Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.37 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67933 | 1.18746 | 0.593731 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593731 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.820135 | 0.410067 | ||||||||
\(5\) | 3.59386 | 1.60722 | 0.803611 | − | 0.595155i | \(-0.202909\pi\) | ||||
0.803611 | + | 0.595155i | \(0.202909\pi\) | |||||||
\(6\) | −1.67933 | −0.685582 | ||||||||
\(7\) | 1.09506 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433647\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433647\pi\) | |||||||
\(8\) | −1.98138 | −0.700523 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.03526 | 1.90852 | ||||||||
\(11\) | −1.52969 | −0.461220 | −0.230610 | − | 0.973046i | \(-0.574072\pi\) | ||||
−0.230610 | + | 0.973046i | \(0.574072\pi\) | |||||||
\(12\) | −0.820135 | −0.236752 | ||||||||
\(13\) | −0.0461842 | −0.0128092 | −0.00640459 | − | 0.999979i | \(-0.502039\pi\) | ||||
−0.00640459 | + | 0.999979i | \(0.502039\pi\) | |||||||
\(14\) | 1.83896 | 0.491482 | ||||||||
\(15\) | −3.59386 | −0.927930 | ||||||||
\(16\) | −4.96765 | −1.24191 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.67933 | 0.395821 | ||||||||
\(19\) | −1.91613 | −0.439591 | −0.219796 | − | 0.975546i | \(-0.570539\pi\) | ||||
−0.219796 | + | 0.975546i | \(0.570539\pi\) | |||||||
\(20\) | 2.94745 | 0.659069 | ||||||||
\(21\) | −1.09506 | −0.238961 | ||||||||
\(22\) | −2.56885 | −0.547681 | ||||||||
\(23\) | −5.70497 | −1.18957 | −0.594785 | − | 0.803885i | \(-0.702763\pi\) | ||||
−0.594785 | + | 0.803885i | \(0.702763\pi\) | |||||||
\(24\) | 1.98138 | 0.404447 | ||||||||
\(25\) | 7.91581 | 1.58316 | ||||||||
\(26\) | −0.0775583 | −0.0152104 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.898094 | 0.169724 | ||||||||
\(29\) | −8.96107 | −1.66403 | −0.832014 | − | 0.554754i | \(-0.812812\pi\) | ||||
−0.832014 | + | 0.554754i | \(0.812812\pi\) | |||||||
\(30\) | −6.03526 | −1.10188 | ||||||||
\(31\) | 1.93639 | 0.347786 | 0.173893 | − | 0.984765i | \(-0.444365\pi\) | ||||
0.173893 | + | 0.984765i | \(0.444365\pi\) | |||||||
\(32\) | −4.37954 | −0.774201 | ||||||||
\(33\) | 1.52969 | 0.266285 | ||||||||
\(34\) | −1.67933 | −0.288002 | ||||||||
\(35\) | 3.93548 | 0.665217 | ||||||||
\(36\) | 0.820135 | 0.136689 | ||||||||
\(37\) | −6.02148 | −0.989925 | −0.494962 | − | 0.868914i | \(-0.664818\pi\) | ||||
−0.494962 | + | 0.868914i | \(0.664818\pi\) | |||||||
\(38\) | −3.21781 | −0.521998 | ||||||||
\(39\) | 0.0461842 | 0.00739539 | ||||||||
\(40\) | −7.12079 | −1.12590 | ||||||||
\(41\) | −4.24287 | −0.662625 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(42\) | −1.83896 | −0.283757 | ||||||||
\(43\) | −0.305192 | −0.0465414 | −0.0232707 | − | 0.999729i | \(-0.507408\pi\) | ||||
−0.0232707 | + | 0.999729i | \(0.507408\pi\) | |||||||
\(44\) | −1.25455 | −0.189131 | ||||||||
\(45\) | 3.59386 | 0.535741 | ||||||||
\(46\) | −9.58051 | −1.41257 | ||||||||
\(47\) | 5.72249 | 0.834712 | 0.417356 | − | 0.908743i | \(-0.362957\pi\) | ||||
0.417356 | + | 0.908743i | \(0.362957\pi\) | |||||||
\(48\) | 4.96765 | 0.717018 | ||||||||
\(49\) | −5.80085 | −0.828693 | ||||||||
\(50\) | 13.2932 | 1.87995 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.0378772 | −0.00525263 | ||||||||
\(53\) | 0.193461 | 0.0265740 | 0.0132870 | − | 0.999912i | \(-0.495770\pi\) | ||||
0.0132870 | + | 0.999912i | \(0.495770\pi\) | |||||||
\(54\) | −1.67933 | −0.228527 | ||||||||
\(55\) | −5.49749 | −0.741282 | ||||||||
\(56\) | −2.16972 | −0.289941 | ||||||||
\(57\) | 1.91613 | 0.253798 | ||||||||
\(58\) | −15.0486 | −1.97597 | ||||||||
\(59\) | −2.32265 | −0.302383 | −0.151191 | − | 0.988505i | \(-0.548311\pi\) | ||||
−0.151191 | + | 0.988505i | \(0.548311\pi\) | |||||||
\(60\) | −2.94745 | −0.380514 | ||||||||
\(61\) | −14.8783 | −1.90497 | −0.952485 | − | 0.304587i | \(-0.901482\pi\) | ||||
−0.952485 | + | 0.304587i | \(0.901482\pi\) | |||||||
\(62\) | 3.25183 | 0.412983 | ||||||||
\(63\) | 1.09506 | 0.137964 | ||||||||
\(64\) | 2.58062 | 0.322577 | ||||||||
\(65\) | −0.165979 | −0.0205872 | ||||||||
\(66\) | 2.56885 | 0.316204 | ||||||||
\(67\) | −4.82522 | −0.589495 | −0.294747 | − | 0.955575i | \(-0.595236\pi\) | ||||
−0.294747 | + | 0.955575i | \(0.595236\pi\) | |||||||
\(68\) | −0.820135 | −0.0994559 | ||||||||
\(69\) | 5.70497 | 0.686798 | ||||||||
\(70\) | 6.60895 | 0.789920 | ||||||||
\(71\) | −8.61413 | −1.02231 | −0.511155 | − | 0.859489i | \(-0.670782\pi\) | ||||
−0.511155 | + | 0.859489i | \(0.670782\pi\) | |||||||
\(72\) | −1.98138 | −0.233508 | ||||||||
\(73\) | 14.1239 | 1.65307 | 0.826537 | − | 0.562883i | \(-0.190308\pi\) | ||||
0.826537 | + | 0.562883i | \(0.190308\pi\) | |||||||
\(74\) | −10.1120 | −1.17550 | ||||||||
\(75\) | −7.91581 | −0.914039 | ||||||||
\(76\) | −1.57149 | −0.180262 | ||||||||
\(77\) | −1.67510 | −0.190895 | ||||||||
\(78\) | 0.0775583 | 0.00878174 | ||||||||
\(79\) | 4.00757 | 0.450887 | 0.225443 | − | 0.974256i | \(-0.427617\pi\) | ||||
0.225443 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(80\) | −17.8530 | −1.99603 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.12516 | −0.786842 | ||||||||
\(83\) | −3.07445 | −0.337465 | −0.168732 | − | 0.985662i | \(-0.553967\pi\) | ||||
−0.168732 | + | 0.985662i | \(0.553967\pi\) | |||||||
\(84\) | −0.898094 | −0.0979900 | ||||||||
\(85\) | −3.59386 | −0.389809 | ||||||||
\(86\) | −0.512517 | −0.0552662 | ||||||||
\(87\) | 8.96107 | 0.960727 | ||||||||
\(88\) | 3.03090 | 0.323095 | ||||||||
\(89\) | −2.17593 | −0.230648 | −0.115324 | − | 0.993328i | \(-0.536791\pi\) | ||||
−0.115324 | + | 0.993328i | \(0.536791\pi\) | |||||||
\(90\) | 6.03526 | 0.636172 | ||||||||
\(91\) | −0.0505743 | −0.00530162 | ||||||||
\(92\) | −4.67885 | −0.487803 | ||||||||
\(93\) | −1.93639 | −0.200794 | ||||||||
\(94\) | 9.60993 | 0.991189 | ||||||||
\(95\) | −6.88631 | −0.706521 | ||||||||
\(96\) | 4.37954 | 0.446985 | ||||||||
\(97\) | −15.4254 | −1.56621 | −0.783105 | − | 0.621889i | \(-0.786365\pi\) | ||||
−0.783105 | + | 0.621889i | \(0.786365\pi\) | |||||||
\(98\) | −9.74152 | −0.984042 | ||||||||
\(99\) | −1.52969 | −0.153740 | ||||||||
\(100\) | 6.49203 | 0.649203 | ||||||||
\(101\) | 11.1376 | 1.10823 | 0.554116 | − | 0.832440i | \(-0.313057\pi\) | ||||
0.554116 | + | 0.832440i | \(0.313057\pi\) | |||||||
\(102\) | 1.67933 | 0.166278 | ||||||||
\(103\) | 4.16853 | 0.410737 | 0.205369 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205369 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(104\) | 0.0915083 | 0.00897313 | ||||||||
\(105\) | −3.93548 | −0.384063 | ||||||||
\(106\) | 0.324885 | 0.0315556 | ||||||||
\(107\) | 9.95303 | 0.962196 | 0.481098 | − | 0.876667i | \(-0.340238\pi\) | ||||
0.481098 | + | 0.876667i | \(0.340238\pi\) | |||||||
\(108\) | −0.820135 | −0.0789175 | ||||||||
\(109\) | −6.25723 | −0.599334 | −0.299667 | − | 0.954044i | \(-0.596876\pi\) | ||||
−0.299667 | + | 0.954044i | \(0.596876\pi\) | |||||||
\(110\) | −9.23208 | −0.880245 | ||||||||
\(111\) | 6.02148 | 0.571533 | ||||||||
\(112\) | −5.43986 | −0.514018 | ||||||||
\(113\) | 3.19648 | 0.300700 | 0.150350 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150350 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(114\) | 3.21781 | 0.301376 | ||||||||
\(115\) | −20.5029 | −1.91190 | ||||||||
\(116\) | −7.34928 | −0.682364 | ||||||||
\(117\) | −0.0461842 | −0.00426973 | ||||||||
\(118\) | −3.90048 | −0.359068 | ||||||||
\(119\) | −1.09506 | −0.100384 | ||||||||
\(120\) | 7.12079 | 0.650036 | ||||||||
\(121\) | −8.66004 | −0.787277 | ||||||||
\(122\) | −24.9855 | −2.26208 | ||||||||
\(123\) | 4.24287 | 0.382567 | ||||||||
\(124\) | 1.58810 | 0.142616 | ||||||||
\(125\) | 10.4790 | 0.937270 | ||||||||
\(126\) | 1.83896 | 0.163827 | ||||||||
\(127\) | −6.53383 | −0.579784 | −0.289892 | − | 0.957059i | \(-0.593619\pi\) | ||||
−0.289892 | + | 0.957059i | \(0.593619\pi\) | |||||||
\(128\) | 13.0928 | 1.15725 | ||||||||
\(129\) | 0.305192 | 0.0268707 | ||||||||
\(130\) | −0.278733 | −0.0244465 | ||||||||
\(131\) | 6.42075 | 0.560983 | 0.280492 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280492 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(132\) | 1.25455 | 0.109195 | ||||||||
\(133\) | −2.09828 | −0.181944 | ||||||||
\(134\) | −8.10312 | −0.700003 | ||||||||
\(135\) | −3.59386 | −0.309310 | ||||||||
\(136\) | 1.98138 | 0.169902 | ||||||||
\(137\) | 8.79125 | 0.751087 | 0.375543 | − | 0.926805i | \(-0.377456\pi\) | ||||
0.375543 | + | 0.926805i | \(0.377456\pi\) | |||||||
\(138\) | 9.58051 | 0.815547 | ||||||||
\(139\) | −0.593136 | −0.0503091 | −0.0251546 | − | 0.999684i | \(-0.508008\pi\) | ||||
−0.0251546 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(140\) | 3.22762 | 0.272784 | ||||||||
\(141\) | −5.72249 | −0.481921 | ||||||||
\(142\) | −14.4659 | −1.21395 | ||||||||
\(143\) | 0.0706476 | 0.00590785 | ||||||||
\(144\) | −4.96765 | −0.413971 | ||||||||
\(145\) | −32.2048 | −2.67446 | ||||||||
\(146\) | 23.7186 | 1.96296 | ||||||||
\(147\) | 5.80085 | 0.478446 | ||||||||
\(148\) | −4.93842 | −0.405936 | ||||||||
\(149\) | 9.44340 | 0.773634 | 0.386817 | − | 0.922157i | \(-0.373575\pi\) | ||||
0.386817 | + | 0.922157i | \(0.373575\pi\) | |||||||
\(150\) | −13.2932 | −1.08539 | ||||||||
\(151\) | 15.8001 | 1.28580 | 0.642899 | − | 0.765951i | \(-0.277732\pi\) | ||||
0.642899 | + | 0.765951i | \(0.277732\pi\) | |||||||
\(152\) | 3.79659 | 0.307944 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −2.81304 | −0.226681 | ||||||||
\(155\) | 6.95911 | 0.558969 | ||||||||
\(156\) | 0.0378772 | 0.00303261 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 6.73001 | 0.535411 | ||||||||
\(159\) | −0.193461 | −0.0153425 | ||||||||
\(160\) | −15.7395 | −1.24431 | ||||||||
\(161\) | −6.24727 | −0.492354 | ||||||||
\(162\) | 1.67933 | 0.131940 | ||||||||
\(163\) | 8.56463 | 0.670834 | 0.335417 | − | 0.942070i | \(-0.391123\pi\) | ||||
0.335417 | + | 0.942070i | \(0.391123\pi\) | |||||||
\(164\) | −3.47972 | −0.271721 | ||||||||
\(165\) | 5.49749 | 0.427979 | ||||||||
\(166\) | −5.16300 | −0.400727 | ||||||||
\(167\) | −12.1584 | −0.940844 | −0.470422 | − | 0.882442i | \(-0.655898\pi\) | ||||
−0.470422 | + | 0.882442i | \(0.655898\pi\) | |||||||
\(168\) | 2.16972 | 0.167398 | ||||||||
\(169\) | −12.9979 | −0.999836 | ||||||||
\(170\) | −6.03526 | −0.462883 | ||||||||
\(171\) | −1.91613 | −0.146530 | ||||||||
\(172\) | −0.250299 | −0.0190851 | ||||||||
\(173\) | −13.0161 | −0.989598 | −0.494799 | − | 0.869007i | \(-0.664758\pi\) | ||||
−0.494799 | + | 0.869007i | \(0.664758\pi\) | |||||||
\(174\) | 15.0486 | 1.14083 | ||||||||
\(175\) | 8.66826 | 0.655259 | ||||||||
\(176\) | 7.59897 | 0.572794 | ||||||||
\(177\) | 2.32265 | 0.174581 | ||||||||
\(178\) | −3.65409 | −0.273886 | ||||||||
\(179\) | 5.06732 | 0.378749 | 0.189375 | − | 0.981905i | \(-0.439354\pi\) | ||||
0.189375 | + | 0.981905i | \(0.439354\pi\) | |||||||
\(180\) | 2.94745 | 0.219690 | ||||||||
\(181\) | −5.21426 | −0.387573 | −0.193786 | − | 0.981044i | \(-0.562077\pi\) | ||||
−0.193786 | + | 0.981044i | \(0.562077\pi\) | |||||||
\(182\) | −0.0849307 | −0.00629548 | ||||||||
\(183\) | 14.8783 | 1.09983 | ||||||||
\(184\) | 11.3037 | 0.833321 | ||||||||
\(185\) | −21.6403 | −1.59103 | ||||||||
\(186\) | −3.25183 | −0.238436 | ||||||||
\(187\) | 1.52969 | 0.111862 | ||||||||
\(188\) | 4.69322 | 0.342288 | ||||||||
\(189\) | −1.09506 | −0.0796536 | ||||||||
\(190\) | −11.5644 | −0.838967 | ||||||||
\(191\) | 5.91599 | 0.428066 | 0.214033 | − | 0.976826i | \(-0.431340\pi\) | ||||
0.214033 | + | 0.976826i | \(0.431340\pi\) | |||||||
\(192\) | −2.58062 | −0.186240 | ||||||||
\(193\) | 22.8297 | 1.64332 | 0.821660 | − | 0.569978i | \(-0.193048\pi\) | ||||
0.821660 | + | 0.569978i | \(0.193048\pi\) | |||||||
\(194\) | −25.9042 | −1.85982 | ||||||||
\(195\) | 0.165979 | 0.0118860 | ||||||||
\(196\) | −4.75748 | −0.339820 | ||||||||
\(197\) | −0.855946 | −0.0609836 | −0.0304918 | − | 0.999535i | \(-0.509707\pi\) | ||||
−0.0304918 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(198\) | −2.56885 | −0.182560 | ||||||||
\(199\) | 19.4670 | 1.37998 | 0.689988 | − | 0.723820i | \(-0.257616\pi\) | ||||
0.689988 | + | 0.723820i | \(0.257616\pi\) | |||||||
\(200\) | −15.6842 | −1.10904 | ||||||||
\(201\) | 4.82522 | 0.340345 | ||||||||
\(202\) | 18.7036 | 1.31598 | ||||||||
\(203\) | −9.81288 | −0.688729 | ||||||||
\(204\) | 0.820135 | 0.0574209 | ||||||||
\(205\) | −15.2483 | −1.06499 | ||||||||
\(206\) | 7.00031 | 0.487735 | ||||||||
\(207\) | −5.70497 | −0.396523 | ||||||||
\(208\) | 0.229427 | 0.0159079 | ||||||||
\(209\) | 2.93110 | 0.202748 | ||||||||
\(210\) | −6.60895 | −0.456061 | ||||||||
\(211\) | −9.18507 | −0.632327 | −0.316163 | − | 0.948705i | \(-0.602395\pi\) | ||||
−0.316163 | + | 0.948705i | \(0.602395\pi\) | |||||||
\(212\) | 0.158664 | 0.0108971 | ||||||||
\(213\) | 8.61413 | 0.590231 | ||||||||
\(214\) | 16.7144 | 1.14257 | ||||||||
\(215\) | −1.09682 | −0.0748023 | ||||||||
\(216\) | 1.98138 | 0.134816 | ||||||||
\(217\) | 2.12046 | 0.143946 | ||||||||
\(218\) | −10.5079 | −0.711687 | ||||||||
\(219\) | −14.1239 | −0.954402 | ||||||||
\(220\) | −4.50869 | −0.303976 | ||||||||
\(221\) | 0.0461842 | 0.00310668 | ||||||||
\(222\) | 10.1120 | 0.678674 | ||||||||
\(223\) | −15.0124 | −1.00530 | −0.502652 | − | 0.864489i | \(-0.667642\pi\) | ||||
−0.502652 | + | 0.864489i | \(0.667642\pi\) | |||||||
\(224\) | −4.79585 | −0.320436 | ||||||||
\(225\) | 7.91581 | 0.527721 | ||||||||
\(226\) | 5.36794 | 0.357070 | ||||||||
\(227\) | 19.0896 | 1.26702 | 0.633509 | − | 0.773735i | \(-0.281614\pi\) | ||||
0.633509 | + | 0.773735i | \(0.281614\pi\) | |||||||
\(228\) | 1.57149 | 0.104074 | ||||||||
\(229\) | −14.5725 | −0.962978 | −0.481489 | − | 0.876452i | \(-0.659904\pi\) | ||||
−0.481489 | + | 0.876452i | \(0.659904\pi\) | |||||||
\(230\) | −34.4310 | −2.27031 | ||||||||
\(231\) | 1.67510 | 0.110213 | ||||||||
\(232\) | 17.7553 | 1.16569 | ||||||||
\(233\) | −9.19047 | −0.602087 | −0.301044 | − | 0.953610i | \(-0.597335\pi\) | ||||
−0.301044 | + | 0.953610i | \(0.597335\pi\) | |||||||
\(234\) | −0.0775583 | −0.00507014 | ||||||||
\(235\) | 20.5658 | 1.34157 | ||||||||
\(236\) | −1.90488 | −0.123997 | ||||||||
\(237\) | −4.00757 | −0.260320 | ||||||||
\(238\) | −1.83896 | −0.119202 | ||||||||
\(239\) | −29.9619 | −1.93808 | −0.969038 | − | 0.246911i | \(-0.920584\pi\) | ||||
−0.969038 | + | 0.246911i | \(0.920584\pi\) | |||||||
\(240\) | 17.8530 | 1.15241 | ||||||||
\(241\) | −0.260683 | −0.0167921 | −0.00839604 | − | 0.999965i | \(-0.502673\pi\) | ||||
−0.00839604 | + | 0.999965i | \(0.502673\pi\) | |||||||
\(242\) | −14.5430 | −0.934861 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.2022 | −0.781166 | ||||||||
\(245\) | −20.8474 | −1.33189 | ||||||||
\(246\) | 7.12516 | 0.454284 | ||||||||
\(247\) | 0.0884951 | 0.00563081 | ||||||||
\(248\) | −3.83672 | −0.243632 | ||||||||
\(249\) | 3.07445 | 0.194835 | ||||||||
\(250\) | 17.5976 | 1.11297 | ||||||||
\(251\) | 28.8017 | 1.81795 | 0.908974 | − | 0.416853i | \(-0.136867\pi\) | ||||
0.908974 | + | 0.416853i | \(0.136867\pi\) | |||||||
\(252\) | 0.898094 | 0.0565746 | ||||||||
\(253\) | 8.72685 | 0.548653 | ||||||||
\(254\) | −10.9724 | −0.688472 | ||||||||
\(255\) | 3.59386 | 0.225056 | ||||||||
\(256\) | 16.8258 | 1.05161 | ||||||||
\(257\) | −13.0022 | −0.811057 | −0.405529 | − | 0.914082i | \(-0.632913\pi\) | ||||
−0.405529 | + | 0.914082i | \(0.632913\pi\) | |||||||
\(258\) | 0.512517 | 0.0319079 | ||||||||
\(259\) | −6.59386 | −0.409722 | ||||||||
\(260\) | −0.136125 | −0.00844214 | ||||||||
\(261\) | −8.96107 | −0.554676 | ||||||||
\(262\) | 10.7825 | 0.666147 | ||||||||
\(263\) | 11.3986 | 0.702866 | 0.351433 | − | 0.936213i | \(-0.385695\pi\) | ||||
0.351433 | + | 0.936213i | \(0.385695\pi\) | |||||||
\(264\) | −3.03090 | −0.186539 | ||||||||
\(265\) | 0.695273 | 0.0427103 | ||||||||
\(266\) | −3.52369 | −0.216051 | ||||||||
\(267\) | 2.17593 | 0.133165 | ||||||||
\(268\) | −3.95733 | −0.241733 | ||||||||
\(269\) | −10.6849 | −0.651473 | −0.325736 | − | 0.945461i | \(-0.605612\pi\) | ||||
−0.325736 | + | 0.945461i | \(0.605612\pi\) | |||||||
\(270\) | −6.03526 | −0.367294 | ||||||||
\(271\) | −10.3987 | −0.631677 | −0.315839 | − | 0.948813i | \(-0.602286\pi\) | ||||
−0.315839 | + | 0.948813i | \(0.602286\pi\) | |||||||
\(272\) | 4.96765 | 0.301208 | ||||||||
\(273\) | 0.0505743 | 0.00306089 | ||||||||
\(274\) | 14.7634 | 0.891888 | ||||||||
\(275\) | −12.1087 | −0.730185 | ||||||||
\(276\) | 4.67885 | 0.281633 | ||||||||
\(277\) | −4.41176 | −0.265077 | −0.132538 | − | 0.991178i | \(-0.542313\pi\) | ||||
−0.132538 | + | 0.991178i | \(0.542313\pi\) | |||||||
\(278\) | −0.996069 | −0.0597402 | ||||||||
\(279\) | 1.93639 | 0.115929 | ||||||||
\(280\) | −7.79767 | −0.466000 | ||||||||
\(281\) | −2.71894 | −0.162198 | −0.0810992 | − | 0.996706i | \(-0.525843\pi\) | ||||
−0.0810992 | + | 0.996706i | \(0.525843\pi\) | |||||||
\(282\) | −9.60993 | −0.572263 | ||||||||
\(283\) | −9.80213 | −0.582676 | −0.291338 | − | 0.956620i | \(-0.594100\pi\) | ||||
−0.291338 | + | 0.956620i | \(0.594100\pi\) | |||||||
\(284\) | −7.06475 | −0.419216 | ||||||||
\(285\) | 6.88631 | 0.407910 | ||||||||
\(286\) | 0.118640 | 0.00701535 | ||||||||
\(287\) | −4.64618 | −0.274255 | ||||||||
\(288\) | −4.37954 | −0.258067 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −54.0823 | −3.17582 | ||||||||
\(291\) | 15.4254 | 0.904252 | ||||||||
\(292\) | 11.5835 | 0.677871 | ||||||||
\(293\) | 18.5396 | 1.08309 | 0.541547 | − | 0.840670i | \(-0.317839\pi\) | ||||
0.541547 | + | 0.840670i | \(0.317839\pi\) | |||||||
\(294\) | 9.74152 | 0.568137 | ||||||||
\(295\) | −8.34726 | −0.485996 | ||||||||
\(296\) | 11.9308 | 0.693465 | ||||||||
\(297\) | 1.52969 | 0.0887617 | ||||||||
\(298\) | 15.8585 | 0.918661 | ||||||||
\(299\) | 0.263479 | 0.0152374 | ||||||||
\(300\) | −6.49203 | −0.374817 | ||||||||
\(301\) | −0.334203 | −0.0192631 | ||||||||
\(302\) | 26.5336 | 1.52684 | ||||||||
\(303\) | −11.1376 | −0.639837 | ||||||||
\(304\) | 9.51868 | 0.545934 | ||||||||
\(305\) | −53.4704 | −3.06171 | ||||||||
\(306\) | −1.67933 | −0.0960007 | ||||||||
\(307\) | 12.4781 | 0.712161 | 0.356080 | − | 0.934455i | \(-0.384113\pi\) | ||||
0.356080 | + | 0.934455i | \(0.384113\pi\) | |||||||
\(308\) | −1.37381 | −0.0782799 | ||||||||
\(309\) | −4.16853 | −0.237139 | ||||||||
\(310\) | 11.6866 | 0.663755 | ||||||||
\(311\) | −5.40547 | −0.306516 | −0.153258 | − | 0.988186i | \(-0.548977\pi\) | ||||
−0.153258 | + | 0.988186i | \(0.548977\pi\) | |||||||
\(312\) | −0.0915083 | −0.00518064 | ||||||||
\(313\) | 22.9439 | 1.29687 | 0.648433 | − | 0.761272i | \(-0.275425\pi\) | ||||
0.648433 | + | 0.761272i | \(0.275425\pi\) | |||||||
\(314\) | −1.67933 | −0.0947698 | ||||||||
\(315\) | 3.93548 | 0.221739 | ||||||||
\(316\) | 3.28674 | 0.184894 | ||||||||
\(317\) | 32.7680 | 1.84043 | 0.920217 | − | 0.391410i | \(-0.128012\pi\) | ||||
0.920217 | + | 0.391410i | \(0.128012\pi\) | |||||||
\(318\) | −0.324885 | −0.0182186 | ||||||||
\(319\) | 13.7077 | 0.767483 | ||||||||
\(320\) | 9.27437 | 0.518453 | ||||||||
\(321\) | −9.95303 | −0.555524 | ||||||||
\(322\) | −10.4912 | −0.584652 | ||||||||
\(323\) | 1.91613 | 0.106617 | ||||||||
\(324\) | 0.820135 | 0.0455630 | ||||||||
\(325\) | −0.365585 | −0.0202790 | ||||||||
\(326\) | 14.3828 | 0.796590 | ||||||||
\(327\) | 6.25723 | 0.346026 | ||||||||
\(328\) | 8.40673 | 0.464184 | ||||||||
\(329\) | 6.26645 | 0.345481 | ||||||||
\(330\) | 9.23208 | 0.508210 | ||||||||
\(331\) | −3.68621 | −0.202613 | −0.101306 | − | 0.994855i | \(-0.532302\pi\) | ||||
−0.101306 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(332\) | −2.52146 | −0.138383 | ||||||||
\(333\) | −6.02148 | −0.329975 | ||||||||
\(334\) | −20.4179 | −1.11722 | ||||||||
\(335\) | −17.3412 | −0.947449 | ||||||||
\(336\) | 5.43986 | 0.296768 | ||||||||
\(337\) | 12.2642 | 0.668074 | 0.334037 | − | 0.942560i | \(-0.391589\pi\) | ||||
0.334037 | + | 0.942560i | \(0.391589\pi\) | |||||||
\(338\) | −21.8277 | −1.18727 | ||||||||
\(339\) | −3.19648 | −0.173609 | ||||||||
\(340\) | −2.94745 | −0.159848 | ||||||||
\(341\) | −2.96208 | −0.160406 | ||||||||
\(342\) | −3.21781 | −0.173999 | ||||||||
\(343\) | −14.0177 | −0.756882 | ||||||||
\(344\) | 0.604702 | 0.0326033 | ||||||||
\(345\) | 20.5029 | 1.10384 | ||||||||
\(346\) | −21.8583 | −1.17511 | ||||||||
\(347\) | 9.28716 | 0.498561 | 0.249280 | − | 0.968431i | \(-0.419806\pi\) | ||||
0.249280 | + | 0.968431i | \(0.419806\pi\) | |||||||
\(348\) | 7.34928 | 0.393963 | ||||||||
\(349\) | −29.4998 | −1.57909 | −0.789544 | − | 0.613695i | \(-0.789683\pi\) | ||||
−0.789544 | + | 0.613695i | \(0.789683\pi\) | |||||||
\(350\) | 14.5568 | 0.778095 | ||||||||
\(351\) | 0.0461842 | 0.00246513 | ||||||||
\(352\) | 6.69935 | 0.357077 | ||||||||
\(353\) | −15.0848 | −0.802882 | −0.401441 | − | 0.915885i | \(-0.631491\pi\) | ||||
−0.401441 | + | 0.915885i | \(0.631491\pi\) | |||||||
\(354\) | 3.90048 | 0.207308 | ||||||||
\(355\) | −30.9580 | −1.64308 | ||||||||
\(356\) | −1.78455 | −0.0945812 | ||||||||
\(357\) | 1.09506 | 0.0579565 | ||||||||
\(358\) | 8.50968 | 0.449750 | ||||||||
\(359\) | 3.23478 | 0.170725 | 0.0853626 | − | 0.996350i | \(-0.472795\pi\) | ||||
0.0853626 | + | 0.996350i | \(0.472795\pi\) | |||||||
\(360\) | −7.12079 | −0.375299 | ||||||||
\(361\) | −15.3284 | −0.806759 | ||||||||
\(362\) | −8.75644 | −0.460228 | ||||||||
\(363\) | 8.66004 | 0.454534 | ||||||||
\(364\) | −0.0414777 | −0.00217402 | ||||||||
\(365\) | 50.7591 | 2.65686 | ||||||||
\(366\) | 24.9855 | 1.30601 | ||||||||
\(367\) | 0.561855 | 0.0293286 | 0.0146643 | − | 0.999892i | \(-0.495332\pi\) | ||||
0.0146643 | + | 0.999892i | \(0.495332\pi\) | |||||||
\(368\) | 28.3403 | 1.47734 | ||||||||
\(369\) | −4.24287 | −0.220875 | ||||||||
\(370\) | −36.3412 | −1.88929 | ||||||||
\(371\) | 0.211851 | 0.0109988 | ||||||||
\(372\) | −1.58810 | −0.0823392 | ||||||||
\(373\) | 27.4552 | 1.42158 | 0.710789 | − | 0.703405i | \(-0.248338\pi\) | ||||
0.710789 | + | 0.703405i | \(0.248338\pi\) | |||||||
\(374\) | 2.56885 | 0.132832 | ||||||||
\(375\) | −10.4790 | −0.541133 | ||||||||
\(376\) | −11.3384 | −0.584735 | ||||||||
\(377\) | 0.413859 | 0.0213148 | ||||||||
\(378\) | −1.83896 | −0.0945857 | ||||||||
\(379\) | 9.73443 | 0.500024 | 0.250012 | − | 0.968243i | \(-0.419565\pi\) | ||||
0.250012 | + | 0.968243i | \(0.419565\pi\) | |||||||
\(380\) | −5.64770 | −0.289721 | ||||||||
\(381\) | 6.53383 | 0.334738 | ||||||||
\(382\) | 9.93488 | 0.508313 | ||||||||
\(383\) | −16.8676 | −0.861892 | −0.430946 | − | 0.902378i | \(-0.641820\pi\) | ||||
−0.430946 | + | 0.902378i | \(0.641820\pi\) | |||||||
\(384\) | −13.0928 | −0.668138 | ||||||||
\(385\) | −6.02007 | −0.306811 | ||||||||
\(386\) | 38.3386 | 1.95138 | ||||||||
\(387\) | −0.305192 | −0.0155138 | ||||||||
\(388\) | −12.6509 | −0.642252 | ||||||||
\(389\) | 11.4566 | 0.580873 | 0.290437 | − | 0.956894i | \(-0.406199\pi\) | ||||
0.290437 | + | 0.956894i | \(0.406199\pi\) | |||||||
\(390\) | 0.278733 | 0.0141142 | ||||||||
\(391\) | 5.70497 | 0.288513 | ||||||||
\(392\) | 11.4937 | 0.580519 | ||||||||
\(393\) | −6.42075 | −0.323884 | ||||||||
\(394\) | −1.43741 | −0.0724158 | ||||||||
\(395\) | 14.4026 | 0.724675 | ||||||||
\(396\) | −1.25455 | −0.0630437 | ||||||||
\(397\) | −32.8386 | −1.64812 | −0.824061 | − | 0.566501i | \(-0.808297\pi\) | ||||
−0.824061 | + | 0.566501i | \(0.808297\pi\) | |||||||
\(398\) | 32.6914 | 1.63867 | ||||||||
\(399\) | 2.09828 | 0.105045 | ||||||||
\(400\) | −39.3230 | −1.96615 | ||||||||
\(401\) | −36.5893 | −1.82718 | −0.913590 | − | 0.406636i | \(-0.866702\pi\) | ||||
−0.913590 | + | 0.406636i | \(0.866702\pi\) | |||||||
\(402\) | 8.10312 | 0.404147 | ||||||||
\(403\) | −0.0894306 | −0.00445486 | ||||||||
\(404\) | 9.13432 | 0.454449 | ||||||||
\(405\) | 3.59386 | 0.178580 | ||||||||
\(406\) | −16.4790 | −0.817840 | ||||||||
\(407\) | 9.21100 | 0.456573 | ||||||||
\(408\) | −1.98138 | −0.0980928 | ||||||||
\(409\) | −12.4925 | −0.617715 | −0.308858 | − | 0.951108i | \(-0.599947\pi\) | ||||
−0.308858 | + | 0.951108i | \(0.599947\pi\) | |||||||
\(410\) | −25.6068 | −1.26463 | ||||||||
\(411\) | −8.79125 | −0.433640 | ||||||||
\(412\) | 3.41875 | 0.168430 | ||||||||
\(413\) | −2.54343 | −0.125154 | ||||||||
\(414\) | −9.58051 | −0.470856 | ||||||||
\(415\) | −11.0491 | −0.542381 | ||||||||
\(416\) | 0.202266 | 0.00991688 | ||||||||
\(417\) | 0.593136 | 0.0290460 | ||||||||
\(418\) | 4.92226 | 0.240756 | ||||||||
\(419\) | −27.6888 | −1.35269 | −0.676344 | − | 0.736586i | \(-0.736437\pi\) | ||||
−0.676344 | + | 0.736586i | \(0.736437\pi\) | |||||||
\(420\) | −3.22762 | −0.157492 | ||||||||
\(421\) | 21.9880 | 1.07163 | 0.535815 | − | 0.844335i | \(-0.320004\pi\) | ||||
0.535815 | + | 0.844335i | \(0.320004\pi\) | |||||||
\(422\) | −15.4247 | −0.750864 | ||||||||
\(423\) | 5.72249 | 0.278237 | ||||||||
\(424\) | −0.383320 | −0.0186157 | ||||||||
\(425\) | −7.91581 | −0.383973 | ||||||||
\(426\) | 14.4659 | 0.700877 | ||||||||
\(427\) | −16.2926 | −0.788452 | ||||||||
\(428\) | 8.16283 | 0.394565 | ||||||||
\(429\) | −0.0706476 | −0.00341090 | ||||||||
\(430\) | −1.84191 | −0.0888250 | ||||||||
\(431\) | 4.78198 | 0.230340 | 0.115170 | − | 0.993346i | \(-0.463259\pi\) | ||||
0.115170 | + | 0.993346i | \(0.463259\pi\) | |||||||
\(432\) | 4.96765 | 0.239006 | ||||||||
\(433\) | −17.8643 | −0.858503 | −0.429251 | − | 0.903185i | \(-0.641223\pi\) | ||||
−0.429251 | + | 0.903185i | \(0.641223\pi\) | |||||||
\(434\) | 3.56094 | 0.170931 | ||||||||
\(435\) | 32.2048 | 1.54410 | ||||||||
\(436\) | −5.13177 | −0.245767 | ||||||||
\(437\) | 10.9315 | 0.522924 | ||||||||
\(438\) | −23.7186 | −1.13332 | ||||||||
\(439\) | 12.3881 | 0.591252 | 0.295626 | − | 0.955304i | \(-0.404472\pi\) | ||||
0.295626 | + | 0.955304i | \(0.404472\pi\) | |||||||
\(440\) | 10.8926 | 0.519285 | ||||||||
\(441\) | −5.80085 | −0.276231 | ||||||||
\(442\) | 0.0775583 | 0.00368907 | ||||||||
\(443\) | −19.2163 | −0.912995 | −0.456498 | − | 0.889725i | \(-0.650896\pi\) | ||||
−0.456498 | + | 0.889725i | \(0.650896\pi\) | |||||||
\(444\) | 4.93842 | 0.234367 | ||||||||
\(445\) | −7.81998 | −0.370703 | ||||||||
\(446\) | −25.2107 | −1.19376 | ||||||||
\(447\) | −9.44340 | −0.446658 | ||||||||
\(448\) | 2.82592 | 0.133512 | ||||||||
\(449\) | −8.50966 | −0.401596 | −0.200798 | − | 0.979633i | \(-0.564353\pi\) | ||||
−0.200798 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(450\) | 13.2932 | 0.626648 | ||||||||
\(451\) | 6.49028 | 0.305616 | ||||||||
\(452\) | 2.62155 | 0.123307 | ||||||||
\(453\) | −15.8001 | −0.742356 | ||||||||
\(454\) | 32.0576 | 1.50454 | ||||||||
\(455\) | −0.181757 | −0.00852088 | ||||||||
\(456\) | −3.79659 | −0.177791 | ||||||||
\(457\) | −30.1291 | −1.40938 | −0.704689 | − | 0.709516i | \(-0.748914\pi\) | ||||
−0.704689 | + | 0.709516i | \(0.748914\pi\) | |||||||
\(458\) | −24.4720 | −1.14350 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −16.8151 | −0.784008 | ||||||||
\(461\) | 16.4091 | 0.764249 | 0.382124 | − | 0.924111i | \(-0.375193\pi\) | ||||
0.382124 | + | 0.924111i | \(0.375193\pi\) | |||||||
\(462\) | 2.81304 | 0.130874 | ||||||||
\(463\) | −31.4518 | −1.46169 | −0.730844 | − | 0.682545i | \(-0.760873\pi\) | ||||
−0.730844 | + | 0.682545i | \(0.760873\pi\) | |||||||
\(464\) | 44.5154 | 2.06658 | ||||||||
\(465\) | −6.95911 | −0.322721 | ||||||||
\(466\) | −15.4338 | −0.714956 | ||||||||
\(467\) | 4.39800 | 0.203515 | 0.101757 | − | 0.994809i | \(-0.467553\pi\) | ||||
0.101757 | + | 0.994809i | \(0.467553\pi\) | |||||||
\(468\) | −0.0378772 | −0.00175088 | ||||||||
\(469\) | −5.28389 | −0.243987 | ||||||||
\(470\) | 34.5367 | 1.59306 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 4.60204 | 0.211826 | ||||||||
\(473\) | 0.466850 | 0.0214658 | ||||||||
\(474\) | −6.73001 | −0.309120 | ||||||||
\(475\) | −15.1678 | −0.695944 | ||||||||
\(476\) | −0.898094 | −0.0411641 | ||||||||
\(477\) | 0.193461 | 0.00885799 | ||||||||
\(478\) | −50.3158 | −2.30139 | ||||||||
\(479\) | −15.6060 | −0.713056 | −0.356528 | − | 0.934285i | \(-0.616040\pi\) | ||||
−0.356528 | + | 0.934285i | \(0.616040\pi\) | |||||||
\(480\) | 15.7395 | 0.718404 | ||||||||
\(481\) | 0.278097 | 0.0126801 | ||||||||
\(482\) | −0.437772 | −0.0199400 | ||||||||
\(483\) | 6.24727 | 0.284261 | ||||||||
\(484\) | −7.10240 | −0.322836 | ||||||||
\(485\) | −55.4366 | −2.51725 | ||||||||
\(486\) | −1.67933 | −0.0761758 | ||||||||
\(487\) | 40.2640 | 1.82454 | 0.912268 | − | 0.409594i | \(-0.134330\pi\) | ||||
0.912268 | + | 0.409594i | \(0.134330\pi\) | |||||||
\(488\) | 29.4795 | 1.33447 | ||||||||
\(489\) | −8.56463 | −0.387306 | ||||||||
\(490\) | −35.0096 | −1.58157 | ||||||||
\(491\) | −30.9388 | −1.39625 | −0.698124 | − | 0.715976i | \(-0.745982\pi\) | ||||
−0.698124 | + | 0.715976i | \(0.745982\pi\) | |||||||
\(492\) | 3.47972 | 0.156878 | ||||||||
\(493\) | 8.96107 | 0.403586 | ||||||||
\(494\) | 0.148612 | 0.00668637 | ||||||||
\(495\) | −5.49749 | −0.247094 | ||||||||
\(496\) | −9.61931 | −0.431920 | ||||||||
\(497\) | −9.43296 | −0.423126 | ||||||||
\(498\) | 5.16300 | 0.231360 | ||||||||
\(499\) | −5.81475 | −0.260304 | −0.130152 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130152 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(500\) | 8.59419 | 0.384344 | ||||||||
\(501\) | 12.1584 | 0.543197 | ||||||||
\(502\) | 48.3674 | 2.15874 | ||||||||
\(503\) | −26.0840 | −1.16303 | −0.581514 | − | 0.813536i | \(-0.697539\pi\) | ||||
−0.581514 | + | 0.813536i | \(0.697539\pi\) | |||||||
\(504\) | −2.16972 | −0.0966471 | ||||||||
\(505\) | 40.0269 | 1.78117 | ||||||||
\(506\) | 14.6552 | 0.651504 | ||||||||
\(507\) | 12.9979 | 0.577256 | ||||||||
\(508\) | −5.35862 | −0.237750 | ||||||||
\(509\) | −4.63729 | −0.205544 | −0.102772 | − | 0.994705i | \(-0.532771\pi\) | ||||
−0.102772 | + | 0.994705i | \(0.532771\pi\) | |||||||
\(510\) | 6.03526 | 0.267246 | ||||||||
\(511\) | 15.4664 | 0.684195 | ||||||||
\(512\) | 2.07045 | 0.0915017 | ||||||||
\(513\) | 1.91613 | 0.0845994 | ||||||||
\(514\) | −21.8350 | −0.963100 | ||||||||
\(515\) | 14.9811 | 0.660146 | ||||||||
\(516\) | 0.250299 | 0.0110188 | ||||||||
\(517\) | −8.75366 | −0.384985 | ||||||||
\(518\) | −11.0732 | −0.486530 | ||||||||
\(519\) | 13.0161 | 0.571345 | ||||||||
\(520\) | 0.328868 | 0.0144218 | ||||||||
\(521\) | −14.0071 | −0.613662 | −0.306831 | − | 0.951764i | \(-0.599269\pi\) | ||||
−0.306831 | + | 0.951764i | \(0.599269\pi\) | |||||||
\(522\) | −15.0486 | −0.658657 | ||||||||
\(523\) | 19.8939 | 0.869901 | 0.434951 | − | 0.900454i | \(-0.356766\pi\) | ||||
0.434951 | + | 0.900454i | \(0.356766\pi\) | |||||||
\(524\) | 5.26588 | 0.230041 | ||||||||
\(525\) | −8.66826 | −0.378314 | ||||||||
\(526\) | 19.1419 | 0.834627 | ||||||||
\(527\) | −1.93639 | −0.0843505 | ||||||||
\(528\) | −7.59897 | −0.330703 | ||||||||
\(529\) | 9.54673 | 0.415075 | ||||||||
\(530\) | 1.16759 | 0.0507168 | ||||||||
\(531\) | −2.32265 | −0.100794 | ||||||||
\(532\) | −1.72087 | −0.0746091 | ||||||||
\(533\) | 0.195953 | 0.00848768 | ||||||||
\(534\) | 3.65409 | 0.158128 | ||||||||
\(535\) | 35.7698 | 1.54646 | ||||||||
\(536\) | 9.56059 | 0.412955 | ||||||||
\(537\) | −5.06732 | −0.218671 | ||||||||
\(538\) | −17.9435 | −0.773599 | ||||||||
\(539\) | 8.87352 | 0.382209 | ||||||||
\(540\) | −2.94745 | −0.126838 | ||||||||
\(541\) | −28.7557 | −1.23631 | −0.618153 | − | 0.786058i | \(-0.712119\pi\) | ||||
−0.618153 | + | 0.786058i | \(0.712119\pi\) | |||||||
\(542\) | −17.4628 | −0.750093 | ||||||||
\(543\) | 5.21426 | 0.223765 | ||||||||
\(544\) | 4.37954 | 0.187771 | ||||||||
\(545\) | −22.4876 | −0.963263 | ||||||||
\(546\) | 0.0849307 | 0.00363470 | ||||||||
\(547\) | −4.15252 | −0.177549 | −0.0887745 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887745 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(548\) | 7.21001 | 0.307996 | ||||||||
\(549\) | −14.8783 | −0.634990 | ||||||||
\(550\) | −20.3345 | −0.867067 | ||||||||
\(551\) | 17.1706 | 0.731493 | ||||||||
\(552\) | −11.3037 | −0.481118 | ||||||||
\(553\) | 4.38851 | 0.186619 | ||||||||
\(554\) | −7.40878 | −0.314769 | ||||||||
\(555\) | 21.6403 | 0.918581 | ||||||||
\(556\) | −0.486451 | −0.0206301 | ||||||||
\(557\) | −33.7307 | −1.42922 | −0.714609 | − | 0.699524i | \(-0.753395\pi\) | ||||
−0.714609 | + | 0.699524i | \(0.753395\pi\) | |||||||
\(558\) | 3.25183 | 0.137661 | ||||||||
\(559\) | 0.0140951 | 0.000596157 0 | ||||||||
\(560\) | −19.5501 | −0.826141 | ||||||||
\(561\) | −1.52969 | −0.0645837 | ||||||||
\(562\) | −4.56599 | −0.192605 | ||||||||
\(563\) | 33.3227 | 1.40439 | 0.702193 | − | 0.711987i | \(-0.252204\pi\) | ||||
0.702193 | + | 0.711987i | \(0.252204\pi\) | |||||||
\(564\) | −4.69322 | −0.197620 | ||||||||
\(565\) | 11.4877 | 0.483291 | ||||||||
\(566\) | −16.4610 | −0.691906 | ||||||||
\(567\) | 1.09506 | 0.0459880 | ||||||||
\(568\) | 17.0679 | 0.716151 | ||||||||
\(569\) | −37.3867 | −1.56733 | −0.783665 | − | 0.621183i | \(-0.786652\pi\) | ||||
−0.783665 | + | 0.621183i | \(0.786652\pi\) | |||||||
\(570\) | 11.5644 | 0.484378 | ||||||||
\(571\) | 0.500722 | 0.0209546 | 0.0104773 | − | 0.999945i | \(-0.496665\pi\) | ||||
0.0104773 | + | 0.999945i | \(0.496665\pi\) | |||||||
\(572\) | 0.0579405 | 0.00242261 | ||||||||
\(573\) | −5.91599 | −0.247144 | ||||||||
\(574\) | −7.80245 | −0.325668 | ||||||||
\(575\) | −45.1595 | −1.88328 | ||||||||
\(576\) | 2.58062 | 0.107526 | ||||||||
\(577\) | −8.80915 | −0.366730 | −0.183365 | − | 0.983045i | \(-0.558699\pi\) | ||||
−0.183365 | + | 0.983045i | \(0.558699\pi\) | |||||||
\(578\) | 1.67933 | 0.0698507 | ||||||||
\(579\) | −22.8297 | −0.948772 | ||||||||
\(580\) | −26.4123 | −1.09671 | ||||||||
\(581\) | −3.36670 | −0.139674 | ||||||||
\(582\) | 25.9042 | 1.07377 | ||||||||
\(583\) | −0.295936 | −0.0122564 | ||||||||
\(584\) | −27.9847 | −1.15802 | ||||||||
\(585\) | −0.165979 | −0.00686240 | ||||||||
\(586\) | 31.1340 | 1.28613 | ||||||||
\(587\) | 47.2663 | 1.95089 | 0.975444 | − | 0.220246i | \(-0.0706860\pi\) | ||||
0.975444 | + | 0.220246i | \(0.0706860\pi\) | |||||||
\(588\) | 4.75748 | 0.196195 | ||||||||
\(589\) | −3.71039 | −0.152884 | ||||||||
\(590\) | −14.0178 | −0.577102 | ||||||||
\(591\) | 0.855946 | 0.0352089 | ||||||||
\(592\) | 29.9126 | 1.22940 | ||||||||
\(593\) | −0.274025 | −0.0112528 | −0.00562642 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562642 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(594\) | 2.56885 | 0.105401 | ||||||||
\(595\) | −3.93548 | −0.161339 | ||||||||
\(596\) | 7.74486 | 0.317242 | ||||||||
\(597\) | −19.4670 | −0.796730 | ||||||||
\(598\) | 0.442468 | 0.0180939 | ||||||||
\(599\) | 36.0529 | 1.47308 | 0.736542 | − | 0.676392i | \(-0.236458\pi\) | ||||
0.736542 | + | 0.676392i | \(0.236458\pi\) | |||||||
\(600\) | 15.6842 | 0.640305 | ||||||||
\(601\) | −14.6526 | −0.597693 | −0.298846 | − | 0.954301i | \(-0.596602\pi\) | ||||
−0.298846 | + | 0.954301i | \(0.596602\pi\) | |||||||
\(602\) | −0.561235 | −0.0228742 | ||||||||
\(603\) | −4.82522 | −0.196498 | ||||||||
\(604\) | 12.9582 | 0.527264 | ||||||||
\(605\) | −31.1230 | −1.26533 | ||||||||
\(606\) | −18.7036 | −0.759783 | ||||||||
\(607\) | −15.6217 | −0.634064 | −0.317032 | − | 0.948415i | \(-0.602686\pi\) | ||||
−0.317032 | + | 0.948415i | \(0.602686\pi\) | |||||||
\(608\) | 8.39179 | 0.340332 | ||||||||
\(609\) | 9.81288 | 0.397638 | ||||||||
\(610\) | −89.7943 | −3.63566 | ||||||||
\(611\) | −0.264289 | −0.0106920 | ||||||||
\(612\) | −0.820135 | −0.0331520 | ||||||||
\(613\) | 12.0078 | 0.484991 | 0.242496 | − | 0.970152i | \(-0.422034\pi\) | ||||
0.242496 | + | 0.970152i | \(0.422034\pi\) | |||||||
\(614\) | 20.9547 | 0.845664 | ||||||||
\(615\) | 15.2483 | 0.614870 | ||||||||
\(616\) | 3.31901 | 0.133727 | ||||||||
\(617\) | 14.9841 | 0.603237 | 0.301619 | − | 0.953429i | \(-0.402473\pi\) | ||||
0.301619 | + | 0.953429i | \(0.402473\pi\) | |||||||
\(618\) | −7.00031 | −0.281594 | ||||||||
\(619\) | −1.87009 | −0.0751654 | −0.0375827 | − | 0.999294i | \(-0.511966\pi\) | ||||
−0.0375827 | + | 0.999294i | \(0.511966\pi\) | |||||||
\(620\) | 5.70741 | 0.229215 | ||||||||
\(621\) | 5.70497 | 0.228933 | ||||||||
\(622\) | −9.07755 | −0.363977 | ||||||||
\(623\) | −2.38277 | −0.0954635 | ||||||||
\(624\) | −0.229427 | −0.00918442 | ||||||||
\(625\) | −1.91902 | −0.0767608 | ||||||||
\(626\) | 38.5303 | 1.53998 | ||||||||
\(627\) | −2.93110 | −0.117057 | ||||||||
\(628\) | −0.820135 | −0.0327269 | ||||||||
\(629\) | 6.02148 | 0.240092 | ||||||||
\(630\) | 6.60895 | 0.263307 | ||||||||
\(631\) | 45.2024 | 1.79948 | 0.899739 | − | 0.436428i | \(-0.143756\pi\) | ||||
0.899739 | + | 0.436428i | \(0.143756\pi\) | |||||||
\(632\) | −7.94051 | −0.315856 | ||||||||
\(633\) | 9.18507 | 0.365074 | ||||||||
\(634\) | 55.0281 | 2.18545 | ||||||||
\(635\) | −23.4817 | −0.931841 | ||||||||
\(636\) | −0.158664 | −0.00629145 | ||||||||
\(637\) | 0.267907 | 0.0106149 | ||||||||
\(638\) | 23.0197 | 0.911357 | ||||||||
\(639\) | −8.61413 | −0.340770 | ||||||||
\(640\) | 47.0536 | 1.85996 | ||||||||
\(641\) | −21.0744 | −0.832388 | −0.416194 | − | 0.909276i | \(-0.636636\pi\) | ||||
−0.416194 | + | 0.909276i | \(0.636636\pi\) | |||||||
\(642\) | −16.7144 | −0.659664 | ||||||||
\(643\) | −10.7588 | −0.424284 | −0.212142 | − | 0.977239i | \(-0.568044\pi\) | ||||
−0.212142 | + | 0.977239i | \(0.568044\pi\) | |||||||
\(644\) | −5.12360 | −0.201898 | ||||||||
\(645\) | 1.09682 | 0.0431872 | ||||||||
\(646\) | 3.21781 | 0.126603 | ||||||||
\(647\) | −43.4902 | −1.70978 | −0.854888 | − | 0.518812i | \(-0.826374\pi\) | ||||
−0.854888 | + | 0.518812i | \(0.826374\pi\) | |||||||
\(648\) | −1.98138 | −0.0778359 | ||||||||
\(649\) | 3.55293 | 0.139465 | ||||||||
\(650\) | −0.613936 | −0.0240806 | ||||||||
\(651\) | −2.12046 | −0.0831073 | ||||||||
\(652\) | 7.02415 | 0.275087 | ||||||||
\(653\) | 18.7651 | 0.734334 | 0.367167 | − | 0.930155i | \(-0.380328\pi\) | ||||
0.367167 | + | 0.930155i | \(0.380328\pi\) | |||||||
\(654\) | 10.5079 | 0.410893 | ||||||||
\(655\) | 23.0752 | 0.901625 | ||||||||
\(656\) | 21.0771 | 0.822922 | ||||||||
\(657\) | 14.1239 | 0.551024 | ||||||||
\(658\) | 10.5234 | 0.410246 | ||||||||
\(659\) | −9.87754 | −0.384774 | −0.192387 | − | 0.981319i | \(-0.561623\pi\) | ||||
−0.192387 | + | 0.981319i | \(0.561623\pi\) | |||||||
\(660\) | 4.50869 | 0.175500 | ||||||||
\(661\) | 44.2858 | 1.72252 | 0.861259 | − | 0.508167i | \(-0.169677\pi\) | ||||
0.861259 | + | 0.508167i | \(0.169677\pi\) | |||||||
\(662\) | −6.19035 | −0.240595 | ||||||||
\(663\) | −0.0461842 | −0.00179364 | ||||||||
\(664\) | 6.09165 | 0.236402 | ||||||||
\(665\) | −7.54090 | −0.292424 | ||||||||
\(666\) | −10.1120 | −0.391833 | ||||||||
\(667\) | 51.1227 | 1.97948 | ||||||||
\(668\) | −9.97151 | −0.385809 | ||||||||
\(669\) | 15.0124 | 0.580413 | ||||||||
\(670\) | −29.1215 | −1.12506 | ||||||||
\(671\) | 22.7592 | 0.878609 | ||||||||
\(672\) | 4.79585 | 0.185004 | ||||||||
\(673\) | 33.3030 | 1.28374 | 0.641868 | − | 0.766815i | \(-0.278160\pi\) | ||||
0.641868 | + | 0.766815i | \(0.278160\pi\) | |||||||
\(674\) | 20.5956 | 0.793312 | ||||||||
\(675\) | −7.91581 | −0.304680 | ||||||||
\(676\) | −10.6600 | −0.410000 | ||||||||
\(677\) | −37.4141 | −1.43794 | −0.718970 | − | 0.695041i | \(-0.755386\pi\) | ||||
−0.718970 | + | 0.695041i | \(0.755386\pi\) | |||||||
\(678\) | −5.36794 | −0.206154 | ||||||||
\(679\) | −16.8917 | −0.648243 | ||||||||
\(680\) | 7.12079 | 0.273070 | ||||||||
\(681\) | −19.0896 | −0.731513 | ||||||||
\(682\) | −4.97430 | −0.190476 | ||||||||
\(683\) | −18.1151 | −0.693156 | −0.346578 | − | 0.938021i | \(-0.612656\pi\) | ||||
−0.346578 | + | 0.938021i | \(0.612656\pi\) | |||||||
\(684\) | −1.57149 | −0.0600873 | ||||||||
\(685\) | 31.5945 | 1.20716 | ||||||||
\(686\) | −23.5402 | −0.898769 | ||||||||
\(687\) | 14.5725 | 0.555976 | ||||||||
\(688\) | 1.51609 | 0.0578003 | ||||||||
\(689\) | −0.00893485 | −0.000340391 0 | ||||||||
\(690\) | 34.4310 | 1.31076 | ||||||||
\(691\) | 39.2338 | 1.49252 | 0.746261 | − | 0.665653i | \(-0.231847\pi\) | ||||
0.746261 | + | 0.665653i | \(0.231847\pi\) | |||||||
\(692\) | −10.6750 | −0.405802 | ||||||||
\(693\) | −1.67510 | −0.0636318 | ||||||||
\(694\) | 15.5962 | 0.592022 | ||||||||
\(695\) | −2.13165 | −0.0808579 | ||||||||
\(696\) | −17.7553 | −0.673012 | ||||||||
\(697\) | 4.24287 | 0.160710 | ||||||||
\(698\) | −49.5397 | −1.87511 | ||||||||
\(699\) | 9.19047 | 0.347615 | ||||||||
\(700\) | 7.10914 | 0.268700 | ||||||||
\(701\) | 45.6812 | 1.72535 | 0.862677 | − | 0.505756i | \(-0.168786\pi\) | ||||
0.862677 | + | 0.505756i | \(0.168786\pi\) | |||||||
\(702\) | 0.0775583 | 0.00292725 | ||||||||
\(703\) | 11.5380 | 0.435162 | ||||||||
\(704\) | −3.94755 | −0.148779 | ||||||||
\(705\) | −20.5658 | −0.774554 | ||||||||
\(706\) | −25.3323 | −0.953392 | ||||||||
\(707\) | 12.1963 | 0.458688 | ||||||||
\(708\) | 1.90488 | 0.0715899 | ||||||||
\(709\) | −41.7290 | −1.56717 | −0.783583 | − | 0.621287i | \(-0.786610\pi\) | ||||
−0.783583 | + | 0.621287i | \(0.786610\pi\) | |||||||
\(710\) | −51.9885 | −1.95109 | ||||||||
\(711\) | 4.00757 | 0.150296 | ||||||||
\(712\) | 4.31134 | 0.161574 | ||||||||
\(713\) | −11.0471 | −0.413716 | ||||||||
\(714\) | 1.83896 | 0.0688212 | ||||||||
\(715\) | 0.253897 | 0.00949522 | ||||||||
\(716\) | 4.15588 | 0.155313 | ||||||||
\(717\) | 29.9619 | 1.11895 | ||||||||
\(718\) | 5.43225 | 0.202730 | ||||||||
\(719\) | 35.2895 | 1.31608 | 0.658038 | − | 0.752985i | \(-0.271387\pi\) | ||||
0.658038 | + | 0.752985i | \(0.271387\pi\) | |||||||
\(720\) | −17.8530 | −0.665343 | ||||||||
\(721\) | 4.56477 | 0.170001 | ||||||||
\(722\) | −25.7414 | −0.957997 | ||||||||
\(723\) | 0.260683 | 0.00969491 | ||||||||
\(724\) | −4.27639 | −0.158931 | ||||||||
\(725\) | −70.9341 | −2.63443 | ||||||||
\(726\) | 14.5430 | 0.539742 | ||||||||
\(727\) | −15.0621 | −0.558621 | −0.279311 | − | 0.960201i | \(-0.590106\pi\) | ||||
−0.279311 | + | 0.960201i | \(0.590106\pi\) | |||||||
\(728\) | 0.100207 | 0.00371391 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 85.2411 | 3.15492 | ||||||||
\(731\) | 0.305192 | 0.0112879 | ||||||||
\(732\) | 12.2022 | 0.451006 | ||||||||
\(733\) | −5.35920 | −0.197947 | −0.0989733 | − | 0.995090i | \(-0.531556\pi\) | ||||
−0.0989733 | + | 0.995090i | \(0.531556\pi\) | |||||||
\(734\) | 0.943537 | 0.0348266 | ||||||||
\(735\) | 20.8474 | 0.768969 | ||||||||
\(736\) | 24.9852 | 0.920966 | ||||||||
\(737\) | 7.38111 | 0.271887 | ||||||||
\(738\) | −7.12516 | −0.262281 | ||||||||
\(739\) | 21.0427 | 0.774067 | 0.387033 | − | 0.922066i | \(-0.373500\pi\) | ||||
0.387033 | + | 0.922066i | \(0.373500\pi\) | |||||||
\(740\) | −17.7480 | −0.652429 | ||||||||
\(741\) | −0.0884951 | −0.00325095 | ||||||||
\(742\) | 0.355767 | 0.0130606 | ||||||||
\(743\) | 38.4467 | 1.41047 | 0.705236 | − | 0.708973i | \(-0.250841\pi\) | ||||
0.705236 | + | 0.708973i | \(0.250841\pi\) | |||||||
\(744\) | 3.83672 | 0.140661 | ||||||||
\(745\) | 33.9382 | 1.24340 | ||||||||
\(746\) | 46.1063 | 1.68807 | ||||||||
\(747\) | −3.07445 | −0.112488 | ||||||||
\(748\) | 1.25455 | 0.0458710 | ||||||||
\(749\) | 10.8991 | 0.398246 | ||||||||
\(750\) | −17.5976 | −0.642575 | ||||||||
\(751\) | −14.4525 | −0.527377 | −0.263689 | − | 0.964608i | \(-0.584939\pi\) | ||||
−0.263689 | + | 0.964608i | \(0.584939\pi\) | |||||||
\(752\) | −28.4273 | −1.03664 | ||||||||
\(753\) | −28.8017 | −1.04959 | ||||||||
\(754\) | 0.695005 | 0.0253106 | ||||||||
\(755\) | 56.7835 | 2.06656 | ||||||||
\(756\) | −0.898094 | −0.0326633 | ||||||||
\(757\) | 16.9998 | 0.617867 | 0.308934 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308934 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(758\) | 16.3473 | 0.593760 | ||||||||
\(759\) | −8.72685 | −0.316765 | ||||||||
\(760\) | 13.6444 | 0.494934 | ||||||||
\(761\) | −7.92681 | −0.287346 | −0.143673 | − | 0.989625i | \(-0.545891\pi\) | ||||
−0.143673 | + | 0.989625i | \(0.545891\pi\) | |||||||
\(762\) | 10.9724 | 0.397489 | ||||||||
\(763\) | −6.85202 | −0.248060 | ||||||||
\(764\) | 4.85191 | 0.175536 | ||||||||
\(765\) | −3.59386 | −0.129936 | ||||||||
\(766\) | −28.3261 | −1.02346 | ||||||||
\(767\) | 0.107270 | 0.00387328 | ||||||||
\(768\) | −16.8258 | −0.607149 | ||||||||
\(769\) | −3.34933 | −0.120780 | −0.0603900 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603900 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(770\) | −10.1097 | −0.364327 | ||||||||
\(771\) | 13.0022 | 0.468264 | ||||||||
\(772\) | 18.7235 | 0.673872 | ||||||||
\(773\) | 30.4161 | 1.09399 | 0.546996 | − | 0.837135i | \(-0.315771\pi\) | ||||
0.546996 | + | 0.837135i | \(0.315771\pi\) | |||||||
\(774\) | −0.512517 | −0.0184221 | ||||||||
\(775\) | 15.3281 | 0.550602 | ||||||||
\(776\) | 30.5635 | 1.09717 | ||||||||
\(777\) | 6.59386 | 0.236553 | ||||||||
\(778\) | 19.2394 | 0.689765 | ||||||||
\(779\) | 8.12991 | 0.291284 | ||||||||
\(780\) | 0.136125 | 0.00487407 | ||||||||
\(781\) | 13.1770 | 0.471509 | ||||||||
\(782\) | 9.58051 | 0.342598 | ||||||||
\(783\) | 8.96107 | 0.320242 | ||||||||
\(784\) | 28.8166 | 1.02916 | ||||||||
\(785\) | −3.59386 | −0.128270 | ||||||||
\(786\) | −10.7825 | −0.384600 | ||||||||
\(787\) | −8.20172 | −0.292360 | −0.146180 | − | 0.989258i | \(-0.546698\pi\) | ||||
−0.146180 | + | 0.989258i | \(0.546698\pi\) | |||||||
\(788\) | −0.701991 | −0.0250074 | ||||||||
\(789\) | −11.3986 | −0.405800 | ||||||||
\(790\) | 24.1867 | 0.860524 | ||||||||
\(791\) | 3.50033 | 0.124457 | ||||||||
\(792\) | 3.03090 | 0.107698 | ||||||||
\(793\) | 0.687141 | 0.0244011 | ||||||||
\(794\) | −55.1467 | −1.95708 | ||||||||
\(795\) | −0.695273 | −0.0246588 | ||||||||
\(796\) | 15.9655 | 0.565883 | ||||||||
\(797\) | −21.7121 | −0.769083 | −0.384541 | − | 0.923108i | \(-0.625640\pi\) | ||||
−0.384541 | + | 0.923108i | \(0.625640\pi\) | |||||||
\(798\) | 3.52369 | 0.124737 | ||||||||
\(799\) | −5.72249 | −0.202447 | ||||||||
\(800\) | −34.6676 | −1.22569 | ||||||||
\(801\) | −2.17593 | −0.0768827 | ||||||||
\(802\) | −61.4453 | −2.16971 | ||||||||
\(803\) | −21.6052 | −0.762430 | ||||||||
\(804\) | 3.95733 | 0.139564 | ||||||||
\(805\) | −22.4518 | −0.791322 | ||||||||
\(806\) | −0.150183 | −0.00528998 | ||||||||
\(807\) | 10.6849 | 0.376128 | ||||||||
\(808\) | −22.0678 | −0.776341 | ||||||||
\(809\) | −43.3879 | −1.52544 | −0.762718 | − | 0.646731i | \(-0.776136\pi\) | ||||
−0.762718 | + | 0.646731i | \(0.776136\pi\) | |||||||
\(810\) | 6.03526 | 0.212057 | ||||||||
\(811\) | −46.3570 | −1.62781 | −0.813907 | − | 0.580995i | \(-0.802664\pi\) | ||||
−0.813907 | + | 0.580995i | \(0.802664\pi\) | |||||||
\(812\) | −8.04788 | −0.282425 | ||||||||
\(813\) | 10.3987 | 0.364699 | ||||||||
\(814\) | 15.4683 | 0.542163 | ||||||||
\(815\) | 30.7801 | 1.07818 | ||||||||
\(816\) | −4.96765 | −0.173902 | ||||||||
\(817\) | 0.584790 | 0.0204592 | ||||||||
\(818\) | −20.9790 | −0.733514 | ||||||||
\(819\) | −0.0505743 | −0.00176721 | ||||||||
\(820\) | −12.5056 | −0.436716 | ||||||||
\(821\) | −0.510003 | −0.0177992 | −0.00889961 | − | 0.999960i | \(-0.502833\pi\) | ||||
−0.00889961 | + | 0.999960i | \(0.502833\pi\) | |||||||
\(822\) | −14.7634 | −0.514932 | ||||||||
\(823\) | −33.4611 | −1.16638 | −0.583190 | − | 0.812336i | \(-0.698196\pi\) | ||||
−0.583190 | + | 0.812336i | \(0.698196\pi\) | |||||||
\(824\) | −8.25943 | −0.287731 | ||||||||
\(825\) | 12.1087 | 0.421573 | ||||||||
\(826\) | −4.27125 | −0.148616 | ||||||||
\(827\) | −40.2051 | −1.39807 | −0.699035 | − | 0.715088i | \(-0.746387\pi\) | ||||
−0.699035 | + | 0.715088i | \(0.746387\pi\) | |||||||
\(828\) | −4.67885 | −0.162601 | ||||||||
\(829\) | 16.1426 | 0.560655 | 0.280327 | − | 0.959904i | \(-0.409557\pi\) | ||||
0.280327 | + | 0.959904i | \(0.409557\pi\) | |||||||
\(830\) | −18.5551 | −0.644057 | ||||||||
\(831\) | 4.41176 | 0.153042 | ||||||||
\(832\) | −0.119184 | −0.00413195 | ||||||||
\(833\) | 5.80085 | 0.200988 | ||||||||
\(834\) | 0.996069 | 0.0344910 | ||||||||
\(835\) | −43.6955 | −1.51214 | ||||||||
\(836\) | 2.40389 | 0.0831404 | ||||||||
\(837\) | −1.93639 | −0.0669315 | ||||||||
\(838\) | −46.4985 | −1.60627 | ||||||||
\(839\) | 49.4308 | 1.70654 | 0.853270 | − | 0.521469i | \(-0.174616\pi\) | ||||
0.853270 | + | 0.521469i | \(0.174616\pi\) | |||||||
\(840\) | 7.79767 | 0.269045 | ||||||||
\(841\) | 51.3008 | 1.76899 | ||||||||
\(842\) | 36.9251 | 1.27252 | ||||||||
\(843\) | 2.71894 | 0.0936453 | ||||||||
\(844\) | −7.53300 | −0.259296 | ||||||||
\(845\) | −46.7125 | −1.60696 | ||||||||
\(846\) | 9.60993 | 0.330396 | ||||||||
\(847\) | −9.48323 | −0.325848 | ||||||||
\(848\) | −0.961048 | −0.0330025 | ||||||||
\(849\) | 9.80213 | 0.336408 | ||||||||
\(850\) | −13.2932 | −0.455954 | ||||||||
\(851\) | 34.3524 | 1.17758 | ||||||||
\(852\) | 7.06475 | 0.242034 | ||||||||
\(853\) | 17.4755 | 0.598351 | 0.299176 | − | 0.954198i | \(-0.403288\pi\) | ||||
0.299176 | + | 0.954198i | \(0.403288\pi\) | |||||||
\(854\) | −27.3605 | −0.936258 | ||||||||
\(855\) | −6.88631 | −0.235507 | ||||||||
\(856\) | −19.7207 | −0.674040 | ||||||||
\(857\) | −15.6295 | −0.533892 | −0.266946 | − | 0.963711i | \(-0.586015\pi\) | ||||
−0.266946 | + | 0.963711i | \(0.586015\pi\) | |||||||
\(858\) | −0.118640 | −0.00405031 | ||||||||
\(859\) | 7.67136 | 0.261743 | 0.130872 | − | 0.991399i | \(-0.458222\pi\) | ||||
0.130872 | + | 0.991399i | \(0.458222\pi\) | |||||||
\(860\) | −0.899538 | −0.0306740 | ||||||||
\(861\) | 4.64618 | 0.158341 | ||||||||
\(862\) | 8.03050 | 0.273520 | ||||||||
\(863\) | 22.4197 | 0.763176 | 0.381588 | − | 0.924333i | \(-0.375377\pi\) | ||||
0.381588 | + | 0.924333i | \(0.375377\pi\) | |||||||
\(864\) | 4.37954 | 0.148995 | ||||||||
\(865\) | −46.7781 | −1.59050 | ||||||||
\(866\) | −29.9999 | −1.01944 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 1.73906 | 0.0590276 | ||||||||
\(869\) | −6.13035 | −0.207958 | ||||||||
\(870\) | 54.0823 | 1.83356 | ||||||||
\(871\) | 0.222849 | 0.00755095 | ||||||||
\(872\) | 12.3979 | 0.419847 | ||||||||
\(873\) | −15.4254 | −0.522070 | ||||||||
\(874\) | 18.3575 | 0.620953 | ||||||||
\(875\) | 11.4751 | 0.387929 | ||||||||
\(876\) | −11.5835 | −0.391369 | ||||||||
\(877\) | 6.51262 | 0.219915 | 0.109958 | − | 0.993936i | \(-0.464928\pi\) | ||||
0.109958 | + | 0.993936i | \(0.464928\pi\) | |||||||
\(878\) | 20.8037 | 0.702089 | ||||||||
\(879\) | −18.5396 | −0.625325 | ||||||||
\(880\) | 27.3096 | 0.920607 | ||||||||
\(881\) | −8.28718 | −0.279202 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(882\) | −9.74152 | −0.328014 | ||||||||
\(883\) | 13.4417 | 0.452348 | 0.226174 | − | 0.974087i | \(-0.427378\pi\) | ||||
0.226174 | + | 0.974087i | \(0.427378\pi\) | |||||||
\(884\) | 0.0378772 | 0.00127395 | ||||||||
\(885\) | 8.34726 | 0.280590 | ||||||||
\(886\) | −32.2705 | −1.08415 | ||||||||
\(887\) | 15.7191 | 0.527794 | 0.263897 | − | 0.964551i | \(-0.414992\pi\) | ||||
0.263897 | + | 0.964551i | \(0.414992\pi\) | |||||||
\(888\) | −11.9308 | −0.400372 | ||||||||
\(889\) | −7.15491 | −0.239968 | ||||||||
\(890\) | −13.1323 | −0.440195 | ||||||||
\(891\) | −1.52969 | −0.0512466 | ||||||||
\(892\) | −12.3122 | −0.412243 | ||||||||
\(893\) | −10.9651 | −0.366932 | ||||||||
\(894\) | −15.8585 | −0.530389 | ||||||||
\(895\) | 18.2112 | 0.608734 | ||||||||
\(896\) | 14.3373 | 0.478977 | ||||||||
\(897\) | −0.263479 | −0.00879732 | ||||||||
\(898\) | −14.2905 | −0.476880 | ||||||||
\(899\) | −17.3521 | −0.578726 | ||||||||
\(900\) | 6.49203 | 0.216401 | ||||||||
\(901\) | −0.193461 | −0.00644513 | ||||||||
\(902\) | 10.8993 | 0.362907 | ||||||||
\(903\) | 0.334203 | 0.0111216 | ||||||||
\(904\) | −6.33344 | −0.210647 | ||||||||
\(905\) | −18.7393 | −0.622915 | ||||||||
\(906\) | −26.5336 | −0.881520 | ||||||||
\(907\) | 45.1858 | 1.50037 | 0.750185 | − | 0.661228i | \(-0.229965\pi\) | ||||
0.750185 | + | 0.661228i | \(0.229965\pi\) | |||||||
\(908\) | 15.6560 | 0.519563 | ||||||||
\(909\) | 11.1376 | 0.369410 | ||||||||
\(910\) | −0.305229 | −0.0101182 | ||||||||
\(911\) | 52.5562 | 1.74127 | 0.870633 | − | 0.491933i | \(-0.163710\pi\) | ||||
0.870633 | + | 0.491933i | \(0.163710\pi\) | |||||||
\(912\) | −9.51868 | −0.315195 | ||||||||
\(913\) | 4.70296 | 0.155645 | ||||||||
\(914\) | −50.5965 | −1.67358 | ||||||||
\(915\) | 53.4704 | 1.76768 | ||||||||
\(916\) | −11.9514 | −0.394886 | ||||||||
\(917\) | 7.03108 | 0.232187 | ||||||||
\(918\) | 1.67933 | 0.0554260 | ||||||||
\(919\) | 59.2062 | 1.95303 | 0.976517 | − | 0.215441i | \(-0.0691188\pi\) | ||||
0.976517 | + | 0.215441i | \(0.0691188\pi\) | |||||||
\(920\) | 40.6239 | 1.33933 | ||||||||
\(921\) | −12.4781 | −0.411166 | ||||||||
\(922\) | 27.5563 | 0.907517 | ||||||||
\(923\) | 0.397837 | 0.0130950 | ||||||||
\(924\) | 1.37381 | 0.0451949 | ||||||||
\(925\) | −47.6649 | −1.56721 | ||||||||
\(926\) | −52.8178 | −1.73570 | ||||||||
\(927\) | 4.16853 | 0.136912 | ||||||||
\(928\) | 39.2454 | 1.28829 | ||||||||
\(929\) | 54.0557 | 1.77351 | 0.886755 | − | 0.462239i | \(-0.152954\pi\) | ||||
0.886755 | + | 0.462239i | \(0.152954\pi\) | |||||||
\(930\) | −11.6866 | −0.383219 | ||||||||
\(931\) | 11.1152 | 0.364286 | ||||||||
\(932\) | −7.53742 | −0.246896 | ||||||||
\(933\) | 5.40547 | 0.176967 | ||||||||
\(934\) | 7.38567 | 0.241666 | ||||||||
\(935\) | 5.49749 | 0.179787 | ||||||||
\(936\) | 0.0915083 | 0.00299104 | ||||||||
\(937\) | −56.3169 | −1.83979 | −0.919897 | − | 0.392160i | \(-0.871728\pi\) | ||||
−0.919897 | + | 0.392160i | \(0.871728\pi\) | |||||||
\(938\) | −8.87338 | −0.289726 | ||||||||
\(939\) | −22.9439 | −0.748746 | ||||||||
\(940\) | 16.8667 | 0.550133 | ||||||||
\(941\) | 32.9031 | 1.07261 | 0.536305 | − | 0.844024i | \(-0.319820\pi\) | ||||
0.536305 | + | 0.844024i | \(0.319820\pi\) | |||||||
\(942\) | 1.67933 | 0.0547154 | ||||||||
\(943\) | 24.2055 | 0.788238 | ||||||||
\(944\) | 11.5381 | 0.375533 | ||||||||
\(945\) | −3.93548 | −0.128021 | ||||||||
\(946\) | 0.783994 | 0.0254898 | ||||||||
\(947\) | −24.3724 | −0.791995 | −0.395998 | − | 0.918252i | \(-0.629601\pi\) | ||||
−0.395998 | + | 0.918252i | \(0.629601\pi\) | |||||||
\(948\) | −3.28674 | −0.106749 | ||||||||
\(949\) | −0.652299 | −0.0211745 | ||||||||
\(950\) | −25.4716 | −0.826408 | ||||||||
\(951\) | −32.7680 | −1.06257 | ||||||||
\(952\) | 2.16972 | 0.0703211 | ||||||||
\(953\) | 19.9179 | 0.645204 | 0.322602 | − | 0.946535i | \(-0.395442\pi\) | ||||
0.322602 | + | 0.946535i | \(0.395442\pi\) | |||||||
\(954\) | 0.324885 | 0.0105185 | ||||||||
\(955\) | 21.2612 | 0.687997 | ||||||||
\(956\) | −24.5728 | −0.794742 | ||||||||
\(957\) | −13.7077 | −0.443106 | ||||||||
\(958\) | −26.2075 | −0.846727 | ||||||||
\(959\) | 9.62691 | 0.310869 | ||||||||
\(960\) | −9.27437 | −0.299329 | ||||||||
\(961\) | −27.2504 | −0.879045 | ||||||||
\(962\) | 0.467015 | 0.0150572 | ||||||||
\(963\) | 9.95303 | 0.320732 | ||||||||
\(964\) | −0.213795 | −0.00688588 | ||||||||
\(965\) | 82.0468 | 2.64118 | ||||||||
\(966\) | 10.4912 | 0.337549 | ||||||||
\(967\) | −23.6814 | −0.761542 | −0.380771 | − | 0.924669i | \(-0.624341\pi\) | ||||
−0.380771 | + | 0.924669i | \(0.624341\pi\) | |||||||
\(968\) | 17.1588 | 0.551505 | ||||||||
\(969\) | −1.91613 | −0.0615551 | ||||||||
\(970\) | −93.0962 | −2.98914 | ||||||||
\(971\) | −7.95210 | −0.255195 | −0.127598 | − | 0.991826i | \(-0.540727\pi\) | ||||
−0.127598 | + | 0.991826i | \(0.540727\pi\) | |||||||
\(972\) | −0.820135 | −0.0263058 | ||||||||
\(973\) | −0.649517 | −0.0208226 | ||||||||
\(974\) | 67.6164 | 2.16657 | ||||||||
\(975\) | 0.365585 | 0.0117081 | ||||||||
\(976\) | 73.9101 | 2.36580 | ||||||||
\(977\) | 58.5191 | 1.87219 | 0.936095 | − | 0.351747i | \(-0.114412\pi\) | ||||
0.936095 | + | 0.351747i | \(0.114412\pi\) | |||||||
\(978\) | −14.3828 | −0.459911 | ||||||||
\(979\) | 3.32850 | 0.106379 | ||||||||
\(980\) | −17.0977 | −0.546166 | ||||||||
\(981\) | −6.25723 | −0.199778 | ||||||||
\(982\) | −51.9563 | −1.65799 | ||||||||
\(983\) | 15.3438 | 0.489390 | 0.244695 | − | 0.969600i | \(-0.421312\pi\) | ||||
0.244695 | + | 0.969600i | \(0.421312\pi\) | |||||||
\(984\) | −8.40673 | −0.267997 | ||||||||
\(985\) | −3.07615 | −0.0980142 | ||||||||
\(986\) | 15.0486 | 0.479244 | ||||||||
\(987\) | −6.26645 | −0.199463 | ||||||||
\(988\) | 0.0725779 | 0.00230901 | ||||||||
\(989\) | 1.74111 | 0.0553642 | ||||||||
\(990\) | −9.23208 | −0.293415 | ||||||||
\(991\) | 15.1365 | 0.480825 | 0.240413 | − | 0.970671i | \(-0.422717\pi\) | ||||
0.240413 | + | 0.970671i | \(0.422717\pi\) | |||||||
\(992\) | −8.48051 | −0.269256 | ||||||||
\(993\) | 3.68621 | 0.116978 | ||||||||
\(994\) | −15.8410 | −0.502446 | ||||||||
\(995\) | 69.9615 | 2.21793 | ||||||||
\(996\) | 2.52146 | 0.0798956 | ||||||||
\(997\) | −37.3031 | −1.18140 | −0.590701 | − | 0.806890i | \(-0.701149\pi\) | ||||
−0.590701 | + | 0.806890i | \(0.701149\pi\) | |||||||
\(998\) | −9.76486 | −0.309101 | ||||||||
\(999\) | 6.02148 | 0.190511 |
(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 | 8007.2.a.f.1.37 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.37 | ✓ | 48 | 1.1 | even | 1 | trivial |