Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83395 | −1.29680 | −0.648399 | − | 0.761301i | \(-0.724561\pi\) | ||||
−0.648399 | + | 0.761301i | \(0.724561\pi\) | |||||||
\(3\) | 2.22148 | 1.28257 | 0.641286 | − | 0.767302i | \(-0.278401\pi\) | ||||
0.641286 | + | 0.767302i | \(0.278401\pi\) | |||||||
\(4\) | 1.36337 | 0.681684 | ||||||||
\(5\) | 1.24306 | 0.555911 | 0.277956 | − | 0.960594i | \(-0.410343\pi\) | ||||
0.277956 | + | 0.960594i | \(0.410343\pi\) | |||||||
\(6\) | −4.07408 | −1.66324 | ||||||||
\(7\) | 2.01007 | 0.759736 | 0.379868 | − | 0.925041i | \(-0.375969\pi\) | ||||
0.379868 | + | 0.925041i | \(0.375969\pi\) | |||||||
\(8\) | 1.16755 | 0.412791 | ||||||||
\(9\) | 1.93497 | 0.644990 | ||||||||
\(10\) | −2.27970 | −0.720905 | ||||||||
\(11\) | −5.64415 | −1.70178 | −0.850888 | − | 0.525347i | \(-0.823935\pi\) | ||||
−0.850888 | + | 0.525347i | \(0.823935\pi\) | |||||||
\(12\) | 3.02870 | 0.874309 | ||||||||
\(13\) | −2.77843 | −0.770598 | −0.385299 | − | 0.922792i | \(-0.625902\pi\) | ||||
−0.385299 | + | 0.922792i | \(0.625902\pi\) | |||||||
\(14\) | −3.68637 | −0.985224 | ||||||||
\(15\) | 2.76142 | 0.712996 | ||||||||
\(16\) | −4.86796 | −1.21699 | ||||||||
\(17\) | 0.668588 | 0.162156 | 0.0810782 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810782 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(18\) | −3.54864 | −0.836422 | ||||||||
\(19\) | 4.24245 | 0.973285 | 0.486642 | − | 0.873601i | \(-0.338221\pi\) | ||||
0.486642 | + | 0.873601i | \(0.338221\pi\) | |||||||
\(20\) | 1.69474 | 0.378956 | ||||||||
\(21\) | 4.46534 | 0.974416 | ||||||||
\(22\) | 10.3511 | 2.20686 | ||||||||
\(23\) | −4.21670 | −0.879242 | −0.439621 | − | 0.898183i | \(-0.644887\pi\) | ||||
−0.439621 | + | 0.898183i | \(0.644887\pi\) | |||||||
\(24\) | 2.59369 | 0.529434 | ||||||||
\(25\) | −3.45481 | −0.690963 | ||||||||
\(26\) | 5.09550 | 0.999310 | ||||||||
\(27\) | −2.36594 | −0.455326 | ||||||||
\(28\) | 2.74047 | 0.517900 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −5.06431 | −0.924612 | ||||||||
\(31\) | −5.44314 | −0.977616 | −0.488808 | − | 0.872391i | \(-0.662568\pi\) | ||||
−0.488808 | + | 0.872391i | \(0.662568\pi\) | |||||||
\(32\) | 6.59250 | 1.16540 | ||||||||
\(33\) | −12.5384 | −2.18265 | ||||||||
\(34\) | −1.22616 | −0.210284 | ||||||||
\(35\) | 2.49863 | 0.422346 | ||||||||
\(36\) | 2.63808 | 0.439680 | ||||||||
\(37\) | −1.36287 | −0.224055 | −0.112027 | − | 0.993705i | \(-0.535734\pi\) | ||||
−0.112027 | + | 0.993705i | \(0.535734\pi\) | |||||||
\(38\) | −7.78044 | −1.26215 | ||||||||
\(39\) | −6.17223 | −0.988348 | ||||||||
\(40\) | 1.45133 | 0.229475 | ||||||||
\(41\) | 5.79632 | 0.905234 | 0.452617 | − | 0.891705i | \(-0.350491\pi\) | ||||
0.452617 | + | 0.891705i | \(0.350491\pi\) | |||||||
\(42\) | −8.18920 | −1.26362 | ||||||||
\(43\) | 4.48081 | 0.683316 | 0.341658 | − | 0.939824i | \(-0.389011\pi\) | ||||
0.341658 | + | 0.939824i | \(0.389011\pi\) | |||||||
\(44\) | −7.69506 | −1.16007 | ||||||||
\(45\) | 2.40528 | 0.358557 | ||||||||
\(46\) | 7.73321 | 1.14020 | ||||||||
\(47\) | −2.51083 | −0.366242 | −0.183121 | − | 0.983090i | \(-0.558620\pi\) | ||||
−0.183121 | + | 0.983090i | \(0.558620\pi\) | |||||||
\(48\) | −10.8141 | −1.56088 | ||||||||
\(49\) | −2.95961 | −0.422801 | ||||||||
\(50\) | 6.33595 | 0.896039 | ||||||||
\(51\) | 1.48525 | 0.207977 | ||||||||
\(52\) | −3.78803 | −0.525305 | ||||||||
\(53\) | 9.20963 | 1.26504 | 0.632520 | − | 0.774544i | \(-0.282021\pi\) | ||||
0.632520 | + | 0.774544i | \(0.282021\pi\) | |||||||
\(54\) | 4.33902 | 0.590465 | ||||||||
\(55\) | −7.01600 | −0.946037 | ||||||||
\(56\) | 2.34686 | 0.313612 | ||||||||
\(57\) | 9.42452 | 1.24831 | ||||||||
\(58\) | 1.83395 | 0.240809 | ||||||||
\(59\) | −8.56719 | −1.11535 | −0.557677 | − | 0.830058i | \(-0.688307\pi\) | ||||
−0.557677 | + | 0.830058i | \(0.688307\pi\) | |||||||
\(60\) | 3.76484 | 0.486038 | ||||||||
\(61\) | −9.37884 | −1.20084 | −0.600419 | − | 0.799686i | \(-0.704999\pi\) | ||||
−0.600419 | + | 0.799686i | \(0.704999\pi\) | |||||||
\(62\) | 9.98243 | 1.26777 | ||||||||
\(63\) | 3.88943 | 0.490022 | ||||||||
\(64\) | −2.35438 | −0.294297 | ||||||||
\(65\) | −3.45375 | −0.428384 | ||||||||
\(66\) | 22.9947 | 2.83045 | ||||||||
\(67\) | −1.24871 | −0.152555 | −0.0762774 | − | 0.997087i | \(-0.524303\pi\) | ||||
−0.0762774 | + | 0.997087i | \(0.524303\pi\) | |||||||
\(68\) | 0.911532 | 0.110540 | ||||||||
\(69\) | −9.36731 | −1.12769 | ||||||||
\(70\) | −4.58236 | −0.547697 | ||||||||
\(71\) | 0.728297 | 0.0864329 | 0.0432165 | − | 0.999066i | \(-0.486239\pi\) | ||||
0.0432165 | + | 0.999066i | \(0.486239\pi\) | |||||||
\(72\) | 2.25917 | 0.266246 | ||||||||
\(73\) | −9.77556 | −1.14414 | −0.572072 | − | 0.820204i | \(-0.693860\pi\) | ||||
−0.572072 | + | 0.820204i | \(0.693860\pi\) | |||||||
\(74\) | 2.49944 | 0.290554 | ||||||||
\(75\) | −7.67479 | −0.886209 | ||||||||
\(76\) | 5.78402 | 0.663473 | ||||||||
\(77\) | −11.3452 | −1.29290 | ||||||||
\(78\) | 11.3196 | 1.28169 | ||||||||
\(79\) | −4.46664 | −0.502536 | −0.251268 | − | 0.967918i | \(-0.580848\pi\) | ||||
−0.251268 | + | 0.967918i | \(0.580848\pi\) | |||||||
\(80\) | −6.05115 | −0.676539 | ||||||||
\(81\) | −11.0608 | −1.22898 | ||||||||
\(82\) | −10.6302 | −1.17390 | ||||||||
\(83\) | 2.99039 | 0.328237 | 0.164119 | − | 0.986441i | \(-0.447522\pi\) | ||||
0.164119 | + | 0.986441i | \(0.447522\pi\) | |||||||
\(84\) | 6.08790 | 0.664244 | ||||||||
\(85\) | 0.831092 | 0.0901446 | ||||||||
\(86\) | −8.21757 | −0.886123 | ||||||||
\(87\) | −2.22148 | −0.238168 | ||||||||
\(88\) | −6.58982 | −0.702478 | ||||||||
\(89\) | −7.01453 | −0.743539 | −0.371769 | − | 0.928325i | \(-0.621249\pi\) | ||||
−0.371769 | + | 0.928325i | \(0.621249\pi\) | |||||||
\(90\) | −4.41115 | −0.464976 | ||||||||
\(91\) | −5.58485 | −0.585451 | ||||||||
\(92\) | −5.74891 | −0.599366 | ||||||||
\(93\) | −12.0918 | −1.25386 | ||||||||
\(94\) | 4.60473 | 0.474942 | ||||||||
\(95\) | 5.27360 | 0.541060 | ||||||||
\(96\) | 14.6451 | 1.49471 | ||||||||
\(97\) | −9.31278 | −0.945569 | −0.472785 | − | 0.881178i | \(-0.656751\pi\) | ||||
−0.472785 | + | 0.881178i | \(0.656751\pi\) | |||||||
\(98\) | 5.42777 | 0.548287 | ||||||||
\(99\) | −10.9213 | −1.09763 | ||||||||
\(100\) | −4.71018 | −0.471018 | ||||||||
\(101\) | 10.5508 | 1.04984 | 0.524920 | − | 0.851152i | \(-0.324095\pi\) | ||||
0.524920 | + | 0.851152i | \(0.324095\pi\) | |||||||
\(102\) | −2.72388 | −0.269704 | ||||||||
\(103\) | −9.80880 | −0.966490 | −0.483245 | − | 0.875485i | \(-0.660542\pi\) | ||||
−0.483245 | + | 0.875485i | \(0.660542\pi\) | |||||||
\(104\) | −3.24396 | −0.318096 | ||||||||
\(105\) | 5.55066 | 0.541689 | ||||||||
\(106\) | −16.8900 | −1.64050 | ||||||||
\(107\) | 1.87151 | 0.180926 | 0.0904629 | − | 0.995900i | \(-0.471165\pi\) | ||||
0.0904629 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(108\) | −3.22565 | −0.310388 | ||||||||
\(109\) | −8.38731 | −0.803358 | −0.401679 | − | 0.915780i | \(-0.631573\pi\) | ||||
−0.401679 | + | 0.915780i | \(0.631573\pi\) | |||||||
\(110\) | 12.8670 | 1.22682 | ||||||||
\(111\) | −3.02759 | −0.287366 | ||||||||
\(112\) | −9.78496 | −0.924592 | ||||||||
\(113\) | −0.291141 | −0.0273882 | −0.0136941 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136941 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(114\) | −17.2841 | −1.61880 | ||||||||
\(115\) | −5.24159 | −0.488781 | ||||||||
\(116\) | −1.36337 | −0.126586 | ||||||||
\(117\) | −5.37618 | −0.497028 | ||||||||
\(118\) | 15.7118 | 1.44639 | ||||||||
\(119\) | 1.34391 | 0.123196 | ||||||||
\(120\) | 3.22410 | 0.294318 | ||||||||
\(121\) | 20.8564 | 1.89604 | ||||||||
\(122\) | 17.2003 | 1.55724 | ||||||||
\(123\) | 12.8764 | 1.16103 | ||||||||
\(124\) | −7.42100 | −0.666426 | ||||||||
\(125\) | −10.5098 | −0.940025 | ||||||||
\(126\) | −7.13302 | −0.635460 | ||||||||
\(127\) | 2.71896 | 0.241269 | 0.120634 | − | 0.992697i | \(-0.461507\pi\) | ||||
0.120634 | + | 0.992697i | \(0.461507\pi\) | |||||||
\(128\) | −8.86719 | −0.783756 | ||||||||
\(129\) | 9.95402 | 0.876402 | ||||||||
\(130\) | 6.33399 | 0.555528 | ||||||||
\(131\) | −1.46073 | −0.127624 | −0.0638122 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638122 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(132\) | −17.0944 | −1.48788 | ||||||||
\(133\) | 8.52763 | 0.739440 | ||||||||
\(134\) | 2.29008 | 0.197833 | ||||||||
\(135\) | −2.94100 | −0.253121 | ||||||||
\(136\) | 0.780609 | 0.0669367 | ||||||||
\(137\) | 5.65497 | 0.483137 | 0.241569 | − | 0.970384i | \(-0.422338\pi\) | ||||
0.241569 | + | 0.970384i | \(0.422338\pi\) | |||||||
\(138\) | 17.1792 | 1.46239 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 3.40656 | 0.287907 | ||||||||
\(141\) | −5.57776 | −0.469732 | ||||||||
\(142\) | −1.33566 | −0.112086 | ||||||||
\(143\) | 15.6819 | 1.31139 | ||||||||
\(144\) | −9.41936 | −0.784947 | ||||||||
\(145\) | −1.24306 | −0.103230 | ||||||||
\(146\) | 17.9279 | 1.48372 | ||||||||
\(147\) | −6.57471 | −0.542273 | ||||||||
\(148\) | −1.85810 | −0.152735 | ||||||||
\(149\) | −13.6240 | −1.11612 | −0.558060 | − | 0.829801i | \(-0.688454\pi\) | ||||
−0.558060 | + | 0.829801i | \(0.688454\pi\) | |||||||
\(150\) | 14.0752 | 1.14923 | ||||||||
\(151\) | 20.1573 | 1.64038 | 0.820191 | − | 0.572090i | \(-0.193867\pi\) | ||||
0.820191 | + | 0.572090i | \(0.193867\pi\) | |||||||
\(152\) | 4.95327 | 0.401763 | ||||||||
\(153\) | 1.29370 | 0.104589 | ||||||||
\(154\) | 20.8064 | 1.67663 | ||||||||
\(155\) | −6.76612 | −0.543468 | ||||||||
\(156\) | −8.41503 | −0.673741 | ||||||||
\(157\) | −4.29784 | −0.343005 | −0.171502 | − | 0.985184i | \(-0.554862\pi\) | ||||
−0.171502 | + | 0.985184i | \(0.554862\pi\) | |||||||
\(158\) | 8.19159 | 0.651688 | ||||||||
\(159\) | 20.4590 | 1.62250 | ||||||||
\(160\) | 8.19484 | 0.647859 | ||||||||
\(161\) | −8.47587 | −0.667992 | ||||||||
\(162\) | 20.2849 | 1.59374 | ||||||||
\(163\) | −7.44700 | −0.583294 | −0.291647 | − | 0.956526i | \(-0.594203\pi\) | ||||
−0.291647 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(164\) | 7.90253 | 0.617084 | ||||||||
\(165\) | −15.5859 | −1.21336 | ||||||||
\(166\) | −5.48421 | −0.425658 | ||||||||
\(167\) | −7.21906 | −0.558627 | −0.279314 | − | 0.960200i | \(-0.590107\pi\) | ||||
−0.279314 | + | 0.960200i | \(0.590107\pi\) | |||||||
\(168\) | 5.21350 | 0.402230 | ||||||||
\(169\) | −5.28031 | −0.406178 | ||||||||
\(170\) | −1.52418 | −0.116899 | ||||||||
\(171\) | 8.20901 | 0.627759 | ||||||||
\(172\) | 6.10899 | 0.465806 | ||||||||
\(173\) | −5.14445 | −0.391125 | −0.195563 | − | 0.980691i | \(-0.562653\pi\) | ||||
−0.195563 | + | 0.980691i | \(0.562653\pi\) | |||||||
\(174\) | 4.07408 | 0.308855 | ||||||||
\(175\) | −6.94443 | −0.524949 | ||||||||
\(176\) | 27.4755 | 2.07105 | ||||||||
\(177\) | −19.0318 | −1.43052 | ||||||||
\(178\) | 12.8643 | 0.964219 | ||||||||
\(179\) | 15.9114 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(180\) | 3.27928 | 0.244423 | ||||||||
\(181\) | 17.1925 | 1.27791 | 0.638956 | − | 0.769244i | \(-0.279367\pi\) | ||||
0.638956 | + | 0.769244i | \(0.279367\pi\) | |||||||
\(182\) | 10.2423 | 0.759212 | ||||||||
\(183\) | −20.8349 | −1.54016 | ||||||||
\(184\) | −4.92320 | −0.362943 | ||||||||
\(185\) | −1.69413 | −0.124555 | ||||||||
\(186\) | 22.1758 | 1.62601 | ||||||||
\(187\) | −3.77361 | −0.275954 | ||||||||
\(188\) | −3.42319 | −0.249662 | ||||||||
\(189\) | −4.75572 | −0.345927 | ||||||||
\(190\) | −9.67152 | −0.701646 | ||||||||
\(191\) | −19.4927 | −1.41044 | −0.705222 | − | 0.708987i | \(-0.749153\pi\) | ||||
−0.705222 | + | 0.708987i | \(0.749153\pi\) | |||||||
\(192\) | −5.23020 | −0.377457 | ||||||||
\(193\) | −12.5093 | −0.900442 | −0.450221 | − | 0.892917i | \(-0.648655\pi\) | ||||
−0.450221 | + | 0.892917i | \(0.648655\pi\) | |||||||
\(194\) | 17.0792 | 1.22621 | ||||||||
\(195\) | −7.67243 | −0.549434 | ||||||||
\(196\) | −4.03504 | −0.288217 | ||||||||
\(197\) | 19.0707 | 1.35873 | 0.679367 | − | 0.733799i | \(-0.262255\pi\) | ||||
0.679367 | + | 0.733799i | \(0.262255\pi\) | |||||||
\(198\) | 20.0290 | 1.42340 | ||||||||
\(199\) | −10.5371 | −0.746958 | −0.373479 | − | 0.927639i | \(-0.621835\pi\) | ||||
−0.373479 | + | 0.927639i | \(0.621835\pi\) | |||||||
\(200\) | −4.03366 | −0.285223 | ||||||||
\(201\) | −2.77399 | −0.195662 | ||||||||
\(202\) | −19.3495 | −1.36143 | ||||||||
\(203\) | −2.01007 | −0.141079 | ||||||||
\(204\) | 2.02495 | 0.141775 | ||||||||
\(205\) | 7.20515 | 0.503230 | ||||||||
\(206\) | 17.9888 | 1.25334 | ||||||||
\(207\) | −8.15918 | −0.567102 | ||||||||
\(208\) | 13.5253 | 0.937811 | ||||||||
\(209\) | −23.9450 | −1.65631 | ||||||||
\(210\) | −10.1796 | −0.702461 | ||||||||
\(211\) | 0.922142 | 0.0634829 | 0.0317414 | − | 0.999496i | \(-0.489895\pi\) | ||||
0.0317414 | + | 0.999496i | \(0.489895\pi\) | |||||||
\(212\) | 12.5561 | 0.862358 | ||||||||
\(213\) | 1.61790 | 0.110856 | ||||||||
\(214\) | −3.43225 | −0.234624 | ||||||||
\(215\) | 5.56989 | 0.379863 | ||||||||
\(216\) | −2.76235 | −0.187954 | ||||||||
\(217\) | −10.9411 | −0.742730 | ||||||||
\(218\) | 15.3819 | 1.04179 | ||||||||
\(219\) | −21.7162 | −1.46745 | ||||||||
\(220\) | −9.56539 | −0.644898 | ||||||||
\(221\) | −1.85763 | −0.124957 | ||||||||
\(222\) | 5.55245 | 0.372656 | ||||||||
\(223\) | 15.0369 | 1.00694 | 0.503472 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503472 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(224\) | 13.2514 | 0.885396 | ||||||||
\(225\) | −6.68496 | −0.445664 | ||||||||
\(226\) | 0.533937 | 0.0355170 | ||||||||
\(227\) | −3.88589 | −0.257916 | −0.128958 | − | 0.991650i | \(-0.541163\pi\) | ||||
−0.128958 | + | 0.991650i | \(0.541163\pi\) | |||||||
\(228\) | 12.8491 | 0.850952 | ||||||||
\(229\) | 11.7843 | 0.778728 | 0.389364 | − | 0.921084i | \(-0.372695\pi\) | ||||
0.389364 | + | 0.921084i | \(0.372695\pi\) | |||||||
\(230\) | 9.61281 | 0.633850 | ||||||||
\(231\) | −25.2030 | −1.65824 | ||||||||
\(232\) | −1.16755 | −0.0766534 | ||||||||
\(233\) | 12.3496 | 0.809047 | 0.404523 | − | 0.914528i | \(-0.367437\pi\) | ||||
0.404523 | + | 0.914528i | \(0.367437\pi\) | |||||||
\(234\) | 9.85965 | 0.644545 | ||||||||
\(235\) | −3.12110 | −0.203598 | ||||||||
\(236\) | −11.6802 | −0.760319 | ||||||||
\(237\) | −9.92255 | −0.644539 | ||||||||
\(238\) | −2.46466 | −0.159760 | ||||||||
\(239\) | 23.9266 | 1.54768 | 0.773842 | − | 0.633379i | \(-0.218333\pi\) | ||||
0.773842 | + | 0.633379i | \(0.218333\pi\) | |||||||
\(240\) | −13.4425 | −0.867710 | ||||||||
\(241\) | 10.2786 | 0.662106 | 0.331053 | − | 0.943612i | \(-0.392596\pi\) | ||||
0.331053 | + | 0.943612i | \(0.392596\pi\) | |||||||
\(242\) | −38.2497 | −2.45878 | ||||||||
\(243\) | −17.4735 | −1.12093 | ||||||||
\(244\) | −12.7868 | −0.818592 | ||||||||
\(245\) | −3.67896 | −0.235040 | ||||||||
\(246\) | −23.6147 | −1.50562 | ||||||||
\(247\) | −11.7874 | −0.750012 | ||||||||
\(248\) | −6.35513 | −0.403551 | ||||||||
\(249\) | 6.64308 | 0.420988 | ||||||||
\(250\) | 19.2744 | 1.21902 | ||||||||
\(251\) | −0.569540 | −0.0359491 | −0.0179745 | − | 0.999838i | \(-0.505722\pi\) | ||||
−0.0179745 | + | 0.999838i | \(0.505722\pi\) | |||||||
\(252\) | 5.30273 | 0.334041 | ||||||||
\(253\) | 23.7997 | 1.49627 | ||||||||
\(254\) | −4.98644 | −0.312877 | ||||||||
\(255\) | 1.84625 | 0.115617 | ||||||||
\(256\) | 20.9707 | 1.31067 | ||||||||
\(257\) | 2.78147 | 0.173504 | 0.0867518 | − | 0.996230i | \(-0.472351\pi\) | ||||
0.0867518 | + | 0.996230i | \(0.472351\pi\) | |||||||
\(258\) | −18.2552 | −1.13652 | ||||||||
\(259\) | −2.73947 | −0.170222 | ||||||||
\(260\) | −4.70873 | −0.292023 | ||||||||
\(261\) | −1.93497 | −0.119772 | ||||||||
\(262\) | 2.67890 | 0.165503 | ||||||||
\(263\) | −21.4959 | −1.32549 | −0.662746 | − | 0.748844i | \(-0.730609\pi\) | ||||
−0.662746 | + | 0.748844i | \(0.730609\pi\) | |||||||
\(264\) | −14.6392 | −0.900978 | ||||||||
\(265\) | 11.4481 | 0.703250 | ||||||||
\(266\) | −15.6392 | −0.958904 | ||||||||
\(267\) | −15.5826 | −0.953641 | ||||||||
\(268\) | −1.70246 | −0.103994 | ||||||||
\(269\) | 7.66060 | 0.467075 | 0.233537 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233537 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(270\) | 5.39364 | 0.328246 | ||||||||
\(271\) | 29.6818 | 1.80304 | 0.901519 | − | 0.432739i | \(-0.142453\pi\) | ||||
0.901519 | + | 0.432739i | \(0.142453\pi\) | |||||||
\(272\) | −3.25466 | −0.197343 | ||||||||
\(273\) | −12.4066 | −0.750883 | ||||||||
\(274\) | −10.3709 | −0.626531 | ||||||||
\(275\) | 19.4995 | 1.17586 | ||||||||
\(276\) | −12.7711 | −0.768730 | ||||||||
\(277\) | −25.8068 | −1.55058 | −0.775289 | − | 0.631607i | \(-0.782396\pi\) | ||||
−0.775289 | + | 0.631607i | \(0.782396\pi\) | |||||||
\(278\) | 1.83395 | 0.109993 | ||||||||
\(279\) | −10.5323 | −0.630553 | ||||||||
\(280\) | 2.91728 | 0.174341 | ||||||||
\(281\) | 4.18325 | 0.249552 | 0.124776 | − | 0.992185i | \(-0.460179\pi\) | ||||
0.124776 | + | 0.992185i | \(0.460179\pi\) | |||||||
\(282\) | 10.2293 | 0.609147 | ||||||||
\(283\) | 11.3202 | 0.672917 | 0.336458 | − | 0.941698i | \(-0.390771\pi\) | ||||
0.336458 | + | 0.941698i | \(0.390771\pi\) | |||||||
\(284\) | 0.992937 | 0.0589200 | ||||||||
\(285\) | 11.7152 | 0.693948 | ||||||||
\(286\) | −28.7598 | −1.70060 | ||||||||
\(287\) | 11.6510 | 0.687739 | ||||||||
\(288\) | 12.7563 | 0.751671 | ||||||||
\(289\) | −16.5530 | −0.973705 | ||||||||
\(290\) | 2.27970 | 0.133869 | ||||||||
\(291\) | −20.6881 | −1.21276 | ||||||||
\(292\) | −13.3277 | −0.779945 | ||||||||
\(293\) | 5.66212 | 0.330785 | 0.165392 | − | 0.986228i | \(-0.447111\pi\) | ||||
0.165392 | + | 0.986228i | \(0.447111\pi\) | |||||||
\(294\) | 12.0577 | 0.703218 | ||||||||
\(295\) | −10.6495 | −0.620038 | ||||||||
\(296\) | −1.59122 | −0.0924878 | ||||||||
\(297\) | 13.3537 | 0.774862 | ||||||||
\(298\) | 24.9857 | 1.44738 | ||||||||
\(299\) | 11.7158 | 0.677543 | ||||||||
\(300\) | −10.4636 | −0.604115 | ||||||||
\(301\) | 9.00675 | 0.519140 | ||||||||
\(302\) | −36.9675 | −2.12724 | ||||||||
\(303\) | 23.4383 | 1.34649 | ||||||||
\(304\) | −20.6521 | −1.18448 | ||||||||
\(305\) | −11.6584 | −0.667559 | ||||||||
\(306\) | −2.37258 | −0.135631 | ||||||||
\(307\) | −19.2092 | −1.09632 | −0.548162 | − | 0.836372i | \(-0.684672\pi\) | ||||
−0.548162 | + | 0.836372i | \(0.684672\pi\) | |||||||
\(308\) | −15.4676 | −0.881350 | ||||||||
\(309\) | −21.7901 | −1.23959 | ||||||||
\(310\) | 12.4087 | 0.704768 | ||||||||
\(311\) | 6.41115 | 0.363543 | 0.181772 | − | 0.983341i | \(-0.441817\pi\) | ||||
0.181772 | + | 0.983341i | \(0.441817\pi\) | |||||||
\(312\) | −7.20638 | −0.407981 | ||||||||
\(313\) | 11.3444 | 0.641221 | 0.320611 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320611 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(314\) | 7.88201 | 0.444808 | ||||||||
\(315\) | 4.83478 | 0.272409 | ||||||||
\(316\) | −6.08968 | −0.342571 | ||||||||
\(317\) | −12.2839 | −0.689931 | −0.344966 | − | 0.938615i | \(-0.612109\pi\) | ||||
−0.344966 | + | 0.938615i | \(0.612109\pi\) | |||||||
\(318\) | −37.5208 | −2.10406 | ||||||||
\(319\) | 5.64415 | 0.316012 | ||||||||
\(320\) | −2.92662 | −0.163603 | ||||||||
\(321\) | 4.15752 | 0.232050 | ||||||||
\(322\) | 15.5443 | 0.866251 | ||||||||
\(323\) | 2.83645 | 0.157824 | ||||||||
\(324\) | −15.0800 | −0.837775 | ||||||||
\(325\) | 9.59896 | 0.532455 | ||||||||
\(326\) | 13.6574 | 0.756415 | ||||||||
\(327\) | −18.6322 | −1.03036 | ||||||||
\(328\) | 6.76749 | 0.373672 | ||||||||
\(329\) | −5.04695 | −0.278247 | ||||||||
\(330\) | 28.5837 | 1.57348 | ||||||||
\(331\) | −13.0588 | −0.717774 | −0.358887 | − | 0.933381i | \(-0.616844\pi\) | ||||
−0.358887 | + | 0.933381i | \(0.616844\pi\) | |||||||
\(332\) | 4.07700 | 0.223754 | ||||||||
\(333\) | −2.63712 | −0.144513 | ||||||||
\(334\) | 13.2394 | 0.724427 | ||||||||
\(335\) | −1.55222 | −0.0848069 | ||||||||
\(336\) | −21.7371 | −1.18586 | ||||||||
\(337\) | 2.95532 | 0.160987 | 0.0804933 | − | 0.996755i | \(-0.474350\pi\) | ||||
0.0804933 | + | 0.996755i | \(0.474350\pi\) | |||||||
\(338\) | 9.68383 | 0.526731 | ||||||||
\(339\) | −0.646763 | −0.0351274 | ||||||||
\(340\) | 1.13309 | 0.0614502 | ||||||||
\(341\) | 30.7219 | 1.66368 | ||||||||
\(342\) | −15.0549 | −0.814077 | ||||||||
\(343\) | −20.0195 | −1.08095 | ||||||||
\(344\) | 5.23156 | 0.282067 | ||||||||
\(345\) | −11.6441 | −0.626896 | ||||||||
\(346\) | 9.43466 | 0.507211 | ||||||||
\(347\) | −32.6814 | −1.75443 | −0.877216 | − | 0.480096i | \(-0.840602\pi\) | ||||
−0.877216 | + | 0.480096i | \(0.840602\pi\) | |||||||
\(348\) | −3.02870 | −0.162355 | ||||||||
\(349\) | −15.7430 | −0.842704 | −0.421352 | − | 0.906897i | \(-0.638444\pi\) | ||||
−0.421352 | + | 0.906897i | \(0.638444\pi\) | |||||||
\(350\) | 12.7357 | 0.680753 | ||||||||
\(351\) | 6.57361 | 0.350873 | ||||||||
\(352\) | −37.2091 | −1.98325 | ||||||||
\(353\) | 33.0831 | 1.76084 | 0.880419 | − | 0.474197i | \(-0.157262\pi\) | ||||
0.880419 | + | 0.474197i | \(0.157262\pi\) | |||||||
\(354\) | 34.9034 | 1.85510 | ||||||||
\(355\) | 0.905313 | 0.0480490 | ||||||||
\(356\) | −9.56339 | −0.506859 | ||||||||
\(357\) | 2.98547 | 0.158008 | ||||||||
\(358\) | −29.1806 | −1.54224 | ||||||||
\(359\) | 19.6864 | 1.03901 | 0.519505 | − | 0.854468i | \(-0.326117\pi\) | ||||
0.519505 | + | 0.854468i | \(0.326117\pi\) | |||||||
\(360\) | 2.80828 | 0.148009 | ||||||||
\(361\) | −1.00161 | −0.0527165 | ||||||||
\(362\) | −31.5302 | −1.65719 | ||||||||
\(363\) | 46.3322 | 2.43181 | ||||||||
\(364\) | −7.61421 | −0.399093 | ||||||||
\(365\) | −12.1516 | −0.636042 | ||||||||
\(366\) | 38.2101 | 1.99728 | ||||||||
\(367\) | 33.4889 | 1.74810 | 0.874052 | − | 0.485832i | \(-0.161483\pi\) | ||||
0.874052 | + | 0.485832i | \(0.161483\pi\) | |||||||
\(368\) | 20.5267 | 1.07003 | ||||||||
\(369\) | 11.2157 | 0.583867 | ||||||||
\(370\) | 3.10694 | 0.161522 | ||||||||
\(371\) | 18.5120 | 0.961096 | ||||||||
\(372\) | −16.4856 | −0.854739 | ||||||||
\(373\) | −29.0100 | −1.50208 | −0.751041 | − | 0.660256i | \(-0.770448\pi\) | ||||
−0.751041 | + | 0.660256i | \(0.770448\pi\) | |||||||
\(374\) | 6.92061 | 0.357856 | ||||||||
\(375\) | −23.3473 | −1.20565 | ||||||||
\(376\) | −2.93152 | −0.151181 | ||||||||
\(377\) | 2.77843 | 0.143097 | ||||||||
\(378\) | 8.72174 | 0.448598 | ||||||||
\(379\) | −13.5860 | −0.697865 | −0.348933 | − | 0.937148i | \(-0.613456\pi\) | ||||
−0.348933 | + | 0.937148i | \(0.613456\pi\) | |||||||
\(380\) | 7.18986 | 0.368832 | ||||||||
\(381\) | 6.04012 | 0.309445 | ||||||||
\(382\) | 35.7486 | 1.82906 | ||||||||
\(383\) | 2.55541 | 0.130576 | 0.0652878 | − | 0.997866i | \(-0.479203\pi\) | ||||
0.0652878 | + | 0.997866i | \(0.479203\pi\) | |||||||
\(384\) | −19.6983 | −1.00522 | ||||||||
\(385\) | −14.1027 | −0.718738 | ||||||||
\(386\) | 22.9415 | 1.16769 | ||||||||
\(387\) | 8.67022 | 0.440732 | ||||||||
\(388\) | −12.6967 | −0.644580 | ||||||||
\(389\) | 26.1040 | 1.32352 | 0.661762 | − | 0.749714i | \(-0.269809\pi\) | ||||
0.661762 | + | 0.749714i | \(0.269809\pi\) | |||||||
\(390\) | 14.0708 | 0.712504 | ||||||||
\(391\) | −2.81923 | −0.142575 | ||||||||
\(392\) | −3.45549 | −0.174528 | ||||||||
\(393\) | −3.24498 | −0.163688 | ||||||||
\(394\) | −34.9747 | −1.76200 | ||||||||
\(395\) | −5.55228 | −0.279366 | ||||||||
\(396\) | −14.8897 | −0.748236 | ||||||||
\(397\) | −24.5293 | −1.23109 | −0.615545 | − | 0.788102i | \(-0.711064\pi\) | ||||
−0.615545 | + | 0.788102i | \(0.711064\pi\) | |||||||
\(398\) | 19.3246 | 0.968654 | ||||||||
\(399\) | 18.9440 | 0.948384 | ||||||||
\(400\) | 16.8179 | 0.840895 | ||||||||
\(401\) | −14.0012 | −0.699188 | −0.349594 | − | 0.936901i | \(-0.613681\pi\) | ||||
−0.349594 | + | 0.936901i | \(0.613681\pi\) | |||||||
\(402\) | 5.08736 | 0.253734 | ||||||||
\(403\) | 15.1234 | 0.753349 | ||||||||
\(404\) | 14.3846 | 0.715659 | ||||||||
\(405\) | −13.7492 | −0.683203 | ||||||||
\(406\) | 3.68637 | 0.182952 | ||||||||
\(407\) | 7.69226 | 0.381291 | ||||||||
\(408\) | 1.73411 | 0.0858511 | ||||||||
\(409\) | 9.37308 | 0.463469 | 0.231735 | − | 0.972779i | \(-0.425560\pi\) | ||||
0.231735 | + | 0.972779i | \(0.425560\pi\) | |||||||
\(410\) | −13.2139 | −0.652587 | ||||||||
\(411\) | 12.5624 | 0.619658 | ||||||||
\(412\) | −13.3730 | −0.658841 | ||||||||
\(413\) | −17.2207 | −0.847374 | ||||||||
\(414\) | 14.9635 | 0.735417 | ||||||||
\(415\) | 3.71722 | 0.182471 | ||||||||
\(416\) | −18.3168 | −0.898055 | ||||||||
\(417\) | −2.22148 | −0.108786 | ||||||||
\(418\) | 43.9140 | 2.14790 | ||||||||
\(419\) | 1.38486 | 0.0676548 | 0.0338274 | − | 0.999428i | \(-0.489230\pi\) | ||||
0.0338274 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(420\) | 7.56760 | 0.369261 | ||||||||
\(421\) | −33.1640 | −1.61631 | −0.808157 | − | 0.588967i | \(-0.799535\pi\) | ||||
−0.808157 | + | 0.588967i | \(0.799535\pi\) | |||||||
\(422\) | −1.69116 | −0.0823245 | ||||||||
\(423\) | −4.85838 | −0.236223 | ||||||||
\(424\) | 10.7527 | 0.522197 | ||||||||
\(425\) | −2.30985 | −0.112044 | ||||||||
\(426\) | −2.96714 | −0.143758 | ||||||||
\(427\) | −18.8521 | −0.912319 | ||||||||
\(428\) | 2.55156 | 0.123334 | ||||||||
\(429\) | 34.8370 | 1.68195 | ||||||||
\(430\) | −10.2149 | −0.492606 | ||||||||
\(431\) | −1.17561 | −0.0566270 | −0.0283135 | − | 0.999599i | \(-0.509014\pi\) | ||||
−0.0283135 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(432\) | 11.5173 | 0.554127 | ||||||||
\(433\) | −10.3946 | −0.499532 | −0.249766 | − | 0.968306i | \(-0.580354\pi\) | ||||
−0.249766 | + | 0.968306i | \(0.580354\pi\) | |||||||
\(434\) | 20.0654 | 0.963171 | ||||||||
\(435\) | −2.76142 | −0.132400 | ||||||||
\(436\) | −11.4350 | −0.547637 | ||||||||
\(437\) | −17.8891 | −0.855753 | ||||||||
\(438\) | 39.8264 | 1.90298 | ||||||||
\(439\) | 11.8005 | 0.563206 | 0.281603 | − | 0.959531i | \(-0.409134\pi\) | ||||
0.281603 | + | 0.959531i | \(0.409134\pi\) | |||||||
\(440\) | −8.19152 | −0.390515 | ||||||||
\(441\) | −5.72675 | −0.272702 | ||||||||
\(442\) | 3.40679 | 0.162045 | ||||||||
\(443\) | −18.0992 | −0.859918 | −0.429959 | − | 0.902848i | \(-0.641472\pi\) | ||||
−0.429959 | + | 0.902848i | \(0.641472\pi\) | |||||||
\(444\) | −4.12772 | −0.195893 | ||||||||
\(445\) | −8.71945 | −0.413342 | ||||||||
\(446\) | −27.5768 | −1.30580 | ||||||||
\(447\) | −30.2654 | −1.43150 | ||||||||
\(448\) | −4.73247 | −0.223588 | ||||||||
\(449\) | 39.4251 | 1.86059 | 0.930293 | − | 0.366818i | \(-0.119553\pi\) | ||||
0.930293 | + | 0.366818i | \(0.119553\pi\) | |||||||
\(450\) | 12.2599 | 0.577936 | ||||||||
\(451\) | −32.7153 | −1.54050 | ||||||||
\(452\) | −0.396932 | −0.0186701 | ||||||||
\(453\) | 44.7791 | 2.10391 | ||||||||
\(454\) | 7.12653 | 0.334465 | ||||||||
\(455\) | −6.94228 | −0.325459 | ||||||||
\(456\) | 11.0036 | 0.515290 | ||||||||
\(457\) | 8.62277 | 0.403356 | 0.201678 | − | 0.979452i | \(-0.435361\pi\) | ||||
0.201678 | + | 0.979452i | \(0.435361\pi\) | |||||||
\(458\) | −21.6118 | −1.00985 | ||||||||
\(459\) | −1.58184 | −0.0738340 | ||||||||
\(460\) | −7.14622 | −0.333194 | ||||||||
\(461\) | −35.4156 | −1.64947 | −0.824734 | − | 0.565521i | \(-0.808675\pi\) | ||||
−0.824734 | + | 0.565521i | \(0.808675\pi\) | |||||||
\(462\) | 46.2211 | 2.15040 | ||||||||
\(463\) | −24.5238 | −1.13972 | −0.569859 | − | 0.821743i | \(-0.693002\pi\) | ||||
−0.569859 | + | 0.821743i | \(0.693002\pi\) | |||||||
\(464\) | 4.86796 | 0.225990 | ||||||||
\(465\) | −15.0308 | −0.697037 | ||||||||
\(466\) | −22.6485 | −1.04917 | ||||||||
\(467\) | 31.9863 | 1.48015 | 0.740075 | − | 0.672525i | \(-0.234790\pi\) | ||||
0.740075 | + | 0.672525i | \(0.234790\pi\) | |||||||
\(468\) | −7.32972 | −0.338816 | ||||||||
\(469\) | −2.51001 | −0.115901 | ||||||||
\(470\) | 5.72394 | 0.264026 | ||||||||
\(471\) | −9.54755 | −0.439928 | ||||||||
\(472\) | −10.0026 | −0.460408 | ||||||||
\(473\) | −25.2903 | −1.16285 | ||||||||
\(474\) | 18.1974 | 0.835836 | ||||||||
\(475\) | −14.6569 | −0.672503 | ||||||||
\(476\) | 1.83225 | 0.0839809 | ||||||||
\(477\) | 17.8204 | 0.815938 | ||||||||
\(478\) | −43.8802 | −2.00703 | ||||||||
\(479\) | 11.1474 | 0.509337 | 0.254669 | − | 0.967028i | \(-0.418034\pi\) | ||||
0.254669 | + | 0.967028i | \(0.418034\pi\) | |||||||
\(480\) | 18.2047 | 0.830926 | ||||||||
\(481\) | 3.78665 | 0.172656 | ||||||||
\(482\) | −18.8505 | −0.858617 | ||||||||
\(483\) | −18.8290 | −0.856748 | ||||||||
\(484\) | 28.4350 | 1.29250 | ||||||||
\(485\) | −11.5763 | −0.525653 | ||||||||
\(486\) | 32.0455 | 1.45361 | ||||||||
\(487\) | −16.3167 | −0.739381 | −0.369691 | − | 0.929155i | \(-0.620536\pi\) | ||||
−0.369691 | + | 0.929155i | \(0.620536\pi\) | |||||||
\(488\) | −10.9503 | −0.495695 | ||||||||
\(489\) | −16.5434 | −0.748117 | ||||||||
\(490\) | 6.74702 | 0.304799 | ||||||||
\(491\) | 9.01831 | 0.406990 | 0.203495 | − | 0.979076i | \(-0.434770\pi\) | ||||
0.203495 | + | 0.979076i | \(0.434770\pi\) | |||||||
\(492\) | 17.5553 | 0.791454 | ||||||||
\(493\) | −0.668588 | −0.0301117 | ||||||||
\(494\) | 21.6174 | 0.972614 | ||||||||
\(495\) | −13.5757 | −0.610184 | ||||||||
\(496\) | 26.4970 | 1.18975 | ||||||||
\(497\) | 1.46393 | 0.0656662 | ||||||||
\(498\) | −12.1831 | −0.545936 | ||||||||
\(499\) | −15.3650 | −0.687832 | −0.343916 | − | 0.939000i | \(-0.611754\pi\) | ||||
−0.343916 | + | 0.939000i | \(0.611754\pi\) | |||||||
\(500\) | −14.3287 | −0.640801 | ||||||||
\(501\) | −16.0370 | −0.716479 | ||||||||
\(502\) | 1.04451 | 0.0466187 | ||||||||
\(503\) | 3.02824 | 0.135023 | 0.0675114 | − | 0.997719i | \(-0.478494\pi\) | ||||
0.0675114 | + | 0.997719i | \(0.478494\pi\) | |||||||
\(504\) | 4.54110 | 0.202277 | ||||||||
\(505\) | 13.1152 | 0.583618 | ||||||||
\(506\) | −43.6474 | −1.94036 | ||||||||
\(507\) | −11.7301 | −0.520952 | ||||||||
\(508\) | 3.70695 | 0.164469 | ||||||||
\(509\) | −18.3653 | −0.814026 | −0.407013 | − | 0.913422i | \(-0.633430\pi\) | ||||
−0.407013 | + | 0.913422i | \(0.633430\pi\) | |||||||
\(510\) | −3.38594 | −0.149932 | ||||||||
\(511\) | −19.6496 | −0.869247 | ||||||||
\(512\) | −20.7249 | −0.915918 | ||||||||
\(513\) | −10.0374 | −0.443162 | ||||||||
\(514\) | −5.10108 | −0.224999 | ||||||||
\(515\) | −12.1929 | −0.537283 | ||||||||
\(516\) | 13.5710 | 0.597430 | ||||||||
\(517\) | 14.1715 | 0.623262 | ||||||||
\(518\) | 5.02405 | 0.220744 | ||||||||
\(519\) | −11.4283 | −0.501646 | ||||||||
\(520\) | −4.03242 | −0.176833 | ||||||||
\(521\) | 21.7085 | 0.951066 | 0.475533 | − | 0.879698i | \(-0.342255\pi\) | ||||
0.475533 | + | 0.879698i | \(0.342255\pi\) | |||||||
\(522\) | 3.54864 | 0.155320 | ||||||||
\(523\) | 4.98493 | 0.217976 | 0.108988 | − | 0.994043i | \(-0.465239\pi\) | ||||
0.108988 | + | 0.994043i | \(0.465239\pi\) | |||||||
\(524\) | −1.99151 | −0.0869996 | ||||||||
\(525\) | −15.4269 | −0.673285 | ||||||||
\(526\) | 39.4223 | 1.71890 | ||||||||
\(527\) | −3.63922 | −0.158527 | ||||||||
\(528\) | 61.0363 | 2.65626 | ||||||||
\(529\) | −5.21946 | −0.226933 | ||||||||
\(530\) | −20.9952 | −0.911973 | ||||||||
\(531\) | −16.5773 | −0.719392 | ||||||||
\(532\) | 11.6263 | 0.504065 | ||||||||
\(533\) | −16.1047 | −0.697572 | ||||||||
\(534\) | 28.5777 | 1.23668 | ||||||||
\(535\) | 2.32639 | 0.100579 | ||||||||
\(536\) | −1.45794 | −0.0629732 | ||||||||
\(537\) | 35.3467 | 1.52532 | ||||||||
\(538\) | −14.0491 | −0.605702 | ||||||||
\(539\) | 16.7045 | 0.719513 | ||||||||
\(540\) | −4.00966 | −0.172548 | ||||||||
\(541\) | 6.47617 | 0.278432 | 0.139216 | − | 0.990262i | \(-0.455542\pi\) | ||||
0.139216 | + | 0.990262i | \(0.455542\pi\) | |||||||
\(542\) | −54.4348 | −2.33818 | ||||||||
\(543\) | 38.1929 | 1.63901 | ||||||||
\(544\) | 4.40767 | 0.188977 | ||||||||
\(545\) | −10.4259 | −0.446596 | ||||||||
\(546\) | 22.7531 | 0.973744 | ||||||||
\(547\) | −26.3303 | −1.12580 | −0.562901 | − | 0.826524i | \(-0.690315\pi\) | ||||
−0.562901 | + | 0.826524i | \(0.690315\pi\) | |||||||
\(548\) | 7.70981 | 0.329347 | ||||||||
\(549\) | −18.1478 | −0.774528 | ||||||||
\(550\) | −35.7611 | −1.52486 | ||||||||
\(551\) | −4.24245 | −0.180734 | ||||||||
\(552\) | −10.9368 | −0.465501 | ||||||||
\(553\) | −8.97827 | −0.381795 | ||||||||
\(554\) | 47.3283 | 2.01079 | ||||||||
\(555\) | −3.76347 | −0.159750 | ||||||||
\(556\) | −1.36337 | −0.0578197 | ||||||||
\(557\) | −31.9958 | −1.35570 | −0.677852 | − | 0.735199i | \(-0.737089\pi\) | ||||
−0.677852 | + | 0.735199i | \(0.737089\pi\) | |||||||
\(558\) | 19.3157 | 0.817699 | ||||||||
\(559\) | −12.4496 | −0.526563 | ||||||||
\(560\) | −12.1633 | −0.513991 | ||||||||
\(561\) | −8.38300 | −0.353931 | ||||||||
\(562\) | −7.67186 | −0.323618 | ||||||||
\(563\) | −3.91721 | −0.165091 | −0.0825453 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825453 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(564\) | −7.60454 | −0.320209 | ||||||||
\(565\) | −0.361904 | −0.0152254 | ||||||||
\(566\) | −20.7607 | −0.872637 | ||||||||
\(567\) | −22.2330 | −0.933699 | ||||||||
\(568\) | 0.850322 | 0.0356787 | ||||||||
\(569\) | −14.6616 | −0.614645 | −0.307322 | − | 0.951605i | \(-0.599433\pi\) | ||||
−0.307322 | + | 0.951605i | \(0.599433\pi\) | |||||||
\(570\) | −21.4851 | −0.899911 | ||||||||
\(571\) | 22.3749 | 0.936362 | 0.468181 | − | 0.883633i | \(-0.344910\pi\) | ||||
0.468181 | + | 0.883633i | \(0.344910\pi\) | |||||||
\(572\) | 21.3802 | 0.893951 | ||||||||
\(573\) | −43.3027 | −1.80899 | ||||||||
\(574\) | −21.3674 | −0.891858 | ||||||||
\(575\) | 14.5679 | 0.607523 | ||||||||
\(576\) | −4.55565 | −0.189819 | ||||||||
\(577\) | 45.6063 | 1.89861 | 0.949307 | − | 0.314351i | \(-0.101787\pi\) | ||||
0.949307 | + | 0.314351i | \(0.101787\pi\) | |||||||
\(578\) | 30.3573 | 1.26270 | ||||||||
\(579\) | −27.7892 | −1.15488 | ||||||||
\(580\) | −1.69474 | −0.0703704 | ||||||||
\(581\) | 6.01089 | 0.249374 | ||||||||
\(582\) | 37.9410 | 1.57270 | ||||||||
\(583\) | −51.9805 | −2.15281 | ||||||||
\(584\) | −11.4135 | −0.472292 | ||||||||
\(585\) | −6.68290 | −0.276304 | ||||||||
\(586\) | −10.3840 | −0.428961 | ||||||||
\(587\) | −35.4247 | −1.46213 | −0.731067 | − | 0.682305i | \(-0.760977\pi\) | ||||
−0.731067 | + | 0.682305i | \(0.760977\pi\) | |||||||
\(588\) | −8.96375 | −0.369659 | ||||||||
\(589\) | −23.0922 | −0.951499 | ||||||||
\(590\) | 19.5306 | 0.804063 | ||||||||
\(591\) | 42.3652 | 1.74267 | ||||||||
\(592\) | 6.63441 | 0.272673 | ||||||||
\(593\) | 1.00484 | 0.0412636 | 0.0206318 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206318 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(594\) | −24.4901 | −1.00484 | ||||||||
\(595\) | 1.67056 | 0.0684861 | ||||||||
\(596\) | −18.5745 | −0.760841 | ||||||||
\(597\) | −23.4080 | −0.958028 | ||||||||
\(598\) | −21.4862 | −0.878636 | ||||||||
\(599\) | 41.4102 | 1.69197 | 0.845987 | − | 0.533203i | \(-0.179012\pi\) | ||||
0.845987 | + | 0.533203i | \(0.179012\pi\) | |||||||
\(600\) | −8.96070 | −0.365819 | ||||||||
\(601\) | −32.0025 | −1.30541 | −0.652704 | − | 0.757613i | \(-0.726365\pi\) | ||||
−0.652704 | + | 0.757613i | \(0.726365\pi\) | |||||||
\(602\) | −16.5179 | −0.673220 | ||||||||
\(603\) | −2.41622 | −0.0983963 | ||||||||
\(604\) | 27.4819 | 1.11822 | ||||||||
\(605\) | 25.9257 | 1.05403 | ||||||||
\(606\) | −42.9846 | −1.74613 | ||||||||
\(607\) | −2.93277 | −0.119037 | −0.0595187 | − | 0.998227i | \(-0.518957\pi\) | ||||
−0.0595187 | + | 0.998227i | \(0.518957\pi\) | |||||||
\(608\) | 27.9683 | 1.13427 | ||||||||
\(609\) | −4.46534 | −0.180945 | ||||||||
\(610\) | 21.3809 | 0.865689 | ||||||||
\(611\) | 6.97617 | 0.282226 | ||||||||
\(612\) | 1.76379 | 0.0712969 | ||||||||
\(613\) | −35.3141 | −1.42632 | −0.713162 | − | 0.700999i | \(-0.752738\pi\) | ||||
−0.713162 | + | 0.700999i | \(0.752738\pi\) | |||||||
\(614\) | 35.2286 | 1.42171 | ||||||||
\(615\) | 16.0061 | 0.645428 | ||||||||
\(616\) | −13.2460 | −0.533698 | ||||||||
\(617\) | −19.1939 | −0.772718 | −0.386359 | − | 0.922348i | \(-0.626267\pi\) | ||||
−0.386359 | + | 0.922348i | \(0.626267\pi\) | |||||||
\(618\) | 39.9618 | 1.60750 | ||||||||
\(619\) | −10.1164 | −0.406611 | −0.203306 | − | 0.979115i | \(-0.565168\pi\) | ||||
−0.203306 | + | 0.979115i | \(0.565168\pi\) | |||||||
\(620\) | −9.22472 | −0.370474 | ||||||||
\(621\) | 9.97646 | 0.400342 | ||||||||
\(622\) | −11.7577 | −0.471442 | ||||||||
\(623\) | −14.0997 | −0.564893 | ||||||||
\(624\) | 30.0462 | 1.20281 | ||||||||
\(625\) | 4.20979 | 0.168392 | ||||||||
\(626\) | −20.8050 | −0.831534 | ||||||||
\(627\) | −53.1934 | −2.12434 | ||||||||
\(628\) | −5.85954 | −0.233821 | ||||||||
\(629\) | −0.911200 | −0.0363319 | ||||||||
\(630\) | −8.86674 | −0.353259 | ||||||||
\(631\) | −30.4959 | −1.21402 | −0.607011 | − | 0.794694i | \(-0.707632\pi\) | ||||
−0.607011 | + | 0.794694i | \(0.707632\pi\) | |||||||
\(632\) | −5.21502 | −0.207442 | ||||||||
\(633\) | 2.04852 | 0.0814213 | ||||||||
\(634\) | 22.5280 | 0.894701 | ||||||||
\(635\) | 3.37982 | 0.134124 | ||||||||
\(636\) | 27.8932 | 1.10604 | ||||||||
\(637\) | 8.22307 | 0.325810 | ||||||||
\(638\) | −10.3511 | −0.409803 | ||||||||
\(639\) | 1.40923 | 0.0557484 | ||||||||
\(640\) | −11.0224 | −0.435699 | ||||||||
\(641\) | 28.8594 | 1.13988 | 0.569938 | − | 0.821688i | \(-0.306967\pi\) | ||||
0.569938 | + | 0.821688i | \(0.306967\pi\) | |||||||
\(642\) | −7.62468 | −0.300922 | ||||||||
\(643\) | 15.3497 | 0.605334 | 0.302667 | − | 0.953096i | \(-0.402123\pi\) | ||||
0.302667 | + | 0.953096i | \(0.402123\pi\) | |||||||
\(644\) | −11.5557 | −0.455360 | ||||||||
\(645\) | 12.3734 | 0.487202 | ||||||||
\(646\) | −5.20191 | −0.204666 | ||||||||
\(647\) | −36.9647 | −1.45323 | −0.726615 | − | 0.687045i | \(-0.758908\pi\) | ||||
−0.726615 | + | 0.687045i | \(0.758908\pi\) | |||||||
\(648\) | −12.9140 | −0.507311 | ||||||||
\(649\) | 48.3545 | 1.89808 | ||||||||
\(650\) | −17.6040 | −0.690486 | ||||||||
\(651\) | −24.3054 | −0.952605 | ||||||||
\(652\) | −10.1530 | −0.397623 | ||||||||
\(653\) | 41.4900 | 1.62363 | 0.811815 | − | 0.583914i | \(-0.198480\pi\) | ||||
0.811815 | + | 0.583914i | \(0.198480\pi\) | |||||||
\(654\) | 34.1706 | 1.33617 | ||||||||
\(655\) | −1.81577 | −0.0709479 | ||||||||
\(656\) | −28.2163 | −1.10166 | ||||||||
\(657\) | −18.9154 | −0.737961 | ||||||||
\(658\) | 9.25585 | 0.360831 | ||||||||
\(659\) | 44.7917 | 1.74484 | 0.872418 | − | 0.488760i | \(-0.162551\pi\) | ||||
0.872418 | + | 0.488760i | \(0.162551\pi\) | |||||||
\(660\) | −21.2493 | −0.827128 | ||||||||
\(661\) | −0.574409 | −0.0223419 | −0.0111710 | − | 0.999938i | \(-0.503556\pi\) | ||||
−0.0111710 | + | 0.999938i | \(0.503556\pi\) | |||||||
\(662\) | 23.9491 | 0.930808 | ||||||||
\(663\) | −4.12668 | −0.160267 | ||||||||
\(664\) | 3.49142 | 0.135493 | ||||||||
\(665\) | 10.6003 | 0.411063 | ||||||||
\(666\) | 4.83634 | 0.187404 | ||||||||
\(667\) | 4.21670 | 0.163271 | ||||||||
\(668\) | −9.84223 | −0.380807 | ||||||||
\(669\) | 33.4041 | 1.29148 | ||||||||
\(670\) | 2.84669 | 0.109977 | ||||||||
\(671\) | 52.9356 | 2.04356 | ||||||||
\(672\) | 29.4377 | 1.13558 | ||||||||
\(673\) | 26.8878 | 1.03645 | 0.518225 | − | 0.855245i | \(-0.326593\pi\) | ||||
0.518225 | + | 0.855245i | \(0.326593\pi\) | |||||||
\(674\) | −5.41991 | −0.208767 | ||||||||
\(675\) | 8.17389 | 0.314613 | ||||||||
\(676\) | −7.19902 | −0.276885 | ||||||||
\(677\) | −45.8867 | −1.76357 | −0.881785 | − | 0.471651i | \(-0.843658\pi\) | ||||
−0.881785 | + | 0.471651i | \(0.843658\pi\) | |||||||
\(678\) | 1.18613 | 0.0455531 | ||||||||
\(679\) | −18.7194 | −0.718383 | ||||||||
\(680\) | 0.970341 | 0.0372109 | ||||||||
\(681\) | −8.63243 | −0.330795 | ||||||||
\(682\) | −56.3424 | −2.15746 | ||||||||
\(683\) | −29.3011 | −1.12118 | −0.560588 | − | 0.828095i | \(-0.689425\pi\) | ||||
−0.560588 | + | 0.828095i | \(0.689425\pi\) | |||||||
\(684\) | 11.1919 | 0.427934 | ||||||||
\(685\) | 7.02945 | 0.268581 | ||||||||
\(686\) | 36.7148 | 1.40178 | ||||||||
\(687\) | 26.1786 | 0.998775 | ||||||||
\(688\) | −21.8124 | −0.831590 | ||||||||
\(689\) | −25.5883 | −0.974838 | ||||||||
\(690\) | 21.3547 | 0.812958 | ||||||||
\(691\) | 9.87689 | 0.375735 | 0.187867 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187867 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(692\) | −7.01378 | −0.266624 | ||||||||
\(693\) | −21.9525 | −0.833908 | ||||||||
\(694\) | 59.9361 | 2.27514 | ||||||||
\(695\) | −1.24306 | −0.0471518 | ||||||||
\(696\) | −2.59369 | −0.0983134 | ||||||||
\(697\) | 3.87535 | 0.146789 | ||||||||
\(698\) | 28.8719 | 1.09282 | ||||||||
\(699\) | 27.4343 | 1.03766 | ||||||||
\(700\) | −9.46781 | −0.357850 | ||||||||
\(701\) | 8.23788 | 0.311140 | 0.155570 | − | 0.987825i | \(-0.450279\pi\) | ||||
0.155570 | + | 0.987825i | \(0.450279\pi\) | |||||||
\(702\) | −12.0557 | −0.455012 | ||||||||
\(703\) | −5.78192 | −0.218069 | ||||||||
\(704\) | 13.2885 | 0.500828 | ||||||||
\(705\) | −6.93346 | −0.261129 | ||||||||
\(706\) | −60.6728 | −2.28345 | ||||||||
\(707\) | 21.2078 | 0.797601 | ||||||||
\(708\) | −25.9474 | −0.975164 | ||||||||
\(709\) | −30.7693 | −1.15557 | −0.577783 | − | 0.816190i | \(-0.696082\pi\) | ||||
−0.577783 | + | 0.816190i | \(0.696082\pi\) | |||||||
\(710\) | −1.66030 | −0.0623099 | ||||||||
\(711\) | −8.64281 | −0.324131 | ||||||||
\(712\) | −8.18981 | −0.306926 | ||||||||
\(713\) | 22.9521 | 0.859561 | ||||||||
\(714\) | −5.47520 | −0.204904 | ||||||||
\(715\) | 19.4935 | 0.729014 | ||||||||
\(716\) | 21.6930 | 0.810707 | ||||||||
\(717\) | 53.1525 | 1.98501 | ||||||||
\(718\) | −36.1039 | −1.34738 | ||||||||
\(719\) | −5.42888 | −0.202463 | −0.101231 | − | 0.994863i | \(-0.532278\pi\) | ||||
−0.101231 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(720\) | −11.7088 | −0.436361 | ||||||||
\(721\) | −19.7164 | −0.734278 | ||||||||
\(722\) | 1.83691 | 0.0683627 | ||||||||
\(723\) | 22.8338 | 0.849198 | ||||||||
\(724\) | 23.4398 | 0.871132 | ||||||||
\(725\) | 3.45481 | 0.128309 | ||||||||
\(726\) | −84.9708 | −3.15356 | ||||||||
\(727\) | −10.3202 | −0.382754 | −0.191377 | − | 0.981517i | \(-0.561295\pi\) | ||||
−0.191377 | + | 0.981517i | \(0.561295\pi\) | |||||||
\(728\) | −6.52059 | −0.241669 | ||||||||
\(729\) | −5.63465 | −0.208691 | ||||||||
\(730\) | 22.2854 | 0.824818 | ||||||||
\(731\) | 2.99581 | 0.110804 | ||||||||
\(732\) | −28.4056 | −1.04990 | ||||||||
\(733\) | 0.0447480 | 0.00165280 | 0.000826402 | − | 1.00000i | \(-0.499737\pi\) | ||||
0.000826402 | 1.00000i | \(0.499737\pi\) | ||||||||
\(734\) | −61.4169 | −2.26694 | ||||||||
\(735\) | −8.17273 | −0.301456 | ||||||||
\(736\) | −27.7986 | −1.02467 | ||||||||
\(737\) | 7.04793 | 0.259614 | ||||||||
\(738\) | −20.5690 | −0.757157 | ||||||||
\(739\) | 38.5738 | 1.41896 | 0.709480 | − | 0.704725i | \(-0.248930\pi\) | ||||
0.709480 | + | 0.704725i | \(0.248930\pi\) | |||||||
\(740\) | −2.30972 | −0.0849069 | ||||||||
\(741\) | −26.1854 | −0.961944 | ||||||||
\(742\) | −33.9501 | −1.24635 | ||||||||
\(743\) | 39.8310 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239227\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239227\pi\) | |||||||
\(744\) | −14.1178 | −0.517583 | ||||||||
\(745\) | −16.9354 | −0.620464 | ||||||||
\(746\) | 53.2029 | 1.94790 | ||||||||
\(747\) | 5.78631 | 0.211710 | ||||||||
\(748\) | −5.14483 | −0.188113 | ||||||||
\(749\) | 3.76187 | 0.137456 | ||||||||
\(750\) | 42.8178 | 1.56348 | ||||||||
\(751\) | −30.2442 | −1.10363 | −0.551813 | − | 0.833968i | \(-0.686064\pi\) | ||||
−0.551813 | + | 0.833968i | \(0.686064\pi\) | |||||||
\(752\) | 12.2226 | 0.445713 | ||||||||
\(753\) | −1.26522 | −0.0461073 | ||||||||
\(754\) | −5.09550 | −0.185567 | ||||||||
\(755\) | 25.0567 | 0.911907 | ||||||||
\(756\) | −6.48379 | −0.235813 | ||||||||
\(757\) | 51.6913 | 1.87875 | 0.939377 | − | 0.342887i | \(-0.111405\pi\) | ||||
0.939377 | + | 0.342887i | \(0.111405\pi\) | |||||||
\(758\) | 24.9160 | 0.904990 | ||||||||
\(759\) | 52.8705 | 1.91908 | ||||||||
\(760\) | 6.15719 | 0.223345 | ||||||||
\(761\) | −4.69002 | −0.170013 | −0.0850066 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850066 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(762\) | −11.0773 | −0.401287 | ||||||||
\(763\) | −16.8591 | −0.610340 | ||||||||
\(764\) | −26.5758 | −0.961477 | ||||||||
\(765\) | 1.60814 | 0.0581424 | ||||||||
\(766\) | −4.68650 | −0.169330 | ||||||||
\(767\) | 23.8034 | 0.859490 | ||||||||
\(768\) | 46.5860 | 1.68103 | ||||||||
\(769\) | −26.4507 | −0.953835 | −0.476917 | − | 0.878948i | \(-0.658246\pi\) | ||||
−0.476917 | + | 0.878948i | \(0.658246\pi\) | |||||||
\(770\) | 25.8636 | 0.932058 | ||||||||
\(771\) | 6.17898 | 0.222531 | ||||||||
\(772\) | −17.0548 | −0.613817 | ||||||||
\(773\) | −6.88315 | −0.247570 | −0.123785 | − | 0.992309i | \(-0.539503\pi\) | ||||
−0.123785 | + | 0.992309i | \(0.539503\pi\) | |||||||
\(774\) | −15.9007 | −0.571541 | ||||||||
\(775\) | 18.8050 | 0.675496 | ||||||||
\(776\) | −10.8731 | −0.390322 | ||||||||
\(777\) | −6.08568 | −0.218323 | ||||||||
\(778\) | −47.8733 | −1.71634 | ||||||||
\(779\) | 24.5906 | 0.881050 | ||||||||
\(780\) | −10.4603 | −0.374540 | ||||||||
\(781\) | −4.11062 | −0.147089 | ||||||||
\(782\) | 5.17033 | 0.184891 | ||||||||
\(783\) | 2.36594 | 0.0845519 | ||||||||
\(784\) | 14.4073 | 0.514545 | ||||||||
\(785\) | −5.34245 | −0.190680 | ||||||||
\(786\) | 5.95113 | 0.212270 | ||||||||
\(787\) | −2.82562 | −0.100722 | −0.0503612 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503612 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(788\) | 26.0004 | 0.926227 | ||||||||
\(789\) | −47.7526 | −1.70004 | ||||||||
\(790\) | 10.1826 | 0.362281 | ||||||||
\(791\) | −0.585214 | −0.0208078 | ||||||||
\(792\) | −12.7511 | −0.453091 | ||||||||
\(793\) | 26.0585 | 0.925363 | ||||||||
\(794\) | 44.9854 | 1.59647 | ||||||||
\(795\) | 25.4317 | 0.901969 | ||||||||
\(796\) | −14.3660 | −0.509190 | ||||||||
\(797\) | 15.2976 | 0.541868 | 0.270934 | − | 0.962598i | \(-0.412668\pi\) | ||||
0.270934 | + | 0.962598i | \(0.412668\pi\) | |||||||
\(798\) | −34.7423 | −1.22986 | ||||||||
\(799\) | −1.67871 | −0.0593885 | ||||||||
\(800\) | −22.7758 | −0.805248 | ||||||||
\(801\) | −13.5729 | −0.479575 | ||||||||
\(802\) | 25.6776 | 0.906706 | ||||||||
\(803\) | 55.1748 | 1.94708 | ||||||||
\(804\) | −3.78197 | −0.133380 | ||||||||
\(805\) | −10.5360 | −0.371344 | ||||||||
\(806\) | −27.7355 | −0.976942 | ||||||||
\(807\) | 17.0179 | 0.599057 | ||||||||
\(808\) | 12.3185 | 0.433364 | ||||||||
\(809\) | −19.0327 | −0.669154 | −0.334577 | − | 0.942368i | \(-0.608593\pi\) | ||||
−0.334577 | + | 0.942368i | \(0.608593\pi\) | |||||||
\(810\) | 25.2153 | 0.885976 | ||||||||
\(811\) | 23.2544 | 0.816574 | 0.408287 | − | 0.912854i | \(-0.366126\pi\) | ||||
0.408287 | + | 0.912854i | \(0.366126\pi\) | |||||||
\(812\) | −2.74047 | −0.0961717 | ||||||||
\(813\) | 65.9374 | 2.31253 | ||||||||
\(814\) | −14.1072 | −0.494457 | ||||||||
\(815\) | −9.25704 | −0.324260 | ||||||||
\(816\) | −7.23016 | −0.253106 | ||||||||
\(817\) | 19.0096 | 0.665062 | ||||||||
\(818\) | −17.1898 | −0.601026 | ||||||||
\(819\) | −10.8065 | −0.377610 | ||||||||
\(820\) | 9.82328 | 0.343044 | ||||||||
\(821\) | 2.47894 | 0.0865157 | 0.0432578 | − | 0.999064i | \(-0.486226\pi\) | ||||
0.0432578 | + | 0.999064i | \(0.486226\pi\) | |||||||
\(822\) | −23.0388 | −0.803571 | ||||||||
\(823\) | 2.75618 | 0.0960746 | 0.0480373 | − | 0.998846i | \(-0.484703\pi\) | ||||
0.0480373 | + | 0.998846i | \(0.484703\pi\) | |||||||
\(824\) | −11.4523 | −0.398958 | ||||||||
\(825\) | 43.3177 | 1.50813 | ||||||||
\(826\) | 31.5818 | 1.09887 | ||||||||
\(827\) | 31.2781 | 1.08765 | 0.543823 | − | 0.839200i | \(-0.316976\pi\) | ||||
0.543823 | + | 0.839200i | \(0.316976\pi\) | |||||||
\(828\) | −11.1240 | −0.386585 | ||||||||
\(829\) | −12.3196 | −0.427878 | −0.213939 | − | 0.976847i | \(-0.568629\pi\) | ||||
−0.213939 | + | 0.976847i | \(0.568629\pi\) | |||||||
\(830\) | −6.81718 | −0.236628 | ||||||||
\(831\) | −57.3292 | −1.98873 | ||||||||
\(832\) | 6.54148 | 0.226785 | ||||||||
\(833\) | −1.97876 | −0.0685599 | ||||||||
\(834\) | 4.07408 | 0.141074 | ||||||||
\(835\) | −8.97369 | −0.310547 | ||||||||
\(836\) | −32.6459 | −1.12908 | ||||||||
\(837\) | 12.8781 | 0.445134 | ||||||||
\(838\) | −2.53976 | −0.0877345 | ||||||||
\(839\) | −7.27794 | −0.251262 | −0.125631 | − | 0.992077i | \(-0.540096\pi\) | ||||
−0.125631 | + | 0.992077i | \(0.540096\pi\) | |||||||
\(840\) | 6.48067 | 0.223604 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 60.8211 | 2.09603 | ||||||||
\(843\) | 9.29300 | 0.320068 | ||||||||
\(844\) | 1.25722 | 0.0432753 | ||||||||
\(845\) | −6.56372 | −0.225799 | ||||||||
\(846\) | 8.91002 | 0.306333 | ||||||||
\(847\) | 41.9230 | 1.44049 | ||||||||
\(848\) | −44.8321 | −1.53954 | ||||||||
\(849\) | 25.1476 | 0.863064 | ||||||||
\(850\) | 4.23614 | 0.145298 | ||||||||
\(851\) | 5.74682 | 0.196998 | ||||||||
\(852\) | 2.20579 | 0.0755691 | ||||||||
\(853\) | 29.2283 | 1.00076 | 0.500378 | − | 0.865807i | \(-0.333194\pi\) | ||||
0.500378 | + | 0.865807i | \(0.333194\pi\) | |||||||
\(854\) | 34.5739 | 1.18309 | ||||||||
\(855\) | 10.2043 | 0.348978 | ||||||||
\(856\) | 2.18508 | 0.0746845 | ||||||||
\(857\) | −47.8387 | −1.63414 | −0.817069 | − | 0.576539i | \(-0.804403\pi\) | ||||
−0.817069 | + | 0.576539i | \(0.804403\pi\) | |||||||
\(858\) | −63.8893 | −2.18114 | ||||||||
\(859\) | −35.9446 | −1.22641 | −0.613207 | − | 0.789922i | \(-0.710121\pi\) | ||||
−0.613207 | + | 0.789922i | \(0.710121\pi\) | |||||||
\(860\) | 7.59382 | 0.258947 | ||||||||
\(861\) | 25.8825 | 0.882074 | ||||||||
\(862\) | 2.15600 | 0.0734338 | ||||||||
\(863\) | −16.0074 | −0.544897 | −0.272449 | − | 0.962170i | \(-0.587834\pi\) | ||||
−0.272449 | + | 0.962170i | \(0.587834\pi\) | |||||||
\(864\) | −15.5975 | −0.530637 | ||||||||
\(865\) | −6.39484 | −0.217431 | ||||||||
\(866\) | 19.0631 | 0.647792 | ||||||||
\(867\) | −36.7721 | −1.24885 | ||||||||
\(868\) | −14.9168 | −0.506308 | ||||||||
\(869\) | 25.2104 | 0.855204 | ||||||||
\(870\) | 5.06431 | 0.171696 | ||||||||
\(871\) | 3.46947 | 0.117558 | ||||||||
\(872\) | −9.79259 | −0.331619 | ||||||||
\(873\) | −18.0199 | −0.609883 | ||||||||
\(874\) | 32.8078 | 1.10974 | ||||||||
\(875\) | −21.1255 | −0.714171 | ||||||||
\(876\) | −29.6072 | −1.00033 | ||||||||
\(877\) | 39.1682 | 1.32262 | 0.661308 | − | 0.750115i | \(-0.270002\pi\) | ||||
0.661308 | + | 0.750115i | \(0.270002\pi\) | |||||||
\(878\) | −21.6415 | −0.730364 | ||||||||
\(879\) | 12.5783 | 0.424255 | ||||||||
\(880\) | 34.1536 | 1.15132 | ||||||||
\(881\) | 11.6314 | 0.391872 | 0.195936 | − | 0.980617i | \(-0.437225\pi\) | ||||
0.195936 | + | 0.980617i | \(0.437225\pi\) | |||||||
\(882\) | 10.5026 | 0.353640 | ||||||||
\(883\) | −21.0579 | −0.708656 | −0.354328 | − | 0.935121i | \(-0.615290\pi\) | ||||
−0.354328 | + | 0.935121i | \(0.615290\pi\) | |||||||
\(884\) | −2.53263 | −0.0851816 | ||||||||
\(885\) | −23.6576 | −0.795243 | ||||||||
\(886\) | 33.1930 | 1.11514 | ||||||||
\(887\) | 8.46040 | 0.284072 | 0.142036 | − | 0.989861i | \(-0.454635\pi\) | ||||
0.142036 | + | 0.989861i | \(0.454635\pi\) | |||||||
\(888\) | −3.53486 | −0.118622 | ||||||||
\(889\) | 5.46531 | 0.183301 | ||||||||
\(890\) | 15.9910 | 0.536020 | ||||||||
\(891\) | 62.4288 | 2.09144 | ||||||||
\(892\) | 20.5008 | 0.686417 | ||||||||
\(893\) | −10.6521 | −0.356458 | ||||||||
\(894\) | 55.5052 | 1.85637 | ||||||||
\(895\) | 19.7787 | 0.661129 | ||||||||
\(896\) | −17.8237 | −0.595448 | ||||||||
\(897\) | 26.0264 | 0.868997 | ||||||||
\(898\) | −72.3036 | −2.41280 | ||||||||
\(899\) | 5.44314 | 0.181539 | ||||||||
\(900\) | −9.11406 | −0.303802 | ||||||||
\(901\) | 6.15745 | 0.205134 | ||||||||
\(902\) | 59.9982 | 1.99772 | ||||||||
\(903\) | 20.0083 | 0.665834 | ||||||||
\(904\) | −0.339921 | −0.0113056 | ||||||||
\(905\) | 21.3713 | 0.710406 | ||||||||
\(906\) | −82.1226 | −2.72834 | ||||||||
\(907\) | −23.6662 | −0.785823 | −0.392911 | − | 0.919576i | \(-0.628532\pi\) | ||||
−0.392911 | + | 0.919576i | \(0.628532\pi\) | |||||||
\(908\) | −5.29791 | −0.175817 | ||||||||
\(909\) | 20.4154 | 0.677136 | ||||||||
\(910\) | 12.7318 | 0.422055 | ||||||||
\(911\) | −6.05842 | −0.200724 | −0.100362 | − | 0.994951i | \(-0.532000\pi\) | ||||
−0.100362 | + | 0.994951i | \(0.532000\pi\) | |||||||
\(912\) | −45.8782 | −1.51918 | ||||||||
\(913\) | −16.8782 | −0.558587 | ||||||||
\(914\) | −15.8137 | −0.523071 | ||||||||
\(915\) | −25.8989 | −0.856192 | ||||||||
\(916\) | 16.0663 | 0.530847 | ||||||||
\(917\) | −2.93617 | −0.0969609 | ||||||||
\(918\) | 2.90101 | 0.0957478 | ||||||||
\(919\) | 0.232766 | 0.00767825 | 0.00383912 | − | 0.999993i | \(-0.498778\pi\) | ||||
0.00383912 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(920\) | −6.11981 | −0.201764 | ||||||||
\(921\) | −42.6728 | −1.40612 | ||||||||
\(922\) | 64.9504 | 2.13903 | ||||||||
\(923\) | −2.02352 | −0.0666051 | ||||||||
\(924\) | −34.3610 | −1.13039 | ||||||||
\(925\) | 4.70847 | 0.154813 | ||||||||
\(926\) | 44.9754 | 1.47798 | ||||||||
\(927\) | −18.9797 | −0.623377 | ||||||||
\(928\) | −6.59250 | −0.216409 | ||||||||
\(929\) | 28.9222 | 0.948908 | 0.474454 | − | 0.880280i | \(-0.342645\pi\) | ||||
0.474454 | + | 0.880280i | \(0.342645\pi\) | |||||||
\(930\) | 27.5657 | 0.903915 | ||||||||
\(931\) | −12.5560 | −0.411506 | ||||||||
\(932\) | 16.8370 | 0.551515 | ||||||||
\(933\) | 14.2422 | 0.466270 | ||||||||
\(934\) | −58.6612 | −1.91945 | ||||||||
\(935\) | −4.69081 | −0.153406 | ||||||||
\(936\) | −6.27696 | −0.205169 | ||||||||
\(937\) | −3.08688 | −0.100844 | −0.0504220 | − | 0.998728i | \(-0.516057\pi\) | ||||
−0.0504220 | + | 0.998728i | \(0.516057\pi\) | |||||||
\(938\) | 4.60322 | 0.150301 | ||||||||
\(939\) | 25.2013 | 0.822412 | ||||||||
\(940\) | −4.25521 | −0.138790 | ||||||||
\(941\) | −54.7851 | −1.78594 | −0.892972 | − | 0.450113i | \(-0.851384\pi\) | ||||
−0.892972 | + | 0.450113i | \(0.851384\pi\) | |||||||
\(942\) | 17.5097 | 0.570498 | ||||||||
\(943\) | −24.4413 | −0.795920 | ||||||||
\(944\) | 41.7048 | 1.35737 | ||||||||
\(945\) | −5.91162 | −0.192305 | ||||||||
\(946\) | 46.3812 | 1.50798 | ||||||||
\(947\) | 21.6168 | 0.702452 | 0.351226 | − | 0.936291i | \(-0.385765\pi\) | ||||
0.351226 | + | 0.936291i | \(0.385765\pi\) | |||||||
\(948\) | −13.5281 | −0.439372 | ||||||||
\(949\) | 27.1607 | 0.881675 | ||||||||
\(950\) | 26.8800 | 0.872101 | ||||||||
\(951\) | −27.2884 | −0.884886 | ||||||||
\(952\) | 1.56908 | 0.0508542 | ||||||||
\(953\) | 10.1315 | 0.328191 | 0.164096 | − | 0.986444i | \(-0.447529\pi\) | ||||
0.164096 | + | 0.986444i | \(0.447529\pi\) | |||||||
\(954\) | −32.6816 | −1.05811 | ||||||||
\(955\) | −24.2305 | −0.784081 | ||||||||
\(956\) | 32.6208 | 1.05503 | ||||||||
\(957\) | 12.5384 | 0.405308 | ||||||||
\(958\) | −20.4437 | −0.660507 | ||||||||
\(959\) | 11.3669 | 0.367057 | ||||||||
\(960\) | −6.50143 | −0.209833 | ||||||||
\(961\) | −1.37227 | −0.0442669 | ||||||||
\(962\) | −6.94452 | −0.223900 | ||||||||
\(963\) | 3.62132 | 0.116695 | ||||||||
\(964\) | 14.0136 | 0.451347 | ||||||||
\(965\) | −15.5498 | −0.500566 | ||||||||
\(966\) | 34.5314 | 1.11103 | ||||||||
\(967\) | 27.3427 | 0.879283 | 0.439641 | − | 0.898173i | \(-0.355106\pi\) | ||||
0.439641 | + | 0.898173i | \(0.355106\pi\) | |||||||
\(968\) | 24.3509 | 0.782669 | ||||||||
\(969\) | 6.30112 | 0.202421 | ||||||||
\(970\) | 21.2303 | 0.681665 | ||||||||
\(971\) | 41.6142 | 1.33546 | 0.667732 | − | 0.744402i | \(-0.267265\pi\) | ||||
0.667732 | + | 0.744402i | \(0.267265\pi\) | |||||||
\(972\) | −23.8228 | −0.764118 | ||||||||
\(973\) | −2.01007 | −0.0644400 | ||||||||
\(974\) | 29.9240 | 0.958828 | ||||||||
\(975\) | 21.3239 | 0.682911 | ||||||||
\(976\) | 45.6558 | 1.46141 | ||||||||
\(977\) | −3.08971 | −0.0988486 | −0.0494243 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494243 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(978\) | 30.3397 | 0.970156 | ||||||||
\(979\) | 39.5911 | 1.26534 | ||||||||
\(980\) | −5.01577 | −0.160223 | ||||||||
\(981\) | −16.2292 | −0.518158 | ||||||||
\(982\) | −16.5391 | −0.527784 | ||||||||
\(983\) | 39.5890 | 1.26269 | 0.631346 | − | 0.775501i | \(-0.282503\pi\) | ||||
0.631346 | + | 0.775501i | \(0.282503\pi\) | |||||||
\(984\) | 15.0338 | 0.479261 | ||||||||
\(985\) | 23.7060 | 0.755335 | ||||||||
\(986\) | 1.22616 | 0.0390488 | ||||||||
\(987\) | −11.2117 | −0.356872 | ||||||||
\(988\) | −16.0705 | −0.511271 | ||||||||
\(989\) | −18.8942 | −0.600801 | ||||||||
\(990\) | 24.8972 | 0.791285 | ||||||||
\(991\) | 42.8562 | 1.36137 | 0.680686 | − | 0.732575i | \(-0.261682\pi\) | ||||
0.680686 | + | 0.732575i | \(0.261682\pi\) | |||||||
\(992\) | −35.8839 | −1.13931 | ||||||||
\(993\) | −29.0098 | −0.920597 | ||||||||
\(994\) | −2.68477 | −0.0851558 | ||||||||
\(995\) | −13.0983 | −0.415243 | ||||||||
\(996\) | 9.05697 | 0.286981 | ||||||||
\(997\) | 28.2944 | 0.896094 | 0.448047 | − | 0.894010i | \(-0.352120\pi\) | ||||
0.448047 | + | 0.894010i | \(0.352120\pi\) | |||||||
\(998\) | 28.1786 | 0.891979 | ||||||||
\(999\) | 3.22448 | 0.102018 |
(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 | 4031.2.a.c.1.12 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.12 | ✓ | 61 | 1.1 | even | 1 | trivial |