Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39408 | −1.69287 | −0.846434 | − | 0.532493i | \(-0.821255\pi\) | ||||
−0.846434 | + | 0.532493i | \(0.821255\pi\) | |||||||
\(3\) | −0.179689 | −0.103743 | −0.0518717 | − | 0.998654i | \(-0.516519\pi\) | ||||
−0.0518717 | + | 0.998654i | \(0.516519\pi\) | |||||||
\(4\) | 3.73161 | 1.86580 | ||||||||
\(5\) | −1.83517 | −0.820711 | −0.410356 | − | 0.911926i | \(-0.634595\pi\) | ||||
−0.410356 | + | 0.911926i | \(0.634595\pi\) | |||||||
\(6\) | 0.430189 | 0.175624 | ||||||||
\(7\) | 0.373924 | 0.141330 | 0.0706650 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706650 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(8\) | −4.14560 | −1.46569 | ||||||||
\(9\) | −2.96771 | −0.989237 | ||||||||
\(10\) | 4.39353 | 1.38936 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.670529 | −0.193565 | ||||||||
\(13\) | 6.01413 | 1.66802 | 0.834009 | − | 0.551750i | \(-0.186040\pi\) | ||||
0.834009 | + | 0.551750i | \(0.186040\pi\) | |||||||
\(14\) | −0.895203 | −0.239253 | ||||||||
\(15\) | 0.329759 | 0.0851434 | ||||||||
\(16\) | 2.46168 | 0.615419 | ||||||||
\(17\) | 5.84884 | 1.41855 | 0.709276 | − | 0.704931i | \(-0.249022\pi\) | ||||
0.709276 | + | 0.704931i | \(0.249022\pi\) | |||||||
\(18\) | 7.10493 | 1.67465 | ||||||||
\(19\) | −3.17074 | −0.727418 | −0.363709 | − | 0.931513i | \(-0.618490\pi\) | ||||
−0.363709 | + | 0.931513i | \(0.618490\pi\) | |||||||
\(20\) | −6.84812 | −1.53129 | ||||||||
\(21\) | −0.0671900 | −0.0146621 | ||||||||
\(22\) | −2.39408 | −0.510419 | ||||||||
\(23\) | 0.679989 | 0.141788 | 0.0708938 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708938 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(24\) | 0.744919 | 0.152056 | ||||||||
\(25\) | −1.63217 | −0.326433 | ||||||||
\(26\) | −14.3983 | −2.82374 | ||||||||
\(27\) | 1.07233 | 0.206370 | ||||||||
\(28\) | 1.39534 | 0.263694 | ||||||||
\(29\) | 5.00335 | 0.929099 | 0.464549 | − | 0.885547i | \(-0.346216\pi\) | ||||
0.464549 | + | 0.885547i | \(0.346216\pi\) | |||||||
\(30\) | −0.789469 | −0.144137 | ||||||||
\(31\) | −9.34384 | −1.67820 | −0.839101 | − | 0.543975i | \(-0.816919\pi\) | ||||
−0.839101 | + | 0.543975i | \(0.816919\pi\) | |||||||
\(32\) | 2.39776 | 0.423868 | ||||||||
\(33\) | −0.179689 | −0.0312798 | ||||||||
\(34\) | −14.0026 | −2.40142 | ||||||||
\(35\) | −0.686213 | −0.115991 | ||||||||
\(36\) | −11.0743 | −1.84572 | ||||||||
\(37\) | −3.30410 | −0.543190 | −0.271595 | − | 0.962412i | \(-0.587551\pi\) | ||||
−0.271595 | + | 0.962412i | \(0.587551\pi\) | |||||||
\(38\) | 7.59100 | 1.23142 | ||||||||
\(39\) | −1.08067 | −0.173046 | ||||||||
\(40\) | 7.60787 | 1.20291 | ||||||||
\(41\) | 0.161876 | 0.0252809 | 0.0126404 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126404 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(42\) | 0.160858 | 0.0248209 | ||||||||
\(43\) | 3.21975 | 0.491007 | 0.245504 | − | 0.969396i | \(-0.421047\pi\) | ||||
0.245504 | + | 0.969396i | \(0.421047\pi\) | |||||||
\(44\) | 3.73161 | 0.562561 | ||||||||
\(45\) | 5.44624 | 0.811878 | ||||||||
\(46\) | −1.62795 | −0.240028 | ||||||||
\(47\) | −5.62611 | −0.820652 | −0.410326 | − | 0.911939i | \(-0.634585\pi\) | ||||
−0.410326 | + | 0.911939i | \(0.634585\pi\) | |||||||
\(48\) | −0.442336 | −0.0638457 | ||||||||
\(49\) | −6.86018 | −0.980026 | ||||||||
\(50\) | 3.90753 | 0.552608 | ||||||||
\(51\) | −1.05097 | −0.147165 | ||||||||
\(52\) | 22.4424 | 3.11220 | ||||||||
\(53\) | −3.08764 | −0.424120 | −0.212060 | − | 0.977257i | \(-0.568017\pi\) | ||||
−0.212060 | + | 0.977257i | \(0.568017\pi\) | |||||||
\(54\) | −2.56725 | −0.349358 | ||||||||
\(55\) | −1.83517 | −0.247454 | ||||||||
\(56\) | −1.55014 | −0.207146 | ||||||||
\(57\) | 0.569747 | 0.0754648 | ||||||||
\(58\) | −11.9784 | −1.57284 | ||||||||
\(59\) | −8.99236 | −1.17071 | −0.585353 | − | 0.810778i | \(-0.699044\pi\) | ||||
−0.585353 | + | 0.810778i | \(0.699044\pi\) | |||||||
\(60\) | 1.23053 | 0.158861 | ||||||||
\(61\) | −2.58651 | −0.331168 | −0.165584 | − | 0.986196i | \(-0.552951\pi\) | ||||
−0.165584 | + | 0.986196i | \(0.552951\pi\) | |||||||
\(62\) | 22.3699 | 2.84098 | ||||||||
\(63\) | −1.10970 | −0.139809 | ||||||||
\(64\) | −10.6638 | −1.33297 | ||||||||
\(65\) | −11.0369 | −1.36896 | ||||||||
\(66\) | 0.430189 | 0.0529526 | ||||||||
\(67\) | 7.79770 | 0.952641 | 0.476320 | − | 0.879272i | \(-0.341970\pi\) | ||||
0.476320 | + | 0.879272i | \(0.341970\pi\) | |||||||
\(68\) | 21.8256 | 2.64674 | ||||||||
\(69\) | −0.122187 | −0.0147095 | ||||||||
\(70\) | 1.64285 | 0.196358 | ||||||||
\(71\) | −11.9224 | −1.41493 | −0.707466 | − | 0.706748i | \(-0.750162\pi\) | ||||
−0.707466 | + | 0.706748i | \(0.750162\pi\) | |||||||
\(72\) | 12.3029 | 1.44992 | ||||||||
\(73\) | −5.11901 | −0.599135 | −0.299567 | − | 0.954075i | \(-0.596842\pi\) | ||||
−0.299567 | + | 0.954075i | \(0.596842\pi\) | |||||||
\(74\) | 7.91026 | 0.919550 | ||||||||
\(75\) | 0.293282 | 0.0338653 | ||||||||
\(76\) | −11.8320 | −1.35722 | ||||||||
\(77\) | 0.373924 | 0.0426126 | ||||||||
\(78\) | 2.58721 | 0.292944 | ||||||||
\(79\) | −1.78467 | −0.200791 | −0.100396 | − | 0.994948i | \(-0.532011\pi\) | ||||
−0.100396 | + | 0.994948i | \(0.532011\pi\) | |||||||
\(80\) | −4.51758 | −0.505081 | ||||||||
\(81\) | 8.71045 | 0.967828 | ||||||||
\(82\) | −0.387545 | −0.0427972 | ||||||||
\(83\) | 13.2223 | 1.45133 | 0.725666 | − | 0.688047i | \(-0.241532\pi\) | ||||
0.725666 | + | 0.688047i | \(0.241532\pi\) | |||||||
\(84\) | −0.250727 | −0.0273565 | ||||||||
\(85\) | −10.7336 | −1.16422 | ||||||||
\(86\) | −7.70833 | −0.831211 | ||||||||
\(87\) | −0.899047 | −0.0963879 | ||||||||
\(88\) | −4.14560 | −0.441923 | ||||||||
\(89\) | 17.1332 | 1.81612 | 0.908058 | − | 0.418844i | \(-0.137565\pi\) | ||||
0.908058 | + | 0.418844i | \(0.137565\pi\) | |||||||
\(90\) | −13.0387 | −1.37440 | ||||||||
\(91\) | 2.24883 | 0.235741 | ||||||||
\(92\) | 2.53745 | 0.264548 | ||||||||
\(93\) | 1.67898 | 0.174103 | ||||||||
\(94\) | 13.4693 | 1.38926 | ||||||||
\(95\) | 5.81883 | 0.597000 | ||||||||
\(96\) | −0.430851 | −0.0439735 | ||||||||
\(97\) | 15.6825 | 1.59231 | 0.796157 | − | 0.605090i | \(-0.206863\pi\) | ||||
0.796157 | + | 0.605090i | \(0.206863\pi\) | |||||||
\(98\) | 16.4238 | 1.65905 | ||||||||
\(99\) | −2.96771 | −0.298266 | ||||||||
\(100\) | −6.09060 | −0.609060 | ||||||||
\(101\) | 15.1463 | 1.50711 | 0.753555 | − | 0.657385i | \(-0.228337\pi\) | ||||
0.753555 | + | 0.657385i | \(0.228337\pi\) | |||||||
\(102\) | 2.51611 | 0.249132 | ||||||||
\(103\) | −0.217065 | −0.0213881 | −0.0106940 | − | 0.999943i | \(-0.503404\pi\) | ||||
−0.0106940 | + | 0.999943i | \(0.503404\pi\) | |||||||
\(104\) | −24.9322 | −2.44480 | ||||||||
\(105\) | 0.123305 | 0.0120333 | ||||||||
\(106\) | 7.39205 | 0.717979 | ||||||||
\(107\) | −1.51562 | −0.146521 | −0.0732604 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732604 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(108\) | 4.00152 | 0.385047 | ||||||||
\(109\) | 2.48417 | 0.237941 | 0.118970 | − | 0.992898i | \(-0.462041\pi\) | ||||
0.118970 | + | 0.992898i | \(0.462041\pi\) | |||||||
\(110\) | 4.39353 | 0.418907 | ||||||||
\(111\) | 0.593710 | 0.0563524 | ||||||||
\(112\) | 0.920479 | 0.0869771 | ||||||||
\(113\) | −7.35374 | −0.691781 | −0.345891 | − | 0.938275i | \(-0.612423\pi\) | ||||
−0.345891 | + | 0.938275i | \(0.612423\pi\) | |||||||
\(114\) | −1.36402 | −0.127752 | ||||||||
\(115\) | −1.24789 | −0.116367 | ||||||||
\(116\) | 18.6705 | 1.73352 | ||||||||
\(117\) | −17.8482 | −1.65007 | ||||||||
\(118\) | 21.5284 | 1.98185 | ||||||||
\(119\) | 2.18702 | 0.200484 | ||||||||
\(120\) | −1.36705 | −0.124794 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.19230 | 0.560624 | ||||||||
\(123\) | −0.0290874 | −0.00262272 | ||||||||
\(124\) | −34.8675 | −3.13120 | ||||||||
\(125\) | 12.1711 | 1.08862 | ||||||||
\(126\) | 2.65670 | 0.236678 | ||||||||
\(127\) | 10.4142 | 0.924114 | 0.462057 | − | 0.886850i | \(-0.347112\pi\) | ||||
0.462057 | + | 0.886850i | \(0.347112\pi\) | |||||||
\(128\) | 20.7344 | 1.83268 | ||||||||
\(129\) | −0.578554 | −0.0509388 | ||||||||
\(130\) | 26.4232 | 2.31747 | ||||||||
\(131\) | −2.04204 | −0.178413 | −0.0892067 | − | 0.996013i | \(-0.528433\pi\) | ||||
−0.0892067 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(132\) | −0.670529 | −0.0583620 | ||||||||
\(133\) | −1.18562 | −0.102806 | ||||||||
\(134\) | −18.6683 | −1.61270 | ||||||||
\(135\) | −1.96791 | −0.169371 | ||||||||
\(136\) | −24.2469 | −2.07916 | ||||||||
\(137\) | 14.0680 | 1.20191 | 0.600954 | − | 0.799283i | \(-0.294787\pi\) | ||||
0.600954 | + | 0.799283i | \(0.294787\pi\) | |||||||
\(138\) | 0.292524 | 0.0249013 | ||||||||
\(139\) | −10.3244 | −0.875706 | −0.437853 | − | 0.899047i | \(-0.644261\pi\) | ||||
−0.437853 | + | 0.899047i | \(0.644261\pi\) | |||||||
\(140\) | −2.56068 | −0.216417 | ||||||||
\(141\) | 1.01095 | 0.0851373 | ||||||||
\(142\) | 28.5432 | 2.39529 | ||||||||
\(143\) | 6.01413 | 0.502927 | ||||||||
\(144\) | −7.30554 | −0.608795 | ||||||||
\(145\) | −9.18198 | −0.762522 | ||||||||
\(146\) | 12.2553 | 1.01426 | ||||||||
\(147\) | 1.23270 | 0.101671 | ||||||||
\(148\) | −12.3296 | −1.01349 | ||||||||
\(149\) | −19.0969 | −1.56448 | −0.782238 | − | 0.622980i | \(-0.785922\pi\) | ||||
−0.782238 | + | 0.622980i | \(0.785922\pi\) | |||||||
\(150\) | −0.702140 | −0.0573295 | ||||||||
\(151\) | −17.1066 | −1.39212 | −0.696059 | − | 0.717984i | \(-0.745065\pi\) | ||||
−0.696059 | + | 0.717984i | \(0.745065\pi\) | |||||||
\(152\) | 13.1446 | 1.06617 | ||||||||
\(153\) | −17.3577 | −1.40328 | ||||||||
\(154\) | −0.895203 | −0.0721375 | ||||||||
\(155\) | 17.1475 | 1.37732 | ||||||||
\(156\) | −4.03264 | −0.322870 | ||||||||
\(157\) | −20.7553 | −1.65646 | −0.828228 | − | 0.560391i | \(-0.810651\pi\) | ||||
−0.828228 | + | 0.560391i | \(0.810651\pi\) | |||||||
\(158\) | 4.27264 | 0.339913 | ||||||||
\(159\) | 0.554815 | 0.0439997 | ||||||||
\(160\) | −4.40029 | −0.347873 | ||||||||
\(161\) | 0.254264 | 0.0200388 | ||||||||
\(162\) | −20.8535 | −1.63840 | ||||||||
\(163\) | −16.2746 | −1.27473 | −0.637363 | − | 0.770564i | \(-0.719975\pi\) | ||||
−0.637363 | + | 0.770564i | \(0.719975\pi\) | |||||||
\(164\) | 0.604059 | 0.0471691 | ||||||||
\(165\) | 0.329759 | 0.0256717 | ||||||||
\(166\) | −31.6551 | −2.45692 | ||||||||
\(167\) | −1.72474 | −0.133464 | −0.0667320 | − | 0.997771i | \(-0.521257\pi\) | ||||
−0.0667320 | + | 0.997771i | \(0.521257\pi\) | |||||||
\(168\) | 0.278543 | 0.0214901 | ||||||||
\(169\) | 23.1697 | 1.78229 | ||||||||
\(170\) | 25.6970 | 1.97087 | ||||||||
\(171\) | 9.40984 | 0.719589 | ||||||||
\(172\) | 12.0148 | 0.916123 | ||||||||
\(173\) | 9.09979 | 0.691844 | 0.345922 | − | 0.938263i | \(-0.387566\pi\) | ||||
0.345922 | + | 0.938263i | \(0.387566\pi\) | |||||||
\(174\) | 2.15239 | 0.163172 | ||||||||
\(175\) | −0.610306 | −0.0461348 | ||||||||
\(176\) | 2.46168 | 0.185556 | ||||||||
\(177\) | 1.61583 | 0.121453 | ||||||||
\(178\) | −41.0182 | −3.07445 | ||||||||
\(179\) | −20.0313 | −1.49721 | −0.748605 | − | 0.663017i | \(-0.769276\pi\) | ||||
−0.748605 | + | 0.663017i | \(0.769276\pi\) | |||||||
\(180\) | 20.3232 | 1.51481 | ||||||||
\(181\) | 9.25128 | 0.687642 | 0.343821 | − | 0.939035i | \(-0.388279\pi\) | ||||
0.343821 | + | 0.939035i | \(0.388279\pi\) | |||||||
\(182\) | −5.38386 | −0.399079 | ||||||||
\(183\) | 0.464767 | 0.0343565 | ||||||||
\(184\) | −2.81896 | −0.207817 | ||||||||
\(185\) | 6.06357 | 0.445802 | ||||||||
\(186\) | −4.01962 | −0.294733 | ||||||||
\(187\) | 5.84884 | 0.427709 | ||||||||
\(188\) | −20.9944 | −1.53117 | ||||||||
\(189\) | 0.400971 | 0.0291663 | ||||||||
\(190\) | −13.9307 | −1.01064 | ||||||||
\(191\) | 11.0791 | 0.801657 | 0.400828 | − | 0.916153i | \(-0.368722\pi\) | ||||
0.400828 | + | 0.916153i | \(0.368722\pi\) | |||||||
\(192\) | 1.91616 | 0.138287 | ||||||||
\(193\) | 15.1622 | 1.09140 | 0.545699 | − | 0.837982i | \(-0.316264\pi\) | ||||
0.545699 | + | 0.837982i | \(0.316264\pi\) | |||||||
\(194\) | −37.5451 | −2.69558 | ||||||||
\(195\) | 1.98321 | 0.142021 | ||||||||
\(196\) | −25.5995 | −1.82854 | ||||||||
\(197\) | −16.6652 | −1.18735 | −0.593673 | − | 0.804707i | \(-0.702323\pi\) | ||||
−0.593673 | + | 0.804707i | \(0.702323\pi\) | |||||||
\(198\) | 7.10493 | 0.504926 | ||||||||
\(199\) | −22.9383 | −1.62605 | −0.813027 | − | 0.582226i | \(-0.802182\pi\) | ||||
−0.813027 | + | 0.582226i | \(0.802182\pi\) | |||||||
\(200\) | 6.76630 | 0.478450 | ||||||||
\(201\) | −1.40116 | −0.0988303 | ||||||||
\(202\) | −36.2613 | −2.55134 | ||||||||
\(203\) | 1.87087 | 0.131309 | ||||||||
\(204\) | −3.92181 | −0.274582 | ||||||||
\(205\) | −0.297070 | −0.0207483 | ||||||||
\(206\) | 0.519670 | 0.0362072 | ||||||||
\(207\) | −2.01801 | −0.140262 | ||||||||
\(208\) | 14.8048 | 1.02653 | ||||||||
\(209\) | −3.17074 | −0.219325 | ||||||||
\(210\) | −0.295201 | −0.0203708 | ||||||||
\(211\) | 2.81573 | 0.193843 | 0.0969213 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969213 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(212\) | −11.5219 | −0.791324 | ||||||||
\(213\) | 2.14233 | 0.146790 | ||||||||
\(214\) | 3.62852 | 0.248041 | ||||||||
\(215\) | −5.90878 | −0.402975 | ||||||||
\(216\) | −4.44546 | −0.302475 | ||||||||
\(217\) | −3.49388 | −0.237180 | ||||||||
\(218\) | −5.94731 | −0.402802 | ||||||||
\(219\) | 0.919830 | 0.0621563 | ||||||||
\(220\) | −6.84812 | −0.461700 | ||||||||
\(221\) | 35.1756 | 2.36617 | ||||||||
\(222\) | −1.42139 | −0.0953973 | ||||||||
\(223\) | −23.4098 | −1.56763 | −0.783817 | − | 0.620992i | \(-0.786730\pi\) | ||||
−0.783817 | + | 0.620992i | \(0.786730\pi\) | |||||||
\(224\) | 0.896580 | 0.0599053 | ||||||||
\(225\) | 4.84380 | 0.322920 | ||||||||
\(226\) | 17.6054 | 1.17109 | ||||||||
\(227\) | −9.86918 | −0.655041 | −0.327520 | − | 0.944844i | \(-0.606213\pi\) | ||||
−0.327520 | + | 0.944844i | \(0.606213\pi\) | |||||||
\(228\) | 2.12607 | 0.140803 | ||||||||
\(229\) | −2.01835 | −0.133376 | −0.0666880 | − | 0.997774i | \(-0.521243\pi\) | ||||
−0.0666880 | + | 0.997774i | \(0.521243\pi\) | |||||||
\(230\) | 2.98755 | 0.196993 | ||||||||
\(231\) | −0.0671900 | −0.00442078 | ||||||||
\(232\) | −20.7419 | −1.36177 | ||||||||
\(233\) | 16.8723 | 1.10534 | 0.552670 | − | 0.833400i | \(-0.313609\pi\) | ||||
0.552670 | + | 0.833400i | \(0.313609\pi\) | |||||||
\(234\) | 42.7300 | 2.79335 | ||||||||
\(235\) | 10.3248 | 0.673518 | ||||||||
\(236\) | −33.5560 | −2.18431 | ||||||||
\(237\) | 0.320686 | 0.0208308 | ||||||||
\(238\) | −5.23589 | −0.339393 | ||||||||
\(239\) | 28.1658 | 1.82190 | 0.910948 | − | 0.412522i | \(-0.135352\pi\) | ||||
0.910948 | + | 0.412522i | \(0.135352\pi\) | |||||||
\(240\) | 0.811760 | 0.0523989 | ||||||||
\(241\) | 11.9948 | 0.772656 | 0.386328 | − | 0.922361i | \(-0.373743\pi\) | ||||
0.386328 | + | 0.922361i | \(0.373743\pi\) | |||||||
\(242\) | −2.39408 | −0.153897 | ||||||||
\(243\) | −4.78217 | −0.306776 | ||||||||
\(244\) | −9.65182 | −0.617895 | ||||||||
\(245\) | 12.5896 | 0.804318 | ||||||||
\(246\) | 0.0696375 | 0.00443993 | ||||||||
\(247\) | −19.0692 | −1.21335 | ||||||||
\(248\) | 38.7358 | 2.45973 | ||||||||
\(249\) | −2.37590 | −0.150566 | ||||||||
\(250\) | −29.1386 | −1.84289 | ||||||||
\(251\) | −9.30790 | −0.587509 | −0.293755 | − | 0.955881i | \(-0.594905\pi\) | ||||
−0.293755 | + | 0.955881i | \(0.594905\pi\) | |||||||
\(252\) | −4.14096 | −0.260856 | ||||||||
\(253\) | 0.679989 | 0.0427506 | ||||||||
\(254\) | −24.9325 | −1.56440 | ||||||||
\(255\) | 1.92871 | 0.120780 | ||||||||
\(256\) | −28.3122 | −1.76951 | ||||||||
\(257\) | 12.7303 | 0.794092 | 0.397046 | − | 0.917799i | \(-0.370035\pi\) | ||||
0.397046 | + | 0.917799i | \(0.370035\pi\) | |||||||
\(258\) | 1.38510 | 0.0862327 | ||||||||
\(259\) | −1.23548 | −0.0767691 | ||||||||
\(260\) | −41.1855 | −2.55421 | ||||||||
\(261\) | −14.8485 | −0.919099 | ||||||||
\(262\) | 4.88879 | 0.302031 | ||||||||
\(263\) | 14.7742 | 0.911016 | 0.455508 | − | 0.890232i | \(-0.349458\pi\) | ||||
0.455508 | + | 0.890232i | \(0.349458\pi\) | |||||||
\(264\) | 0.744919 | 0.0458466 | ||||||||
\(265\) | 5.66633 | 0.348080 | ||||||||
\(266\) | 2.83846 | 0.174037 | ||||||||
\(267\) | −3.07865 | −0.188410 | ||||||||
\(268\) | 29.0980 | 1.77744 | ||||||||
\(269\) | 25.5398 | 1.55719 | 0.778594 | − | 0.627528i | \(-0.215933\pi\) | ||||
0.778594 | + | 0.627528i | \(0.215933\pi\) | |||||||
\(270\) | 4.71132 | 0.286722 | ||||||||
\(271\) | 1.65583 | 0.100584 | 0.0502922 | − | 0.998735i | \(-0.483985\pi\) | ||||
0.0502922 | + | 0.998735i | \(0.483985\pi\) | |||||||
\(272\) | 14.3979 | 0.873003 | ||||||||
\(273\) | −0.404089 | −0.0244566 | ||||||||
\(274\) | −33.6798 | −2.03467 | ||||||||
\(275\) | −1.63217 | −0.0984233 | ||||||||
\(276\) | −0.455952 | −0.0274451 | ||||||||
\(277\) | −17.5359 | −1.05363 | −0.526815 | − | 0.849980i | \(-0.676614\pi\) | ||||
−0.526815 | + | 0.849980i | \(0.676614\pi\) | |||||||
\(278\) | 24.7175 | 1.48245 | ||||||||
\(279\) | 27.7298 | 1.66014 | ||||||||
\(280\) | 2.84476 | 0.170007 | ||||||||
\(281\) | −19.5215 | −1.16456 | −0.582278 | − | 0.812990i | \(-0.697839\pi\) | ||||
−0.582278 | + | 0.812990i | \(0.697839\pi\) | |||||||
\(282\) | −2.42029 | −0.144126 | ||||||||
\(283\) | −0.449425 | −0.0267155 | −0.0133578 | − | 0.999911i | \(-0.504252\pi\) | ||||
−0.0133578 | + | 0.999911i | \(0.504252\pi\) | |||||||
\(284\) | −44.4898 | −2.63998 | ||||||||
\(285\) | −1.04558 | −0.0619348 | ||||||||
\(286\) | −14.3983 | −0.851389 | ||||||||
\(287\) | 0.0605295 | 0.00357294 | ||||||||
\(288\) | −7.11586 | −0.419306 | ||||||||
\(289\) | 17.2089 | 1.01229 | ||||||||
\(290\) | 21.9824 | 1.29085 | ||||||||
\(291\) | −2.81797 | −0.165192 | ||||||||
\(292\) | −19.1021 | −1.11787 | ||||||||
\(293\) | 2.21724 | 0.129533 | 0.0647663 | − | 0.997900i | \(-0.479370\pi\) | ||||
0.0647663 | + | 0.997900i | \(0.479370\pi\) | |||||||
\(294\) | −2.95118 | −0.172116 | ||||||||
\(295\) | 16.5025 | 0.960812 | ||||||||
\(296\) | 13.6975 | 0.796149 | ||||||||
\(297\) | 1.07233 | 0.0622230 | ||||||||
\(298\) | 45.7194 | 2.64845 | ||||||||
\(299\) | 4.08954 | 0.236504 | ||||||||
\(300\) | 1.09441 | 0.0631860 | ||||||||
\(301\) | 1.20394 | 0.0693940 | ||||||||
\(302\) | 40.9546 | 2.35667 | ||||||||
\(303\) | −2.72162 | −0.156353 | ||||||||
\(304\) | −7.80533 | −0.447666 | ||||||||
\(305\) | 4.74667 | 0.271793 | ||||||||
\(306\) | 41.5556 | 2.37557 | ||||||||
\(307\) | −16.4096 | −0.936544 | −0.468272 | − | 0.883584i | \(-0.655123\pi\) | ||||
−0.468272 | + | 0.883584i | \(0.655123\pi\) | |||||||
\(308\) | 1.39534 | 0.0795067 | ||||||||
\(309\) | 0.0390042 | 0.00221887 | ||||||||
\(310\) | −41.0524 | −2.33162 | ||||||||
\(311\) | 29.3948 | 1.66683 | 0.833414 | − | 0.552648i | \(-0.186383\pi\) | ||||
0.833414 | + | 0.552648i | \(0.186383\pi\) | |||||||
\(312\) | 4.48004 | 0.253632 | ||||||||
\(313\) | 17.9042 | 1.01201 | 0.506003 | − | 0.862532i | \(-0.331122\pi\) | ||||
0.506003 | + | 0.862532i | \(0.331122\pi\) | |||||||
\(314\) | 49.6899 | 2.80416 | ||||||||
\(315\) | 2.03648 | 0.114743 | ||||||||
\(316\) | −6.65969 | −0.374637 | ||||||||
\(317\) | −26.2139 | −1.47232 | −0.736159 | − | 0.676808i | \(-0.763363\pi\) | ||||
−0.736159 | + | 0.676808i | \(0.763363\pi\) | |||||||
\(318\) | −1.32827 | −0.0744857 | ||||||||
\(319\) | 5.00335 | 0.280134 | ||||||||
\(320\) | 19.5698 | 1.09398 | ||||||||
\(321\) | 0.272341 | 0.0152006 | ||||||||
\(322\) | −0.608728 | −0.0339231 | ||||||||
\(323\) | −18.5451 | −1.03188 | ||||||||
\(324\) | 32.5040 | 1.80578 | ||||||||
\(325\) | −9.81605 | −0.544496 | ||||||||
\(326\) | 38.9627 | 2.15794 | ||||||||
\(327\) | −0.446379 | −0.0246848 | ||||||||
\(328\) | −0.671075 | −0.0370539 | ||||||||
\(329\) | −2.10374 | −0.115983 | ||||||||
\(330\) | −0.789469 | −0.0434588 | ||||||||
\(331\) | −6.00895 | −0.330282 | −0.165141 | − | 0.986270i | \(-0.552808\pi\) | ||||
−0.165141 | + | 0.986270i | \(0.552808\pi\) | |||||||
\(332\) | 49.3403 | 2.70790 | ||||||||
\(333\) | 9.80561 | 0.537344 | ||||||||
\(334\) | 4.12915 | 0.225937 | ||||||||
\(335\) | −14.3101 | −0.781843 | ||||||||
\(336\) | −0.165400 | −0.00902331 | ||||||||
\(337\) | 0.779994 | 0.0424890 | 0.0212445 | − | 0.999774i | \(-0.493237\pi\) | ||||
0.0212445 | + | 0.999774i | \(0.493237\pi\) | |||||||
\(338\) | −55.4701 | −3.01718 | ||||||||
\(339\) | 1.32139 | 0.0717678 | ||||||||
\(340\) | −40.0535 | −2.17221 | ||||||||
\(341\) | −9.34384 | −0.505997 | ||||||||
\(342\) | −22.5279 | −1.21817 | ||||||||
\(343\) | −5.18265 | −0.279837 | ||||||||
\(344\) | −13.3478 | −0.719665 | ||||||||
\(345\) | 0.224233 | 0.0120723 | ||||||||
\(346\) | −21.7856 | −1.17120 | ||||||||
\(347\) | 14.2370 | 0.764280 | 0.382140 | − | 0.924104i | \(-0.375187\pi\) | ||||
0.382140 | + | 0.924104i | \(0.375187\pi\) | |||||||
\(348\) | −3.35489 | −0.179841 | ||||||||
\(349\) | −32.3854 | −1.73355 | −0.866775 | − | 0.498700i | \(-0.833811\pi\) | ||||
−0.866775 | + | 0.498700i | \(0.833811\pi\) | |||||||
\(350\) | 1.46112 | 0.0781001 | ||||||||
\(351\) | 6.44914 | 0.344230 | ||||||||
\(352\) | 2.39776 | 0.127801 | ||||||||
\(353\) | −9.89812 | −0.526824 | −0.263412 | − | 0.964683i | \(-0.584848\pi\) | ||||
−0.263412 | + | 0.964683i | \(0.584848\pi\) | |||||||
\(354\) | −3.86842 | −0.205604 | ||||||||
\(355\) | 21.8796 | 1.16125 | ||||||||
\(356\) | 63.9344 | 3.38852 | ||||||||
\(357\) | −0.392983 | −0.0207989 | ||||||||
\(358\) | 47.9565 | 2.53458 | ||||||||
\(359\) | −21.5311 | −1.13637 | −0.568184 | − | 0.822902i | \(-0.692354\pi\) | ||||
−0.568184 | + | 0.822902i | \(0.692354\pi\) | |||||||
\(360\) | −22.5780 | −1.18996 | ||||||||
\(361\) | −8.94641 | −0.470864 | ||||||||
\(362\) | −22.1483 | −1.16409 | ||||||||
\(363\) | −0.179689 | −0.00943123 | ||||||||
\(364\) | 8.39174 | 0.439846 | ||||||||
\(365\) | 9.39424 | 0.491717 | ||||||||
\(366\) | −1.11269 | −0.0581611 | ||||||||
\(367\) | −8.90435 | −0.464803 | −0.232402 | − | 0.972620i | \(-0.574658\pi\) | ||||
−0.232402 | + | 0.972620i | \(0.574658\pi\) | |||||||
\(368\) | 1.67391 | 0.0872587 | ||||||||
\(369\) | −0.480403 | −0.0250088 | ||||||||
\(370\) | −14.5167 | −0.754685 | ||||||||
\(371\) | −1.15454 | −0.0599409 | ||||||||
\(372\) | 6.26531 | 0.324841 | ||||||||
\(373\) | −13.5296 | −0.700534 | −0.350267 | − | 0.936650i | \(-0.613909\pi\) | ||||
−0.350267 | + | 0.936650i | \(0.613909\pi\) | |||||||
\(374\) | −14.0026 | −0.724055 | ||||||||
\(375\) | −2.18702 | −0.112937 | ||||||||
\(376\) | 23.3236 | 1.20282 | ||||||||
\(377\) | 30.0908 | 1.54975 | ||||||||
\(378\) | −0.959955 | −0.0493747 | ||||||||
\(379\) | −7.85566 | −0.403518 | −0.201759 | − | 0.979435i | \(-0.564666\pi\) | ||||
−0.201759 | + | 0.979435i | \(0.564666\pi\) | |||||||
\(380\) | 21.7136 | 1.11388 | ||||||||
\(381\) | −1.87132 | −0.0958708 | ||||||||
\(382\) | −26.5243 | −1.35710 | ||||||||
\(383\) | 4.79601 | 0.245065 | 0.122532 | − | 0.992465i | \(-0.460898\pi\) | ||||
0.122532 | + | 0.992465i | \(0.460898\pi\) | |||||||
\(384\) | −3.72574 | −0.190128 | ||||||||
\(385\) | −0.686213 | −0.0349726 | ||||||||
\(386\) | −36.2994 | −1.84759 | ||||||||
\(387\) | −9.55529 | −0.485723 | ||||||||
\(388\) | 58.5208 | 2.97095 | ||||||||
\(389\) | 5.34323 | 0.270913 | 0.135456 | − | 0.990783i | \(-0.456750\pi\) | ||||
0.135456 | + | 0.990783i | \(0.456750\pi\) | |||||||
\(390\) | −4.74797 | −0.240423 | ||||||||
\(391\) | 3.97715 | 0.201133 | ||||||||
\(392\) | 28.4396 | 1.43642 | ||||||||
\(393\) | 0.366931 | 0.0185092 | ||||||||
\(394\) | 39.8977 | 2.01002 | ||||||||
\(395\) | 3.27517 | 0.164792 | ||||||||
\(396\) | −11.0743 | −0.556506 | ||||||||
\(397\) | −13.1684 | −0.660901 | −0.330451 | − | 0.943823i | \(-0.607201\pi\) | ||||
−0.330451 | + | 0.943823i | \(0.607201\pi\) | |||||||
\(398\) | 54.9161 | 2.75270 | ||||||||
\(399\) | 0.213042 | 0.0106654 | ||||||||
\(400\) | −4.01786 | −0.200893 | ||||||||
\(401\) | −34.0103 | −1.69839 | −0.849197 | − | 0.528076i | \(-0.822914\pi\) | ||||
−0.849197 | + | 0.528076i | \(0.822914\pi\) | |||||||
\(402\) | 3.35449 | 0.167307 | ||||||||
\(403\) | −56.1950 | −2.79927 | ||||||||
\(404\) | 56.5199 | 2.81197 | ||||||||
\(405\) | −15.9851 | −0.794307 | ||||||||
\(406\) | −4.47901 | −0.222290 | ||||||||
\(407\) | −3.30410 | −0.163778 | ||||||||
\(408\) | 4.35691 | 0.215699 | ||||||||
\(409\) | 9.68204 | 0.478746 | 0.239373 | − | 0.970928i | \(-0.423058\pi\) | ||||
0.239373 | + | 0.970928i | \(0.423058\pi\) | |||||||
\(410\) | 0.711209 | 0.0351241 | ||||||||
\(411\) | −2.52786 | −0.124690 | ||||||||
\(412\) | −0.810001 | −0.0399059 | ||||||||
\(413\) | −3.36246 | −0.165456 | ||||||||
\(414\) | 4.83128 | 0.237444 | ||||||||
\(415\) | −24.2651 | −1.19113 | ||||||||
\(416\) | 14.4204 | 0.707020 | ||||||||
\(417\) | 1.85518 | 0.0908488 | ||||||||
\(418\) | 7.59100 | 0.371288 | ||||||||
\(419\) | −13.2652 | −0.648048 | −0.324024 | − | 0.946049i | \(-0.605036\pi\) | ||||
−0.324024 | + | 0.946049i | \(0.605036\pi\) | |||||||
\(420\) | 0.460125 | 0.0224518 | ||||||||
\(421\) | 10.2365 | 0.498898 | 0.249449 | − | 0.968388i | \(-0.419751\pi\) | ||||
0.249449 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(422\) | −6.74107 | −0.328150 | ||||||||
\(423\) | 16.6967 | 0.811819 | ||||||||
\(424\) | 12.8001 | 0.621629 | ||||||||
\(425\) | −9.54627 | −0.463062 | ||||||||
\(426\) | −5.12890 | −0.248496 | ||||||||
\(427\) | −0.967157 | −0.0468040 | ||||||||
\(428\) | −5.65571 | −0.273379 | ||||||||
\(429\) | −1.08067 | −0.0521754 | ||||||||
\(430\) | 14.1461 | 0.682184 | ||||||||
\(431\) | 19.1015 | 0.920085 | 0.460042 | − | 0.887897i | \(-0.347834\pi\) | ||||
0.460042 | + | 0.887897i | \(0.347834\pi\) | |||||||
\(432\) | 2.63973 | 0.127004 | ||||||||
\(433\) | −27.6484 | −1.32870 | −0.664348 | − | 0.747423i | \(-0.731291\pi\) | ||||
−0.664348 | + | 0.747423i | \(0.731291\pi\) | |||||||
\(434\) | 8.36463 | 0.401515 | ||||||||
\(435\) | 1.64990 | 0.0791067 | ||||||||
\(436\) | 9.26996 | 0.443951 | ||||||||
\(437\) | −2.15607 | −0.103139 | ||||||||
\(438\) | −2.20214 | −0.105223 | ||||||||
\(439\) | 17.3620 | 0.828642 | 0.414321 | − | 0.910131i | \(-0.364019\pi\) | ||||
0.414321 | + | 0.910131i | \(0.364019\pi\) | |||||||
\(440\) | 7.60787 | 0.362691 | ||||||||
\(441\) | 20.3590 | 0.969478 | ||||||||
\(442\) | −84.2132 | −4.00561 | ||||||||
\(443\) | −18.2415 | −0.866680 | −0.433340 | − | 0.901230i | \(-0.642665\pi\) | ||||
−0.433340 | + | 0.901230i | \(0.642665\pi\) | |||||||
\(444\) | 2.21549 | 0.105143 | ||||||||
\(445\) | −31.4423 | −1.49051 | ||||||||
\(446\) | 56.0448 | 2.65380 | ||||||||
\(447\) | 3.43150 | 0.162304 | ||||||||
\(448\) | −3.98744 | −0.188389 | ||||||||
\(449\) | −20.2317 | −0.954793 | −0.477397 | − | 0.878688i | \(-0.658419\pi\) | ||||
−0.477397 | + | 0.878688i | \(0.658419\pi\) | |||||||
\(450\) | −11.5964 | −0.546661 | ||||||||
\(451\) | 0.161876 | 0.00762246 | ||||||||
\(452\) | −27.4413 | −1.29073 | ||||||||
\(453\) | 3.07388 | 0.144423 | ||||||||
\(454\) | 23.6276 | 1.10890 | ||||||||
\(455\) | −4.12697 | −0.193475 | ||||||||
\(456\) | −2.36194 | −0.110608 | ||||||||
\(457\) | 19.0925 | 0.893107 | 0.446554 | − | 0.894757i | \(-0.352651\pi\) | ||||
0.446554 | + | 0.894757i | \(0.352651\pi\) | |||||||
\(458\) | 4.83208 | 0.225788 | ||||||||
\(459\) | 6.27189 | 0.292747 | ||||||||
\(460\) | −4.65665 | −0.217117 | ||||||||
\(461\) | −20.8789 | −0.972429 | −0.486214 | − | 0.873840i | \(-0.661623\pi\) | ||||
−0.486214 | + | 0.873840i | \(0.661623\pi\) | |||||||
\(462\) | 0.160858 | 0.00748380 | ||||||||
\(463\) | 15.7557 | 0.732227 | 0.366114 | − | 0.930570i | \(-0.380688\pi\) | ||||
0.366114 | + | 0.930570i | \(0.380688\pi\) | |||||||
\(464\) | 12.3166 | 0.571785 | ||||||||
\(465\) | −3.08122 | −0.142888 | ||||||||
\(466\) | −40.3936 | −1.87120 | ||||||||
\(467\) | −13.7584 | −0.636662 | −0.318331 | − | 0.947980i | \(-0.603122\pi\) | ||||
−0.318331 | + | 0.947980i | \(0.603122\pi\) | |||||||
\(468\) | −66.6025 | −3.07870 | ||||||||
\(469\) | 2.91575 | 0.134637 | ||||||||
\(470\) | −24.7185 | −1.14018 | ||||||||
\(471\) | 3.72951 | 0.171847 | ||||||||
\(472\) | 37.2788 | 1.71589 | ||||||||
\(473\) | 3.21975 | 0.148044 | ||||||||
\(474\) | −0.767746 | −0.0352638 | ||||||||
\(475\) | 5.17517 | 0.237453 | ||||||||
\(476\) | 8.16110 | 0.374063 | ||||||||
\(477\) | 9.16322 | 0.419555 | ||||||||
\(478\) | −67.4312 | −3.08423 | ||||||||
\(479\) | −4.62159 | −0.211166 | −0.105583 | − | 0.994411i | \(-0.533671\pi\) | ||||
−0.105583 | + | 0.994411i | \(0.533671\pi\) | |||||||
\(480\) | 0.790683 | 0.0360896 | ||||||||
\(481\) | −19.8713 | −0.906052 | ||||||||
\(482\) | −28.7166 | −1.30800 | ||||||||
\(483\) | −0.0456885 | −0.00207890 | ||||||||
\(484\) | 3.73161 | 0.169618 | ||||||||
\(485\) | −28.7800 | −1.30683 | ||||||||
\(486\) | 11.4489 | 0.519332 | ||||||||
\(487\) | −11.0234 | −0.499519 | −0.249759 | − | 0.968308i | \(-0.580352\pi\) | ||||
−0.249759 | + | 0.968308i | \(0.580352\pi\) | |||||||
\(488\) | 10.7226 | 0.485390 | ||||||||
\(489\) | 2.92437 | 0.132244 | ||||||||
\(490\) | −30.1404 | −1.36160 | ||||||||
\(491\) | 25.9101 | 1.16931 | 0.584653 | − | 0.811284i | \(-0.301231\pi\) | ||||
0.584653 | + | 0.811284i | \(0.301231\pi\) | |||||||
\(492\) | −0.108543 | −0.00489349 | ||||||||
\(493\) | 29.2638 | 1.31797 | ||||||||
\(494\) | 45.6532 | 2.05404 | ||||||||
\(495\) | 5.44624 | 0.244790 | ||||||||
\(496\) | −23.0015 | −1.03280 | ||||||||
\(497\) | −4.45808 | −0.199972 | ||||||||
\(498\) | 5.68808 | 0.254889 | ||||||||
\(499\) | −0.375967 | −0.0168306 | −0.00841530 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841530 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(500\) | 45.4179 | 2.03115 | ||||||||
\(501\) | 0.309916 | 0.0138460 | ||||||||
\(502\) | 22.2838 | 0.994576 | ||||||||
\(503\) | 7.27713 | 0.324471 | 0.162236 | − | 0.986752i | \(-0.448130\pi\) | ||||
0.162236 | + | 0.986752i | \(0.448130\pi\) | |||||||
\(504\) | 4.60037 | 0.204917 | ||||||||
\(505\) | −27.7959 | −1.23690 | ||||||||
\(506\) | −1.62795 | −0.0723711 | ||||||||
\(507\) | −4.16335 | −0.184901 | ||||||||
\(508\) | 38.8618 | 1.72421 | ||||||||
\(509\) | −11.5444 | −0.511696 | −0.255848 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255848 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(510\) | −4.61747 | −0.204465 | ||||||||
\(511\) | −1.91412 | −0.0846757 | ||||||||
\(512\) | 26.3128 | 1.16287 | ||||||||
\(513\) | −3.40009 | −0.150117 | ||||||||
\(514\) | −30.4772 | −1.34429 | ||||||||
\(515\) | 0.398350 | 0.0175534 | ||||||||
\(516\) | −2.15893 | −0.0950418 | ||||||||
\(517\) | −5.62611 | −0.247436 | ||||||||
\(518\) | 2.95784 | 0.129960 | ||||||||
\(519\) | −1.63513 | −0.0717743 | ||||||||
\(520\) | 45.7547 | 2.00648 | ||||||||
\(521\) | 30.7442 | 1.34693 | 0.673465 | − | 0.739219i | \(-0.264805\pi\) | ||||
0.673465 | + | 0.739219i | \(0.264805\pi\) | |||||||
\(522\) | 35.5485 | 1.55591 | ||||||||
\(523\) | 17.6245 | 0.770666 | 0.385333 | − | 0.922778i | \(-0.374087\pi\) | ||||
0.385333 | + | 0.922778i | \(0.374087\pi\) | |||||||
\(524\) | −7.62007 | −0.332884 | ||||||||
\(525\) | 0.109665 | 0.00478618 | ||||||||
\(526\) | −35.3706 | −1.54223 | ||||||||
\(527\) | −54.6506 | −2.38062 | ||||||||
\(528\) | −0.442336 | −0.0192502 | ||||||||
\(529\) | −22.5376 | −0.979896 | ||||||||
\(530\) | −13.5656 | −0.589254 | ||||||||
\(531\) | 26.6867 | 1.15811 | ||||||||
\(532\) | −4.42425 | −0.191816 | ||||||||
\(533\) | 0.973546 | 0.0421689 | ||||||||
\(534\) | 7.37052 | 0.318954 | ||||||||
\(535\) | 2.78142 | 0.120251 | ||||||||
\(536\) | −32.3262 | −1.39628 | ||||||||
\(537\) | 3.59940 | 0.155326 | ||||||||
\(538\) | −61.1442 | −2.63611 | ||||||||
\(539\) | −6.86018 | −0.295489 | ||||||||
\(540\) | −7.34346 | −0.316012 | ||||||||
\(541\) | 20.1138 | 0.864759 | 0.432380 | − | 0.901692i | \(-0.357674\pi\) | ||||
0.432380 | + | 0.901692i | \(0.357674\pi\) | |||||||
\(542\) | −3.96418 | −0.170276 | ||||||||
\(543\) | −1.66235 | −0.0713384 | ||||||||
\(544\) | 14.0241 | 0.601278 | ||||||||
\(545\) | −4.55887 | −0.195281 | ||||||||
\(546\) | 0.967421 | 0.0414018 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 52.4962 | 2.24252 | ||||||||
\(549\) | 7.67600 | 0.327604 | ||||||||
\(550\) | 3.90753 | 0.166618 | ||||||||
\(551\) | −15.8643 | −0.675843 | ||||||||
\(552\) | 0.506537 | 0.0215596 | ||||||||
\(553\) | −0.667331 | −0.0283778 | ||||||||
\(554\) | 41.9823 | 1.78366 | ||||||||
\(555\) | −1.08956 | −0.0462491 | ||||||||
\(556\) | −38.5267 | −1.63389 | ||||||||
\(557\) | 25.4636 | 1.07893 | 0.539464 | − | 0.842009i | \(-0.318627\pi\) | ||||
0.539464 | + | 0.842009i | \(0.318627\pi\) | |||||||
\(558\) | −66.3873 | −2.81040 | ||||||||
\(559\) | 19.3640 | 0.819009 | ||||||||
\(560\) | −1.68923 | −0.0713831 | ||||||||
\(561\) | −1.05097 | −0.0443720 | ||||||||
\(562\) | 46.7360 | 1.97144 | ||||||||
\(563\) | −39.2615 | −1.65467 | −0.827337 | − | 0.561706i | \(-0.810145\pi\) | ||||
−0.827337 | + | 0.561706i | \(0.810145\pi\) | |||||||
\(564\) | 3.77246 | 0.158849 | ||||||||
\(565\) | 13.4953 | 0.567753 | ||||||||
\(566\) | 1.07596 | 0.0452259 | ||||||||
\(567\) | 3.25705 | 0.136783 | ||||||||
\(568\) | 49.4256 | 2.07385 | ||||||||
\(569\) | −33.7635 | −1.41544 | −0.707720 | − | 0.706493i | \(-0.750276\pi\) | ||||
−0.707720 | + | 0.706493i | \(0.750276\pi\) | |||||||
\(570\) | 2.50320 | 0.104848 | ||||||||
\(571\) | 29.8914 | 1.25092 | 0.625458 | − | 0.780257i | \(-0.284912\pi\) | ||||
0.625458 | + | 0.780257i | \(0.284912\pi\) | |||||||
\(572\) | 22.4424 | 0.938362 | ||||||||
\(573\) | −1.99080 | −0.0831667 | ||||||||
\(574\) | −0.144912 | −0.00604852 | ||||||||
\(575\) | −1.10985 | −0.0462841 | ||||||||
\(576\) | 31.6470 | 1.31863 | ||||||||
\(577\) | −9.61989 | −0.400481 | −0.200241 | − | 0.979747i | \(-0.564172\pi\) | ||||
−0.200241 | + | 0.979747i | \(0.564172\pi\) | |||||||
\(578\) | −41.1994 | −1.71367 | ||||||||
\(579\) | −2.72448 | −0.113225 | ||||||||
\(580\) | −34.2635 | −1.42272 | ||||||||
\(581\) | 4.94412 | 0.205117 | ||||||||
\(582\) | 6.74644 | 0.279649 | ||||||||
\(583\) | −3.08764 | −0.127877 | ||||||||
\(584\) | 21.2214 | 0.878147 | ||||||||
\(585\) | 32.7544 | 1.35423 | ||||||||
\(586\) | −5.30824 | −0.219282 | ||||||||
\(587\) | −16.7346 | −0.690711 | −0.345355 | − | 0.938472i | \(-0.612242\pi\) | ||||
−0.345355 | + | 0.938472i | \(0.612242\pi\) | |||||||
\(588\) | 4.59995 | 0.189699 | ||||||||
\(589\) | 29.6269 | 1.22075 | ||||||||
\(590\) | −39.5082 | −1.62653 | ||||||||
\(591\) | 2.99455 | 0.123179 | ||||||||
\(592\) | −8.13361 | −0.334290 | ||||||||
\(593\) | −9.13613 | −0.375176 | −0.187588 | − | 0.982248i | \(-0.560067\pi\) | ||||
−0.187588 | + | 0.982248i | \(0.560067\pi\) | |||||||
\(594\) | −2.56725 | −0.105335 | ||||||||
\(595\) | −4.01354 | −0.164539 | ||||||||
\(596\) | −71.2620 | −2.91900 | ||||||||
\(597\) | 4.12176 | 0.168692 | ||||||||
\(598\) | −9.79068 | −0.400371 | ||||||||
\(599\) | 15.4926 | 0.633009 | 0.316505 | − | 0.948591i | \(-0.397491\pi\) | ||||
0.316505 | + | 0.948591i | \(0.397491\pi\) | |||||||
\(600\) | −1.21583 | −0.0496361 | ||||||||
\(601\) | −24.0874 | −0.982547 | −0.491273 | − | 0.871005i | \(-0.663468\pi\) | ||||
−0.491273 | + | 0.871005i | \(0.663468\pi\) | |||||||
\(602\) | −2.88233 | −0.117475 | ||||||||
\(603\) | −23.1413 | −0.942388 | ||||||||
\(604\) | −63.8353 | −2.59742 | ||||||||
\(605\) | −1.83517 | −0.0746101 | ||||||||
\(606\) | 6.51576 | 0.264685 | ||||||||
\(607\) | −19.9915 | −0.811432 | −0.405716 | − | 0.913999i | \(-0.632978\pi\) | ||||
−0.405716 | + | 0.913999i | \(0.632978\pi\) | |||||||
\(608\) | −7.60267 | −0.308329 | ||||||||
\(609\) | −0.336175 | −0.0136225 | ||||||||
\(610\) | −11.3639 | −0.460111 | ||||||||
\(611\) | −33.8361 | −1.36886 | ||||||||
\(612\) | −64.7720 | −2.61825 | ||||||||
\(613\) | −4.93254 | −0.199223 | −0.0996117 | − | 0.995026i | \(-0.531760\pi\) | ||||
−0.0996117 | + | 0.995026i | \(0.531760\pi\) | |||||||
\(614\) | 39.2858 | 1.58545 | ||||||||
\(615\) | 0.0533802 | 0.00215250 | ||||||||
\(616\) | −1.55014 | −0.0624569 | ||||||||
\(617\) | −1.73132 | −0.0697004 | −0.0348502 | − | 0.999393i | \(-0.511095\pi\) | ||||
−0.0348502 | + | 0.999393i | \(0.511095\pi\) | |||||||
\(618\) | −0.0933791 | −0.00375626 | ||||||||
\(619\) | −7.82980 | −0.314706 | −0.157353 | − | 0.987542i | \(-0.550296\pi\) | ||||
−0.157353 | + | 0.987542i | \(0.550296\pi\) | |||||||
\(620\) | 63.9877 | 2.56981 | ||||||||
\(621\) | 0.729174 | 0.0292608 | ||||||||
\(622\) | −70.3735 | −2.82172 | ||||||||
\(623\) | 6.40652 | 0.256672 | ||||||||
\(624\) | −2.66026 | −0.106496 | ||||||||
\(625\) | −14.1752 | −0.567008 | ||||||||
\(626\) | −42.8641 | −1.71319 | ||||||||
\(627\) | 0.569747 | 0.0227535 | ||||||||
\(628\) | −77.4508 | −3.09062 | ||||||||
\(629\) | −19.3251 | −0.770543 | ||||||||
\(630\) | −4.87549 | −0.194244 | ||||||||
\(631\) | −46.0076 | −1.83154 | −0.915768 | − | 0.401708i | \(-0.868417\pi\) | ||||
−0.915768 | + | 0.401708i | \(0.868417\pi\) | |||||||
\(632\) | 7.39853 | 0.294298 | ||||||||
\(633\) | −0.505955 | −0.0201099 | ||||||||
\(634\) | 62.7581 | 2.49244 | ||||||||
\(635\) | −19.1118 | −0.758430 | ||||||||
\(636\) | 2.07035 | 0.0820947 | ||||||||
\(637\) | −41.2580 | −1.63470 | ||||||||
\(638\) | −11.9784 | −0.474230 | ||||||||
\(639\) | 35.3823 | 1.39970 | ||||||||
\(640\) | −38.0510 | −1.50410 | ||||||||
\(641\) | −12.4823 | −0.493022 | −0.246511 | − | 0.969140i | \(-0.579284\pi\) | ||||
−0.246511 | + | 0.969140i | \(0.579284\pi\) | |||||||
\(642\) | −0.652005 | −0.0257326 | ||||||||
\(643\) | 18.6708 | 0.736304 | 0.368152 | − | 0.929766i | \(-0.379991\pi\) | ||||
0.368152 | + | 0.929766i | \(0.379991\pi\) | |||||||
\(644\) | 0.948814 | 0.0373885 | ||||||||
\(645\) | 1.06174 | 0.0418060 | ||||||||
\(646\) | 44.3985 | 1.74684 | ||||||||
\(647\) | −9.76447 | −0.383881 | −0.191940 | − | 0.981407i | \(-0.561478\pi\) | ||||
−0.191940 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(648\) | −36.1100 | −1.41854 | ||||||||
\(649\) | −8.99236 | −0.352981 | ||||||||
\(650\) | 23.5004 | 0.921761 | ||||||||
\(651\) | 0.627813 | 0.0246059 | ||||||||
\(652\) | −60.7304 | −2.37839 | ||||||||
\(653\) | 22.2247 | 0.869719 | 0.434859 | − | 0.900498i | \(-0.356798\pi\) | ||||
0.434859 | + | 0.900498i | \(0.356798\pi\) | |||||||
\(654\) | 1.06867 | 0.0417881 | ||||||||
\(655\) | 3.74747 | 0.146426 | ||||||||
\(656\) | 0.398487 | 0.0155583 | ||||||||
\(657\) | 15.1917 | 0.592687 | ||||||||
\(658\) | 5.03651 | 0.196343 | ||||||||
\(659\) | −4.16800 | −0.162362 | −0.0811812 | − | 0.996699i | \(-0.525869\pi\) | ||||
−0.0811812 | + | 0.996699i | \(0.525869\pi\) | |||||||
\(660\) | 1.23053 | 0.0478984 | ||||||||
\(661\) | −41.1100 | −1.59900 | −0.799498 | − | 0.600669i | \(-0.794901\pi\) | ||||
−0.799498 | + | 0.600669i | \(0.794901\pi\) | |||||||
\(662\) | 14.3859 | 0.559123 | ||||||||
\(663\) | −6.32068 | −0.245475 | ||||||||
\(664\) | −54.8143 | −2.12721 | ||||||||
\(665\) | 2.17580 | 0.0843740 | ||||||||
\(666\) | −23.4754 | −0.909653 | ||||||||
\(667\) | 3.40222 | 0.131735 | ||||||||
\(668\) | −6.43604 | −0.249018 | ||||||||
\(669\) | 4.20648 | 0.162632 | ||||||||
\(670\) | 34.2594 | 1.32356 | ||||||||
\(671\) | −2.58651 | −0.0998510 | ||||||||
\(672\) | −0.161106 | −0.00621478 | ||||||||
\(673\) | −42.9971 | −1.65742 | −0.828709 | − | 0.559680i | \(-0.810924\pi\) | ||||
−0.828709 | + | 0.559680i | \(0.810924\pi\) | |||||||
\(674\) | −1.86737 | −0.0719282 | ||||||||
\(675\) | −1.75022 | −0.0673661 | ||||||||
\(676\) | 86.4603 | 3.32540 | ||||||||
\(677\) | −9.36046 | −0.359752 | −0.179876 | − | 0.983689i | \(-0.557570\pi\) | ||||
−0.179876 | + | 0.983689i | \(0.557570\pi\) | |||||||
\(678\) | −3.16350 | −0.121493 | ||||||||
\(679\) | 5.86405 | 0.225042 | ||||||||
\(680\) | 44.4972 | 1.70639 | ||||||||
\(681\) | 1.77338 | 0.0679562 | ||||||||
\(682\) | 22.3699 | 0.856587 | ||||||||
\(683\) | −45.6073 | −1.74512 | −0.872558 | − | 0.488511i | \(-0.837540\pi\) | ||||
−0.872558 | + | 0.488511i | \(0.837540\pi\) | |||||||
\(684\) | 35.1138 | 1.34261 | ||||||||
\(685\) | −25.8171 | −0.986420 | ||||||||
\(686\) | 12.4077 | 0.473727 | ||||||||
\(687\) | 0.362675 | 0.0138369 | ||||||||
\(688\) | 7.92598 | 0.302175 | ||||||||
\(689\) | −18.5695 | −0.707440 | ||||||||
\(690\) | −0.536830 | −0.0204368 | ||||||||
\(691\) | −48.4304 | −1.84238 | −0.921190 | − | 0.389113i | \(-0.872782\pi\) | ||||
−0.921190 | + | 0.389113i | \(0.872782\pi\) | |||||||
\(692\) | 33.9568 | 1.29085 | ||||||||
\(693\) | −1.10970 | −0.0421540 | ||||||||
\(694\) | −34.0844 | −1.29383 | ||||||||
\(695\) | 18.9470 | 0.718702 | ||||||||
\(696\) | 3.72709 | 0.141275 | ||||||||
\(697\) | 0.946789 | 0.0358622 | ||||||||
\(698\) | 77.5331 | 2.93467 | ||||||||
\(699\) | −3.03177 | −0.114672 | ||||||||
\(700\) | −2.27742 | −0.0860784 | ||||||||
\(701\) | −36.7901 | −1.38954 | −0.694771 | − | 0.719231i | \(-0.744494\pi\) | ||||
−0.694771 | + | 0.719231i | \(0.744494\pi\) | |||||||
\(702\) | −15.4397 | −0.582736 | ||||||||
\(703\) | 10.4764 | 0.395126 | ||||||||
\(704\) | −10.6638 | −0.401906 | ||||||||
\(705\) | −1.85526 | −0.0698731 | ||||||||
\(706\) | 23.6969 | 0.891843 | ||||||||
\(707\) | 5.66355 | 0.213000 | ||||||||
\(708\) | 6.02964 | 0.226608 | ||||||||
\(709\) | −40.0097 | −1.50260 | −0.751299 | − | 0.659962i | \(-0.770572\pi\) | ||||
−0.751299 | + | 0.659962i | \(0.770572\pi\) | |||||||
\(710\) | −52.3815 | −1.96584 | ||||||||
\(711\) | 5.29639 | 0.198630 | ||||||||
\(712\) | −71.0274 | −2.66187 | ||||||||
\(713\) | −6.35371 | −0.237948 | ||||||||
\(714\) | 0.940833 | 0.0352098 | ||||||||
\(715\) | −11.0369 | −0.412758 | ||||||||
\(716\) | −74.7489 | −2.79350 | ||||||||
\(717\) | −5.06109 | −0.189010 | ||||||||
\(718\) | 51.5471 | 1.92372 | ||||||||
\(719\) | −42.4355 | −1.58258 | −0.791288 | − | 0.611444i | \(-0.790589\pi\) | ||||
−0.791288 | + | 0.611444i | \(0.790589\pi\) | |||||||
\(720\) | 13.4069 | 0.499645 | ||||||||
\(721\) | −0.0811658 | −0.00302277 | ||||||||
\(722\) | 21.4184 | 0.797110 | ||||||||
\(723\) | −2.15534 | −0.0801580 | ||||||||
\(724\) | 34.5221 | 1.28300 | ||||||||
\(725\) | −8.16629 | −0.303288 | ||||||||
\(726\) | 0.430189 | 0.0159658 | ||||||||
\(727\) | −35.7945 | −1.32754 | −0.663772 | − | 0.747935i | \(-0.731045\pi\) | ||||
−0.663772 | + | 0.747935i | \(0.731045\pi\) | |||||||
\(728\) | −9.32274 | −0.345524 | ||||||||
\(729\) | −25.2720 | −0.936002 | ||||||||
\(730\) | −22.4905 | −0.832412 | ||||||||
\(731\) | 18.8318 | 0.696519 | ||||||||
\(732\) | 1.73433 | 0.0641025 | ||||||||
\(733\) | −28.8373 | −1.06513 | −0.532565 | − | 0.846389i | \(-0.678772\pi\) | ||||
−0.532565 | + | 0.846389i | \(0.678772\pi\) | |||||||
\(734\) | 21.3177 | 0.786851 | ||||||||
\(735\) | −2.26221 | −0.0834428 | ||||||||
\(736\) | 1.63045 | 0.0600992 | ||||||||
\(737\) | 7.79770 | 0.287232 | ||||||||
\(738\) | 1.15012 | 0.0423365 | ||||||||
\(739\) | 36.9636 | 1.35973 | 0.679864 | − | 0.733338i | \(-0.262039\pi\) | ||||
0.679864 | + | 0.733338i | \(0.262039\pi\) | |||||||
\(740\) | 22.6269 | 0.831780 | ||||||||
\(741\) | 3.42653 | 0.125877 | ||||||||
\(742\) | 2.76406 | 0.101472 | ||||||||
\(743\) | 11.5690 | 0.424426 | 0.212213 | − | 0.977223i | \(-0.431933\pi\) | ||||
0.212213 | + | 0.977223i | \(0.431933\pi\) | |||||||
\(744\) | −6.96040 | −0.255181 | ||||||||
\(745\) | 35.0459 | 1.28398 | ||||||||
\(746\) | 32.3908 | 1.18591 | ||||||||
\(747\) | −39.2399 | −1.43571 | ||||||||
\(748\) | 21.8256 | 0.798021 | ||||||||
\(749\) | −0.566728 | −0.0207078 | ||||||||
\(750\) | 5.23589 | 0.191188 | ||||||||
\(751\) | −26.6400 | −0.972107 | −0.486054 | − | 0.873929i | \(-0.661564\pi\) | ||||
−0.486054 | + | 0.873929i | \(0.661564\pi\) | |||||||
\(752\) | −13.8496 | −0.505045 | ||||||||
\(753\) | 1.67253 | 0.0609503 | ||||||||
\(754\) | −72.0397 | −2.62353 | ||||||||
\(755\) | 31.3935 | 1.14253 | ||||||||
\(756\) | 1.49626 | 0.0544186 | ||||||||
\(757\) | 14.0705 | 0.511401 | 0.255701 | − | 0.966756i | \(-0.417694\pi\) | ||||
0.255701 | + | 0.966756i | \(0.417694\pi\) | |||||||
\(758\) | 18.8071 | 0.683103 | ||||||||
\(759\) | −0.122187 | −0.00443509 | ||||||||
\(760\) | −24.1226 | −0.875017 | ||||||||
\(761\) | 24.4898 | 0.887755 | 0.443878 | − | 0.896087i | \(-0.353602\pi\) | ||||
0.443878 | + | 0.896087i | \(0.353602\pi\) | |||||||
\(762\) | 4.48009 | 0.162297 | ||||||||
\(763\) | 0.928892 | 0.0336282 | ||||||||
\(764\) | 41.3429 | 1.49573 | ||||||||
\(765\) | 31.8542 | 1.15169 | ||||||||
\(766\) | −11.4820 | −0.414862 | ||||||||
\(767\) | −54.0812 | −1.95276 | ||||||||
\(768\) | 5.08738 | 0.183575 | ||||||||
\(769\) | 24.9108 | 0.898306 | 0.449153 | − | 0.893455i | \(-0.351726\pi\) | ||||
0.449153 | + | 0.893455i | \(0.351726\pi\) | |||||||
\(770\) | 1.64285 | 0.0592041 | ||||||||
\(771\) | −2.28749 | −0.0823819 | ||||||||
\(772\) | 56.5793 | 2.03633 | ||||||||
\(773\) | 7.70709 | 0.277205 | 0.138602 | − | 0.990348i | \(-0.455739\pi\) | ||||
0.138602 | + | 0.990348i | \(0.455739\pi\) | |||||||
\(774\) | 22.8761 | 0.822264 | ||||||||
\(775\) | 15.2507 | 0.547821 | ||||||||
\(776\) | −65.0133 | −2.33384 | ||||||||
\(777\) | 0.222002 | 0.00796429 | ||||||||
\(778\) | −12.7921 | −0.458619 | ||||||||
\(779\) | −0.513268 | −0.0183897 | ||||||||
\(780\) | 7.40057 | 0.264983 | ||||||||
\(781\) | −11.9224 | −0.426618 | ||||||||
\(782\) | −9.52159 | −0.340492 | ||||||||
\(783\) | 5.36525 | 0.191738 | ||||||||
\(784\) | −16.8875 | −0.603126 | ||||||||
\(785\) | 38.0895 | 1.35947 | ||||||||
\(786\) | −0.878462 | −0.0313337 | ||||||||
\(787\) | 16.1483 | 0.575626 | 0.287813 | − | 0.957687i | \(-0.407072\pi\) | ||||
0.287813 | + | 0.957687i | \(0.407072\pi\) | |||||||
\(788\) | −62.1879 | −2.21535 | ||||||||
\(789\) | −2.65476 | −0.0945119 | ||||||||
\(790\) | −7.84101 | −0.278970 | ||||||||
\(791\) | −2.74974 | −0.0977694 | ||||||||
\(792\) | 12.3029 | 0.437166 | ||||||||
\(793\) | −15.5556 | −0.552395 | ||||||||
\(794\) | 31.5261 | 1.11882 | ||||||||
\(795\) | −1.01818 | −0.0361110 | ||||||||
\(796\) | −85.5968 | −3.03390 | ||||||||
\(797\) | 26.0244 | 0.921832 | 0.460916 | − | 0.887444i | \(-0.347521\pi\) | ||||
0.460916 | + | 0.887444i | \(0.347521\pi\) | |||||||
\(798\) | −0.510039 | −0.0180552 | ||||||||
\(799\) | −32.9062 | −1.16414 | ||||||||
\(800\) | −3.91354 | −0.138365 | ||||||||
\(801\) | −50.8464 | −1.79657 | ||||||||
\(802\) | 81.4233 | 2.87516 | ||||||||
\(803\) | −5.11901 | −0.180646 | ||||||||
\(804\) | −5.22858 | −0.184398 | ||||||||
\(805\) | −0.466617 | −0.0164461 | ||||||||
\(806\) | 134.535 | 4.73880 | ||||||||
\(807\) | −4.58922 | −0.161548 | ||||||||
\(808\) | −62.7904 | −2.20896 | ||||||||
\(809\) | 24.2338 | 0.852016 | 0.426008 | − | 0.904720i | \(-0.359920\pi\) | ||||
0.426008 | + | 0.904720i | \(0.359920\pi\) | |||||||
\(810\) | 38.2696 | 1.34466 | ||||||||
\(811\) | 29.1767 | 1.02453 | 0.512267 | − | 0.858826i | \(-0.328806\pi\) | ||||
0.512267 | + | 0.858826i | \(0.328806\pi\) | |||||||
\(812\) | 6.98136 | 0.244998 | ||||||||
\(813\) | −0.297534 | −0.0104350 | ||||||||
\(814\) | 7.91026 | 0.277255 | ||||||||
\(815\) | 29.8666 | 1.04618 | ||||||||
\(816\) | −2.58715 | −0.0905684 | ||||||||
\(817\) | −10.2090 | −0.357167 | ||||||||
\(818\) | −23.1795 | −0.810454 | ||||||||
\(819\) | −6.67387 | −0.233204 | ||||||||
\(820\) | −1.10855 | −0.0387122 | ||||||||
\(821\) | 10.4657 | 0.365255 | 0.182627 | − | 0.983182i | \(-0.441540\pi\) | ||||
0.182627 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(822\) | 6.05189 | 0.211084 | ||||||||
\(823\) | 37.0842 | 1.29267 | 0.646337 | − | 0.763052i | \(-0.276300\pi\) | ||||
0.646337 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(824\) | 0.899865 | 0.0313483 | ||||||||
\(825\) | 0.293282 | 0.0102108 | ||||||||
\(826\) | 8.04999 | 0.280095 | ||||||||
\(827\) | −23.1002 | −0.803274 | −0.401637 | − | 0.915799i | \(-0.631559\pi\) | ||||
−0.401637 | + | 0.915799i | \(0.631559\pi\) | |||||||
\(828\) | −7.53043 | −0.261700 | ||||||||
\(829\) | 26.6561 | 0.925804 | 0.462902 | − | 0.886410i | \(-0.346808\pi\) | ||||
0.462902 | + | 0.886410i | \(0.346808\pi\) | |||||||
\(830\) | 58.0924 | 2.01642 | ||||||||
\(831\) | 3.15101 | 0.109307 | ||||||||
\(832\) | −64.1333 | −2.22342 | ||||||||
\(833\) | −40.1241 | −1.39022 | ||||||||
\(834\) | −4.44145 | −0.153795 | ||||||||
\(835\) | 3.16518 | 0.109535 | ||||||||
\(836\) | −11.8320 | −0.409217 | ||||||||
\(837\) | −10.0197 | −0.346331 | ||||||||
\(838\) | 31.7579 | 1.09706 | ||||||||
\(839\) | 28.1012 | 0.970163 | 0.485081 | − | 0.874469i | \(-0.338790\pi\) | ||||
0.485081 | + | 0.874469i | \(0.338790\pi\) | |||||||
\(840\) | −0.511173 | −0.0176371 | ||||||||
\(841\) | −3.96650 | −0.136776 | ||||||||
\(842\) | −24.5070 | −0.844568 | ||||||||
\(843\) | 3.50780 | 0.120815 | ||||||||
\(844\) | 10.5072 | 0.361672 | ||||||||
\(845\) | −42.5203 | −1.46274 | ||||||||
\(846\) | −39.9731 | −1.37430 | ||||||||
\(847\) | 0.373924 | 0.0128482 | ||||||||
\(848\) | −7.60077 | −0.261011 | ||||||||
\(849\) | 0.0807566 | 0.00277156 | ||||||||
\(850\) | 22.8545 | 0.783903 | ||||||||
\(851\) | −2.24675 | −0.0770176 | ||||||||
\(852\) | 7.99433 | 0.273881 | ||||||||
\(853\) | 6.03852 | 0.206755 | 0.103377 | − | 0.994642i | \(-0.467035\pi\) | ||||
0.103377 | + | 0.994642i | \(0.467035\pi\) | |||||||
\(854\) | 2.31545 | 0.0792330 | ||||||||
\(855\) | −17.2686 | −0.590574 | ||||||||
\(856\) | 6.28317 | 0.214754 | ||||||||
\(857\) | −27.8148 | −0.950135 | −0.475068 | − | 0.879949i | \(-0.657576\pi\) | ||||
−0.475068 | + | 0.879949i | \(0.657576\pi\) | |||||||
\(858\) | 2.58721 | 0.0883260 | ||||||||
\(859\) | 33.1787 | 1.13204 | 0.566022 | − | 0.824390i | \(-0.308482\pi\) | ||||
0.566022 | + | 0.824390i | \(0.308482\pi\) | |||||||
\(860\) | −22.0492 | −0.751872 | ||||||||
\(861\) | −0.0108765 | −0.000370669 0 | ||||||||
\(862\) | −45.7304 | −1.55758 | ||||||||
\(863\) | 9.26982 | 0.315548 | 0.157774 | − | 0.987475i | \(-0.449568\pi\) | ||||
0.157774 | + | 0.987475i | \(0.449568\pi\) | |||||||
\(864\) | 2.57119 | 0.0874738 | ||||||||
\(865\) | −16.6996 | −0.567804 | ||||||||
\(866\) | 66.1924 | 2.24931 | ||||||||
\(867\) | −3.09225 | −0.105018 | ||||||||
\(868\) | −13.0378 | −0.442532 | ||||||||
\(869\) | −1.78467 | −0.0605408 | ||||||||
\(870\) | −3.94999 | −0.133917 | ||||||||
\(871\) | 46.8964 | 1.58902 | ||||||||
\(872\) | −10.2984 | −0.348748 | ||||||||
\(873\) | −46.5411 | −1.57518 | ||||||||
\(874\) | 5.16180 | 0.174600 | ||||||||
\(875\) | 4.55108 | 0.153854 | ||||||||
\(876\) | 3.43244 | 0.115972 | ||||||||
\(877\) | −33.5835 | −1.13403 | −0.567017 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567017 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(878\) | −41.5659 | −1.40278 | ||||||||
\(879\) | −0.398414 | −0.0134382 | ||||||||
\(880\) | −4.51758 | −0.152288 | ||||||||
\(881\) | −27.8492 | −0.938264 | −0.469132 | − | 0.883128i | \(-0.655433\pi\) | ||||
−0.469132 | + | 0.883128i | \(0.655433\pi\) | |||||||
\(882\) | −48.7411 | −1.64120 | ||||||||
\(883\) | 55.4365 | 1.86559 | 0.932794 | − | 0.360410i | \(-0.117363\pi\) | ||||
0.932794 | + | 0.360410i | \(0.117363\pi\) | |||||||
\(884\) | 131.262 | 4.41481 | ||||||||
\(885\) | −2.96531 | −0.0996780 | ||||||||
\(886\) | 43.6716 | 1.46718 | ||||||||
\(887\) | −22.4463 | −0.753673 | −0.376837 | − | 0.926280i | \(-0.622988\pi\) | ||||
−0.376837 | + | 0.926280i | \(0.622988\pi\) | |||||||
\(888\) | −2.46128 | −0.0825953 | ||||||||
\(889\) | 3.89413 | 0.130605 | ||||||||
\(890\) | 75.2753 | 2.52323 | ||||||||
\(891\) | 8.71045 | 0.291811 | ||||||||
\(892\) | −87.3560 | −2.92490 | ||||||||
\(893\) | 17.8389 | 0.596957 | ||||||||
\(894\) | −8.21527 | −0.274760 | ||||||||
\(895\) | 36.7608 | 1.22878 | ||||||||
\(896\) | 7.75308 | 0.259012 | ||||||||
\(897\) | −0.734846 | −0.0245358 | ||||||||
\(898\) | 48.4363 | 1.61634 | ||||||||
\(899\) | −46.7505 | −1.55922 | ||||||||
\(900\) | 18.0751 | 0.602505 | ||||||||
\(901\) | −18.0591 | −0.601636 | ||||||||
\(902\) | −0.387545 | −0.0129038 | ||||||||
\(903\) | −0.216335 | −0.00719918 | ||||||||
\(904\) | 30.4857 | 1.01394 | ||||||||
\(905\) | −16.9776 | −0.564356 | ||||||||
\(906\) | −7.35909 | −0.244490 | ||||||||
\(907\) | −54.4198 | −1.80698 | −0.903490 | − | 0.428609i | \(-0.859004\pi\) | ||||
−0.903490 | + | 0.428609i | \(0.859004\pi\) | |||||||
\(908\) | −36.8279 | −1.22218 | ||||||||
\(909\) | −44.9497 | −1.49089 | ||||||||
\(910\) | 9.88029 | 0.327528 | ||||||||
\(911\) | −33.5387 | −1.11119 | −0.555594 | − | 0.831454i | \(-0.687509\pi\) | ||||
−0.555594 | + | 0.831454i | \(0.687509\pi\) | |||||||
\(912\) | 1.40253 | 0.0464425 | ||||||||
\(913\) | 13.2223 | 0.437593 | ||||||||
\(914\) | −45.7088 | −1.51191 | ||||||||
\(915\) | −0.852924 | −0.0281968 | ||||||||
\(916\) | −7.53167 | −0.248854 | ||||||||
\(917\) | −0.763566 | −0.0252152 | ||||||||
\(918\) | −15.0154 | −0.495582 | ||||||||
\(919\) | −25.1655 | −0.830132 | −0.415066 | − | 0.909791i | \(-0.636241\pi\) | ||||
−0.415066 | + | 0.909791i | \(0.636241\pi\) | |||||||
\(920\) | 5.17327 | 0.170558 | ||||||||
\(921\) | 2.94862 | 0.0971603 | ||||||||
\(922\) | 49.9858 | 1.64619 | ||||||||
\(923\) | −71.7030 | −2.36013 | ||||||||
\(924\) | −0.250727 | −0.00824830 | ||||||||
\(925\) | 5.39283 | 0.177315 | ||||||||
\(926\) | −37.7203 | −1.23956 | ||||||||
\(927\) | 0.644186 | 0.0211579 | ||||||||
\(928\) | 11.9968 | 0.393815 | ||||||||
\(929\) | −28.1816 | −0.924609 | −0.462305 | − | 0.886721i | \(-0.652977\pi\) | ||||
−0.462305 | + | 0.886721i | \(0.652977\pi\) | |||||||
\(930\) | 7.37667 | 0.241891 | ||||||||
\(931\) | 21.7518 | 0.712888 | ||||||||
\(932\) | 62.9608 | 2.06235 | ||||||||
\(933\) | −5.28193 | −0.172923 | ||||||||
\(934\) | 32.9386 | 1.07779 | ||||||||
\(935\) | −10.7336 | −0.351026 | ||||||||
\(936\) | 73.9915 | 2.41849 | ||||||||
\(937\) | −7.64808 | −0.249852 | −0.124926 | − | 0.992166i | \(-0.539869\pi\) | ||||
−0.124926 | + | 0.992166i | \(0.539869\pi\) | |||||||
\(938\) | −6.98053 | −0.227922 | ||||||||
\(939\) | −3.21719 | −0.104989 | ||||||||
\(940\) | 38.5282 | 1.25665 | ||||||||
\(941\) | −9.55744 | −0.311564 | −0.155782 | − | 0.987791i | \(-0.549790\pi\) | ||||
−0.155782 | + | 0.987791i | \(0.549790\pi\) | |||||||
\(942\) | −8.92873 | −0.290914 | ||||||||
\(943\) | 0.110074 | 0.00358451 | ||||||||
\(944\) | −22.1363 | −0.720475 | ||||||||
\(945\) | −0.735848 | −0.0239371 | ||||||||
\(946\) | −7.70833 | −0.250619 | ||||||||
\(947\) | −0.547314 | −0.0177853 | −0.00889265 | − | 0.999960i | \(-0.502831\pi\) | ||||
−0.00889265 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(948\) | 1.19667 | 0.0388661 | ||||||||
\(949\) | −30.7864 | −0.999368 | ||||||||
\(950\) | −12.3898 | −0.401977 | ||||||||
\(951\) | 4.71035 | 0.152743 | ||||||||
\(952\) | −9.06651 | −0.293847 | ||||||||
\(953\) | −37.2177 | −1.20560 | −0.602800 | − | 0.797892i | \(-0.705948\pi\) | ||||
−0.602800 | + | 0.797892i | \(0.705948\pi\) | |||||||
\(954\) | −21.9375 | −0.710252 | ||||||||
\(955\) | −20.3320 | −0.657929 | ||||||||
\(956\) | 105.104 | 3.39930 | ||||||||
\(957\) | −0.899047 | −0.0290621 | ||||||||
\(958\) | 11.0644 | 0.357476 | ||||||||
\(959\) | 5.26035 | 0.169866 | ||||||||
\(960\) | −3.51648 | −0.113494 | ||||||||
\(961\) | 56.3073 | 1.81636 | ||||||||
\(962\) | 47.5733 | 1.53383 | ||||||||
\(963\) | 4.49794 | 0.144944 | ||||||||
\(964\) | 44.7600 | 1.44162 | ||||||||
\(965\) | −27.8251 | −0.895722 | ||||||||
\(966\) | 0.109382 | 0.00351930 | ||||||||
\(967\) | 51.6346 | 1.66046 | 0.830228 | − | 0.557424i | \(-0.188210\pi\) | ||||
0.830228 | + | 0.557424i | \(0.188210\pi\) | |||||||
\(968\) | −4.14560 | −0.133245 | ||||||||
\(969\) | 3.33236 | 0.107051 | ||||||||
\(970\) | 68.9014 | 2.21229 | ||||||||
\(971\) | 12.3419 | 0.396070 | 0.198035 | − | 0.980195i | \(-0.436544\pi\) | ||||
0.198035 | + | 0.980195i | \(0.436544\pi\) | |||||||
\(972\) | −17.8452 | −0.572384 | ||||||||
\(973\) | −3.86055 | −0.123763 | ||||||||
\(974\) | 26.3909 | 0.845619 | ||||||||
\(975\) | 1.76384 | 0.0564880 | ||||||||
\(976\) | −6.36714 | −0.203807 | ||||||||
\(977\) | −27.9991 | −0.895772 | −0.447886 | − | 0.894091i | \(-0.647823\pi\) | ||||
−0.447886 | + | 0.894091i | \(0.647823\pi\) | |||||||
\(978\) | −7.00116 | −0.223873 | ||||||||
\(979\) | 17.1332 | 0.547580 | ||||||||
\(980\) | 46.9793 | 1.50070 | ||||||||
\(981\) | −7.37231 | −0.235380 | ||||||||
\(982\) | −62.0307 | −1.97948 | ||||||||
\(983\) | 26.0186 | 0.829864 | 0.414932 | − | 0.909852i | \(-0.363805\pi\) | ||||
0.414932 | + | 0.909852i | \(0.363805\pi\) | |||||||
\(984\) | 0.120585 | 0.00384410 | ||||||||
\(985\) | 30.5834 | 0.974468 | ||||||||
\(986\) | −70.0597 | −2.23116 | ||||||||
\(987\) | 0.378018 | 0.0120324 | ||||||||
\(988\) | −71.1589 | −2.26387 | ||||||||
\(989\) | 2.18940 | 0.0696187 | ||||||||
\(990\) | −13.0387 | −0.414398 | ||||||||
\(991\) | −7.37456 | −0.234260 | −0.117130 | − | 0.993117i | \(-0.537369\pi\) | ||||
−0.117130 | + | 0.993117i | \(0.537369\pi\) | |||||||
\(992\) | −22.4043 | −0.711337 | ||||||||
\(993\) | 1.07974 | 0.0342646 | ||||||||
\(994\) | 10.6730 | 0.338527 | ||||||||
\(995\) | 42.0956 | 1.33452 | ||||||||
\(996\) | −8.86591 | −0.280927 | ||||||||
\(997\) | 9.38484 | 0.297221 | 0.148610 | − | 0.988896i | \(-0.452520\pi\) | ||||
0.148610 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(998\) | 0.900094 | 0.0284920 | ||||||||
\(999\) | −3.54309 | −0.112098 |
(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 | 6017.2.a.c.1.12 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.12 | ✓ | 106 | 1.1 | even | 1 | trivial |