277 | −0.668748 | ||||||||
\(486\) | −2.42203 | −0.109866 | ||||||||
\(487\) | 6.79824 | 0.308058 | 0.154029 | − | 0.988066i | \(-0.450775\pi\) | ||||
0.154029 | + | 0.988066i | \(0.450775\pi\) | |||||||
\(488\) | −4.01073 | −0.181557 | ||||||||
\(489\) | 22.4360 | 1.01459 | ||||||||
\(490\) | −3.64681 | −0.164746 | ||||||||
\(491\) | 13.1347 | 0.592759 | 0.296380 | − | 0.955070i | \(-0.404221\pi\) | ||||
0.296380 | + | 0.955070i | \(0.404221\pi\) | |||||||
\(492\) | −27.9204 | −1.25875 | ||||||||
\(493\) | −6.32163 | −0.284712 | ||||||||
\(494\) | 63.3008 | 2.84804 | ||||||||
\(495\) | −3.45929 | −0.155484 | ||||||||
\(496\) | 15.7814 | 0.708608 | ||||||||
\(497\) | 2.31105 | 0.103665 | ||||||||
\(498\) | −31.0798 | −1.39272 | ||||||||
\(499\) | 31.2157 | 1.39741 | 0.698704 | − | 0.715411i | \(-0.253761\pi\) | ||||
0.698704 | + | 0.715411i | \(0.253761\pi\) | |||||||
\(500\) | −45.0160 | −2.01317 | ||||||||
\(501\) | −13.3217 | −0.595168 | ||||||||
\(502\) | −71.9804 | −3.21264 | ||||||||
\(503\) | −13.9842 | −0.623523 | −0.311761 | − | 0.950160i | \(-0.600919\pi\) | ||||
−0.311761 | + | 0.950160i | \(0.600919\pi\) | |||||||
\(504\) | −4.52011 | −0.201342 | ||||||||
\(505\) | −8.36669 | −0.372313 | ||||||||
\(506\) | 46.0521 | 2.04727 | ||||||||
\(507\) | 2.67141 | 0.118641 | ||||||||
\(508\) | 0.961001 | 0.0426375 | ||||||||
\(509\) | 43.9490 | 1.94801 | 0.974003 | − | 0.226537i | \(-0.0727403\pi\) | ||||
0.974003 | + | 0.226537i | \(0.0727403\pi\) | |||||||
\(510\) | −24.6743 | −1.09260 | ||||||||
\(511\) | 4.70238 | 0.208021 | ||||||||
\(512\) | 33.0949 | 1.46260 | ||||||||
\(513\) | 6.60199 | 0.291485 | ||||||||
\(514\) | 17.6188 | 0.777132 | ||||||||
\(515\) | −15.1182 | −0.666188 | ||||||||
\(516\) | −44.7363 | −1.96940 | ||||||||
\(517\) | 9.68880 | 0.426113 | ||||||||
\(518\) | −2.18247 | −0.0958924 | ||||||||
\(519\) | −21.8313 | −0.958287 | ||||||||
\(520\) | 26.9424 | 1.18150 | ||||||||
\(521\) | 26.3981 | 1.15652 | 0.578262 | − | 0.815851i | \(-0.303731\pi\) | ||||
0.578262 | + | 0.815851i | \(0.303731\pi\) | |||||||
\(522\) | 2.26297 | 0.0990474 | ||||||||
\(523\) | 23.8046 | 1.04090 | 0.520452 | − | 0.853891i | \(-0.325764\pi\) | ||||
0.520452 | + | 0.853891i | \(0.325764\pi\) | |||||||
\(524\) | −9.78486 | −0.427453 | ||||||||
\(525\) | −2.73292 | −0.119274 | ||||||||
\(526\) | 4.61163 | 0.201077 | ||||||||
\(527\) | 33.2083 | 1.44657 | ||||||||
\(528\) | −7.38729 | −0.321491 | ||||||||
\(529\) | 45.4906 | 1.97785 | ||||||||
\(530\) | −36.6813 | −1.59333 | ||||||||
\(531\) | 7.86728 | 0.341411 | ||||||||
\(532\) | 25.5249 | 1.10665 | ||||||||
\(533\) | 28.5881 | 1.23829 | ||||||||
\(534\) | −6.19183 | −0.267947 | ||||||||
\(535\) | −11.7622 | −0.508523 | ||||||||
\(536\) | 33.5717 | 1.45008 | ||||||||
\(537\) | −5.30716 | −0.229021 | ||||||||
\(538\) | −21.5127 | −0.927480 | ||||||||
\(539\) | −2.29749 | −0.0989599 | ||||||||
\(540\) | 5.82134 | 0.250511 | ||||||||
\(541\) | −41.4961 | −1.78406 | −0.892028 | − | 0.451980i | \(-0.850718\pi\) | ||||
−0.892028 | + | 0.451980i | \(0.850718\pi\) | |||||||
\(542\) | 52.8211 | 2.26886 | ||||||||
\(543\) | −11.0696 | −0.475041 | ||||||||
\(544\) | 8.47428 | 0.363332 | ||||||||
\(545\) | −13.8229 | −0.592107 | ||||||||
\(546\) | 9.58814 | 0.410334 | ||||||||
\(547\) | −9.68451 | −0.414080 | −0.207040 | − | 0.978333i | \(-0.566383\pi\) | ||||
−0.207040 | + | 0.978333i | \(0.566383\pi\) | |||||||
\(548\) | 65.7825 | 2.81009 | ||||||||
\(549\) | 0.887307 | 0.0378693 | ||||||||
\(550\) | −15.2076 | −0.648455 | ||||||||
\(551\) | −6.16841 | −0.262783 | ||||||||
\(552\) | −37.4080 | −1.59219 | ||||||||
\(553\) | 11.8751 | 0.504982 | ||||||||
\(554\) | −15.2305 | −0.647084 | ||||||||
\(555\) | 1.35676 | 0.0575911 | ||||||||
\(556\) | 72.1407 | 3.05945 | ||||||||
\(557\) | 0.0830489 | 0.00351890 | 0.00175945 | − | 0.999998i | \(-0.499440\pi\) | ||||
0.00175945 | + | 0.999998i | \(0.499440\pi\) | |||||||
\(558\) | −11.8876 | −0.503244 | ||||||||
\(559\) | 45.8062 | 1.93739 | ||||||||
\(560\) | 4.84133 | 0.204584 | ||||||||
\(561\) | −15.5448 | −0.656301 | ||||||||
\(562\) | 0.551272 | 0.0232540 | ||||||||
\(563\) | −27.2775 | −1.14961 | −0.574804 | − | 0.818291i | \(-0.694922\pi\) | ||||
−0.574804 | + | 0.818291i | \(0.694922\pi\) | |||||||
\(564\) | −16.3044 | −0.686541 | ||||||||
\(565\) | 22.9272 | 0.964556 | ||||||||
\(566\) | 6.76752 | 0.284460 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −10.4462 | −0.438314 | ||||||||
\(569\) | −9.45734 | −0.396472 | −0.198236 | − | 0.980154i | \(-0.563521\pi\) | ||||
−0.198236 | + | 0.980154i | \(0.563521\pi\) | |||||||
\(570\) | −24.0762 | −1.00844 | ||||||||
\(571\) | −7.32078 | −0.306365 | −0.153183 | − | 0.988198i | \(-0.548952\pi\) | ||||
−0.153183 | + | 0.988198i | \(0.548952\pi\) | |||||||
\(572\) | 35.1639 | 1.47028 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | 17.4909 | 0.730056 | ||||||||
\(575\) | −22.6174 | −0.943211 | ||||||||
\(576\) | −9.46431 | −0.394346 | ||||||||
\(577\) | 5.75849 | 0.239729 | 0.119864 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119864 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(578\) | −69.7025 | −2.89924 | ||||||||
\(579\) | −6.75705 | −0.280813 | ||||||||
\(580\) | −5.43902 | −0.225843 | ||||||||
\(581\) | 12.8321 | 0.532366 | ||||||||
\(582\) | 23.6908 | 0.982017 | ||||||||
\(583\) | −23.1092 | −0.957086 | ||||||||
\(584\) | −21.2553 | −0.879550 | ||||||||
\(585\) | −5.96056 | −0.246439 | ||||||||
\(586\) | −42.6930 | −1.76363 | ||||||||
\(587\) | −32.8516 | −1.35593 | −0.677965 | − | 0.735095i | \(-0.737138\pi\) | ||||
−0.677965 | + | 0.735095i | \(0.737138\pi\) | |||||||
\(588\) | 3.86625 | 0.159441 | ||||||||
\(589\) | 32.4034 | 1.33516 | ||||||||
\(590\) | −28.6905 | −1.18117 | ||||||||
\(591\) | 22.5867 | 0.929095 | ||||||||
\(592\) | 2.89735 | 0.119080 | ||||||||
\(593\) | 29.8685 | 1.22655 | 0.613277 | − | 0.789868i | \(-0.289851\pi\) | ||||
0.613277 | + | 0.789868i | \(0.289851\pi\) | |||||||
\(594\) | 5.56460 | 0.228318 | ||||||||
\(595\) | 10.1874 | 0.417643 | ||||||||
\(596\) | 69.3512 | 2.84074 | ||||||||
\(597\) | 8.40653 | 0.344056 | ||||||||
\(598\) | 79.3505 | 3.24488 | ||||||||
\(599\) | −45.1692 | −1.84556 | −0.922781 | − | 0.385324i | \(-0.874090\pi\) | ||||
−0.922781 | + | 0.385324i | \(0.874090\pi\) | |||||||
\(600\) | 12.3531 | 0.504314 | ||||||||
\(601\) | −31.1745 | −1.27164 | −0.635818 | − | 0.771839i | \(-0.719337\pi\) | ||||
−0.635818 | + | 0.771839i | \(0.719337\pi\) | |||||||
\(602\) | 28.0253 | 1.14223 | ||||||||
\(603\) | −7.42719 | −0.302458 | ||||||||
\(604\) | −23.3110 | −0.948513 | ||||||||
\(605\) | −8.61481 | −0.350242 | ||||||||
\(606\) | 13.4586 | 0.546719 | ||||||||
\(607\) | −17.3429 | −0.703926 | −0.351963 | − | 0.936014i | \(-0.614486\pi\) | ||||
−0.351963 | + | 0.936014i | \(0.614486\pi\) | |||||||
\(608\) | 8.26889 | 0.335348 | ||||||||
\(609\) | −0.934325 | −0.0378608 | ||||||||
\(610\) | −3.23584 | −0.131015 | ||||||||
\(611\) | 16.6944 | 0.675382 | ||||||||
\(612\) | 26.1590 | 1.05741 | ||||||||
\(613\) | 18.3956 | 0.742990 | 0.371495 | − | 0.928435i | \(-0.378845\pi\) | ||||
0.371495 | + | 0.928435i | \(0.378845\pi\) | |||||||
\(614\) | −37.4380 | −1.51087 | ||||||||
\(615\) | −10.8734 | −0.438458 | ||||||||
\(616\) | 10.3849 | 0.418420 | ||||||||
\(617\) | −21.0229 | −0.846351 | −0.423176 | − | 0.906048i | \(-0.639085\pi\) | ||||
−0.423176 | + | 0.906048i | \(0.639085\pi\) | |||||||
\(618\) | 24.3191 | 0.978258 | ||||||||
\(619\) | −16.2023 | −0.651224 | −0.325612 | − | 0.945503i | \(-0.605570\pi\) | ||||
−0.325612 | + | 0.945503i | \(0.605570\pi\) | |||||||
\(620\) | 28.5718 | 1.14747 | ||||||||
\(621\) | 8.27590 | 0.332101 | ||||||||
\(622\) | 16.6713 | 0.668460 | ||||||||
\(623\) | 2.55646 | 0.102422 | ||||||||
\(624\) | −12.7287 | −0.509558 | ||||||||
\(625\) | −3.86653 | −0.154661 | ||||||||
\(626\) | −5.09287 | −0.203552 | ||||||||
\(627\) | −15.1680 | −0.605752 | ||||||||
\(628\) | 26.4568 | 1.05574 | ||||||||
\(629\) | 6.09677 | 0.243094 | ||||||||
\(630\) | −3.64681 | −0.145292 | ||||||||
\(631\) | 40.3438 | 1.60606 | 0.803030 | − | 0.595938i | \(-0.203220\pi\) | ||||
0.803030 | + | 0.595938i | \(0.203220\pi\) | |||||||
\(632\) | −53.6769 | −2.13515 | ||||||||
\(633\) | 17.4880 | 0.695087 | ||||||||
\(634\) | 44.6102 | 1.77170 | ||||||||
\(635\) | 0.374255 | 0.0148519 | ||||||||
\(636\) | 38.8885 | 1.54203 | ||||||||
\(637\) | −3.95871 | −0.156850 | ||||||||
\(638\) | −5.19915 | −0.205836 | ||||||||
\(639\) | 2.31105 | 0.0914238 | ||||||||
\(640\) | 30.7429 | 1.21522 | ||||||||
\(641\) | 46.3877 | 1.83221 | 0.916103 | − | 0.400943i | \(-0.131317\pi\) | ||||
0.916103 | + | 0.400943i | \(0.131317\pi\) | |||||||
\(642\) | 18.9206 | 0.746735 | ||||||||
\(643\) | −15.5280 | −0.612363 | −0.306182 | − | 0.951973i | \(-0.599051\pi\) | ||||
−0.306182 | + | 0.951973i | \(0.599051\pi\) | |||||||
\(644\) | 31.9967 | 1.26085 | ||||||||
\(645\) | −17.4222 | −0.685999 | ||||||||
\(646\) | −108.190 | −4.25667 | ||||||||
\(647\) | −29.4139 | −1.15638 | −0.578190 | − | 0.815902i | \(-0.696241\pi\) | ||||
−0.578190 | + | 0.815902i | \(0.696241\pi\) | |||||||
\(648\) | −4.52011 | −0.177567 | ||||||||
\(649\) | −18.0750 | −0.709506 | ||||||||
\(650\) | −26.2036 | −1.02779 | ||||||||
\(651\) | 4.90812 | 0.192364 | ||||||||
\(652\) | 86.7433 | 3.39713 | ||||||||
\(653\) | 16.5609 | 0.648077 | 0.324038 | − | 0.946044i | \(-0.394959\pi\) | ||||
0.324038 | + | 0.946044i | \(0.394959\pi\) | |||||||
\(654\) | 22.2354 | 0.869473 | ||||||||
\(655\) | −3.81064 | −0.148894 | ||||||||
\(656\) | −23.2201 | −0.906591 | ||||||||
\(657\) | 4.70238 | 0.183457 | ||||||||
\(658\) | 10.2140 | 0.398184 | ||||||||
\(659\) | 2.12582 | 0.0828102 | 0.0414051 | − | 0.999142i | \(-0.486817\pi\) | ||||
0.0414051 | + | 0.999142i | \(0.486817\pi\) | |||||||
\(660\) | −13.3745 | −0.520601 | ||||||||
\(661\) | −5.39501 | −0.209842 | −0.104921 | − | 0.994481i | \(-0.533459\pi\) | ||||
−0.104921 | + | 0.994481i | \(0.533459\pi\) | |||||||
\(662\) | −6.39208 | −0.248435 | ||||||||
\(663\) | −26.7846 | −1.04023 | ||||||||
\(664\) | −58.0027 | −2.25094 | ||||||||
\(665\) | 9.94050 | 0.385476 | ||||||||
\(666\) | −2.18247 | −0.0845692 | ||||||||
\(667\) | −7.73239 | −0.299399 | ||||||||
\(668\) | −51.5049 | −1.99278 | ||||||||
\(669\) | 9.19635 | 0.355552 | ||||||||
\(670\) | 27.0856 | 1.04641 | ||||||||
\(671\) | −2.03858 | −0.0786985 | ||||||||
\(672\) | 1.25248 | 0.0483156 | ||||||||
\(673\) | −23.4623 | −0.904404 | −0.452202 | − | 0.891916i | \(-0.649361\pi\) | ||||
−0.452202 | + | 0.891916i | \(0.649361\pi\) | |||||||
\(674\) | −39.9131 | −1.53740 | ||||||||
\(675\) | −2.73292 | −0.105190 | ||||||||
\(676\) | 10.3283 | 0.397243 | ||||||||
\(677\) | 35.3478 | 1.35853 | 0.679263 | − | 0.733895i | \(-0.262300\pi\) | ||||
0.679263 | + | 0.733895i | \(0.262300\pi\) | |||||||
\(678\) | −36.8806 | −1.41639 | ||||||||
\(679\) | −9.78138 | −0.375375 | ||||||||
\(680\) | −46.0483 | −1.76587 | ||||||||
\(681\) | 9.49722 | 0.363934 | ||||||||
\(682\) | 27.3117 | 1.04582 | ||||||||
\(683\) | 23.4038 | 0.895520 | 0.447760 | − | 0.894154i | \(-0.352222\pi\) | ||||
0.447760 | + | 0.894154i | \(0.352222\pi\) | |||||||
\(684\) | 25.5249 | 0.975970 | ||||||||
\(685\) | 25.6185 | 0.978833 | ||||||||
\(686\) | −2.42203 | −0.0924737 | ||||||||
\(687\) | −1.97384 | −0.0753066 | ||||||||
\(688\) | −37.2050 | −1.41843 | ||||||||
\(689\) | −39.8186 | −1.51697 | ||||||||
\(690\) | −30.1807 | −1.14896 | ||||||||
\(691\) | 9.73574 | 0.370365 | 0.185182 | − | 0.982704i | \(-0.440712\pi\) | ||||
0.185182 | + | 0.982704i | \(0.440712\pi\) | |||||||
\(692\) | −84.4051 | −3.20860 | ||||||||
\(693\) | −2.29749 | −0.0872745 | ||||||||
\(694\) | 72.7988 | 2.76340 | ||||||||
\(695\) | 28.0947 | 1.06569 | ||||||||
\(696\) | 4.22326 | 0.160082 | ||||||||
\(697\) | −48.8611 | −1.85074 | ||||||||
\(698\) | −64.2560 | −2.43213 | ||||||||
\(699\) | −8.23215 | −0.311368 | ||||||||
\(700\) | −10.5662 | −0.399363 | ||||||||
\(701\) | 22.1987 | 0.838433 | 0.419216 | − | 0.907886i | \(-0.362305\pi\) | ||||
0.419216 | + | 0.907886i | \(0.362305\pi\) | |||||||
\(702\) | 9.58814 | 0.361881 | ||||||||
\(703\) | 5.94900 | 0.224371 | ||||||||
\(704\) | 21.7442 | 0.819514 | ||||||||
\(705\) | −6.34965 | −0.239142 | ||||||||
\(706\) | 4.84705 | 0.182421 | ||||||||
\(707\) | −5.55675 | −0.208983 | ||||||||
\(708\) | 30.4169 | 1.14314 | ||||||||
\(709\) | 24.3918 | 0.916053 | 0.458027 | − | 0.888938i | \(-0.348556\pi\) | ||||
0.458027 | + | 0.888938i | \(0.348556\pi\) | |||||||
\(710\) | −8.42797 | −0.316296 | ||||||||
\(711\) | 11.8751 | 0.445352 | ||||||||
\(712\) | −11.5555 | −0.433060 | ||||||||
\(713\) | 40.6191 | 1.52120 | ||||||||
\(714\) | −16.3874 | −0.613284 | ||||||||
\(715\) | 13.6943 | 0.512139 | ||||||||
\(716\) | −20.5188 | −0.766823 | ||||||||
\(717\) | 1.35691 | 0.0506746 | ||||||||
\(718\) | −58.7258 | −2.19163 | ||||||||
\(719\) | 41.0246 | 1.52996 | 0.764980 | − | 0.644054i | \(-0.222749\pi\) | ||||
0.764980 | + | 0.644054i | \(0.222749\pi\) | |||||||
\(720\) | 4.84133 | 0.180426 | ||||||||
\(721\) | −10.0408 | −0.373938 | ||||||||
\(722\) | −59.5488 | −2.21618 | ||||||||
\(723\) | −11.2200 | −0.417278 | ||||||||
\(724\) | −42.7977 | −1.59056 | ||||||||
\(725\) | 2.55344 | 0.0948323 | ||||||||
\(726\) | 13.8578 | 0.514310 | ||||||||
\(727\) | −0.708608 | −0.0262808 | −0.0131404 | − | 0.999914i | \(-0.504183\pi\) | ||||
−0.0131404 | + | 0.999914i | \(0.504183\pi\) | |||||||
\(728\) | 17.8938 | 0.663190 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.1487 | −0.634702 | ||||||||
\(731\) | −78.2890 | −2.89562 | ||||||||
\(732\) | 3.43055 | 0.126797 | ||||||||
\(733\) | −43.5004 | −1.60672 | −0.803361 | − | 0.595492i | \(-0.796957\pi\) | ||||
−0.803361 | + | 0.595492i | \(0.796957\pi\) | |||||||
\(734\) | 34.0857 | 1.25813 | ||||||||
\(735\) | 1.50568 | 0.0555379 | ||||||||
\(736\) | 10.3654 | 0.382075 | ||||||||
\(737\) | 17.0639 | 0.628557 | ||||||||
\(738\) | 17.4909 | 0.643849 | ||||||||
\(739\) | 26.2262 | 0.964746 | 0.482373 | − | 0.875966i | \(-0.339775\pi\) | ||||
0.482373 | + | 0.875966i | \(0.339775\pi\) | |||||||
\(740\) | 5.24556 | 0.192831 | ||||||||
\(741\) | −26.1354 | −0.960107 | ||||||||
\(742\) | −24.3619 | −0.894355 | ||||||||
\(743\) | −34.4663 | −1.26445 | −0.632223 | − | 0.774787i | \(-0.717857\pi\) | ||||
−0.632223 | + | 0.774787i | \(0.717857\pi\) | |||||||
\(744\) | −22.1853 | −0.813351 | ||||||||
\(745\) | 27.0083 | 0.989509 | ||||||||
\(746\) | 74.9679 | 2.74477 | ||||||||
\(747\) | 12.8321 | 0.469503 | ||||||||
\(748\) | −60.1000 | −2.19747 | ||||||||
\(749\) | −7.81185 | −0.285439 | ||||||||
\(750\) | 28.2005 | 1.02974 | ||||||||
\(751\) | 25.8639 | 0.943786 | 0.471893 | − | 0.881656i | \(-0.343571\pi\) | ||||
0.471893 | + | 0.881656i | \(0.343571\pi\) | |||||||
\(752\) | −13.5596 | −0.494469 | ||||||||
\(753\) | 29.7190 | 1.08302 | ||||||||
\(754\) | −8.95844 | −0.326247 | ||||||||
\(755\) | −9.07831 | −0.330394 | ||||||||
\(756\) | 3.86625 | 0.140614 | ||||||||
\(757\) | 10.7395 | 0.390333 | 0.195167 | − | 0.980770i | \(-0.437475\pi\) | ||||
0.195167 | + | 0.980770i | \(0.437475\pi\) | |||||||
\(758\) | 49.9740 | 1.81514 | ||||||||
\(759\) | −19.0138 | −0.690158 | ||||||||
\(760\) | −44.9322 | −1.62986 | ||||||||
\(761\) | 1.56636 | 0.0567803 | 0.0283902 | − | 0.999597i | \(-0.490962\pi\) | ||||
0.0283902 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(762\) | −0.602025 | −0.0218091 | ||||||||
\(763\) | −9.18047 | −0.332355 | ||||||||
\(764\) | 3.86625 | 0.139876 | ||||||||
\(765\) | 10.1874 | 0.368327 | ||||||||
\(766\) | −12.4576 | −0.450112 | ||||||||
\(767\) | −31.1443 | −1.12456 | ||||||||
\(768\) | −30.5242 | −1.10145 | ||||||||
\(769\) | −13.6790 | −0.493278 | −0.246639 | − | 0.969107i | \(-0.579326\pi\) | ||||
−0.246639 | + | 0.969107i | \(0.579326\pi\) | |||||||
\(770\) | 8.37852 | 0.301941 | ||||||||
\(771\) | −7.27439 | −0.261981 | ||||||||
\(772\) | −26.1244 | −0.940239 | ||||||||
\(773\) | 39.9255 | 1.43602 | 0.718010 | − | 0.696033i | \(-0.245053\pi\) | ||||
0.718010 | + | 0.696033i | \(0.245053\pi\) | |||||||
\(774\) | 28.0253 | 1.00735 | ||||||||
\(775\) | −13.4135 | −0.481828 | ||||||||
\(776\) | 44.2130 | 1.58715 | ||||||||
\(777\) | 0.901092 | 0.0323265 | ||||||||
\(778\) | −50.7216 | −1.81846 | ||||||||
\(779\) | −47.6768 | −1.70820 | ||||||||
\(780\) | −23.0450 | −0.825144 | ||||||||
\(781\) | −5.30962 | −0.189993 | ||||||||
\(782\) | −135.621 | −4.84979 | ||||||||
\(783\) | −0.934325 | −0.0333901 | ||||||||
\(784\) | 3.21537 | 0.114835 | ||||||||
\(785\) | 10.3034 | 0.367745 | ||||||||
\(786\) | 6.12978 | 0.218642 | ||||||||
\(787\) | 49.4286 | 1.76194 | 0.880970 | − | 0.473171i | \(-0.156891\pi\) | ||||
0.880970 | + | 0.473171i | \(0.156891\pi\) | |||||||
\(788\) | 87.3260 | 3.11086 | ||||||||
\(789\) | −1.90403 | −0.0677854 | ||||||||
\(790\) | −43.3064 | −1.54077 | ||||||||
\(791\) | 15.2271 | 0.541415 | ||||||||
\(792\) | 10.3849 | 0.369012 | ||||||||
\(793\) | −3.51259 | −0.124736 | ||||||||
\(794\) | 4.04175 | 0.143436 | ||||||||
\(795\) | 15.1448 | 0.537132 | ||||||||
\(796\) | 32.5017 | 1.15199 | ||||||||
\(797\) | 17.6121 | 0.623854 | 0.311927 | − | 0.950106i | \(-0.399026\pi\) | ||||
0.311927 | + | 0.950106i | \(0.399026\pi\) | |||||||
\(798\) | −15.9902 | −0.566049 | ||||||||
\(799\) | −28.5330 | −1.00942 | ||||||||
\(800\) | −3.42294 | −0.121019 | ||||||||
\(801\) | 2.55646 | 0.0903281 | ||||||||
\(802\) | −4.74713 | −0.167627 | ||||||||
\(803\) | −10.8037 | −0.381253 | ||||||||
\(804\) | −28.7153 | −1.01271 | ||||||||
\(805\) | 12.4609 | 0.439188 | ||||||||
\(806\) | 47.0597 | 1.65761 | ||||||||
\(807\) | 8.88210 | 0.312665 | ||||||||
\(808\) | 25.1171 | 0.883617 | ||||||||
\(809\) | −46.3539 | −1.62972 | −0.814858 | − | 0.579661i | \(-0.803185\pi\) | ||||
−0.814858 | + | 0.579661i | \(0.803185\pi\) | |||||||
\(810\) | −3.64681 | −0.128136 | ||||||||
\(811\) | −30.5558 | −1.07296 | −0.536480 | − | 0.843913i | \(-0.680246\pi\) | ||||
−0.536480 | + | 0.843913i | \(0.680246\pi\) | |||||||
\(812\) | −3.61233 | −0.126768 | ||||||||
\(813\) | −21.8086 | −0.764860 | ||||||||
\(814\) | 5.01421 | 0.175748 | ||||||||
\(815\) | 33.7815 | 1.18332 | ||||||||
\(816\) | 21.7552 | 0.761583 | ||||||||
\(817\) | −76.3915 | −2.67260 | ||||||||
\(818\) | 27.8866 | 0.975031 | ||||||||
\(819\) | −3.95871 | −0.138329 | ||||||||
\(820\) | −42.0392 | −1.46807 | ||||||||
\(821\) | 5.23138 | 0.182577 | 0.0912883 | − | 0.995825i | \(-0.470902\pi\) | ||||
0.0912883 | + | 0.995825i | \(0.470902\pi\) | |||||||
\(822\) | −41.2098 | −1.43736 | ||||||||
\(823\) | 42.5634 | 1.48367 | 0.741833 | − | 0.670585i | \(-0.233957\pi\) | ||||
0.741833 | + | 0.670585i | \(0.233957\pi\) | |||||||
\(824\) | 45.3855 | 1.58108 | ||||||||
\(825\) | 6.27886 | 0.218602 | ||||||||
\(826\) | −19.0548 | −0.663002 | ||||||||
\(827\) | 7.80292 | 0.271334 | 0.135667 | − | 0.990754i | \(-0.456682\pi\) | ||||
0.135667 | + | 0.990754i | \(0.456682\pi\) | |||||||
\(828\) | 31.9967 | 1.11196 | ||||||||
\(829\) | −20.8746 | −0.725006 | −0.362503 | − | 0.931983i | \(-0.618078\pi\) | ||||
−0.362503 | + | 0.931983i | \(0.618078\pi\) | |||||||
\(830\) | −46.7963 | −1.62432 | ||||||||
\(831\) | 6.28833 | 0.218140 | ||||||||
\(832\) | 37.4665 | 1.29892 | ||||||||
\(833\) | 6.76598 | 0.234427 | ||||||||
\(834\) | −45.1930 | −1.56490 | ||||||||
\(835\) | −20.0582 | −0.694143 | ||||||||
\(836\) | −58.6433 | −2.02822 | ||||||||
\(837\) | 4.90812 | 0.169649 | ||||||||
\(838\) | −25.3301 | −0.875015 | ||||||||
\(839\) | −40.7290 | −1.40612 | −0.703061 | − | 0.711130i | \(-0.748184\pi\) | ||||
−0.703061 | + | 0.711130i | \(0.748184\pi\) | |||||||
\(840\) | −6.80585 | −0.234824 | ||||||||
\(841\) | −28.1270 | −0.969898 | ||||||||
\(842\) | −90.4230 | −3.11618 | ||||||||
\(843\) | −0.227607 | −0.00783920 | ||||||||
\(844\) | 67.6130 | 2.32734 | ||||||||
\(845\) | 4.02229 | 0.138371 | ||||||||
\(846\) | 10.2140 | 0.351165 | ||||||||
\(847\) | −5.72154 | −0.196594 | ||||||||
\(848\) | 32.3417 | 1.11062 | ||||||||
\(849\) | −2.79415 | −0.0958949 | ||||||||
\(850\) | 44.7856 | 1.53613 | ||||||||
\(851\) | 7.45735 | 0.255635 | ||||||||
\(852\) | 8.93510 | 0.306111 | ||||||||
\(853\) | 11.8387 | 0.405350 | 0.202675 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202675 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(854\) | −2.14909 | −0.0735403 | ||||||||
\(855\) | 9.94050 | 0.339958 | ||||||||
\(856\) | 35.3104 | 1.20689 | ||||||||
\(857\) | −32.3341 | −1.10451 | −0.552256 | − | 0.833675i | \(-0.686233\pi\) | ||||
−0.552256 | + | 0.833675i | \(0.686233\pi\) | |||||||
\(858\) | −22.0287 | −0.752046 | ||||||||
\(859\) | 39.5374 | 1.34900 | 0.674499 | − | 0.738275i | \(-0.264359\pi\) | ||||
0.674499 | + | 0.738275i | \(0.264359\pi\) | |||||||
\(860\) | −67.3586 | −2.29691 | ||||||||
\(861\) | −7.22158 | −0.246111 | ||||||||
\(862\) | 44.5224 | 1.51644 | ||||||||
\(863\) | −52.0310 | −1.77115 | −0.885577 | − | 0.464492i | \(-0.846237\pi\) | ||||
−0.885577 | + | 0.464492i | \(0.846237\pi\) | |||||||
\(864\) | 1.25248 | 0.0426104 | ||||||||
\(865\) | −32.8710 | −1.11765 | ||||||||
\(866\) | 22.3306 | 0.758823 | ||||||||
\(867\) | 28.7785 | 0.977370 | ||||||||
\(868\) | 18.9760 | 0.644088 | ||||||||
\(869\) | −27.2830 | −0.925512 | ||||||||
\(870\) | 3.40731 | 0.115519 | ||||||||
\(871\) | 29.4021 | 0.996252 | ||||||||
\(872\) | 41.4968 | 1.40526 | ||||||||
\(873\) | −9.78138 | −0.331050 | ||||||||
\(874\) | −132.334 | −4.47625 | ||||||||
\(875\) | −11.6433 | −0.393616 | ||||||||
\(876\) | 18.1806 | 0.614264 | ||||||||
\(877\) | 11.4947 | 0.388148 | 0.194074 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194074 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(878\) | −41.4099 | −1.39752 | ||||||||
\(879\) | 17.6269 | 0.594541 | ||||||||
\(880\) | −11.1229 | −0.374953 | ||||||||
\(881\) | −14.4514 | −0.486880 | −0.243440 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243440 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(882\) | −2.42203 | −0.0815541 | ||||||||
\(883\) | −51.4627 | −1.73186 | −0.865930 | − | 0.500166i | \(-0.833272\pi\) | ||||
−0.865930 | + | 0.500166i | \(0.833272\pi\) | |||||||
\(884\) | −103.556 | −3.48296 | ||||||||
\(885\) | 11.8456 | 0.398186 | ||||||||
\(886\) | 61.4458 | 2.06431 | ||||||||
\(887\) | −1.06718 | −0.0358324 | −0.0179162 | − | 0.999839i | \(-0.505703\pi\) | ||||
−0.0179162 | + | 0.999839i | \(0.505703\pi\) | |||||||
\(888\) | −4.07304 | −0.136682 | ||||||||
\(889\) | 0.248562 | 0.00833649 | ||||||||
\(890\) | −9.32293 | −0.312505 | ||||||||
\(891\) | −2.29749 | −0.0769688 | ||||||||
\(892\) | 35.5554 | 1.19048 | ||||||||
\(893\) | −27.8414 | −0.931677 | ||||||||
\(894\) | −43.4455 | −1.45303 | ||||||||
\(895\) | −7.99089 | −0.267106 | ||||||||
\(896\) | 20.4179 | 0.682114 | ||||||||
\(897\) | −32.7619 | −1.09389 | ||||||||
\(898\) | −84.2269 | −2.81069 | ||||||||
\(899\) | −4.58578 | −0.152944 | ||||||||
\(900\) | −10.5662 | −0.352205 | ||||||||
\(901\) | 68.0554 | 2.26725 | ||||||||
\(902\) | −40.1852 | −1.33802 | ||||||||
\(903\) | −11.5710 | −0.385058 | ||||||||
\(904\) | −68.8284 | −2.28920 | ||||||||
\(905\) | −16.6673 | −0.554038 | ||||||||
\(906\) | 14.6033 | 0.485163 | ||||||||
\(907\) | 16.9844 | 0.563957 | 0.281979 | − | 0.959421i | \(-0.409009\pi\) | ||||
0.281979 | + | 0.959421i | \(0.409009\pi\) | |||||||
\(908\) | 36.7186 | 1.21855 | ||||||||
\(909\) | −5.55675 | −0.184306 | ||||||||
\(910\) | 14.4367 | 0.478571 | ||||||||
\(911\) | 16.9254 | 0.560763 | 0.280382 | − | 0.959889i | \(-0.409539\pi\) | ||||
0.280382 | + | 0.959889i | \(0.409539\pi\) | |||||||
\(912\) | 21.2279 | 0.702925 | ||||||||
\(913\) | −29.4817 | −0.975701 | ||||||||
\(914\) | 57.3221 | 1.89605 | ||||||||
\(915\) | 1.33600 | 0.0441669 | ||||||||
\(916\) | −7.63134 | −0.252147 | ||||||||
\(917\) | −2.53084 | −0.0835757 | ||||||||
\(918\) | −16.3874 | −0.540866 | ||||||||
\(919\) | −35.4670 | −1.16995 | −0.584974 | − | 0.811052i | \(-0.698895\pi\) | ||||
−0.584974 | + | 0.811052i | \(0.698895\pi\) | |||||||
\(920\) | −56.3246 | −1.85697 | ||||||||
\(921\) | 15.4572 | 0.509333 | ||||||||
\(922\) | 14.6548 | 0.482631 | ||||||||
\(923\) | −9.14879 | −0.301136 | ||||||||
\(924\) | −8.88267 | −0.292218 | ||||||||
\(925\) | −2.46261 | −0.0809702 | ||||||||
\(926\) | −11.0056 | −0.361666 | ||||||||
\(927\) | −10.0408 | −0.329782 | ||||||||
\(928\) | −1.17023 | −0.0384146 | ||||||||
\(929\) | −40.6823 | −1.33474 | −0.667372 | − | 0.744724i | \(-0.732581\pi\) | ||||
−0.667372 | + | 0.744724i | \(0.732581\pi\) | |||||||
\(930\) | −17.8990 | −0.586931 | ||||||||
\(931\) | 6.60199 | 0.216372 | ||||||||
\(932\) | −31.8275 | −1.04254 | ||||||||
\(933\) | −6.88320 | −0.225346 | ||||||||
\(934\) | 15.4796 | 0.506508 | ||||||||
\(935\) | −23.4055 | −0.765442 | ||||||||
\(936\) | 17.8938 | 0.584878 | ||||||||
\(937\) | 37.7286 | 1.23254 | 0.616271 | − | 0.787534i | \(-0.288643\pi\) | ||||
0.616271 | + | 0.787534i | \(0.288643\pi\) | |||||||
\(938\) | 17.9889 | 0.587358 | ||||||||
\(939\) | 2.10273 | 0.0686199 | ||||||||
\(940\) | −24.5493 | −0.800710 | ||||||||
\(941\) | 3.27413 | 0.106734 | 0.0533669 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533669 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(942\) | −16.5740 | −0.540011 | ||||||||
\(943\) | −59.7651 | −1.94622 | ||||||||
\(944\) | 25.2963 | 0.823323 | ||||||||
\(945\) | 1.50568 | 0.0489798 | ||||||||
\(946\) | −64.3879 | −2.09343 | ||||||||
\(947\) | −53.4843 | −1.73801 | −0.869004 | − | 0.494806i | \(-0.835239\pi\) | ||||
−0.869004 | + | 0.494806i | \(0.835239\pi\) | |||||||
\(948\) | 45.9122 | 1.49116 | ||||||||
\(949\) | −18.6154 | −0.604280 | ||||||||
\(950\) | 43.7001 | 1.41782 | ||||||||
\(951\) | −18.4185 | −0.597260 | ||||||||
\(952\) | −30.5830 | −0.991201 | ||||||||
\(953\) | −20.2477 | −0.655886 | −0.327943 | − | 0.944697i | \(-0.606355\pi\) | ||||
−0.327943 | + | 0.944697i | \(0.606355\pi\) | |||||||
\(954\) | −24.3619 | −0.788747 | ||||||||
\(955\) | 1.50568 | 0.0487227 | ||||||||
\(956\) | 5.24613 | 0.169672 | ||||||||
\(957\) | 2.14660 | 0.0693898 | ||||||||
\(958\) | 60.2562 | 1.94679 | ||||||||
\(959\) | 17.0146 | 0.549429 | ||||||||
\(960\) | −14.2502 | −0.459924 | ||||||||
\(961\) | −6.91034 | −0.222914 | ||||||||
\(962\) | 8.63979 | 0.278558 | ||||||||
\(963\) | −7.81185 | −0.251733 | ||||||||
\(964\) | −43.3795 | −1.39716 | ||||||||
\(965\) | −10.1740 | −0.327512 | ||||||||
\(966\) | −20.0445 | −0.644922 | ||||||||
\(967\) | −29.4057 | −0.945624 | −0.472812 | − | 0.881163i | \(-0.656761\pi\) | ||||
−0.472812 | + | 0.881163i | \(0.656761\pi\) | |||||||
\(968\) | 25.8620 | 0.831236 | ||||||||
\(969\) | 44.6690 | 1.43497 | ||||||||
\(970\) | 35.6709 | 1.14532 | ||||||||
\(971\) | 29.6780 | 0.952413 | 0.476206 | − | 0.879334i | \(-0.342012\pi\) | ||||
0.476206 | + | 0.879334i | \(0.342012\pi\) | |||||||
\(972\) | 3.86625 | 0.124010 | ||||||||
\(973\) | 18.6591 | 0.598183 | ||||||||
\(974\) | −16.4656 | −0.527591 | ||||||||
\(975\) | 10.8189 | 0.346481 | ||||||||
\(976\) | 2.85302 | 0.0913231 | ||||||||
\(977\) | −21.9357 | −0.701785 | −0.350893 | − | 0.936416i | \(-0.614122\pi\) | ||||
−0.350893 | + | 0.936416i | \(0.614122\pi\) | |||||||
\(978\) | −54.3408 | −1.73763 | ||||||||
\(979\) | −5.87344 | −0.187716 | ||||||||
\(980\) | 5.82134 | 0.185956 | ||||||||
\(981\) | −9.18047 | −0.293110 | ||||||||
\(982\) | −31.8126 | −1.01518 | ||||||||
\(983\) | −14.5214 | −0.463160 | −0.231580 | − | 0.972816i | \(-0.574390\pi\) | ||||
−0.231580 | + | 0.972816i | \(0.574390\pi\) | |||||||
\(984\) | 32.6423 | 1.04060 | ||||||||
\(985\) | 34.0085 | 1.08360 | ||||||||
\(986\) | 15.3112 | 0.487608 | ||||||||
\(987\) | −4.21712 | −0.134233 | ||||||||
\(988\) | −101.046 | −3.21470 | ||||||||
\(989\) | −95.7603 | −3.04500 | ||||||||
\(990\) | 8.37852 | 0.266287 | ||||||||
\(991\) | −23.3065 | −0.740356 | −0.370178 | − | 0.928961i | \(-0.620703\pi\) | ||||
−0.370178 | + | 0.928961i | \(0.620703\pi\) | |||||||
\(992\) | 6.14734 | 0.195178 | ||||||||
\(993\) | 2.63914 | 0.0837505 | ||||||||
\(994\) | −5.59745 | −0.177540 | ||||||||
\(995\) | 12.6576 | 0.401271 | ||||||||
\(996\) | 49.6122 | 1.57202 | ||||||||
\(997\) | −19.7195 | −0.624521 | −0.312261 | − | 0.949996i | \(-0.601086\pi\) | ||||
−0.312261 | + | 0.949996i | \(0.601086\pi\) | |||||||
\(998\) | −75.6055 | −2.39325 | ||||||||
\(999\) | 0.901092 | 0.0285093 |
(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 | 4011.2.a.k.1.3 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.k.1.3 | ✓ | 27 | 1.1 | even | 1 | trivial |