Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.31191\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31191 | −1.63477 | −0.817385 | − | 0.576092i | \(-0.804577\pi\) | ||||
−0.817385 | + | 0.576092i | \(0.804577\pi\) | |||||||
\(3\) | −0.910509 | −0.525683 | −0.262841 | − | 0.964839i | \(-0.584660\pi\) | ||||
−0.262841 | + | 0.964839i | \(0.584660\pi\) | |||||||
\(4\) | 3.34494 | 1.67247 | ||||||||
\(5\) | −2.04187 | −0.913153 | −0.456576 | − | 0.889684i | \(-0.650924\pi\) | ||||
−0.456576 | + | 0.889684i | \(0.650924\pi\) | |||||||
\(6\) | 2.10502 | 0.859370 | ||||||||
\(7\) | 2.45270 | 0.927034 | 0.463517 | − | 0.886088i | \(-0.346587\pi\) | ||||
0.463517 | + | 0.886088i | \(0.346587\pi\) | |||||||
\(8\) | −3.10939 | −1.09934 | ||||||||
\(9\) | −2.17097 | −0.723658 | ||||||||
\(10\) | 4.72063 | 1.49279 | ||||||||
\(11\) | 6.34679 | 1.91363 | 0.956814 | − | 0.290700i | \(-0.0938882\pi\) | ||||
0.956814 | + | 0.290700i | \(0.0938882\pi\) | |||||||
\(12\) | −3.04560 | −0.879189 | ||||||||
\(13\) | 1.40584 | 0.389911 | 0.194956 | − | 0.980812i | \(-0.437544\pi\) | ||||
0.194956 | + | 0.980812i | \(0.437544\pi\) | |||||||
\(14\) | −5.67043 | −1.51549 | ||||||||
\(15\) | 1.85914 | 0.480028 | ||||||||
\(16\) | 0.498758 | 0.124690 | ||||||||
\(17\) | 6.68943 | 1.62242 | 0.811212 | − | 0.584751i | \(-0.198808\pi\) | ||||
0.811212 | + | 0.584751i | \(0.198808\pi\) | |||||||
\(18\) | 5.01910 | 1.18301 | ||||||||
\(19\) | 0.707650 | 0.162346 | 0.0811731 | − | 0.996700i | \(-0.474133\pi\) | ||||
0.0811731 | + | 0.996700i | \(0.474133\pi\) | |||||||
\(20\) | −6.82994 | −1.52722 | ||||||||
\(21\) | −2.23321 | −0.487325 | ||||||||
\(22\) | −14.6732 | −3.12834 | ||||||||
\(23\) | 1.78915 | 0.373063 | 0.186532 | − | 0.982449i | \(-0.440275\pi\) | ||||
0.186532 | + | 0.982449i | \(0.440275\pi\) | |||||||
\(24\) | 2.83113 | 0.577902 | ||||||||
\(25\) | −0.830761 | −0.166152 | ||||||||
\(26\) | −3.25019 | −0.637415 | ||||||||
\(27\) | 4.70822 | 0.906097 | ||||||||
\(28\) | 8.20414 | 1.55044 | ||||||||
\(29\) | 6.38701 | 1.18604 | 0.593019 | − | 0.805188i | \(-0.297936\pi\) | ||||
0.593019 | + | 0.805188i | \(0.297936\pi\) | |||||||
\(30\) | −4.29818 | −0.784736 | ||||||||
\(31\) | −1.00414 | −0.180348 | −0.0901742 | − | 0.995926i | \(-0.528742\pi\) | ||||
−0.0901742 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(32\) | 5.06570 | 0.895497 | ||||||||
\(33\) | −5.77881 | −1.00596 | ||||||||
\(34\) | −15.4654 | −2.65229 | ||||||||
\(35\) | −5.00810 | −0.846523 | ||||||||
\(36\) | −7.26178 | −1.21030 | ||||||||
\(37\) | −5.42485 | −0.891840 | −0.445920 | − | 0.895073i | \(-0.647123\pi\) | ||||
−0.445920 | + | 0.895073i | \(0.647123\pi\) | |||||||
\(38\) | −1.63603 | −0.265399 | ||||||||
\(39\) | −1.28003 | −0.204969 | ||||||||
\(40\) | 6.34898 | 1.00386 | ||||||||
\(41\) | −0.748756 | −0.116936 | −0.0584680 | − | 0.998289i | \(-0.518622\pi\) | ||||
−0.0584680 | + | 0.998289i | \(0.518622\pi\) | |||||||
\(42\) | 5.16298 | 0.796665 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 21.2296 | 3.20049 | ||||||||
\(45\) | 4.43285 | 0.660810 | ||||||||
\(46\) | −4.13636 | −0.609873 | ||||||||
\(47\) | −4.05984 | −0.592188 | −0.296094 | − | 0.955159i | \(-0.595684\pi\) | ||||
−0.296094 | + | 0.955159i | \(0.595684\pi\) | |||||||
\(48\) | −0.454124 | −0.0655471 | ||||||||
\(49\) | −0.984262 | −0.140609 | ||||||||
\(50\) | 1.92065 | 0.271621 | ||||||||
\(51\) | −6.09079 | −0.852881 | ||||||||
\(52\) | 4.70247 | 0.652115 | ||||||||
\(53\) | 6.12798 | 0.841742 | 0.420871 | − | 0.907120i | \(-0.361724\pi\) | ||||
0.420871 | + | 0.907120i | \(0.361724\pi\) | |||||||
\(54\) | −10.8850 | −1.48126 | ||||||||
\(55\) | −12.9593 | −1.74743 | ||||||||
\(56\) | −7.62641 | −1.01912 | ||||||||
\(57\) | −0.644322 | −0.0853425 | ||||||||
\(58\) | −14.7662 | −1.93890 | ||||||||
\(59\) | 9.78062 | 1.27333 | 0.636664 | − | 0.771141i | \(-0.280314\pi\) | ||||
0.636664 | + | 0.771141i | \(0.280314\pi\) | |||||||
\(60\) | 6.21872 | 0.802834 | ||||||||
\(61\) | 3.52420 | 0.451227 | 0.225614 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(62\) | 2.32148 | 0.294828 | ||||||||
\(63\) | −5.32475 | −0.670855 | ||||||||
\(64\) | −12.7090 | −1.58862 | ||||||||
\(65\) | −2.87055 | −0.356048 | ||||||||
\(66\) | 13.3601 | 1.64451 | ||||||||
\(67\) | −10.2096 | −1.24730 | −0.623652 | − | 0.781702i | \(-0.714352\pi\) | ||||
−0.623652 | + | 0.781702i | \(0.714352\pi\) | |||||||
\(68\) | 22.3758 | 2.71346 | ||||||||
\(69\) | −1.62904 | −0.196113 | ||||||||
\(70\) | 11.5783 | 1.38387 | ||||||||
\(71\) | −7.49541 | −0.889541 | −0.444771 | − | 0.895645i | \(-0.646715\pi\) | ||||
−0.444771 | + | 0.895645i | \(0.646715\pi\) | |||||||
\(72\) | 6.75041 | 0.795543 | ||||||||
\(73\) | −1.37573 | −0.161017 | −0.0805085 | − | 0.996754i | \(-0.525654\pi\) | ||||
−0.0805085 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(74\) | 12.5418 | 1.45795 | ||||||||
\(75\) | 0.756416 | 0.0873433 | ||||||||
\(76\) | 2.36705 | 0.271519 | ||||||||
\(77\) | 15.5668 | 1.77400 | ||||||||
\(78\) | 2.95933 | 0.335078 | ||||||||
\(79\) | 7.46275 | 0.839625 | 0.419812 | − | 0.907611i | \(-0.362096\pi\) | ||||
0.419812 | + | 0.907611i | \(0.362096\pi\) | |||||||
\(80\) | −1.01840 | −0.113861 | ||||||||
\(81\) | 2.22605 | 0.247339 | ||||||||
\(82\) | 1.73106 | 0.191163 | ||||||||
\(83\) | −12.8225 | −1.40745 | −0.703726 | − | 0.710472i | \(-0.748482\pi\) | ||||
−0.703726 | + | 0.710472i | \(0.748482\pi\) | |||||||
\(84\) | −7.46994 | −0.815038 | ||||||||
\(85\) | −13.6590 | −1.48152 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.81543 | −0.623480 | ||||||||
\(88\) | −19.7346 | −2.10372 | ||||||||
\(89\) | 15.4830 | 1.64120 | 0.820598 | − | 0.571506i | \(-0.193641\pi\) | ||||
0.820598 | + | 0.571506i | \(0.193641\pi\) | |||||||
\(90\) | −10.2484 | −1.08027 | ||||||||
\(91\) | 3.44811 | 0.361461 | ||||||||
\(92\) | 5.98460 | 0.623938 | ||||||||
\(93\) | 0.914276 | 0.0948060 | ||||||||
\(94\) | 9.38600 | 0.968092 | ||||||||
\(95\) | −1.44493 | −0.148247 | ||||||||
\(96\) | −4.61236 | −0.470747 | ||||||||
\(97\) | −0.288669 | −0.0293099 | −0.0146550 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146550 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(98\) | 2.27553 | 0.229863 | ||||||||
\(99\) | −13.7787 | −1.38481 | ||||||||
\(100\) | −2.77885 | −0.277885 | ||||||||
\(101\) | −12.2140 | −1.21534 | −0.607669 | − | 0.794190i | \(-0.707895\pi\) | ||||
−0.607669 | + | 0.794190i | \(0.707895\pi\) | |||||||
\(102\) | 14.0814 | 1.39426 | ||||||||
\(103\) | −2.16466 | −0.213290 | −0.106645 | − | 0.994297i | \(-0.534011\pi\) | ||||
−0.106645 | + | 0.994297i | \(0.534011\pi\) | |||||||
\(104\) | −4.37132 | −0.428643 | ||||||||
\(105\) | 4.55992 | 0.445002 | ||||||||
\(106\) | −14.1673 | −1.37605 | ||||||||
\(107\) | −6.57548 | −0.635676 | −0.317838 | − | 0.948145i | \(-0.602957\pi\) | ||||
−0.317838 | + | 0.948145i | \(0.602957\pi\) | |||||||
\(108\) | 15.7487 | 1.51542 | ||||||||
\(109\) | −0.909544 | −0.0871185 | −0.0435593 | − | 0.999051i | \(-0.513870\pi\) | ||||
−0.0435593 | + | 0.999051i | \(0.513870\pi\) | |||||||
\(110\) | 29.9608 | 2.85665 | ||||||||
\(111\) | 4.93937 | 0.468825 | ||||||||
\(112\) | 1.22330 | 0.115591 | ||||||||
\(113\) | −1.74932 | −0.164563 | −0.0822813 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822813 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(114\) | 1.48962 | 0.139515 | ||||||||
\(115\) | −3.65321 | −0.340664 | ||||||||
\(116\) | 21.3642 | 1.98362 | ||||||||
\(117\) | −3.05205 | −0.282162 | ||||||||
\(118\) | −22.6119 | −2.08160 | ||||||||
\(119\) | 16.4072 | 1.50404 | ||||||||
\(120\) | −5.78080 | −0.527713 | ||||||||
\(121\) | 29.2817 | 2.66197 | ||||||||
\(122\) | −8.14764 | −0.737653 | ||||||||
\(123\) | 0.681749 | 0.0614712 | ||||||||
\(124\) | −3.35878 | −0.301628 | ||||||||
\(125\) | 11.9057 | 1.06488 | ||||||||
\(126\) | 12.3104 | 1.09669 | ||||||||
\(127\) | 3.16793 | 0.281108 | 0.140554 | − | 0.990073i | \(-0.455112\pi\) | ||||
0.140554 | + | 0.990073i | \(0.455112\pi\) | |||||||
\(128\) | 19.2506 | 1.70153 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.63647 | 0.582057 | ||||||||
\(131\) | −9.84378 | −0.860055 | −0.430028 | − | 0.902816i | \(-0.641496\pi\) | ||||
−0.430028 | + | 0.902816i | \(0.641496\pi\) | |||||||
\(132\) | −19.3298 | −1.68244 | ||||||||
\(133\) | 1.73565 | 0.150500 | ||||||||
\(134\) | 23.6038 | 2.03906 | ||||||||
\(135\) | −9.61357 | −0.827405 | ||||||||
\(136\) | −20.8001 | −1.78359 | ||||||||
\(137\) | 4.94440 | 0.422428 | 0.211214 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211214 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(138\) | 3.76619 | 0.320599 | ||||||||
\(139\) | −3.10229 | −0.263133 | −0.131566 | − | 0.991307i | \(-0.542001\pi\) | ||||
−0.131566 | + | 0.991307i | \(0.542001\pi\) | |||||||
\(140\) | −16.7518 | −1.41579 | ||||||||
\(141\) | 3.69652 | 0.311303 | ||||||||
\(142\) | 17.3287 | 1.45419 | ||||||||
\(143\) | 8.92260 | 0.746145 | ||||||||
\(144\) | −1.08279 | −0.0902326 | ||||||||
\(145\) | −13.0415 | −1.08303 | ||||||||
\(146\) | 3.18057 | 0.263226 | ||||||||
\(147\) | 0.896179 | 0.0739156 | ||||||||
\(148\) | −18.1458 | −1.49158 | ||||||||
\(149\) | 9.62541 | 0.788544 | 0.394272 | − | 0.918994i | \(-0.370997\pi\) | ||||
0.394272 | + | 0.918994i | \(0.370997\pi\) | |||||||
\(150\) | −1.74877 | −0.142786 | ||||||||
\(151\) | −1.65716 | −0.134857 | −0.0674287 | − | 0.997724i | \(-0.521480\pi\) | ||||
−0.0674287 | + | 0.997724i | \(0.521480\pi\) | |||||||
\(152\) | −2.20036 | −0.178473 | ||||||||
\(153\) | −14.5226 | −1.17408 | ||||||||
\(154\) | −35.9890 | −2.90008 | ||||||||
\(155\) | 2.05032 | 0.164686 | ||||||||
\(156\) | −4.28164 | −0.342806 | ||||||||
\(157\) | 13.8628 | 1.10637 | 0.553185 | − | 0.833059i | \(-0.313412\pi\) | ||||
0.553185 | + | 0.833059i | \(0.313412\pi\) | |||||||
\(158\) | −17.2532 | −1.37259 | ||||||||
\(159\) | −5.57958 | −0.442489 | ||||||||
\(160\) | −10.3435 | −0.817726 | ||||||||
\(161\) | 4.38825 | 0.345842 | ||||||||
\(162\) | −5.14643 | −0.404341 | ||||||||
\(163\) | 9.47410 | 0.742068 | 0.371034 | − | 0.928619i | \(-0.379003\pi\) | ||||
0.371034 | + | 0.928619i | \(0.379003\pi\) | |||||||
\(164\) | −2.50455 | −0.195572 | ||||||||
\(165\) | 11.7996 | 0.918596 | ||||||||
\(166\) | 29.6445 | 2.30086 | ||||||||
\(167\) | 10.7402 | 0.831100 | 0.415550 | − | 0.909570i | \(-0.363589\pi\) | ||||
0.415550 | + | 0.909570i | \(0.363589\pi\) | |||||||
\(168\) | 6.94391 | 0.535734 | ||||||||
\(169\) | −11.0236 | −0.847969 | ||||||||
\(170\) | 31.5783 | 2.42195 | ||||||||
\(171\) | −1.53629 | −0.117483 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.8095 | −1.88623 | −0.943115 | − | 0.332465i | \(-0.892120\pi\) | ||||
−0.943115 | + | 0.332465i | \(0.892120\pi\) | |||||||
\(174\) | 13.4448 | 1.01925 | ||||||||
\(175\) | −2.03761 | −0.154029 | ||||||||
\(176\) | 3.16551 | 0.238609 | ||||||||
\(177\) | −8.90534 | −0.669366 | ||||||||
\(178\) | −35.7954 | −2.68298 | ||||||||
\(179\) | 11.6400 | 0.870012 | 0.435006 | − | 0.900428i | \(-0.356746\pi\) | ||||
0.435006 | + | 0.900428i | \(0.356746\pi\) | |||||||
\(180\) | 14.8276 | 1.10519 | ||||||||
\(181\) | 20.5083 | 1.52437 | 0.762184 | − | 0.647361i | \(-0.224127\pi\) | ||||
0.762184 | + | 0.647361i | \(0.224127\pi\) | |||||||
\(182\) | −7.97174 | −0.590905 | ||||||||
\(183\) | −3.20881 | −0.237202 | ||||||||
\(184\) | −5.56317 | −0.410122 | ||||||||
\(185\) | 11.0768 | 0.814386 | ||||||||
\(186\) | −2.11373 | −0.154986 | ||||||||
\(187\) | 42.4564 | 3.10472 | ||||||||
\(188\) | −13.5799 | −0.990418 | ||||||||
\(189\) | 11.5478 | 0.839982 | ||||||||
\(190\) | 3.34056 | 0.242349 | ||||||||
\(191\) | 19.2993 | 1.39645 | 0.698224 | − | 0.715880i | \(-0.253974\pi\) | ||||
0.698224 | + | 0.715880i | \(0.253974\pi\) | |||||||
\(192\) | 11.5716 | 0.835111 | ||||||||
\(193\) | 11.5762 | 0.833271 | 0.416635 | − | 0.909074i | \(-0.363209\pi\) | ||||
0.416635 | + | 0.909074i | \(0.363209\pi\) | |||||||
\(194\) | 0.667378 | 0.0479150 | ||||||||
\(195\) | 2.61366 | 0.187168 | ||||||||
\(196\) | −3.29230 | −0.235164 | ||||||||
\(197\) | 16.1457 | 1.15033 | 0.575166 | − | 0.818036i | \(-0.304937\pi\) | ||||
0.575166 | + | 0.818036i | \(0.304937\pi\) | |||||||
\(198\) | 31.8552 | 2.26385 | ||||||||
\(199\) | 15.9222 | 1.12870 | 0.564349 | − | 0.825536i | \(-0.309127\pi\) | ||||
0.564349 | + | 0.825536i | \(0.309127\pi\) | |||||||
\(200\) | 2.58316 | 0.182657 | ||||||||
\(201\) | 9.29596 | 0.655686 | ||||||||
\(202\) | 28.2377 | 1.98680 | ||||||||
\(203\) | 15.6654 | 1.09950 | ||||||||
\(204\) | −20.3733 | −1.42642 | ||||||||
\(205\) | 1.52886 | 0.106780 | ||||||||
\(206\) | 5.00450 | 0.348680 | ||||||||
\(207\) | −3.88420 | −0.269970 | ||||||||
\(208\) | 0.701176 | 0.0486178 | ||||||||
\(209\) | 4.49131 | 0.310670 | ||||||||
\(210\) | −10.5421 | −0.727476 | ||||||||
\(211\) | 3.82377 | 0.263239 | 0.131619 | − | 0.991300i | \(-0.457982\pi\) | ||||
0.131619 | + | 0.991300i | \(0.457982\pi\) | |||||||
\(212\) | 20.4977 | 1.40779 | ||||||||
\(213\) | 6.82463 | 0.467616 | ||||||||
\(214\) | 15.2019 | 1.03918 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6397 | −0.996105 | ||||||||
\(217\) | −2.46285 | −0.167189 | ||||||||
\(218\) | 2.10279 | 0.142419 | ||||||||
\(219\) | 1.25261 | 0.0846438 | ||||||||
\(220\) | −43.3482 | −2.92254 | ||||||||
\(221\) | 9.40430 | 0.632601 | ||||||||
\(222\) | −11.4194 | −0.766420 | ||||||||
\(223\) | −24.0546 | −1.61082 | −0.805409 | − | 0.592720i | \(-0.798054\pi\) | ||||
−0.805409 | + | 0.592720i | \(0.798054\pi\) | |||||||
\(224\) | 12.4246 | 0.830156 | ||||||||
\(225\) | 1.80356 | 0.120237 | ||||||||
\(226\) | 4.04429 | 0.269022 | ||||||||
\(227\) | 7.24312 | 0.480743 | 0.240371 | − | 0.970681i | \(-0.422731\pi\) | ||||
0.240371 | + | 0.970681i | \(0.422731\pi\) | |||||||
\(228\) | −2.15522 | −0.142733 | ||||||||
\(229\) | 6.96410 | 0.460201 | 0.230100 | − | 0.973167i | \(-0.426095\pi\) | ||||
0.230100 | + | 0.973167i | \(0.426095\pi\) | |||||||
\(230\) | 8.44591 | 0.556907 | ||||||||
\(231\) | −14.1737 | −0.932560 | ||||||||
\(232\) | −19.8597 | −1.30385 | ||||||||
\(233\) | −5.50612 | −0.360718 | −0.180359 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180359 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(234\) | 7.05608 | 0.461270 | ||||||||
\(235\) | 8.28967 | 0.540758 | ||||||||
\(236\) | 32.7156 | 2.12960 | ||||||||
\(237\) | −6.79490 | −0.441376 | ||||||||
\(238\) | −37.9319 | −2.45876 | ||||||||
\(239\) | 3.48155 | 0.225203 | 0.112601 | − | 0.993640i | \(-0.464082\pi\) | ||||
0.112601 | + | 0.993640i | \(0.464082\pi\) | |||||||
\(240\) | 0.927262 | 0.0598545 | ||||||||
\(241\) | 1.62945 | 0.104962 | 0.0524812 | − | 0.998622i | \(-0.483287\pi\) | ||||
0.0524812 | + | 0.998622i | \(0.483287\pi\) | |||||||
\(242\) | −67.6968 | −4.35171 | ||||||||
\(243\) | −16.1515 | −1.03612 | ||||||||
\(244\) | 11.7882 | 0.754665 | ||||||||
\(245\) | 2.00974 | 0.128397 | ||||||||
\(246\) | −1.57614 | −0.100491 | ||||||||
\(247\) | 0.994846 | 0.0633005 | ||||||||
\(248\) | 3.12226 | 0.198264 | ||||||||
\(249\) | 11.6750 | 0.739873 | ||||||||
\(250\) | −27.5249 | −1.74083 | ||||||||
\(251\) | 14.8497 | 0.937306 | 0.468653 | − | 0.883382i | \(-0.344739\pi\) | ||||
0.468653 | + | 0.883382i | \(0.344739\pi\) | |||||||
\(252\) | −17.8110 | −1.12199 | ||||||||
\(253\) | 11.3554 | 0.713905 | ||||||||
\(254\) | −7.32397 | −0.459547 | ||||||||
\(255\) | 12.4366 | 0.778810 | ||||||||
\(256\) | −19.0879 | −1.19299 | ||||||||
\(257\) | −3.05501 | −0.190566 | −0.0952832 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952832 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.3055 | −0.826765 | ||||||||
\(260\) | −9.60184 | −0.595481 | ||||||||
\(261\) | −13.8660 | −0.858286 | ||||||||
\(262\) | 22.7580 | 1.40599 | ||||||||
\(263\) | −7.41792 | −0.457408 | −0.228704 | − | 0.973496i | \(-0.573449\pi\) | ||||
−0.228704 | + | 0.973496i | \(0.573449\pi\) | |||||||
\(264\) | 17.9686 | 1.10589 | ||||||||
\(265\) | −12.5125 | −0.768639 | ||||||||
\(266\) | −4.01268 | −0.246033 | ||||||||
\(267\) | −14.0974 | −0.862748 | ||||||||
\(268\) | −34.1506 | −2.08608 | ||||||||
\(269\) | 16.2509 | 0.990834 | 0.495417 | − | 0.868655i | \(-0.335015\pi\) | ||||
0.495417 | + | 0.868655i | \(0.335015\pi\) | |||||||
\(270\) | 22.2258 | 1.35262 | ||||||||
\(271\) | 26.6634 | 1.61969 | 0.809845 | − | 0.586645i | \(-0.199551\pi\) | ||||
0.809845 | + | 0.586645i | \(0.199551\pi\) | |||||||
\(272\) | 3.33641 | 0.202299 | ||||||||
\(273\) | −3.13954 | −0.190014 | ||||||||
\(274\) | −11.4310 | −0.690573 | ||||||||
\(275\) | −5.27267 | −0.317954 | ||||||||
\(276\) | −5.44903 | −0.327993 | ||||||||
\(277\) | −18.3038 | −1.09977 | −0.549886 | − | 0.835240i | \(-0.685329\pi\) | ||||
−0.549886 | + | 0.835240i | \(0.685329\pi\) | |||||||
\(278\) | 7.17222 | 0.430161 | ||||||||
\(279\) | 2.17996 | 0.130511 | ||||||||
\(280\) | 15.5721 | 0.930613 | ||||||||
\(281\) | −11.8249 | −0.705417 | −0.352708 | − | 0.935733i | \(-0.614739\pi\) | ||||
−0.352708 | + | 0.935733i | \(0.614739\pi\) | |||||||
\(282\) | −8.54603 | −0.508909 | ||||||||
\(283\) | 1.73915 | 0.103382 | 0.0516910 | − | 0.998663i | \(-0.483539\pi\) | ||||
0.0516910 | + | 0.998663i | \(0.483539\pi\) | |||||||
\(284\) | −25.0717 | −1.48773 | ||||||||
\(285\) | 1.31562 | 0.0779308 | ||||||||
\(286\) | −20.6283 | −1.21978 | ||||||||
\(287\) | −1.83647 | −0.108404 | ||||||||
\(288\) | −10.9975 | −0.648034 | ||||||||
\(289\) | 27.7485 | 1.63226 | ||||||||
\(290\) | 30.1507 | 1.77051 | ||||||||
\(291\) | 0.262836 | 0.0154077 | ||||||||
\(292\) | −4.60174 | −0.269296 | ||||||||
\(293\) | 10.6521 | 0.622303 | 0.311152 | − | 0.950360i | \(-0.399285\pi\) | ||||
0.311152 | + | 0.950360i | \(0.399285\pi\) | |||||||
\(294\) | −2.07189 | −0.120835 | ||||||||
\(295\) | −19.9708 | −1.16274 | ||||||||
\(296\) | 16.8680 | 0.980431 | ||||||||
\(297\) | 29.8821 | 1.73393 | ||||||||
\(298\) | −22.2531 | −1.28909 | ||||||||
\(299\) | 2.51527 | 0.145462 | ||||||||
\(300\) | 2.53017 | 0.146079 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.83120 | 0.220461 | ||||||||
\(303\) | 11.1210 | 0.638882 | ||||||||
\(304\) | 0.352946 | 0.0202429 | ||||||||
\(305\) | −7.19596 | −0.412040 | ||||||||
\(306\) | 33.5749 | 1.91935 | ||||||||
\(307\) | 5.49017 | 0.313341 | 0.156670 | − | 0.987651i | \(-0.449924\pi\) | ||||
0.156670 | + | 0.987651i | \(0.449924\pi\) | |||||||
\(308\) | 52.0700 | 2.96696 | ||||||||
\(309\) | 1.97094 | 0.112123 | ||||||||
\(310\) | −4.74016 | −0.269223 | ||||||||
\(311\) | −6.50028 | −0.368597 | −0.184299 | − | 0.982870i | \(-0.559001\pi\) | ||||
−0.184299 | + | 0.982870i | \(0.559001\pi\) | |||||||
\(312\) | 3.98013 | 0.225330 | ||||||||
\(313\) | −19.7542 | −1.11657 | −0.558285 | − | 0.829649i | \(-0.688541\pi\) | ||||
−0.558285 | + | 0.829649i | \(0.688541\pi\) | |||||||
\(314\) | −32.0495 | −1.80866 | ||||||||
\(315\) | 10.8724 | 0.612593 | ||||||||
\(316\) | 24.9625 | 1.40425 | ||||||||
\(317\) | 13.8919 | 0.780250 | 0.390125 | − | 0.920762i | \(-0.372432\pi\) | ||||
0.390125 | + | 0.920762i | \(0.372432\pi\) | |||||||
\(318\) | 12.8995 | 0.723368 | ||||||||
\(319\) | 40.5370 | 2.26964 | ||||||||
\(320\) | 25.9501 | 1.45065 | ||||||||
\(321\) | 5.98703 | 0.334164 | ||||||||
\(322\) | −10.1452 | −0.565373 | ||||||||
\(323\) | 4.73378 | 0.263394 | ||||||||
\(324\) | 7.44600 | 0.413667 | ||||||||
\(325\) | −1.16792 | −0.0647846 | ||||||||
\(326\) | −21.9033 | −1.21311 | ||||||||
\(327\) | 0.828148 | 0.0457967 | ||||||||
\(328\) | 2.32818 | 0.128552 | ||||||||
\(329\) | −9.95757 | −0.548979 | ||||||||
\(330\) | −27.2796 | −1.50169 | ||||||||
\(331\) | 14.6176 | 0.803459 | 0.401729 | − | 0.915758i | \(-0.368409\pi\) | ||||
0.401729 | + | 0.915758i | \(0.368409\pi\) | |||||||
\(332\) | −42.8905 | −2.35392 | ||||||||
\(333\) | 11.7772 | 0.645387 | ||||||||
\(334\) | −24.8304 | −1.35866 | ||||||||
\(335\) | 20.8467 | 1.13898 | ||||||||
\(336\) | −1.11383 | −0.0607644 | ||||||||
\(337\) | −24.4065 | −1.32951 | −0.664753 | − | 0.747063i | \(-0.731463\pi\) | ||||
−0.664753 | + | 0.747063i | \(0.731463\pi\) | |||||||
\(338\) | 25.4856 | 1.38623 | ||||||||
\(339\) | 1.59278 | 0.0865077 | ||||||||
\(340\) | −45.6884 | −2.47780 | ||||||||
\(341\) | −6.37305 | −0.345120 | ||||||||
\(342\) | 3.55177 | 0.192058 | ||||||||
\(343\) | −19.5830 | −1.05738 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.32628 | 0.179081 | ||||||||
\(346\) | 57.3574 | 3.08355 | ||||||||
\(347\) | 7.52857 | 0.404155 | 0.202077 | − | 0.979370i | \(-0.435231\pi\) | ||||
0.202077 | + | 0.979370i | \(0.435231\pi\) | |||||||
\(348\) | −19.4523 | −1.04275 | ||||||||
\(349\) | 13.5757 | 0.726692 | 0.363346 | − | 0.931654i | \(-0.381634\pi\) | ||||
0.363346 | + | 0.931654i | \(0.381634\pi\) | |||||||
\(350\) | 4.71077 | 0.251801 | ||||||||
\(351\) | 6.61902 | 0.353297 | ||||||||
\(352\) | 32.1509 | 1.71365 | ||||||||
\(353\) | −30.2021 | −1.60750 | −0.803748 | − | 0.594970i | \(-0.797164\pi\) | ||||
−0.803748 | + | 0.594970i | \(0.797164\pi\) | |||||||
\(354\) | 20.5884 | 1.09426 | ||||||||
\(355\) | 15.3047 | 0.812287 | ||||||||
\(356\) | 51.7898 | 2.74485 | ||||||||
\(357\) | −14.9389 | −0.790649 | ||||||||
\(358\) | −26.9106 | −1.42227 | ||||||||
\(359\) | −12.0540 | −0.636187 | −0.318093 | − | 0.948059i | \(-0.603043\pi\) | ||||
−0.318093 | + | 0.948059i | \(0.603043\pi\) | |||||||
\(360\) | −13.7835 | −0.726452 | ||||||||
\(361\) | −18.4992 | −0.973644 | ||||||||
\(362\) | −47.4133 | −2.49199 | ||||||||
\(363\) | −26.6613 | −1.39935 | ||||||||
\(364\) | 11.5337 | 0.604533 | ||||||||
\(365\) | 2.80906 | 0.147033 | ||||||||
\(366\) | 7.41850 | 0.387771 | ||||||||
\(367\) | 31.5354 | 1.64614 | 0.823068 | − | 0.567943i | \(-0.192261\pi\) | ||||
0.823068 | + | 0.567943i | \(0.192261\pi\) | |||||||
\(368\) | 0.892353 | 0.0465171 | ||||||||
\(369\) | 1.62553 | 0.0846217 | ||||||||
\(370\) | −25.6087 | −1.33133 | ||||||||
\(371\) | 15.0301 | 0.780323 | ||||||||
\(372\) | 3.05820 | 0.158560 | ||||||||
\(373\) | −19.3174 | −1.00022 | −0.500109 | − | 0.865963i | \(-0.666707\pi\) | ||||
−0.500109 | + | 0.865963i | \(0.666707\pi\) | |||||||
\(374\) | −98.1555 | −5.07550 | ||||||||
\(375\) | −10.8402 | −0.559786 | ||||||||
\(376\) | 12.6236 | 0.651014 | ||||||||
\(377\) | 8.97914 | 0.462449 | ||||||||
\(378\) | −26.6976 | −1.37318 | ||||||||
\(379\) | −19.4777 | −1.00050 | −0.500250 | − | 0.865881i | \(-0.666759\pi\) | ||||
−0.500250 | + | 0.865881i | \(0.666759\pi\) | |||||||
\(380\) | −4.83321 | −0.247939 | ||||||||
\(381\) | −2.88442 | −0.147774 | ||||||||
\(382\) | −44.6183 | −2.28287 | ||||||||
\(383\) | −23.8663 | −1.21951 | −0.609755 | − | 0.792590i | \(-0.708732\pi\) | ||||
−0.609755 | + | 0.792590i | \(0.708732\pi\) | |||||||
\(384\) | −17.5279 | −0.894466 | ||||||||
\(385\) | −31.7853 | −1.61993 | ||||||||
\(386\) | −26.7631 | −1.36221 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.965582 | −0.0490200 | ||||||||
\(389\) | −4.95237 | −0.251095 | −0.125547 | − | 0.992088i | \(-0.540069\pi\) | ||||
−0.125547 | + | 0.992088i | \(0.540069\pi\) | |||||||
\(390\) | −6.04257 | −0.305977 | ||||||||
\(391\) | 11.9684 | 0.605267 | ||||||||
\(392\) | 3.06046 | 0.154576 | ||||||||
\(393\) | 8.96285 | 0.452116 | ||||||||
\(394\) | −37.3274 | −1.88053 | ||||||||
\(395\) | −15.2380 | −0.766706 | ||||||||
\(396\) | −46.0890 | −2.31606 | ||||||||
\(397\) | 8.51276 | 0.427243 | 0.213622 | − | 0.976916i | \(-0.431474\pi\) | ||||
0.213622 | + | 0.976916i | \(0.431474\pi\) | |||||||
\(398\) | −36.8108 | −1.84516 | ||||||||
\(399\) | −1.58033 | −0.0791154 | ||||||||
\(400\) | −0.414349 | −0.0207174 | ||||||||
\(401\) | 5.71984 | 0.285635 | 0.142818 | − | 0.989749i | \(-0.454384\pi\) | ||||
0.142818 | + | 0.989749i | \(0.454384\pi\) | |||||||
\(402\) | −21.4914 | −1.07190 | ||||||||
\(403\) | −1.41166 | −0.0703199 | ||||||||
\(404\) | −40.8551 | −2.03262 | ||||||||
\(405\) | −4.54530 | −0.225858 | ||||||||
\(406\) | −36.2171 | −1.79742 | ||||||||
\(407\) | −34.4304 | −1.70665 | ||||||||
\(408\) | 18.9386 | 0.937602 | ||||||||
\(409\) | 17.5608 | 0.868325 | 0.434163 | − | 0.900835i | \(-0.357044\pi\) | ||||
0.434163 | + | 0.900835i | \(0.357044\pi\) | |||||||
\(410\) | −3.53460 | −0.174561 | ||||||||
\(411\) | −4.50192 | −0.222063 | ||||||||
\(412\) | −7.24066 | −0.356722 | ||||||||
\(413\) | 23.9889 | 1.18042 | ||||||||
\(414\) | 8.97992 | 0.441339 | ||||||||
\(415\) | 26.1819 | 1.28522 | ||||||||
\(416\) | 7.12158 | 0.349164 | ||||||||
\(417\) | 2.82466 | 0.138324 | ||||||||
\(418\) | −10.3835 | −0.507874 | ||||||||
\(419\) | −29.9639 | −1.46383 | −0.731917 | − | 0.681393i | \(-0.761374\pi\) | ||||
−0.731917 | + | 0.681393i | \(0.761374\pi\) | |||||||
\(420\) | 15.2527 | 0.744254 | ||||||||
\(421\) | −37.1590 | −1.81102 | −0.905510 | − | 0.424325i | \(-0.860511\pi\) | ||||
−0.905510 | + | 0.424325i | \(0.860511\pi\) | |||||||
\(422\) | −8.84021 | −0.430335 | ||||||||
\(423\) | 8.81380 | 0.428542 | ||||||||
\(424\) | −19.0543 | −0.925357 | ||||||||
\(425\) | −5.55732 | −0.269570 | ||||||||
\(426\) | −15.7780 | −0.764445 | ||||||||
\(427\) | 8.64380 | 0.418303 | ||||||||
\(428\) | −21.9946 | −1.06315 | ||||||||
\(429\) | −8.12410 | −0.392235 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.0938 | 1.20872 | 0.604362 | − | 0.796710i | \(-0.293428\pi\) | ||||
0.604362 | + | 0.796710i | \(0.293428\pi\) | |||||||
\(432\) | 2.34826 | 0.112981 | ||||||||
\(433\) | 29.2470 | 1.40552 | 0.702760 | − | 0.711427i | \(-0.251951\pi\) | ||||
0.702760 | + | 0.711427i | \(0.251951\pi\) | |||||||
\(434\) | 5.69389 | 0.273316 | ||||||||
\(435\) | 11.8744 | 0.569332 | ||||||||
\(436\) | −3.04237 | −0.145703 | ||||||||
\(437\) | 1.26609 | 0.0605654 | ||||||||
\(438\) | −2.89594 | −0.138373 | ||||||||
\(439\) | 10.5083 | 0.501534 | 0.250767 | − | 0.968047i | \(-0.419317\pi\) | ||||
0.250767 | + | 0.968047i | \(0.419317\pi\) | |||||||
\(440\) | 40.2956 | 1.92102 | ||||||||
\(441\) | 2.13681 | 0.101753 | ||||||||
\(442\) | −21.7419 | −1.03416 | ||||||||
\(443\) | −8.51248 | −0.404440 | −0.202220 | − | 0.979340i | \(-0.564816\pi\) | ||||
−0.202220 | + | 0.979340i | \(0.564816\pi\) | |||||||
\(444\) | 16.5219 | 0.784096 | ||||||||
\(445\) | −31.6143 | −1.49866 | ||||||||
\(446\) | 55.6122 | 2.63332 | ||||||||
\(447\) | −8.76402 | −0.414524 | ||||||||
\(448\) | −31.1713 | −1.47271 | ||||||||
\(449\) | 34.8622 | 1.64525 | 0.822626 | − | 0.568583i | \(-0.192508\pi\) | ||||
0.822626 | + | 0.568583i | \(0.192508\pi\) | |||||||
\(450\) | −4.16968 | −0.196560 | ||||||||
\(451\) | −4.75219 | −0.223772 | ||||||||
\(452\) | −5.85139 | −0.275226 | ||||||||
\(453\) | 1.50886 | 0.0708922 | ||||||||
\(454\) | −16.7455 | −0.785904 | ||||||||
\(455\) | −7.04061 | −0.330069 | ||||||||
\(456\) | 2.00345 | 0.0938201 | ||||||||
\(457\) | 32.7436 | 1.53168 | 0.765841 | − | 0.643030i | \(-0.222323\pi\) | ||||
0.765841 | + | 0.643030i | \(0.222323\pi\) | |||||||
\(458\) | −16.1004 | −0.752322 | ||||||||
\(459\) | 31.4953 | 1.47007 | ||||||||
\(460\) | −12.2198 | −0.569751 | ||||||||
\(461\) | −39.7806 | −1.85277 | −0.926383 | − | 0.376582i | \(-0.877099\pi\) | ||||
−0.926383 | + | 0.376582i | \(0.877099\pi\) | |||||||
\(462\) | 32.7683 | 1.52452 | ||||||||
\(463\) | −12.6595 | −0.588336 | −0.294168 | − | 0.955754i | \(-0.595042\pi\) | ||||
−0.294168 | + | 0.955754i | \(0.595042\pi\) | |||||||
\(464\) | 3.18557 | 0.147887 | ||||||||
\(465\) | −1.86683 | −0.0865724 | ||||||||
\(466\) | 12.7297 | 0.589690 | ||||||||
\(467\) | −34.9711 | −1.61827 | −0.809136 | − | 0.587622i | \(-0.800064\pi\) | ||||
−0.809136 | + | 0.587622i | \(0.800064\pi\) | |||||||
\(468\) | −10.2089 | −0.471908 | ||||||||
\(469\) | −25.0412 | −1.15629 | ||||||||
\(470\) | −19.1650 | −0.884015 | ||||||||
\(471\) | −12.6222 | −0.581599 | ||||||||
\(472\) | −30.4118 | −1.39982 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15.7092 | 0.721548 | ||||||||
\(475\) | −0.587889 | −0.0269742 | ||||||||
\(476\) | 54.8810 | 2.51547 | ||||||||
\(477\) | −13.3037 | −0.609133 | ||||||||
\(478\) | −8.04904 | −0.368155 | ||||||||
\(479\) | 21.9996 | 1.00519 | 0.502593 | − | 0.864523i | \(-0.332380\pi\) | ||||
0.502593 | + | 0.864523i | \(0.332380\pi\) | |||||||
\(480\) | 9.41785 | 0.429864 | ||||||||
\(481\) | −7.62649 | −0.347738 | ||||||||
\(482\) | −3.76716 | −0.171589 | ||||||||
\(483\) | −3.99554 | −0.181803 | ||||||||
\(484\) | 97.9457 | 4.45208 | ||||||||
\(485\) | 0.589425 | 0.0267644 | ||||||||
\(486\) | 37.3408 | 1.69381 | ||||||||
\(487\) | −6.49327 | −0.294238 | −0.147119 | − | 0.989119i | \(-0.547000\pi\) | ||||
−0.147119 | + | 0.989119i | \(0.547000\pi\) | |||||||
\(488\) | −10.9581 | −0.496051 | ||||||||
\(489\) | −8.62625 | −0.390092 | ||||||||
\(490\) | −4.64634 | −0.209900 | ||||||||
\(491\) | −7.19968 | −0.324917 | −0.162459 | − | 0.986715i | \(-0.551942\pi\) | ||||
−0.162459 | + | 0.986715i | \(0.551942\pi\) | |||||||
\(492\) | 2.28041 | 0.102809 | ||||||||
\(493\) | 42.7255 | 1.92426 | ||||||||
\(494\) | −2.30000 | −0.103482 | ||||||||
\(495\) | 28.1343 | 1.26454 | ||||||||
\(496\) | −0.500822 | −0.0224876 | ||||||||
\(497\) | −18.3840 | −0.824634 | ||||||||
\(498\) | −26.9916 | −1.20952 | ||||||||
\(499\) | −37.0430 | −1.65827 | −0.829135 | − | 0.559048i | \(-0.811167\pi\) | ||||
−0.829135 | + | 0.559048i | \(0.811167\pi\) | |||||||
\(500\) | 39.8238 | 1.78097 | ||||||||
\(501\) | −9.77902 | −0.436895 | ||||||||
\(502\) | −34.3313 | −1.53228 | ||||||||
\(503\) | 5.21326 | 0.232448 | 0.116224 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116224 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(504\) | 16.5567 | 0.737495 | ||||||||
\(505\) | 24.9394 | 1.10979 | ||||||||
\(506\) | −26.2526 | −1.16707 | ||||||||
\(507\) | 10.0371 | 0.445763 | ||||||||
\(508\) | 10.5965 | 0.470145 | ||||||||
\(509\) | 19.2599 | 0.853680 | 0.426840 | − | 0.904327i | \(-0.359627\pi\) | ||||
0.426840 | + | 0.904327i | \(0.359627\pi\) | |||||||
\(510\) | −28.7523 | −1.27318 | ||||||||
\(511\) | −3.37425 | −0.149268 | ||||||||
\(512\) | 5.62823 | 0.248735 | ||||||||
\(513\) | 3.33177 | 0.147101 | ||||||||
\(514\) | 7.06292 | 0.311532 | ||||||||
\(515\) | 4.41995 | 0.194766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.7669 | −1.13323 | ||||||||
\(518\) | 30.7612 | 1.35157 | ||||||||
\(519\) | 22.5893 | 0.991559 | ||||||||
\(520\) | 8.92567 | 0.391417 | ||||||||
\(521\) | −20.9839 | −0.919322 | −0.459661 | − | 0.888094i | \(-0.652029\pi\) | ||||
−0.459661 | + | 0.888094i | \(0.652029\pi\) | |||||||
\(522\) | 32.0571 | 1.40310 | ||||||||
\(523\) | 8.38255 | 0.366543 | 0.183272 | − | 0.983062i | \(-0.441331\pi\) | ||||
0.183272 | + | 0.983062i | \(0.441331\pi\) | |||||||
\(524\) | −32.9269 | −1.43842 | ||||||||
\(525\) | 1.85526 | 0.0809702 | ||||||||
\(526\) | 17.1496 | 0.747757 | ||||||||
\(527\) | −6.71711 | −0.292602 | ||||||||
\(528\) | −2.88223 | −0.125433 | ||||||||
\(529\) | −19.7989 | −0.860824 | ||||||||
\(530\) | 28.9279 | 1.25655 | ||||||||
\(531\) | −21.2335 | −0.921454 | ||||||||
\(532\) | 5.80566 | 0.251707 | ||||||||
\(533\) | −1.05263 | −0.0455946 | ||||||||
\(534\) | 32.5920 | 1.41039 | ||||||||
\(535\) | 13.4263 | 0.580469 | ||||||||
\(536\) | 31.7457 | 1.37121 | ||||||||
\(537\) | −10.5983 | −0.457350 | ||||||||
\(538\) | −37.5706 | −1.61978 | ||||||||
\(539\) | −6.24690 | −0.269073 | ||||||||
\(540\) | −32.1569 | −1.38381 | ||||||||
\(541\) | 34.2947 | 1.47444 | 0.737222 | − | 0.675651i | \(-0.236137\pi\) | ||||
0.737222 | + | 0.675651i | \(0.236137\pi\) | |||||||
\(542\) | −61.6436 | −2.64782 | ||||||||
\(543\) | −18.6730 | −0.801333 | ||||||||
\(544\) | 33.8866 | 1.45288 | ||||||||
\(545\) | 1.85717 | 0.0795525 | ||||||||
\(546\) | 7.25834 | 0.310628 | ||||||||
\(547\) | −1.93445 | −0.0827112 | −0.0413556 | − | 0.999144i | \(-0.513168\pi\) | ||||
−0.0413556 | + | 0.999144i | \(0.513168\pi\) | |||||||
\(548\) | 16.5387 | 0.706500 | ||||||||
\(549\) | −7.65094 | −0.326534 | ||||||||
\(550\) | 12.1899 | 0.519781 | ||||||||
\(551\) | 4.51977 | 0.192549 | ||||||||
\(552\) | 5.06531 | 0.215594 | ||||||||
\(553\) | 18.3039 | 0.778360 | ||||||||
\(554\) | 42.3169 | 1.79787 | ||||||||
\(555\) | −10.0856 | −0.428108 | ||||||||
\(556\) | −10.3770 | −0.440082 | ||||||||
\(557\) | −26.5867 | −1.12651 | −0.563257 | − | 0.826282i | \(-0.690452\pi\) | ||||
−0.563257 | + | 0.826282i | \(0.690452\pi\) | |||||||
\(558\) | −5.03987 | −0.213355 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.49783 | −0.105553 | ||||||||
\(561\) | −38.6569 | −1.63210 | ||||||||
\(562\) | 27.3382 | 1.15319 | ||||||||
\(563\) | 20.4328 | 0.861139 | 0.430570 | − | 0.902557i | \(-0.358313\pi\) | ||||
0.430570 | + | 0.902557i | \(0.358313\pi\) | |||||||
\(564\) | 12.3646 | 0.520646 | ||||||||
\(565\) | 3.57190 | 0.150271 | ||||||||
\(566\) | −4.02077 | −0.169006 | ||||||||
\(567\) | 5.45983 | 0.229291 | ||||||||
\(568\) | 23.3062 | 0.977905 | ||||||||
\(569\) | 32.1027 | 1.34581 | 0.672907 | − | 0.739727i | \(-0.265045\pi\) | ||||
0.672907 | + | 0.739727i | \(0.265045\pi\) | |||||||
\(570\) | −3.04161 | −0.127399 | ||||||||
\(571\) | −13.4605 | −0.563303 | −0.281651 | − | 0.959517i | \(-0.590882\pi\) | ||||
−0.281651 | + | 0.959517i | \(0.590882\pi\) | |||||||
\(572\) | 29.8456 | 1.24791 | ||||||||
\(573\) | −17.5722 | −0.734088 | ||||||||
\(574\) | 4.24577 | 0.177215 | ||||||||
\(575\) | −1.48636 | −0.0619853 | ||||||||
\(576\) | 27.5908 | 1.14962 | ||||||||
\(577\) | −24.7963 | −1.03228 | −0.516141 | − | 0.856504i | \(-0.672632\pi\) | ||||
−0.516141 | + | 0.856504i | \(0.672632\pi\) | |||||||
\(578\) | −64.1521 | −2.66837 | ||||||||
\(579\) | −10.5402 | −0.438036 | ||||||||
\(580\) | −43.6229 | −1.81134 | ||||||||
\(581\) | −31.4497 | −1.30475 | ||||||||
\(582\) | −0.607654 | −0.0251881 | ||||||||
\(583\) | 38.8930 | 1.61078 | ||||||||
\(584\) | 4.27768 | 0.177012 | ||||||||
\(585\) | 6.23190 | 0.257657 | ||||||||
\(586\) | −24.6268 | −1.01732 | ||||||||
\(587\) | 12.2593 | 0.505998 | 0.252999 | − | 0.967467i | \(-0.418583\pi\) | ||||
0.252999 | + | 0.967467i | \(0.418583\pi\) | |||||||
\(588\) | 2.99767 | 0.123622 | ||||||||
\(589\) | −0.710578 | −0.0292789 | ||||||||
\(590\) | 46.1707 | 1.90082 | ||||||||
\(591\) | −14.7008 | −0.604710 | ||||||||
\(592\) | −2.70569 | −0.111203 | ||||||||
\(593\) | −33.0810 | −1.35847 | −0.679236 | − | 0.733920i | \(-0.737689\pi\) | ||||
−0.679236 | + | 0.733920i | \(0.737689\pi\) | |||||||
\(594\) | −69.0847 | −2.83458 | ||||||||
\(595\) | −33.5013 | −1.37342 | ||||||||
\(596\) | 32.1965 | 1.31882 | ||||||||
\(597\) | −14.4973 | −0.593337 | ||||||||
\(598\) | −5.81508 | −0.237796 | ||||||||
\(599\) | 35.0641 | 1.43268 | 0.716339 | − | 0.697752i | \(-0.245816\pi\) | ||||
0.716339 | + | 0.697752i | \(0.245816\pi\) | |||||||
\(600\) | −2.35199 | −0.0960197 | ||||||||
\(601\) | 37.9483 | 1.54794 | 0.773972 | − | 0.633220i | \(-0.218267\pi\) | ||||
0.773972 | + | 0.633220i | \(0.218267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.1648 | 0.902622 | ||||||||
\(604\) | −5.54309 | −0.225545 | ||||||||
\(605\) | −59.7895 | −2.43079 | ||||||||
\(606\) | −25.7107 | −1.04442 | ||||||||
\(607\) | −35.9199 | −1.45794 | −0.728971 | − | 0.684544i | \(-0.760001\pi\) | ||||
−0.728971 | + | 0.684544i | \(0.760001\pi\) | |||||||
\(608\) | 3.58474 | 0.145381 | ||||||||
\(609\) | −14.2635 | −0.577986 | ||||||||
\(610\) | 16.6364 | 0.673590 | ||||||||
\(611\) | −5.70750 | −0.230901 | ||||||||
\(612\) | −48.5772 | −1.96362 | ||||||||
\(613\) | 3.16067 | 0.127658 | 0.0638292 | − | 0.997961i | \(-0.479669\pi\) | ||||
0.0638292 | + | 0.997961i | \(0.479669\pi\) | |||||||
\(614\) | −12.6928 | −0.512240 | ||||||||
\(615\) | −1.39204 | −0.0561326 | ||||||||
\(616\) | −48.4032 | −1.95022 | ||||||||
\(617\) | 16.3852 | 0.659642 | 0.329821 | − | 0.944044i | \(-0.393012\pi\) | ||||
0.329821 | + | 0.944044i | \(0.393012\pi\) | |||||||
\(618\) | −4.55664 | −0.183295 | ||||||||
\(619\) | −4.92740 | −0.198049 | −0.0990244 | − | 0.995085i | \(-0.531572\pi\) | ||||
−0.0990244 | + | 0.995085i | \(0.531572\pi\) | |||||||
\(620\) | 6.85820 | 0.275432 | ||||||||
\(621\) | 8.42370 | 0.338032 | ||||||||
\(622\) | 15.0281 | 0.602571 | ||||||||
\(623\) | 37.9752 | 1.52144 | ||||||||
\(624\) | −0.638427 | −0.0255575 | ||||||||
\(625\) | −20.1560 | −0.806241 | ||||||||
\(626\) | 45.6699 | 1.82534 | ||||||||
\(627\) | −4.08937 | −0.163314 | ||||||||
\(628\) | 46.3702 | 1.85037 | ||||||||
\(629\) | −36.2891 | −1.44694 | ||||||||
\(630\) | −25.1362 | −1.00145 | ||||||||
\(631\) | 6.97783 | 0.277783 | 0.138892 | − | 0.990308i | \(-0.455646\pi\) | ||||
0.138892 | + | 0.990308i | \(0.455646\pi\) | |||||||
\(632\) | −23.2046 | −0.923030 | ||||||||
\(633\) | −3.48157 | −0.138380 | ||||||||
\(634\) | −32.1170 | −1.27553 | ||||||||
\(635\) | −6.46850 | −0.256695 | ||||||||
\(636\) | −18.6634 | −0.740051 | ||||||||
\(637\) | −1.38372 | −0.0548249 | ||||||||
\(638\) | −93.7180 | −3.71033 | ||||||||
\(639\) | 16.2723 | 0.643723 | ||||||||
\(640\) | −39.3073 | −1.55376 | ||||||||
\(641\) | 26.5976 | 1.05054 | 0.525271 | − | 0.850935i | \(-0.323964\pi\) | ||||
0.525271 | + | 0.850935i | \(0.323964\pi\) | |||||||
\(642\) | −13.8415 | −0.546281 | ||||||||
\(643\) | 8.22463 | 0.324348 | 0.162174 | − | 0.986762i | \(-0.448149\pi\) | ||||
0.162174 | + | 0.986762i | \(0.448149\pi\) | |||||||
\(644\) | 14.6784 | 0.578411 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.9441 | −0.430589 | ||||||||
\(647\) | 37.9614 | 1.49242 | 0.746209 | − | 0.665712i | \(-0.231872\pi\) | ||||
0.746209 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(648\) | −6.92165 | −0.271908 | ||||||||
\(649\) | 62.0755 | 2.43668 | ||||||||
\(650\) | 2.70013 | 0.105908 | ||||||||
\(651\) | 2.24245 | 0.0878884 | ||||||||
\(652\) | 31.6903 | 1.24109 | ||||||||
\(653\) | −1.96304 | −0.0768198 | −0.0384099 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384099 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(654\) | −1.91461 | −0.0748670 | ||||||||
\(655\) | 20.0997 | 0.785362 | ||||||||
\(656\) | −0.373448 | −0.0145807 | ||||||||
\(657\) | 2.98667 | 0.116521 | ||||||||
\(658\) | 23.0210 | 0.897453 | ||||||||
\(659\) | 26.0591 | 1.01512 | 0.507560 | − | 0.861617i | \(-0.330548\pi\) | ||||
0.507560 | + | 0.861617i | \(0.330548\pi\) | |||||||
\(660\) | 39.4689 | 1.53633 | ||||||||
\(661\) | −14.5776 | −0.567001 | −0.283501 | − | 0.958972i | \(-0.591496\pi\) | ||||
−0.283501 | + | 0.958972i | \(0.591496\pi\) | |||||||
\(662\) | −33.7947 | −1.31347 | ||||||||
\(663\) | −8.56270 | −0.332548 | ||||||||
\(664\) | 39.8701 | 1.54726 | ||||||||
\(665\) | −3.54398 | −0.137430 | ||||||||
\(666\) | −27.2279 | −1.05506 | ||||||||
\(667\) | 11.4273 | 0.442467 | ||||||||
\(668\) | 35.9253 | 1.38999 | ||||||||
\(669\) | 21.9020 | 0.846779 | ||||||||
\(670\) | −48.1959 | −1.86197 | ||||||||
\(671\) | 22.3673 | 0.863482 | ||||||||
\(672\) | −11.3127 | −0.436399 | ||||||||
\(673\) | −26.0002 | −1.00224 | −0.501118 | − | 0.865379i | \(-0.667078\pi\) | ||||
−0.501118 | + | 0.865379i | \(0.667078\pi\) | |||||||
\(674\) | 56.4257 | 2.17344 | ||||||||
\(675\) | −3.91140 | −0.150550 | ||||||||
\(676\) | −36.8733 | −1.41820 | ||||||||
\(677\) | 22.0690 | 0.848182 | 0.424091 | − | 0.905620i | \(-0.360594\pi\) | ||||
0.424091 | + | 0.905620i | \(0.360594\pi\) | |||||||
\(678\) | −3.68236 | −0.141420 | ||||||||
\(679\) | −0.708019 | −0.0271713 | ||||||||
\(680\) | 42.4710 | 1.62869 | ||||||||
\(681\) | −6.59493 | −0.252718 | ||||||||
\(682\) | 14.7339 | 0.564192 | ||||||||
\(683\) | 4.70251 | 0.179937 | 0.0899684 | − | 0.995945i | \(-0.471323\pi\) | ||||
0.0899684 | + | 0.995945i | \(0.471323\pi\) | |||||||
\(684\) | −5.13880 | −0.196487 | ||||||||
\(685\) | −10.0958 | −0.385742 | ||||||||
\(686\) | 45.2742 | 1.72858 | ||||||||
\(687\) | −6.34088 | −0.241920 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.61498 | 0.328205 | ||||||||
\(690\) | −7.69008 | −0.292756 | ||||||||
\(691\) | −36.0380 | −1.37095 | −0.685475 | − | 0.728096i | \(-0.740406\pi\) | ||||
−0.685475 | + | 0.728096i | \(0.740406\pi\) | |||||||
\(692\) | −82.9863 | −3.15467 | ||||||||
\(693\) | −33.7950 | −1.28377 | ||||||||
\(694\) | −17.4054 | −0.660700 | ||||||||
\(695\) | 6.33447 | 0.240280 | ||||||||
\(696\) | 18.0825 | 0.685414 | ||||||||
\(697\) | −5.00875 | −0.189720 | ||||||||
\(698\) | −31.3859 | −1.18797 | ||||||||
\(699\) | 5.01337 | 0.189623 | ||||||||
\(700\) | −6.81568 | −0.257609 | ||||||||
\(701\) | −39.9027 | −1.50711 | −0.753553 | − | 0.657387i | \(-0.771662\pi\) | ||||
−0.753553 | + | 0.657387i | \(0.771662\pi\) | |||||||
\(702\) | −15.3026 | −0.577559 | ||||||||
\(703\) | −3.83890 | −0.144787 | ||||||||
\(704\) | −80.6611 | −3.04003 | ||||||||
\(705\) | −7.54782 | −0.284267 | ||||||||
\(706\) | 69.8246 | 2.62789 | ||||||||
\(707\) | −29.9573 | −1.12666 | ||||||||
\(708\) | −29.7878 | −1.11950 | ||||||||
\(709\) | −1.96754 | −0.0738927 | −0.0369463 | − | 0.999317i | \(-0.511763\pi\) | ||||
−0.0369463 | + | 0.999317i | \(0.511763\pi\) | |||||||
\(710\) | −35.3830 | −1.32790 | ||||||||
\(711\) | −16.2014 | −0.607601 | ||||||||
\(712\) | −48.1428 | −1.80423 | ||||||||
\(713\) | −1.79655 | −0.0672814 | ||||||||
\(714\) | 34.5374 | 1.29253 | ||||||||
\(715\) | −18.2188 | −0.681344 | ||||||||
\(716\) | 38.9350 | 1.45507 | ||||||||
\(717\) | −3.16998 | −0.118385 | ||||||||
\(718\) | 27.8678 | 1.04002 | ||||||||
\(719\) | 29.1938 | 1.08875 | 0.544373 | − | 0.838843i | \(-0.316768\pi\) | ||||
0.544373 | + | 0.838843i | \(0.316768\pi\) | |||||||
\(720\) | 2.21092 | 0.0823961 | ||||||||
\(721\) | −5.30926 | −0.197727 | ||||||||
\(722\) | 42.7686 | 1.59168 | ||||||||
\(723\) | −1.48363 | −0.0551769 | ||||||||
\(724\) | 68.5990 | 2.54946 | ||||||||
\(725\) | −5.30608 | −0.197063 | ||||||||
\(726\) | 61.6385 | 2.28762 | ||||||||
\(727\) | 41.5692 | 1.54172 | 0.770858 | − | 0.637007i | \(-0.219828\pi\) | ||||
0.770858 | + | 0.637007i | \(0.219828\pi\) | |||||||
\(728\) | −10.7215 | −0.397367 | ||||||||
\(729\) | 8.02793 | 0.297331 | ||||||||
\(730\) | −6.49431 | −0.240365 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −10.7333 | −0.396714 | ||||||||
\(733\) | −30.0670 | −1.11055 | −0.555275 | − | 0.831667i | \(-0.687387\pi\) | ||||
−0.555275 | + | 0.831667i | \(0.687387\pi\) | |||||||
\(734\) | −72.9072 | −2.69105 | ||||||||
\(735\) | −1.82988 | −0.0674962 | ||||||||
\(736\) | 9.06329 | 0.334077 | ||||||||
\(737\) | −64.7983 | −2.38688 | ||||||||
\(738\) | −3.75808 | −0.138337 | ||||||||
\(739\) | 3.87146 | 0.142414 | 0.0712071 | − | 0.997462i | \(-0.477315\pi\) | ||||
0.0712071 | + | 0.997462i | \(0.477315\pi\) | |||||||
\(740\) | 37.0514 | 1.36204 | ||||||||
\(741\) | −0.905816 | −0.0332760 | ||||||||
\(742\) | −34.7483 | −1.27565 | ||||||||
\(743\) | 52.0970 | 1.91125 | 0.955626 | − | 0.294582i | \(-0.0951804\pi\) | ||||
0.955626 | + | 0.294582i | \(0.0951804\pi\) | |||||||
\(744\) | −2.84284 | −0.104224 | ||||||||
\(745\) | −19.6539 | −0.720061 | ||||||||
\(746\) | 44.6602 | 1.63512 | ||||||||
\(747\) | 27.8373 | 1.01851 | ||||||||
\(748\) | 142.014 | 5.19255 | ||||||||
\(749\) | −16.1277 | −0.589293 | ||||||||
\(750\) | 25.0616 | 0.915121 | ||||||||
\(751\) | −29.7160 | −1.08435 | −0.542177 | − | 0.840264i | \(-0.682400\pi\) | ||||
−0.542177 | + | 0.840264i | \(0.682400\pi\) | |||||||
\(752\) | −2.02488 | −0.0738397 | ||||||||
\(753\) | −13.5208 | −0.492725 | ||||||||
\(754\) | −20.7590 | −0.755998 | ||||||||
\(755\) | 3.38370 | 0.123145 | ||||||||
\(756\) | 38.6269 | 1.40485 | ||||||||
\(757\) | 18.1870 | 0.661018 | 0.330509 | − | 0.943803i | \(-0.392780\pi\) | ||||
0.330509 | + | 0.943803i | \(0.392780\pi\) | |||||||
\(758\) | 45.0307 | 1.63559 | ||||||||
\(759\) | −10.3391 | −0.375287 | ||||||||
\(760\) | 4.49286 | 0.162973 | ||||||||
\(761\) | −12.4175 | −0.450133 | −0.225066 | − | 0.974343i | \(-0.572260\pi\) | ||||
−0.225066 | + | 0.974343i | \(0.572260\pi\) | |||||||
\(762\) | 6.66854 | 0.241576 | ||||||||
\(763\) | −2.23084 | −0.0807618 | ||||||||
\(764\) | 64.5550 | 2.33552 | ||||||||
\(765\) | 29.6532 | 1.07211 | ||||||||
\(766\) | 55.1768 | 1.99362 | ||||||||
\(767\) | 13.7500 | 0.496485 | ||||||||
\(768\) | 17.3797 | 0.627135 | ||||||||
\(769\) | 13.6399 | 0.491868 | 0.245934 | − | 0.969287i | \(-0.420905\pi\) | ||||
0.245934 | + | 0.969287i | \(0.420905\pi\) | |||||||
\(770\) | 73.4849 | 2.64821 | ||||||||
\(771\) | 2.78161 | 0.100177 | ||||||||
\(772\) | 38.7216 | 1.39362 | ||||||||
\(773\) | 31.9270 | 1.14833 | 0.574167 | − | 0.818738i | \(-0.305326\pi\) | ||||
0.574167 | + | 0.818738i | \(0.305326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.834199 | 0.0299653 | ||||||||
\(776\) | 0.897586 | 0.0322215 | ||||||||
\(777\) | 12.1148 | 0.434616 | ||||||||
\(778\) | 11.4494 | 0.410482 | ||||||||
\(779\) | −0.529857 | −0.0189841 | ||||||||
\(780\) | 8.74256 | 0.313034 | ||||||||
\(781\) | −47.5718 | −1.70225 | ||||||||
\(782\) | −27.6699 | −0.989473 | ||||||||
\(783\) | 30.0714 | 1.07467 | ||||||||
\(784\) | −0.490909 | −0.0175325 | ||||||||
\(785\) | −28.3060 | −1.01028 | ||||||||
\(786\) | −20.7213 | −0.739106 | ||||||||
\(787\) | 30.6799 | 1.09362 | 0.546811 | − | 0.837256i | \(-0.315842\pi\) | ||||
0.546811 | + | 0.837256i | \(0.315842\pi\) | |||||||
\(788\) | 54.0064 | 1.92390 | ||||||||
\(789\) | 6.75408 | 0.240452 | ||||||||
\(790\) | 35.2289 | 1.25339 | ||||||||
\(791\) | −4.29057 | −0.152555 | ||||||||
\(792\) | 42.8434 | 1.52237 | ||||||||
\(793\) | 4.95448 | 0.175939 | ||||||||
\(794\) | −19.6808 | −0.698444 | ||||||||
\(795\) | 11.3928 | 0.404060 | ||||||||
\(796\) | 53.2590 | 1.88771 | ||||||||
\(797\) | 18.4303 | 0.652835 | 0.326417 | − | 0.945226i | \(-0.394159\pi\) | ||||
0.326417 | + | 0.945226i | \(0.394159\pi\) | |||||||
\(798\) | 3.65358 | 0.129335 | ||||||||
\(799\) | −27.1580 | −0.960781 | ||||||||
\(800\) | −4.20839 | −0.148789 | ||||||||
\(801\) | −33.6132 | −1.18766 | ||||||||
\(802\) | −13.2238 | −0.466948 | ||||||||
\(803\) | −8.73147 | −0.308127 | ||||||||
\(804\) | 31.0944 | 1.09662 | ||||||||
\(805\) | −8.96024 | −0.315807 | ||||||||
\(806\) | 3.26364 | 0.114957 | ||||||||
\(807\) | −14.7966 | −0.520864 | ||||||||
\(808\) | 37.9781 | 1.33606 | ||||||||
\(809\) | −14.2481 | −0.500938 | −0.250469 | − | 0.968125i | \(-0.580585\pi\) | ||||
−0.250469 | + | 0.968125i | \(0.580585\pi\) | |||||||
\(810\) | 10.5083 | 0.369225 | ||||||||
\(811\) | −6.10231 | −0.214281 | −0.107141 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107141 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(812\) | 52.3999 | 1.83888 | ||||||||
\(813\) | −24.2773 | −0.851442 | ||||||||
\(814\) | 79.6000 | 2.78998 | ||||||||
\(815\) | −19.3449 | −0.677622 | ||||||||
\(816\) | −3.03783 | −0.106345 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −40.5990 | −1.41951 | ||||||||
\(819\) | −7.48577 | −0.261574 | ||||||||
\(820\) | 5.11396 | 0.178587 | ||||||||
\(821\) | 34.2987 | 1.19703 | 0.598516 | − | 0.801111i | \(-0.295757\pi\) | ||||
0.598516 | + | 0.801111i | \(0.295757\pi\) | |||||||
\(822\) | 10.4080 | 0.363022 | ||||||||
\(823\) | 42.4031 | 1.47808 | 0.739040 | − | 0.673662i | \(-0.235280\pi\) | ||||
0.739040 | + | 0.673662i | \(0.235280\pi\) | |||||||
\(824\) | 6.73077 | 0.234477 | ||||||||
\(825\) | 4.80081 | 0.167143 | ||||||||
\(826\) | −55.4603 | −1.92971 | ||||||||
\(827\) | 9.85209 | 0.342591 | 0.171295 | − | 0.985220i | \(-0.445205\pi\) | ||||
0.171295 | + | 0.985220i | \(0.445205\pi\) | |||||||
\(828\) | −12.9924 | −0.451518 | ||||||||
\(829\) | −3.03968 | −0.105573 | −0.0527863 | − | 0.998606i | \(-0.516810\pi\) | ||||
−0.0527863 | + | 0.998606i | \(0.516810\pi\) | |||||||
\(830\) | −60.5302 | −2.10103 | ||||||||
\(831\) | 16.6658 | 0.578131 | ||||||||
\(832\) | −17.8668 | −0.619421 | ||||||||
\(833\) | −6.58415 | −0.228127 | ||||||||
\(834\) | −6.53037 | −0.226128 | ||||||||
\(835\) | −21.9301 | −0.758921 | ||||||||
\(836\) | 15.0232 | 0.519587 | ||||||||
\(837\) | −4.72770 | −0.163413 | ||||||||
\(838\) | 69.2740 | 2.39303 | ||||||||
\(839\) | 46.5265 | 1.60627 | 0.803137 | − | 0.595794i | \(-0.203163\pi\) | ||||
0.803137 | + | 0.595794i | \(0.203163\pi\) | |||||||
\(840\) | −14.1786 | −0.489207 | ||||||||
\(841\) | 11.7939 | 0.406686 | ||||||||
\(842\) | 85.9084 | 2.96060 | ||||||||
\(843\) | 10.7667 | 0.370825 | ||||||||
\(844\) | 12.7903 | 0.440260 | ||||||||
\(845\) | 22.5088 | 0.774325 | ||||||||
\(846\) | −20.3768 | −0.700567 | ||||||||
\(847\) | 71.8193 | 2.46774 | ||||||||
\(848\) | 3.05638 | 0.104956 | ||||||||
\(849\) | −1.58352 | −0.0543461 | ||||||||
\(850\) | 12.8480 | 0.440684 | ||||||||
\(851\) | −9.70586 | −0.332713 | ||||||||
\(852\) | 22.8280 | 0.782075 | ||||||||
\(853\) | 16.9716 | 0.581098 | 0.290549 | − | 0.956860i | \(-0.406162\pi\) | ||||
0.290549 | + | 0.956860i | \(0.406162\pi\) | |||||||
\(854\) | −19.9837 | −0.683829 | ||||||||
\(855\) | 3.13691 | 0.107280 | ||||||||
\(856\) | 20.4457 | 0.698821 | ||||||||
\(857\) | 15.9929 | 0.546308 | 0.273154 | − | 0.961970i | \(-0.411933\pi\) | ||||
0.273154 | + | 0.961970i | \(0.411933\pi\) | |||||||
\(858\) | 18.7822 | 0.641214 | ||||||||
\(859\) | 49.8888 | 1.70219 | 0.851093 | − | 0.525015i | \(-0.175940\pi\) | ||||
0.851093 | + | 0.525015i | \(0.175940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.67213 | 0.0569859 | ||||||||
\(862\) | −58.0146 | −1.97599 | ||||||||
\(863\) | 12.5338 | 0.426657 | 0.213328 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213328 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(864\) | 23.8504 | 0.811407 | ||||||||
\(865\) | 50.6578 | 1.72242 | ||||||||
\(866\) | −67.6164 | −2.29770 | ||||||||
\(867\) | −25.2652 | −0.858052 | ||||||||
\(868\) | −8.23809 | −0.279619 | ||||||||
\(869\) | 47.3645 | 1.60673 | ||||||||
\(870\) | −27.4525 | −0.930727 | ||||||||
\(871\) | −14.3531 | −0.486338 | ||||||||
\(872\) | 2.82813 | 0.0957725 | ||||||||
\(873\) | 0.626693 | 0.0212104 | ||||||||
\(874\) | −2.92710 | −0.0990105 | ||||||||
\(875\) | 29.2010 | 0.987175 | ||||||||
\(876\) | 4.18992 | 0.141564 | ||||||||
\(877\) | −33.8971 | −1.14463 | −0.572313 | − | 0.820035i | \(-0.693954\pi\) | ||||
−0.572313 | + | 0.820035i | \(0.693954\pi\) | |||||||
\(878\) | −24.2943 | −0.819893 | ||||||||
\(879\) | −9.69884 | −0.327134 | ||||||||
\(880\) | −6.46357 | −0.217887 | ||||||||
\(881\) | 38.1336 | 1.28475 | 0.642377 | − | 0.766389i | \(-0.277948\pi\) | ||||
0.642377 | + | 0.766389i | \(0.277948\pi\) | |||||||
\(882\) | −4.94011 | −0.166342 | ||||||||
\(883\) | −9.47384 | −0.318820 | −0.159410 | − | 0.987212i | \(-0.550959\pi\) | ||||
−0.159410 | + | 0.987212i | \(0.550959\pi\) | |||||||
\(884\) | 31.4568 | 1.05801 | ||||||||
\(885\) | 18.1836 | 0.611234 | ||||||||
\(886\) | 19.6801 | 0.661166 | ||||||||
\(887\) | 23.4875 | 0.788633 | 0.394317 | − | 0.918975i | \(-0.370981\pi\) | ||||
0.394317 | + | 0.918975i | \(0.370981\pi\) | |||||||
\(888\) | −15.3584 | −0.515396 | ||||||||
\(889\) | 7.76997 | 0.260597 | ||||||||
\(890\) | 73.0896 | 2.44997 | ||||||||
\(891\) | 14.1282 | 0.473314 | ||||||||
\(892\) | −80.4614 | −2.69405 | ||||||||
\(893\) | −2.87295 | −0.0961395 | ||||||||
\(894\) | 20.2617 | 0.677651 | ||||||||
\(895\) | −23.7673 | −0.794454 | ||||||||
\(896\) | 47.2161 | 1.57738 | ||||||||
\(897\) | −2.29017 | −0.0764666 | ||||||||
\(898\) | −80.5985 | −2.68961 | ||||||||
\(899\) | −6.41344 | −0.213900 | ||||||||
\(900\) | 6.03281 | 0.201094 | ||||||||
\(901\) | 40.9927 | 1.36566 | ||||||||
\(902\) | 10.9867 | 0.365816 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.43933 | 0.180910 | ||||||||
\(905\) | −41.8752 | −1.39198 | ||||||||
\(906\) | −3.48834 | −0.115892 | ||||||||
\(907\) | −56.7976 | −1.88593 | −0.942966 | − | 0.332889i | \(-0.891977\pi\) | ||||
−0.942966 | + | 0.332889i | \(0.891977\pi\) | |||||||
\(908\) | 24.2278 | 0.804029 | ||||||||
\(909\) | 26.5163 | 0.879489 | ||||||||
\(910\) | 16.2773 | 0.539586 | ||||||||
\(911\) | 24.2739 | 0.804229 | 0.402114 | − | 0.915589i | \(-0.368275\pi\) | ||||
0.402114 | + | 0.915589i | \(0.368275\pi\) | |||||||
\(912\) | −0.321361 | −0.0106413 | ||||||||
\(913\) | −81.3816 | −2.69334 | ||||||||
\(914\) | −75.7004 | −2.50395 | ||||||||
\(915\) | 6.55199 | 0.216602 | ||||||||
\(916\) | 23.2945 | 0.769673 | ||||||||
\(917\) | −24.1438 | −0.797300 | ||||||||
\(918\) | −72.8144 | −2.40323 | ||||||||
\(919\) | 9.60014 | 0.316680 | 0.158340 | − | 0.987385i | \(-0.449386\pi\) | ||||
0.158340 | + | 0.987385i | \(0.449386\pi\) | |||||||
\(920\) | 11.3593 | 0.374504 | ||||||||
\(921\) | −4.99885 | −0.164718 | ||||||||
\(922\) | 91.9692 | 3.02885 | ||||||||
\(923\) | −10.5374 | −0.346842 | ||||||||
\(924\) | −47.4102 | −1.55968 | ||||||||
\(925\) | 4.50675 | 0.148181 | ||||||||
\(926\) | 29.2676 | 0.961794 | ||||||||
\(927\) | 4.69941 | 0.154349 | ||||||||
\(928\) | 32.3547 | 1.06209 | ||||||||
\(929\) | 12.0757 | 0.396190 | 0.198095 | − | 0.980183i | \(-0.436525\pi\) | ||||
0.198095 | + | 0.980183i | \(0.436525\pi\) | |||||||
\(930\) | 4.31596 | 0.141526 | ||||||||
\(931\) | −0.696513 | −0.0228273 | ||||||||
\(932\) | −18.4177 | −0.603290 | ||||||||
\(933\) | 5.91856 | 0.193765 | ||||||||
\(934\) | 80.8503 | 2.64550 | ||||||||
\(935\) | −86.6905 | −2.83508 | ||||||||
\(936\) | 9.49002 | 0.310191 | ||||||||
\(937\) | −48.4179 | −1.58174 | −0.790872 | − | 0.611982i | \(-0.790373\pi\) | ||||
−0.790872 | + | 0.611982i | \(0.790373\pi\) | |||||||
\(938\) | 57.8930 | 1.89027 | ||||||||
\(939\) | 17.9863 | 0.586962 | ||||||||
\(940\) | 27.7285 | 0.904403 | ||||||||
\(941\) | −26.1750 | −0.853279 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(942\) | 29.1814 | 0.950781 | ||||||||
\(943\) | −1.33964 | −0.0436246 | ||||||||
\(944\) | 4.87816 | 0.158771 | ||||||||
\(945\) | −23.5792 | −0.767032 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.3957 | 1.63764 | 0.818820 | − | 0.574050i | \(-0.194628\pi\) | ||||
0.818820 | + | 0.574050i | \(0.194628\pi\) | |||||||
\(948\) | −22.7286 | −0.738189 | ||||||||
\(949\) | −1.93406 | −0.0627823 | ||||||||
\(950\) | 1.35915 | 0.0440966 | ||||||||
\(951\) | −12.6487 | −0.410164 | ||||||||
\(952\) | −51.0163 | −1.65345 | ||||||||
\(953\) | 2.40711 | 0.0779740 | 0.0389870 | − | 0.999240i | \(-0.487587\pi\) | ||||
0.0389870 | + | 0.999240i | \(0.487587\pi\) | |||||||
\(954\) | 30.7569 | 0.995793 | ||||||||
\(955\) | −39.4067 | −1.27517 | ||||||||
\(956\) | 11.6456 | 0.376645 | ||||||||
\(957\) | −36.9093 | −1.19311 | ||||||||
\(958\) | −50.8611 | −1.64325 | ||||||||
\(959\) | 12.1271 | 0.391605 | ||||||||
\(960\) | −23.6278 | −0.762583 | ||||||||
\(961\) | −29.9917 | −0.967474 | ||||||||
\(962\) | 17.6318 | 0.568472 | ||||||||
\(963\) | 14.2752 | 0.460012 | ||||||||
\(964\) | 5.45043 | 0.175547 | ||||||||
\(965\) | −23.6370 | −0.760903 | ||||||||
\(966\) | 9.23734 | 0.297206 | ||||||||
\(967\) | −31.2564 | −1.00514 | −0.502568 | − | 0.864538i | \(-0.667611\pi\) | ||||
−0.502568 | + | 0.864538i | \(0.667611\pi\) | |||||||
\(968\) | −91.0483 | −2.92640 | ||||||||
\(969\) | −4.31015 | −0.138462 | ||||||||
\(970\) | −1.36270 | −0.0437537 | ||||||||
\(971\) | −0.00187696 | −6.02345e−5 0 | −3.01173e−5 | − | 1.00000i | \(-0.500010\pi\) | ||||
−3.01173e−5 | 1.00000i | \(0.500010\pi\) | ||||||||
\(972\) | −54.0258 | −1.73288 | ||||||||
\(973\) | −7.60898 | −0.243933 | ||||||||
\(974\) | 15.0119 | 0.481012 | ||||||||
\(975\) | 1.06340 | 0.0340561 | ||||||||
\(976\) | 1.75772 | 0.0562633 | ||||||||
\(977\) | −25.3298 | −0.810372 | −0.405186 | − | 0.914234i | \(-0.632793\pi\) | ||||
−0.405186 | + | 0.914234i | \(0.632793\pi\) | |||||||
\(978\) | 19.9431 | 0.637711 | ||||||||
\(979\) | 98.2674 | 3.14064 | ||||||||
\(980\) | 6.72245 | 0.214741 | ||||||||
\(981\) | 1.97460 | 0.0630440 | ||||||||
\(982\) | 16.6450 | 0.531164 | ||||||||
\(983\) | 37.1682 | 1.18548 | 0.592741 | − | 0.805393i | \(-0.298046\pi\) | ||||
0.592741 | + | 0.805393i | \(0.298046\pi\) | |||||||
\(984\) | −2.11982 | −0.0675775 | ||||||||
\(985\) | −32.9674 | −1.05043 | ||||||||
\(986\) | −98.7776 | −3.14572 | ||||||||
\(987\) | 9.06646 | 0.288588 | ||||||||
\(988\) | 3.32770 | 0.105868 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −65.0442 | −2.06724 | ||||||||
\(991\) | 0.390175 | 0.0123943 | 0.00619716 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619716 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(992\) | −5.08666 | −0.161502 | ||||||||
\(993\) | −13.3095 | −0.422364 | ||||||||
\(994\) | 42.5022 | 1.34809 | ||||||||
\(995\) | −32.5112 | −1.03067 | ||||||||
\(996\) | 39.0522 | 1.23742 | ||||||||
\(997\) | 14.6123 | 0.462777 | 0.231388 | − | 0.972861i | \(-0.425673\pi\) | ||||
0.231388 | + | 0.972861i | \(0.425673\pi\) | |||||||
\(998\) | 85.6401 | 2.71089 | ||||||||
\(999\) | −25.5414 | −0.808093 |
(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 | 1849.2.a.p.1.5 | ✓ | 20 | |
43.42 | odd | 2 | 1849.2.a.r.1.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.p.1.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1849.2.a.r.1.16 | yes | 20 | 43.42 | odd | 2 |