Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50108 | −1.76853 | −0.884266 | − | 0.466983i | \(-0.845341\pi\) | ||||
−0.884266 | + | 0.466983i | \(0.845341\pi\) | |||||||
\(3\) | −2.74712 | −1.58605 | −0.793026 | − | 0.609188i | \(-0.791495\pi\) | ||||
−0.793026 | + | 0.609188i | \(0.791495\pi\) | |||||||
\(4\) | 4.25541 | 2.12771 | ||||||||
\(5\) | 3.75941 | 1.68126 | 0.840629 | − | 0.541612i | \(-0.182186\pi\) | ||||
0.840629 | + | 0.541612i | \(0.182186\pi\) | |||||||
\(6\) | 6.87078 | 2.80498 | ||||||||
\(7\) | −1.77571 | −0.671155 | −0.335577 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335577 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(8\) | −5.64098 | −1.99439 | ||||||||
\(9\) | 4.54668 | 1.51556 | ||||||||
\(10\) | −9.40258 | −2.97336 | ||||||||
\(11\) | 4.50342 | 1.35783 | 0.678916 | − | 0.734216i | \(-0.262450\pi\) | ||||
0.678916 | + | 0.734216i | \(0.262450\pi\) | |||||||
\(12\) | −11.6901 | −3.37465 | ||||||||
\(13\) | −2.22949 | −0.618350 | −0.309175 | − | 0.951005i | \(-0.600053\pi\) | ||||
−0.309175 | + | 0.951005i | \(0.600053\pi\) | |||||||
\(14\) | 4.44119 | 1.18696 | ||||||||
\(15\) | −10.3275 | −2.66656 | ||||||||
\(16\) | 5.59772 | 1.39943 | ||||||||
\(17\) | 2.78903 | 0.676438 | 0.338219 | − | 0.941067i | \(-0.390176\pi\) | ||||
0.338219 | + | 0.941067i | \(0.390176\pi\) | |||||||
\(18\) | −11.3716 | −2.68032 | ||||||||
\(19\) | −6.60953 | −1.51633 | −0.758165 | − | 0.652063i | \(-0.773904\pi\) | ||||
−0.758165 | + | 0.652063i | \(0.773904\pi\) | |||||||
\(20\) | 15.9978 | 3.57722 | ||||||||
\(21\) | 4.87809 | 1.06449 | ||||||||
\(22\) | −11.2634 | −2.40137 | ||||||||
\(23\) | 5.39913 | 1.12580 | 0.562898 | − | 0.826526i | \(-0.309686\pi\) | ||||
0.562898 | + | 0.826526i | \(0.309686\pi\) | |||||||
\(24\) | 15.4965 | 3.16320 | ||||||||
\(25\) | 9.13313 | 1.82663 | ||||||||
\(26\) | 5.57615 | 1.09357 | ||||||||
\(27\) | −4.24891 | −0.817703 | ||||||||
\(28\) | −7.55638 | −1.42802 | ||||||||
\(29\) | 1.55088 | 0.287991 | 0.143996 | − | 0.989578i | \(-0.454005\pi\) | ||||
0.143996 | + | 0.989578i | \(0.454005\pi\) | |||||||
\(30\) | 25.8300 | 4.71590 | ||||||||
\(31\) | −4.02437 | −0.722797 | −0.361399 | − | 0.932411i | \(-0.617701\pi\) | ||||
−0.361399 | + | 0.932411i | \(0.617701\pi\) | |||||||
\(32\) | −2.71842 | −0.480552 | ||||||||
\(33\) | −12.3714 | −2.15359 | ||||||||
\(34\) | −6.97558 | −1.19630 | ||||||||
\(35\) | −6.67561 | −1.12838 | ||||||||
\(36\) | 19.3480 | 3.22467 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 16.5310 | 2.68168 | ||||||||
\(39\) | 6.12469 | 0.980736 | ||||||||
\(40\) | −21.2067 | −3.35308 | ||||||||
\(41\) | 11.6153 | 1.81400 | 0.907001 | − | 0.421128i | \(-0.138366\pi\) | ||||
0.907001 | + | 0.421128i | \(0.138366\pi\) | |||||||
\(42\) | −12.2005 | −1.88258 | ||||||||
\(43\) | −10.9960 | −1.67688 | −0.838438 | − | 0.544997i | \(-0.816531\pi\) | ||||
−0.838438 | + | 0.544997i | \(0.816531\pi\) | |||||||
\(44\) | 19.1639 | 2.88907 | ||||||||
\(45\) | 17.0928 | 2.54804 | ||||||||
\(46\) | −13.5037 | −1.99101 | ||||||||
\(47\) | −9.73430 | −1.41989 | −0.709947 | − | 0.704255i | \(-0.751281\pi\) | ||||
−0.709947 | + | 0.704255i | \(0.751281\pi\) | |||||||
\(48\) | −15.3776 | −2.21957 | ||||||||
\(49\) | −3.84686 | −0.549551 | ||||||||
\(50\) | −22.8427 | −3.23045 | ||||||||
\(51\) | −7.66179 | −1.07287 | ||||||||
\(52\) | −9.48742 | −1.31567 | ||||||||
\(53\) | −10.7722 | −1.47968 | −0.739841 | − | 0.672782i | \(-0.765099\pi\) | ||||
−0.739841 | + | 0.672782i | \(0.765099\pi\) | |||||||
\(54\) | 10.6269 | 1.44613 | ||||||||
\(55\) | 16.9302 | 2.28286 | ||||||||
\(56\) | 10.0167 | 1.33854 | ||||||||
\(57\) | 18.1572 | 2.40498 | ||||||||
\(58\) | −3.87888 | −0.509322 | ||||||||
\(59\) | −2.95304 | −0.384453 | −0.192227 | − | 0.981351i | \(-0.561571\pi\) | ||||
−0.192227 | + | 0.981351i | \(0.561571\pi\) | |||||||
\(60\) | −43.9480 | −5.67366 | ||||||||
\(61\) | 6.72393 | 0.860911 | 0.430456 | − | 0.902612i | \(-0.358353\pi\) | ||||
0.430456 | + | 0.902612i | \(0.358353\pi\) | |||||||
\(62\) | 10.0653 | 1.27829 | ||||||||
\(63\) | −8.07357 | −1.01717 | ||||||||
\(64\) | −4.39647 | −0.549559 | ||||||||
\(65\) | −8.38157 | −1.03961 | ||||||||
\(66\) | 30.9420 | 3.80870 | ||||||||
\(67\) | −3.18113 | −0.388636 | −0.194318 | − | 0.980939i | \(-0.562249\pi\) | ||||
−0.194318 | + | 0.980939i | \(0.562249\pi\) | |||||||
\(68\) | 11.8685 | 1.43926 | ||||||||
\(69\) | −14.8321 | −1.78557 | ||||||||
\(70\) | 16.6962 | 1.99558 | ||||||||
\(71\) | 10.1420 | 1.20364 | 0.601818 | − | 0.798633i | \(-0.294443\pi\) | ||||
0.601818 | + | 0.798633i | \(0.294443\pi\) | |||||||
\(72\) | −25.6477 | −3.02261 | ||||||||
\(73\) | −6.37886 | −0.746589 | −0.373294 | − | 0.927713i | \(-0.621772\pi\) | ||||
−0.373294 | + | 0.927713i | \(0.621772\pi\) | |||||||
\(74\) | 2.50108 | 0.290745 | ||||||||
\(75\) | −25.0898 | −2.89712 | ||||||||
\(76\) | −28.1263 | −3.22631 | ||||||||
\(77\) | −7.99676 | −0.911315 | ||||||||
\(78\) | −15.3184 | −1.73446 | ||||||||
\(79\) | −10.5416 | −1.18602 | −0.593009 | − | 0.805196i | \(-0.702060\pi\) | ||||
−0.593009 | + | 0.805196i | \(0.702060\pi\) | |||||||
\(80\) | 21.0441 | 2.35280 | ||||||||
\(81\) | −1.96776 | −0.218640 | ||||||||
\(82\) | −29.0508 | −3.20812 | ||||||||
\(83\) | −6.27102 | −0.688334 | −0.344167 | − | 0.938908i | \(-0.611839\pi\) | ||||
−0.344167 | + | 0.938908i | \(0.611839\pi\) | |||||||
\(84\) | 20.7583 | 2.26491 | ||||||||
\(85\) | 10.4851 | 1.13727 | ||||||||
\(86\) | 27.5019 | 2.96561 | ||||||||
\(87\) | −4.26046 | −0.456769 | ||||||||
\(88\) | −25.4037 | −2.70804 | ||||||||
\(89\) | −16.4692 | −1.74573 | −0.872864 | − | 0.487964i | \(-0.837740\pi\) | ||||
−0.872864 | + | 0.487964i | \(0.837740\pi\) | |||||||
\(90\) | −42.7505 | −4.50630 | ||||||||
\(91\) | 3.95893 | 0.415009 | ||||||||
\(92\) | 22.9755 | 2.39536 | ||||||||
\(93\) | 11.0554 | 1.14639 | ||||||||
\(94\) | 24.3463 | 2.51113 | ||||||||
\(95\) | −24.8479 | −2.54934 | ||||||||
\(96\) | 7.46782 | 0.762181 | ||||||||
\(97\) | −12.3723 | −1.25622 | −0.628111 | − | 0.778124i | \(-0.716171\pi\) | ||||
−0.628111 | + | 0.778124i | \(0.716171\pi\) | |||||||
\(98\) | 9.62132 | 0.971900 | ||||||||
\(99\) | 20.4756 | 2.05787 | ||||||||
\(100\) | 38.8652 | 3.88652 | ||||||||
\(101\) | 3.73452 | 0.371598 | 0.185799 | − | 0.982588i | \(-0.440513\pi\) | ||||
0.185799 | + | 0.982588i | \(0.440513\pi\) | |||||||
\(102\) | 19.1628 | 1.89740 | ||||||||
\(103\) | 1.87238 | 0.184491 | 0.0922456 | − | 0.995736i | \(-0.470596\pi\) | ||||
0.0922456 | + | 0.995736i | \(0.470596\pi\) | |||||||
\(104\) | 12.5765 | 1.23323 | ||||||||
\(105\) | 18.3387 | 1.78967 | ||||||||
\(106\) | 26.9423 | 2.61687 | ||||||||
\(107\) | −5.66160 | −0.547328 | −0.273664 | − | 0.961825i | \(-0.588236\pi\) | ||||
−0.273664 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(108\) | −18.0809 | −1.73983 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −42.3438 | −4.03732 | ||||||||
\(111\) | 2.74712 | 0.260745 | ||||||||
\(112\) | −9.93993 | −0.939235 | ||||||||
\(113\) | −7.62153 | −0.716974 | −0.358487 | − | 0.933535i | \(-0.616707\pi\) | ||||
−0.358487 | + | 0.933535i | \(0.616707\pi\) | |||||||
\(114\) | −45.4126 | −4.25328 | ||||||||
\(115\) | 20.2975 | 1.89275 | ||||||||
\(116\) | 6.59964 | 0.612761 | ||||||||
\(117\) | −10.1368 | −0.937146 | ||||||||
\(118\) | 7.38580 | 0.679918 | ||||||||
\(119\) | −4.95250 | −0.453995 | ||||||||
\(120\) | 58.2574 | 5.31815 | ||||||||
\(121\) | 9.28078 | 0.843707 | ||||||||
\(122\) | −16.8171 | −1.52255 | ||||||||
\(123\) | −31.9086 | −2.87710 | ||||||||
\(124\) | −17.1253 | −1.53790 | ||||||||
\(125\) | 15.5381 | 1.38977 | ||||||||
\(126\) | 20.1927 | 1.79891 | ||||||||
\(127\) | −5.33994 | −0.473843 | −0.236921 | − | 0.971529i | \(-0.576138\pi\) | ||||
−0.236921 | + | 0.971529i | \(0.576138\pi\) | |||||||
\(128\) | 16.4328 | 1.45246 | ||||||||
\(129\) | 30.2074 | 2.65961 | ||||||||
\(130\) | 20.9630 | 1.83858 | ||||||||
\(131\) | 2.03375 | 0.177689 | 0.0888447 | − | 0.996045i | \(-0.471683\pi\) | ||||
0.0888447 | + | 0.996045i | \(0.471683\pi\) | |||||||
\(132\) | −52.6456 | −4.58221 | ||||||||
\(133\) | 11.7366 | 1.01769 | ||||||||
\(134\) | 7.95626 | 0.687316 | ||||||||
\(135\) | −15.9734 | −1.37477 | ||||||||
\(136\) | −15.7328 | −1.34908 | ||||||||
\(137\) | −3.64660 | −0.311550 | −0.155775 | − | 0.987793i | \(-0.549788\pi\) | ||||
−0.155775 | + | 0.987793i | \(0.549788\pi\) | |||||||
\(138\) | 37.0962 | 3.15784 | ||||||||
\(139\) | 20.6974 | 1.75553 | 0.877766 | − | 0.479090i | \(-0.159033\pi\) | ||||
0.877766 | + | 0.479090i | \(0.159033\pi\) | |||||||
\(140\) | −28.4075 | −2.40087 | ||||||||
\(141\) | 26.7413 | 2.25202 | ||||||||
\(142\) | −25.3660 | −2.12867 | ||||||||
\(143\) | −10.0403 | −0.839616 | ||||||||
\(144\) | 25.4510 | 2.12092 | ||||||||
\(145\) | 5.83039 | 0.484187 | ||||||||
\(146\) | 15.9540 | 1.32037 | ||||||||
\(147\) | 10.5678 | 0.871617 | ||||||||
\(148\) | −4.25541 | −0.349793 | ||||||||
\(149\) | 13.8189 | 1.13209 | 0.566044 | − | 0.824375i | \(-0.308473\pi\) | ||||
0.566044 | + | 0.824375i | \(0.308473\pi\) | |||||||
\(150\) | 62.7517 | 5.12365 | ||||||||
\(151\) | 4.94410 | 0.402345 | 0.201172 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201172 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(152\) | 37.2842 | 3.02415 | ||||||||
\(153\) | 12.6808 | 1.02518 | ||||||||
\(154\) | 20.0006 | 1.61169 | ||||||||
\(155\) | −15.1292 | −1.21521 | ||||||||
\(156\) | 26.0631 | 2.08672 | ||||||||
\(157\) | 22.3443 | 1.78327 | 0.891634 | − | 0.452756i | \(-0.149559\pi\) | ||||
0.891634 | + | 0.452756i | \(0.149559\pi\) | |||||||
\(158\) | 26.3653 | 2.09751 | ||||||||
\(159\) | 29.5927 | 2.34685 | ||||||||
\(160\) | −10.2196 | −0.807932 | ||||||||
\(161\) | −9.58728 | −0.755583 | ||||||||
\(162\) | 4.92154 | 0.386673 | ||||||||
\(163\) | −9.37314 | −0.734161 | −0.367081 | − | 0.930189i | \(-0.619643\pi\) | ||||
−0.367081 | + | 0.930189i | \(0.619643\pi\) | |||||||
\(164\) | 49.4278 | 3.85967 | ||||||||
\(165\) | −46.5092 | −3.62074 | ||||||||
\(166\) | 15.6843 | 1.21734 | ||||||||
\(167\) | 14.8931 | 1.15246 | 0.576231 | − | 0.817287i | \(-0.304523\pi\) | ||||
0.576231 | + | 0.817287i | \(0.304523\pi\) | |||||||
\(168\) | −27.5172 | −2.12300 | ||||||||
\(169\) | −8.02936 | −0.617643 | ||||||||
\(170\) | −26.2240 | −2.01129 | ||||||||
\(171\) | −30.0514 | −2.29809 | ||||||||
\(172\) | −46.7926 | −3.56790 | ||||||||
\(173\) | 20.4389 | 1.55394 | 0.776971 | − | 0.629536i | \(-0.216755\pi\) | ||||
0.776971 | + | 0.629536i | \(0.216755\pi\) | |||||||
\(174\) | 10.6558 | 0.807810 | ||||||||
\(175\) | −16.2178 | −1.22595 | ||||||||
\(176\) | 25.2089 | 1.90019 | ||||||||
\(177\) | 8.11237 | 0.609763 | ||||||||
\(178\) | 41.1907 | 3.08738 | ||||||||
\(179\) | −15.7357 | −1.17614 | −0.588070 | − | 0.808810i | \(-0.700112\pi\) | ||||
−0.588070 | + | 0.808810i | \(0.700112\pi\) | |||||||
\(180\) | 72.7369 | 5.42149 | ||||||||
\(181\) | −5.37184 | −0.399286 | −0.199643 | − | 0.979869i | \(-0.563978\pi\) | ||||
−0.199643 | + | 0.979869i | \(0.563978\pi\) | |||||||
\(182\) | −9.90161 | −0.733957 | ||||||||
\(183\) | −18.4715 | −1.36545 | ||||||||
\(184\) | −30.4564 | −2.24527 | ||||||||
\(185\) | −3.75941 | −0.276397 | ||||||||
\(186\) | −27.6505 | −2.02743 | ||||||||
\(187\) | 12.5602 | 0.918489 | ||||||||
\(188\) | −41.4235 | −3.02112 | ||||||||
\(189\) | 7.54482 | 0.548805 | ||||||||
\(190\) | 62.1466 | 4.50859 | ||||||||
\(191\) | 5.53808 | 0.400722 | 0.200361 | − | 0.979722i | \(-0.435789\pi\) | ||||
0.200361 | + | 0.979722i | \(0.435789\pi\) | |||||||
\(192\) | 12.0776 | 0.871628 | ||||||||
\(193\) | −10.0808 | −0.725628 | −0.362814 | − | 0.931862i | \(-0.618184\pi\) | ||||
−0.362814 | + | 0.931862i | \(0.618184\pi\) | |||||||
\(194\) | 30.9443 | 2.22167 | ||||||||
\(195\) | 23.0252 | 1.64887 | ||||||||
\(196\) | −16.3700 | −1.16928 | ||||||||
\(197\) | −0.686420 | −0.0489054 | −0.0244527 | − | 0.999701i | \(-0.507784\pi\) | ||||
−0.0244527 | + | 0.999701i | \(0.507784\pi\) | |||||||
\(198\) | −51.2111 | −3.63942 | ||||||||
\(199\) | −17.1729 | −1.21735 | −0.608676 | − | 0.793419i | \(-0.708299\pi\) | ||||
−0.608676 | + | 0.793419i | \(0.708299\pi\) | |||||||
\(200\) | −51.5198 | −3.64300 | ||||||||
\(201\) | 8.73894 | 0.616397 | ||||||||
\(202\) | −9.34033 | −0.657184 | ||||||||
\(203\) | −2.75391 | −0.193287 | ||||||||
\(204\) | −32.6041 | −2.28274 | ||||||||
\(205\) | 43.6666 | 3.04980 | ||||||||
\(206\) | −4.68298 | −0.326279 | ||||||||
\(207\) | 24.5481 | 1.70621 | ||||||||
\(208\) | −12.4801 | −0.865339 | ||||||||
\(209\) | −29.7655 | −2.05892 | ||||||||
\(210\) | −45.8666 | −3.16510 | ||||||||
\(211\) | −4.67839 | −0.322073 | −0.161037 | − | 0.986948i | \(-0.551484\pi\) | ||||
−0.161037 | + | 0.986948i | \(0.551484\pi\) | |||||||
\(212\) | −45.8404 | −3.14833 | ||||||||
\(213\) | −27.8614 | −1.90903 | ||||||||
\(214\) | 14.1601 | 0.967967 | ||||||||
\(215\) | −41.3385 | −2.81926 | ||||||||
\(216\) | 23.9680 | 1.63082 | ||||||||
\(217\) | 7.14610 | 0.485109 | ||||||||
\(218\) | 2.50108 | 0.169395 | ||||||||
\(219\) | 17.5235 | 1.18413 | ||||||||
\(220\) | 72.0449 | 4.85727 | ||||||||
\(221\) | −6.21812 | −0.418276 | ||||||||
\(222\) | −6.87078 | −0.461136 | ||||||||
\(223\) | −4.38034 | −0.293329 | −0.146665 | − | 0.989186i | \(-0.546854\pi\) | ||||
−0.146665 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(224\) | 4.82711 | 0.322525 | ||||||||
\(225\) | 41.5254 | 2.76836 | ||||||||
\(226\) | 19.0621 | 1.26799 | ||||||||
\(227\) | −4.94781 | −0.328398 | −0.164199 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164199 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(228\) | 77.2663 | 5.11709 | ||||||||
\(229\) | −2.70576 | −0.178802 | −0.0894008 | − | 0.995996i | \(-0.528495\pi\) | ||||
−0.0894008 | + | 0.995996i | \(0.528495\pi\) | |||||||
\(230\) | −50.7657 | −3.34739 | ||||||||
\(231\) | 21.9681 | 1.44539 | ||||||||
\(232\) | −8.74848 | −0.574366 | ||||||||
\(233\) | 28.9503 | 1.89660 | 0.948299 | − | 0.317379i | \(-0.102803\pi\) | ||||
0.948299 | + | 0.317379i | \(0.102803\pi\) | |||||||
\(234\) | 25.3529 | 1.65737 | ||||||||
\(235\) | −36.5952 | −2.38721 | ||||||||
\(236\) | −12.5664 | −0.818004 | ||||||||
\(237\) | 28.9590 | 1.88109 | ||||||||
\(238\) | 12.3866 | 0.802904 | ||||||||
\(239\) | −0.0952732 | −0.00616271 | −0.00308136 | − | 0.999995i | \(-0.500981\pi\) | ||||
−0.00308136 | + | 0.999995i | \(0.500981\pi\) | |||||||
\(240\) | −57.8107 | −3.73167 | ||||||||
\(241\) | 4.45281 | 0.286831 | 0.143415 | − | 0.989663i | \(-0.454191\pi\) | ||||
0.143415 | + | 0.989663i | \(0.454191\pi\) | |||||||
\(242\) | −23.2120 | −1.49212 | ||||||||
\(243\) | 18.1524 | 1.16448 | ||||||||
\(244\) | 28.6131 | 1.83177 | ||||||||
\(245\) | −14.4619 | −0.923937 | ||||||||
\(246\) | 79.8060 | 5.08825 | ||||||||
\(247\) | 14.7359 | 0.937623 | ||||||||
\(248\) | 22.7014 | 1.44154 | ||||||||
\(249\) | 17.2273 | 1.09173 | ||||||||
\(250\) | −38.8621 | −2.45785 | ||||||||
\(251\) | −11.9965 | −0.757215 | −0.378607 | − | 0.925557i | \(-0.623597\pi\) | ||||
−0.378607 | + | 0.925557i | \(0.623597\pi\) | |||||||
\(252\) | −34.3564 | −2.16425 | ||||||||
\(253\) | 24.3145 | 1.52864 | ||||||||
\(254\) | 13.3556 | 0.838006 | ||||||||
\(255\) | −28.8038 | −1.80376 | ||||||||
\(256\) | −32.3068 | −2.01917 | ||||||||
\(257\) | −5.09848 | −0.318035 | −0.159017 | − | 0.987276i | \(-0.550833\pi\) | ||||
−0.159017 | + | 0.987276i | \(0.550833\pi\) | |||||||
\(258\) | −75.5512 | −4.70361 | ||||||||
\(259\) | 1.77571 | 0.110337 | ||||||||
\(260\) | −35.6671 | −2.21198 | ||||||||
\(261\) | 7.05135 | 0.436468 | ||||||||
\(262\) | −5.08657 | −0.314249 | ||||||||
\(263\) | −19.2074 | −1.18438 | −0.592188 | − | 0.805800i | \(-0.701736\pi\) | ||||
−0.592188 | + | 0.805800i | \(0.701736\pi\) | |||||||
\(264\) | 69.7870 | 4.29509 | ||||||||
\(265\) | −40.4972 | −2.48773 | ||||||||
\(266\) | −29.3542 | −1.79982 | ||||||||
\(267\) | 45.2428 | 2.76881 | ||||||||
\(268\) | −13.5370 | −0.826904 | ||||||||
\(269\) | −10.2788 | −0.626711 | −0.313356 | − | 0.949636i | \(-0.601453\pi\) | ||||
−0.313356 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(270\) | 39.9507 | 2.43132 | ||||||||
\(271\) | 5.71771 | 0.347326 | 0.173663 | − | 0.984805i | \(-0.444440\pi\) | ||||
0.173663 | + | 0.984805i | \(0.444440\pi\) | |||||||
\(272\) | 15.6122 | 0.946629 | ||||||||
\(273\) | −10.8757 | −0.658225 | ||||||||
\(274\) | 9.12045 | 0.550987 | ||||||||
\(275\) | 41.1303 | 2.48025 | ||||||||
\(276\) | −63.1166 | −3.79917 | ||||||||
\(277\) | 22.7137 | 1.36474 | 0.682368 | − | 0.731009i | \(-0.260950\pi\) | ||||
0.682368 | + | 0.731009i | \(0.260950\pi\) | |||||||
\(278\) | −51.7660 | −3.10472 | ||||||||
\(279\) | −18.2975 | −1.09544 | ||||||||
\(280\) | 37.6570 | 2.25043 | ||||||||
\(281\) | −22.4531 | −1.33944 | −0.669721 | − | 0.742613i | \(-0.733586\pi\) | ||||
−0.669721 | + | 0.742613i | \(0.733586\pi\) | |||||||
\(282\) | −66.8822 | −3.98278 | ||||||||
\(283\) | −15.9034 | −0.945360 | −0.472680 | − | 0.881234i | \(-0.656713\pi\) | ||||
−0.472680 | + | 0.881234i | \(0.656713\pi\) | |||||||
\(284\) | 43.1585 | 2.56098 | ||||||||
\(285\) | 68.2602 | 4.04338 | ||||||||
\(286\) | 25.1117 | 1.48489 | ||||||||
\(287\) | −20.6254 | −1.21748 | ||||||||
\(288\) | −12.3598 | −0.728305 | ||||||||
\(289\) | −9.22133 | −0.542431 | ||||||||
\(290\) | −14.5823 | −0.856301 | ||||||||
\(291\) | 33.9883 | 1.99243 | ||||||||
\(292\) | −27.1447 | −1.58852 | ||||||||
\(293\) | 28.0829 | 1.64062 | 0.820311 | − | 0.571918i | \(-0.193800\pi\) | ||||
0.820311 | + | 0.571918i | \(0.193800\pi\) | |||||||
\(294\) | −26.4309 | −1.54148 | ||||||||
\(295\) | −11.1017 | −0.646365 | ||||||||
\(296\) | 5.64098 | 0.327875 | ||||||||
\(297\) | −19.1346 | −1.11030 | ||||||||
\(298\) | −34.5622 | −2.00214 | ||||||||
\(299\) | −12.0373 | −0.696136 | ||||||||
\(300\) | −106.768 | −6.16423 | ||||||||
\(301\) | 19.5257 | 1.12544 | ||||||||
\(302\) | −12.3656 | −0.711560 | ||||||||
\(303\) | −10.2592 | −0.589374 | ||||||||
\(304\) | −36.9983 | −2.12200 | ||||||||
\(305\) | 25.2780 | 1.44741 | ||||||||
\(306\) | −31.7157 | −1.81307 | ||||||||
\(307\) | −12.7842 | −0.729633 | −0.364816 | − | 0.931079i | \(-0.618868\pi\) | ||||
−0.364816 | + | 0.931079i | \(0.618868\pi\) | |||||||
\(308\) | −34.0295 | −1.93901 | ||||||||
\(309\) | −5.14366 | −0.292613 | ||||||||
\(310\) | 37.8394 | 2.14914 | ||||||||
\(311\) | 14.7539 | 0.836619 | 0.418309 | − | 0.908305i | \(-0.362623\pi\) | ||||
0.418309 | + | 0.908305i | \(0.362623\pi\) | |||||||
\(312\) | −34.5493 | −1.95597 | ||||||||
\(313\) | −5.22249 | −0.295192 | −0.147596 | − | 0.989048i | \(-0.547154\pi\) | ||||
−0.147596 | + | 0.989048i | \(0.547154\pi\) | |||||||
\(314\) | −55.8849 | −3.15377 | ||||||||
\(315\) | −30.3518 | −1.71013 | ||||||||
\(316\) | −44.8587 | −2.52350 | ||||||||
\(317\) | −2.84700 | −0.159904 | −0.0799518 | − | 0.996799i | \(-0.525477\pi\) | ||||
−0.0799518 | + | 0.996799i | \(0.525477\pi\) | |||||||
\(318\) | −74.0137 | −4.15048 | ||||||||
\(319\) | 6.98426 | 0.391044 | ||||||||
\(320\) | −16.5281 | −0.923949 | ||||||||
\(321\) | 15.5531 | 0.868090 | ||||||||
\(322\) | 23.9786 | 1.33627 | ||||||||
\(323\) | −18.4341 | −1.02570 | ||||||||
\(324\) | −8.37365 | −0.465203 | ||||||||
\(325\) | −20.3623 | −1.12949 | ||||||||
\(326\) | 23.4430 | 1.29839 | ||||||||
\(327\) | 2.74712 | 0.151916 | ||||||||
\(328\) | −65.5216 | −3.61782 | ||||||||
\(329\) | 17.2853 | 0.952968 | ||||||||
\(330\) | 116.323 | 6.40340 | ||||||||
\(331\) | −17.4093 | −0.956902 | −0.478451 | − | 0.878114i | \(-0.658802\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(332\) | −26.6858 | −1.46457 | ||||||||
\(333\) | −4.54668 | −0.249156 | ||||||||
\(334\) | −37.2488 | −2.03817 | ||||||||
\(335\) | −11.9591 | −0.653398 | ||||||||
\(336\) | 27.3062 | 1.48967 | ||||||||
\(337\) | −12.7783 | −0.696078 | −0.348039 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348039 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(338\) | 20.0821 | 1.09232 | ||||||||
\(339\) | 20.9373 | 1.13716 | ||||||||
\(340\) | 44.6184 | 2.41977 | ||||||||
\(341\) | −18.1234 | −0.981437 | ||||||||
\(342\) | 75.1610 | 4.06424 | ||||||||
\(343\) | 19.2609 | 1.03999 | ||||||||
\(344\) | 62.0283 | 3.34434 | ||||||||
\(345\) | −55.7597 | −3.00200 | ||||||||
\(346\) | −51.1194 | −2.74820 | ||||||||
\(347\) | 16.9491 | 0.909875 | 0.454938 | − | 0.890523i | \(-0.349662\pi\) | ||||
0.454938 | + | 0.890523i | \(0.349662\pi\) | |||||||
\(348\) | −18.1300 | −0.971870 | ||||||||
\(349\) | −6.61386 | −0.354032 | −0.177016 | − | 0.984208i | \(-0.556644\pi\) | ||||
−0.177016 | + | 0.984208i | \(0.556644\pi\) | |||||||
\(350\) | 40.5620 | 2.16813 | ||||||||
\(351\) | 9.47292 | 0.505627 | ||||||||
\(352\) | −12.2422 | −0.652509 | ||||||||
\(353\) | −17.1758 | −0.914178 | −0.457089 | − | 0.889421i | \(-0.651108\pi\) | ||||
−0.457089 | + | 0.889421i | \(0.651108\pi\) | |||||||
\(354\) | −20.2897 | −1.07839 | ||||||||
\(355\) | 38.1279 | 2.02362 | ||||||||
\(356\) | −70.0831 | −3.71440 | ||||||||
\(357\) | 13.6051 | 0.720059 | ||||||||
\(358\) | 39.3562 | 2.08004 | ||||||||
\(359\) | 5.68775 | 0.300188 | 0.150094 | − | 0.988672i | \(-0.452042\pi\) | ||||
0.150094 | + | 0.988672i | \(0.452042\pi\) | |||||||
\(360\) | −96.4201 | −5.08179 | ||||||||
\(361\) | 24.6859 | 1.29926 | ||||||||
\(362\) | 13.4354 | 0.706150 | ||||||||
\(363\) | −25.4954 | −1.33816 | ||||||||
\(364\) | 16.8469 | 0.883017 | ||||||||
\(365\) | −23.9807 | −1.25521 | ||||||||
\(366\) | 46.1986 | 2.41484 | ||||||||
\(367\) | 10.7412 | 0.560686 | 0.280343 | − | 0.959900i | \(-0.409552\pi\) | ||||
0.280343 | + | 0.959900i | \(0.409552\pi\) | |||||||
\(368\) | 30.2228 | 1.57547 | ||||||||
\(369\) | 52.8109 | 2.74923 | ||||||||
\(370\) | 9.40258 | 0.488817 | ||||||||
\(371\) | 19.1284 | 0.993095 | ||||||||
\(372\) | 47.0454 | 2.43919 | ||||||||
\(373\) | −29.8133 | −1.54367 | −0.771836 | − | 0.635821i | \(-0.780662\pi\) | ||||
−0.771836 | + | 0.635821i | \(0.780662\pi\) | |||||||
\(374\) | −31.4140 | −1.62438 | ||||||||
\(375\) | −42.6851 | −2.20425 | ||||||||
\(376\) | 54.9110 | 2.83182 | ||||||||
\(377\) | −3.45768 | −0.178079 | ||||||||
\(378\) | −18.8702 | −0.970579 | ||||||||
\(379\) | −30.0416 | −1.54313 | −0.771567 | − | 0.636149i | \(-0.780527\pi\) | ||||
−0.771567 | + | 0.636149i | \(0.780527\pi\) | |||||||
\(380\) | −105.738 | −5.42425 | ||||||||
\(381\) | 14.6695 | 0.751539 | ||||||||
\(382\) | −13.8512 | −0.708689 | ||||||||
\(383\) | 18.5881 | 0.949810 | 0.474905 | − | 0.880037i | \(-0.342482\pi\) | ||||
0.474905 | + | 0.880037i | \(0.342482\pi\) | |||||||
\(384\) | −45.1428 | −2.30368 | ||||||||
\(385\) | −30.0631 | −1.53216 | ||||||||
\(386\) | 25.2128 | 1.28330 | ||||||||
\(387\) | −49.9953 | −2.54140 | ||||||||
\(388\) | −52.6495 | −2.67287 | ||||||||
\(389\) | 34.1304 | 1.73048 | 0.865241 | − | 0.501356i | \(-0.167165\pi\) | ||||
0.865241 | + | 0.501356i | \(0.167165\pi\) | |||||||
\(390\) | −57.5879 | −2.91608 | ||||||||
\(391\) | 15.0583 | 0.761531 | ||||||||
\(392\) | 21.7001 | 1.09602 | ||||||||
\(393\) | −5.58695 | −0.281824 | ||||||||
\(394\) | 1.71679 | 0.0864908 | ||||||||
\(395\) | −39.6300 | −1.99400 | ||||||||
\(396\) | 87.1321 | 4.37855 | ||||||||
\(397\) | −26.9599 | −1.35308 | −0.676540 | − | 0.736405i | \(-0.736522\pi\) | ||||
−0.676540 | + | 0.736405i | \(0.736522\pi\) | |||||||
\(398\) | 42.9507 | 2.15293 | ||||||||
\(399\) | −32.2418 | −1.61411 | ||||||||
\(400\) | 51.1247 | 2.55624 | ||||||||
\(401\) | −13.5162 | −0.674968 | −0.337484 | − | 0.941331i | \(-0.609576\pi\) | ||||
−0.337484 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(402\) | −21.8568 | −1.09012 | ||||||||
\(403\) | 8.97230 | 0.446942 | ||||||||
\(404\) | 15.8919 | 0.790652 | ||||||||
\(405\) | −7.39762 | −0.367591 | ||||||||
\(406\) | 6.88776 | 0.341834 | ||||||||
\(407\) | −4.50342 | −0.223226 | ||||||||
\(408\) | 43.2200 | 2.13971 | ||||||||
\(409\) | 13.2780 | 0.656556 | 0.328278 | − | 0.944581i | \(-0.393532\pi\) | ||||
0.328278 | + | 0.944581i | \(0.393532\pi\) | |||||||
\(410\) | −109.214 | −5.39368 | ||||||||
\(411\) | 10.0177 | 0.494135 | ||||||||
\(412\) | 7.96776 | 0.392543 | ||||||||
\(413\) | 5.24374 | 0.258028 | ||||||||
\(414\) | −61.3968 | −3.01749 | ||||||||
\(415\) | −23.5753 | −1.15727 | ||||||||
\(416\) | 6.06069 | 0.297150 | ||||||||
\(417\) | −56.8583 | −2.78436 | ||||||||
\(418\) | 74.4459 | 3.64127 | ||||||||
\(419\) | −29.3218 | −1.43247 | −0.716233 | − | 0.697861i | \(-0.754135\pi\) | ||||
−0.716233 | + | 0.697861i | \(0.754135\pi\) | |||||||
\(420\) | 78.0388 | 3.80790 | ||||||||
\(421\) | 28.5734 | 1.39258 | 0.696291 | − | 0.717760i | \(-0.254832\pi\) | ||||
0.696291 | + | 0.717760i | \(0.254832\pi\) | |||||||
\(422\) | 11.7010 | 0.569597 | ||||||||
\(423\) | −44.2587 | −2.15193 | ||||||||
\(424\) | 60.7660 | 2.95106 | ||||||||
\(425\) | 25.4725 | 1.23560 | ||||||||
\(426\) | 69.6835 | 3.37618 | ||||||||
\(427\) | −11.9397 | −0.577804 | ||||||||
\(428\) | −24.0925 | −1.16455 | ||||||||
\(429\) | 27.5820 | 1.33167 | ||||||||
\(430\) | 103.391 | 4.98595 | ||||||||
\(431\) | 29.3912 | 1.41573 | 0.707863 | − | 0.706350i | \(-0.249659\pi\) | ||||
0.707863 | + | 0.706350i | \(0.249659\pi\) | |||||||
\(432\) | −23.7842 | −1.14432 | ||||||||
\(433\) | −30.0483 | −1.44403 | −0.722014 | − | 0.691879i | \(-0.756783\pi\) | ||||
−0.722014 | + | 0.691879i | \(0.756783\pi\) | |||||||
\(434\) | −17.8730 | −0.857931 | ||||||||
\(435\) | −16.0168 | −0.767946 | ||||||||
\(436\) | −4.25541 | −0.203797 | ||||||||
\(437\) | −35.6857 | −1.70708 | ||||||||
\(438\) | −43.8277 | −2.09417 | ||||||||
\(439\) | −1.81365 | −0.0865608 | −0.0432804 | − | 0.999063i | \(-0.513781\pi\) | ||||
−0.0432804 | + | 0.999063i | \(0.513781\pi\) | |||||||
\(440\) | −95.5028 | −4.55292 | ||||||||
\(441\) | −17.4904 | −0.832878 | ||||||||
\(442\) | 15.5520 | 0.739734 | ||||||||
\(443\) | 9.68617 | 0.460204 | 0.230102 | − | 0.973167i | \(-0.426094\pi\) | ||||
0.230102 | + | 0.973167i | \(0.426094\pi\) | |||||||
\(444\) | 11.6901 | 0.554790 | ||||||||
\(445\) | −61.9143 | −2.93502 | ||||||||
\(446\) | 10.9556 | 0.518762 | ||||||||
\(447\) | −37.9622 | −1.79555 | ||||||||
\(448\) | 7.80685 | 0.368839 | ||||||||
\(449\) | 9.52376 | 0.449454 | 0.224727 | − | 0.974422i | \(-0.427851\pi\) | ||||
0.224727 | + | 0.974422i | \(0.427851\pi\) | |||||||
\(450\) | −103.858 | −4.89593 | ||||||||
\(451\) | 52.3085 | 2.46311 | ||||||||
\(452\) | −32.4328 | −1.52551 | ||||||||
\(453\) | −13.5820 | −0.638140 | ||||||||
\(454\) | 12.3749 | 0.580782 | ||||||||
\(455\) | 14.8832 | 0.697736 | ||||||||
\(456\) | −102.424 | −4.79645 | ||||||||
\(457\) | 25.1797 | 1.17786 | 0.588929 | − | 0.808185i | \(-0.299550\pi\) | ||||
0.588929 | + | 0.808185i | \(0.299550\pi\) | |||||||
\(458\) | 6.76733 | 0.316217 | ||||||||
\(459\) | −11.8503 | −0.553125 | ||||||||
\(460\) | 86.3743 | 4.02722 | ||||||||
\(461\) | 22.1288 | 1.03064 | 0.515319 | − | 0.856998i | \(-0.327673\pi\) | ||||
0.515319 | + | 0.856998i | \(0.327673\pi\) | |||||||
\(462\) | −54.9439 | −2.55622 | ||||||||
\(463\) | 21.1050 | 0.980834 | 0.490417 | − | 0.871488i | \(-0.336845\pi\) | ||||
0.490417 | + | 0.871488i | \(0.336845\pi\) | |||||||
\(464\) | 8.68140 | 0.403024 | ||||||||
\(465\) | 41.5618 | 1.92738 | ||||||||
\(466\) | −72.4071 | −3.35420 | ||||||||
\(467\) | −36.7561 | −1.70087 | −0.850435 | − | 0.526080i | \(-0.823661\pi\) | ||||
−0.850435 | + | 0.526080i | \(0.823661\pi\) | |||||||
\(468\) | −43.1362 | −1.99397 | ||||||||
\(469\) | 5.64875 | 0.260835 | ||||||||
\(470\) | 91.5276 | 4.22185 | ||||||||
\(471\) | −61.3825 | −2.82836 | ||||||||
\(472\) | 16.6581 | 0.766749 | ||||||||
\(473\) | −49.5197 | −2.27692 | ||||||||
\(474\) | −72.4288 | −3.32676 | ||||||||
\(475\) | −60.3657 | −2.76977 | ||||||||
\(476\) | −21.0749 | −0.965968 | ||||||||
\(477\) | −48.9779 | −2.24254 | ||||||||
\(478\) | 0.238286 | 0.0108990 | ||||||||
\(479\) | −30.3823 | −1.38820 | −0.694102 | − | 0.719876i | \(-0.744199\pi\) | ||||
−0.694102 | + | 0.719876i | \(0.744199\pi\) | |||||||
\(480\) | 28.0745 | 1.28142 | ||||||||
\(481\) | 2.22949 | 0.101656 | ||||||||
\(482\) | −11.1369 | −0.507270 | ||||||||
\(483\) | 26.3374 | 1.19839 | ||||||||
\(484\) | 39.4936 | 1.79516 | ||||||||
\(485\) | −46.5127 | −2.11203 | ||||||||
\(486\) | −45.4007 | −2.05942 | ||||||||
\(487\) | 33.0725 | 1.49866 | 0.749330 | − | 0.662197i | \(-0.230376\pi\) | ||||
0.749330 | + | 0.662197i | \(0.230376\pi\) | |||||||
\(488\) | −37.9295 | −1.71699 | ||||||||
\(489\) | 25.7492 | 1.16442 | ||||||||
\(490\) | 36.1704 | 1.63401 | ||||||||
\(491\) | 8.48729 | 0.383026 | 0.191513 | − | 0.981490i | \(-0.438661\pi\) | ||||
0.191513 | + | 0.981490i | \(0.438661\pi\) | |||||||
\(492\) | −135.784 | −6.12163 | ||||||||
\(493\) | 4.32544 | 0.194808 | ||||||||
\(494\) | −36.8557 | −1.65822 | ||||||||
\(495\) | 76.9760 | 3.45982 | ||||||||
\(496\) | −22.5273 | −1.01151 | ||||||||
\(497\) | −18.0093 | −0.807826 | ||||||||
\(498\) | −43.0868 | −1.93077 | ||||||||
\(499\) | 2.15049 | 0.0962692 | 0.0481346 | − | 0.998841i | \(-0.484672\pi\) | ||||
0.0481346 | + | 0.998841i | \(0.484672\pi\) | |||||||
\(500\) | 66.1211 | 2.95702 | ||||||||
\(501\) | −40.9131 | −1.82786 | ||||||||
\(502\) | 30.0043 | 1.33916 | ||||||||
\(503\) | −2.94521 | −0.131320 | −0.0656601 | − | 0.997842i | \(-0.520915\pi\) | ||||
−0.0656601 | + | 0.997842i | \(0.520915\pi\) | |||||||
\(504\) | 45.5428 | 2.02864 | ||||||||
\(505\) | 14.0396 | 0.624752 | ||||||||
\(506\) | −60.8127 | −2.70345 | ||||||||
\(507\) | 22.0576 | 0.979613 | ||||||||
\(508\) | −22.7236 | −1.00820 | ||||||||
\(509\) | 27.1085 | 1.20156 | 0.600782 | − | 0.799413i | \(-0.294856\pi\) | ||||
0.600782 | + | 0.799413i | \(0.294856\pi\) | |||||||
\(510\) | 72.0406 | 3.19001 | ||||||||
\(511\) | 11.3270 | 0.501076 | ||||||||
\(512\) | 47.9364 | 2.11851 | ||||||||
\(513\) | 28.0833 | 1.23991 | ||||||||
\(514\) | 12.7517 | 0.562454 | ||||||||
\(515\) | 7.03904 | 0.310177 | ||||||||
\(516\) | 128.545 | 5.65888 | ||||||||
\(517\) | −43.8376 | −1.92798 | ||||||||
\(518\) | −4.44119 | −0.195135 | ||||||||
\(519\) | −56.1482 | −2.46463 | ||||||||
\(520\) | 47.2803 | 2.07338 | ||||||||
\(521\) | −28.5679 | −1.25158 | −0.625790 | − | 0.779991i | \(-0.715223\pi\) | ||||
−0.625790 | + | 0.779991i | \(0.715223\pi\) | |||||||
\(522\) | −17.6360 | −0.771907 | ||||||||
\(523\) | 8.28521 | 0.362287 | 0.181143 | − | 0.983457i | \(-0.442020\pi\) | ||||
0.181143 | + | 0.983457i | \(0.442020\pi\) | |||||||
\(524\) | 8.65444 | 0.378071 | ||||||||
\(525\) | 44.5522 | 1.94442 | ||||||||
\(526\) | 48.0392 | 2.09461 | ||||||||
\(527\) | −11.2241 | −0.488928 | ||||||||
\(528\) | −69.2519 | −3.01380 | ||||||||
\(529\) | 6.15058 | 0.267416 | ||||||||
\(530\) | 101.287 | 4.39962 | ||||||||
\(531\) | −13.4265 | −0.582662 | ||||||||
\(532\) | 49.9441 | 2.16535 | ||||||||
\(533\) | −25.8962 | −1.12169 | ||||||||
\(534\) | −113.156 | −4.89674 | ||||||||
\(535\) | −21.2842 | −0.920198 | ||||||||
\(536\) | 17.9447 | 0.775091 | ||||||||
\(537\) | 43.2278 | 1.86542 | ||||||||
\(538\) | 25.7082 | 1.10836 | ||||||||
\(539\) | −17.3240 | −0.746198 | ||||||||
\(540\) | −67.9733 | −2.92510 | ||||||||
\(541\) | 9.46904 | 0.407106 | 0.203553 | − | 0.979064i | \(-0.434751\pi\) | ||||
0.203553 | + | 0.979064i | \(0.434751\pi\) | |||||||
\(542\) | −14.3005 | −0.614258 | ||||||||
\(543\) | 14.7571 | 0.633288 | ||||||||
\(544\) | −7.58173 | −0.325064 | ||||||||
\(545\) | −3.75941 | −0.161035 | ||||||||
\(546\) | 27.2009 | 1.16409 | ||||||||
\(547\) | −39.1040 | −1.67197 | −0.835983 | − | 0.548755i | \(-0.815102\pi\) | ||||
−0.835983 | + | 0.548755i | \(0.815102\pi\) | |||||||
\(548\) | −15.5178 | −0.662888 | ||||||||
\(549\) | 30.5715 | 1.30476 | ||||||||
\(550\) | −102.870 | −4.38640 | ||||||||
\(551\) | −10.2506 | −0.436690 | ||||||||
\(552\) | 83.6673 | 3.56112 | ||||||||
\(553\) | 18.7187 | 0.796002 | ||||||||
\(554\) | −56.8089 | −2.41358 | ||||||||
\(555\) | 10.3275 | 0.438380 | ||||||||
\(556\) | 88.0761 | 3.73526 | ||||||||
\(557\) | −8.96933 | −0.380043 | −0.190021 | − | 0.981780i | \(-0.560856\pi\) | ||||
−0.190021 | + | 0.981780i | \(0.560856\pi\) | |||||||
\(558\) | 45.7635 | 1.93732 | ||||||||
\(559\) | 24.5156 | 1.03690 | ||||||||
\(560\) | −37.3682 | −1.57910 | ||||||||
\(561\) | −34.5043 | −1.45677 | ||||||||
\(562\) | 56.1571 | 2.36885 | ||||||||
\(563\) | −36.8971 | −1.55503 | −0.777513 | − | 0.628867i | \(-0.783519\pi\) | ||||
−0.777513 | + | 0.628867i | \(0.783519\pi\) | |||||||
\(564\) | 113.795 | 4.79165 | ||||||||
\(565\) | −28.6524 | −1.20542 | ||||||||
\(566\) | 39.7758 | 1.67190 | ||||||||
\(567\) | 3.49417 | 0.146742 | ||||||||
\(568\) | −57.2109 | −2.40052 | ||||||||
\(569\) | −6.15740 | −0.258131 | −0.129066 | − | 0.991636i | \(-0.541198\pi\) | ||||
−0.129066 | + | 0.991636i | \(0.541198\pi\) | |||||||
\(570\) | −170.724 | −7.15086 | ||||||||
\(571\) | −14.5119 | −0.607303 | −0.303652 | − | 0.952783i | \(-0.598206\pi\) | ||||
−0.303652 | + | 0.952783i | \(0.598206\pi\) | |||||||
\(572\) | −42.7258 | −1.78646 | ||||||||
\(573\) | −15.2138 | −0.635565 | ||||||||
\(574\) | 51.5857 | 2.15315 | ||||||||
\(575\) | 49.3109 | 2.05641 | ||||||||
\(576\) | −19.9893 | −0.832888 | ||||||||
\(577\) | −42.7898 | −1.78136 | −0.890681 | − | 0.454629i | \(-0.849772\pi\) | ||||
−0.890681 | + | 0.454629i | \(0.849772\pi\) | |||||||
\(578\) | 23.0633 | 0.959308 | ||||||||
\(579\) | 27.6930 | 1.15088 | ||||||||
\(580\) | 24.8107 | 1.03021 | ||||||||
\(581\) | 11.1355 | 0.461978 | ||||||||
\(582\) | −85.0076 | −3.52368 | ||||||||
\(583\) | −48.5119 | −2.00916 | ||||||||
\(584\) | 35.9830 | 1.48899 | ||||||||
\(585\) | −38.1083 | −1.57558 | ||||||||
\(586\) | −70.2377 | −2.90149 | ||||||||
\(587\) | −29.9670 | −1.23687 | −0.618436 | − | 0.785835i | \(-0.712233\pi\) | ||||
−0.618436 | + | 0.785835i | \(0.712233\pi\) | |||||||
\(588\) | 44.9703 | 1.85455 | ||||||||
\(589\) | 26.5992 | 1.09600 | ||||||||
\(590\) | 27.7662 | 1.14312 | ||||||||
\(591\) | 1.88568 | 0.0775665 | ||||||||
\(592\) | −5.59772 | −0.230065 | ||||||||
\(593\) | −16.3470 | −0.671292 | −0.335646 | − | 0.941988i | \(-0.608955\pi\) | ||||
−0.335646 | + | 0.941988i | \(0.608955\pi\) | |||||||
\(594\) | 47.8572 | 1.96361 | ||||||||
\(595\) | −18.6184 | −0.763282 | ||||||||
\(596\) | 58.8052 | 2.40875 | ||||||||
\(597\) | 47.1759 | 1.93078 | ||||||||
\(598\) | 30.1063 | 1.23114 | ||||||||
\(599\) | −21.9570 | −0.897138 | −0.448569 | − | 0.893748i | \(-0.648066\pi\) | ||||
−0.448569 | + | 0.893748i | \(0.648066\pi\) | |||||||
\(600\) | 141.531 | 5.77798 | ||||||||
\(601\) | −17.1625 | −0.700073 | −0.350036 | − | 0.936736i | \(-0.613831\pi\) | ||||
−0.350036 | + | 0.936736i | \(0.613831\pi\) | |||||||
\(602\) | −48.8354 | −1.99038 | ||||||||
\(603\) | −14.4635 | −0.589001 | ||||||||
\(604\) | 21.0392 | 0.856072 | ||||||||
\(605\) | 34.8902 | 1.41849 | ||||||||
\(606\) | 25.6590 | 1.04233 | ||||||||
\(607\) | −40.3817 | −1.63904 | −0.819521 | − | 0.573049i | \(-0.805760\pi\) | ||||
−0.819521 | + | 0.573049i | \(0.805760\pi\) | |||||||
\(608\) | 17.9674 | 0.728676 | ||||||||
\(609\) | 7.56533 | 0.306562 | ||||||||
\(610\) | −63.2223 | −2.55980 | ||||||||
\(611\) | 21.7026 | 0.877992 | ||||||||
\(612\) | 53.9621 | 2.18129 | ||||||||
\(613\) | −38.1289 | −1.54001 | −0.770007 | − | 0.638036i | \(-0.779747\pi\) | ||||
−0.770007 | + | 0.638036i | \(0.779747\pi\) | |||||||
\(614\) | 31.9743 | 1.29038 | ||||||||
\(615\) | −119.957 | −4.83715 | ||||||||
\(616\) | 45.1095 | 1.81752 | ||||||||
\(617\) | 39.2989 | 1.58211 | 0.791057 | − | 0.611743i | \(-0.209531\pi\) | ||||
0.791057 | + | 0.611743i | \(0.209531\pi\) | |||||||
\(618\) | 12.8647 | 0.517495 | ||||||||
\(619\) | 47.8885 | 1.92480 | 0.962400 | − | 0.271637i | \(-0.0875651\pi\) | ||||
0.962400 | + | 0.271637i | \(0.0875651\pi\) | |||||||
\(620\) | −64.3811 | −2.58561 | ||||||||
\(621\) | −22.9404 | −0.920566 | ||||||||
\(622\) | −36.9008 | −1.47959 | ||||||||
\(623\) | 29.2444 | 1.17165 | ||||||||
\(624\) | 34.2843 | 1.37247 | ||||||||
\(625\) | 12.7484 | 0.509936 | ||||||||
\(626\) | 13.0619 | 0.522057 | ||||||||
\(627\) | 81.7694 | 3.26555 | ||||||||
\(628\) | 95.0842 | 3.79427 | ||||||||
\(629\) | −2.78903 | −0.111206 | ||||||||
\(630\) | 75.9124 | 3.02442 | ||||||||
\(631\) | −3.39586 | −0.135187 | −0.0675935 | − | 0.997713i | \(-0.521532\pi\) | ||||
−0.0675935 | + | 0.997713i | \(0.521532\pi\) | |||||||
\(632\) | 59.4647 | 2.36538 | ||||||||
\(633\) | 12.8521 | 0.510825 | ||||||||
\(634\) | 7.12059 | 0.282795 | ||||||||
\(635\) | −20.0750 | −0.796651 | ||||||||
\(636\) | 125.929 | 4.99341 | ||||||||
\(637\) | 8.57655 | 0.339815 | ||||||||
\(638\) | −17.4682 | −0.691573 | ||||||||
\(639\) | 46.1125 | 1.82418 | ||||||||
\(640\) | 61.7774 | 2.44197 | ||||||||
\(641\) | −4.24075 | −0.167499 | −0.0837497 | − | 0.996487i | \(-0.526690\pi\) | ||||
−0.0837497 | + | 0.996487i | \(0.526690\pi\) | |||||||
\(642\) | −38.8996 | −1.53524 | ||||||||
\(643\) | 36.9933 | 1.45888 | 0.729438 | − | 0.684047i | \(-0.239782\pi\) | ||||
0.729438 | + | 0.684047i | \(0.239782\pi\) | |||||||
\(644\) | −40.7978 | −1.60766 | ||||||||
\(645\) | 113.562 | 4.47149 | ||||||||
\(646\) | 46.1053 | 1.81399 | ||||||||
\(647\) | 1.07387 | 0.0422183 | 0.0211092 | − | 0.999777i | \(-0.493280\pi\) | ||||
0.0211092 | + | 0.999777i | \(0.493280\pi\) | |||||||
\(648\) | 11.1001 | 0.436054 | ||||||||
\(649\) | −13.2988 | −0.522023 | ||||||||
\(650\) | 50.9277 | 1.99755 | ||||||||
\(651\) | −19.6312 | −0.769407 | ||||||||
\(652\) | −39.8866 | −1.56208 | ||||||||
\(653\) | −5.36182 | −0.209824 | −0.104912 | − | 0.994481i | \(-0.533456\pi\) | ||||
−0.104912 | + | 0.994481i | \(0.533456\pi\) | |||||||
\(654\) | −6.87078 | −0.268669 | ||||||||
\(655\) | 7.64568 | 0.298742 | ||||||||
\(656\) | 65.0192 | 2.53857 | ||||||||
\(657\) | −29.0026 | −1.13150 | ||||||||
\(658\) | −43.2319 | −1.68536 | ||||||||
\(659\) | 45.0898 | 1.75645 | 0.878224 | − | 0.478250i | \(-0.158729\pi\) | ||||
0.878224 | + | 0.478250i | \(0.158729\pi\) | |||||||
\(660\) | −197.916 | −7.70388 | ||||||||
\(661\) | −21.3253 | −0.829457 | −0.414729 | − | 0.909945i | \(-0.636123\pi\) | ||||
−0.414729 | + | 0.909945i | \(0.636123\pi\) | |||||||
\(662\) | 43.5421 | 1.69231 | ||||||||
\(663\) | 17.0819 | 0.663407 | ||||||||
\(664\) | 35.3747 | 1.37280 | ||||||||
\(665\) | 44.1226 | 1.71100 | ||||||||
\(666\) | 11.3716 | 0.440641 | ||||||||
\(667\) | 8.37340 | 0.324219 | ||||||||
\(668\) | 63.3762 | 2.45210 | ||||||||
\(669\) | 12.0333 | 0.465235 | ||||||||
\(670\) | 29.9108 | 1.15555 | ||||||||
\(671\) | 30.2807 | 1.16897 | ||||||||
\(672\) | −13.2607 | −0.511541 | ||||||||
\(673\) | 41.9257 | 1.61612 | 0.808058 | − | 0.589103i | \(-0.200519\pi\) | ||||
0.808058 | + | 0.589103i | \(0.200519\pi\) | |||||||
\(674\) | 31.9596 | 1.23104 | ||||||||
\(675\) | −38.8058 | −1.49364 | ||||||||
\(676\) | −34.1682 | −1.31416 | ||||||||
\(677\) | 15.6844 | 0.602799 | 0.301399 | − | 0.953498i | \(-0.402546\pi\) | ||||
0.301399 | + | 0.953498i | \(0.402546\pi\) | |||||||
\(678\) | −52.3659 | −2.01110 | ||||||||
\(679\) | 21.9697 | 0.843119 | ||||||||
\(680\) | −59.1461 | −2.26815 | ||||||||
\(681\) | 13.5922 | 0.520856 | ||||||||
\(682\) | 45.3281 | 1.73570 | ||||||||
\(683\) | 47.2032 | 1.80618 | 0.903090 | − | 0.429451i | \(-0.141293\pi\) | ||||
0.903090 | + | 0.429451i | \(0.141293\pi\) | |||||||
\(684\) | −127.881 | −4.88966 | ||||||||
\(685\) | −13.7091 | −0.523796 | ||||||||
\(686\) | −48.1730 | −1.83925 | ||||||||
\(687\) | 7.43305 | 0.283589 | ||||||||
\(688\) | −61.5527 | −2.34667 | ||||||||
\(689\) | 24.0167 | 0.914962 | ||||||||
\(690\) | 139.460 | 5.30914 | ||||||||
\(691\) | −35.3951 | −1.34649 | −0.673246 | − | 0.739419i | \(-0.735101\pi\) | ||||
−0.673246 | + | 0.739419i | \(0.735101\pi\) | |||||||
\(692\) | 86.9761 | 3.30633 | ||||||||
\(693\) | −36.3587 | −1.38115 | ||||||||
\(694\) | −42.3911 | −1.60914 | ||||||||
\(695\) | 77.8100 | 2.95150 | ||||||||
\(696\) | 24.0331 | 0.910974 | ||||||||
\(697\) | 32.3953 | 1.22706 | ||||||||
\(698\) | 16.5418 | 0.626117 | ||||||||
\(699\) | −79.5300 | −3.00810 | ||||||||
\(700\) | −69.0133 | −2.60846 | ||||||||
\(701\) | 38.7447 | 1.46337 | 0.731683 | − | 0.681645i | \(-0.238735\pi\) | ||||
0.731683 | + | 0.681645i | \(0.238735\pi\) | |||||||
\(702\) | −23.6925 | −0.894217 | ||||||||
\(703\) | 6.60953 | 0.249283 | ||||||||
\(704\) | −19.7991 | −0.746208 | ||||||||
\(705\) | 100.531 | 3.78623 | ||||||||
\(706\) | 42.9582 | 1.61675 | ||||||||
\(707\) | −6.63141 | −0.249400 | ||||||||
\(708\) | 34.5215 | 1.29740 | ||||||||
\(709\) | −37.8365 | −1.42098 | −0.710490 | − | 0.703707i | \(-0.751527\pi\) | ||||
−0.710490 | + | 0.703707i | \(0.751527\pi\) | |||||||
\(710\) | −95.3612 | −3.57884 | ||||||||
\(711\) | −47.9291 | −1.79748 | ||||||||
\(712\) | 92.9022 | 3.48166 | ||||||||
\(713\) | −21.7281 | −0.813722 | ||||||||
\(714\) | −34.0275 | −1.27345 | ||||||||
\(715\) | −37.7457 | −1.41161 | ||||||||
\(716\) | −66.9618 | −2.50248 | ||||||||
\(717\) | 0.261727 | 0.00977438 | ||||||||
\(718\) | −14.2255 | −0.530892 | ||||||||
\(719\) | −26.3921 | −0.984259 | −0.492129 | − | 0.870522i | \(-0.663781\pi\) | ||||
−0.492129 | + | 0.870522i | \(0.663781\pi\) | |||||||
\(720\) | 95.6808 | 3.56581 | ||||||||
\(721\) | −3.32480 | −0.123822 | ||||||||
\(722\) | −61.7414 | −2.29778 | ||||||||
\(723\) | −12.2324 | −0.454929 | ||||||||
\(724\) | −22.8594 | −0.849563 | ||||||||
\(725\) | 14.1644 | 0.526052 | ||||||||
\(726\) | 63.7662 | 2.36658 | ||||||||
\(727\) | 4.00161 | 0.148411 | 0.0742057 | − | 0.997243i | \(-0.476358\pi\) | ||||
0.0742057 | + | 0.997243i | \(0.476358\pi\) | |||||||
\(728\) | −22.3322 | −0.827688 | ||||||||
\(729\) | −43.9636 | −1.62828 | ||||||||
\(730\) | 59.9777 | 2.21988 | ||||||||
\(731\) | −30.6682 | −1.13430 | ||||||||
\(732\) | −78.6037 | −2.90528 | ||||||||
\(733\) | −24.6358 | −0.909944 | −0.454972 | − | 0.890506i | \(-0.650351\pi\) | ||||
−0.454972 | + | 0.890506i | \(0.650351\pi\) | |||||||
\(734\) | −26.8646 | −0.991591 | ||||||||
\(735\) | 39.7286 | 1.46541 | ||||||||
\(736\) | −14.6771 | −0.541004 | ||||||||
\(737\) | −14.3259 | −0.527703 | ||||||||
\(738\) | −132.085 | −4.86210 | ||||||||
\(739\) | −8.83046 | −0.324834 | −0.162417 | − | 0.986722i | \(-0.551929\pi\) | ||||
−0.162417 | + | 0.986722i | \(0.551929\pi\) | |||||||
\(740\) | −15.9978 | −0.588092 | ||||||||
\(741\) | −40.4813 | −1.48712 | ||||||||
\(742\) | −47.8416 | −1.75632 | ||||||||
\(743\) | −23.7277 | −0.870485 | −0.435242 | − | 0.900313i | \(-0.643337\pi\) | ||||
−0.435242 | + | 0.900313i | \(0.643337\pi\) | |||||||
\(744\) | −62.3634 | −2.28635 | ||||||||
\(745\) | 51.9509 | 1.90333 | ||||||||
\(746\) | 74.5655 | 2.73004 | ||||||||
\(747\) | −28.5123 | −1.04321 | ||||||||
\(748\) | 53.4487 | 1.95428 | ||||||||
\(749\) | 10.0533 | 0.367341 | ||||||||
\(750\) | 106.759 | 3.89828 | ||||||||
\(751\) | −18.5947 | −0.678530 | −0.339265 | − | 0.940691i | \(-0.610178\pi\) | ||||
−0.339265 | + | 0.940691i | \(0.610178\pi\) | |||||||
\(752\) | −54.4899 | −1.98704 | ||||||||
\(753\) | 32.9559 | 1.20098 | ||||||||
\(754\) | 8.64794 | 0.314939 | ||||||||
\(755\) | 18.5869 | 0.676445 | ||||||||
\(756\) | 32.1063 | 1.16770 | ||||||||
\(757\) | 25.8715 | 0.940315 | 0.470157 | − | 0.882583i | \(-0.344197\pi\) | ||||
0.470157 | + | 0.882583i | \(0.344197\pi\) | |||||||
\(758\) | 75.1365 | 2.72908 | ||||||||
\(759\) | −66.7950 | −2.42450 | ||||||||
\(760\) | 140.166 | 5.08437 | ||||||||
\(761\) | 21.1880 | 0.768065 | 0.384032 | − | 0.923320i | \(-0.374535\pi\) | ||||
0.384032 | + | 0.923320i | \(0.374535\pi\) | |||||||
\(762\) | −36.6895 | −1.32912 | ||||||||
\(763\) | 1.77571 | 0.0642850 | ||||||||
\(764\) | 23.5668 | 0.852618 | ||||||||
\(765\) | 47.6723 | 1.72359 | ||||||||
\(766\) | −46.4905 | −1.67977 | ||||||||
\(767\) | 6.58379 | 0.237727 | ||||||||
\(768\) | 88.7506 | 3.20251 | ||||||||
\(769\) | 18.3133 | 0.660394 | 0.330197 | − | 0.943912i | \(-0.392885\pi\) | ||||
0.330197 | + | 0.943912i | \(0.392885\pi\) | |||||||
\(770\) | 75.1902 | 2.70967 | ||||||||
\(771\) | 14.0061 | 0.504419 | ||||||||
\(772\) | −42.8978 | −1.54392 | ||||||||
\(773\) | 24.6088 | 0.885118 | 0.442559 | − | 0.896740i | \(-0.354071\pi\) | ||||
0.442559 | + | 0.896740i | \(0.354071\pi\) | |||||||
\(774\) | 125.042 | 4.49456 | ||||||||
\(775\) | −36.7550 | −1.32028 | ||||||||
\(776\) | 69.7921 | 2.50539 | ||||||||
\(777\) | −4.87809 | −0.175000 | ||||||||
\(778\) | −85.3630 | −3.06041 | ||||||||
\(779\) | −76.7715 | −2.75063 | ||||||||
\(780\) | 97.9818 | 3.50831 | ||||||||
\(781\) | 45.6737 | 1.63434 | ||||||||
\(782\) | −37.6621 | −1.34679 | ||||||||
\(783\) | −6.58955 | −0.235491 | ||||||||
\(784\) | −21.5337 | −0.769059 | ||||||||
\(785\) | 84.0013 | 2.99813 | ||||||||
\(786\) | 13.9734 | 0.498416 | ||||||||
\(787\) | 24.0390 | 0.856897 | 0.428449 | − | 0.903566i | \(-0.359060\pi\) | ||||
0.428449 | + | 0.903566i | \(0.359060\pi\) | |||||||
\(788\) | −2.92100 | −0.104056 | ||||||||
\(789\) | 52.7649 | 1.87848 | ||||||||
\(790\) | 99.1180 | 3.52646 | ||||||||
\(791\) | 13.5336 | 0.481200 | ||||||||
\(792\) | −115.502 | −4.10420 | ||||||||
\(793\) | −14.9910 | −0.532345 | ||||||||
\(794\) | 67.4291 | 2.39297 | ||||||||
\(795\) | 111.251 | 3.94566 | ||||||||
\(796\) | −73.0776 | −2.59017 | ||||||||
\(797\) | −51.9727 | −1.84097 | −0.920484 | − | 0.390779i | \(-0.872206\pi\) | ||||
−0.920484 | + | 0.390779i | \(0.872206\pi\) | |||||||
\(798\) | 80.6395 | 2.85461 | ||||||||
\(799\) | −27.1492 | −0.960470 | ||||||||
\(800\) | −24.8276 | −0.877789 | ||||||||
\(801\) | −74.8800 | −2.64575 | ||||||||
\(802\) | 33.8052 | 1.19370 | ||||||||
\(803\) | −28.7267 | −1.01374 | ||||||||
\(804\) | 37.1878 | 1.31151 | ||||||||
\(805\) | −36.0425 | −1.27033 | ||||||||
\(806\) | −22.4405 | −0.790432 | ||||||||
\(807\) | 28.2372 | 0.993996 | ||||||||
\(808\) | −21.0663 | −0.741111 | ||||||||
\(809\) | −51.6974 | −1.81759 | −0.908793 | − | 0.417248i | \(-0.862995\pi\) | ||||
−0.908793 | + | 0.417248i | \(0.862995\pi\) | |||||||
\(810\) | 18.5021 | 0.650096 | ||||||||
\(811\) | −36.2942 | −1.27446 | −0.637230 | − | 0.770674i | \(-0.719920\pi\) | ||||
−0.637230 | + | 0.770674i | \(0.719920\pi\) | |||||||
\(812\) | −11.7190 | −0.411257 | ||||||||
\(813\) | −15.7073 | −0.550877 | ||||||||
\(814\) | 11.2634 | 0.394783 | ||||||||
\(815\) | −35.2374 | −1.23431 | ||||||||
\(816\) | −42.8886 | −1.50140 | ||||||||
\(817\) | 72.6785 | 2.54270 | ||||||||
\(818\) | −33.2094 | −1.16114 | ||||||||
\(819\) | 18.0000 | 0.628970 | ||||||||
\(820\) | 185.819 | 6.48909 | ||||||||
\(821\) | 6.98642 | 0.243828 | 0.121914 | − | 0.992541i | \(-0.461097\pi\) | ||||
0.121914 | + | 0.992541i | \(0.461097\pi\) | |||||||
\(822\) | −25.0550 | −0.873893 | ||||||||
\(823\) | 37.5741 | 1.30975 | 0.654875 | − | 0.755737i | \(-0.272721\pi\) | ||||
0.654875 | + | 0.755737i | \(0.272721\pi\) | |||||||
\(824\) | −10.5621 | −0.367947 | ||||||||
\(825\) | −112.990 | −3.93380 | ||||||||
\(826\) | −13.1150 | −0.456330 | ||||||||
\(827\) | 32.0081 | 1.11303 | 0.556516 | − | 0.830837i | \(-0.312138\pi\) | ||||
0.556516 | + | 0.830837i | \(0.312138\pi\) | |||||||
\(828\) | 104.462 | 3.63032 | ||||||||
\(829\) | 5.74489 | 0.199528 | 0.0997642 | − | 0.995011i | \(-0.468191\pi\) | ||||
0.0997642 | + | 0.995011i | \(0.468191\pi\) | |||||||
\(830\) | 58.9638 | 2.04666 | ||||||||
\(831\) | −62.3974 | −2.16454 | ||||||||
\(832\) | 9.80190 | 0.339820 | ||||||||
\(833\) | −10.7290 | −0.371738 | ||||||||
\(834\) | 142.207 | 4.92424 | ||||||||
\(835\) | 55.9891 | 1.93758 | ||||||||
\(836\) | −126.664 | −4.38078 | ||||||||
\(837\) | 17.0992 | 0.591033 | ||||||||
\(838\) | 73.3364 | 2.53336 | ||||||||
\(839\) | −1.50858 | −0.0520820 | −0.0260410 | − | 0.999661i | \(-0.508290\pi\) | ||||
−0.0260410 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(840\) | −103.448 | −3.56930 | ||||||||
\(841\) | −26.5948 | −0.917061 | ||||||||
\(842\) | −71.4644 | −2.46283 | ||||||||
\(843\) | 61.6815 | 2.12442 | ||||||||
\(844\) | −19.9085 | −0.685278 | ||||||||
\(845\) | −30.1856 | −1.03842 | ||||||||
\(846\) | 110.695 | 3.80576 | ||||||||
\(847\) | −16.4800 | −0.566258 | ||||||||
\(848\) | −60.3001 | −2.07071 | ||||||||
\(849\) | 43.6886 | 1.49939 | ||||||||
\(850\) | −63.7089 | −2.18520 | ||||||||
\(851\) | −5.39913 | −0.185080 | ||||||||
\(852\) | −118.562 | −4.06185 | ||||||||
\(853\) | −42.4939 | −1.45496 | −0.727482 | − | 0.686127i | \(-0.759309\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759309\pi\) | |||||||
\(854\) | 29.8623 | 1.02187 | ||||||||
\(855\) | −112.975 | −3.86367 | ||||||||
\(856\) | 31.9370 | 1.09158 | ||||||||
\(857\) | 14.0921 | 0.481376 | 0.240688 | − | 0.970603i | \(-0.422627\pi\) | ||||
0.240688 | + | 0.970603i | \(0.422627\pi\) | |||||||
\(858\) | −68.9850 | −2.35511 | ||||||||
\(859\) | 22.2933 | 0.760636 | 0.380318 | − | 0.924856i | \(-0.375815\pi\) | ||||
0.380318 | + | 0.924856i | \(0.375815\pi\) | |||||||
\(860\) | −175.912 | −5.99856 | ||||||||
\(861\) | 56.6604 | 1.93098 | ||||||||
\(862\) | −73.5099 | −2.50376 | ||||||||
\(863\) | 50.3130 | 1.71267 | 0.856337 | − | 0.516417i | \(-0.172734\pi\) | ||||
0.856337 | + | 0.516417i | \(0.172734\pi\) | |||||||
\(864\) | 11.5503 | 0.392949 | ||||||||
\(865\) | 76.8382 | 2.61258 | ||||||||
\(866\) | 75.1532 | 2.55381 | ||||||||
\(867\) | 25.3321 | 0.860324 | ||||||||
\(868\) | 30.4096 | 1.03217 | ||||||||
\(869\) | −47.4731 | −1.61041 | ||||||||
\(870\) | 40.0593 | 1.35814 | ||||||||
\(871\) | 7.09230 | 0.240313 | ||||||||
\(872\) | 5.64098 | 0.191028 | ||||||||
\(873\) | −56.2530 | −1.90388 | ||||||||
\(874\) | 89.2529 | 3.01902 | ||||||||
\(875\) | −27.5911 | −0.932751 | ||||||||
\(876\) | 74.5697 | 2.51948 | ||||||||
\(877\) | −10.1060 | −0.341256 | −0.170628 | − | 0.985336i | \(-0.554580\pi\) | ||||
−0.170628 | + | 0.985336i | \(0.554580\pi\) | |||||||
\(878\) | 4.53609 | 0.153086 | ||||||||
\(879\) | −77.1472 | −2.60211 | ||||||||
\(880\) | 94.7705 | 3.19471 | ||||||||
\(881\) | −47.2631 | −1.59233 | −0.796167 | − | 0.605077i | \(-0.793142\pi\) | ||||
−0.796167 | + | 0.605077i | \(0.793142\pi\) | |||||||
\(882\) | 43.7450 | 1.47297 | ||||||||
\(883\) | 49.0860 | 1.65187 | 0.825937 | − | 0.563762i | \(-0.190647\pi\) | ||||
0.825937 | + | 0.563762i | \(0.190647\pi\) | |||||||
\(884\) | −26.4607 | −0.889969 | ||||||||
\(885\) | 30.4977 | 1.02517 | ||||||||
\(886\) | −24.2259 | −0.813886 | ||||||||
\(887\) | −8.79015 | −0.295144 | −0.147572 | − | 0.989051i | \(-0.547146\pi\) | ||||
−0.147572 | + | 0.989051i | \(0.547146\pi\) | |||||||
\(888\) | −15.4965 | −0.520027 | ||||||||
\(889\) | 9.48217 | 0.318022 | ||||||||
\(890\) | 154.853 | 5.19067 | ||||||||
\(891\) | −8.86166 | −0.296877 | ||||||||
\(892\) | −18.6402 | −0.624118 | ||||||||
\(893\) | 64.3391 | 2.15303 | ||||||||
\(894\) | 94.9466 | 3.17549 | ||||||||
\(895\) | −59.1568 | −1.97739 | ||||||||
\(896\) | −29.1798 | −0.974828 | ||||||||
\(897\) | 33.0680 | 1.10411 | ||||||||
\(898\) | −23.8197 | −0.794874 | ||||||||
\(899\) | −6.24131 | −0.208159 | ||||||||
\(900\) | 176.708 | 5.89026 | ||||||||
\(901\) | −30.0441 | −1.00091 | ||||||||
\(902\) | −130.828 | −4.35609 | ||||||||
\(903\) | −53.6395 | −1.78501 | ||||||||
\(904\) | 42.9929 | 1.42992 | ||||||||
\(905\) | −20.1949 | −0.671302 | ||||||||
\(906\) | 33.9698 | 1.12857 | ||||||||
\(907\) | 36.5862 | 1.21483 | 0.607413 | − | 0.794386i | \(-0.292207\pi\) | ||||
0.607413 | + | 0.794386i | \(0.292207\pi\) | |||||||
\(908\) | −21.0550 | −0.698735 | ||||||||
\(909\) | 16.9796 | 0.563179 | ||||||||
\(910\) | −37.2242 | −1.23397 | ||||||||
\(911\) | −52.0158 | −1.72336 | −0.861679 | − | 0.507453i | \(-0.830587\pi\) | ||||
−0.861679 | + | 0.507453i | \(0.830587\pi\) | |||||||
\(912\) | 101.639 | 3.36560 | ||||||||
\(913\) | −28.2410 | −0.934642 | ||||||||
\(914\) | −62.9765 | −2.08308 | ||||||||
\(915\) | −69.4417 | −2.29567 | ||||||||
\(916\) | −11.5141 | −0.380438 | ||||||||
\(917\) | −3.61134 | −0.119257 | ||||||||
\(918\) | 29.6386 | 0.978220 | ||||||||
\(919\) | −30.5085 | −1.00638 | −0.503191 | − | 0.864175i | \(-0.667841\pi\) | ||||
−0.503191 | + | 0.864175i | \(0.667841\pi\) | |||||||
\(920\) | −114.498 | −3.77488 | ||||||||
\(921\) | 35.1197 | 1.15724 | ||||||||
\(922\) | −55.3459 | −1.82272 | ||||||||
\(923\) | −22.6116 | −0.744269 | ||||||||
\(924\) | 93.4832 | 3.07537 | ||||||||
\(925\) | −9.13313 | −0.300295 | ||||||||
\(926\) | −52.7854 | −1.73464 | ||||||||
\(927\) | 8.51311 | 0.279607 | ||||||||
\(928\) | −4.21593 | −0.138395 | ||||||||
\(929\) | −17.6283 | −0.578367 | −0.289183 | − | 0.957274i | \(-0.593384\pi\) | ||||
−0.289183 | + | 0.957274i | \(0.593384\pi\) | |||||||
\(930\) | −103.950 | −3.40864 | ||||||||
\(931\) | 25.4259 | 0.833301 | ||||||||
\(932\) | 123.196 | 4.03541 | ||||||||
\(933\) | −40.5308 | −1.32692 | ||||||||
\(934\) | 91.9301 | 3.00804 | ||||||||
\(935\) | 47.2187 | 1.54422 | ||||||||
\(936\) | 57.1814 | 1.86903 | ||||||||
\(937\) | −13.6281 | −0.445211 | −0.222606 | − | 0.974909i | \(-0.571456\pi\) | ||||
−0.222606 | + | 0.974909i | \(0.571456\pi\) | |||||||
\(938\) | −14.1280 | −0.461295 | ||||||||
\(939\) | 14.3468 | 0.468190 | ||||||||
\(940\) | −155.728 | −5.07928 | ||||||||
\(941\) | −16.9766 | −0.553421 | −0.276711 | − | 0.960953i | \(-0.589244\pi\) | ||||
−0.276711 | + | 0.960953i | \(0.589244\pi\) | |||||||
\(942\) | 153.523 | 5.00204 | ||||||||
\(943\) | 62.7124 | 2.04220 | ||||||||
\(944\) | −16.5303 | −0.538016 | ||||||||
\(945\) | 28.3640 | 0.922682 | ||||||||
\(946\) | 123.853 | 4.02680 | ||||||||
\(947\) | −52.7863 | −1.71532 | −0.857662 | − | 0.514214i | \(-0.828084\pi\) | ||||
−0.857662 | + | 0.514214i | \(0.828084\pi\) | |||||||
\(948\) | 123.232 | 4.00240 | ||||||||
\(949\) | 14.2216 | 0.461653 | ||||||||
\(950\) | 150.980 | 4.89842 | ||||||||
\(951\) | 7.82106 | 0.253615 | ||||||||
\(952\) | 27.9369 | 0.905441 | ||||||||
\(953\) | −29.5778 | −0.958120 | −0.479060 | − | 0.877782i | \(-0.659022\pi\) | ||||
−0.479060 | + | 0.877782i | \(0.659022\pi\) | |||||||
\(954\) | 122.498 | 3.96601 | ||||||||
\(955\) | 20.8199 | 0.673716 | ||||||||
\(956\) | −0.405427 | −0.0131124 | ||||||||
\(957\) | −19.1866 | −0.620215 | ||||||||
\(958\) | 75.9888 | 2.45509 | ||||||||
\(959\) | 6.47530 | 0.209098 | ||||||||
\(960\) | 45.4047 | 1.46543 | ||||||||
\(961\) | −14.8045 | −0.477564 | ||||||||
\(962\) | −5.57615 | −0.179782 | ||||||||
\(963\) | −25.7415 | −0.829507 | ||||||||
\(964\) | 18.9486 | 0.610292 | ||||||||
\(965\) | −37.8976 | −1.21997 | ||||||||
\(966\) | −65.8720 | −2.11940 | ||||||||
\(967\) | −20.1261 | −0.647210 | −0.323605 | − | 0.946192i | \(-0.604895\pi\) | ||||
−0.323605 | + | 0.946192i | \(0.604895\pi\) | |||||||
\(968\) | −52.3527 | −1.68268 | ||||||||
\(969\) | 50.6408 | 1.62682 | ||||||||
\(970\) | 116.332 | 3.73520 | ||||||||
\(971\) | −11.7292 | −0.376407 | −0.188203 | − | 0.982130i | \(-0.560266\pi\) | ||||
−0.188203 | + | 0.982130i | \(0.560266\pi\) | |||||||
\(972\) | 77.2460 | 2.47767 | ||||||||
\(973\) | −36.7526 | −1.17823 | ||||||||
\(974\) | −82.7171 | −2.65043 | ||||||||
\(975\) | 55.9376 | 1.79144 | ||||||||
\(976\) | 37.6387 | 1.20479 | ||||||||
\(977\) | 31.0277 | 0.992665 | 0.496333 | − | 0.868132i | \(-0.334680\pi\) | ||||
0.496333 | + | 0.868132i | \(0.334680\pi\) | |||||||
\(978\) | −64.4008 | −2.05931 | ||||||||
\(979\) | −74.1675 | −2.37040 | ||||||||
\(980\) | −61.5414 | −1.96587 | ||||||||
\(981\) | −4.54668 | −0.145164 | ||||||||
\(982\) | −21.2274 | −0.677394 | ||||||||
\(983\) | −25.3519 | −0.808599 | −0.404299 | − | 0.914627i | \(-0.632485\pi\) | ||||
−0.404299 | + | 0.914627i | \(0.632485\pi\) | |||||||
\(984\) | 179.996 | 5.73805 | ||||||||
\(985\) | −2.58053 | −0.0822226 | ||||||||
\(986\) | −10.8183 | −0.344525 | ||||||||
\(987\) | −47.4848 | −1.51146 | ||||||||
\(988\) | 62.7074 | 1.99499 | ||||||||
\(989\) | −59.3689 | −1.88782 | ||||||||
\(990\) | −192.523 | −6.11880 | ||||||||
\(991\) | −46.7573 | −1.48529 | −0.742647 | − | 0.669683i | \(-0.766430\pi\) | ||||
−0.742647 | + | 0.669683i | \(0.766430\pi\) | |||||||
\(992\) | 10.9399 | 0.347342 | ||||||||
\(993\) | 47.8255 | 1.51770 | ||||||||
\(994\) | 45.0427 | 1.42867 | ||||||||
\(995\) | −64.5597 | −2.04668 | ||||||||
\(996\) | 73.3091 | 2.32289 | ||||||||
\(997\) | −5.36141 | −0.169798 | −0.0848989 | − | 0.996390i | \(-0.527057\pi\) | ||||
−0.0848989 | + | 0.996390i | \(0.527057\pi\) | |||||||
\(998\) | −5.37856 | −0.170255 | ||||||||
\(999\) | 4.24891 | 0.134429 |
(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 | 4033.2.a.d.1.9 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.9 | ✓ | 79 | 1.1 | even | 1 | trivial |