Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, 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("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66752 | −1.88622 | −0.943112 | − | 0.332476i | \(-0.892116\pi\) | ||||
−0.943112 | + | 0.332476i | \(0.892116\pi\) | |||||||
\(3\) | 1.67561 | 0.967412 | 0.483706 | − | 0.875231i | \(-0.339290\pi\) | ||||
0.483706 | + | 0.875231i | \(0.339290\pi\) | |||||||
\(4\) | 5.11568 | 2.55784 | ||||||||
\(5\) | −2.95924 | −1.32341 | −0.661707 | − | 0.749762i | \(-0.730168\pi\) | ||||
−0.661707 | + | 0.749762i | \(0.730168\pi\) | |||||||
\(6\) | −4.46972 | −1.82475 | ||||||||
\(7\) | −2.28368 | −0.863148 | −0.431574 | − | 0.902078i | \(-0.642042\pi\) | ||||
−0.431574 | + | 0.902078i | \(0.642042\pi\) | |||||||
\(8\) | −8.31114 | −2.93843 | ||||||||
\(9\) | −0.192344 | −0.0641145 | ||||||||
\(10\) | 7.89385 | 2.49625 | ||||||||
\(11\) | −3.02794 | −0.912958 | −0.456479 | − | 0.889734i | \(-0.650890\pi\) | ||||
−0.456479 | + | 0.889734i | \(0.650890\pi\) | |||||||
\(12\) | 8.57186 | 2.47448 | ||||||||
\(13\) | 0.947331 | 0.262742 | 0.131371 | − | 0.991333i | \(-0.458062\pi\) | ||||
0.131371 | + | 0.991333i | \(0.458062\pi\) | |||||||
\(14\) | 6.09176 | 1.62809 | ||||||||
\(15\) | −4.95853 | −1.28029 | ||||||||
\(16\) | 11.9388 | 2.98470 | ||||||||
\(17\) | 5.89642 | 1.43009 | 0.715046 | − | 0.699078i | \(-0.246406\pi\) | ||||
0.715046 | + | 0.699078i | \(0.246406\pi\) | |||||||
\(18\) | 0.513081 | 0.120934 | ||||||||
\(19\) | −7.66287 | −1.75798 | −0.878992 | − | 0.476837i | \(-0.841783\pi\) | ||||
−0.878992 | + | 0.476837i | \(0.841783\pi\) | |||||||
\(20\) | −15.1385 | −3.38508 | ||||||||
\(21\) | −3.82654 | −0.835020 | ||||||||
\(22\) | 8.07710 | 1.72204 | ||||||||
\(23\) | −1.63367 | −0.340643 | −0.170322 | − | 0.985389i | \(-0.554481\pi\) | ||||
−0.170322 | + | 0.985389i | \(0.554481\pi\) | |||||||
\(24\) | −13.9262 | −2.84267 | ||||||||
\(25\) | 3.75713 | 0.751425 | ||||||||
\(26\) | −2.52703 | −0.495590 | ||||||||
\(27\) | −5.34911 | −1.02944 | ||||||||
\(28\) | −11.6825 | −2.20779 | ||||||||
\(29\) | 7.16324 | 1.33018 | 0.665091 | − | 0.746763i | \(-0.268393\pi\) | ||||
0.665091 | + | 0.746763i | \(0.268393\pi\) | |||||||
\(30\) | 13.2270 | 2.41491 | ||||||||
\(31\) | −3.55148 | −0.637864 | −0.318932 | − | 0.947778i | \(-0.603324\pi\) | ||||
−0.318932 | + | 0.947778i | \(0.603324\pi\) | |||||||
\(32\) | −15.2247 | −2.69138 | ||||||||
\(33\) | −5.07364 | −0.883207 | ||||||||
\(34\) | −15.7288 | −2.69747 | ||||||||
\(35\) | 6.75795 | 1.14230 | ||||||||
\(36\) | −0.983968 | −0.163995 | ||||||||
\(37\) | −6.75814 | −1.11103 | −0.555516 | − | 0.831506i | \(-0.687479\pi\) | ||||
−0.555516 | + | 0.831506i | \(0.687479\pi\) | |||||||
\(38\) | 20.4409 | 3.31595 | ||||||||
\(39\) | 1.58735 | 0.254180 | ||||||||
\(40\) | 24.5947 | 3.88876 | ||||||||
\(41\) | −2.81195 | −0.439153 | −0.219576 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219576 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(42\) | 10.2074 | 1.57503 | ||||||||
\(43\) | −12.3624 | −1.88524 | −0.942621 | − | 0.333865i | \(-0.891647\pi\) | ||||
−0.942621 | + | 0.333865i | \(0.891647\pi\) | |||||||
\(44\) | −15.4900 | −2.33520 | ||||||||
\(45\) | 0.569192 | 0.0848501 | ||||||||
\(46\) | 4.35784 | 0.642529 | ||||||||
\(47\) | −4.25096 | −0.620067 | −0.310033 | − | 0.950726i | \(-0.600340\pi\) | ||||
−0.310033 | + | 0.950726i | \(0.600340\pi\) | |||||||
\(48\) | 20.0047 | 2.88743 | ||||||||
\(49\) | −1.78483 | −0.254975 | ||||||||
\(50\) | −10.0222 | −1.41736 | ||||||||
\(51\) | 9.88007 | 1.38349 | ||||||||
\(52\) | 4.84624 | 0.672052 | ||||||||
\(53\) | −3.22130 | −0.442480 | −0.221240 | − | 0.975219i | \(-0.571010\pi\) | ||||
−0.221240 | + | 0.975219i | \(0.571010\pi\) | |||||||
\(54\) | 14.2689 | 1.94175 | ||||||||
\(55\) | 8.96042 | 1.20822 | ||||||||
\(56\) | 18.9799 | 2.53630 | ||||||||
\(57\) | −12.8400 | −1.70069 | ||||||||
\(58\) | −19.1081 | −2.50902 | ||||||||
\(59\) | −3.55040 | −0.462223 | −0.231112 | − | 0.972927i | \(-0.574236\pi\) | ||||
−0.231112 | + | 0.972927i | \(0.574236\pi\) | |||||||
\(60\) | −25.3662 | −3.27477 | ||||||||
\(61\) | −8.64493 | −1.10687 | −0.553435 | − | 0.832892i | \(-0.686683\pi\) | ||||
−0.553435 | + | 0.832892i | \(0.686683\pi\) | |||||||
\(62\) | 9.47364 | 1.20315 | ||||||||
\(63\) | 0.439250 | 0.0553403 | ||||||||
\(64\) | 16.7347 | 2.09184 | ||||||||
\(65\) | −2.80338 | −0.347717 | ||||||||
\(66\) | 13.5340 | 1.66593 | ||||||||
\(67\) | 9.86666 | 1.20540 | 0.602702 | − | 0.797966i | \(-0.294091\pi\) | ||||
0.602702 | + | 0.797966i | \(0.294091\pi\) | |||||||
\(68\) | 30.1642 | 3.65794 | ||||||||
\(69\) | −2.73738 | −0.329542 | ||||||||
\(70\) | −18.0270 | −2.15464 | ||||||||
\(71\) | 6.24835 | 0.741542 | 0.370771 | − | 0.928724i | \(-0.379093\pi\) | ||||
0.370771 | + | 0.928724i | \(0.379093\pi\) | |||||||
\(72\) | 1.59859 | 0.188396 | ||||||||
\(73\) | 8.63808 | 1.01101 | 0.505506 | − | 0.862823i | \(-0.331306\pi\) | ||||
0.505506 | + | 0.862823i | \(0.331306\pi\) | |||||||
\(74\) | 18.0275 | 2.09565 | ||||||||
\(75\) | 6.29546 | 0.726937 | ||||||||
\(76\) | −39.2008 | −4.49664 | ||||||||
\(77\) | 6.91483 | 0.788018 | ||||||||
\(78\) | −4.23430 | −0.479440 | ||||||||
\(79\) | −6.90866 | −0.777285 | −0.388642 | − | 0.921389i | \(-0.627056\pi\) | ||||
−0.388642 | + | 0.921389i | \(0.627056\pi\) | |||||||
\(80\) | −35.3298 | −3.94999 | ||||||||
\(81\) | −8.38597 | −0.931775 | ||||||||
\(82\) | 7.50094 | 0.828341 | ||||||||
\(83\) | 3.20341 | 0.351620 | 0.175810 | − | 0.984424i | \(-0.443746\pi\) | ||||
0.175810 | + | 0.984424i | \(0.443746\pi\) | |||||||
\(84\) | −19.5753 | −2.13585 | ||||||||
\(85\) | −17.4489 | −1.89260 | ||||||||
\(86\) | 32.9769 | 3.55599 | ||||||||
\(87\) | 12.0028 | 1.28683 | ||||||||
\(88\) | 25.1656 | 2.68267 | ||||||||
\(89\) | 8.25139 | 0.874646 | 0.437323 | − | 0.899305i | \(-0.355927\pi\) | ||||
0.437323 | + | 0.899305i | \(0.355927\pi\) | |||||||
\(90\) | −1.51833 | −0.160046 | ||||||||
\(91\) | −2.16340 | −0.226785 | ||||||||
\(92\) | −8.35731 | −0.871310 | ||||||||
\(93\) | −5.95088 | −0.617077 | ||||||||
\(94\) | 11.3395 | 1.16958 | ||||||||
\(95\) | 22.6763 | 2.32654 | ||||||||
\(96\) | −25.5107 | −2.60367 | ||||||||
\(97\) | −8.96631 | −0.910391 | −0.455196 | − | 0.890391i | \(-0.650431\pi\) | ||||
−0.455196 | + | 0.890391i | \(0.650431\pi\) | |||||||
\(98\) | 4.76107 | 0.480940 | ||||||||
\(99\) | 0.582405 | 0.0585339 | ||||||||
\(100\) | 19.2202 | 1.92202 | ||||||||
\(101\) | 4.03848 | 0.401844 | 0.200922 | − | 0.979607i | \(-0.435606\pi\) | ||||
0.200922 | + | 0.979607i | \(0.435606\pi\) | |||||||
\(102\) | −26.3553 | −2.60957 | ||||||||
\(103\) | 11.3163 | 1.11502 | 0.557512 | − | 0.830169i | \(-0.311756\pi\) | ||||
0.557512 | + | 0.830169i | \(0.311756\pi\) | |||||||
\(104\) | −7.87340 | −0.772050 | ||||||||
\(105\) | 11.3237 | 1.10508 | ||||||||
\(106\) | 8.59290 | 0.834616 | ||||||||
\(107\) | −9.41035 | −0.909733 | −0.454866 | − | 0.890560i | \(-0.650313\pi\) | ||||
−0.454866 | + | 0.890560i | \(0.650313\pi\) | |||||||
\(108\) | −27.3643 | −2.63313 | ||||||||
\(109\) | −18.6652 | −1.78780 | −0.893902 | − | 0.448263i | \(-0.852043\pi\) | ||||
−0.893902 | + | 0.448263i | \(0.852043\pi\) | |||||||
\(110\) | −23.9021 | −2.27898 | ||||||||
\(111\) | −11.3240 | −1.07482 | ||||||||
\(112\) | −27.2643 | −2.57624 | ||||||||
\(113\) | 3.91702 | 0.368482 | 0.184241 | − | 0.982881i | \(-0.441017\pi\) | ||||
0.184241 | + | 0.982881i | \(0.441017\pi\) | |||||||
\(114\) | 34.2509 | 3.20789 | ||||||||
\(115\) | 4.83442 | 0.450812 | ||||||||
\(116\) | 36.6448 | 3.40239 | ||||||||
\(117\) | −0.182213 | −0.0168456 | ||||||||
\(118\) | 9.47078 | 0.871856 | ||||||||
\(119\) | −13.4655 | −1.23438 | ||||||||
\(120\) | 41.2110 | 3.76203 | ||||||||
\(121\) | −1.83158 | −0.166507 | ||||||||
\(122\) | 23.0605 | 2.08780 | ||||||||
\(123\) | −4.71172 | −0.424842 | ||||||||
\(124\) | −18.1682 | −1.63155 | ||||||||
\(125\) | 3.67797 | 0.328968 | ||||||||
\(126\) | −1.17171 | −0.104384 | ||||||||
\(127\) | −16.4276 | −1.45771 | −0.728855 | − | 0.684668i | \(-0.759947\pi\) | ||||
−0.728855 | + | 0.684668i | \(0.759947\pi\) | |||||||
\(128\) | −14.1908 | −1.25430 | ||||||||
\(129\) | −20.7144 | −1.82381 | ||||||||
\(130\) | 7.47809 | 0.655871 | ||||||||
\(131\) | −1.69660 | −0.148233 | −0.0741164 | − | 0.997250i | \(-0.523614\pi\) | ||||
−0.0741164 | + | 0.997250i | \(0.523614\pi\) | |||||||
\(132\) | −25.9551 | −2.25910 | ||||||||
\(133\) | 17.4995 | 1.51740 | ||||||||
\(134\) | −26.3195 | −2.27366 | ||||||||
\(135\) | 15.8293 | 1.36237 | ||||||||
\(136\) | −49.0060 | −4.20223 | ||||||||
\(137\) | −22.5290 | −1.92478 | −0.962391 | − | 0.271667i | \(-0.912425\pi\) | ||||
−0.962391 | + | 0.271667i | \(0.912425\pi\) | |||||||
\(138\) | 7.30203 | 0.621590 | ||||||||
\(139\) | 16.1229 | 1.36753 | 0.683763 | − | 0.729704i | \(-0.260342\pi\) | ||||
0.683763 | + | 0.729704i | \(0.260342\pi\) | |||||||
\(140\) | 34.5715 | 2.92183 | ||||||||
\(141\) | −7.12294 | −0.599860 | ||||||||
\(142\) | −16.6676 | −1.39871 | ||||||||
\(143\) | −2.86846 | −0.239873 | ||||||||
\(144\) | −2.29635 | −0.191363 | ||||||||
\(145\) | −21.1978 | −1.76038 | ||||||||
\(146\) | −23.0423 | −1.90699 | ||||||||
\(147\) | −2.99067 | −0.246666 | ||||||||
\(148\) | −34.5725 | −2.84184 | ||||||||
\(149\) | −16.9777 | −1.39086 | −0.695432 | − | 0.718592i | \(-0.744787\pi\) | ||||
−0.695432 | + | 0.718592i | \(0.744787\pi\) | |||||||
\(150\) | −16.7933 | −1.37117 | ||||||||
\(151\) | −15.3917 | −1.25256 | −0.626279 | − | 0.779599i | \(-0.715423\pi\) | ||||
−0.626279 | + | 0.779599i | \(0.715423\pi\) | |||||||
\(152\) | 63.6872 | 5.16571 | ||||||||
\(153\) | −1.13414 | −0.0916896 | ||||||||
\(154\) | −18.4455 | −1.48638 | ||||||||
\(155\) | 10.5097 | 0.844158 | ||||||||
\(156\) | 8.12039 | 0.650151 | ||||||||
\(157\) | 18.8211 | 1.50209 | 0.751045 | − | 0.660251i | \(-0.229550\pi\) | ||||
0.751045 | + | 0.660251i | \(0.229550\pi\) | |||||||
\(158\) | 18.4290 | 1.46613 | ||||||||
\(159\) | −5.39763 | −0.428060 | ||||||||
\(160\) | 45.0537 | 3.56181 | ||||||||
\(161\) | 3.73076 | 0.294025 | ||||||||
\(162\) | 22.3698 | 1.75754 | ||||||||
\(163\) | −18.2232 | −1.42735 | −0.713677 | − | 0.700475i | \(-0.752972\pi\) | ||||
−0.713677 | + | 0.700475i | \(0.752972\pi\) | |||||||
\(164\) | −14.3850 | −1.12328 | ||||||||
\(165\) | 15.0141 | 1.16885 | ||||||||
\(166\) | −8.54518 | −0.663234 | ||||||||
\(167\) | −5.14879 | −0.398426 | −0.199213 | − | 0.979956i | \(-0.563839\pi\) | ||||
−0.199213 | + | 0.979956i | \(0.563839\pi\) | |||||||
\(168\) | 31.8029 | 2.45365 | ||||||||
\(169\) | −12.1026 | −0.930967 | ||||||||
\(170\) | 46.5454 | 3.56987 | ||||||||
\(171\) | 1.47390 | 0.112712 | ||||||||
\(172\) | −63.2418 | −4.82215 | ||||||||
\(173\) | 5.86979 | 0.446272 | 0.223136 | − | 0.974787i | \(-0.428371\pi\) | ||||
0.223136 | + | 0.974787i | \(0.428371\pi\) | |||||||
\(174\) | −32.0177 | −2.42725 | ||||||||
\(175\) | −8.58005 | −0.648591 | ||||||||
\(176\) | −36.1500 | −2.72491 | ||||||||
\(177\) | −5.94908 | −0.447160 | ||||||||
\(178\) | −22.0108 | −1.64978 | ||||||||
\(179\) | −12.6060 | −0.942213 | −0.471107 | − | 0.882076i | \(-0.656145\pi\) | ||||
−0.471107 | + | 0.882076i | \(0.656145\pi\) | |||||||
\(180\) | 2.91180 | 0.217033 | ||||||||
\(181\) | 18.1081 | 1.34596 | 0.672981 | − | 0.739660i | \(-0.265014\pi\) | ||||
0.672981 | + | 0.739660i | \(0.265014\pi\) | |||||||
\(182\) | 5.77091 | 0.427768 | ||||||||
\(183\) | −14.4855 | −1.07080 | ||||||||
\(184\) | 13.5776 | 1.00096 | ||||||||
\(185\) | 19.9990 | 1.47035 | ||||||||
\(186\) | 15.8741 | 1.16395 | ||||||||
\(187\) | −17.8540 | −1.30561 | ||||||||
\(188\) | −21.7466 | −1.58603 | ||||||||
\(189\) | 12.2156 | 0.888557 | ||||||||
\(190\) | −60.4896 | −4.38837 | ||||||||
\(191\) | −1.74370 | −0.126170 | −0.0630848 | − | 0.998008i | \(-0.520094\pi\) | ||||
−0.0630848 | + | 0.998008i | \(0.520094\pi\) | |||||||
\(192\) | 28.0408 | 2.02367 | ||||||||
\(193\) | 2.25746 | 0.162495 | 0.0812477 | − | 0.996694i | \(-0.474110\pi\) | ||||
0.0812477 | + | 0.996694i | \(0.474110\pi\) | |||||||
\(194\) | 23.9178 | 1.71720 | ||||||||
\(195\) | −4.69736 | −0.336385 | ||||||||
\(196\) | −9.13060 | −0.652186 | ||||||||
\(197\) | 5.47249 | 0.389898 | 0.194949 | − | 0.980813i | \(-0.437546\pi\) | ||||
0.194949 | + | 0.980813i | \(0.437546\pi\) | |||||||
\(198\) | −1.55358 | −0.110408 | ||||||||
\(199\) | 1.28842 | 0.0913338 | 0.0456669 | − | 0.998957i | \(-0.485459\pi\) | ||||
0.0456669 | + | 0.998957i | \(0.485459\pi\) | |||||||
\(200\) | −31.2260 | −2.20801 | ||||||||
\(201\) | 16.5326 | 1.16612 | ||||||||
\(202\) | −10.7727 | −0.757967 | ||||||||
\(203\) | −16.3585 | −1.14814 | ||||||||
\(204\) | 50.5433 | 3.53874 | ||||||||
\(205\) | 8.32125 | 0.581181 | ||||||||
\(206\) | −30.1864 | −2.10319 | ||||||||
\(207\) | 0.314225 | 0.0218402 | ||||||||
\(208\) | 11.3100 | 0.784207 | ||||||||
\(209\) | 23.2027 | 1.60497 | ||||||||
\(210\) | −30.2061 | −2.08442 | ||||||||
\(211\) | 3.27165 | 0.225230 | 0.112615 | − | 0.993639i | \(-0.464077\pi\) | ||||
0.112615 | + | 0.993639i | \(0.464077\pi\) | |||||||
\(212\) | −16.4791 | −1.13179 | ||||||||
\(213\) | 10.4698 | 0.717377 | ||||||||
\(214\) | 25.1023 | 1.71596 | ||||||||
\(215\) | 36.5832 | 2.49496 | ||||||||
\(216\) | 44.4572 | 3.02493 | ||||||||
\(217\) | 8.11042 | 0.550571 | ||||||||
\(218\) | 49.7899 | 3.37220 | ||||||||
\(219\) | 14.4740 | 0.978064 | ||||||||
\(220\) | 45.8386 | 3.09044 | ||||||||
\(221\) | 5.58586 | 0.375745 | ||||||||
\(222\) | 30.2070 | 2.02736 | ||||||||
\(223\) | −12.5804 | −0.842448 | −0.421224 | − | 0.906957i | \(-0.638399\pi\) | ||||
−0.421224 | + | 0.906957i | \(0.638399\pi\) | |||||||
\(224\) | 34.7684 | 2.32306 | ||||||||
\(225\) | −0.722659 | −0.0481773 | ||||||||
\(226\) | −10.4487 | −0.695040 | ||||||||
\(227\) | 28.8962 | 1.91791 | 0.958955 | − | 0.283558i | \(-0.0915149\pi\) | ||||
0.958955 | + | 0.283558i | \(0.0915149\pi\) | |||||||
\(228\) | −65.6851 | −4.35010 | ||||||||
\(229\) | 1.04679 | 0.0691738 | 0.0345869 | − | 0.999402i | \(-0.488988\pi\) | ||||
0.0345869 | + | 0.999402i | \(0.488988\pi\) | |||||||
\(230\) | −12.8959 | −0.850332 | ||||||||
\(231\) | 11.5865 | 0.762338 | ||||||||
\(232\) | −59.5347 | −3.90865 | ||||||||
\(233\) | 11.6114 | 0.760685 | 0.380343 | − | 0.924846i | \(-0.375806\pi\) | ||||
0.380343 | + | 0.924846i | \(0.375806\pi\) | |||||||
\(234\) | 0.486057 | 0.0317746 | ||||||||
\(235\) | 12.5796 | 0.820605 | ||||||||
\(236\) | −18.1627 | −1.18229 | ||||||||
\(237\) | −11.5762 | −0.751954 | ||||||||
\(238\) | 35.9195 | 2.32832 | ||||||||
\(239\) | 4.91271 | 0.317777 | 0.158888 | − | 0.987297i | \(-0.449209\pi\) | ||||
0.158888 | + | 0.987297i | \(0.449209\pi\) | |||||||
\(240\) | −59.1989 | −3.82127 | ||||||||
\(241\) | 22.7747 | 1.46704 | 0.733522 | − | 0.679665i | \(-0.237875\pi\) | ||||
0.733522 | + | 0.679665i | \(0.237875\pi\) | |||||||
\(242\) | 4.88577 | 0.314069 | ||||||||
\(243\) | 1.99574 | 0.128027 | ||||||||
\(244\) | −44.2247 | −2.83119 | ||||||||
\(245\) | 5.28174 | 0.337438 | ||||||||
\(246\) | 12.5686 | 0.801346 | ||||||||
\(247\) | −7.25927 | −0.461896 | ||||||||
\(248\) | 29.5168 | 1.87432 | ||||||||
\(249\) | 5.36766 | 0.340162 | ||||||||
\(250\) | −9.81107 | −0.620506 | ||||||||
\(251\) | −11.1052 | −0.700957 | −0.350479 | − | 0.936571i | \(-0.613981\pi\) | ||||
−0.350479 | + | 0.936571i | \(0.613981\pi\) | |||||||
\(252\) | 2.24706 | 0.141552 | ||||||||
\(253\) | 4.94665 | 0.310993 | ||||||||
\(254\) | 43.8209 | 2.74957 | ||||||||
\(255\) | −29.2376 | −1.83093 | ||||||||
\(256\) | 4.38484 | 0.274052 | ||||||||
\(257\) | 14.4664 | 0.902386 | 0.451193 | − | 0.892426i | \(-0.350999\pi\) | ||||
0.451193 | + | 0.892426i | \(0.350999\pi\) | |||||||
\(258\) | 55.2563 | 3.44010 | ||||||||
\(259\) | 15.4334 | 0.958985 | ||||||||
\(260\) | −14.3412 | −0.889403 | ||||||||
\(261\) | −1.37780 | −0.0852839 | ||||||||
\(262\) | 4.52572 | 0.279600 | ||||||||
\(263\) | −26.0580 | −1.60680 | −0.803402 | − | 0.595437i | \(-0.796979\pi\) | ||||
−0.803402 | + | 0.595437i | \(0.796979\pi\) | |||||||
\(264\) | 42.1677 | 2.59524 | ||||||||
\(265\) | 9.53262 | 0.585584 | ||||||||
\(266\) | −46.6803 | −2.86216 | ||||||||
\(267\) | 13.8261 | 0.846142 | ||||||||
\(268\) | 50.4746 | 3.08323 | ||||||||
\(269\) | 0.895258 | 0.0545848 | 0.0272924 | − | 0.999627i | \(-0.491311\pi\) | ||||
0.0272924 | + | 0.999627i | \(0.491311\pi\) | |||||||
\(270\) | −42.2251 | −2.56974 | ||||||||
\(271\) | −0.566173 | −0.0343926 | −0.0171963 | − | 0.999852i | \(-0.505474\pi\) | ||||
−0.0171963 | + | 0.999852i | \(0.505474\pi\) | |||||||
\(272\) | 70.3961 | 4.26839 | ||||||||
\(273\) | −3.62500 | −0.219395 | ||||||||
\(274\) | 60.0966 | 3.63057 | ||||||||
\(275\) | −11.3764 | −0.686020 | ||||||||
\(276\) | −14.0036 | −0.842916 | ||||||||
\(277\) | −8.10132 | −0.486761 | −0.243381 | − | 0.969931i | \(-0.578256\pi\) | ||||
−0.243381 | + | 0.969931i | \(0.578256\pi\) | |||||||
\(278\) | −43.0082 | −2.57946 | ||||||||
\(279\) | 0.683104 | 0.0408964 | ||||||||
\(280\) | −56.1663 | −3.35658 | ||||||||
\(281\) | 9.16231 | 0.546578 | 0.273289 | − | 0.961932i | \(-0.411889\pi\) | ||||
0.273289 | + | 0.961932i | \(0.411889\pi\) | |||||||
\(282\) | 19.0006 | 1.13147 | ||||||||
\(283\) | −21.9242 | −1.30326 | −0.651628 | − | 0.758538i | \(-0.725914\pi\) | ||||
−0.651628 | + | 0.758538i | \(0.725914\pi\) | |||||||
\(284\) | 31.9645 | 1.89675 | ||||||||
\(285\) | 37.9966 | 2.25072 | ||||||||
\(286\) | 7.65168 | 0.452454 | ||||||||
\(287\) | 6.42158 | 0.379054 | ||||||||
\(288\) | 2.92838 | 0.172557 | ||||||||
\(289\) | 17.7677 | 1.04516 | ||||||||
\(290\) | 56.5456 | 3.32047 | ||||||||
\(291\) | −15.0240 | −0.880723 | ||||||||
\(292\) | 44.1896 | 2.58600 | ||||||||
\(293\) | −7.44075 | −0.434693 | −0.217347 | − | 0.976094i | \(-0.569740\pi\) | ||||
−0.217347 | + | 0.976094i | \(0.569740\pi\) | |||||||
\(294\) | 7.97767 | 0.465267 | ||||||||
\(295\) | 10.5065 | 0.611713 | ||||||||
\(296\) | 56.1678 | 3.26469 | ||||||||
\(297\) | 16.1968 | 0.939833 | ||||||||
\(298\) | 45.2883 | 2.62348 | ||||||||
\(299\) | −1.54762 | −0.0895013 | ||||||||
\(300\) | 32.2056 | 1.85939 | ||||||||
\(301\) | 28.2316 | 1.62724 | ||||||||
\(302\) | 41.0577 | 2.36260 | ||||||||
\(303\) | 6.76690 | 0.388749 | ||||||||
\(304\) | −91.4855 | −5.24705 | ||||||||
\(305\) | 25.5825 | 1.46485 | ||||||||
\(306\) | 3.02534 | 0.172947 | ||||||||
\(307\) | −12.2830 | −0.701028 | −0.350514 | − | 0.936557i | \(-0.613993\pi\) | ||||
−0.350514 | + | 0.936557i | \(0.613993\pi\) | |||||||
\(308\) | 35.3741 | 2.01562 | ||||||||
\(309\) | 18.9616 | 1.07869 | ||||||||
\(310\) | −28.0348 | −1.59227 | ||||||||
\(311\) | 19.9688 | 1.13233 | 0.566164 | − | 0.824293i | \(-0.308427\pi\) | ||||
0.566164 | + | 0.824293i | \(0.308427\pi\) | |||||||
\(312\) | −13.1927 | −0.746890 | ||||||||
\(313\) | 6.40673 | 0.362130 | 0.181065 | − | 0.983471i | \(-0.442046\pi\) | ||||
0.181065 | + | 0.983471i | \(0.442046\pi\) | |||||||
\(314\) | −50.2058 | −2.83328 | ||||||||
\(315\) | −1.29985 | −0.0732382 | ||||||||
\(316\) | −35.3425 | −1.98817 | ||||||||
\(317\) | −7.96801 | −0.447528 | −0.223764 | − | 0.974643i | \(-0.571834\pi\) | ||||
−0.223764 | + | 0.974643i | \(0.571834\pi\) | |||||||
\(318\) | 14.3983 | 0.807417 | ||||||||
\(319\) | −21.6899 | −1.21440 | ||||||||
\(320\) | −49.5222 | −2.76837 | ||||||||
\(321\) | −15.7680 | −0.880086 | ||||||||
\(322\) | −9.95190 | −0.554598 | ||||||||
\(323\) | −45.1835 | −2.51408 | ||||||||
\(324\) | −42.8999 | −2.38333 | ||||||||
\(325\) | 3.55924 | 0.197431 | ||||||||
\(326\) | 48.6109 | 2.69231 | ||||||||
\(327\) | −31.2756 | −1.72954 | ||||||||
\(328\) | 23.3705 | 1.29042 | ||||||||
\(329\) | 9.70782 | 0.535210 | ||||||||
\(330\) | −40.0505 | −2.20471 | ||||||||
\(331\) | 9.40042 | 0.516694 | 0.258347 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258347 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(332\) | 16.3876 | 0.899388 | ||||||||
\(333\) | 1.29988 | 0.0712333 | ||||||||
\(334\) | 13.7345 | 0.751520 | ||||||||
\(335\) | −29.1979 | −1.59525 | ||||||||
\(336\) | −45.6843 | −2.49228 | ||||||||
\(337\) | −8.67640 | −0.472634 | −0.236317 | − | 0.971676i | \(-0.575940\pi\) | ||||
−0.236317 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(338\) | 32.2839 | 1.75601 | ||||||||
\(339\) | 6.56338 | 0.356474 | ||||||||
\(340\) | −89.2631 | −4.84097 | ||||||||
\(341\) | 10.7537 | 0.582343 | ||||||||
\(342\) | −3.93167 | −0.212601 | ||||||||
\(343\) | 20.0617 | 1.08323 | ||||||||
\(344\) | 102.745 | 5.53966 | ||||||||
\(345\) | 8.10058 | 0.436121 | ||||||||
\(346\) | −15.6578 | −0.841768 | ||||||||
\(347\) | 9.07737 | 0.487299 | 0.243649 | − | 0.969863i | \(-0.421655\pi\) | ||||
0.243649 | + | 0.969863i | \(0.421655\pi\) | |||||||
\(348\) | 61.4023 | 3.29151 | ||||||||
\(349\) | 34.0324 | 1.82171 | 0.910857 | − | 0.412723i | \(-0.135422\pi\) | ||||
0.910857 | + | 0.412723i | \(0.135422\pi\) | |||||||
\(350\) | 22.8875 | 1.22339 | ||||||||
\(351\) | −5.06738 | −0.270477 | ||||||||
\(352\) | 46.0996 | 2.45712 | ||||||||
\(353\) | −1.92632 | −0.102528 | −0.0512639 | − | 0.998685i | \(-0.516325\pi\) | ||||
−0.0512639 | + | 0.998685i | \(0.516325\pi\) | |||||||
\(354\) | 15.8693 | 0.843444 | ||||||||
\(355\) | −18.4904 | −0.981368 | ||||||||
\(356\) | 42.2114 | 2.23720 | ||||||||
\(357\) | −22.5629 | −1.19415 | ||||||||
\(358\) | 33.6267 | 1.77722 | ||||||||
\(359\) | −12.6811 | −0.669283 | −0.334641 | − | 0.942346i | \(-0.608615\pi\) | ||||
−0.334641 | + | 0.942346i | \(0.608615\pi\) | |||||||
\(360\) | −4.73063 | −0.249326 | ||||||||
\(361\) | 39.7196 | 2.09051 | ||||||||
\(362\) | −48.3037 | −2.53878 | ||||||||
\(363\) | −3.06900 | −0.161081 | ||||||||
\(364\) | −11.0672 | −0.580081 | ||||||||
\(365\) | −25.5622 | −1.33799 | ||||||||
\(366\) | 38.6404 | 2.01977 | ||||||||
\(367\) | −12.8098 | −0.668667 | −0.334334 | − | 0.942455i | \(-0.608511\pi\) | ||||
−0.334334 | + | 0.942455i | \(0.608511\pi\) | |||||||
\(368\) | −19.5040 | −1.01672 | ||||||||
\(369\) | 0.540861 | 0.0281561 | ||||||||
\(370\) | −53.3477 | −2.77342 | ||||||||
\(371\) | 7.35641 | 0.381926 | ||||||||
\(372\) | −30.4428 | −1.57838 | ||||||||
\(373\) | −12.6473 | −0.654852 | −0.327426 | − | 0.944877i | \(-0.606181\pi\) | ||||
−0.327426 | + | 0.944877i | \(0.606181\pi\) | |||||||
\(374\) | 47.6260 | 2.46268 | ||||||||
\(375\) | 6.16283 | 0.318247 | ||||||||
\(376\) | 35.3304 | 1.82202 | ||||||||
\(377\) | 6.78596 | 0.349495 | ||||||||
\(378\) | −32.5855 | −1.67602 | ||||||||
\(379\) | 30.0712 | 1.54465 | 0.772327 | − | 0.635225i | \(-0.219093\pi\) | ||||
0.772327 | + | 0.635225i | \(0.219093\pi\) | |||||||
\(380\) | 116.005 | 5.95091 | ||||||||
\(381\) | −27.5261 | −1.41021 | ||||||||
\(382\) | 4.65136 | 0.237984 | ||||||||
\(383\) | 31.8222 | 1.62604 | 0.813018 | − | 0.582238i | \(-0.197823\pi\) | ||||
0.813018 | + | 0.582238i | \(0.197823\pi\) | |||||||
\(384\) | −23.7782 | −1.21343 | ||||||||
\(385\) | −20.4627 | −1.04287 | ||||||||
\(386\) | −6.02182 | −0.306503 | ||||||||
\(387\) | 2.37782 | 0.120871 | ||||||||
\(388\) | −45.8688 | −2.32863 | ||||||||
\(389\) | −0.700445 | −0.0355140 | −0.0177570 | − | 0.999842i | \(-0.505653\pi\) | ||||
−0.0177570 | + | 0.999842i | \(0.505653\pi\) | |||||||
\(390\) | 12.5303 | 0.634498 | ||||||||
\(391\) | −9.63278 | −0.487151 | ||||||||
\(392\) | 14.8339 | 0.749227 | ||||||||
\(393\) | −2.84284 | −0.143402 | ||||||||
\(394\) | −14.5980 | −0.735436 | ||||||||
\(395\) | 20.4444 | 1.02867 | ||||||||
\(396\) | 2.97940 | 0.149720 | ||||||||
\(397\) | 38.4405 | 1.92927 | 0.964637 | − | 0.263581i | \(-0.0849037\pi\) | ||||
0.964637 | + | 0.263581i | \(0.0849037\pi\) | |||||||
\(398\) | −3.43689 | −0.172276 | ||||||||
\(399\) | 29.3223 | 1.46795 | ||||||||
\(400\) | 44.8556 | 2.24278 | ||||||||
\(401\) | −20.3458 | −1.01602 | −0.508010 | − | 0.861351i | \(-0.669619\pi\) | ||||
−0.508010 | + | 0.861351i | \(0.669619\pi\) | |||||||
\(402\) | −44.1012 | −2.19957 | ||||||||
\(403\) | −3.36442 | −0.167594 | ||||||||
\(404\) | 20.6596 | 1.02785 | ||||||||
\(405\) | 24.8161 | 1.23312 | ||||||||
\(406\) | 43.6367 | 2.16565 | ||||||||
\(407\) | 20.4632 | 1.01433 | ||||||||
\(408\) | −82.1147 | −4.06528 | ||||||||
\(409\) | 8.89191 | 0.439677 | 0.219838 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219838 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(410\) | −22.1971 | −1.09624 | ||||||||
\(411\) | −37.7497 | −1.86206 | ||||||||
\(412\) | 57.8903 | 2.85205 | ||||||||
\(413\) | 8.10797 | 0.398967 | ||||||||
\(414\) | −0.838203 | −0.0411954 | ||||||||
\(415\) | −9.47968 | −0.465339 | ||||||||
\(416\) | −14.4229 | −0.707139 | ||||||||
\(417\) | 27.0156 | 1.32296 | ||||||||
\(418\) | −61.8938 | −3.02732 | ||||||||
\(419\) | −14.8732 | −0.726603 | −0.363301 | − | 0.931672i | \(-0.618350\pi\) | ||||
−0.363301 | + | 0.931672i | \(0.618350\pi\) | |||||||
\(420\) | 57.9282 | 2.82661 | ||||||||
\(421\) | −1.42604 | −0.0695008 | −0.0347504 | − | 0.999396i | \(-0.511064\pi\) | ||||
−0.0347504 | + | 0.999396i | \(0.511064\pi\) | |||||||
\(422\) | −8.72720 | −0.424834 | ||||||||
\(423\) | 0.817646 | 0.0397553 | ||||||||
\(424\) | 26.7727 | 1.30020 | ||||||||
\(425\) | 22.1536 | 1.07461 | ||||||||
\(426\) | −27.9283 | −1.35313 | ||||||||
\(427\) | 19.7422 | 0.955393 | ||||||||
\(428\) | −48.1403 | −2.32695 | ||||||||
\(429\) | −4.80641 | −0.232056 | ||||||||
\(430\) | −97.5866 | −4.70604 | ||||||||
\(431\) | −10.4355 | −0.502660 | −0.251330 | − | 0.967901i | \(-0.580868\pi\) | ||||
−0.251330 | + | 0.967901i | \(0.580868\pi\) | |||||||
\(432\) | −63.8620 | −3.07256 | ||||||||
\(433\) | −23.0379 | −1.10713 | −0.553565 | − | 0.832806i | \(-0.686733\pi\) | ||||
−0.553565 | + | 0.832806i | \(0.686733\pi\) | |||||||
\(434\) | −21.6347 | −1.03850 | ||||||||
\(435\) | −35.5191 | −1.70301 | ||||||||
\(436\) | −95.4852 | −4.57291 | ||||||||
\(437\) | 12.5186 | 0.598845 | ||||||||
\(438\) | −38.6098 | −1.84485 | ||||||||
\(439\) | −15.7702 | −0.752669 | −0.376334 | − | 0.926484i | \(-0.622816\pi\) | ||||
−0.376334 | + | 0.926484i | \(0.622816\pi\) | |||||||
\(440\) | −74.4713 | −3.55028 | ||||||||
\(441\) | 0.343300 | 0.0163476 | ||||||||
\(442\) | −14.9004 | −0.708740 | ||||||||
\(443\) | −13.9520 | −0.662882 | −0.331441 | − | 0.943476i | \(-0.607535\pi\) | ||||
−0.331441 | + | 0.943476i | \(0.607535\pi\) | |||||||
\(444\) | −57.9298 | −2.74923 | ||||||||
\(445\) | −24.4179 | −1.15752 | ||||||||
\(446\) | 33.5586 | 1.58904 | ||||||||
\(447\) | −28.4479 | −1.34554 | ||||||||
\(448\) | −38.2167 | −1.80557 | ||||||||
\(449\) | −0.593025 | −0.0279866 | −0.0139933 | − | 0.999902i | \(-0.504454\pi\) | ||||
−0.0139933 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(450\) | 1.92771 | 0.0908731 | ||||||||
\(451\) | 8.51442 | 0.400928 | ||||||||
\(452\) | 20.0382 | 0.942518 | ||||||||
\(453\) | −25.7904 | −1.21174 | ||||||||
\(454\) | −77.0813 | −3.61761 | ||||||||
\(455\) | 6.40201 | 0.300131 | ||||||||
\(456\) | 106.715 | 4.99737 | ||||||||
\(457\) | 13.4204 | 0.627779 | 0.313890 | − | 0.949459i | \(-0.398368\pi\) | ||||
0.313890 | + | 0.949459i | \(0.398368\pi\) | |||||||
\(458\) | −2.79233 | −0.130477 | ||||||||
\(459\) | −31.5406 | −1.47219 | ||||||||
\(460\) | 24.7313 | 1.15310 | ||||||||
\(461\) | 20.2794 | 0.944504 | 0.472252 | − | 0.881463i | \(-0.343441\pi\) | ||||
0.472252 | + | 0.881463i | \(0.343441\pi\) | |||||||
\(462\) | −30.9074 | −1.43794 | ||||||||
\(463\) | −41.0949 | −1.90984 | −0.954921 | − | 0.296861i | \(-0.904060\pi\) | ||||
−0.954921 | + | 0.296861i | \(0.904060\pi\) | |||||||
\(464\) | 85.5205 | 3.97019 | ||||||||
\(465\) | 17.6101 | 0.816649 | ||||||||
\(466\) | −30.9736 | −1.43482 | ||||||||
\(467\) | 22.0758 | 1.02155 | 0.510773 | − | 0.859716i | \(-0.329359\pi\) | ||||
0.510773 | + | 0.859716i | \(0.329359\pi\) | |||||||
\(468\) | −0.932143 | −0.0430883 | ||||||||
\(469\) | −22.5322 | −1.04044 | ||||||||
\(470\) | −33.5565 | −1.54784 | ||||||||
\(471\) | 31.5368 | 1.45314 | ||||||||
\(472\) | 29.5079 | 1.35821 | ||||||||
\(473\) | 37.4325 | 1.72115 | ||||||||
\(474\) | 30.8797 | 1.41835 | ||||||||
\(475\) | −28.7904 | −1.32099 | ||||||||
\(476\) | −68.8852 | −3.15735 | ||||||||
\(477\) | 0.619597 | 0.0283694 | ||||||||
\(478\) | −13.1048 | −0.599398 | ||||||||
\(479\) | 15.1393 | 0.691734 | 0.345867 | − | 0.938284i | \(-0.387585\pi\) | ||||
0.345867 | + | 0.938284i | \(0.387585\pi\) | |||||||
\(480\) | 75.4923 | 3.44574 | ||||||||
\(481\) | −6.40219 | −0.291915 | ||||||||
\(482\) | −60.7519 | −2.76717 | ||||||||
\(483\) | 6.25129 | 0.284444 | ||||||||
\(484\) | −9.36975 | −0.425898 | ||||||||
\(485\) | 26.5335 | 1.20482 | ||||||||
\(486\) | −5.32369 | −0.241488 | ||||||||
\(487\) | −5.66374 | −0.256649 | −0.128324 | − | 0.991732i | \(-0.540960\pi\) | ||||
−0.128324 | + | 0.991732i | \(0.540960\pi\) | |||||||
\(488\) | 71.8492 | 3.25246 | ||||||||
\(489\) | −30.5350 | −1.38084 | ||||||||
\(490\) | −14.0892 | −0.636483 | ||||||||
\(491\) | −10.3558 | −0.467351 | −0.233676 | − | 0.972315i | \(-0.575075\pi\) | ||||
−0.233676 | + | 0.972315i | \(0.575075\pi\) | |||||||
\(492\) | −24.1037 | −1.08668 | ||||||||
\(493\) | 42.2375 | 1.90228 | ||||||||
\(494\) | 19.3643 | 0.871240 | ||||||||
\(495\) | −1.72348 | −0.0774646 | ||||||||
\(496\) | −42.4004 | −1.90383 | ||||||||
\(497\) | −14.2692 | −0.640061 | ||||||||
\(498\) | −14.3184 | −0.641621 | ||||||||
\(499\) | 37.0368 | 1.65799 | 0.828997 | − | 0.559253i | \(-0.188912\pi\) | ||||
0.828997 | + | 0.559253i | \(0.188912\pi\) | |||||||
\(500\) | 18.8153 | 0.841446 | ||||||||
\(501\) | −8.62735 | −0.385442 | ||||||||
\(502\) | 29.6235 | 1.32216 | ||||||||
\(503\) | 22.9747 | 1.02439 | 0.512195 | − | 0.858869i | \(-0.328832\pi\) | ||||
0.512195 | + | 0.858869i | \(0.328832\pi\) | |||||||
\(504\) | −3.65067 | −0.162614 | ||||||||
\(505\) | −11.9509 | −0.531806 | ||||||||
\(506\) | −13.1953 | −0.586602 | ||||||||
\(507\) | −20.2791 | −0.900628 | ||||||||
\(508\) | −84.0381 | −3.72859 | ||||||||
\(509\) | 25.8533 | 1.14593 | 0.572964 | − | 0.819581i | \(-0.305793\pi\) | ||||
0.572964 | + | 0.819581i | \(0.305793\pi\) | |||||||
\(510\) | 77.9918 | 3.45354 | ||||||||
\(511\) | −19.7266 | −0.872652 | ||||||||
\(512\) | 16.6850 | 0.737378 | ||||||||
\(513\) | 40.9896 | 1.80973 | ||||||||
\(514\) | −38.5893 | −1.70210 | ||||||||
\(515\) | −33.4876 | −1.47564 | ||||||||
\(516\) | −105.968 | −4.66500 | ||||||||
\(517\) | 12.8717 | 0.566095 | ||||||||
\(518\) | −41.1689 | −1.80886 | ||||||||
\(519\) | 9.83545 | 0.431728 | ||||||||
\(520\) | 23.2993 | 1.02174 | ||||||||
\(521\) | −10.8019 | −0.473239 | −0.236619 | − | 0.971602i | \(-0.576039\pi\) | ||||
−0.236619 | + | 0.971602i | \(0.576039\pi\) | |||||||
\(522\) | 3.67532 | 0.160865 | ||||||||
\(523\) | 14.7037 | 0.642946 | 0.321473 | − | 0.946919i | \(-0.395822\pi\) | ||||
0.321473 | + | 0.946919i | \(0.395822\pi\) | |||||||
\(524\) | −8.67927 | −0.379156 | ||||||||
\(525\) | −14.3768 | −0.627455 | ||||||||
\(526\) | 69.5103 | 3.03079 | ||||||||
\(527\) | −20.9410 | −0.912204 | ||||||||
\(528\) | −60.5731 | −2.63611 | ||||||||
\(529\) | −20.3311 | −0.883962 | ||||||||
\(530\) | −25.4285 | −1.10454 | ||||||||
\(531\) | 0.682898 | 0.0296352 | ||||||||
\(532\) | 89.5219 | 3.88126 | ||||||||
\(533\) | −2.66385 | −0.115384 | ||||||||
\(534\) | −36.8814 | −1.59601 | ||||||||
\(535\) | 27.8475 | 1.20395 | ||||||||
\(536\) | −82.0032 | −3.54200 | ||||||||
\(537\) | −21.1226 | −0.911508 | ||||||||
\(538\) | −2.38812 | −0.102959 | ||||||||
\(539\) | 5.40435 | 0.232782 | ||||||||
\(540\) | 80.9777 | 3.48473 | ||||||||
\(541\) | 10.8235 | 0.465337 | 0.232669 | − | 0.972556i | \(-0.425254\pi\) | ||||
0.232669 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(542\) | 1.51028 | 0.0648721 | ||||||||
\(543\) | 30.3420 | 1.30210 | ||||||||
\(544\) | −89.7714 | −3.84892 | ||||||||
\(545\) | 55.2349 | 2.36600 | ||||||||
\(546\) | 9.66977 | 0.413828 | ||||||||
\(547\) | 38.6655 | 1.65322 | 0.826609 | − | 0.562777i | \(-0.190267\pi\) | ||||
0.826609 | + | 0.562777i | \(0.190267\pi\) | |||||||
\(548\) | −115.251 | −4.92328 | ||||||||
\(549\) | 1.66280 | 0.0709664 | ||||||||
\(550\) | 30.3467 | 1.29399 | ||||||||
\(551\) | −54.8910 | −2.33844 | ||||||||
\(552\) | 22.7508 | 0.968337 | ||||||||
\(553\) | 15.7771 | 0.670912 | ||||||||
\(554\) | 21.6105 | 0.918140 | ||||||||
\(555\) | 33.5104 | 1.42244 | ||||||||
\(556\) | 82.4795 | 3.49791 | ||||||||
\(557\) | 11.4708 | 0.486033 | 0.243017 | − | 0.970022i | \(-0.421863\pi\) | ||||
0.243017 | + | 0.970022i | \(0.421863\pi\) | |||||||
\(558\) | −1.82219 | −0.0771397 | ||||||||
\(559\) | −11.7112 | −0.495333 | ||||||||
\(560\) | 80.6818 | 3.40943 | ||||||||
\(561\) | −29.9163 | −1.26307 | ||||||||
\(562\) | −24.4407 | −1.03097 | ||||||||
\(563\) | −19.1123 | −0.805486 | −0.402743 | − | 0.915313i | \(-0.631943\pi\) | ||||
−0.402743 | + | 0.915313i | \(0.631943\pi\) | |||||||
\(564\) | −36.4387 | −1.53435 | ||||||||
\(565\) | −11.5914 | −0.487654 | ||||||||
\(566\) | 58.4832 | 2.45823 | ||||||||
\(567\) | 19.1508 | 0.804260 | ||||||||
\(568\) | −51.9309 | −2.17897 | ||||||||
\(569\) | 38.9786 | 1.63407 | 0.817034 | − | 0.576589i | \(-0.195617\pi\) | ||||
0.817034 | + | 0.576589i | \(0.195617\pi\) | |||||||
\(570\) | −101.357 | −4.24536 | ||||||||
\(571\) | 2.17452 | 0.0910008 | 0.0455004 | − | 0.998964i | \(-0.485512\pi\) | ||||
0.0455004 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(572\) | −14.6741 | −0.613556 | ||||||||
\(573\) | −2.92175 | −0.122058 | ||||||||
\(574\) | −17.1297 | −0.714981 | ||||||||
\(575\) | −6.13789 | −0.255968 | ||||||||
\(576\) | −3.21882 | −0.134117 | ||||||||
\(577\) | −14.4405 | −0.601165 | −0.300583 | − | 0.953756i | \(-0.597181\pi\) | ||||
−0.300583 | + | 0.953756i | \(0.597181\pi\) | |||||||
\(578\) | −47.3959 | −1.97141 | ||||||||
\(579\) | 3.78261 | 0.157200 | ||||||||
\(580\) | −108.441 | −4.50277 | ||||||||
\(581\) | −7.31556 | −0.303500 | ||||||||
\(582\) | 40.0769 | 1.66124 | ||||||||
\(583\) | 9.75391 | 0.403966 | ||||||||
\(584\) | −71.7923 | −2.97079 | ||||||||
\(585\) | 0.539213 | 0.0222937 | ||||||||
\(586\) | 19.8484 | 0.819929 | ||||||||
\(587\) | −20.6851 | −0.853763 | −0.426882 | − | 0.904307i | \(-0.640388\pi\) | ||||
−0.426882 | + | 0.904307i | \(0.640388\pi\) | |||||||
\(588\) | −15.2993 | −0.630932 | ||||||||
\(589\) | 27.2145 | 1.12135 | ||||||||
\(590\) | −28.0264 | −1.15383 | ||||||||
\(591\) | 9.16973 | 0.377192 | ||||||||
\(592\) | −80.6841 | −3.31609 | ||||||||
\(593\) | 30.9756 | 1.27202 | 0.636009 | − | 0.771682i | \(-0.280584\pi\) | ||||
0.636009 | + | 0.771682i | \(0.280584\pi\) | |||||||
\(594\) | −43.2053 | −1.77274 | ||||||||
\(595\) | 39.8477 | 1.63360 | ||||||||
\(596\) | −86.8522 | −3.55761 | ||||||||
\(597\) | 2.15889 | 0.0883574 | ||||||||
\(598\) | 4.12832 | 0.168819 | ||||||||
\(599\) | 14.0833 | 0.575428 | 0.287714 | − | 0.957716i | \(-0.407105\pi\) | ||||
0.287714 | + | 0.957716i | \(0.407105\pi\) | |||||||
\(600\) | −52.3225 | −2.13606 | ||||||||
\(601\) | −31.6167 | −1.28967 | −0.644837 | − | 0.764320i | \(-0.723075\pi\) | ||||
−0.644837 | + | 0.764320i | \(0.723075\pi\) | |||||||
\(602\) | −75.3085 | −3.06934 | ||||||||
\(603\) | −1.89779 | −0.0772839 | ||||||||
\(604\) | −78.7389 | −3.20384 | ||||||||
\(605\) | 5.42008 | 0.220358 | ||||||||
\(606\) | −18.0509 | −0.733267 | ||||||||
\(607\) | 8.12864 | 0.329931 | 0.164966 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164966 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(608\) | 116.665 | 4.73140 | ||||||||
\(609\) | −27.4104 | −1.11073 | ||||||||
\(610\) | −68.2418 | −2.76303 | ||||||||
\(611\) | −4.02707 | −0.162918 | ||||||||
\(612\) | −5.80189 | −0.234527 | ||||||||
\(613\) | 24.7448 | 0.999434 | 0.499717 | − | 0.866189i | \(-0.333437\pi\) | ||||
0.499717 | + | 0.866189i | \(0.333437\pi\) | |||||||
\(614\) | 32.7652 | 1.32230 | ||||||||
\(615\) | 13.9431 | 0.562242 | ||||||||
\(616\) | −57.4701 | −2.31554 | ||||||||
\(617\) | −42.0895 | −1.69446 | −0.847229 | − | 0.531228i | \(-0.821731\pi\) | ||||
−0.847229 | + | 0.531228i | \(0.821731\pi\) | |||||||
\(618\) | −50.5805 | −2.03465 | ||||||||
\(619\) | 48.8247 | 1.96243 | 0.981216 | − | 0.192913i | \(-0.0617936\pi\) | ||||
0.981216 | + | 0.192913i | \(0.0617936\pi\) | |||||||
\(620\) | 53.7642 | 2.15922 | ||||||||
\(621\) | 8.73867 | 0.350671 | ||||||||
\(622\) | −53.2673 | −2.13582 | ||||||||
\(623\) | −18.8435 | −0.754949 | ||||||||
\(624\) | 18.9511 | 0.758651 | ||||||||
\(625\) | −29.6696 | −1.18679 | ||||||||
\(626\) | −17.0901 | −0.683057 | ||||||||
\(627\) | 38.8786 | 1.55266 | ||||||||
\(628\) | 96.2828 | 3.84210 | ||||||||
\(629\) | −39.8488 | −1.58888 | ||||||||
\(630\) | 3.46738 | 0.138144 | ||||||||
\(631\) | −42.3507 | −1.68595 | −0.842977 | − | 0.537949i | \(-0.819199\pi\) | ||||
−0.842977 | + | 0.537949i | \(0.819199\pi\) | |||||||
\(632\) | 57.4188 | 2.28400 | ||||||||
\(633\) | 5.48200 | 0.217890 | ||||||||
\(634\) | 21.2548 | 0.844137 | ||||||||
\(635\) | 48.6132 | 1.92915 | ||||||||
\(636\) | −27.6126 | −1.09491 | ||||||||
\(637\) | −1.69082 | −0.0669928 | ||||||||
\(638\) | 57.8582 | 2.29063 | ||||||||
\(639\) | −1.20183 | −0.0475436 | ||||||||
\(640\) | 41.9941 | 1.65996 | ||||||||
\(641\) | −47.9125 | −1.89243 | −0.946215 | − | 0.323537i | \(-0.895128\pi\) | ||||
−0.946215 | + | 0.323537i | \(0.895128\pi\) | |||||||
\(642\) | 42.0616 | 1.66004 | ||||||||
\(643\) | −33.1186 | −1.30607 | −0.653036 | − | 0.757327i | \(-0.726505\pi\) | ||||
−0.653036 | + | 0.757327i | \(0.726505\pi\) | |||||||
\(644\) | 19.0854 | 0.752070 | ||||||||
\(645\) | 61.2991 | 2.41365 | ||||||||
\(646\) | 120.528 | 4.74211 | ||||||||
\(647\) | 22.6387 | 0.890018 | 0.445009 | − | 0.895526i | \(-0.353201\pi\) | ||||
0.445009 | + | 0.895526i | \(0.353201\pi\) | |||||||
\(648\) | 69.6970 | 2.73796 | ||||||||
\(649\) | 10.7504 | 0.421991 | ||||||||
\(650\) | −9.49435 | −0.372399 | ||||||||
\(651\) | 13.5899 | 0.532629 | ||||||||
\(652\) | −93.2242 | −3.65094 | ||||||||
\(653\) | −31.0970 | −1.21692 | −0.608460 | − | 0.793584i | \(-0.708213\pi\) | ||||
−0.608460 | + | 0.793584i | \(0.708213\pi\) | |||||||
\(654\) | 83.4282 | 3.26230 | ||||||||
\(655\) | 5.02066 | 0.196173 | ||||||||
\(656\) | −33.5713 | −1.31074 | ||||||||
\(657\) | −1.66148 | −0.0648205 | ||||||||
\(658\) | −25.8958 | −1.00952 | ||||||||
\(659\) | 24.1812 | 0.941966 | 0.470983 | − | 0.882142i | \(-0.343899\pi\) | ||||
0.470983 | + | 0.882142i | \(0.343899\pi\) | |||||||
\(660\) | 76.8074 | 2.98973 | ||||||||
\(661\) | 14.0027 | 0.544640 | 0.272320 | − | 0.962207i | \(-0.412209\pi\) | ||||
0.272320 | + | 0.962207i | \(0.412209\pi\) | |||||||
\(662\) | −25.0758 | −0.974600 | ||||||||
\(663\) | 9.35970 | 0.363500 | ||||||||
\(664\) | −26.6240 | −1.03321 | ||||||||
\(665\) | −51.7853 | −2.00815 | ||||||||
\(666\) | −3.46747 | −0.134362 | ||||||||
\(667\) | −11.7024 | −0.453117 | ||||||||
\(668\) | −26.3396 | −1.01911 | ||||||||
\(669\) | −21.0798 | −0.814994 | ||||||||
\(670\) | 77.8859 | 3.00900 | ||||||||
\(671\) | 26.1763 | 1.01053 | ||||||||
\(672\) | 58.2581 | 2.24735 | ||||||||
\(673\) | −37.4592 | −1.44394 | −0.721972 | − | 0.691922i | \(-0.756764\pi\) | ||||
−0.721972 | + | 0.691922i | \(0.756764\pi\) | |||||||
\(674\) | 23.1445 | 0.891493 | ||||||||
\(675\) | −20.0973 | −0.773545 | ||||||||
\(676\) | −61.9128 | −2.38126 | ||||||||
\(677\) | 43.5235 | 1.67274 | 0.836371 | − | 0.548163i | \(-0.184673\pi\) | ||||
0.836371 | + | 0.548163i | \(0.184673\pi\) | |||||||
\(678\) | −17.5080 | −0.672389 | ||||||||
\(679\) | 20.4761 | 0.785802 | ||||||||
\(680\) | 145.021 | 5.56129 | ||||||||
\(681\) | 48.4187 | 1.85541 | ||||||||
\(682\) | −28.6856 | −1.09843 | ||||||||
\(683\) | −17.6853 | −0.676708 | −0.338354 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338354 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(684\) | 7.54002 | 0.288300 | ||||||||
\(685\) | 66.6688 | 2.54728 | ||||||||
\(686\) | −53.5150 | −2.04321 | ||||||||
\(687\) | 1.75401 | 0.0669195 | ||||||||
\(688\) | −147.592 | −5.62688 | ||||||||
\(689\) | −3.05164 | −0.116258 | ||||||||
\(690\) | −21.6085 | −0.822621 | ||||||||
\(691\) | −19.6308 | −0.746791 | −0.373395 | − | 0.927672i | \(-0.621807\pi\) | ||||
−0.373395 | + | 0.927672i | \(0.621807\pi\) | |||||||
\(692\) | 30.0279 | 1.14149 | ||||||||
\(693\) | −1.33002 | −0.0505234 | ||||||||
\(694\) | −24.2141 | −0.919154 | ||||||||
\(695\) | −47.7116 | −1.80980 | ||||||||
\(696\) | −99.7568 | −3.78127 | ||||||||
\(697\) | −16.5804 | −0.628029 | ||||||||
\(698\) | −90.7822 | −3.43616 | ||||||||
\(699\) | 19.4561 | 0.735896 | ||||||||
\(700\) | −43.8928 | −1.65899 | ||||||||
\(701\) | 12.2379 | 0.462220 | 0.231110 | − | 0.972928i | \(-0.425764\pi\) | ||||
0.231110 | + | 0.972928i | \(0.425764\pi\) | |||||||
\(702\) | 13.5173 | 0.510179 | ||||||||
\(703\) | 51.7868 | 1.95317 | ||||||||
\(704\) | −50.6718 | −1.90976 | ||||||||
\(705\) | 21.0785 | 0.793863 | ||||||||
\(706\) | 5.13851 | 0.193390 | ||||||||
\(707\) | −9.22258 | −0.346851 | ||||||||
\(708\) | −30.4336 | −1.14376 | ||||||||
\(709\) | 17.1224 | 0.643046 | 0.321523 | − | 0.946902i | \(-0.395805\pi\) | ||||
0.321523 | + | 0.946902i | \(0.395805\pi\) | |||||||
\(710\) | 49.3235 | 1.85108 | ||||||||
\(711\) | 1.32884 | 0.0498352 | ||||||||
\(712\) | −68.5785 | −2.57009 | ||||||||
\(713\) | 5.80193 | 0.217284 | ||||||||
\(714\) | 60.1870 | 2.25244 | ||||||||
\(715\) | 8.48847 | 0.317451 | ||||||||
\(716\) | −64.4880 | −2.41003 | ||||||||
\(717\) | 8.23177 | 0.307421 | ||||||||
\(718\) | 33.8271 | 1.26242 | ||||||||
\(719\) | 41.8356 | 1.56020 | 0.780102 | − | 0.625653i | \(-0.215167\pi\) | ||||
0.780102 | + | 0.625653i | \(0.215167\pi\) | |||||||
\(720\) | 6.79547 | 0.253252 | ||||||||
\(721\) | −25.8427 | −0.962431 | ||||||||
\(722\) | −105.953 | −3.94316 | ||||||||
\(723\) | 38.1614 | 1.41924 | ||||||||
\(724\) | 92.6350 | 3.44275 | ||||||||
\(725\) | 26.9132 | 0.999531 | ||||||||
\(726\) | 8.18663 | 0.303834 | ||||||||
\(727\) | −45.0775 | −1.67183 | −0.835916 | − | 0.548857i | \(-0.815063\pi\) | ||||
−0.835916 | + | 0.548857i | \(0.815063\pi\) | |||||||
\(728\) | 17.9803 | 0.666394 | ||||||||
\(729\) | 28.5020 | 1.05563 | ||||||||
\(730\) | 68.1877 | 2.52374 | ||||||||
\(731\) | −72.8936 | −2.69607 | ||||||||
\(732\) | −74.1031 | −2.73893 | ||||||||
\(733\) | 15.1009 | 0.557764 | 0.278882 | − | 0.960325i | \(-0.410036\pi\) | ||||
0.278882 | + | 0.960325i | \(0.410036\pi\) | |||||||
\(734\) | 34.1705 | 1.26126 | ||||||||
\(735\) | 8.85012 | 0.326441 | ||||||||
\(736\) | 24.8721 | 0.916800 | ||||||||
\(737\) | −29.8757 | −1.10048 | ||||||||
\(738\) | −1.44276 | −0.0531087 | ||||||||
\(739\) | 39.8828 | 1.46711 | 0.733557 | − | 0.679628i | \(-0.237859\pi\) | ||||
0.733557 | + | 0.679628i | \(0.237859\pi\) | |||||||
\(740\) | 102.308 | 3.76093 | ||||||||
\(741\) | −12.1637 | −0.446844 | ||||||||
\(742\) | −19.6234 | −0.720397 | ||||||||
\(743\) | 20.7790 | 0.762306 | 0.381153 | − | 0.924512i | \(-0.375527\pi\) | ||||
0.381153 | + | 0.924512i | \(0.375527\pi\) | |||||||
\(744\) | 49.4586 | 1.81324 | ||||||||
\(745\) | 50.2410 | 1.84069 | ||||||||
\(746\) | 33.7369 | 1.23520 | ||||||||
\(747\) | −0.616156 | −0.0225440 | ||||||||
\(748\) | −91.3353 | −3.33955 | ||||||||
\(749\) | 21.4902 | 0.785234 | ||||||||
\(750\) | −16.4395 | −0.600285 | ||||||||
\(751\) | −10.5944 | −0.386596 | −0.193298 | − | 0.981140i | \(-0.561918\pi\) | ||||
−0.193298 | + | 0.981140i | \(0.561918\pi\) | |||||||
\(752\) | −50.7514 | −1.85071 | ||||||||
\(753\) | −18.6080 | −0.678114 | ||||||||
\(754\) | −18.1017 | −0.659225 | ||||||||
\(755\) | 45.5478 | 1.65765 | ||||||||
\(756\) | 62.4912 | 2.27278 | ||||||||
\(757\) | 27.3635 | 0.994543 | 0.497271 | − | 0.867595i | \(-0.334335\pi\) | ||||
0.497271 | + | 0.867595i | \(0.334335\pi\) | |||||||
\(758\) | −80.2156 | −2.91356 | ||||||||
\(759\) | 8.28863 | 0.300858 | ||||||||
\(760\) | −188.466 | −6.83638 | ||||||||
\(761\) | 19.1211 | 0.693139 | 0.346569 | − | 0.938024i | \(-0.387347\pi\) | ||||
0.346569 | + | 0.938024i | \(0.387347\pi\) | |||||||
\(762\) | 73.4266 | 2.65996 | ||||||||
\(763\) | 42.6253 | 1.54314 | ||||||||
\(764\) | −8.92020 | −0.322722 | ||||||||
\(765\) | 3.35619 | 0.121343 | ||||||||
\(766\) | −84.8863 | −3.06707 | ||||||||
\(767\) | −3.36341 | −0.121446 | ||||||||
\(768\) | 7.34726 | 0.265121 | ||||||||
\(769\) | −3.91719 | −0.141258 | −0.0706288 | − | 0.997503i | \(-0.522501\pi\) | ||||
−0.0706288 | + | 0.997503i | \(0.522501\pi\) | |||||||
\(770\) | 54.5847 | 1.96709 | ||||||||
\(771\) | 24.2399 | 0.872979 | ||||||||
\(772\) | 11.5484 | 0.415637 | ||||||||
\(773\) | 4.52051 | 0.162591 | 0.0812957 | − | 0.996690i | \(-0.474094\pi\) | ||||
0.0812957 | + | 0.996690i | \(0.474094\pi\) | |||||||
\(774\) | −6.34289 | −0.227991 | ||||||||
\(775\) | −13.3433 | −0.479307 | ||||||||
\(776\) | 74.5203 | 2.67512 | ||||||||
\(777\) | 25.8603 | 0.927733 | ||||||||
\(778\) | 1.86845 | 0.0669873 | ||||||||
\(779\) | 21.5476 | 0.772024 | ||||||||
\(780\) | −24.0302 | −0.860419 | ||||||||
\(781\) | −18.9196 | −0.676997 | ||||||||
\(782\) | 25.6957 | 0.918875 | ||||||||
\(783\) | −38.3170 | −1.36934 | ||||||||
\(784\) | −21.3087 | −0.761025 | ||||||||
\(785\) | −55.6963 | −1.98789 | ||||||||
\(786\) | 7.58333 | 0.270489 | ||||||||
\(787\) | 32.7245 | 1.16650 | 0.583251 | − | 0.812292i | \(-0.301780\pi\) | ||||
0.583251 | + | 0.812292i | \(0.301780\pi\) | |||||||
\(788\) | 27.9955 | 0.997297 | ||||||||
\(789\) | −43.6629 | −1.55444 | ||||||||
\(790\) | −54.5359 | −1.94030 | ||||||||
\(791\) | −8.94520 | −0.318055 | ||||||||
\(792\) | −4.84045 | −0.171998 | ||||||||
\(793\) | −8.18961 | −0.290821 | ||||||||
\(794\) | −102.541 | −3.63904 | ||||||||
\(795\) | 15.9729 | 0.566501 | ||||||||
\(796\) | 6.59115 | 0.233617 | ||||||||
\(797\) | −24.1889 | −0.856814 | −0.428407 | − | 0.903586i | \(-0.640925\pi\) | ||||
−0.428407 | + | 0.903586i | \(0.640925\pi\) | |||||||
\(798\) | −78.2179 | −2.76888 | ||||||||
\(799\) | −25.0655 | −0.886752 | ||||||||
\(800\) | −57.2012 | −2.02237 | ||||||||
\(801\) | −1.58710 | −0.0560775 | ||||||||
\(802\) | 54.2729 | 1.91644 | ||||||||
\(803\) | −26.1556 | −0.923011 | ||||||||
\(804\) | 84.5756 | 2.98275 | ||||||||
\(805\) | −11.0402 | −0.389117 | ||||||||
\(806\) | 8.97467 | 0.316119 | ||||||||
\(807\) | 1.50010 | 0.0528060 | ||||||||
\(808\) | −33.5644 | −1.18079 | ||||||||
\(809\) | 4.80521 | 0.168942 | 0.0844712 | − | 0.996426i | \(-0.473080\pi\) | ||||
0.0844712 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(810\) | −66.1976 | −2.32595 | ||||||||
\(811\) | −30.3017 | −1.06404 | −0.532018 | − | 0.846733i | \(-0.678566\pi\) | ||||
−0.532018 | + | 0.846733i | \(0.678566\pi\) | |||||||
\(812\) | −83.6849 | −2.93677 | ||||||||
\(813\) | −0.948684 | −0.0332718 | ||||||||
\(814\) | −54.5862 | −1.91324 | ||||||||
\(815\) | 53.9270 | 1.88898 | ||||||||
\(816\) | 117.956 | 4.12929 | ||||||||
\(817\) | 94.7312 | 3.31422 | ||||||||
\(818\) | −23.7194 | −0.829328 | ||||||||
\(819\) | 0.416115 | 0.0145402 | ||||||||
\(820\) | 42.5688 | 1.48657 | ||||||||
\(821\) | −38.5463 | −1.34528 | −0.672638 | − | 0.739972i | \(-0.734839\pi\) | ||||
−0.672638 | + | 0.739972i | \(0.734839\pi\) | |||||||
\(822\) | 100.698 | 3.51226 | ||||||||
\(823\) | −2.65886 | −0.0926819 | −0.0463410 | − | 0.998926i | \(-0.514756\pi\) | ||||
−0.0463410 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(824\) | −94.0510 | −3.27642 | ||||||||
\(825\) | −19.0623 | −0.663664 | ||||||||
\(826\) | −21.6282 | −0.752541 | ||||||||
\(827\) | −9.74827 | −0.338981 | −0.169490 | − | 0.985532i | \(-0.554212\pi\) | ||||
−0.169490 | + | 0.985532i | \(0.554212\pi\) | |||||||
\(828\) | 1.60748 | 0.0558636 | ||||||||
\(829\) | 49.1290 | 1.70632 | 0.853161 | − | 0.521648i | \(-0.174682\pi\) | ||||
0.853161 | + | 0.521648i | \(0.174682\pi\) | |||||||
\(830\) | 25.2873 | 0.877734 | ||||||||
\(831\) | −13.5746 | −0.470898 | ||||||||
\(832\) | 15.8533 | 0.549615 | ||||||||
\(833\) | −10.5241 | −0.364638 | ||||||||
\(834\) | −72.0648 | −2.49540 | ||||||||
\(835\) | 15.2365 | 0.527282 | ||||||||
\(836\) | 118.698 | 4.10524 | ||||||||
\(837\) | 18.9972 | 0.656641 | ||||||||
\(838\) | 39.6746 | 1.37054 | ||||||||
\(839\) | −17.6872 | −0.610630 | −0.305315 | − | 0.952251i | \(-0.598762\pi\) | ||||
−0.305315 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(840\) | −94.1126 | −3.24719 | ||||||||
\(841\) | 22.3121 | 0.769382 | ||||||||
\(842\) | 3.80399 | 0.131094 | ||||||||
\(843\) | 15.3524 | 0.528766 | ||||||||
\(844\) | 16.7367 | 0.576101 | ||||||||
\(845\) | 35.8144 | 1.23205 | ||||||||
\(846\) | −2.18109 | −0.0749874 | ||||||||
\(847\) | 4.18272 | 0.143720 | ||||||||
\(848\) | −38.4585 | −1.32067 | ||||||||
\(849\) | −36.7363 | −1.26079 | ||||||||
\(850\) | −59.0952 | −2.02695 | ||||||||
\(851\) | 11.0405 | 0.378465 | ||||||||
\(852\) | 53.5600 | 1.83493 | ||||||||
\(853\) | 6.64201 | 0.227418 | 0.113709 | − | 0.993514i | \(-0.463727\pi\) | ||||
0.113709 | + | 0.993514i | \(0.463727\pi\) | |||||||
\(854\) | −52.6628 | −1.80208 | ||||||||
\(855\) | −4.36164 | −0.149165 | ||||||||
\(856\) | 78.2107 | 2.67319 | ||||||||
\(857\) | −17.1577 | −0.586097 | −0.293049 | − | 0.956098i | \(-0.594670\pi\) | ||||
−0.293049 | + | 0.956098i | \(0.594670\pi\) | |||||||
\(858\) | 12.8212 | 0.437709 | ||||||||
\(859\) | 5.19035 | 0.177092 | 0.0885462 | − | 0.996072i | \(-0.471778\pi\) | ||||
0.0885462 | + | 0.996072i | \(0.471778\pi\) | |||||||
\(860\) | 187.148 | 6.38170 | ||||||||
\(861\) | 10.7600 | 0.366701 | ||||||||
\(862\) | 27.8369 | 0.948129 | ||||||||
\(863\) | 0.869663 | 0.0296037 | 0.0148018 | − | 0.999890i | \(-0.495288\pi\) | ||||
0.0148018 | + | 0.999890i | \(0.495288\pi\) | |||||||
\(864\) | 81.4388 | 2.77060 | ||||||||
\(865\) | −17.3701 | −0.590602 | ||||||||
\(866\) | 61.4541 | 2.08830 | ||||||||
\(867\) | 29.7717 | 1.01110 | ||||||||
\(868\) | 41.4903 | 1.40827 | ||||||||
\(869\) | 20.9190 | 0.709629 | ||||||||
\(870\) | 94.7481 | 3.21226 | ||||||||
\(871\) | 9.34699 | 0.316711 | ||||||||
\(872\) | 155.129 | 5.25334 | ||||||||
\(873\) | 1.72461 | 0.0583693 | ||||||||
\(874\) | −33.3936 | −1.12956 | ||||||||
\(875\) | −8.39929 | −0.283948 | ||||||||
\(876\) | 74.0444 | 2.50173 | ||||||||
\(877\) | 14.5132 | 0.490075 | 0.245038 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245038 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(878\) | 42.0673 | 1.41970 | ||||||||
\(879\) | −12.4678 | −0.420527 | ||||||||
\(880\) | 106.977 | 3.60618 | ||||||||
\(881\) | −28.5486 | −0.961828 | −0.480914 | − | 0.876768i | \(-0.659695\pi\) | ||||
−0.480914 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(882\) | −0.915761 | −0.0308353 | ||||||||
\(883\) | −12.0171 | −0.404409 | −0.202205 | − | 0.979343i | \(-0.564811\pi\) | ||||
−0.202205 | + | 0.979343i | \(0.564811\pi\) | |||||||
\(884\) | 28.5754 | 0.961096 | ||||||||
\(885\) | 17.6048 | 0.591778 | ||||||||
\(886\) | 37.2174 | 1.25034 | ||||||||
\(887\) | −16.9674 | −0.569710 | −0.284855 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284855 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(888\) | 94.1152 | 3.15830 | ||||||||
\(889\) | 37.5152 | 1.25822 | ||||||||
\(890\) | 65.1352 | 2.18334 | ||||||||
\(891\) | 25.3922 | 0.850672 | ||||||||
\(892\) | −64.3574 | −2.15485 | ||||||||
\(893\) | 32.5746 | 1.09007 | ||||||||
\(894\) | 75.8853 | 2.53799 | ||||||||
\(895\) | 37.3041 | 1.24694 | ||||||||
\(896\) | 32.4072 | 1.08265 | ||||||||
\(897\) | −2.59321 | −0.0865846 | ||||||||
\(898\) | 1.58191 | 0.0527890 | ||||||||
\(899\) | −25.4401 | −0.848475 | ||||||||
\(900\) | −3.69689 | −0.123230 | ||||||||
\(901\) | −18.9941 | −0.632787 | ||||||||
\(902\) | −22.7124 | −0.756240 | ||||||||
\(903\) | 47.3051 | 1.57421 | ||||||||
\(904\) | −32.5549 | −1.08276 | ||||||||
\(905\) | −53.5862 | −1.78126 | ||||||||
\(906\) | 68.7965 | 2.28561 | ||||||||
\(907\) | 22.6963 | 0.753617 | 0.376809 | − | 0.926291i | \(-0.377021\pi\) | ||||
0.376809 | + | 0.926291i | \(0.377021\pi\) | |||||||
\(908\) | 147.824 | 4.90570 | ||||||||
\(909\) | −0.776776 | −0.0257640 | ||||||||
\(910\) | −17.0775 | −0.566114 | ||||||||
\(911\) | 38.6284 | 1.27982 | 0.639908 | − | 0.768451i | \(-0.278972\pi\) | ||||
0.639908 | + | 0.768451i | \(0.278972\pi\) | |||||||
\(912\) | −153.294 | −5.07606 | ||||||||
\(913\) | −9.69975 | −0.321015 | ||||||||
\(914\) | −35.7992 | −1.18413 | ||||||||
\(915\) | 42.8661 | 1.41711 | ||||||||
\(916\) | 5.35504 | 0.176935 | ||||||||
\(917\) | 3.87449 | 0.127947 | ||||||||
\(918\) | 84.1352 | 2.77688 | ||||||||
\(919\) | −21.9472 | −0.723970 | −0.361985 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361985 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(920\) | −40.1795 | −1.32468 | ||||||||
\(921\) | −20.5815 | −0.678183 | ||||||||
\(922\) | −54.0957 | −1.78155 | ||||||||
\(923\) | 5.91925 | 0.194834 | ||||||||
\(924\) | 59.2730 | 1.94994 | ||||||||
\(925\) | −25.3912 | −0.834857 | ||||||||
\(926\) | 109.622 | 3.60239 | ||||||||
\(927\) | −2.17661 | −0.0714893 | ||||||||
\(928\) | −109.059 | −3.58002 | ||||||||
\(929\) | 55.6957 | 1.82732 | 0.913658 | − | 0.406483i | \(-0.133245\pi\) | ||||
0.913658 | + | 0.406483i | \(0.133245\pi\) | |||||||
\(930\) | −46.9753 | −1.54038 | ||||||||
\(931\) | 13.6769 | 0.448242 | ||||||||
\(932\) | 59.3999 | 1.94571 | ||||||||
\(933\) | 33.4599 | 1.09543 | ||||||||
\(934\) | −58.8876 | −1.92686 | ||||||||
\(935\) | 52.8344 | 1.72787 | ||||||||
\(936\) | 1.51440 | 0.0494996 | ||||||||
\(937\) | −4.37763 | −0.143011 | −0.0715054 | − | 0.997440i | \(-0.522780\pi\) | ||||
−0.0715054 | + | 0.997440i | \(0.522780\pi\) | |||||||
\(938\) | 60.1053 | 1.96251 | ||||||||
\(939\) | 10.7351 | 0.350328 | ||||||||
\(940\) | 64.3534 | 2.09898 | ||||||||
\(941\) | 23.6834 | 0.772055 | 0.386028 | − | 0.922487i | \(-0.373847\pi\) | ||||
0.386028 | + | 0.922487i | \(0.373847\pi\) | |||||||
\(942\) | −84.1251 | −2.74095 | ||||||||
\(943\) | 4.59379 | 0.149594 | ||||||||
\(944\) | −42.3876 | −1.37960 | ||||||||
\(945\) | −36.1490 | −1.17593 | ||||||||
\(946\) | −99.8520 | −3.24647 | ||||||||
\(947\) | −7.08558 | −0.230250 | −0.115125 | − | 0.993351i | \(-0.536727\pi\) | ||||
−0.115125 | + | 0.993351i | \(0.536727\pi\) | |||||||
\(948\) | −59.2200 | −1.92338 | ||||||||
\(949\) | 8.18312 | 0.265635 | ||||||||
\(950\) | 76.7990 | 2.49169 | ||||||||
\(951\) | −13.3512 | −0.432944 | ||||||||
\(952\) | 111.914 | 3.62714 | ||||||||
\(953\) | 38.8102 | 1.25719 | 0.628593 | − | 0.777734i | \(-0.283631\pi\) | ||||
0.628593 | + | 0.777734i | \(0.283631\pi\) | |||||||
\(954\) | −1.65279 | −0.0535110 | ||||||||
\(955\) | 5.16003 | 0.166975 | ||||||||
\(956\) | 25.1319 | 0.812822 | ||||||||
\(957\) | −36.3437 | −1.17482 | ||||||||
\(958\) | −40.3845 | −1.30477 | ||||||||
\(959\) | 51.4489 | 1.66137 | ||||||||
\(960\) | −82.9796 | −2.67816 | ||||||||
\(961\) | −18.3870 | −0.593130 | ||||||||
\(962\) | 17.0780 | 0.550617 | ||||||||
\(963\) | 1.81002 | 0.0583271 | ||||||||
\(964\) | 116.508 | 3.75246 | ||||||||
\(965\) | −6.68037 | −0.215049 | ||||||||
\(966\) | −16.6755 | −0.536524 | ||||||||
\(967\) | 6.82336 | 0.219424 | 0.109712 | − | 0.993963i | \(-0.465007\pi\) | ||||
0.109712 | + | 0.993963i | \(0.465007\pi\) | |||||||
\(968\) | 15.2225 | 0.489269 | ||||||||
\(969\) | −75.7097 | −2.43215 | ||||||||
\(970\) | −70.7787 | −2.27257 | ||||||||
\(971\) | −1.33232 | −0.0427562 | −0.0213781 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213781 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(972\) | 10.2096 | 0.327472 | ||||||||
\(973\) | −36.8194 | −1.18038 | ||||||||
\(974\) | 15.1082 | 0.484097 | ||||||||
\(975\) | 5.96388 | 0.190997 | ||||||||
\(976\) | −103.210 | −3.30367 | ||||||||
\(977\) | −4.93022 | −0.157732 | −0.0788658 | − | 0.996885i | \(-0.525130\pi\) | ||||
−0.0788658 | + | 0.996885i | \(0.525130\pi\) | |||||||
\(978\) | 81.4527 | 2.60457 | ||||||||
\(979\) | −24.9847 | −0.798515 | ||||||||
\(980\) | 27.0197 | 0.863112 | ||||||||
\(981\) | 3.59014 | 0.114624 | ||||||||
\(982\) | 27.6244 | 0.881529 | ||||||||
\(983\) | −14.5594 | −0.464373 | −0.232186 | − | 0.972671i | \(-0.574588\pi\) | ||||
−0.232186 | + | 0.972671i | \(0.574588\pi\) | |||||||
\(984\) | 39.1598 | 1.24837 | ||||||||
\(985\) | −16.1944 | −0.515997 | ||||||||
\(986\) | −112.669 | −3.58813 | ||||||||
\(987\) | 16.2665 | 0.517768 | ||||||||
\(988\) | −37.1361 | −1.18146 | ||||||||
\(989\) | 20.1960 | 0.642195 | ||||||||
\(990\) | 4.59742 | 0.146116 | ||||||||
\(991\) | 37.1791 | 1.18103 | 0.590517 | − | 0.807025i | \(-0.298924\pi\) | ||||
0.590517 | + | 0.807025i | \(0.298924\pi\) | |||||||
\(992\) | 54.0703 | 1.71673 | ||||||||
\(993\) | 15.7514 | 0.499856 | ||||||||
\(994\) | 38.0634 | 1.20730 | ||||||||
\(995\) | −3.81275 | −0.120872 | ||||||||
\(996\) | 27.4592 | 0.870078 | ||||||||
\(997\) | 35.6219 | 1.12816 | 0.564079 | − | 0.825721i | \(-0.309231\pi\) | ||||
0.564079 | + | 0.825721i | \(0.309231\pi\) | |||||||
\(998\) | −98.7965 | −3.12735 | ||||||||
\(999\) | 36.1500 | 1.14374 |
(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 | 8011.2.a.b.1.10 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.10 | ✓ | 358 | 1.1 | even | 1 | trivial |