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 | 1.28 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.498945 | 0.352807 | 0.176404 | − | 0.984318i | \(-0.443554\pi\) | ||||
0.176404 | + | 0.984318i | \(0.443554\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.75105 | −0.875527 | ||||||||
\(5\) | 0.622534 | 0.278406 | 0.139203 | − | 0.990264i | \(-0.455546\pi\) | ||||
0.139203 | + | 0.990264i | \(0.455546\pi\) | |||||||
\(6\) | −0.498945 | −0.203693 | ||||||||
\(7\) | 0.110017 | 0.0415824 | 0.0207912 | − | 0.999784i | \(-0.493381\pi\) | ||||
0.0207912 | + | 0.999784i | \(0.493381\pi\) | |||||||
\(8\) | −1.87157 | −0.661699 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.310610 | 0.0982235 | ||||||||
\(11\) | 0.189879 | 0.0572508 | 0.0286254 | − | 0.999590i | \(-0.490887\pi\) | ||||
0.0286254 | + | 0.999590i | \(0.490887\pi\) | |||||||
\(12\) | 1.75105 | 0.505486 | ||||||||
\(13\) | 6.61917 | 1.83583 | 0.917913 | − | 0.396781i | \(-0.129873\pi\) | ||||
0.917913 | + | 0.396781i | \(0.129873\pi\) | |||||||
\(14\) | 0.0548922 | 0.0146706 | ||||||||
\(15\) | −0.622534 | −0.160738 | ||||||||
\(16\) | 2.56830 | 0.642075 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.498945 | 0.117602 | ||||||||
\(19\) | −0.0616562 | −0.0141449 | −0.00707245 | − | 0.999975i | \(-0.502251\pi\) | ||||
−0.00707245 | + | 0.999975i | \(0.502251\pi\) | |||||||
\(20\) | −1.09009 | −0.243752 | ||||||||
\(21\) | −0.110017 | −0.0240076 | ||||||||
\(22\) | 0.0947393 | 0.0201985 | ||||||||
\(23\) | −5.46866 | −1.14029 | −0.570147 | − | 0.821543i | \(-0.693114\pi\) | ||||
−0.570147 | + | 0.821543i | \(0.693114\pi\) | |||||||
\(24\) | 1.87157 | 0.382032 | ||||||||
\(25\) | −4.61245 | −0.922490 | ||||||||
\(26\) | 3.30260 | 0.647693 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.192645 | −0.0364065 | ||||||||
\(29\) | −5.28863 | −0.982073 | −0.491037 | − | 0.871139i | \(-0.663382\pi\) | ||||
−0.491037 | + | 0.871139i | \(0.663382\pi\) | |||||||
\(30\) | −0.310610 | −0.0567094 | ||||||||
\(31\) | −4.08323 | −0.733370 | −0.366685 | − | 0.930345i | \(-0.619507\pi\) | ||||
−0.366685 | + | 0.930345i | \(0.619507\pi\) | |||||||
\(32\) | 5.02458 | 0.888228 | ||||||||
\(33\) | −0.189879 | −0.0330537 | ||||||||
\(34\) | −0.498945 | −0.0855683 | ||||||||
\(35\) | 0.0684891 | 0.0115768 | ||||||||
\(36\) | −1.75105 | −0.291842 | ||||||||
\(37\) | 7.61954 | 1.25264 | 0.626322 | − | 0.779565i | \(-0.284560\pi\) | ||||
0.626322 | + | 0.779565i | \(0.284560\pi\) | |||||||
\(38\) | −0.0307630 | −0.00499042 | ||||||||
\(39\) | −6.61917 | −1.05991 | ||||||||
\(40\) | −1.16512 | −0.184221 | ||||||||
\(41\) | −8.53971 | −1.33368 | −0.666840 | − | 0.745201i | \(-0.732353\pi\) | ||||
−0.666840 | + | 0.745201i | \(0.732353\pi\) | |||||||
\(42\) | −0.0548922 | −0.00847006 | ||||||||
\(43\) | −1.22669 | −0.187068 | −0.0935342 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935342 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(44\) | −0.332489 | −0.0501246 | ||||||||
\(45\) | 0.622534 | 0.0928019 | ||||||||
\(46\) | −2.72856 | −0.402304 | ||||||||
\(47\) | 11.0065 | 1.60546 | 0.802730 | − | 0.596343i | \(-0.203380\pi\) | ||||
0.802730 | + | 0.596343i | \(0.203380\pi\) | |||||||
\(48\) | −2.56830 | −0.370702 | ||||||||
\(49\) | −6.98790 | −0.998271 | ||||||||
\(50\) | −2.30136 | −0.325461 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −11.5905 | −1.60732 | ||||||||
\(53\) | −0.0568805 | −0.00781314 | −0.00390657 | − | 0.999992i | \(-0.501244\pi\) | ||||
−0.00390657 | + | 0.999992i | \(0.501244\pi\) | |||||||
\(54\) | −0.498945 | −0.0678978 | ||||||||
\(55\) | 0.118206 | 0.0159389 | ||||||||
\(56\) | −0.205904 | −0.0275150 | ||||||||
\(57\) | 0.0616562 | 0.00816656 | ||||||||
\(58\) | −2.63873 | −0.346483 | ||||||||
\(59\) | 3.88617 | 0.505936 | 0.252968 | − | 0.967475i | \(-0.418593\pi\) | ||||
0.252968 | + | 0.967475i | \(0.418593\pi\) | |||||||
\(60\) | 1.09009 | 0.140730 | ||||||||
\(61\) | 3.47610 | 0.445069 | 0.222535 | − | 0.974925i | \(-0.428567\pi\) | ||||
0.222535 | + | 0.974925i | \(0.428567\pi\) | |||||||
\(62\) | −2.03731 | −0.258738 | ||||||||
\(63\) | 0.110017 | 0.0138608 | ||||||||
\(64\) | −2.62961 | −0.328702 | ||||||||
\(65\) | 4.12066 | 0.511105 | ||||||||
\(66\) | −0.0947393 | −0.0116616 | ||||||||
\(67\) | −10.7555 | −1.31399 | −0.656994 | − | 0.753896i | \(-0.728172\pi\) | ||||
−0.656994 | + | 0.753896i | \(0.728172\pi\) | |||||||
\(68\) | 1.75105 | 0.212347 | ||||||||
\(69\) | 5.46866 | 0.658349 | ||||||||
\(70\) | 0.0341723 | 0.00408437 | ||||||||
\(71\) | 6.87507 | 0.815921 | 0.407960 | − | 0.913000i | \(-0.366240\pi\) | ||||
0.407960 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(72\) | −1.87157 | −0.220566 | ||||||||
\(73\) | −6.33728 | −0.741723 | −0.370861 | − | 0.928688i | \(-0.620937\pi\) | ||||
−0.370861 | + | 0.928688i | \(0.620937\pi\) | |||||||
\(74\) | 3.80173 | 0.441942 | ||||||||
\(75\) | 4.61245 | 0.532600 | ||||||||
\(76\) | 0.107963 | 0.0123842 | ||||||||
\(77\) | 0.0208899 | 0.00238062 | ||||||||
\(78\) | −3.30260 | −0.373946 | ||||||||
\(79\) | −2.39038 | −0.268939 | −0.134469 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134469 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(80\) | 1.59885 | 0.178757 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.26084 | −0.470532 | ||||||||
\(83\) | 17.9437 | 1.96958 | 0.984790 | − | 0.173746i | \(-0.0555872\pi\) | ||||
0.984790 | + | 0.173746i | \(0.0555872\pi\) | |||||||
\(84\) | 0.192645 | 0.0210193 | ||||||||
\(85\) | −0.622534 | −0.0675233 | ||||||||
\(86\) | −0.612050 | −0.0659991 | ||||||||
\(87\) | 5.28863 | 0.567000 | ||||||||
\(88\) | −0.355372 | −0.0378828 | ||||||||
\(89\) | 12.7186 | 1.34817 | 0.674084 | − | 0.738655i | \(-0.264539\pi\) | ||||
0.674084 | + | 0.738655i | \(0.264539\pi\) | |||||||
\(90\) | 0.310610 | 0.0327412 | ||||||||
\(91\) | 0.728219 | 0.0763381 | ||||||||
\(92\) | 9.57592 | 0.998359 | ||||||||
\(93\) | 4.08323 | 0.423411 | ||||||||
\(94\) | 5.49162 | 0.566418 | ||||||||
\(95\) | −0.0383831 | −0.00393802 | ||||||||
\(96\) | −5.02458 | −0.512819 | ||||||||
\(97\) | 9.70831 | 0.985730 | 0.492865 | − | 0.870106i | \(-0.335950\pi\) | ||||
0.492865 | + | 0.870106i | \(0.335950\pi\) | |||||||
\(98\) | −3.48657 | −0.352197 | ||||||||
\(99\) | 0.189879 | 0.0190836 | ||||||||
\(100\) | 8.07665 | 0.807665 | ||||||||
\(101\) | −1.38802 | −0.138114 | −0.0690568 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690568 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(102\) | 0.498945 | 0.0494029 | ||||||||
\(103\) | −1.57120 | −0.154815 | −0.0774073 | − | 0.997000i | \(-0.524664\pi\) | ||||
−0.0774073 | + | 0.997000i | \(0.524664\pi\) | |||||||
\(104\) | −12.3882 | −1.21477 | ||||||||
\(105\) | −0.0684891 | −0.00668386 | ||||||||
\(106\) | −0.0283802 | −0.00275653 | ||||||||
\(107\) | 7.18961 | 0.695046 | 0.347523 | − | 0.937672i | \(-0.387023\pi\) | ||||
0.347523 | + | 0.937672i | \(0.387023\pi\) | |||||||
\(108\) | 1.75105 | 0.168495 | ||||||||
\(109\) | −11.7603 | −1.12643 | −0.563216 | − | 0.826310i | \(-0.690436\pi\) | ||||
−0.563216 | + | 0.826310i | \(0.690436\pi\) | |||||||
\(110\) | 0.0589784 | 0.00562337 | ||||||||
\(111\) | −7.61954 | −0.723214 | ||||||||
\(112\) | 0.282556 | 0.0266990 | ||||||||
\(113\) | 5.36524 | 0.504719 | 0.252360 | − | 0.967633i | \(-0.418793\pi\) | ||||
0.252360 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(114\) | 0.0307630 | 0.00288122 | ||||||||
\(115\) | −3.40443 | −0.317465 | ||||||||
\(116\) | 9.26067 | 0.859832 | ||||||||
\(117\) | 6.61917 | 0.611942 | ||||||||
\(118\) | 1.93898 | 0.178498 | ||||||||
\(119\) | −0.110017 | −0.0100852 | ||||||||
\(120\) | 1.16512 | 0.106360 | ||||||||
\(121\) | −10.9639 | −0.996722 | ||||||||
\(122\) | 1.73438 | 0.157024 | ||||||||
\(123\) | 8.53971 | 0.770000 | ||||||||
\(124\) | 7.14996 | 0.642085 | ||||||||
\(125\) | −5.98408 | −0.535232 | ||||||||
\(126\) | 0.0548922 | 0.00489019 | ||||||||
\(127\) | 11.9742 | 1.06254 | 0.531269 | − | 0.847203i | \(-0.321715\pi\) | ||||
0.531269 | + | 0.847203i | \(0.321715\pi\) | |||||||
\(128\) | −11.3612 | −1.00420 | ||||||||
\(129\) | 1.22669 | 0.108004 | ||||||||
\(130\) | 2.05598 | 0.180321 | ||||||||
\(131\) | −5.31945 | −0.464763 | −0.232381 | − | 0.972625i | \(-0.574652\pi\) | ||||
−0.232381 | + | 0.972625i | \(0.574652\pi\) | |||||||
\(132\) | 0.332489 | 0.0289395 | ||||||||
\(133\) | −0.00678321 | −0.000588179 0 | ||||||||
\(134\) | −5.36638 | −0.463584 | ||||||||
\(135\) | −0.622534 | −0.0535792 | ||||||||
\(136\) | 1.87157 | 0.160486 | ||||||||
\(137\) | −4.30047 | −0.367414 | −0.183707 | − | 0.982981i | \(-0.558810\pi\) | ||||
−0.183707 | + | 0.982981i | \(0.558810\pi\) | |||||||
\(138\) | 2.72856 | 0.232270 | ||||||||
\(139\) | −21.3093 | −1.80743 | −0.903716 | − | 0.428133i | \(-0.859172\pi\) | ||||
−0.903716 | + | 0.428133i | \(0.859172\pi\) | |||||||
\(140\) | −0.119928 | −0.0101358 | ||||||||
\(141\) | −11.0065 | −0.926913 | ||||||||
\(142\) | 3.43028 | 0.287863 | ||||||||
\(143\) | 1.25684 | 0.105102 | ||||||||
\(144\) | 2.56830 | 0.214025 | ||||||||
\(145\) | −3.29235 | −0.273415 | ||||||||
\(146\) | −3.16195 | −0.261685 | ||||||||
\(147\) | 6.98790 | 0.576352 | ||||||||
\(148\) | −13.3422 | −1.09672 | ||||||||
\(149\) | −14.5703 | −1.19365 | −0.596823 | − | 0.802373i | \(-0.703570\pi\) | ||||
−0.596823 | + | 0.802373i | \(0.703570\pi\) | |||||||
\(150\) | 2.30136 | 0.187905 | ||||||||
\(151\) | 7.31852 | 0.595573 | 0.297786 | − | 0.954633i | \(-0.403752\pi\) | ||||
0.297786 | + | 0.954633i | \(0.403752\pi\) | |||||||
\(152\) | 0.115394 | 0.00935967 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.0104229 | 0.000839901 0 | ||||||||
\(155\) | −2.54195 | −0.204174 | ||||||||
\(156\) | 11.5905 | 0.927984 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −1.19267 | −0.0948836 | ||||||||
\(159\) | 0.0568805 | 0.00451092 | ||||||||
\(160\) | 3.12797 | 0.247288 | ||||||||
\(161\) | −0.601644 | −0.0474162 | ||||||||
\(162\) | 0.498945 | 0.0392008 | ||||||||
\(163\) | 10.7686 | 0.843463 | 0.421731 | − | 0.906721i | \(-0.361423\pi\) | ||||
0.421731 | + | 0.906721i | \(0.361423\pi\) | |||||||
\(164\) | 14.9535 | 1.16767 | ||||||||
\(165\) | −0.118206 | −0.00920235 | ||||||||
\(166\) | 8.95293 | 0.694882 | ||||||||
\(167\) | −5.12239 | −0.396382 | −0.198191 | − | 0.980163i | \(-0.563507\pi\) | ||||
−0.198191 | + | 0.980163i | \(0.563507\pi\) | |||||||
\(168\) | 0.205904 | 0.0158858 | ||||||||
\(169\) | 30.8134 | 2.37026 | ||||||||
\(170\) | −0.310610 | −0.0238227 | ||||||||
\(171\) | −0.0616562 | −0.00471496 | ||||||||
\(172\) | 2.14800 | 0.163783 | ||||||||
\(173\) | −17.7180 | −1.34707 | −0.673536 | − | 0.739154i | \(-0.735225\pi\) | ||||
−0.673536 | + | 0.739154i | \(0.735225\pi\) | |||||||
\(174\) | 2.63873 | 0.200042 | ||||||||
\(175\) | −0.507447 | −0.0383594 | ||||||||
\(176\) | 0.487667 | 0.0367593 | ||||||||
\(177\) | −3.88617 | −0.292102 | ||||||||
\(178\) | 6.34587 | 0.475643 | ||||||||
\(179\) | −7.02296 | −0.524921 | −0.262460 | − | 0.964943i | \(-0.584534\pi\) | ||||
−0.262460 | + | 0.964943i | \(0.584534\pi\) | |||||||
\(180\) | −1.09009 | −0.0812506 | ||||||||
\(181\) | −11.5729 | −0.860207 | −0.430103 | − | 0.902780i | \(-0.641523\pi\) | ||||
−0.430103 | + | 0.902780i | \(0.641523\pi\) | |||||||
\(182\) | 0.363341 | 0.0269326 | ||||||||
\(183\) | −3.47610 | −0.256961 | ||||||||
\(184\) | 10.2350 | 0.754532 | ||||||||
\(185\) | 4.74342 | 0.348743 | ||||||||
\(186\) | 2.03731 | 0.149382 | ||||||||
\(187\) | −0.189879 | −0.0138854 | ||||||||
\(188\) | −19.2729 | −1.40562 | ||||||||
\(189\) | −0.110017 | −0.00800254 | ||||||||
\(190\) | −0.0191510 | −0.00138936 | ||||||||
\(191\) | 4.83937 | 0.350164 | 0.175082 | − | 0.984554i | \(-0.443981\pi\) | ||||
0.175082 | + | 0.984554i | \(0.443981\pi\) | |||||||
\(192\) | 2.62961 | 0.189776 | ||||||||
\(193\) | −10.6120 | −0.763865 | −0.381933 | − | 0.924190i | \(-0.624741\pi\) | ||||
−0.381933 | + | 0.924190i | \(0.624741\pi\) | |||||||
\(194\) | 4.84391 | 0.347772 | ||||||||
\(195\) | −4.12066 | −0.295086 | ||||||||
\(196\) | 12.2362 | 0.874013 | ||||||||
\(197\) | 1.33752 | 0.0952941 | 0.0476470 | − | 0.998864i | \(-0.484828\pi\) | ||||
0.0476470 | + | 0.998864i | \(0.484828\pi\) | |||||||
\(198\) | 0.0947393 | 0.00673283 | ||||||||
\(199\) | −13.6565 | −0.968080 | −0.484040 | − | 0.875046i | \(-0.660831\pi\) | ||||
−0.484040 | + | 0.875046i | \(0.660831\pi\) | |||||||
\(200\) | 8.63252 | 0.610411 | ||||||||
\(201\) | 10.7555 | 0.758631 | ||||||||
\(202\) | −0.692548 | −0.0487275 | ||||||||
\(203\) | −0.581837 | −0.0408370 | ||||||||
\(204\) | −1.75105 | −0.122598 | ||||||||
\(205\) | −5.31626 | −0.371304 | ||||||||
\(206\) | −0.783940 | −0.0546197 | ||||||||
\(207\) | −5.46866 | −0.380098 | ||||||||
\(208\) | 17.0000 | 1.17874 | ||||||||
\(209\) | −0.0117072 | −0.000809806 0 | ||||||||
\(210\) | −0.0341723 | −0.00235811 | ||||||||
\(211\) | −7.25466 | −0.499432 | −0.249716 | − | 0.968319i | \(-0.580337\pi\) | ||||
−0.249716 | + | 0.968319i | \(0.580337\pi\) | |||||||
\(212\) | 0.0996009 | 0.00684062 | ||||||||
\(213\) | −6.87507 | −0.471072 | ||||||||
\(214\) | 3.58722 | 0.245217 | ||||||||
\(215\) | −0.763656 | −0.0520809 | ||||||||
\(216\) | 1.87157 | 0.127344 | ||||||||
\(217\) | −0.449223 | −0.0304953 | ||||||||
\(218\) | −5.86773 | −0.397413 | ||||||||
\(219\) | 6.33728 | 0.428234 | ||||||||
\(220\) | −0.206986 | −0.0139550 | ||||||||
\(221\) | −6.61917 | −0.445253 | ||||||||
\(222\) | −3.80173 | −0.255155 | ||||||||
\(223\) | −25.7018 | −1.72112 | −0.860562 | − | 0.509347i | \(-0.829887\pi\) | ||||
−0.860562 | + | 0.509347i | \(0.829887\pi\) | |||||||
\(224\) | 0.552787 | 0.0369346 | ||||||||
\(225\) | −4.61245 | −0.307497 | ||||||||
\(226\) | 2.67696 | 0.178069 | ||||||||
\(227\) | −0.0456610 | −0.00303063 | −0.00151531 | − | 0.999999i | \(-0.500482\pi\) | ||||
−0.00151531 | + | 0.999999i | \(0.500482\pi\) | |||||||
\(228\) | −0.107963 | −0.00715004 | ||||||||
\(229\) | −5.83691 | −0.385714 | −0.192857 | − | 0.981227i | \(-0.561775\pi\) | ||||
−0.192857 | + | 0.981227i | \(0.561775\pi\) | |||||||
\(230\) | −1.69862 | −0.112004 | ||||||||
\(231\) | −0.0208899 | −0.00137445 | ||||||||
\(232\) | 9.89803 | 0.649837 | ||||||||
\(233\) | −7.68536 | −0.503485 | −0.251742 | − | 0.967794i | \(-0.581004\pi\) | ||||
−0.251742 | + | 0.967794i | \(0.581004\pi\) | |||||||
\(234\) | 3.30260 | 0.215898 | ||||||||
\(235\) | 6.85191 | 0.446969 | ||||||||
\(236\) | −6.80489 | −0.442961 | ||||||||
\(237\) | 2.39038 | 0.155272 | ||||||||
\(238\) | −0.0548922 | −0.00355813 | ||||||||
\(239\) | 6.81710 | 0.440962 | 0.220481 | − | 0.975391i | \(-0.429237\pi\) | ||||
0.220481 | + | 0.975391i | \(0.429237\pi\) | |||||||
\(240\) | −1.59885 | −0.103206 | ||||||||
\(241\) | −23.3281 | −1.50270 | −0.751348 | − | 0.659907i | \(-0.770596\pi\) | ||||
−0.751348 | + | 0.659907i | \(0.770596\pi\) | |||||||
\(242\) | −5.47040 | −0.351651 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.08684 | −0.389670 | ||||||||
\(245\) | −4.35020 | −0.277924 | ||||||||
\(246\) | 4.26084 | 0.271662 | ||||||||
\(247\) | −0.408112 | −0.0259676 | ||||||||
\(248\) | 7.64204 | 0.485270 | ||||||||
\(249\) | −17.9437 | −1.13714 | ||||||||
\(250\) | −2.98572 | −0.188834 | ||||||||
\(251\) | 2.30713 | 0.145625 | 0.0728124 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728124 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(252\) | −0.192645 | −0.0121355 | ||||||||
\(253\) | −1.03839 | −0.0652827 | ||||||||
\(254\) | 5.97446 | 0.374871 | ||||||||
\(255\) | 0.622534 | 0.0389846 | ||||||||
\(256\) | −0.409375 | −0.0255859 | ||||||||
\(257\) | −11.9923 | −0.748059 | −0.374030 | − | 0.927417i | \(-0.622024\pi\) | ||||
−0.374030 | + | 0.927417i | \(0.622024\pi\) | |||||||
\(258\) | 0.612050 | 0.0381046 | ||||||||
\(259\) | 0.838276 | 0.0520879 | ||||||||
\(260\) | −7.21549 | −0.447486 | ||||||||
\(261\) | −5.28863 | −0.327358 | ||||||||
\(262\) | −2.65411 | −0.163972 | ||||||||
\(263\) | 20.1830 | 1.24454 | 0.622270 | − | 0.782803i | \(-0.286211\pi\) | ||||
0.622270 | + | 0.782803i | \(0.286211\pi\) | |||||||
\(264\) | 0.355372 | 0.0218716 | ||||||||
\(265\) | −0.0354101 | −0.00217522 | ||||||||
\(266\) | −0.00338444 | −0.000207514 0 | ||||||||
\(267\) | −12.7186 | −0.778365 | ||||||||
\(268\) | 18.8334 | 1.15043 | ||||||||
\(269\) | −29.9514 | −1.82617 | −0.913085 | − | 0.407769i | \(-0.866307\pi\) | ||||
−0.913085 | + | 0.407769i | \(0.866307\pi\) | |||||||
\(270\) | −0.310610 | −0.0189031 | ||||||||
\(271\) | −6.64163 | −0.403450 | −0.201725 | − | 0.979442i | \(-0.564655\pi\) | ||||
−0.201725 | + | 0.979442i | \(0.564655\pi\) | |||||||
\(272\) | −2.56830 | −0.155726 | ||||||||
\(273\) | −0.728219 | −0.0440738 | ||||||||
\(274\) | −2.14570 | −0.129626 | ||||||||
\(275\) | −0.875809 | −0.0528133 | ||||||||
\(276\) | −9.57592 | −0.576403 | ||||||||
\(277\) | −0.752550 | −0.0452163 | −0.0226082 | − | 0.999744i | \(-0.507197\pi\) | ||||
−0.0226082 | + | 0.999744i | \(0.507197\pi\) | |||||||
\(278\) | −10.6322 | −0.637675 | ||||||||
\(279\) | −4.08323 | −0.244457 | ||||||||
\(280\) | −0.128182 | −0.00766035 | ||||||||
\(281\) | −17.1481 | −1.02297 | −0.511484 | − | 0.859293i | \(-0.670904\pi\) | ||||
−0.511484 | + | 0.859293i | \(0.670904\pi\) | |||||||
\(282\) | −5.49162 | −0.327021 | ||||||||
\(283\) | −19.3556 | −1.15057 | −0.575285 | − | 0.817953i | \(-0.695109\pi\) | ||||
−0.575285 | + | 0.817953i | \(0.695109\pi\) | |||||||
\(284\) | −12.0386 | −0.714361 | ||||||||
\(285\) | 0.0383831 | 0.00227362 | ||||||||
\(286\) | 0.627095 | 0.0370809 | ||||||||
\(287\) | −0.939511 | −0.0554576 | ||||||||
\(288\) | 5.02458 | 0.296076 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.64270 | −0.0964627 | ||||||||
\(291\) | −9.70831 | −0.569111 | ||||||||
\(292\) | 11.0969 | 0.649398 | ||||||||
\(293\) | 31.7072 | 1.85235 | 0.926177 | − | 0.377089i | \(-0.123075\pi\) | ||||
0.926177 | + | 0.377089i | \(0.123075\pi\) | |||||||
\(294\) | 3.48657 | 0.203341 | ||||||||
\(295\) | 2.41927 | 0.140855 | ||||||||
\(296\) | −14.2605 | −0.828874 | ||||||||
\(297\) | −0.189879 | −0.0110179 | ||||||||
\(298\) | −7.26977 | −0.421126 | ||||||||
\(299\) | −36.1980 | −2.09338 | ||||||||
\(300\) | −8.07665 | −0.466306 | ||||||||
\(301\) | −0.134956 | −0.00777875 | ||||||||
\(302\) | 3.65154 | 0.210122 | ||||||||
\(303\) | 1.38802 | 0.0797399 | ||||||||
\(304\) | −0.158351 | −0.00908208 | ||||||||
\(305\) | 2.16399 | 0.123910 | ||||||||
\(306\) | −0.498945 | −0.0285228 | ||||||||
\(307\) | 15.3128 | 0.873948 | 0.436974 | − | 0.899474i | \(-0.356050\pi\) | ||||
0.436974 | + | 0.899474i | \(0.356050\pi\) | |||||||
\(308\) | −0.0365793 | −0.00208430 | ||||||||
\(309\) | 1.57120 | 0.0893822 | ||||||||
\(310\) | −1.26829 | −0.0720342 | ||||||||
\(311\) | 20.6581 | 1.17141 | 0.585705 | − | 0.810524i | \(-0.300818\pi\) | ||||
0.585705 | + | 0.810524i | \(0.300818\pi\) | |||||||
\(312\) | 12.3882 | 0.701345 | ||||||||
\(313\) | −17.8717 | −1.01017 | −0.505085 | − | 0.863070i | \(-0.668539\pi\) | ||||
−0.505085 | + | 0.863070i | \(0.668539\pi\) | |||||||
\(314\) | −0.498945 | −0.0281571 | ||||||||
\(315\) | 0.0684891 | 0.00385893 | ||||||||
\(316\) | 4.18569 | 0.235463 | ||||||||
\(317\) | −16.8959 | −0.948969 | −0.474485 | − | 0.880264i | \(-0.657366\pi\) | ||||
−0.474485 | + | 0.880264i | \(0.657366\pi\) | |||||||
\(318\) | 0.0283802 | 0.00159148 | ||||||||
\(319\) | −1.00420 | −0.0562245 | ||||||||
\(320\) | −1.63702 | −0.0915125 | ||||||||
\(321\) | −7.18961 | −0.401285 | ||||||||
\(322\) | −0.300187 | −0.0167288 | ||||||||
\(323\) | 0.0616562 | 0.00343064 | ||||||||
\(324\) | −1.75105 | −0.0972808 | ||||||||
\(325\) | −30.5306 | −1.69353 | ||||||||
\(326\) | 5.37294 | 0.297580 | ||||||||
\(327\) | 11.7603 | 0.650345 | ||||||||
\(328\) | 15.9827 | 0.882495 | ||||||||
\(329\) | 1.21090 | 0.0667589 | ||||||||
\(330\) | −0.0589784 | −0.00324666 | ||||||||
\(331\) | −30.6643 | −1.68546 | −0.842731 | − | 0.538335i | \(-0.819053\pi\) | ||||
−0.842731 | + | 0.538335i | \(0.819053\pi\) | |||||||
\(332\) | −31.4205 | −1.72442 | ||||||||
\(333\) | 7.61954 | 0.417548 | ||||||||
\(334\) | −2.55579 | −0.139846 | ||||||||
\(335\) | −6.69564 | −0.365822 | ||||||||
\(336\) | −0.282556 | −0.0154147 | ||||||||
\(337\) | 5.54873 | 0.302259 | 0.151129 | − | 0.988514i | \(-0.451709\pi\) | ||||
0.151129 | + | 0.988514i | \(0.451709\pi\) | |||||||
\(338\) | 15.3742 | 0.836244 | ||||||||
\(339\) | −5.36524 | −0.291400 | ||||||||
\(340\) | 1.09009 | 0.0591185 | ||||||||
\(341\) | −0.775321 | −0.0419860 | ||||||||
\(342\) | −0.0307630 | −0.00166347 | ||||||||
\(343\) | −1.53890 | −0.0830929 | ||||||||
\(344\) | 2.29583 | 0.123783 | ||||||||
\(345\) | 3.40443 | 0.183288 | ||||||||
\(346\) | −8.84028 | −0.475257 | ||||||||
\(347\) | −17.2327 | −0.925100 | −0.462550 | − | 0.886593i | \(-0.653065\pi\) | ||||
−0.462550 | + | 0.886593i | \(0.653065\pi\) | |||||||
\(348\) | −9.26067 | −0.496424 | ||||||||
\(349\) | −5.90035 | −0.315838 | −0.157919 | − | 0.987452i | \(-0.550479\pi\) | ||||
−0.157919 | + | 0.987452i | \(0.550479\pi\) | |||||||
\(350\) | −0.253188 | −0.0135335 | ||||||||
\(351\) | −6.61917 | −0.353305 | ||||||||
\(352\) | 0.954063 | 0.0508517 | ||||||||
\(353\) | −22.4944 | −1.19725 | −0.598627 | − | 0.801028i | \(-0.704287\pi\) | ||||
−0.598627 | + | 0.801028i | \(0.704287\pi\) | |||||||
\(354\) | −1.93898 | −0.103056 | ||||||||
\(355\) | 4.27997 | 0.227157 | ||||||||
\(356\) | −22.2709 | −1.18036 | ||||||||
\(357\) | 0.110017 | 0.00582270 | ||||||||
\(358\) | −3.50407 | −0.185196 | ||||||||
\(359\) | 5.47971 | 0.289208 | 0.144604 | − | 0.989490i | \(-0.453809\pi\) | ||||
0.144604 | + | 0.989490i | \(0.453809\pi\) | |||||||
\(360\) | −1.16512 | −0.0614070 | ||||||||
\(361\) | −18.9962 | −0.999800 | ||||||||
\(362\) | −5.77424 | −0.303487 | ||||||||
\(363\) | 10.9639 | 0.575458 | ||||||||
\(364\) | −1.27515 | −0.0668360 | ||||||||
\(365\) | −3.94517 | −0.206500 | ||||||||
\(366\) | −1.73438 | −0.0906576 | ||||||||
\(367\) | −19.8785 | −1.03765 | −0.518824 | − | 0.854881i | \(-0.673630\pi\) | ||||
−0.518824 | + | 0.854881i | \(0.673630\pi\) | |||||||
\(368\) | −14.0452 | −0.732154 | ||||||||
\(369\) | −8.53971 | −0.444560 | ||||||||
\(370\) | 2.36670 | 0.123039 | ||||||||
\(371\) | −0.00625781 | −0.000324889 0 | ||||||||
\(372\) | −7.14996 | −0.370708 | ||||||||
\(373\) | 25.6785 | 1.32958 | 0.664791 | − | 0.747030i | \(-0.268521\pi\) | ||||
0.664791 | + | 0.747030i | \(0.268521\pi\) | |||||||
\(374\) | −0.0947393 | −0.00489885 | ||||||||
\(375\) | 5.98408 | 0.309017 | ||||||||
\(376\) | −20.5994 | −1.06233 | ||||||||
\(377\) | −35.0063 | −1.80292 | ||||||||
\(378\) | −0.0548922 | −0.00282335 | ||||||||
\(379\) | 34.8480 | 1.79002 | 0.895012 | − | 0.446043i | \(-0.147167\pi\) | ||||
0.895012 | + | 0.446043i | \(0.147167\pi\) | |||||||
\(380\) | 0.0672108 | 0.00344784 | ||||||||
\(381\) | −11.9742 | −0.613457 | ||||||||
\(382\) | 2.41458 | 0.123540 | ||||||||
\(383\) | 27.5142 | 1.40591 | 0.702955 | − | 0.711235i | \(-0.251864\pi\) | ||||
0.702955 | + | 0.711235i | \(0.251864\pi\) | |||||||
\(384\) | 11.3612 | 0.579773 | ||||||||
\(385\) | 0.0130047 | 0.000662779 0 | ||||||||
\(386\) | −5.29478 | −0.269497 | ||||||||
\(387\) | −1.22669 | −0.0623561 | ||||||||
\(388\) | −16.9998 | −0.863033 | ||||||||
\(389\) | −8.10655 | −0.411019 | −0.205509 | − | 0.978655i | \(-0.565885\pi\) | ||||
−0.205509 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(390\) | −2.05598 | −0.104109 | ||||||||
\(391\) | 5.46866 | 0.276562 | ||||||||
\(392\) | 13.0783 | 0.660555 | ||||||||
\(393\) | 5.31945 | 0.268331 | ||||||||
\(394\) | 0.667346 | 0.0336204 | ||||||||
\(395\) | −1.48809 | −0.0748741 | ||||||||
\(396\) | −0.332489 | −0.0167082 | ||||||||
\(397\) | 16.7794 | 0.842133 | 0.421066 | − | 0.907030i | \(-0.361656\pi\) | ||||
0.421066 | + | 0.907030i | \(0.361656\pi\) | |||||||
\(398\) | −6.81382 | −0.341546 | ||||||||
\(399\) | 0.00678321 | 0.000339585 0 | ||||||||
\(400\) | −11.8462 | −0.592308 | ||||||||
\(401\) | 32.2773 | 1.61185 | 0.805927 | − | 0.592015i | \(-0.201668\pi\) | ||||
0.805927 | + | 0.592015i | \(0.201668\pi\) | |||||||
\(402\) | 5.36638 | 0.267650 | ||||||||
\(403\) | −27.0276 | −1.34634 | ||||||||
\(404\) | 2.43051 | 0.120922 | ||||||||
\(405\) | 0.622534 | 0.0309340 | ||||||||
\(406\) | −0.290305 | −0.0144076 | ||||||||
\(407\) | 1.44679 | 0.0717148 | ||||||||
\(408\) | −1.87157 | −0.0926564 | ||||||||
\(409\) | −7.42351 | −0.367069 | −0.183534 | − | 0.983013i | \(-0.558754\pi\) | ||||
−0.183534 | + | 0.983013i | \(0.558754\pi\) | |||||||
\(410\) | −2.65252 | −0.130999 | ||||||||
\(411\) | 4.30047 | 0.212127 | ||||||||
\(412\) | 2.75125 | 0.135544 | ||||||||
\(413\) | 0.427543 | 0.0210380 | ||||||||
\(414\) | −2.72856 | −0.134101 | ||||||||
\(415\) | 11.1706 | 0.548343 | ||||||||
\(416\) | 33.2585 | 1.63063 | ||||||||
\(417\) | 21.3093 | 1.04352 | ||||||||
\(418\) | −0.00584126 | −0.000285705 0 | ||||||||
\(419\) | −18.9566 | −0.926090 | −0.463045 | − | 0.886335i | \(-0.653243\pi\) | ||||
−0.463045 | + | 0.886335i | \(0.653243\pi\) | |||||||
\(420\) | 0.119928 | 0.00585190 | ||||||||
\(421\) | −23.4129 | −1.14107 | −0.570536 | − | 0.821272i | \(-0.693265\pi\) | ||||
−0.570536 | + | 0.821272i | \(0.693265\pi\) | |||||||
\(422\) | −3.61967 | −0.176203 | ||||||||
\(423\) | 11.0065 | 0.535153 | ||||||||
\(424\) | 0.106456 | 0.00516995 | ||||||||
\(425\) | 4.61245 | 0.223737 | ||||||||
\(426\) | −3.43028 | −0.166198 | ||||||||
\(427\) | 0.382429 | 0.0185071 | ||||||||
\(428\) | −12.5894 | −0.608531 | ||||||||
\(429\) | −1.25684 | −0.0606809 | ||||||||
\(430\) | −0.381022 | −0.0183745 | ||||||||
\(431\) | −25.4864 | −1.22764 | −0.613818 | − | 0.789448i | \(-0.710367\pi\) | ||||
−0.613818 | + | 0.789448i | \(0.710367\pi\) | |||||||
\(432\) | −2.56830 | −0.123567 | ||||||||
\(433\) | −24.5265 | −1.17867 | −0.589335 | − | 0.807889i | \(-0.700610\pi\) | ||||
−0.589335 | + | 0.807889i | \(0.700610\pi\) | |||||||
\(434\) | −0.224138 | −0.0107589 | ||||||||
\(435\) | 3.29235 | 0.157856 | ||||||||
\(436\) | 20.5929 | 0.986221 | ||||||||
\(437\) | 0.337177 | 0.0161293 | ||||||||
\(438\) | 3.16195 | 0.151084 | ||||||||
\(439\) | −9.14738 | −0.436581 | −0.218290 | − | 0.975884i | \(-0.570048\pi\) | ||||
−0.218290 | + | 0.975884i | \(0.570048\pi\) | |||||||
\(440\) | −0.221231 | −0.0105468 | ||||||||
\(441\) | −6.98790 | −0.332757 | ||||||||
\(442\) | −3.30260 | −0.157089 | ||||||||
\(443\) | 31.4276 | 1.49317 | 0.746586 | − | 0.665289i | \(-0.231692\pi\) | ||||
0.746586 | + | 0.665289i | \(0.231692\pi\) | |||||||
\(444\) | 13.3422 | 0.633194 | ||||||||
\(445\) | 7.91776 | 0.375338 | ||||||||
\(446\) | −12.8238 | −0.607224 | ||||||||
\(447\) | 14.5703 | 0.689151 | ||||||||
\(448\) | −0.289301 | −0.0136682 | ||||||||
\(449\) | −39.3579 | −1.85742 | −0.928708 | − | 0.370812i | \(-0.879079\pi\) | ||||
−0.928708 | + | 0.370812i | \(0.879079\pi\) | |||||||
\(450\) | −2.30136 | −0.108487 | ||||||||
\(451\) | −1.62152 | −0.0763542 | ||||||||
\(452\) | −9.39483 | −0.441896 | ||||||||
\(453\) | −7.31852 | −0.343854 | ||||||||
\(454\) | −0.0227823 | −0.00106923 | ||||||||
\(455\) | 0.453341 | 0.0212530 | ||||||||
\(456\) | −0.115394 | −0.00540381 | ||||||||
\(457\) | 6.47916 | 0.303082 | 0.151541 | − | 0.988451i | \(-0.451576\pi\) | ||||
0.151541 | + | 0.988451i | \(0.451576\pi\) | |||||||
\(458\) | −2.91230 | −0.136083 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 5.96134 | 0.277949 | ||||||||
\(461\) | −31.1170 | −1.44926 | −0.724632 | − | 0.689136i | \(-0.757990\pi\) | ||||
−0.724632 | + | 0.689136i | \(0.757990\pi\) | |||||||
\(462\) | −0.0104229 | −0.000484917 0 | ||||||||
\(463\) | −30.5942 | −1.42183 | −0.710916 | − | 0.703277i | \(-0.751720\pi\) | ||||
−0.710916 | + | 0.703277i | \(0.751720\pi\) | |||||||
\(464\) | −13.5828 | −0.630565 | ||||||||
\(465\) | 2.54195 | 0.117880 | ||||||||
\(466\) | −3.83457 | −0.177633 | ||||||||
\(467\) | 26.2418 | 1.21432 | 0.607162 | − | 0.794578i | \(-0.292308\pi\) | ||||
0.607162 | + | 0.794578i | \(0.292308\pi\) | |||||||
\(468\) | −11.5905 | −0.535772 | ||||||||
\(469\) | −1.18328 | −0.0546388 | ||||||||
\(470\) | 3.41872 | 0.157694 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −7.27323 | −0.334777 | ||||||||
\(473\) | −0.232923 | −0.0107098 | ||||||||
\(474\) | 1.19267 | 0.0547811 | ||||||||
\(475\) | 0.284386 | 0.0130485 | ||||||||
\(476\) | 0.192645 | 0.00882988 | ||||||||
\(477\) | −0.0568805 | −0.00260438 | ||||||||
\(478\) | 3.40136 | 0.155574 | ||||||||
\(479\) | 33.8380 | 1.54610 | 0.773050 | − | 0.634346i | \(-0.218730\pi\) | ||||
0.773050 | + | 0.634346i | \(0.218730\pi\) | |||||||
\(480\) | −3.12797 | −0.142772 | ||||||||
\(481\) | 50.4350 | 2.29964 | ||||||||
\(482\) | −11.6394 | −0.530162 | ||||||||
\(483\) | 0.601644 | 0.0273757 | ||||||||
\(484\) | 19.1985 | 0.872657 | ||||||||
\(485\) | 6.04376 | 0.274433 | ||||||||
\(486\) | −0.498945 | −0.0226326 | ||||||||
\(487\) | 11.2538 | 0.509959 | 0.254980 | − | 0.966946i | \(-0.417931\pi\) | ||||
0.254980 | + | 0.966946i | \(0.417931\pi\) | |||||||
\(488\) | −6.50576 | −0.294502 | ||||||||
\(489\) | −10.7686 | −0.486973 | ||||||||
\(490\) | −2.17051 | −0.0980537 | ||||||||
\(491\) | −28.9139 | −1.30487 | −0.652433 | − | 0.757846i | \(-0.726252\pi\) | ||||
−0.652433 | + | 0.757846i | \(0.726252\pi\) | |||||||
\(492\) | −14.9535 | −0.674156 | ||||||||
\(493\) | 5.28863 | 0.238188 | ||||||||
\(494\) | −0.203625 | −0.00916154 | ||||||||
\(495\) | 0.118206 | 0.00531298 | ||||||||
\(496\) | −10.4870 | −0.470878 | ||||||||
\(497\) | 0.756372 | 0.0339279 | ||||||||
\(498\) | −8.95293 | −0.401190 | ||||||||
\(499\) | 37.0687 | 1.65942 | 0.829712 | − | 0.558192i | \(-0.188505\pi\) | ||||
0.829712 | + | 0.558192i | \(0.188505\pi\) | |||||||
\(500\) | 10.4784 | 0.468610 | ||||||||
\(501\) | 5.12239 | 0.228851 | ||||||||
\(502\) | 1.15113 | 0.0513774 | ||||||||
\(503\) | 9.27716 | 0.413648 | 0.206824 | − | 0.978378i | \(-0.433687\pi\) | ||||
0.206824 | + | 0.978378i | \(0.433687\pi\) | |||||||
\(504\) | −0.205904 | −0.00917168 | ||||||||
\(505\) | −0.864093 | −0.0384516 | ||||||||
\(506\) | −0.518097 | −0.0230322 | ||||||||
\(507\) | −30.8134 | −1.36847 | ||||||||
\(508\) | −20.9675 | −0.930281 | ||||||||
\(509\) | −3.67145 | −0.162734 | −0.0813672 | − | 0.996684i | \(-0.525929\pi\) | ||||
−0.0813672 | + | 0.996684i | \(0.525929\pi\) | |||||||
\(510\) | 0.310610 | 0.0137540 | ||||||||
\(511\) | −0.697207 | −0.0308426 | ||||||||
\(512\) | 22.5181 | 0.995169 | ||||||||
\(513\) | 0.0616562 | 0.00272219 | ||||||||
\(514\) | −5.98349 | −0.263921 | ||||||||
\(515\) | −0.978124 | −0.0431013 | ||||||||
\(516\) | −2.14800 | −0.0945604 | ||||||||
\(517\) | 2.08990 | 0.0919138 | ||||||||
\(518\) | 0.418253 | 0.0183770 | ||||||||
\(519\) | 17.7180 | 0.777732 | ||||||||
\(520\) | −7.71209 | −0.338198 | ||||||||
\(521\) | 31.1280 | 1.36374 | 0.681871 | − | 0.731473i | \(-0.261167\pi\) | ||||
0.681871 | + | 0.731473i | \(0.261167\pi\) | |||||||
\(522\) | −2.63873 | −0.115494 | ||||||||
\(523\) | 4.66119 | 0.203820 | 0.101910 | − | 0.994794i | \(-0.467505\pi\) | ||||
0.101910 | + | 0.994794i | \(0.467505\pi\) | |||||||
\(524\) | 9.31465 | 0.406913 | ||||||||
\(525\) | 0.507447 | 0.0221468 | ||||||||
\(526\) | 10.0702 | 0.439082 | ||||||||
\(527\) | 4.08323 | 0.177868 | ||||||||
\(528\) | −0.487667 | −0.0212230 | ||||||||
\(529\) | 6.90624 | 0.300271 | ||||||||
\(530\) | −0.0176677 | −0.000767434 0 | ||||||||
\(531\) | 3.88617 | 0.168645 | ||||||||
\(532\) | 0.0118778 | 0.000514966 0 | ||||||||
\(533\) | −56.5258 | −2.44840 | ||||||||
\(534\) | −6.34587 | −0.274613 | ||||||||
\(535\) | 4.47578 | 0.193505 | ||||||||
\(536\) | 20.1296 | 0.869465 | ||||||||
\(537\) | 7.02296 | 0.303063 | ||||||||
\(538\) | −14.9441 | −0.644286 | ||||||||
\(539\) | −1.32686 | −0.0571518 | ||||||||
\(540\) | 1.09009 | 0.0469101 | ||||||||
\(541\) | −7.36605 | −0.316691 | −0.158346 | − | 0.987384i | \(-0.550616\pi\) | ||||
−0.158346 | + | 0.987384i | \(0.550616\pi\) | |||||||
\(542\) | −3.31380 | −0.142340 | ||||||||
\(543\) | 11.5729 | 0.496641 | ||||||||
\(544\) | −5.02458 | −0.215427 | ||||||||
\(545\) | −7.32118 | −0.313605 | ||||||||
\(546\) | −0.363341 | −0.0155495 | ||||||||
\(547\) | 21.8338 | 0.933544 | 0.466772 | − | 0.884378i | \(-0.345417\pi\) | ||||
0.466772 | + | 0.884378i | \(0.345417\pi\) | |||||||
\(548\) | 7.53036 | 0.321681 | ||||||||
\(549\) | 3.47610 | 0.148356 | ||||||||
\(550\) | −0.436980 | −0.0186329 | ||||||||
\(551\) | 0.326076 | 0.0138913 | ||||||||
\(552\) | −10.2350 | −0.435629 | ||||||||
\(553\) | −0.262982 | −0.0111831 | ||||||||
\(554\) | −0.375481 | −0.0159526 | ||||||||
\(555\) | −4.74342 | −0.201347 | ||||||||
\(556\) | 37.3138 | 1.58246 | ||||||||
\(557\) | 4.08349 | 0.173023 | 0.0865116 | − | 0.996251i | \(-0.472428\pi\) | ||||
0.0865116 | + | 0.996251i | \(0.472428\pi\) | |||||||
\(558\) | −2.03731 | −0.0862460 | ||||||||
\(559\) | −8.11966 | −0.343425 | ||||||||
\(560\) | 0.175901 | 0.00743316 | ||||||||
\(561\) | 0.189879 | 0.00801671 | ||||||||
\(562\) | −8.55594 | −0.360910 | ||||||||
\(563\) | −30.8749 | −1.30122 | −0.650610 | − | 0.759412i | \(-0.725487\pi\) | ||||
−0.650610 | + | 0.759412i | \(0.725487\pi\) | |||||||
\(564\) | 19.2729 | 0.811537 | ||||||||
\(565\) | 3.34005 | 0.140517 | ||||||||
\(566\) | −9.65736 | −0.405929 | ||||||||
\(567\) | 0.110017 | 0.00462027 | ||||||||
\(568\) | −12.8672 | −0.539894 | ||||||||
\(569\) | 24.1268 | 1.01145 | 0.505724 | − | 0.862695i | \(-0.331225\pi\) | ||||
0.505724 | + | 0.862695i | \(0.331225\pi\) | |||||||
\(570\) | 0.0191510 | 0.000802148 0 | ||||||||
\(571\) | 8.49513 | 0.355510 | 0.177755 | − | 0.984075i | \(-0.443117\pi\) | ||||
0.177755 | + | 0.984075i | \(0.443117\pi\) | |||||||
\(572\) | −2.20080 | −0.0920201 | ||||||||
\(573\) | −4.83937 | −0.202167 | ||||||||
\(574\) | −0.468764 | −0.0195658 | ||||||||
\(575\) | 25.2239 | 1.05191 | ||||||||
\(576\) | −2.62961 | −0.109567 | ||||||||
\(577\) | 36.8184 | 1.53277 | 0.766385 | − | 0.642381i | \(-0.222053\pi\) | ||||
0.766385 | + | 0.642381i | \(0.222053\pi\) | |||||||
\(578\) | 0.498945 | 0.0207534 | ||||||||
\(579\) | 10.6120 | 0.441018 | ||||||||
\(580\) | 5.76509 | 0.239382 | ||||||||
\(581\) | 1.97411 | 0.0818999 | ||||||||
\(582\) | −4.84391 | −0.200787 | ||||||||
\(583\) | −0.0108004 | −0.000447308 0 | ||||||||
\(584\) | 11.8607 | 0.490797 | ||||||||
\(585\) | 4.12066 | 0.170368 | ||||||||
\(586\) | 15.8201 | 0.653524 | ||||||||
\(587\) | −15.5905 | −0.643488 | −0.321744 | − | 0.946827i | \(-0.604269\pi\) | ||||
−0.321744 | + | 0.946827i | \(0.604269\pi\) | |||||||
\(588\) | −12.2362 | −0.504612 | ||||||||
\(589\) | 0.251756 | 0.0103734 | ||||||||
\(590\) | 1.20708 | 0.0496948 | ||||||||
\(591\) | −1.33752 | −0.0550181 | ||||||||
\(592\) | 19.5692 | 0.804291 | ||||||||
\(593\) | −35.5948 | −1.46170 | −0.730852 | − | 0.682536i | \(-0.760877\pi\) | ||||
−0.730852 | + | 0.682536i | \(0.760877\pi\) | |||||||
\(594\) | −0.0947393 | −0.00388720 | ||||||||
\(595\) | −0.0684891 | −0.00280778 | ||||||||
\(596\) | 25.5134 | 1.04507 | ||||||||
\(597\) | 13.6565 | 0.558922 | ||||||||
\(598\) | −18.0608 | −0.738560 | ||||||||
\(599\) | −18.9779 | −0.775417 | −0.387708 | − | 0.921782i | \(-0.626733\pi\) | ||||
−0.387708 | + | 0.921782i | \(0.626733\pi\) | |||||||
\(600\) | −8.63252 | −0.352421 | ||||||||
\(601\) | 35.2668 | 1.43856 | 0.719282 | − | 0.694718i | \(-0.244471\pi\) | ||||
0.719282 | + | 0.694718i | \(0.244471\pi\) | |||||||
\(602\) | −0.0673357 | −0.00274440 | ||||||||
\(603\) | −10.7555 | −0.437996 | ||||||||
\(604\) | −12.8151 | −0.521440 | ||||||||
\(605\) | −6.82543 | −0.277493 | ||||||||
\(606\) | 0.692548 | 0.0281328 | ||||||||
\(607\) | −9.22942 | −0.374611 | −0.187305 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187305 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(608\) | −0.309796 | −0.0125639 | ||||||||
\(609\) | 0.581837 | 0.0235772 | ||||||||
\(610\) | 1.07971 | 0.0437163 | ||||||||
\(611\) | 72.8537 | 2.94735 | ||||||||
\(612\) | 1.75105 | 0.0707822 | ||||||||
\(613\) | −9.69926 | −0.391750 | −0.195875 | − | 0.980629i | \(-0.562755\pi\) | ||||
−0.195875 | + | 0.980629i | \(0.562755\pi\) | |||||||
\(614\) | 7.64025 | 0.308335 | ||||||||
\(615\) | 5.31626 | 0.214372 | ||||||||
\(616\) | −0.0390969 | −0.00157526 | ||||||||
\(617\) | −1.65175 | −0.0664970 | −0.0332485 | − | 0.999447i | \(-0.510585\pi\) | ||||
−0.0332485 | + | 0.999447i | \(0.510585\pi\) | |||||||
\(618\) | 0.783940 | 0.0315347 | ||||||||
\(619\) | 13.8044 | 0.554845 | 0.277422 | − | 0.960748i | \(-0.410520\pi\) | ||||
0.277422 | + | 0.960748i | \(0.410520\pi\) | |||||||
\(620\) | 4.45109 | 0.178760 | ||||||||
\(621\) | 5.46866 | 0.219450 | ||||||||
\(622\) | 10.3072 | 0.413282 | ||||||||
\(623\) | 1.39926 | 0.0560600 | ||||||||
\(624\) | −17.0000 | −0.680545 | ||||||||
\(625\) | 19.3370 | 0.773478 | ||||||||
\(626\) | −8.91700 | −0.356395 | ||||||||
\(627\) | 0.0117072 | 0.000467542 0 | ||||||||
\(628\) | 1.75105 | 0.0698747 | ||||||||
\(629\) | −7.61954 | −0.303811 | ||||||||
\(630\) | 0.0341723 | 0.00136146 | ||||||||
\(631\) | −47.9318 | −1.90814 | −0.954068 | − | 0.299591i | \(-0.903150\pi\) | ||||
−0.954068 | + | 0.299591i | \(0.903150\pi\) | |||||||
\(632\) | 4.47376 | 0.177957 | ||||||||
\(633\) | 7.25466 | 0.288347 | ||||||||
\(634\) | −8.43013 | −0.334803 | ||||||||
\(635\) | 7.45435 | 0.295817 | ||||||||
\(636\) | −0.0996009 | −0.00394943 | ||||||||
\(637\) | −46.2540 | −1.83265 | ||||||||
\(638\) | −0.501041 | −0.0198364 | ||||||||
\(639\) | 6.87507 | 0.271974 | ||||||||
\(640\) | −7.07273 | −0.279574 | ||||||||
\(641\) | 15.4994 | 0.612189 | 0.306095 | − | 0.952001i | \(-0.400978\pi\) | ||||
0.306095 | + | 0.952001i | \(0.400978\pi\) | |||||||
\(642\) | −3.58722 | −0.141576 | ||||||||
\(643\) | −12.6980 | −0.500762 | −0.250381 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250381 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(644\) | 1.05351 | 0.0415141 | ||||||||
\(645\) | 0.763656 | 0.0300689 | ||||||||
\(646\) | 0.0307630 | 0.00121035 | ||||||||
\(647\) | 20.5803 | 0.809097 | 0.404548 | − | 0.914517i | \(-0.367429\pi\) | ||||
0.404548 | + | 0.914517i | \(0.367429\pi\) | |||||||
\(648\) | −1.87157 | −0.0735222 | ||||||||
\(649\) | 0.737903 | 0.0289652 | ||||||||
\(650\) | −15.2331 | −0.597490 | ||||||||
\(651\) | 0.449223 | 0.0176065 | ||||||||
\(652\) | −18.8564 | −0.738475 | ||||||||
\(653\) | −3.97714 | −0.155638 | −0.0778188 | − | 0.996968i | \(-0.524796\pi\) | ||||
−0.0778188 | + | 0.996968i | \(0.524796\pi\) | |||||||
\(654\) | 5.86773 | 0.229447 | ||||||||
\(655\) | −3.31154 | −0.129393 | ||||||||
\(656\) | −21.9325 | −0.856322 | ||||||||
\(657\) | −6.33728 | −0.247241 | ||||||||
\(658\) | 0.604170 | 0.0235530 | ||||||||
\(659\) | 10.1460 | 0.395231 | 0.197615 | − | 0.980280i | \(-0.436680\pi\) | ||||
0.197615 | + | 0.980280i | \(0.436680\pi\) | |||||||
\(660\) | 0.206986 | 0.00805691 | ||||||||
\(661\) | −49.2701 | −1.91639 | −0.958193 | − | 0.286121i | \(-0.907634\pi\) | ||||
−0.958193 | + | 0.286121i | \(0.907634\pi\) | |||||||
\(662\) | −15.2998 | −0.594643 | ||||||||
\(663\) | 6.61917 | 0.257067 | ||||||||
\(664\) | −33.5829 | −1.30327 | ||||||||
\(665\) | −0.00422278 | −0.000163752 0 | ||||||||
\(666\) | 3.80173 | 0.147314 | ||||||||
\(667\) | 28.9217 | 1.11985 | ||||||||
\(668\) | 8.96958 | 0.347043 | ||||||||
\(669\) | 25.7018 | 0.993691 | ||||||||
\(670\) | −3.34075 | −0.129065 | ||||||||
\(671\) | 0.660040 | 0.0254806 | ||||||||
\(672\) | −0.552787 | −0.0213242 | ||||||||
\(673\) | 41.3149 | 1.59257 | 0.796286 | − | 0.604921i | \(-0.206795\pi\) | ||||
0.796286 | + | 0.604921i | \(0.206795\pi\) | |||||||
\(674\) | 2.76851 | 0.106639 | ||||||||
\(675\) | 4.61245 | 0.177533 | ||||||||
\(676\) | −53.9559 | −2.07523 | ||||||||
\(677\) | −35.3660 | −1.35923 | −0.679614 | − | 0.733570i | \(-0.737853\pi\) | ||||
−0.679614 | + | 0.733570i | \(0.737853\pi\) | |||||||
\(678\) | −2.67696 | −0.102808 | ||||||||
\(679\) | 1.06808 | 0.0409890 | ||||||||
\(680\) | 1.16512 | 0.0446801 | ||||||||
\(681\) | 0.0456610 | 0.00174973 | ||||||||
\(682\) | −0.386842 | −0.0148130 | ||||||||
\(683\) | −28.1193 | −1.07595 | −0.537977 | − | 0.842960i | \(-0.680811\pi\) | ||||
−0.537977 | + | 0.842960i | \(0.680811\pi\) | |||||||
\(684\) | 0.107963 | 0.00412808 | ||||||||
\(685\) | −2.67719 | −0.102290 | ||||||||
\(686\) | −0.767827 | −0.0293158 | ||||||||
\(687\) | 5.83691 | 0.222692 | ||||||||
\(688\) | −3.15051 | −0.120112 | ||||||||
\(689\) | −0.376502 | −0.0143436 | ||||||||
\(690\) | 1.69862 | 0.0646654 | ||||||||
\(691\) | −23.5978 | −0.897704 | −0.448852 | − | 0.893606i | \(-0.648167\pi\) | ||||
−0.448852 | + | 0.893606i | \(0.648167\pi\) | |||||||
\(692\) | 31.0251 | 1.17940 | ||||||||
\(693\) | 0.0208899 | 0.000793541 0 | ||||||||
\(694\) | −8.59816 | −0.326382 | ||||||||
\(695\) | −13.2658 | −0.503199 | ||||||||
\(696\) | −9.89803 | −0.375184 | ||||||||
\(697\) | 8.53971 | 0.323465 | ||||||||
\(698\) | −2.94395 | −0.111430 | ||||||||
\(699\) | 7.68536 | 0.290687 | ||||||||
\(700\) | 0.888566 | 0.0335847 | ||||||||
\(701\) | −37.4447 | −1.41427 | −0.707133 | − | 0.707081i | \(-0.750012\pi\) | ||||
−0.707133 | + | 0.707081i | \(0.750012\pi\) | |||||||
\(702\) | −3.30260 | −0.124649 | ||||||||
\(703\) | −0.469791 | −0.0177185 | ||||||||
\(704\) | −0.499309 | −0.0188184 | ||||||||
\(705\) | −6.85191 | −0.258058 | ||||||||
\(706\) | −11.2234 | −0.422400 | ||||||||
\(707\) | −0.152706 | −0.00574310 | ||||||||
\(708\) | 6.80489 | 0.255743 | ||||||||
\(709\) | −43.9110 | −1.64911 | −0.824555 | − | 0.565781i | \(-0.808575\pi\) | ||||
−0.824555 | + | 0.565781i | \(0.808575\pi\) | |||||||
\(710\) | 2.13547 | 0.0801426 | ||||||||
\(711\) | −2.39038 | −0.0896463 | ||||||||
\(712\) | −23.8037 | −0.892082 | ||||||||
\(713\) | 22.3298 | 0.836257 | ||||||||
\(714\) | 0.0548922 | 0.00205429 | ||||||||
\(715\) | 0.782428 | 0.0292611 | ||||||||
\(716\) | 12.2976 | 0.459582 | ||||||||
\(717\) | −6.81710 | −0.254589 | ||||||||
\(718\) | 2.73407 | 0.102035 | ||||||||
\(719\) | −15.7143 | −0.586046 | −0.293023 | − | 0.956105i | \(-0.594661\pi\) | ||||
−0.293023 | + | 0.956105i | \(0.594661\pi\) | |||||||
\(720\) | 1.59885 | 0.0595858 | ||||||||
\(721\) | −0.172858 | −0.00643756 | ||||||||
\(722\) | −9.47805 | −0.352737 | ||||||||
\(723\) | 23.3281 | 0.867581 | ||||||||
\(724\) | 20.2648 | 0.753134 | ||||||||
\(725\) | 24.3935 | 0.905953 | ||||||||
\(726\) | 5.47040 | 0.203026 | ||||||||
\(727\) | 18.7455 | 0.695233 | 0.347617 | − | 0.937637i | \(-0.386991\pi\) | ||||
0.347617 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(728\) | −1.36291 | −0.0505128 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.96842 | −0.0728546 | ||||||||
\(731\) | 1.22669 | 0.0453708 | ||||||||
\(732\) | 6.08684 | 0.224976 | ||||||||
\(733\) | −40.9054 | −1.51087 | −0.755437 | − | 0.655221i | \(-0.772576\pi\) | ||||
−0.755437 | + | 0.655221i | \(0.772576\pi\) | |||||||
\(734\) | −9.91825 | −0.366089 | ||||||||
\(735\) | 4.35020 | 0.160460 | ||||||||
\(736\) | −27.4777 | −1.01284 | ||||||||
\(737\) | −2.04224 | −0.0752268 | ||||||||
\(738\) | −4.26084 | −0.156844 | ||||||||
\(739\) | 47.1152 | 1.73316 | 0.866580 | − | 0.499038i | \(-0.166313\pi\) | ||||
0.866580 | + | 0.499038i | \(0.166313\pi\) | |||||||
\(740\) | −8.30599 | −0.305334 | ||||||||
\(741\) | 0.408112 | 0.0149924 | ||||||||
\(742\) | −0.00312230 | −0.000114623 0 | ||||||||
\(743\) | 22.3958 | 0.821620 | 0.410810 | − | 0.911721i | \(-0.365246\pi\) | ||||
0.410810 | + | 0.911721i | \(0.365246\pi\) | |||||||
\(744\) | −7.64204 | −0.280171 | ||||||||
\(745\) | −9.07051 | −0.332318 | ||||||||
\(746\) | 12.8121 | 0.469086 | ||||||||
\(747\) | 17.9437 | 0.656527 | ||||||||
\(748\) | 0.332489 | 0.0121570 | ||||||||
\(749\) | 0.790977 | 0.0289017 | ||||||||
\(750\) | 2.98572 | 0.109023 | ||||||||
\(751\) | −2.90469 | −0.105994 | −0.0529969 | − | 0.998595i | \(-0.516877\pi\) | ||||
−0.0529969 | + | 0.998595i | \(0.516877\pi\) | |||||||
\(752\) | 28.2679 | 1.03083 | ||||||||
\(753\) | −2.30713 | −0.0840765 | ||||||||
\(754\) | −17.4662 | −0.636082 | ||||||||
\(755\) | 4.55603 | 0.165811 | ||||||||
\(756\) | 0.192645 | 0.00700644 | ||||||||
\(757\) | −27.5912 | −1.00282 | −0.501410 | − | 0.865210i | \(-0.667185\pi\) | ||||
−0.501410 | + | 0.865210i | \(0.667185\pi\) | |||||||
\(758\) | 17.3872 | 0.631533 | ||||||||
\(759\) | 1.03839 | 0.0376910 | ||||||||
\(760\) | 0.0718365 | 0.00260579 | ||||||||
\(761\) | 29.3935 | 1.06551 | 0.532757 | − | 0.846268i | \(-0.321156\pi\) | ||||
0.532757 | + | 0.846268i | \(0.321156\pi\) | |||||||
\(762\) | −5.97446 | −0.216432 | ||||||||
\(763\) | −1.29383 | −0.0468397 | ||||||||
\(764\) | −8.47399 | −0.306578 | ||||||||
\(765\) | −0.622534 | −0.0225078 | ||||||||
\(766\) | 13.7281 | 0.496015 | ||||||||
\(767\) | 25.7232 | 0.928810 | ||||||||
\(768\) | 0.409375 | 0.0147720 | ||||||||
\(769\) | 10.5904 | 0.381899 | 0.190950 | − | 0.981600i | \(-0.438843\pi\) | ||||
0.190950 | + | 0.981600i | \(0.438843\pi\) | |||||||
\(770\) | 0.00648861 | 0.000233833 0 | ||||||||
\(771\) | 11.9923 | 0.431892 | ||||||||
\(772\) | 18.5821 | 0.668785 | ||||||||
\(773\) | 41.9637 | 1.50933 | 0.754665 | − | 0.656110i | \(-0.227799\pi\) | ||||
0.754665 | + | 0.656110i | \(0.227799\pi\) | |||||||
\(774\) | −0.612050 | −0.0219997 | ||||||||
\(775\) | 18.8337 | 0.676526 | ||||||||
\(776\) | −18.1698 | −0.652257 | ||||||||
\(777\) | −0.838276 | −0.0300730 | ||||||||
\(778\) | −4.04472 | −0.145010 | ||||||||
\(779\) | 0.526526 | 0.0188647 | ||||||||
\(780\) | 7.21549 | 0.258356 | ||||||||
\(781\) | 1.30543 | 0.0467121 | ||||||||
\(782\) | 2.72856 | 0.0975731 | ||||||||
\(783\) | 5.28863 | 0.189000 | ||||||||
\(784\) | −17.9470 | −0.640965 | ||||||||
\(785\) | −0.622534 | −0.0222192 | ||||||||
\(786\) | 2.65411 | 0.0946691 | ||||||||
\(787\) | −12.7855 | −0.455755 | −0.227877 | − | 0.973690i | \(-0.573179\pi\) | ||||
−0.227877 | + | 0.973690i | \(0.573179\pi\) | |||||||
\(788\) | −2.34206 | −0.0834325 | ||||||||
\(789\) | −20.1830 | −0.718535 | ||||||||
\(790\) | −0.742477 | −0.0264161 | ||||||||
\(791\) | 0.590266 | 0.0209874 | ||||||||
\(792\) | −0.355372 | −0.0126276 | ||||||||
\(793\) | 23.0089 | 0.817070 | ||||||||
\(794\) | 8.37198 | 0.297110 | ||||||||
\(795\) | 0.0354101 | 0.00125587 | ||||||||
\(796\) | 23.9132 | 0.847581 | ||||||||
\(797\) | 30.3721 | 1.07583 | 0.537917 | − | 0.842997i | \(-0.319211\pi\) | ||||
0.537917 | + | 0.842997i | \(0.319211\pi\) | |||||||
\(798\) | 0.00338444 | 0.000119808 0 | ||||||||
\(799\) | −11.0065 | −0.389381 | ||||||||
\(800\) | −23.1756 | −0.819382 | ||||||||
\(801\) | 12.7186 | 0.449389 | ||||||||
\(802\) | 16.1046 | 0.568673 | ||||||||
\(803\) | −1.20332 | −0.0424642 | ||||||||
\(804\) | −18.8334 | −0.664202 | ||||||||
\(805\) | −0.374544 | −0.0132009 | ||||||||
\(806\) | −13.4853 | −0.474998 | ||||||||
\(807\) | 29.9514 | 1.05434 | ||||||||
\(808\) | 2.59778 | 0.0913897 | ||||||||
\(809\) | −19.7563 | −0.694594 | −0.347297 | − | 0.937755i | \(-0.612900\pi\) | ||||
−0.347297 | + | 0.937755i | \(0.612900\pi\) | |||||||
\(810\) | 0.310610 | 0.0109137 | ||||||||
\(811\) | 9.69439 | 0.340416 | 0.170208 | − | 0.985408i | \(-0.445556\pi\) | ||||
0.170208 | + | 0.985408i | \(0.445556\pi\) | |||||||
\(812\) | 1.01883 | 0.0357539 | ||||||||
\(813\) | 6.64163 | 0.232932 | ||||||||
\(814\) | 0.721869 | 0.0253015 | ||||||||
\(815\) | 6.70383 | 0.234825 | ||||||||
\(816\) | 2.56830 | 0.0899085 | ||||||||
\(817\) | 0.0756330 | 0.00264606 | ||||||||
\(818\) | −3.70392 | −0.129505 | ||||||||
\(819\) | 0.728219 | 0.0254460 | ||||||||
\(820\) | 9.30907 | 0.325087 | ||||||||
\(821\) | 11.9684 | 0.417700 | 0.208850 | − | 0.977948i | \(-0.433028\pi\) | ||||
0.208850 | + | 0.977948i | \(0.433028\pi\) | |||||||
\(822\) | 2.14570 | 0.0748398 | ||||||||
\(823\) | 27.7894 | 0.968676 | 0.484338 | − | 0.874881i | \(-0.339061\pi\) | ||||
0.484338 | + | 0.874881i | \(0.339061\pi\) | |||||||
\(824\) | 2.94060 | 0.102441 | ||||||||
\(825\) | 0.875809 | 0.0304918 | ||||||||
\(826\) | 0.213320 | 0.00742237 | ||||||||
\(827\) | −23.8914 | −0.830786 | −0.415393 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415393 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(828\) | 9.57592 | 0.332786 | ||||||||
\(829\) | −51.7532 | −1.79746 | −0.898732 | − | 0.438498i | \(-0.855510\pi\) | ||||
−0.898732 | + | 0.438498i | \(0.855510\pi\) | |||||||
\(830\) | 5.57351 | 0.193459 | ||||||||
\(831\) | 0.752550 | 0.0261057 | ||||||||
\(832\) | −17.4058 | −0.603439 | ||||||||
\(833\) | 6.98790 | 0.242116 | ||||||||
\(834\) | 10.6322 | 0.368162 | ||||||||
\(835\) | −3.18886 | −0.110355 | ||||||||
\(836\) | 0.0205000 | 0.000709007 0 | ||||||||
\(837\) | 4.08323 | 0.141137 | ||||||||
\(838\) | −9.45829 | −0.326731 | ||||||||
\(839\) | −3.45559 | −0.119300 | −0.0596500 | − | 0.998219i | \(-0.518998\pi\) | ||||
−0.0596500 | + | 0.998219i | \(0.518998\pi\) | |||||||
\(840\) | 0.128182 | 0.00442270 | ||||||||
\(841\) | −1.03042 | −0.0355319 | ||||||||
\(842\) | −11.6817 | −0.402579 | ||||||||
\(843\) | 17.1481 | 0.590611 | ||||||||
\(844\) | 12.7033 | 0.437266 | ||||||||
\(845\) | 19.1824 | 0.659894 | ||||||||
\(846\) | 5.49162 | 0.188806 | ||||||||
\(847\) | −1.20622 | −0.0414461 | ||||||||
\(848\) | −0.146086 | −0.00501662 | ||||||||
\(849\) | 19.3556 | 0.664282 | ||||||||
\(850\) | 2.30136 | 0.0789359 | ||||||||
\(851\) | −41.6686 | −1.42838 | ||||||||
\(852\) | 12.0386 | 0.412436 | ||||||||
\(853\) | −21.5188 | −0.736789 | −0.368394 | − | 0.929670i | \(-0.620092\pi\) | ||||
−0.368394 | + | 0.929670i | \(0.620092\pi\) | |||||||
\(854\) | 0.190811 | 0.00652942 | ||||||||
\(855\) | −0.0383831 | −0.00131267 | ||||||||
\(856\) | −13.4558 | −0.459911 | ||||||||
\(857\) | −20.6835 | −0.706535 | −0.353267 | − | 0.935522i | \(-0.614929\pi\) | ||||
−0.353267 | + | 0.935522i | \(0.614929\pi\) | |||||||
\(858\) | −0.627095 | −0.0214087 | ||||||||
\(859\) | 19.2852 | 0.658002 | 0.329001 | − | 0.944329i | \(-0.393288\pi\) | ||||
0.329001 | + | 0.944329i | \(0.393288\pi\) | |||||||
\(860\) | 1.33720 | 0.0455983 | ||||||||
\(861\) | 0.939511 | 0.0320184 | ||||||||
\(862\) | −12.7163 | −0.433118 | ||||||||
\(863\) | −42.0720 | −1.43215 | −0.716075 | − | 0.698024i | \(-0.754063\pi\) | ||||
−0.716075 | + | 0.698024i | \(0.754063\pi\) | |||||||
\(864\) | −5.02458 | −0.170940 | ||||||||
\(865\) | −11.0300 | −0.375033 | ||||||||
\(866\) | −12.2374 | −0.415843 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0.786614 | 0.0266994 | ||||||||
\(869\) | −0.453884 | −0.0153970 | ||||||||
\(870\) | 1.64270 | 0.0556928 | ||||||||
\(871\) | −71.1921 | −2.41225 | ||||||||
\(872\) | 22.0102 | 0.745359 | ||||||||
\(873\) | 9.70831 | 0.328577 | ||||||||
\(874\) | 0.168232 | 0.00569055 | ||||||||
\(875\) | −0.658349 | −0.0222562 | ||||||||
\(876\) | −11.0969 | −0.374930 | ||||||||
\(877\) | 19.3400 | 0.653066 | 0.326533 | − | 0.945186i | \(-0.394120\pi\) | ||||
0.326533 | + | 0.945186i | \(0.394120\pi\) | |||||||
\(878\) | −4.56404 | −0.154029 | ||||||||
\(879\) | −31.7072 | −1.06946 | ||||||||
\(880\) | 0.303589 | 0.0102340 | ||||||||
\(881\) | −20.6559 | −0.695915 | −0.347957 | − | 0.937510i | \(-0.613125\pi\) | ||||
−0.347957 | + | 0.937510i | \(0.613125\pi\) | |||||||
\(882\) | −3.48657 | −0.117399 | ||||||||
\(883\) | −57.3331 | −1.92941 | −0.964705 | − | 0.263331i | \(-0.915179\pi\) | ||||
−0.964705 | + | 0.263331i | \(0.915179\pi\) | |||||||
\(884\) | 11.5905 | 0.389831 | ||||||||
\(885\) | −2.41927 | −0.0813229 | ||||||||
\(886\) | 15.6806 | 0.526802 | ||||||||
\(887\) | −1.67229 | −0.0561500 | −0.0280750 | − | 0.999606i | \(-0.508938\pi\) | ||||
−0.0280750 | + | 0.999606i | \(0.508938\pi\) | |||||||
\(888\) | 14.2605 | 0.478550 | ||||||||
\(889\) | 1.31736 | 0.0441829 | ||||||||
\(890\) | 3.95052 | 0.132422 | ||||||||
\(891\) | 0.189879 | 0.00636120 | ||||||||
\(892\) | 45.0053 | 1.50689 | ||||||||
\(893\) | −0.678617 | −0.0227091 | ||||||||
\(894\) | 7.26977 | 0.243137 | ||||||||
\(895\) | −4.37203 | −0.146141 | ||||||||
\(896\) | −1.24992 | −0.0417569 | ||||||||
\(897\) | 36.1980 | 1.20861 | ||||||||
\(898\) | −19.6374 | −0.655310 | ||||||||
\(899\) | 21.5947 | 0.720223 | ||||||||
\(900\) | 8.07665 | 0.269222 | ||||||||
\(901\) | 0.0568805 | 0.00189496 | ||||||||
\(902\) | −0.809046 | −0.0269383 | ||||||||
\(903\) | 0.134956 | 0.00449107 | ||||||||
\(904\) | −10.0414 | −0.333973 | ||||||||
\(905\) | −7.20452 | −0.239487 | ||||||||
\(906\) | −3.65154 | −0.121314 | ||||||||
\(907\) | −59.1439 | −1.96384 | −0.981921 | − | 0.189292i | \(-0.939381\pi\) | ||||
−0.981921 | + | 0.189292i | \(0.939381\pi\) | |||||||
\(908\) | 0.0799549 | 0.00265340 | ||||||||
\(909\) | −1.38802 | −0.0460379 | ||||||||
\(910\) | 0.226192 | 0.00749819 | ||||||||
\(911\) | 23.3755 | 0.774465 | 0.387232 | − | 0.921982i | \(-0.373431\pi\) | ||||
0.387232 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(912\) | 0.158351 | 0.00524354 | ||||||||
\(913\) | 3.40714 | 0.112760 | ||||||||
\(914\) | 3.23274 | 0.106930 | ||||||||
\(915\) | −2.16399 | −0.0715394 | ||||||||
\(916\) | 10.2207 | 0.337703 | ||||||||
\(917\) | −0.585229 | −0.0193260 | ||||||||
\(918\) | 0.498945 | 0.0164676 | ||||||||
\(919\) | −51.9293 | −1.71299 | −0.856494 | − | 0.516157i | \(-0.827362\pi\) | ||||
−0.856494 | + | 0.516157i | \(0.827362\pi\) | |||||||
\(920\) | 6.37162 | 0.210066 | ||||||||
\(921\) | −15.3128 | −0.504574 | ||||||||
\(922\) | −15.5257 | −0.511311 | ||||||||
\(923\) | 45.5072 | 1.49789 | ||||||||
\(924\) | 0.0365793 | 0.00120337 | ||||||||
\(925\) | −35.1447 | −1.15555 | ||||||||
\(926\) | −15.2648 | −0.501633 | ||||||||
\(927\) | −1.57120 | −0.0516049 | ||||||||
\(928\) | −26.5731 | −0.872305 | ||||||||
\(929\) | 1.07154 | 0.0351560 | 0.0175780 | − | 0.999845i | \(-0.494404\pi\) | ||||
0.0175780 | + | 0.999845i | \(0.494404\pi\) | |||||||
\(930\) | 1.26829 | 0.0415889 | ||||||||
\(931\) | 0.430847 | 0.0141204 | ||||||||
\(932\) | 13.4575 | 0.440815 | ||||||||
\(933\) | −20.6581 | −0.676314 | ||||||||
\(934\) | 13.0932 | 0.428422 | ||||||||
\(935\) | −0.118206 | −0.00386576 | ||||||||
\(936\) | −12.3882 | −0.404922 | ||||||||
\(937\) | −2.80111 | −0.0915084 | −0.0457542 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457542 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(938\) | −0.590391 | −0.0192769 | ||||||||
\(939\) | 17.8717 | 0.583222 | ||||||||
\(940\) | −11.9981 | −0.391334 | ||||||||
\(941\) | 0.510951 | 0.0166565 | 0.00832827 | − | 0.999965i | \(-0.497349\pi\) | ||||
0.00832827 | + | 0.999965i | \(0.497349\pi\) | |||||||
\(942\) | 0.498945 | 0.0162565 | ||||||||
\(943\) | 46.7008 | 1.52079 | ||||||||
\(944\) | 9.98084 | 0.324849 | ||||||||
\(945\) | −0.0684891 | −0.00222795 | ||||||||
\(946\) | −0.116216 | −0.00377850 | ||||||||
\(947\) | 14.4806 | 0.470557 | 0.235278 | − | 0.971928i | \(-0.424400\pi\) | ||||
0.235278 | + | 0.971928i | \(0.424400\pi\) | |||||||
\(948\) | −4.18569 | −0.135945 | ||||||||
\(949\) | −41.9475 | −1.36167 | ||||||||
\(950\) | 0.141893 | 0.00460361 | ||||||||
\(951\) | 16.8959 | 0.547888 | ||||||||
\(952\) | 0.205904 | 0.00667338 | ||||||||
\(953\) | 37.3143 | 1.20873 | 0.604365 | − | 0.796708i | \(-0.293427\pi\) | ||||
0.604365 | + | 0.796708i | \(0.293427\pi\) | |||||||
\(954\) | −0.0283802 | −0.000918844 0 | ||||||||
\(955\) | 3.01267 | 0.0974877 | ||||||||
\(956\) | −11.9371 | −0.386074 | ||||||||
\(957\) | 1.00420 | 0.0324612 | ||||||||
\(958\) | 16.8833 | 0.545475 | ||||||||
\(959\) | −0.473124 | −0.0152780 | ||||||||
\(960\) | 1.63702 | 0.0528347 | ||||||||
\(961\) | −14.3272 | −0.462169 | ||||||||
\(962\) | 25.1643 | 0.811328 | ||||||||
\(963\) | 7.18961 | 0.231682 | ||||||||
\(964\) | 40.8488 | 1.31565 | ||||||||
\(965\) | −6.60630 | −0.212664 | ||||||||
\(966\) | 0.300187 | 0.00965836 | ||||||||
\(967\) | −8.80310 | −0.283089 | −0.141544 | − | 0.989932i | \(-0.545207\pi\) | ||||
−0.141544 | + | 0.989932i | \(0.545207\pi\) | |||||||
\(968\) | 20.5198 | 0.659531 | ||||||||
\(969\) | −0.0616562 | −0.00198068 | ||||||||
\(970\) | 3.01550 | 0.0968219 | ||||||||
\(971\) | 8.92922 | 0.286552 | 0.143276 | − | 0.989683i | \(-0.454236\pi\) | ||||
0.143276 | + | 0.989683i | \(0.454236\pi\) | |||||||
\(972\) | 1.75105 | 0.0561651 | ||||||||
\(973\) | −2.34438 | −0.0751573 | ||||||||
\(974\) | 5.61503 | 0.179917 | ||||||||
\(975\) | 30.5306 | 0.977761 | ||||||||
\(976\) | 8.92767 | 0.285768 | ||||||||
\(977\) | −24.3957 | −0.780488 | −0.390244 | − | 0.920711i | \(-0.627609\pi\) | ||||
−0.390244 | + | 0.920711i | \(0.627609\pi\) | |||||||
\(978\) | −5.37294 | −0.171808 | ||||||||
\(979\) | 2.41500 | 0.0771836 | ||||||||
\(980\) | 7.61744 | 0.243330 | ||||||||
\(981\) | −11.7603 | −0.375477 | ||||||||
\(982\) | −14.4264 | −0.460366 | ||||||||
\(983\) | 52.1478 | 1.66326 | 0.831628 | − | 0.555333i | \(-0.187409\pi\) | ||||
0.831628 | + | 0.555333i | \(0.187409\pi\) | |||||||
\(984\) | −15.9827 | −0.509509 | ||||||||
\(985\) | 0.832649 | 0.0265304 | ||||||||
\(986\) | 2.63873 | 0.0840344 | ||||||||
\(987\) | −1.21090 | −0.0385433 | ||||||||
\(988\) | 0.714627 | 0.0227353 | ||||||||
\(989\) | 6.70835 | 0.213313 | ||||||||
\(990\) | 0.0589784 | 0.00187446 | ||||||||
\(991\) | −21.5669 | −0.685095 | −0.342547 | − | 0.939501i | \(-0.611290\pi\) | ||||
−0.342547 | + | 0.939501i | \(0.611290\pi\) | |||||||
\(992\) | −20.5165 | −0.651399 | ||||||||
\(993\) | 30.6643 | 0.973102 | ||||||||
\(994\) | 0.377388 | 0.0119700 | ||||||||
\(995\) | −8.50161 | −0.269519 | ||||||||
\(996\) | 31.4205 | 0.995595 | ||||||||
\(997\) | −46.4744 | −1.47186 | −0.735930 | − | 0.677058i | \(-0.763255\pi\) | ||||
−0.735930 | + | 0.677058i | \(0.763255\pi\) | |||||||
\(998\) | 18.4952 | 0.585457 | ||||||||
\(999\) | −7.61954 | −0.241071 |
(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.1.28 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.28 | ✓ | 48 | 1.1 | even | 1 | trivial |