Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.31833 | −1.33849 | −0.669244 | − | 0.743043i | \(-0.733382\pi\) | ||||
−0.669244 | + | 0.743043i | \(0.733382\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.68969 | 0.755654 | 0.377827 | − | 0.925876i | \(-0.376671\pi\) | ||||
0.377827 | + | 0.925876i | \(0.376671\pi\) | |||||||
\(6\) | 2.31833 | 0.946454 | ||||||||
\(7\) | −0.814652 | −0.307910 | −0.153955 | − | 0.988078i | \(-0.549201\pi\) | ||||
−0.153955 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.37465 | 0.791551 | ||||||||
\(10\) | −1.68969 | −0.534328 | ||||||||
\(11\) | −5.83910 | −1.76056 | −0.880278 | − | 0.474458i | \(-0.842644\pi\) | ||||
−0.880278 | + | 0.474458i | \(0.842644\pi\) | |||||||
\(12\) | −2.31833 | −0.669244 | ||||||||
\(13\) | −4.73646 | −1.31366 | −0.656828 | − | 0.754040i | \(-0.728102\pi\) | ||||
−0.656828 | + | 0.754040i | \(0.728102\pi\) | |||||||
\(14\) | 0.814652 | 0.217725 | ||||||||
\(15\) | −3.91727 | −1.01143 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.01151 | −0.245326 | −0.122663 | − | 0.992448i | \(-0.539143\pi\) | ||||
−0.122663 | + | 0.992448i | \(0.539143\pi\) | |||||||
\(18\) | −2.37465 | −0.559711 | ||||||||
\(19\) | −2.53939 | −0.582576 | −0.291288 | − | 0.956635i | \(-0.594084\pi\) | ||||
−0.291288 | + | 0.956635i | \(0.594084\pi\) | |||||||
\(20\) | 1.68969 | 0.377827 | ||||||||
\(21\) | 1.88863 | 0.412134 | ||||||||
\(22\) | 5.83910 | 1.24490 | ||||||||
\(23\) | 2.68664 | 0.560204 | 0.280102 | − | 0.959970i | \(-0.409632\pi\) | ||||
0.280102 | + | 0.959970i | \(0.409632\pi\) | |||||||
\(24\) | 2.31833 | 0.473227 | ||||||||
\(25\) | −2.14494 | −0.428987 | ||||||||
\(26\) | 4.73646 | 0.928896 | ||||||||
\(27\) | 1.44976 | 0.279006 | ||||||||
\(28\) | −0.814652 | −0.153955 | ||||||||
\(29\) | −2.75110 | −0.510867 | −0.255434 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255434 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(30\) | 3.91727 | 0.715192 | ||||||||
\(31\) | −4.44777 | −0.798843 | −0.399421 | − | 0.916767i | \(-0.630789\pi\) | ||||
−0.399421 | + | 0.916767i | \(0.630789\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 13.5370 | 2.35648 | ||||||||
\(34\) | 1.01151 | 0.173472 | ||||||||
\(35\) | −1.37651 | −0.232673 | ||||||||
\(36\) | 2.37465 | 0.395776 | ||||||||
\(37\) | −8.47287 | −1.39293 | −0.696465 | − | 0.717591i | \(-0.745245\pi\) | ||||
−0.696465 | + | 0.717591i | \(0.745245\pi\) | |||||||
\(38\) | 2.53939 | 0.411944 | ||||||||
\(39\) | 10.9807 | 1.75831 | ||||||||
\(40\) | −1.68969 | −0.267164 | ||||||||
\(41\) | −8.32697 | −1.30045 | −0.650227 | − | 0.759740i | \(-0.725326\pi\) | ||||
−0.650227 | + | 0.759740i | \(0.725326\pi\) | |||||||
\(42\) | −1.88863 | −0.291422 | ||||||||
\(43\) | −3.72335 | −0.567806 | −0.283903 | − | 0.958853i | \(-0.591629\pi\) | ||||
−0.283903 | + | 0.958853i | \(0.591629\pi\) | |||||||
\(44\) | −5.83910 | −0.880278 | ||||||||
\(45\) | 4.01244 | 0.598139 | ||||||||
\(46\) | −2.68664 | −0.396124 | ||||||||
\(47\) | −0.952924 | −0.138998 | −0.0694991 | − | 0.997582i | \(-0.522140\pi\) | ||||
−0.0694991 | + | 0.997582i | \(0.522140\pi\) | |||||||
\(48\) | −2.31833 | −0.334622 | ||||||||
\(49\) | −6.33634 | −0.905192 | ||||||||
\(50\) | 2.14494 | 0.303340 | ||||||||
\(51\) | 2.34500 | 0.328366 | ||||||||
\(52\) | −4.73646 | −0.656828 | ||||||||
\(53\) | −10.2214 | −1.40401 | −0.702005 | − | 0.712172i | \(-0.747712\pi\) | ||||
−0.702005 | + | 0.712172i | \(0.747712\pi\) | |||||||
\(54\) | −1.44976 | −0.197287 | ||||||||
\(55\) | −9.86630 | −1.33037 | ||||||||
\(56\) | 0.814652 | 0.108863 | ||||||||
\(57\) | 5.88715 | 0.779772 | ||||||||
\(58\) | 2.75110 | 0.361238 | ||||||||
\(59\) | −5.71856 | −0.744493 | −0.372246 | − | 0.928134i | \(-0.621412\pi\) | ||||
−0.372246 | + | 0.928134i | \(0.621412\pi\) | |||||||
\(60\) | −3.91727 | −0.505717 | ||||||||
\(61\) | 10.5287 | 1.34806 | 0.674031 | − | 0.738703i | \(-0.264561\pi\) | ||||
0.674031 | + | 0.738703i | \(0.264561\pi\) | |||||||
\(62\) | 4.44777 | 0.564867 | ||||||||
\(63\) | −1.93452 | −0.243726 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.00316 | −0.992670 | ||||||||
\(66\) | −13.5370 | −1.66629 | ||||||||
\(67\) | 8.23232 | 1.00574 | 0.502869 | − | 0.864362i | \(-0.332278\pi\) | ||||
0.502869 | + | 0.864362i | \(0.332278\pi\) | |||||||
\(68\) | −1.01151 | −0.122663 | ||||||||
\(69\) | −6.22852 | −0.749826 | ||||||||
\(70\) | 1.37651 | 0.164525 | ||||||||
\(71\) | −3.16569 | −0.375699 | −0.187849 | − | 0.982198i | \(-0.560152\pi\) | ||||
−0.187849 | + | 0.982198i | \(0.560152\pi\) | |||||||
\(72\) | −2.37465 | −0.279856 | ||||||||
\(73\) | −2.69014 | −0.314857 | −0.157429 | − | 0.987530i | \(-0.550320\pi\) | ||||
−0.157429 | + | 0.987530i | \(0.550320\pi\) | |||||||
\(74\) | 8.47287 | 0.984951 | ||||||||
\(75\) | 4.97267 | 0.574194 | ||||||||
\(76\) | −2.53939 | −0.291288 | ||||||||
\(77\) | 4.75684 | 0.542092 | ||||||||
\(78\) | −10.9807 | −1.24332 | ||||||||
\(79\) | −5.66322 | −0.637162 | −0.318581 | − | 0.947896i | \(-0.603206\pi\) | ||||
−0.318581 | + | 0.947896i | \(0.603206\pi\) | |||||||
\(80\) | 1.68969 | 0.188914 | ||||||||
\(81\) | −10.4850 | −1.16500 | ||||||||
\(82\) | 8.32697 | 0.919560 | ||||||||
\(83\) | 9.07757 | 0.996393 | 0.498196 | − | 0.867064i | \(-0.333996\pi\) | ||||
0.498196 | + | 0.867064i | \(0.333996\pi\) | |||||||
\(84\) | 1.88863 | 0.206067 | ||||||||
\(85\) | −1.70913 | −0.185382 | ||||||||
\(86\) | 3.72335 | 0.401500 | ||||||||
\(87\) | 6.37797 | 0.683790 | ||||||||
\(88\) | 5.83910 | 0.622451 | ||||||||
\(89\) | −10.1093 | −1.07158 | −0.535790 | − | 0.844352i | \(-0.679986\pi\) | ||||
−0.535790 | + | 0.844352i | \(0.679986\pi\) | |||||||
\(90\) | −4.01244 | −0.422948 | ||||||||
\(91\) | 3.85857 | 0.404488 | ||||||||
\(92\) | 2.68664 | 0.280102 | ||||||||
\(93\) | 10.3114 | 1.06924 | ||||||||
\(94\) | 0.952924 | 0.0982866 | ||||||||
\(95\) | −4.29079 | −0.440226 | ||||||||
\(96\) | 2.31833 | 0.236614 | ||||||||
\(97\) | −18.1792 | −1.84581 | −0.922907 | − | 0.385023i | \(-0.874193\pi\) | ||||
−0.922907 | + | 0.385023i | \(0.874193\pi\) | |||||||
\(98\) | 6.33634 | 0.640067 | ||||||||
\(99\) | −13.8659 | −1.39357 | ||||||||
\(100\) | −2.14494 | −0.214494 | ||||||||
\(101\) | 10.7997 | 1.07461 | 0.537307 | − | 0.843387i | \(-0.319442\pi\) | ||||
0.537307 | + | 0.843387i | \(0.319442\pi\) | |||||||
\(102\) | −2.34500 | −0.232190 | ||||||||
\(103\) | 14.8806 | 1.46623 | 0.733115 | − | 0.680105i | \(-0.238066\pi\) | ||||
0.733115 | + | 0.680105i | \(0.238066\pi\) | |||||||
\(104\) | 4.73646 | 0.464448 | ||||||||
\(105\) | 3.19121 | 0.311430 | ||||||||
\(106\) | 10.2214 | 0.992786 | ||||||||
\(107\) | −12.9105 | −1.24810 | −0.624051 | − | 0.781383i | \(-0.714514\pi\) | ||||
−0.624051 | + | 0.781383i | \(0.714514\pi\) | |||||||
\(108\) | 1.44976 | 0.139503 | ||||||||
\(109\) | 1.66886 | 0.159848 | 0.0799238 | − | 0.996801i | \(-0.474532\pi\) | ||||
0.0799238 | + | 0.996801i | \(0.474532\pi\) | |||||||
\(110\) | 9.86630 | 0.940715 | ||||||||
\(111\) | 19.6429 | 1.86442 | ||||||||
\(112\) | −0.814652 | −0.0769774 | ||||||||
\(113\) | −10.5034 | −0.988073 | −0.494036 | − | 0.869441i | \(-0.664479\pi\) | ||||
−0.494036 | + | 0.869441i | \(0.664479\pi\) | |||||||
\(114\) | −5.88715 | −0.551382 | ||||||||
\(115\) | 4.53960 | 0.423320 | ||||||||
\(116\) | −2.75110 | −0.255434 | ||||||||
\(117\) | −11.2474 | −1.03983 | ||||||||
\(118\) | 5.71856 | 0.526436 | ||||||||
\(119\) | 0.824025 | 0.0755383 | ||||||||
\(120\) | 3.91727 | 0.357596 | ||||||||
\(121\) | 23.0951 | 2.09956 | ||||||||
\(122\) | −10.5287 | −0.953224 | ||||||||
\(123\) | 19.3047 | 1.74064 | ||||||||
\(124\) | −4.44777 | −0.399421 | ||||||||
\(125\) | −12.0728 | −1.07982 | ||||||||
\(126\) | 1.93452 | 0.172341 | ||||||||
\(127\) | 10.3415 | 0.917657 | 0.458828 | − | 0.888525i | \(-0.348269\pi\) | ||||
0.458828 | + | 0.888525i | \(0.348269\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.63196 | 0.760002 | ||||||||
\(130\) | 8.00316 | 0.701924 | ||||||||
\(131\) | 7.81223 | 0.682558 | 0.341279 | − | 0.939962i | \(-0.389140\pi\) | ||||
0.341279 | + | 0.939962i | \(0.389140\pi\) | |||||||
\(132\) | 13.5370 | 1.17824 | ||||||||
\(133\) | 2.06872 | 0.179381 | ||||||||
\(134\) | −8.23232 | −0.711164 | ||||||||
\(135\) | 2.44965 | 0.210832 | ||||||||
\(136\) | 1.01151 | 0.0867359 | ||||||||
\(137\) | −10.2482 | −0.875559 | −0.437780 | − | 0.899082i | \(-0.644235\pi\) | ||||
−0.437780 | + | 0.899082i | \(0.644235\pi\) | |||||||
\(138\) | 6.22852 | 0.530207 | ||||||||
\(139\) | −10.6722 | −0.905205 | −0.452602 | − | 0.891713i | \(-0.649504\pi\) | ||||
−0.452602 | + | 0.891713i | \(0.649504\pi\) | |||||||
\(140\) | −1.37651 | −0.116337 | ||||||||
\(141\) | 2.20919 | 0.186047 | ||||||||
\(142\) | 3.16569 | 0.265659 | ||||||||
\(143\) | 27.6567 | 2.31277 | ||||||||
\(144\) | 2.37465 | 0.197888 | ||||||||
\(145\) | −4.64852 | −0.386039 | ||||||||
\(146\) | 2.69014 | 0.222638 | ||||||||
\(147\) | 14.6897 | 1.21159 | ||||||||
\(148\) | −8.47287 | −0.696465 | ||||||||
\(149\) | −5.21187 | −0.426973 | −0.213487 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213487 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(150\) | −4.97267 | −0.406017 | ||||||||
\(151\) | 6.83386 | 0.556132 | 0.278066 | − | 0.960562i | \(-0.410307\pi\) | ||||
0.278066 | + | 0.960562i | \(0.410307\pi\) | |||||||
\(152\) | 2.53939 | 0.205972 | ||||||||
\(153\) | −2.40198 | −0.194188 | ||||||||
\(154\) | −4.75684 | −0.383317 | ||||||||
\(155\) | −7.51537 | −0.603649 | ||||||||
\(156\) | 10.9807 | 0.879157 | ||||||||
\(157\) | −4.01248 | −0.320231 | −0.160115 | − | 0.987098i | \(-0.551187\pi\) | ||||
−0.160115 | + | 0.987098i | \(0.551187\pi\) | |||||||
\(158\) | 5.66322 | 0.450541 | ||||||||
\(159\) | 23.6965 | 1.87925 | ||||||||
\(160\) | −1.68969 | −0.133582 | ||||||||
\(161\) | −2.18868 | −0.172492 | ||||||||
\(162\) | 10.4850 | 0.823778 | ||||||||
\(163\) | 9.98607 | 0.782170 | 0.391085 | − | 0.920355i | \(-0.372100\pi\) | ||||
0.391085 | + | 0.920355i | \(0.372100\pi\) | |||||||
\(164\) | −8.32697 | −0.650227 | ||||||||
\(165\) | 22.8733 | 1.78069 | ||||||||
\(166\) | −9.07757 | −0.704556 | ||||||||
\(167\) | −16.0394 | −1.24117 | −0.620584 | − | 0.784140i | \(-0.713104\pi\) | ||||
−0.620584 | + | 0.784140i | \(0.713104\pi\) | |||||||
\(168\) | −1.88863 | −0.145711 | ||||||||
\(169\) | 9.43402 | 0.725694 | ||||||||
\(170\) | 1.70913 | 0.131085 | ||||||||
\(171\) | −6.03017 | −0.461139 | ||||||||
\(172\) | −3.72335 | −0.283903 | ||||||||
\(173\) | 2.94315 | 0.223764 | 0.111882 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111882 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(174\) | −6.37797 | −0.483512 | ||||||||
\(175\) | 1.74738 | 0.132089 | ||||||||
\(176\) | −5.83910 | −0.440139 | ||||||||
\(177\) | 13.2575 | 0.996495 | ||||||||
\(178\) | 10.1093 | 0.757721 | ||||||||
\(179\) | 16.8723 | 1.26109 | 0.630547 | − | 0.776151i | \(-0.282831\pi\) | ||||
0.630547 | + | 0.776151i | \(0.282831\pi\) | |||||||
\(180\) | 4.01244 | 0.299069 | ||||||||
\(181\) | −14.1064 | −1.04852 | −0.524261 | − | 0.851558i | \(-0.675658\pi\) | ||||
−0.524261 | + | 0.851558i | \(0.675658\pi\) | |||||||
\(182\) | −3.85857 | −0.286016 | ||||||||
\(183\) | −24.4090 | −1.80437 | ||||||||
\(184\) | −2.68664 | −0.198062 | ||||||||
\(185\) | −14.3165 | −1.05257 | ||||||||
\(186\) | −10.3114 | −0.756068 | ||||||||
\(187\) | 5.90629 | 0.431910 | ||||||||
\(188\) | −0.952924 | −0.0694991 | ||||||||
\(189\) | −1.18105 | −0.0859087 | ||||||||
\(190\) | 4.29079 | 0.311287 | ||||||||
\(191\) | 19.6613 | 1.42264 | 0.711321 | − | 0.702867i | \(-0.248097\pi\) | ||||
0.711321 | + | 0.702867i | \(0.248097\pi\) | |||||||
\(192\) | −2.31833 | −0.167311 | ||||||||
\(193\) | 3.60799 | 0.259709 | 0.129854 | − | 0.991533i | \(-0.458549\pi\) | ||||
0.129854 | + | 0.991533i | \(0.458549\pi\) | |||||||
\(194\) | 18.1792 | 1.30519 | ||||||||
\(195\) | 18.5540 | 1.32868 | ||||||||
\(196\) | −6.33634 | −0.452596 | ||||||||
\(197\) | 5.96776 | 0.425185 | 0.212593 | − | 0.977141i | \(-0.431809\pi\) | ||||
0.212593 | + | 0.977141i | \(0.431809\pi\) | |||||||
\(198\) | 13.8659 | 0.985403 | ||||||||
\(199\) | 7.98637 | 0.566139 | 0.283069 | − | 0.959099i | \(-0.408647\pi\) | ||||
0.283069 | + | 0.959099i | \(0.408647\pi\) | |||||||
\(200\) | 2.14494 | 0.151670 | ||||||||
\(201\) | −19.0852 | −1.34617 | ||||||||
\(202\) | −10.7997 | −0.759867 | ||||||||
\(203\) | 2.24119 | 0.157301 | ||||||||
\(204\) | 2.34500 | 0.164183 | ||||||||
\(205\) | −14.0700 | −0.982694 | ||||||||
\(206\) | −14.8806 | −1.03678 | ||||||||
\(207\) | 6.37985 | 0.443430 | ||||||||
\(208\) | −4.73646 | −0.328414 | ||||||||
\(209\) | 14.8278 | 1.02566 | ||||||||
\(210\) | −3.19121 | −0.220215 | ||||||||
\(211\) | −20.0508 | −1.38035 | −0.690176 | − | 0.723641i | \(-0.742467\pi\) | ||||
−0.690176 | + | 0.723641i | \(0.742467\pi\) | |||||||
\(212\) | −10.2214 | −0.702005 | ||||||||
\(213\) | 7.33912 | 0.502868 | ||||||||
\(214\) | 12.9105 | 0.882542 | ||||||||
\(215\) | −6.29133 | −0.429065 | ||||||||
\(216\) | −1.44976 | −0.0986436 | ||||||||
\(217\) | 3.62339 | 0.245971 | ||||||||
\(218\) | −1.66886 | −0.113029 | ||||||||
\(219\) | 6.23664 | 0.421433 | ||||||||
\(220\) | −9.86630 | −0.665186 | ||||||||
\(221\) | 4.79095 | 0.322274 | ||||||||
\(222\) | −19.6429 | −1.31834 | ||||||||
\(223\) | −20.2576 | −1.35655 | −0.678276 | − | 0.734807i | \(-0.737273\pi\) | ||||
−0.678276 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(224\) | 0.814652 | 0.0544313 | ||||||||
\(225\) | −5.09348 | −0.339565 | ||||||||
\(226\) | 10.5034 | 0.698673 | ||||||||
\(227\) | −22.6304 | −1.50203 | −0.751017 | − | 0.660283i | \(-0.770436\pi\) | ||||
−0.751017 | + | 0.660283i | \(0.770436\pi\) | |||||||
\(228\) | 5.88715 | 0.389886 | ||||||||
\(229\) | 3.41248 | 0.225503 | 0.112752 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112752 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(230\) | −4.53960 | −0.299333 | ||||||||
\(231\) | −11.0279 | −0.725584 | ||||||||
\(232\) | 2.75110 | 0.180619 | ||||||||
\(233\) | −6.91916 | −0.453289 | −0.226645 | − | 0.973978i | \(-0.572776\pi\) | ||||
−0.226645 | + | 0.973978i | \(0.572776\pi\) | |||||||
\(234\) | 11.2474 | 0.735268 | ||||||||
\(235\) | −1.61015 | −0.105035 | ||||||||
\(236\) | −5.71856 | −0.372246 | ||||||||
\(237\) | 13.1292 | 0.852833 | ||||||||
\(238\) | −0.824025 | −0.0534136 | ||||||||
\(239\) | 17.5957 | 1.13817 | 0.569086 | − | 0.822278i | \(-0.307297\pi\) | ||||
0.569086 | + | 0.822278i | \(0.307297\pi\) | |||||||
\(240\) | −3.91727 | −0.252859 | ||||||||
\(241\) | −18.9874 | −1.22308 | −0.611542 | − | 0.791212i | \(-0.709451\pi\) | ||||
−0.611542 | + | 0.791212i | \(0.709451\pi\) | |||||||
\(242\) | −23.0951 | −1.48461 | ||||||||
\(243\) | 19.9584 | 1.28033 | ||||||||
\(244\) | 10.5287 | 0.674031 | ||||||||
\(245\) | −10.7065 | −0.684012 | ||||||||
\(246\) | −19.3047 | −1.23082 | ||||||||
\(247\) | 12.0277 | 0.765305 | ||||||||
\(248\) | 4.44777 | 0.282434 | ||||||||
\(249\) | −21.0448 | −1.33366 | ||||||||
\(250\) | 12.0728 | 0.763548 | ||||||||
\(251\) | −7.75703 | −0.489619 | −0.244810 | − | 0.969571i | \(-0.578725\pi\) | ||||
−0.244810 | + | 0.969571i | \(0.578725\pi\) | |||||||
\(252\) | −1.93452 | −0.121863 | ||||||||
\(253\) | −15.6876 | −0.986270 | ||||||||
\(254\) | −10.3415 | −0.648881 | ||||||||
\(255\) | 3.96234 | 0.248131 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.17545 | 0.322836 | 0.161418 | − | 0.986886i | \(-0.448393\pi\) | ||||
0.161418 | + | 0.986886i | \(0.448393\pi\) | |||||||
\(258\) | −8.63196 | −0.537403 | ||||||||
\(259\) | 6.90244 | 0.428897 | ||||||||
\(260\) | −8.00316 | −0.496335 | ||||||||
\(261\) | −6.53292 | −0.404378 | ||||||||
\(262\) | −7.81223 | −0.482641 | ||||||||
\(263\) | −25.0072 | −1.54201 | −0.771005 | − | 0.636829i | \(-0.780246\pi\) | ||||
−0.771005 | + | 0.636829i | \(0.780246\pi\) | |||||||
\(264\) | −13.5370 | −0.833143 | ||||||||
\(265\) | −17.2710 | −1.06095 | ||||||||
\(266\) | −2.06872 | −0.126841 | ||||||||
\(267\) | 23.4366 | 1.43430 | ||||||||
\(268\) | 8.23232 | 0.502869 | ||||||||
\(269\) | 27.8095 | 1.69557 | 0.847787 | − | 0.530338i | \(-0.177935\pi\) | ||||
0.847787 | + | 0.530338i | \(0.177935\pi\) | |||||||
\(270\) | −2.44965 | −0.149081 | ||||||||
\(271\) | −20.7328 | −1.25943 | −0.629714 | − | 0.776827i | \(-0.716828\pi\) | ||||
−0.629714 | + | 0.776827i | \(0.716828\pi\) | |||||||
\(272\) | −1.01151 | −0.0613315 | ||||||||
\(273\) | −8.94543 | −0.541402 | ||||||||
\(274\) | 10.2482 | 0.619114 | ||||||||
\(275\) | 12.5245 | 0.755256 | ||||||||
\(276\) | −6.22852 | −0.374913 | ||||||||
\(277\) | −4.79540 | −0.288128 | −0.144064 | − | 0.989568i | \(-0.546017\pi\) | ||||
−0.144064 | + | 0.989568i | \(0.546017\pi\) | |||||||
\(278\) | 10.6722 | 0.640076 | ||||||||
\(279\) | −10.5619 | −0.632325 | ||||||||
\(280\) | 1.37651 | 0.0822624 | ||||||||
\(281\) | 7.45939 | 0.444990 | 0.222495 | − | 0.974934i | \(-0.428580\pi\) | ||||
0.222495 | + | 0.974934i | \(0.428580\pi\) | |||||||
\(282\) | −2.20919 | −0.131555 | ||||||||
\(283\) | −29.5915 | −1.75903 | −0.879517 | − | 0.475868i | \(-0.842134\pi\) | ||||
−0.879517 | + | 0.475868i | \(0.842134\pi\) | |||||||
\(284\) | −3.16569 | −0.187849 | ||||||||
\(285\) | 9.94747 | 0.589238 | ||||||||
\(286\) | −27.6567 | −1.63537 | ||||||||
\(287\) | 6.78359 | 0.400423 | ||||||||
\(288\) | −2.37465 | −0.139928 | ||||||||
\(289\) | −15.9769 | −0.939815 | ||||||||
\(290\) | 4.64852 | 0.272971 | ||||||||
\(291\) | 42.1453 | 2.47060 | ||||||||
\(292\) | −2.69014 | −0.157429 | ||||||||
\(293\) | −1.92817 | −0.112645 | −0.0563226 | − | 0.998413i | \(-0.517938\pi\) | ||||
−0.0563226 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(294\) | −14.6897 | −0.856722 | ||||||||
\(295\) | −9.66261 | −0.562579 | ||||||||
\(296\) | 8.47287 | 0.492475 | ||||||||
\(297\) | −8.46529 | −0.491206 | ||||||||
\(298\) | 5.21187 | 0.301916 | ||||||||
\(299\) | −12.7252 | −0.735915 | ||||||||
\(300\) | 4.97267 | 0.287097 | ||||||||
\(301\) | 3.03324 | 0.174833 | ||||||||
\(302\) | −6.83386 | −0.393244 | ||||||||
\(303\) | −25.0373 | −1.43836 | ||||||||
\(304\) | −2.53939 | −0.145644 | ||||||||
\(305\) | 17.7903 | 1.01867 | ||||||||
\(306\) | 2.40198 | 0.137312 | ||||||||
\(307\) | 25.9462 | 1.48083 | 0.740414 | − | 0.672151i | \(-0.234630\pi\) | ||||
0.740414 | + | 0.672151i | \(0.234630\pi\) | |||||||
\(308\) | 4.75684 | 0.271046 | ||||||||
\(309\) | −34.4981 | −1.96253 | ||||||||
\(310\) | 7.51537 | 0.426844 | ||||||||
\(311\) | −12.7681 | −0.724014 | −0.362007 | − | 0.932175i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932175i | \(0.617908\pi\) | |||||||
\(312\) | −10.9807 | −0.621658 | ||||||||
\(313\) | −20.1029 | −1.13629 | −0.568143 | − | 0.822930i | \(-0.692338\pi\) | ||||
−0.568143 | + | 0.822930i | \(0.692338\pi\) | |||||||
\(314\) | 4.01248 | 0.226437 | ||||||||
\(315\) | −3.26874 | −0.184173 | ||||||||
\(316\) | −5.66322 | −0.318581 | ||||||||
\(317\) | −18.3957 | −1.03321 | −0.516604 | − | 0.856224i | \(-0.672804\pi\) | ||||
−0.516604 | + | 0.856224i | \(0.672804\pi\) | |||||||
\(318\) | −23.6965 | −1.32883 | ||||||||
\(319\) | 16.0640 | 0.899410 | ||||||||
\(320\) | 1.68969 | 0.0944568 | ||||||||
\(321\) | 29.9307 | 1.67057 | ||||||||
\(322\) | 2.18868 | 0.121970 | ||||||||
\(323\) | 2.56861 | 0.142921 | ||||||||
\(324\) | −10.4850 | −0.582499 | ||||||||
\(325\) | 10.1594 | 0.563542 | ||||||||
\(326\) | −9.98607 | −0.553078 | ||||||||
\(327\) | −3.86896 | −0.213954 | ||||||||
\(328\) | 8.32697 | 0.459780 | ||||||||
\(329\) | 0.776302 | 0.0427989 | ||||||||
\(330\) | −22.8733 | −1.25914 | ||||||||
\(331\) | 5.06035 | 0.278142 | 0.139071 | − | 0.990282i | \(-0.455588\pi\) | ||||
0.139071 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(332\) | 9.07757 | 0.498196 | ||||||||
\(333\) | −20.1201 | −1.10258 | ||||||||
\(334\) | 16.0394 | 0.877638 | ||||||||
\(335\) | 13.9101 | 0.759990 | ||||||||
\(336\) | 1.88863 | 0.103033 | ||||||||
\(337\) | −20.9144 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(338\) | −9.43402 | −0.513143 | ||||||||
\(339\) | 24.3503 | 1.32252 | ||||||||
\(340\) | −1.70913 | −0.0926908 | ||||||||
\(341\) | 25.9710 | 1.40641 | ||||||||
\(342\) | 6.03017 | 0.326075 | ||||||||
\(343\) | 10.8645 | 0.586627 | ||||||||
\(344\) | 3.72335 | 0.200750 | ||||||||
\(345\) | −10.5243 | −0.566609 | ||||||||
\(346\) | −2.94315 | −0.158225 | ||||||||
\(347\) | 6.57917 | 0.353188 | 0.176594 | − | 0.984284i | \(-0.443492\pi\) | ||||
0.176594 | + | 0.984284i | \(0.443492\pi\) | |||||||
\(348\) | 6.37797 | 0.341895 | ||||||||
\(349\) | 27.1435 | 1.45296 | 0.726479 | − | 0.687188i | \(-0.241155\pi\) | ||||
0.726479 | + | 0.687188i | \(0.241155\pi\) | |||||||
\(350\) | −1.74738 | −0.0934012 | ||||||||
\(351\) | −6.86672 | −0.366518 | ||||||||
\(352\) | 5.83910 | 0.311225 | ||||||||
\(353\) | 5.93866 | 0.316083 | 0.158041 | − | 0.987432i | \(-0.449482\pi\) | ||||
0.158041 | + | 0.987432i | \(0.449482\pi\) | |||||||
\(354\) | −13.2575 | −0.704628 | ||||||||
\(355\) | −5.34905 | −0.283898 | ||||||||
\(356\) | −10.1093 | −0.535790 | ||||||||
\(357\) | −1.91036 | −0.101107 | ||||||||
\(358\) | −16.8723 | −0.891727 | ||||||||
\(359\) | 21.2416 | 1.12109 | 0.560545 | − | 0.828124i | \(-0.310592\pi\) | ||||
0.560545 | + | 0.828124i | \(0.310592\pi\) | |||||||
\(360\) | −4.01244 | −0.211474 | ||||||||
\(361\) | −12.5515 | −0.660605 | ||||||||
\(362\) | 14.1064 | 0.741417 | ||||||||
\(363\) | −53.5422 | −2.81023 | ||||||||
\(364\) | 3.85857 | 0.202244 | ||||||||
\(365\) | −4.54552 | −0.237923 | ||||||||
\(366\) | 24.4090 | 1.27588 | ||||||||
\(367\) | −21.5755 | −1.12623 | −0.563116 | − | 0.826378i | \(-0.690398\pi\) | ||||
−0.563116 | + | 0.826378i | \(0.690398\pi\) | |||||||
\(368\) | 2.68664 | 0.140051 | ||||||||
\(369\) | −19.7737 | −1.02938 | ||||||||
\(370\) | 14.3165 | 0.744282 | ||||||||
\(371\) | 8.32685 | 0.432309 | ||||||||
\(372\) | 10.3114 | 0.534621 | ||||||||
\(373\) | −34.4737 | −1.78498 | −0.892491 | − | 0.451065i | \(-0.851044\pi\) | ||||
−0.892491 | + | 0.451065i | \(0.851044\pi\) | |||||||
\(374\) | −5.90629 | −0.305407 | ||||||||
\(375\) | 27.9886 | 1.44533 | ||||||||
\(376\) | 0.952924 | 0.0491433 | ||||||||
\(377\) | 13.0305 | 0.671104 | ||||||||
\(378\) | 1.18105 | 0.0607466 | ||||||||
\(379\) | 32.4768 | 1.66822 | 0.834110 | − | 0.551598i | \(-0.185982\pi\) | ||||
0.834110 | + | 0.551598i | \(0.185982\pi\) | |||||||
\(380\) | −4.29079 | −0.220113 | ||||||||
\(381\) | −23.9749 | −1.22827 | ||||||||
\(382\) | −19.6613 | −1.00596 | ||||||||
\(383\) | −31.9792 | −1.63406 | −0.817030 | − | 0.576595i | \(-0.804381\pi\) | ||||
−0.817030 | + | 0.576595i | \(0.804381\pi\) | |||||||
\(384\) | 2.31833 | 0.118307 | ||||||||
\(385\) | 8.03760 | 0.409634 | ||||||||
\(386\) | −3.60799 | −0.183642 | ||||||||
\(387\) | −8.84168 | −0.449448 | ||||||||
\(388\) | −18.1792 | −0.922907 | ||||||||
\(389\) | 13.8989 | 0.704705 | 0.352352 | − | 0.935867i | \(-0.385382\pi\) | ||||
0.352352 | + | 0.935867i | \(0.385382\pi\) | |||||||
\(390\) | −18.5540 | −0.939517 | ||||||||
\(391\) | −2.71755 | −0.137433 | ||||||||
\(392\) | 6.33634 | 0.320034 | ||||||||
\(393\) | −18.1113 | −0.913596 | ||||||||
\(394\) | −5.96776 | −0.300651 | ||||||||
\(395\) | −9.56910 | −0.481474 | ||||||||
\(396\) | −13.8659 | −0.696785 | ||||||||
\(397\) | 24.9044 | 1.24991 | 0.624957 | − | 0.780659i | \(-0.285116\pi\) | ||||
0.624957 | + | 0.780659i | \(0.285116\pi\) | |||||||
\(398\) | −7.98637 | −0.400321 | ||||||||
\(399\) | −4.79598 | −0.240099 | ||||||||
\(400\) | −2.14494 | −0.107247 | ||||||||
\(401\) | 10.9571 | 0.547173 | 0.273587 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273587 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(402\) | 19.0852 | 0.951885 | ||||||||
\(403\) | 21.0667 | 1.04941 | ||||||||
\(404\) | 10.7997 | 0.537307 | ||||||||
\(405\) | −17.7164 | −0.880335 | ||||||||
\(406\) | −2.24119 | −0.111229 | ||||||||
\(407\) | 49.4739 | 2.45233 | ||||||||
\(408\) | −2.34500 | −0.116095 | ||||||||
\(409\) | 32.4094 | 1.60254 | 0.801271 | − | 0.598302i | \(-0.204158\pi\) | ||||
0.801271 | + | 0.598302i | \(0.204158\pi\) | |||||||
\(410\) | 14.0700 | 0.694869 | ||||||||
\(411\) | 23.7586 | 1.17193 | ||||||||
\(412\) | 14.8806 | 0.733115 | ||||||||
\(413\) | 4.65864 | 0.229236 | ||||||||
\(414\) | −6.37985 | −0.313552 | ||||||||
\(415\) | 15.3383 | 0.752928 | ||||||||
\(416\) | 4.73646 | 0.232224 | ||||||||
\(417\) | 24.7417 | 1.21161 | ||||||||
\(418\) | −14.8278 | −0.725250 | ||||||||
\(419\) | 3.24424 | 0.158491 | 0.0792457 | − | 0.996855i | \(-0.474749\pi\) | ||||
0.0792457 | + | 0.996855i | \(0.474749\pi\) | |||||||
\(420\) | 3.19121 | 0.155715 | ||||||||
\(421\) | −1.63837 | −0.0798492 | −0.0399246 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399246 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(422\) | 20.0508 | 0.976056 | ||||||||
\(423\) | −2.26286 | −0.110024 | ||||||||
\(424\) | 10.2214 | 0.496393 | ||||||||
\(425\) | 2.16961 | 0.105242 | ||||||||
\(426\) | −7.33912 | −0.355582 | ||||||||
\(427\) | −8.57724 | −0.415082 | ||||||||
\(428\) | −12.9105 | −0.624051 | ||||||||
\(429\) | −64.1173 | −3.09561 | ||||||||
\(430\) | 6.29133 | 0.303395 | ||||||||
\(431\) | 28.6472 | 1.37989 | 0.689943 | − | 0.723863i | \(-0.257635\pi\) | ||||
0.689943 | + | 0.723863i | \(0.257635\pi\) | |||||||
\(432\) | 1.44976 | 0.0697516 | ||||||||
\(433\) | −18.2427 | −0.876690 | −0.438345 | − | 0.898807i | \(-0.644435\pi\) | ||||
−0.438345 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(434\) | −3.62339 | −0.173928 | ||||||||
\(435\) | 10.7768 | 0.516708 | ||||||||
\(436\) | 1.66886 | 0.0799238 | ||||||||
\(437\) | −6.82244 | −0.326361 | ||||||||
\(438\) | −6.23664 | −0.297998 | ||||||||
\(439\) | −39.8164 | −1.90033 | −0.950167 | − | 0.311740i | \(-0.899088\pi\) | ||||
−0.950167 | + | 0.311740i | \(0.899088\pi\) | |||||||
\(440\) | 9.86630 | 0.470357 | ||||||||
\(441\) | −15.0466 | −0.716506 | ||||||||
\(442\) | −4.79095 | −0.227882 | ||||||||
\(443\) | 11.2069 | 0.532455 | 0.266228 | − | 0.963910i | \(-0.414223\pi\) | ||||
0.266228 | + | 0.963910i | \(0.414223\pi\) | |||||||
\(444\) | 19.6429 | 0.932211 | ||||||||
\(445\) | −17.0815 | −0.809743 | ||||||||
\(446\) | 20.2576 | 0.959228 | ||||||||
\(447\) | 12.0828 | 0.571499 | ||||||||
\(448\) | −0.814652 | −0.0384887 | ||||||||
\(449\) | −17.5509 | −0.828277 | −0.414139 | − | 0.910214i | \(-0.635917\pi\) | ||||
−0.414139 | + | 0.910214i | \(0.635917\pi\) | |||||||
\(450\) | 5.09348 | 0.240109 | ||||||||
\(451\) | 48.6221 | 2.28952 | ||||||||
\(452\) | −10.5034 | −0.494036 | ||||||||
\(453\) | −15.8431 | −0.744376 | ||||||||
\(454\) | 22.6304 | 1.06210 | ||||||||
\(455\) | 6.51979 | 0.305653 | ||||||||
\(456\) | −5.88715 | −0.275691 | ||||||||
\(457\) | 5.62948 | 0.263336 | 0.131668 | − | 0.991294i | \(-0.457967\pi\) | ||||
0.131668 | + | 0.991294i | \(0.457967\pi\) | |||||||
\(458\) | −3.41248 | −0.159455 | ||||||||
\(459\) | −1.46644 | −0.0684475 | ||||||||
\(460\) | 4.53960 | 0.211660 | ||||||||
\(461\) | 7.38433 | 0.343923 | 0.171961 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171961 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(462\) | 11.0279 | 0.513066 | ||||||||
\(463\) | 9.48950 | 0.441014 | 0.220507 | − | 0.975385i | \(-0.429229\pi\) | ||||
0.220507 | + | 0.975385i | \(0.429229\pi\) | |||||||
\(464\) | −2.75110 | −0.127717 | ||||||||
\(465\) | 17.4231 | 0.807977 | ||||||||
\(466\) | 6.91916 | 0.320524 | ||||||||
\(467\) | −6.48042 | −0.299878 | −0.149939 | − | 0.988695i | \(-0.547908\pi\) | ||||
−0.149939 | + | 0.988695i | \(0.547908\pi\) | |||||||
\(468\) | −11.2474 | −0.519913 | ||||||||
\(469\) | −6.70648 | −0.309677 | ||||||||
\(470\) | 1.61015 | 0.0742706 | ||||||||
\(471\) | 9.30226 | 0.428625 | ||||||||
\(472\) | 5.71856 | 0.263218 | ||||||||
\(473\) | 21.7411 | 0.999655 | ||||||||
\(474\) | −13.1292 | −0.603044 | ||||||||
\(475\) | 5.44683 | 0.249918 | ||||||||
\(476\) | 0.824025 | 0.0377691 | ||||||||
\(477\) | −24.2722 | −1.11135 | ||||||||
\(478\) | −17.5957 | −0.804809 | ||||||||
\(479\) | −17.1755 | −0.784767 | −0.392383 | − | 0.919802i | \(-0.628349\pi\) | ||||
−0.392383 | + | 0.919802i | \(0.628349\pi\) | |||||||
\(480\) | 3.91727 | 0.178798 | ||||||||
\(481\) | 40.1314 | 1.82983 | ||||||||
\(482\) | 18.9874 | 0.864852 | ||||||||
\(483\) | 5.07408 | 0.230879 | ||||||||
\(484\) | 23.0951 | 1.04978 | ||||||||
\(485\) | −30.7172 | −1.39480 | ||||||||
\(486\) | −19.9584 | −0.905330 | ||||||||
\(487\) | −3.34097 | −0.151394 | −0.0756969 | − | 0.997131i | \(-0.524118\pi\) | ||||
−0.0756969 | + | 0.997131i | \(0.524118\pi\) | |||||||
\(488\) | −10.5287 | −0.476612 | ||||||||
\(489\) | −23.1510 | −1.04693 | ||||||||
\(490\) | 10.7065 | 0.483669 | ||||||||
\(491\) | 7.98483 | 0.360350 | 0.180175 | − | 0.983635i | \(-0.442334\pi\) | ||||
0.180175 | + | 0.983635i | \(0.442334\pi\) | |||||||
\(492\) | 19.3047 | 0.870322 | ||||||||
\(493\) | 2.78276 | 0.125329 | ||||||||
\(494\) | −12.0277 | −0.541153 | ||||||||
\(495\) | −23.4290 | −1.05306 | ||||||||
\(496\) | −4.44777 | −0.199711 | ||||||||
\(497\) | 2.57894 | 0.115681 | ||||||||
\(498\) | 21.0448 | 0.943040 | ||||||||
\(499\) | −17.6200 | −0.788779 | −0.394389 | − | 0.918943i | \(-0.629044\pi\) | ||||
−0.394389 | + | 0.918943i | \(0.629044\pi\) | |||||||
\(500\) | −12.0728 | −0.539910 | ||||||||
\(501\) | 37.1847 | 1.66129 | ||||||||
\(502\) | 7.75703 | 0.346213 | ||||||||
\(503\) | 12.2062 | 0.544248 | 0.272124 | − | 0.962262i | \(-0.412274\pi\) | ||||
0.272124 | + | 0.962262i | \(0.412274\pi\) | |||||||
\(504\) | 1.93452 | 0.0861703 | ||||||||
\(505\) | 18.2482 | 0.812036 | ||||||||
\(506\) | 15.6876 | 0.697398 | ||||||||
\(507\) | −21.8712 | −0.971333 | ||||||||
\(508\) | 10.3415 | 0.458828 | ||||||||
\(509\) | 25.4382 | 1.12753 | 0.563765 | − | 0.825935i | \(-0.309352\pi\) | ||||
0.563765 | + | 0.825935i | \(0.309352\pi\) | |||||||
\(510\) | −3.96234 | −0.175455 | ||||||||
\(511\) | 2.19153 | 0.0969477 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.68150 | −0.162542 | ||||||||
\(514\) | −5.17545 | −0.228279 | ||||||||
\(515\) | 25.1437 | 1.10796 | ||||||||
\(516\) | 8.63196 | 0.380001 | ||||||||
\(517\) | 5.56422 | 0.244714 | ||||||||
\(518\) | −6.90244 | −0.303276 | ||||||||
\(519\) | −6.82320 | −0.299505 | ||||||||
\(520\) | 8.00316 | 0.350962 | ||||||||
\(521\) | −1.37333 | −0.0601666 | −0.0300833 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300833 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(522\) | 6.53292 | 0.285938 | ||||||||
\(523\) | −4.17298 | −0.182472 | −0.0912359 | − | 0.995829i | \(-0.529082\pi\) | ||||
−0.0912359 | + | 0.995829i | \(0.529082\pi\) | |||||||
\(524\) | 7.81223 | 0.341279 | ||||||||
\(525\) | −4.05100 | −0.176800 | ||||||||
\(526\) | 25.0072 | 1.09037 | ||||||||
\(527\) | 4.49894 | 0.195977 | ||||||||
\(528\) | 13.5370 | 0.589121 | ||||||||
\(529\) | −15.7820 | −0.686172 | ||||||||
\(530\) | 17.2710 | 0.750202 | ||||||||
\(531\) | −13.5796 | −0.589304 | ||||||||
\(532\) | 2.06872 | 0.0896904 | ||||||||
\(533\) | 39.4403 | 1.70835 | ||||||||
\(534\) | −23.4366 | −1.01420 | ||||||||
\(535\) | −21.8147 | −0.943134 | ||||||||
\(536\) | −8.23232 | −0.355582 | ||||||||
\(537\) | −39.1155 | −1.68796 | ||||||||
\(538\) | −27.8095 | −1.19895 | ||||||||
\(539\) | 36.9986 | 1.59364 | ||||||||
\(540\) | 2.44965 | 0.105416 | ||||||||
\(541\) | 18.4521 | 0.793317 | 0.396659 | − | 0.917966i | \(-0.370170\pi\) | ||||
0.396659 | + | 0.917966i | \(0.370170\pi\) | |||||||
\(542\) | 20.7328 | 0.890549 | ||||||||
\(543\) | 32.7033 | 1.40343 | ||||||||
\(544\) | 1.01151 | 0.0433679 | ||||||||
\(545\) | 2.81986 | 0.120790 | ||||||||
\(546\) | 8.94543 | 0.382829 | ||||||||
\(547\) | 19.2458 | 0.822892 | 0.411446 | − | 0.911434i | \(-0.365024\pi\) | ||||
0.411446 | + | 0.911434i | \(0.365024\pi\) | |||||||
\(548\) | −10.2482 | −0.437780 | ||||||||
\(549\) | 25.0020 | 1.06706 | ||||||||
\(550\) | −12.5245 | −0.534046 | ||||||||
\(551\) | 6.98613 | 0.297619 | ||||||||
\(552\) | 6.22852 | 0.265104 | ||||||||
\(553\) | 4.61355 | 0.196188 | ||||||||
\(554\) | 4.79540 | 0.203737 | ||||||||
\(555\) | 33.1905 | 1.40886 | ||||||||
\(556\) | −10.6722 | −0.452602 | ||||||||
\(557\) | 34.7973 | 1.47441 | 0.737204 | − | 0.675671i | \(-0.236146\pi\) | ||||
0.737204 | + | 0.675671i | \(0.236146\pi\) | |||||||
\(558\) | 10.5619 | 0.447121 | ||||||||
\(559\) | 17.6355 | 0.745903 | ||||||||
\(560\) | −1.37651 | −0.0581683 | ||||||||
\(561\) | −13.6927 | −0.578107 | ||||||||
\(562\) | −7.45939 | −0.314655 | ||||||||
\(563\) | −13.1064 | −0.552368 | −0.276184 | − | 0.961105i | \(-0.589070\pi\) | ||||
−0.276184 | + | 0.961105i | \(0.589070\pi\) | |||||||
\(564\) | 2.20919 | 0.0930237 | ||||||||
\(565\) | −17.7475 | −0.746641 | ||||||||
\(566\) | 29.5915 | 1.24382 | ||||||||
\(567\) | 8.54162 | 0.358714 | ||||||||
\(568\) | 3.16569 | 0.132830 | ||||||||
\(569\) | −29.3012 | −1.22837 | −0.614184 | − | 0.789163i | \(-0.710515\pi\) | ||||
−0.614184 | + | 0.789163i | \(0.710515\pi\) | |||||||
\(570\) | −9.94747 | −0.416654 | ||||||||
\(571\) | 17.6196 | 0.737357 | 0.368679 | − | 0.929557i | \(-0.379810\pi\) | ||||
0.368679 | + | 0.929557i | \(0.379810\pi\) | |||||||
\(572\) | 27.6567 | 1.15638 | ||||||||
\(573\) | −45.5814 | −1.90419 | ||||||||
\(574\) | −6.78359 | −0.283142 | ||||||||
\(575\) | −5.76267 | −0.240320 | ||||||||
\(576\) | 2.37465 | 0.0989439 | ||||||||
\(577\) | 11.6384 | 0.484514 | 0.242257 | − | 0.970212i | \(-0.422112\pi\) | ||||
0.242257 | + | 0.970212i | \(0.422112\pi\) | |||||||
\(578\) | 15.9769 | 0.664550 | ||||||||
\(579\) | −8.36450 | −0.347617 | ||||||||
\(580\) | −4.64852 | −0.193019 | ||||||||
\(581\) | −7.39506 | −0.306799 | ||||||||
\(582\) | −42.1453 | −1.74698 | ||||||||
\(583\) | 59.6836 | 2.47184 | ||||||||
\(584\) | 2.69014 | 0.111319 | ||||||||
\(585\) | −19.0047 | −0.785749 | ||||||||
\(586\) | 1.92817 | 0.0796522 | ||||||||
\(587\) | 32.0595 | 1.32324 | 0.661618 | − | 0.749841i | \(-0.269870\pi\) | ||||
0.661618 | + | 0.749841i | \(0.269870\pi\) | |||||||
\(588\) | 14.6897 | 0.605794 | ||||||||
\(589\) | 11.2946 | 0.465387 | ||||||||
\(590\) | 9.66261 | 0.397803 | ||||||||
\(591\) | −13.8352 | −0.569105 | ||||||||
\(592\) | −8.47287 | −0.348233 | ||||||||
\(593\) | −33.6691 | −1.38262 | −0.691312 | − | 0.722557i | \(-0.742967\pi\) | ||||
−0.691312 | + | 0.722557i | \(0.742967\pi\) | |||||||
\(594\) | 8.46529 | 0.347335 | ||||||||
\(595\) | 1.39235 | 0.0570808 | ||||||||
\(596\) | −5.21187 | −0.213487 | ||||||||
\(597\) | −18.5150 | −0.757770 | ||||||||
\(598\) | 12.7252 | 0.520371 | ||||||||
\(599\) | −14.2267 | −0.581289 | −0.290644 | − | 0.956831i | \(-0.593870\pi\) | ||||
−0.290644 | + | 0.956831i | \(0.593870\pi\) | |||||||
\(600\) | −4.97267 | −0.203008 | ||||||||
\(601\) | 5.38031 | 0.219467 | 0.109734 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109734 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(602\) | −3.03324 | −0.123626 | ||||||||
\(603\) | 19.5489 | 0.796094 | ||||||||
\(604\) | 6.83386 | 0.278066 | ||||||||
\(605\) | 39.0237 | 1.58654 | ||||||||
\(606\) | 25.0373 | 1.01707 | ||||||||
\(607\) | −5.13074 | −0.208250 | −0.104125 | − | 0.994564i | \(-0.533204\pi\) | ||||
−0.104125 | + | 0.994564i | \(0.533204\pi\) | |||||||
\(608\) | 2.53939 | 0.102986 | ||||||||
\(609\) | −5.19583 | −0.210545 | ||||||||
\(610\) | −17.7903 | −0.720308 | ||||||||
\(611\) | 4.51348 | 0.182596 | ||||||||
\(612\) | −2.40198 | −0.0970941 | ||||||||
\(613\) | 2.40674 | 0.0972072 | 0.0486036 | − | 0.998818i | \(-0.484523\pi\) | ||||
0.0486036 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(614\) | −25.9462 | −1.04710 | ||||||||
\(615\) | 32.6190 | 1.31532 | ||||||||
\(616\) | −4.75684 | −0.191659 | ||||||||
\(617\) | −34.1639 | −1.37539 | −0.687694 | − | 0.726000i | \(-0.741377\pi\) | ||||
−0.687694 | + | 0.726000i | \(0.741377\pi\) | |||||||
\(618\) | 34.4981 | 1.38772 | ||||||||
\(619\) | 34.9211 | 1.40360 | 0.701799 | − | 0.712375i | \(-0.252381\pi\) | ||||
0.701799 | + | 0.712375i | \(0.252381\pi\) | |||||||
\(620\) | −7.51537 | −0.301824 | ||||||||
\(621\) | 3.89498 | 0.156300 | ||||||||
\(622\) | 12.7681 | 0.511955 | ||||||||
\(623\) | 8.23553 | 0.329950 | ||||||||
\(624\) | 10.9807 | 0.439579 | ||||||||
\(625\) | −9.67458 | −0.386983 | ||||||||
\(626\) | 20.1029 | 0.803475 | ||||||||
\(627\) | −34.3757 | −1.37283 | ||||||||
\(628\) | −4.01248 | −0.160115 | ||||||||
\(629\) | 8.57035 | 0.341722 | ||||||||
\(630\) | 3.26874 | 0.130230 | ||||||||
\(631\) | 17.9399 | 0.714177 | 0.357088 | − | 0.934071i | \(-0.383769\pi\) | ||||
0.357088 | + | 0.934071i | \(0.383769\pi\) | |||||||
\(632\) | 5.66322 | 0.225271 | ||||||||
\(633\) | 46.4843 | 1.84759 | ||||||||
\(634\) | 18.3957 | 0.730588 | ||||||||
\(635\) | 17.4739 | 0.693431 | ||||||||
\(636\) | 23.6965 | 0.939626 | ||||||||
\(637\) | 30.0118 | 1.18911 | ||||||||
\(638\) | −16.0640 | −0.635979 | ||||||||
\(639\) | −7.51742 | −0.297385 | ||||||||
\(640\) | −1.68969 | −0.0667910 | ||||||||
\(641\) | 23.8592 | 0.942381 | 0.471191 | − | 0.882031i | \(-0.343824\pi\) | ||||
0.471191 | + | 0.882031i | \(0.343824\pi\) | |||||||
\(642\) | −29.9307 | −1.18127 | ||||||||
\(643\) | −13.6166 | −0.536986 | −0.268493 | − | 0.963282i | \(-0.586526\pi\) | ||||
−0.268493 | + | 0.963282i | \(0.586526\pi\) | |||||||
\(644\) | −2.18868 | −0.0862461 | ||||||||
\(645\) | 14.5854 | 0.574299 | ||||||||
\(646\) | −2.56861 | −0.101061 | ||||||||
\(647\) | 35.0614 | 1.37841 | 0.689203 | − | 0.724568i | \(-0.257961\pi\) | ||||
0.689203 | + | 0.724568i | \(0.257961\pi\) | |||||||
\(648\) | 10.4850 | 0.411889 | ||||||||
\(649\) | 33.3912 | 1.31072 | ||||||||
\(650\) | −10.1594 | −0.398484 | ||||||||
\(651\) | −8.40020 | −0.329230 | ||||||||
\(652\) | 9.98607 | 0.391085 | ||||||||
\(653\) | −4.26953 | −0.167080 | −0.0835399 | − | 0.996504i | \(-0.526623\pi\) | ||||
−0.0835399 | + | 0.996504i | \(0.526623\pi\) | |||||||
\(654\) | 3.86896 | 0.151288 | ||||||||
\(655\) | 13.2003 | 0.515778 | ||||||||
\(656\) | −8.32697 | −0.325114 | ||||||||
\(657\) | −6.38816 | −0.249226 | ||||||||
\(658\) | −0.776302 | −0.0302634 | ||||||||
\(659\) | 14.8169 | 0.577183 | 0.288591 | − | 0.957452i | \(-0.406813\pi\) | ||||
0.288591 | + | 0.957452i | \(0.406813\pi\) | |||||||
\(660\) | 22.8733 | 0.890343 | ||||||||
\(661\) | −28.2238 | −1.09778 | −0.548888 | − | 0.835896i | \(-0.684949\pi\) | ||||
−0.548888 | + | 0.835896i | \(0.684949\pi\) | |||||||
\(662\) | −5.06035 | −0.196676 | ||||||||
\(663\) | −11.1070 | −0.431360 | ||||||||
\(664\) | −9.07757 | −0.352278 | ||||||||
\(665\) | 3.49551 | 0.135550 | ||||||||
\(666\) | 20.1201 | 0.779639 | ||||||||
\(667\) | −7.39123 | −0.286190 | ||||||||
\(668\) | −16.0394 | −0.620584 | ||||||||
\(669\) | 46.9639 | 1.81573 | ||||||||
\(670\) | −13.9101 | −0.537394 | ||||||||
\(671\) | −61.4782 | −2.37334 | ||||||||
\(672\) | −1.88863 | −0.0728556 | ||||||||
\(673\) | −9.10712 | −0.351054 | −0.175527 | − | 0.984475i | \(-0.556163\pi\) | ||||
−0.175527 | + | 0.984475i | \(0.556163\pi\) | |||||||
\(674\) | 20.9144 | 0.805594 | ||||||||
\(675\) | −3.10964 | −0.119690 | ||||||||
\(676\) | 9.43402 | 0.362847 | ||||||||
\(677\) | 45.2018 | 1.73725 | 0.868623 | − | 0.495473i | \(-0.165005\pi\) | ||||
0.868623 | + | 0.495473i | \(0.165005\pi\) | |||||||
\(678\) | −24.3503 | −0.935166 | ||||||||
\(679\) | 14.8097 | 0.568344 | ||||||||
\(680\) | 1.70913 | 0.0655423 | ||||||||
\(681\) | 52.4648 | 2.01046 | ||||||||
\(682\) | −25.9710 | −0.994480 | ||||||||
\(683\) | 39.6810 | 1.51835 | 0.759176 | − | 0.650885i | \(-0.225602\pi\) | ||||
0.759176 | + | 0.650885i | \(0.225602\pi\) | |||||||
\(684\) | −6.03017 | −0.230569 | ||||||||
\(685\) | −17.3162 | −0.661620 | ||||||||
\(686\) | −10.8645 | −0.414808 | ||||||||
\(687\) | −7.91126 | −0.301833 | ||||||||
\(688\) | −3.72335 | −0.141952 | ||||||||
\(689\) | 48.4130 | 1.84439 | ||||||||
\(690\) | 10.5243 | 0.400653 | ||||||||
\(691\) | −18.7323 | −0.712611 | −0.356306 | − | 0.934369i | \(-0.615964\pi\) | ||||
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(692\) | 2.94315 | 0.111882 | ||||||||
\(693\) | 11.2959 | 0.429094 | ||||||||
\(694\) | −6.57917 | −0.249742 | ||||||||
\(695\) | −18.0328 | −0.684021 | ||||||||
\(696\) | −6.37797 | −0.241756 | ||||||||
\(697\) | 8.42278 | 0.319036 | ||||||||
\(698\) | −27.1435 | −1.02740 | ||||||||
\(699\) | 16.0409 | 0.606723 | ||||||||
\(700\) | 1.74738 | 0.0660446 | ||||||||
\(701\) | −7.87974 | −0.297614 | −0.148807 | − | 0.988866i | \(-0.547543\pi\) | ||||
−0.148807 | + | 0.988866i | \(0.547543\pi\) | |||||||
\(702\) | 6.86672 | 0.259168 | ||||||||
\(703\) | 21.5159 | 0.811488 | ||||||||
\(704\) | −5.83910 | −0.220070 | ||||||||
\(705\) | 3.73286 | 0.140588 | ||||||||
\(706\) | −5.93866 | −0.223504 | ||||||||
\(707\) | −8.79803 | −0.330884 | ||||||||
\(708\) | 13.2575 | 0.498247 | ||||||||
\(709\) | 31.3165 | 1.17612 | 0.588058 | − | 0.808819i | \(-0.299893\pi\) | ||||
0.588058 | + | 0.808819i | \(0.299893\pi\) | |||||||
\(710\) | 5.34905 | 0.200746 | ||||||||
\(711\) | −13.4482 | −0.504346 | ||||||||
\(712\) | 10.1093 | 0.378860 | ||||||||
\(713\) | −11.9496 | −0.447515 | ||||||||
\(714\) | 1.91036 | 0.0714935 | ||||||||
\(715\) | 46.7313 | 1.74765 | ||||||||
\(716\) | 16.8723 | 0.630547 | ||||||||
\(717\) | −40.7926 | −1.52343 | ||||||||
\(718\) | −21.2416 | −0.792731 | ||||||||
\(719\) | 9.99954 | 0.372920 | 0.186460 | − | 0.982463i | \(-0.440299\pi\) | ||||
0.186460 | + | 0.982463i | \(0.440299\pi\) | |||||||
\(720\) | 4.01244 | 0.149535 | ||||||||
\(721\) | −12.1225 | −0.451466 | ||||||||
\(722\) | 12.5515 | 0.467118 | ||||||||
\(723\) | 44.0190 | 1.63708 | ||||||||
\(724\) | −14.1064 | −0.524261 | ||||||||
\(725\) | 5.90094 | 0.219155 | ||||||||
\(726\) | 53.5422 | 1.98714 | ||||||||
\(727\) | −20.5279 | −0.761339 | −0.380670 | − | 0.924711i | \(-0.624306\pi\) | ||||
−0.380670 | + | 0.924711i | \(0.624306\pi\) | |||||||
\(728\) | −3.85857 | −0.143008 | ||||||||
\(729\) | −14.8151 | −0.548709 | ||||||||
\(730\) | 4.54552 | 0.168237 | ||||||||
\(731\) | 3.76619 | 0.139298 | ||||||||
\(732\) | −24.4090 | −0.902183 | ||||||||
\(733\) | −22.4019 | −0.827432 | −0.413716 | − | 0.910406i | \(-0.635769\pi\) | ||||
−0.413716 | + | 0.910406i | \(0.635769\pi\) | |||||||
\(734\) | 21.5755 | 0.796367 | ||||||||
\(735\) | 24.8211 | 0.915542 | ||||||||
\(736\) | −2.68664 | −0.0990310 | ||||||||
\(737\) | −48.0694 | −1.77066 | ||||||||
\(738\) | 19.7737 | 0.727879 | ||||||||
\(739\) | 10.6323 | 0.391116 | 0.195558 | − | 0.980692i | \(-0.437348\pi\) | ||||
0.195558 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(740\) | −14.3165 | −0.526287 | ||||||||
\(741\) | −27.8842 | −1.02435 | ||||||||
\(742\) | −8.32685 | −0.305688 | ||||||||
\(743\) | −19.7891 | −0.725990 | −0.362995 | − | 0.931791i | \(-0.618246\pi\) | ||||
−0.362995 | + | 0.931791i | \(0.618246\pi\) | |||||||
\(744\) | −10.3114 | −0.378034 | ||||||||
\(745\) | −8.80647 | −0.322644 | ||||||||
\(746\) | 34.4737 | 1.26217 | ||||||||
\(747\) | 21.5561 | 0.788696 | ||||||||
\(748\) | 5.90629 | 0.215955 | ||||||||
\(749\) | 10.5175 | 0.384303 | ||||||||
\(750\) | −27.9886 | −1.02200 | ||||||||
\(751\) | −36.9204 | −1.34724 | −0.673621 | − | 0.739077i | \(-0.735262\pi\) | ||||
−0.673621 | + | 0.739077i | \(0.735262\pi\) | |||||||
\(752\) | −0.952924 | −0.0347496 | ||||||||
\(753\) | 17.9833 | 0.655350 | ||||||||
\(754\) | −13.0305 | −0.474542 | ||||||||
\(755\) | 11.5471 | 0.420243 | ||||||||
\(756\) | −1.18105 | −0.0429544 | ||||||||
\(757\) | −30.9255 | −1.12400 | −0.562002 | − | 0.827136i | \(-0.689969\pi\) | ||||
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(758\) | −32.4768 | −1.17961 | ||||||||
\(759\) | 36.3690 | 1.32011 | ||||||||
\(760\) | 4.29079 | 0.155643 | ||||||||
\(761\) | 41.3446 | 1.49874 | 0.749370 | − | 0.662151i | \(-0.230356\pi\) | ||||
0.749370 | + | 0.662151i | \(0.230356\pi\) | |||||||
\(762\) | 23.9749 | 0.868520 | ||||||||
\(763\) | −1.35954 | −0.0492186 | ||||||||
\(764\) | 19.6613 | 0.711321 | ||||||||
\(765\) | −4.05860 | −0.146739 | ||||||||
\(766\) | 31.9792 | 1.15545 | ||||||||
\(767\) | 27.0857 | 0.978008 | ||||||||
\(768\) | −2.31833 | −0.0836555 | ||||||||
\(769\) | 21.1501 | 0.762694 | 0.381347 | − | 0.924432i | \(-0.375460\pi\) | ||||
0.381347 | + | 0.924432i | \(0.375460\pi\) | |||||||
\(770\) | −8.03760 | −0.289655 | ||||||||
\(771\) | −11.9984 | −0.432112 | ||||||||
\(772\) | 3.60799 | 0.129854 | ||||||||
\(773\) | 11.1983 | 0.402775 | 0.201387 | − | 0.979512i | \(-0.435455\pi\) | ||||
0.201387 | + | 0.979512i | \(0.435455\pi\) | |||||||
\(774\) | 8.84168 | 0.317808 | ||||||||
\(775\) | 9.54017 | 0.342693 | ||||||||
\(776\) | 18.1792 | 0.652594 | ||||||||
\(777\) | −16.0021 | −0.574073 | ||||||||
\(778\) | −13.8989 | −0.498301 | ||||||||
\(779\) | 21.1454 | 0.757614 | ||||||||
\(780\) | 18.5540 | 0.664339 | ||||||||
\(781\) | 18.4848 | 0.661439 | ||||||||
\(782\) | 2.71755 | 0.0971795 | ||||||||
\(783\) | −3.98844 | −0.142535 | ||||||||
\(784\) | −6.33634 | −0.226298 | ||||||||
\(785\) | −6.77987 | −0.241984 | ||||||||
\(786\) | 18.1113 | 0.646010 | ||||||||
\(787\) | 0.381565 | 0.0136013 | 0.00680066 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680066 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(788\) | 5.96776 | 0.212593 | ||||||||
\(789\) | 57.9750 | 2.06396 | ||||||||
\(790\) | 9.56910 | 0.340453 | ||||||||
\(791\) | 8.55659 | 0.304237 | ||||||||
\(792\) | 13.8659 | 0.492702 | ||||||||
\(793\) | −49.8688 | −1.77089 | ||||||||
\(794\) | −24.9044 | −0.883823 | ||||||||
\(795\) | 40.0398 | 1.42006 | ||||||||
\(796\) | 7.98637 | 0.283069 | ||||||||
\(797\) | −5.35771 | −0.189780 | −0.0948899 | − | 0.995488i | \(-0.530250\pi\) | ||||
−0.0948899 | + | 0.995488i | \(0.530250\pi\) | |||||||
\(798\) | 4.79598 | 0.169776 | ||||||||
\(799\) | 0.963888 | 0.0340999 | ||||||||
\(800\) | 2.14494 | 0.0758349 | ||||||||
\(801\) | −24.0060 | −0.848210 | ||||||||
\(802\) | −10.9571 | −0.386910 | ||||||||
\(803\) | 15.7080 | 0.554324 | ||||||||
\(804\) | −19.0852 | −0.673085 | ||||||||
\(805\) | −3.69820 | −0.130344 | ||||||||
\(806\) | −21.0667 | −0.742041 | ||||||||
\(807\) | −64.4715 | −2.26950 | ||||||||
\(808\) | −10.7997 | −0.379933 | ||||||||
\(809\) | −29.9189 | −1.05189 | −0.525946 | − | 0.850518i | \(-0.676288\pi\) | ||||
−0.525946 | + | 0.850518i | \(0.676288\pi\) | |||||||
\(810\) | 17.7164 | 0.622491 | ||||||||
\(811\) | −42.8165 | −1.50349 | −0.751745 | − | 0.659454i | \(-0.770788\pi\) | ||||
−0.751745 | + | 0.659454i | \(0.770788\pi\) | |||||||
\(812\) | 2.24119 | 0.0786505 | ||||||||
\(813\) | 48.0654 | 1.68573 | ||||||||
\(814\) | −49.4739 | −1.73406 | ||||||||
\(815\) | 16.8734 | 0.591050 | ||||||||
\(816\) | 2.34500 | 0.0820915 | ||||||||
\(817\) | 9.45505 | 0.330790 | ||||||||
\(818\) | −32.4094 | −1.13317 | ||||||||
\(819\) | 9.16276 | 0.320173 | ||||||||
\(820\) | −14.0700 | −0.491347 | ||||||||
\(821\) | −56.2395 | −1.96277 | −0.981386 | − | 0.192047i | \(-0.938488\pi\) | ||||
−0.981386 | + | 0.192047i | \(0.938488\pi\) | |||||||
\(822\) | −23.7586 | −0.828677 | ||||||||
\(823\) | −17.1440 | −0.597603 | −0.298802 | − | 0.954315i | \(-0.596587\pi\) | ||||
−0.298802 | + | 0.954315i | \(0.596587\pi\) | |||||||
\(824\) | −14.8806 | −0.518390 | ||||||||
\(825\) | −29.0359 | −1.01090 | ||||||||
\(826\) | −4.65864 | −0.162095 | ||||||||
\(827\) | −29.3609 | −1.02098 | −0.510490 | − | 0.859884i | \(-0.670536\pi\) | ||||
−0.510490 | + | 0.859884i | \(0.670536\pi\) | |||||||
\(828\) | 6.37985 | 0.221715 | ||||||||
\(829\) | 2.85472 | 0.0991487 | 0.0495743 | − | 0.998770i | \(-0.484214\pi\) | ||||
0.0495743 | + | 0.998770i | \(0.484214\pi\) | |||||||
\(830\) | −15.3383 | −0.532401 | ||||||||
\(831\) | 11.1173 | 0.385655 | ||||||||
\(832\) | −4.73646 | −0.164207 | ||||||||
\(833\) | 6.40924 | 0.222067 | ||||||||
\(834\) | −24.7417 | −0.856735 | ||||||||
\(835\) | −27.1017 | −0.937893 | ||||||||
\(836\) | 14.8278 | 0.512829 | ||||||||
\(837\) | −6.44819 | −0.222882 | ||||||||
\(838\) | −3.24424 | −0.112070 | ||||||||
\(839\) | −37.6460 | −1.29969 | −0.649843 | − | 0.760069i | \(-0.725165\pi\) | ||||
−0.649843 | + | 0.760069i | \(0.725165\pi\) | |||||||
\(840\) | −3.19121 | −0.110107 | ||||||||
\(841\) | −21.4314 | −0.739015 | ||||||||
\(842\) | 1.63837 | 0.0564619 | ||||||||
\(843\) | −17.2933 | −0.595614 | ||||||||
\(844\) | −20.0508 | −0.690176 | ||||||||
\(845\) | 15.9406 | 0.548374 | ||||||||
\(846\) | 2.26286 | 0.0777989 | ||||||||
\(847\) | −18.8145 | −0.646474 | ||||||||
\(848\) | −10.2214 | −0.351003 | ||||||||
\(849\) | 68.6029 | 2.35445 | ||||||||
\(850\) | −2.16961 | −0.0744171 | ||||||||
\(851\) | −22.7636 | −0.780325 | ||||||||
\(852\) | 7.33912 | 0.251434 | ||||||||
\(853\) | 1.03256 | 0.0353543 | 0.0176772 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176772 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(854\) | 8.57724 | 0.293507 | ||||||||
\(855\) | −10.1891 | −0.348462 | ||||||||
\(856\) | 12.9105 | 0.441271 | ||||||||
\(857\) | 26.6100 | 0.908982 | 0.454491 | − | 0.890751i | \(-0.349821\pi\) | ||||
0.454491 | + | 0.890751i | \(0.349821\pi\) | |||||||
\(858\) | 64.1173 | 2.18893 | ||||||||
\(859\) | 7.84080 | 0.267525 | 0.133762 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133762 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(860\) | −6.29133 | −0.214533 | ||||||||
\(861\) | −15.7266 | −0.535961 | ||||||||
\(862\) | −28.6472 | −0.975727 | ||||||||
\(863\) | 30.7488 | 1.04670 | 0.523350 | − | 0.852118i | \(-0.324682\pi\) | ||||
0.523350 | + | 0.852118i | \(0.324682\pi\) | |||||||
\(864\) | −1.44976 | −0.0493218 | ||||||||
\(865\) | 4.97303 | 0.169088 | ||||||||
\(866\) | 18.2427 | 0.619913 | ||||||||
\(867\) | 37.0396 | 1.25793 | ||||||||
\(868\) | 3.62339 | 0.122986 | ||||||||
\(869\) | 33.0681 | 1.12176 | ||||||||
\(870\) | −10.7768 | −0.365368 | ||||||||
\(871\) | −38.9920 | −1.32120 | ||||||||
\(872\) | −1.66886 | −0.0565147 | ||||||||
\(873\) | −43.1692 | −1.46106 | ||||||||
\(874\) | 6.82244 | 0.230772 | ||||||||
\(875\) | 9.83510 | 0.332487 | ||||||||
\(876\) | 6.23664 | 0.210717 | ||||||||
\(877\) | 33.0449 | 1.11585 | 0.557924 | − | 0.829892i | \(-0.311598\pi\) | ||||
0.557924 | + | 0.829892i | \(0.311598\pi\) | |||||||
\(878\) | 39.8164 | 1.34374 | ||||||||
\(879\) | 4.47015 | 0.150774 | ||||||||
\(880\) | −9.86630 | −0.332593 | ||||||||
\(881\) | 14.1286 | 0.476004 | 0.238002 | − | 0.971265i | \(-0.423508\pi\) | ||||
0.238002 | + | 0.971265i | \(0.423508\pi\) | |||||||
\(882\) | 15.0466 | 0.506646 | ||||||||
\(883\) | −25.2623 | −0.850145 | −0.425072 | − | 0.905159i | \(-0.639751\pi\) | ||||
−0.425072 | + | 0.905159i | \(0.639751\pi\) | |||||||
\(884\) | 4.79095 | 0.161137 | ||||||||
\(885\) | 22.4011 | 0.753005 | ||||||||
\(886\) | −11.2069 | −0.376503 | ||||||||
\(887\) | 9.53593 | 0.320185 | 0.160093 | − | 0.987102i | \(-0.448821\pi\) | ||||
0.160093 | + | 0.987102i | \(0.448821\pi\) | |||||||
\(888\) | −19.6429 | −0.659172 | ||||||||
\(889\) | −8.42470 | −0.282555 | ||||||||
\(890\) | 17.0815 | 0.572575 | ||||||||
\(891\) | 61.2229 | 2.05104 | ||||||||
\(892\) | −20.2576 | −0.678276 | ||||||||
\(893\) | 2.41985 | 0.0809771 | ||||||||
\(894\) | −12.0828 | −0.404110 | ||||||||
\(895\) | 28.5090 | 0.952950 | ||||||||
\(896\) | 0.814652 | 0.0272156 | ||||||||
\(897\) | 29.5011 | 0.985014 | ||||||||
\(898\) | 17.5509 | 0.585680 | ||||||||
\(899\) | 12.2363 | 0.408102 | ||||||||
\(900\) | −5.09348 | −0.169783 | ||||||||
\(901\) | 10.3390 | 0.344441 | ||||||||
\(902\) | −48.6221 | −1.61894 | ||||||||
\(903\) | −7.03205 | −0.234012 | ||||||||
\(904\) | 10.5034 | 0.349337 | ||||||||
\(905\) | −23.8355 | −0.792320 | ||||||||
\(906\) | 15.8431 | 0.526353 | ||||||||
\(907\) | −44.7260 | −1.48510 | −0.742551 | − | 0.669790i | \(-0.766384\pi\) | ||||
−0.742551 | + | 0.669790i | \(0.766384\pi\) | |||||||
\(908\) | −22.6304 | −0.751017 | ||||||||
\(909\) | 25.6456 | 0.850612 | ||||||||
\(910\) | −6.51979 | −0.216129 | ||||||||
\(911\) | 17.7793 | 0.589053 | 0.294526 | − | 0.955643i | \(-0.404838\pi\) | ||||
0.294526 | + | 0.955643i | \(0.404838\pi\) | |||||||
\(912\) | 5.88715 | 0.194943 | ||||||||
\(913\) | −53.0049 | −1.75421 | ||||||||
\(914\) | −5.62948 | −0.186207 | ||||||||
\(915\) | −41.2438 | −1.36348 | ||||||||
\(916\) | 3.41248 | 0.112752 | ||||||||
\(917\) | −6.36426 | −0.210166 | ||||||||
\(918\) | 1.46644 | 0.0483997 | ||||||||
\(919\) | 20.6157 | 0.680048 | 0.340024 | − | 0.940417i | \(-0.389565\pi\) | ||||
0.340024 | + | 0.940417i | \(0.389565\pi\) | |||||||
\(920\) | −4.53960 | −0.149666 | ||||||||
\(921\) | −60.1518 | −1.98207 | ||||||||
\(922\) | −7.38433 | −0.243190 | ||||||||
\(923\) | 14.9942 | 0.493539 | ||||||||
\(924\) | −11.0279 | −0.362792 | ||||||||
\(925\) | 18.1737 | 0.597549 | ||||||||
\(926\) | −9.48950 | −0.311844 | ||||||||
\(927\) | 35.3363 | 1.16060 | ||||||||
\(928\) | 2.75110 | 0.0903094 | ||||||||
\(929\) | −21.7672 | −0.714160 | −0.357080 | − | 0.934074i | \(-0.616228\pi\) | ||||
−0.357080 | + | 0.934074i | \(0.616228\pi\) | |||||||
\(930\) | −17.4231 | −0.571326 | ||||||||
\(931\) | 16.0904 | 0.527343 | ||||||||
\(932\) | −6.91916 | −0.226645 | ||||||||
\(933\) | 29.6007 | 0.969084 | ||||||||
\(934\) | 6.48042 | 0.212046 | ||||||||
\(935\) | 9.97982 | 0.326375 | ||||||||
\(936\) | 11.2474 | 0.367634 | ||||||||
\(937\) | 10.8618 | 0.354838 | 0.177419 | − | 0.984135i | \(-0.443225\pi\) | ||||
0.177419 | + | 0.984135i | \(0.443225\pi\) | |||||||
\(938\) | 6.70648 | 0.218974 | ||||||||
\(939\) | 46.6052 | 1.52090 | ||||||||
\(940\) | −1.61015 | −0.0525173 | ||||||||
\(941\) | 38.8475 | 1.26639 | 0.633197 | − | 0.773991i | \(-0.281742\pi\) | ||||
0.633197 | + | 0.773991i | \(0.281742\pi\) | |||||||
\(942\) | −9.30226 | −0.303084 | ||||||||
\(943\) | −22.3716 | −0.728520 | ||||||||
\(944\) | −5.71856 | −0.186123 | ||||||||
\(945\) | −1.99561 | −0.0649173 | ||||||||
\(946\) | −21.7411 | −0.706863 | ||||||||
\(947\) | −25.5164 | −0.829172 | −0.414586 | − | 0.910010i | \(-0.636074\pi\) | ||||
−0.414586 | + | 0.910010i | \(0.636074\pi\) | |||||||
\(948\) | 13.1292 | 0.426417 | ||||||||
\(949\) | 12.7417 | 0.413615 | ||||||||
\(950\) | −5.44683 | −0.176718 | ||||||||
\(951\) | 42.6474 | 1.38294 | ||||||||
\(952\) | −0.824025 | −0.0267068 | ||||||||
\(953\) | −50.2681 | −1.62834 | −0.814172 | − | 0.580624i | \(-0.802809\pi\) | ||||
−0.814172 | + | 0.580624i | \(0.802809\pi\) | |||||||
\(954\) | 24.2722 | 0.785841 | ||||||||
\(955\) | 33.2216 | 1.07503 | ||||||||
\(956\) | 17.5957 | 0.569086 | ||||||||
\(957\) | −37.2416 | −1.20385 | ||||||||
\(958\) | 17.1755 | 0.554914 | ||||||||
\(959\) | 8.34869 | 0.269593 | ||||||||
\(960\) | −3.91727 | −0.126429 | ||||||||
\(961\) | −11.2174 | −0.361850 | ||||||||
\(962\) | −40.1314 | −1.29389 | ||||||||
\(963\) | −30.6579 | −0.987937 | ||||||||
\(964\) | −18.9874 | −0.611542 | ||||||||
\(965\) | 6.09639 | 0.196250 | ||||||||
\(966\) | −5.07408 | −0.163256 | ||||||||
\(967\) | −50.2037 | −1.61444 | −0.807220 | − | 0.590250i | \(-0.799029\pi\) | ||||
−0.807220 | + | 0.590250i | \(0.799029\pi\) | |||||||
\(968\) | −23.0951 | −0.742306 | ||||||||
\(969\) | −5.95488 | −0.191298 | ||||||||
\(970\) | 30.7172 | 0.986270 | ||||||||
\(971\) | 35.4747 | 1.13844 | 0.569218 | − | 0.822187i | \(-0.307246\pi\) | ||||
0.569218 | + | 0.822187i | \(0.307246\pi\) | |||||||
\(972\) | 19.9584 | 0.640165 | ||||||||
\(973\) | 8.69414 | 0.278721 | ||||||||
\(974\) | 3.34097 | 0.107052 | ||||||||
\(975\) | −23.5528 | −0.754294 | ||||||||
\(976\) | 10.5287 | 0.337016 | ||||||||
\(977\) | −42.8878 | −1.37210 | −0.686051 | − | 0.727554i | \(-0.740657\pi\) | ||||
−0.686051 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(978\) | 23.1510 | 0.740288 | ||||||||
\(979\) | 59.0290 | 1.88658 | ||||||||
\(980\) | −10.7065 | −0.342006 | ||||||||
\(981\) | 3.96296 | 0.126528 | ||||||||
\(982\) | −7.98483 | −0.254806 | ||||||||
\(983\) | 7.83095 | 0.249769 | 0.124884 | − | 0.992171i | \(-0.460144\pi\) | ||||
0.124884 | + | 0.992171i | \(0.460144\pi\) | |||||||
\(984\) | −19.3047 | −0.615410 | ||||||||
\(985\) | 10.0837 | 0.321293 | ||||||||
\(986\) | −2.78276 | −0.0886210 | ||||||||
\(987\) | −1.79972 | −0.0572858 | ||||||||
\(988\) | 12.0277 | 0.382653 | ||||||||
\(989\) | −10.0033 | −0.318087 | ||||||||
\(990\) | 23.4290 | 0.744624 | ||||||||
\(991\) | −32.6401 | −1.03685 | −0.518423 | − | 0.855124i | \(-0.673481\pi\) | ||||
−0.518423 | + | 0.855124i | \(0.673481\pi\) | |||||||
\(992\) | 4.44777 | 0.141217 | ||||||||
\(993\) | −11.7316 | −0.372290 | ||||||||
\(994\) | −2.57894 | −0.0817990 | ||||||||
\(995\) | 13.4945 | 0.427805 | ||||||||
\(996\) | −21.0448 | −0.666830 | ||||||||
\(997\) | −21.9360 | −0.694721 | −0.347361 | − | 0.937732i | \(-0.612922\pi\) | ||||
−0.347361 | + | 0.937732i | \(0.612922\pi\) | |||||||
\(998\) | 17.6200 | 0.557751 | ||||||||
\(999\) | −12.2836 | −0.388636 |
(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 | 8026.2.a.c.1.14 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.c.1.14 | ✓ | 86 | 1.1 | even | 1 | trivial |