Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14221 | −1.51477 | −0.757384 | − | 0.652969i | \(-0.773523\pi\) | ||||
−0.757384 | + | 0.652969i | \(0.773523\pi\) | |||||||
\(3\) | 1.83370 | 1.05869 | 0.529343 | − | 0.848408i | \(-0.322439\pi\) | ||||
0.529343 | + | 0.848408i | \(0.322439\pi\) | |||||||
\(4\) | 2.58905 | 1.29452 | ||||||||
\(5\) | −3.64172 | −1.62863 | −0.814314 | − | 0.580425i | \(-0.802886\pi\) | ||||
−0.814314 | + | 0.580425i | \(0.802886\pi\) | |||||||
\(6\) | −3.92816 | −1.60366 | ||||||||
\(7\) | 3.71202 | 1.40301 | 0.701507 | − | 0.712663i | \(-0.252511\pi\) | ||||
0.701507 | + | 0.712663i | \(0.252511\pi\) | |||||||
\(8\) | −1.26186 | −0.446135 | ||||||||
\(9\) | 0.362447 | 0.120816 | ||||||||
\(10\) | 7.80132 | 2.46699 | ||||||||
\(11\) | −5.02675 | −1.51562 | −0.757812 | − | 0.652473i | \(-0.773731\pi\) | ||||
−0.757812 | + | 0.652473i | \(0.773731\pi\) | |||||||
\(12\) | 4.74753 | 1.37049 | ||||||||
\(13\) | −0.605986 | −0.168070 | −0.0840351 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840351 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(14\) | −7.95192 | −2.12524 | ||||||||
\(15\) | −6.67782 | −1.72420 | ||||||||
\(16\) | −2.47493 | −0.618732 | ||||||||
\(17\) | −1.90825 | −0.462818 | −0.231409 | − | 0.972857i | \(-0.574334\pi\) | ||||
−0.231409 | + | 0.972857i | \(0.574334\pi\) | |||||||
\(18\) | −0.776437 | −0.183008 | ||||||||
\(19\) | 3.84573 | 0.882270 | 0.441135 | − | 0.897441i | \(-0.354576\pi\) | ||||
0.441135 | + | 0.897441i | \(0.354576\pi\) | |||||||
\(20\) | −9.42859 | −2.10830 | ||||||||
\(21\) | 6.80673 | 1.48535 | ||||||||
\(22\) | 10.7683 | 2.29582 | ||||||||
\(23\) | 1.83811 | 0.383273 | 0.191636 | − | 0.981466i | \(-0.438621\pi\) | ||||
0.191636 | + | 0.981466i | \(0.438621\pi\) | |||||||
\(24\) | −2.31387 | −0.472317 | ||||||||
\(25\) | 8.26213 | 1.65243 | ||||||||
\(26\) | 1.29815 | 0.254587 | ||||||||
\(27\) | −4.83647 | −0.930780 | ||||||||
\(28\) | 9.61061 | 1.81623 | ||||||||
\(29\) | 2.71114 | 0.503447 | 0.251723 | − | 0.967799i | \(-0.419003\pi\) | ||||
0.251723 | + | 0.967799i | \(0.419003\pi\) | |||||||
\(30\) | 14.3053 | 2.61177 | ||||||||
\(31\) | −0.885966 | −0.159124 | −0.0795621 | − | 0.996830i | \(-0.525352\pi\) | ||||
−0.0795621 | + | 0.996830i | \(0.525352\pi\) | |||||||
\(32\) | 7.82553 | 1.38337 | ||||||||
\(33\) | −9.21755 | −1.60457 | ||||||||
\(34\) | 4.08786 | 0.701062 | ||||||||
\(35\) | −13.5182 | −2.28499 | ||||||||
\(36\) | 0.938393 | 0.156399 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −8.23834 | −1.33643 | ||||||||
\(39\) | −1.11119 | −0.177934 | ||||||||
\(40\) | 4.59535 | 0.726588 | ||||||||
\(41\) | −4.53098 | −0.707620 | −0.353810 | − | 0.935317i | \(-0.615114\pi\) | ||||
−0.353810 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(42\) | −14.5814 | −2.24996 | ||||||||
\(43\) | 6.94191 | 1.05863 | 0.529315 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529315 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(44\) | −13.0145 | −1.96201 | ||||||||
\(45\) | −1.31993 | −0.196764 | ||||||||
\(46\) | −3.93761 | −0.580570 | ||||||||
\(47\) | 7.47993 | 1.09106 | 0.545530 | − | 0.838092i | \(-0.316329\pi\) | ||||
0.545530 | + | 0.838092i | \(0.316329\pi\) | |||||||
\(48\) | −4.53827 | −0.655043 | ||||||||
\(49\) | 6.77912 | 0.968446 | ||||||||
\(50\) | −17.6992 | −2.50304 | ||||||||
\(51\) | −3.49915 | −0.489979 | ||||||||
\(52\) | −1.56893 | −0.217571 | ||||||||
\(53\) | −0.557732 | −0.0766104 | −0.0383052 | − | 0.999266i | \(-0.512196\pi\) | ||||
−0.0383052 | + | 0.999266i | \(0.512196\pi\) | |||||||
\(54\) | 10.3607 | 1.40992 | ||||||||
\(55\) | 18.3060 | 2.46839 | ||||||||
\(56\) | −4.68406 | −0.625934 | ||||||||
\(57\) | 7.05190 | 0.934047 | ||||||||
\(58\) | −5.80783 | −0.762605 | ||||||||
\(59\) | 9.04093 | 1.17703 | 0.588514 | − | 0.808487i | \(-0.299713\pi\) | ||||
0.588514 | + | 0.808487i | \(0.299713\pi\) | |||||||
\(60\) | −17.2892 | −2.23202 | ||||||||
\(61\) | 6.67775 | 0.854998 | 0.427499 | − | 0.904016i | \(-0.359395\pi\) | ||||
0.427499 | + | 0.904016i | \(0.359395\pi\) | |||||||
\(62\) | 1.89792 | 0.241036 | ||||||||
\(63\) | 1.34541 | 0.169506 | ||||||||
\(64\) | −11.8140 | −1.47675 | ||||||||
\(65\) | 2.20683 | 0.273724 | ||||||||
\(66\) | 19.7459 | 2.43055 | ||||||||
\(67\) | −6.85251 | −0.837167 | −0.418584 | − | 0.908178i | \(-0.637473\pi\) | ||||
−0.418584 | + | 0.908178i | \(0.637473\pi\) | |||||||
\(68\) | −4.94054 | −0.599129 | ||||||||
\(69\) | 3.37054 | 0.405765 | ||||||||
\(70\) | 28.9587 | 3.46122 | ||||||||
\(71\) | −1.94708 | −0.231076 | −0.115538 | − | 0.993303i | \(-0.536859\pi\) | ||||
−0.115538 | + | 0.993303i | \(0.536859\pi\) | |||||||
\(72\) | −0.457358 | −0.0539002 | ||||||||
\(73\) | 10.4042 | 1.21772 | 0.608860 | − | 0.793278i | \(-0.291627\pi\) | ||||
0.608860 | + | 0.793278i | \(0.291627\pi\) | |||||||
\(74\) | −2.14221 | −0.249026 | ||||||||
\(75\) | 15.1503 | 1.74940 | ||||||||
\(76\) | 9.95677 | 1.14212 | ||||||||
\(77\) | −18.6594 | −2.12644 | ||||||||
\(78\) | 2.38041 | 0.269528 | ||||||||
\(79\) | −12.0694 | −1.35791 | −0.678956 | − | 0.734179i | \(-0.737567\pi\) | ||||
−0.678956 | + | 0.734179i | \(0.737567\pi\) | |||||||
\(80\) | 9.01300 | 1.00768 | ||||||||
\(81\) | −9.95597 | −1.10622 | ||||||||
\(82\) | 9.70630 | 1.07188 | ||||||||
\(83\) | −0.0731947 | −0.00803416 | −0.00401708 | − | 0.999992i | \(-0.501279\pi\) | ||||
−0.00401708 | + | 0.999992i | \(0.501279\pi\) | |||||||
\(84\) | 17.6229 | 1.92282 | ||||||||
\(85\) | 6.94931 | 0.753758 | ||||||||
\(86\) | −14.8710 | −1.60358 | ||||||||
\(87\) | 4.97142 | 0.532992 | ||||||||
\(88\) | 6.34306 | 0.676173 | ||||||||
\(89\) | −15.3107 | −1.62293 | −0.811464 | − | 0.584402i | \(-0.801329\pi\) | ||||
−0.811464 | + | 0.584402i | \(0.801329\pi\) | |||||||
\(90\) | 2.82757 | 0.298052 | ||||||||
\(91\) | −2.24943 | −0.235805 | ||||||||
\(92\) | 4.75896 | 0.496156 | ||||||||
\(93\) | −1.62459 | −0.168463 | ||||||||
\(94\) | −16.0235 | −1.65270 | ||||||||
\(95\) | −14.0051 | −1.43689 | ||||||||
\(96\) | 14.3497 | 1.46456 | ||||||||
\(97\) | 4.34874 | 0.441547 | 0.220774 | − | 0.975325i | \(-0.429142\pi\) | ||||
0.220774 | + | 0.975325i | \(0.429142\pi\) | |||||||
\(98\) | −14.5223 | −1.46697 | ||||||||
\(99\) | −1.82193 | −0.183111 | ||||||||
\(100\) | 21.3911 | 2.13911 | ||||||||
\(101\) | −1.09555 | −0.109011 | −0.0545055 | − | 0.998513i | \(-0.517358\pi\) | ||||
−0.0545055 | + | 0.998513i | \(0.517358\pi\) | |||||||
\(102\) | 7.49590 | 0.742205 | ||||||||
\(103\) | −6.03515 | −0.594661 | −0.297331 | − | 0.954775i | \(-0.596096\pi\) | ||||
−0.297331 | + | 0.954775i | \(0.596096\pi\) | |||||||
\(104\) | 0.764670 | 0.0749820 | ||||||||
\(105\) | −24.7882 | −2.41908 | ||||||||
\(106\) | 1.19478 | 0.116047 | ||||||||
\(107\) | −5.58628 | −0.540046 | −0.270023 | − | 0.962854i | \(-0.587031\pi\) | ||||
−0.270023 | + | 0.962854i | \(0.587031\pi\) | |||||||
\(108\) | −12.5219 | −1.20492 | ||||||||
\(109\) | −10.4236 | −0.998398 | −0.499199 | − | 0.866488i | \(-0.666372\pi\) | ||||
−0.499199 | + | 0.866488i | \(0.666372\pi\) | |||||||
\(110\) | −39.2153 | −3.73903 | ||||||||
\(111\) | 1.83370 | 0.174047 | ||||||||
\(112\) | −9.18699 | −0.868089 | ||||||||
\(113\) | 0.569617 | 0.0535850 | 0.0267925 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267925 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(114\) | −15.1066 | −1.41486 | ||||||||
\(115\) | −6.69389 | −0.624208 | ||||||||
\(116\) | 7.01928 | 0.651724 | ||||||||
\(117\) | −0.219638 | −0.0203055 | ||||||||
\(118\) | −19.3675 | −1.78293 | ||||||||
\(119\) | −7.08346 | −0.649340 | ||||||||
\(120\) | 8.42647 | 0.769228 | ||||||||
\(121\) | 14.2683 | 1.29711 | ||||||||
\(122\) | −14.3051 | −1.29512 | ||||||||
\(123\) | −8.30845 | −0.749148 | ||||||||
\(124\) | −2.29381 | −0.205990 | ||||||||
\(125\) | −11.8798 | −1.06256 | ||||||||
\(126\) | −2.88215 | −0.256762 | ||||||||
\(127\) | −15.3922 | −1.36584 | −0.682919 | − | 0.730494i | \(-0.739290\pi\) | ||||
−0.682919 | + | 0.730494i | \(0.739290\pi\) | |||||||
\(128\) | 9.65705 | 0.853571 | ||||||||
\(129\) | 12.7294 | 1.12076 | ||||||||
\(130\) | −4.72749 | −0.414628 | ||||||||
\(131\) | 16.6055 | 1.45083 | 0.725415 | − | 0.688312i | \(-0.241648\pi\) | ||||
0.725415 | + | 0.688312i | \(0.241648\pi\) | |||||||
\(132\) | −23.8647 | −2.07715 | ||||||||
\(133\) | 14.2754 | 1.23784 | ||||||||
\(134\) | 14.6795 | 1.26811 | ||||||||
\(135\) | 17.6131 | 1.51589 | ||||||||
\(136\) | 2.40794 | 0.206479 | ||||||||
\(137\) | −18.2082 | −1.55563 | −0.777817 | − | 0.628491i | \(-0.783673\pi\) | ||||
−0.777817 | + | 0.628491i | \(0.783673\pi\) | |||||||
\(138\) | −7.22039 | −0.614641 | ||||||||
\(139\) | 10.2672 | 0.870850 | 0.435425 | − | 0.900225i | \(-0.356598\pi\) | ||||
0.435425 | + | 0.900225i | \(0.356598\pi\) | |||||||
\(140\) | −34.9991 | −2.95797 | ||||||||
\(141\) | 13.7159 | 1.15509 | ||||||||
\(142\) | 4.17105 | 0.350027 | ||||||||
\(143\) | 3.04614 | 0.254731 | ||||||||
\(144\) | −0.897031 | −0.0747526 | ||||||||
\(145\) | −9.87323 | −0.819927 | ||||||||
\(146\) | −22.2879 | −1.84456 | ||||||||
\(147\) | 12.4309 | 1.02528 | ||||||||
\(148\) | 2.58905 | 0.212818 | ||||||||
\(149\) | −8.31623 | −0.681292 | −0.340646 | − | 0.940192i | \(-0.610646\pi\) | ||||
−0.340646 | + | 0.940192i | \(0.610646\pi\) | |||||||
\(150\) | −32.4550 | −2.64994 | ||||||||
\(151\) | 2.52505 | 0.205486 | 0.102743 | − | 0.994708i | \(-0.467238\pi\) | ||||
0.102743 | + | 0.994708i | \(0.467238\pi\) | |||||||
\(152\) | −4.85277 | −0.393612 | ||||||||
\(153\) | −0.691639 | −0.0559157 | ||||||||
\(154\) | 39.9723 | 3.22106 | ||||||||
\(155\) | 3.22644 | 0.259154 | ||||||||
\(156\) | −2.87694 | −0.230339 | ||||||||
\(157\) | −10.4741 | −0.835921 | −0.417960 | − | 0.908465i | \(-0.637255\pi\) | ||||
−0.417960 | + | 0.908465i | \(0.637255\pi\) | |||||||
\(158\) | 25.8551 | 2.05692 | ||||||||
\(159\) | −1.02271 | −0.0811063 | ||||||||
\(160\) | −28.4984 | −2.25300 | ||||||||
\(161\) | 6.82311 | 0.537737 | ||||||||
\(162\) | 21.3277 | 1.67567 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | −11.7309 | −0.916031 | ||||||||
\(165\) | 33.5677 | 2.61324 | ||||||||
\(166\) | 0.156798 | 0.0121699 | ||||||||
\(167\) | 15.1154 | 1.16966 | 0.584832 | − | 0.811154i | \(-0.301160\pi\) | ||||
0.584832 | + | 0.811154i | \(0.301160\pi\) | |||||||
\(168\) | −8.58915 | −0.662667 | ||||||||
\(169\) | −12.6328 | −0.971752 | ||||||||
\(170\) | −14.8868 | −1.14177 | ||||||||
\(171\) | 1.39387 | 0.106592 | ||||||||
\(172\) | 17.9729 | 1.37042 | ||||||||
\(173\) | −5.58827 | −0.424868 | −0.212434 | − | 0.977175i | \(-0.568139\pi\) | ||||
−0.212434 | + | 0.977175i | \(0.568139\pi\) | |||||||
\(174\) | −10.6498 | −0.807359 | ||||||||
\(175\) | 30.6692 | 2.31838 | ||||||||
\(176\) | 12.4409 | 0.937765 | ||||||||
\(177\) | 16.5783 | 1.24610 | ||||||||
\(178\) | 32.7986 | 2.45836 | ||||||||
\(179\) | 2.97615 | 0.222448 | 0.111224 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111224 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(180\) | −3.41737 | −0.254715 | ||||||||
\(181\) | 3.22550 | 0.239750 | 0.119875 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119875 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(182\) | 4.81875 | 0.357190 | ||||||||
\(183\) | 12.2450 | 0.905174 | ||||||||
\(184\) | −2.31944 | −0.170991 | ||||||||
\(185\) | −3.64172 | −0.267745 | ||||||||
\(186\) | 3.48022 | 0.255182 | ||||||||
\(187\) | 9.59229 | 0.701458 | ||||||||
\(188\) | 19.3659 | 1.41240 | ||||||||
\(189\) | −17.9531 | −1.30590 | ||||||||
\(190\) | 30.0017 | 2.17655 | ||||||||
\(191\) | −19.8200 | −1.43412 | −0.717062 | − | 0.697010i | \(-0.754513\pi\) | ||||
−0.717062 | + | 0.697010i | \(0.754513\pi\) | |||||||
\(192\) | −21.6634 | −1.56342 | ||||||||
\(193\) | 1.16580 | 0.0839160 | 0.0419580 | − | 0.999119i | \(-0.486640\pi\) | ||||
0.0419580 | + | 0.999119i | \(0.486640\pi\) | |||||||
\(194\) | −9.31589 | −0.668842 | ||||||||
\(195\) | 4.04666 | 0.289787 | ||||||||
\(196\) | 17.5515 | 1.25368 | ||||||||
\(197\) | −14.2336 | −1.01410 | −0.507050 | − | 0.861916i | \(-0.669264\pi\) | ||||
−0.507050 | + | 0.861916i | \(0.669264\pi\) | |||||||
\(198\) | 3.90296 | 0.277371 | ||||||||
\(199\) | 1.58343 | 0.112246 | 0.0561231 | − | 0.998424i | \(-0.482126\pi\) | ||||
0.0561231 | + | 0.998424i | \(0.482126\pi\) | |||||||
\(200\) | −10.4257 | −0.737206 | ||||||||
\(201\) | −12.5654 | −0.886297 | ||||||||
\(202\) | 2.34689 | 0.165126 | ||||||||
\(203\) | 10.0638 | 0.706342 | ||||||||
\(204\) | −9.05947 | −0.634289 | ||||||||
\(205\) | 16.5006 | 1.15245 | ||||||||
\(206\) | 12.9285 | 0.900774 | ||||||||
\(207\) | 0.666218 | 0.0463054 | ||||||||
\(208\) | 1.49977 | 0.103990 | ||||||||
\(209\) | −19.3315 | −1.33719 | ||||||||
\(210\) | 53.1015 | 3.66435 | ||||||||
\(211\) | −15.3819 | −1.05894 | −0.529468 | − | 0.848330i | \(-0.677608\pi\) | ||||
−0.529468 | + | 0.848330i | \(0.677608\pi\) | |||||||
\(212\) | −1.44399 | −0.0991739 | ||||||||
\(213\) | −3.57036 | −0.244637 | ||||||||
\(214\) | 11.9670 | 0.818045 | ||||||||
\(215\) | −25.2805 | −1.72411 | ||||||||
\(216\) | 6.10296 | 0.415254 | ||||||||
\(217\) | −3.28873 | −0.223253 | ||||||||
\(218\) | 22.3294 | 1.51234 | ||||||||
\(219\) | 19.0782 | 1.28918 | ||||||||
\(220\) | 47.3952 | 3.19538 | ||||||||
\(221\) | 1.15637 | 0.0777859 | ||||||||
\(222\) | −3.92816 | −0.263641 | ||||||||
\(223\) | −22.5512 | −1.51014 | −0.755068 | − | 0.655646i | \(-0.772396\pi\) | ||||
−0.755068 | + | 0.655646i | \(0.772396\pi\) | |||||||
\(224\) | 29.0486 | 1.94089 | ||||||||
\(225\) | 2.99459 | 0.199639 | ||||||||
\(226\) | −1.22024 | −0.0811689 | ||||||||
\(227\) | −17.4414 | −1.15763 | −0.578814 | − | 0.815460i | \(-0.696484\pi\) | ||||
−0.578814 | + | 0.815460i | \(0.696484\pi\) | |||||||
\(228\) | 18.2577 | 1.20915 | ||||||||
\(229\) | −5.67980 | −0.375331 | −0.187666 | − | 0.982233i | \(-0.560092\pi\) | ||||
−0.187666 | + | 0.982233i | \(0.560092\pi\) | |||||||
\(230\) | 14.3397 | 0.945531 | ||||||||
\(231\) | −34.2158 | −2.25123 | ||||||||
\(232\) | −3.42109 | −0.224605 | ||||||||
\(233\) | −20.7250 | −1.35774 | −0.678869 | − | 0.734259i | \(-0.737530\pi\) | ||||
−0.678869 | + | 0.734259i | \(0.737530\pi\) | |||||||
\(234\) | 0.470510 | 0.0307582 | ||||||||
\(235\) | −27.2398 | −1.77693 | ||||||||
\(236\) | 23.4074 | 1.52369 | ||||||||
\(237\) | −22.1316 | −1.43760 | ||||||||
\(238\) | 15.1742 | 0.983600 | ||||||||
\(239\) | 5.48923 | 0.355069 | 0.177534 | − | 0.984115i | \(-0.443188\pi\) | ||||
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(240\) | 16.5271 | 1.06682 | ||||||||
\(241\) | 15.3398 | 0.988122 | 0.494061 | − | 0.869427i | \(-0.335512\pi\) | ||||
0.494061 | + | 0.869427i | \(0.335512\pi\) | |||||||
\(242\) | −30.5655 | −1.96483 | ||||||||
\(243\) | −3.74682 | −0.240359 | ||||||||
\(244\) | 17.2890 | 1.10681 | ||||||||
\(245\) | −24.6877 | −1.57724 | ||||||||
\(246\) | 17.7984 | 1.13479 | ||||||||
\(247\) | −2.33046 | −0.148283 | ||||||||
\(248\) | 1.11797 | 0.0709909 | ||||||||
\(249\) | −0.134217 | −0.00850565 | ||||||||
\(250\) | 25.4489 | 1.60953 | ||||||||
\(251\) | 11.3715 | 0.717762 | 0.358881 | − | 0.933383i | \(-0.383158\pi\) | ||||
0.358881 | + | 0.933383i | \(0.383158\pi\) | |||||||
\(252\) | 3.48334 | 0.219430 | ||||||||
\(253\) | −9.23973 | −0.580897 | ||||||||
\(254\) | 32.9733 | 2.06893 | ||||||||
\(255\) | 12.7429 | 0.797993 | ||||||||
\(256\) | 2.94068 | 0.183793 | ||||||||
\(257\) | 21.1508 | 1.31935 | 0.659675 | − | 0.751551i | \(-0.270694\pi\) | ||||
0.659675 | + | 0.751551i | \(0.270694\pi\) | |||||||
\(258\) | −27.2689 | −1.69769 | ||||||||
\(259\) | 3.71202 | 0.230654 | ||||||||
\(260\) | 5.71359 | 0.354342 | ||||||||
\(261\) | 0.982646 | 0.0608243 | ||||||||
\(262\) | −35.5724 | −2.19767 | ||||||||
\(263\) | −5.20303 | −0.320832 | −0.160416 | − | 0.987049i | \(-0.551284\pi\) | ||||
−0.160416 | + | 0.987049i | \(0.551284\pi\) | |||||||
\(264\) | 11.6313 | 0.715855 | ||||||||
\(265\) | 2.03110 | 0.124770 | ||||||||
\(266\) | −30.5809 | −1.87504 | ||||||||
\(267\) | −28.0751 | −1.71817 | ||||||||
\(268\) | −17.7415 | −1.08373 | ||||||||
\(269\) | −15.3747 | −0.937414 | −0.468707 | − | 0.883354i | \(-0.655280\pi\) | ||||
−0.468707 | + | 0.883354i | \(0.655280\pi\) | |||||||
\(270\) | −37.7309 | −2.29623 | ||||||||
\(271\) | 9.34983 | 0.567962 | 0.283981 | − | 0.958830i | \(-0.408345\pi\) | ||||
0.283981 | + | 0.958830i | \(0.408345\pi\) | |||||||
\(272\) | 4.72278 | 0.286360 | ||||||||
\(273\) | −4.12478 | −0.249643 | ||||||||
\(274\) | 39.0058 | 2.35643 | ||||||||
\(275\) | −41.5317 | −2.50446 | ||||||||
\(276\) | 8.72649 | 0.525273 | ||||||||
\(277\) | −17.9031 | −1.07569 | −0.537846 | − | 0.843043i | \(-0.680762\pi\) | ||||
−0.537846 | + | 0.843043i | \(0.680762\pi\) | |||||||
\(278\) | −21.9944 | −1.31914 | ||||||||
\(279\) | −0.321116 | −0.0192247 | ||||||||
\(280\) | 17.0580 | 1.01941 | ||||||||
\(281\) | 31.4080 | 1.87365 | 0.936823 | − | 0.349803i | \(-0.113751\pi\) | ||||
0.936823 | + | 0.349803i | \(0.113751\pi\) | |||||||
\(282\) | −29.3823 | −1.74969 | ||||||||
\(283\) | 20.6381 | 1.22681 | 0.613404 | − | 0.789769i | \(-0.289800\pi\) | ||||
0.613404 | + | 0.789769i | \(0.289800\pi\) | |||||||
\(284\) | −5.04109 | −0.299133 | ||||||||
\(285\) | −25.6810 | −1.52121 | ||||||||
\(286\) | −6.52546 | −0.385859 | ||||||||
\(287\) | −16.8191 | −0.992801 | ||||||||
\(288\) | 2.83634 | 0.167133 | ||||||||
\(289\) | −13.3586 | −0.785799 | ||||||||
\(290\) | 21.1505 | 1.24200 | ||||||||
\(291\) | 7.97427 | 0.467460 | ||||||||
\(292\) | 26.9370 | 1.57637 | ||||||||
\(293\) | 0.188418 | 0.0110075 | 0.00550375 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550375 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(294\) | −26.6295 | −1.55306 | ||||||||
\(295\) | −32.9245 | −1.91694 | ||||||||
\(296\) | −1.26186 | −0.0733442 | ||||||||
\(297\) | 24.3118 | 1.41071 | ||||||||
\(298\) | 17.8151 | 1.03200 | ||||||||
\(299\) | −1.11387 | −0.0644167 | ||||||||
\(300\) | 39.2247 | 2.26464 | ||||||||
\(301\) | 25.7685 | 1.48527 | ||||||||
\(302\) | −5.40918 | −0.311264 | ||||||||
\(303\) | −2.00890 | −0.115408 | ||||||||
\(304\) | −9.51790 | −0.545889 | ||||||||
\(305\) | −24.3185 | −1.39247 | ||||||||
\(306\) | 1.48163 | 0.0846994 | ||||||||
\(307\) | −6.22454 | −0.355253 | −0.177627 | − | 0.984098i | \(-0.556842\pi\) | ||||
−0.177627 | + | 0.984098i | \(0.556842\pi\) | |||||||
\(308\) | −48.3101 | −2.75273 | ||||||||
\(309\) | −11.0666 | −0.629559 | ||||||||
\(310\) | −6.91170 | −0.392558 | ||||||||
\(311\) | 16.1536 | 0.915985 | 0.457992 | − | 0.888956i | \(-0.348569\pi\) | ||||
0.457992 | + | 0.888956i | \(0.348569\pi\) | |||||||
\(312\) | 1.40217 | 0.0793824 | ||||||||
\(313\) | −26.6523 | −1.50648 | −0.753239 | − | 0.657747i | \(-0.771509\pi\) | ||||
−0.753239 | + | 0.657747i | \(0.771509\pi\) | |||||||
\(314\) | 22.4376 | 1.26623 | ||||||||
\(315\) | −4.89962 | −0.276062 | ||||||||
\(316\) | −31.2482 | −1.75785 | ||||||||
\(317\) | −10.2349 | −0.574848 | −0.287424 | − | 0.957803i | \(-0.592799\pi\) | ||||
−0.287424 | + | 0.957803i | \(0.592799\pi\) | |||||||
\(318\) | 2.19086 | 0.122857 | ||||||||
\(319\) | −13.6282 | −0.763035 | ||||||||
\(320\) | 43.0234 | 2.40508 | ||||||||
\(321\) | −10.2435 | −0.571739 | ||||||||
\(322\) | −14.6165 | −0.814547 | ||||||||
\(323\) | −7.33860 | −0.408331 | ||||||||
\(324\) | −25.7765 | −1.43203 | ||||||||
\(325\) | −5.00674 | −0.277724 | ||||||||
\(326\) | −2.14221 | −0.118646 | ||||||||
\(327\) | −19.1137 | −1.05699 | ||||||||
\(328\) | 5.71747 | 0.315694 | ||||||||
\(329\) | 27.7657 | 1.53077 | ||||||||
\(330\) | −71.9090 | −3.95846 | ||||||||
\(331\) | −4.57311 | −0.251361 | −0.125681 | − | 0.992071i | \(-0.540111\pi\) | ||||
−0.125681 | + | 0.992071i | \(0.540111\pi\) | |||||||
\(332\) | −0.189505 | −0.0104004 | ||||||||
\(333\) | 0.362447 | 0.0198620 | ||||||||
\(334\) | −32.3803 | −1.77177 | ||||||||
\(335\) | 24.9549 | 1.36343 | ||||||||
\(336\) | −16.8462 | −0.919034 | ||||||||
\(337\) | 16.1477 | 0.879622 | 0.439811 | − | 0.898090i | \(-0.355045\pi\) | ||||
0.439811 | + | 0.898090i | \(0.355045\pi\) | |||||||
\(338\) | 27.0620 | 1.47198 | ||||||||
\(339\) | 1.04450 | 0.0567297 | ||||||||
\(340\) | 17.9921 | 0.975758 | ||||||||
\(341\) | 4.45353 | 0.241172 | ||||||||
\(342\) | −2.98596 | −0.161462 | ||||||||
\(343\) | −0.819905 | −0.0442707 | ||||||||
\(344\) | −8.75972 | −0.472293 | ||||||||
\(345\) | −12.2746 | −0.660841 | ||||||||
\(346\) | 11.9712 | 0.643577 | ||||||||
\(347\) | −24.5747 | −1.31924 | −0.659620 | − | 0.751600i | \(-0.729283\pi\) | ||||
−0.659620 | + | 0.751600i | \(0.729283\pi\) | |||||||
\(348\) | 12.8712 | 0.689971 | ||||||||
\(349\) | 19.3442 | 1.03547 | 0.517736 | − | 0.855540i | \(-0.326775\pi\) | ||||
0.517736 | + | 0.855540i | \(0.326775\pi\) | |||||||
\(350\) | −65.6998 | −3.51180 | ||||||||
\(351\) | 2.93083 | 0.156436 | ||||||||
\(352\) | −39.3370 | −2.09667 | ||||||||
\(353\) | −34.7856 | −1.85145 | −0.925725 | − | 0.378198i | \(-0.876544\pi\) | ||||
−0.925725 | + | 0.378198i | \(0.876544\pi\) | |||||||
\(354\) | −35.5142 | −1.88756 | ||||||||
\(355\) | 7.09073 | 0.376337 | ||||||||
\(356\) | −39.6401 | −2.10092 | ||||||||
\(357\) | −12.9889 | −0.687447 | ||||||||
\(358\) | −6.37552 | −0.336957 | ||||||||
\(359\) | 6.73170 | 0.355285 | 0.177643 | − | 0.984095i | \(-0.443153\pi\) | ||||
0.177643 | + | 0.984095i | \(0.443153\pi\) | |||||||
\(360\) | 1.66557 | 0.0877833 | ||||||||
\(361\) | −4.21040 | −0.221600 | ||||||||
\(362\) | −6.90969 | −0.363165 | ||||||||
\(363\) | 26.1637 | 1.37324 | ||||||||
\(364\) | −5.82389 | −0.305255 | ||||||||
\(365\) | −37.8892 | −1.98321 | ||||||||
\(366\) | −26.2312 | −1.37113 | ||||||||
\(367\) | 10.8382 | 0.565749 | 0.282874 | − | 0.959157i | \(-0.408712\pi\) | ||||
0.282874 | + | 0.959157i | \(0.408712\pi\) | |||||||
\(368\) | −4.54919 | −0.237143 | ||||||||
\(369\) | −1.64224 | −0.0854917 | ||||||||
\(370\) | 7.80132 | 0.405571 | ||||||||
\(371\) | −2.07031 | −0.107485 | ||||||||
\(372\) | −4.20615 | −0.218079 | ||||||||
\(373\) | 19.9848 | 1.03477 | 0.517387 | − | 0.855752i | \(-0.326905\pi\) | ||||
0.517387 | + | 0.855752i | \(0.326905\pi\) | |||||||
\(374\) | −20.5487 | −1.06255 | ||||||||
\(375\) | −21.7839 | −1.12492 | ||||||||
\(376\) | −9.43863 | −0.486760 | ||||||||
\(377\) | −1.64291 | −0.0846144 | ||||||||
\(378\) | 38.4593 | 1.97813 | ||||||||
\(379\) | 2.99305 | 0.153742 | 0.0768712 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768712 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(380\) | −36.2598 | −1.86009 | ||||||||
\(381\) | −28.2247 | −1.44599 | ||||||||
\(382\) | 42.4585 | 2.17236 | ||||||||
\(383\) | −7.32975 | −0.374533 | −0.187266 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187266 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(384\) | 17.7081 | 0.903663 | ||||||||
\(385\) | 67.9524 | 3.46318 | ||||||||
\(386\) | −2.49738 | −0.127113 | ||||||||
\(387\) | 2.51607 | 0.127899 | ||||||||
\(388\) | 11.2591 | 0.571593 | ||||||||
\(389\) | −20.3476 | −1.03166 | −0.515831 | − | 0.856690i | \(-0.672517\pi\) | ||||
−0.515831 | + | 0.856690i | \(0.672517\pi\) | |||||||
\(390\) | −8.66878 | −0.438961 | ||||||||
\(391\) | −3.50757 | −0.177386 | ||||||||
\(392\) | −8.55431 | −0.432058 | ||||||||
\(393\) | 30.4495 | 1.53597 | ||||||||
\(394\) | 30.4913 | 1.53613 | ||||||||
\(395\) | 43.9533 | 2.21153 | ||||||||
\(396\) | −4.71707 | −0.237042 | ||||||||
\(397\) | 16.0348 | 0.804761 | 0.402381 | − | 0.915472i | \(-0.368183\pi\) | ||||
0.402381 | + | 0.915472i | \(0.368183\pi\) | |||||||
\(398\) | −3.39203 | −0.170027 | ||||||||
\(399\) | 26.1768 | 1.31048 | ||||||||
\(400\) | −20.4482 | −1.02241 | ||||||||
\(401\) | −12.0144 | −0.599970 | −0.299985 | − | 0.953944i | \(-0.596982\pi\) | ||||
−0.299985 | + | 0.953944i | \(0.596982\pi\) | |||||||
\(402\) | 26.9177 | 1.34253 | ||||||||
\(403\) | 0.536883 | 0.0267440 | ||||||||
\(404\) | −2.83642 | −0.141117 | ||||||||
\(405\) | 36.2569 | 1.80162 | ||||||||
\(406\) | −21.5588 | −1.06994 | ||||||||
\(407\) | −5.02675 | −0.249167 | ||||||||
\(408\) | 4.41544 | 0.218597 | ||||||||
\(409\) | 1.89395 | 0.0936497 | 0.0468248 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468248 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(410\) | −35.3476 | −1.74569 | ||||||||
\(411\) | −33.3884 | −1.64693 | ||||||||
\(412\) | −15.6253 | −0.769803 | ||||||||
\(413\) | 33.5601 | 1.65139 | ||||||||
\(414\) | −1.42718 | −0.0701419 | ||||||||
\(415\) | 0.266555 | 0.0130847 | ||||||||
\(416\) | −4.74216 | −0.232503 | ||||||||
\(417\) | 18.8269 | 0.921957 | ||||||||
\(418\) | 41.4121 | 2.02553 | ||||||||
\(419\) | 11.7530 | 0.574172 | 0.287086 | − | 0.957905i | \(-0.407313\pi\) | ||||
0.287086 | + | 0.957905i | \(0.407313\pi\) | |||||||
\(420\) | −64.1779 | −3.13156 | ||||||||
\(421\) | −30.4242 | −1.48278 | −0.741391 | − | 0.671073i | \(-0.765834\pi\) | ||||
−0.741391 | + | 0.671073i | \(0.765834\pi\) | |||||||
\(422\) | 32.9513 | 1.60404 | ||||||||
\(423\) | 2.71108 | 0.131817 | ||||||||
\(424\) | 0.703780 | 0.0341786 | ||||||||
\(425\) | −15.7662 | −0.764773 | ||||||||
\(426\) | 7.64844 | 0.370568 | ||||||||
\(427\) | 24.7880 | 1.19957 | ||||||||
\(428\) | −14.4631 | −0.699102 | ||||||||
\(429\) | 5.58570 | 0.269680 | ||||||||
\(430\) | 54.1560 | 2.61164 | ||||||||
\(431\) | 8.38501 | 0.403892 | 0.201946 | − | 0.979397i | \(-0.435274\pi\) | ||||
0.201946 | + | 0.979397i | \(0.435274\pi\) | |||||||
\(432\) | 11.9699 | 0.575903 | ||||||||
\(433\) | −16.6152 | −0.798474 | −0.399237 | − | 0.916848i | \(-0.630725\pi\) | ||||
−0.399237 | + | 0.916848i | \(0.630725\pi\) | |||||||
\(434\) | 7.04513 | 0.338177 | ||||||||
\(435\) | −18.1045 | −0.868045 | ||||||||
\(436\) | −26.9871 | −1.29245 | ||||||||
\(437\) | 7.06887 | 0.338150 | ||||||||
\(438\) | −40.8693 | −1.95281 | ||||||||
\(439\) | −39.7234 | −1.89590 | −0.947948 | − | 0.318425i | \(-0.896846\pi\) | ||||
−0.947948 | + | 0.318425i | \(0.896846\pi\) | |||||||
\(440\) | −23.0997 | −1.10123 | ||||||||
\(441\) | 2.45707 | 0.117004 | ||||||||
\(442\) | −2.47719 | −0.117828 | ||||||||
\(443\) | −16.6087 | −0.789104 | −0.394552 | − | 0.918874i | \(-0.629100\pi\) | ||||
−0.394552 | + | 0.918874i | \(0.629100\pi\) | |||||||
\(444\) | 4.74753 | 0.225308 | ||||||||
\(445\) | 55.7572 | 2.64314 | ||||||||
\(446\) | 48.3092 | 2.28751 | ||||||||
\(447\) | −15.2494 | −0.721274 | ||||||||
\(448\) | −43.8540 | −2.07191 | ||||||||
\(449\) | −3.32520 | −0.156926 | −0.0784630 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784630 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(450\) | −6.41502 | −0.302407 | ||||||||
\(451\) | 22.7761 | 1.07249 | ||||||||
\(452\) | 1.47476 | 0.0693671 | ||||||||
\(453\) | 4.63018 | 0.217545 | ||||||||
\(454\) | 37.3631 | 1.75354 | ||||||||
\(455\) | 8.19181 | 0.384038 | ||||||||
\(456\) | −8.89851 | −0.416711 | ||||||||
\(457\) | −10.0365 | −0.469486 | −0.234743 | − | 0.972058i | \(-0.575425\pi\) | ||||
−0.234743 | + | 0.972058i | \(0.575425\pi\) | |||||||
\(458\) | 12.1673 | 0.568540 | ||||||||
\(459\) | 9.22919 | 0.430782 | ||||||||
\(460\) | −17.3308 | −0.808053 | ||||||||
\(461\) | 32.5172 | 1.51447 | 0.757237 | − | 0.653140i | \(-0.226549\pi\) | ||||
0.757237 | + | 0.653140i | \(0.226549\pi\) | |||||||
\(462\) | 73.2972 | 3.41009 | ||||||||
\(463\) | −14.6340 | −0.680099 | −0.340050 | − | 0.940408i | \(-0.610444\pi\) | ||||
−0.340050 | + | 0.940408i | \(0.610444\pi\) | |||||||
\(464\) | −6.70988 | −0.311499 | ||||||||
\(465\) | 5.91632 | 0.274363 | ||||||||
\(466\) | 44.3972 | 2.05666 | ||||||||
\(467\) | −13.6855 | −0.633290 | −0.316645 | − | 0.948544i | \(-0.602556\pi\) | ||||
−0.316645 | + | 0.948544i | \(0.602556\pi\) | |||||||
\(468\) | −0.568653 | −0.0262860 | ||||||||
\(469\) | −25.4367 | −1.17456 | ||||||||
\(470\) | 58.3533 | 2.69164 | ||||||||
\(471\) | −19.2063 | −0.884978 | ||||||||
\(472\) | −11.4084 | −0.525114 | ||||||||
\(473\) | −34.8953 | −1.60449 | ||||||||
\(474\) | 47.4105 | 2.17764 | ||||||||
\(475\) | 31.7739 | 1.45789 | ||||||||
\(476\) | −18.3394 | −0.840586 | ||||||||
\(477\) | −0.202148 | −0.00925574 | ||||||||
\(478\) | −11.7591 | −0.537847 | ||||||||
\(479\) | 34.2918 | 1.56683 | 0.783415 | − | 0.621498i | \(-0.213476\pi\) | ||||
0.783415 | + | 0.621498i | \(0.213476\pi\) | |||||||
\(480\) | −52.2574 | −2.38521 | ||||||||
\(481\) | −0.605986 | −0.0276306 | ||||||||
\(482\) | −32.8610 | −1.49678 | ||||||||
\(483\) | 12.5115 | 0.569294 | ||||||||
\(484\) | 36.9412 | 1.67914 | ||||||||
\(485\) | −15.8369 | −0.719116 | ||||||||
\(486\) | 8.02647 | 0.364088 | ||||||||
\(487\) | −18.3228 | −0.830286 | −0.415143 | − | 0.909756i | \(-0.636268\pi\) | ||||
−0.415143 | + | 0.909756i | \(0.636268\pi\) | |||||||
\(488\) | −8.42639 | −0.381445 | ||||||||
\(489\) | 1.83370 | 0.0829227 | ||||||||
\(490\) | 52.8861 | 2.38915 | ||||||||
\(491\) | 4.16764 | 0.188083 | 0.0940416 | − | 0.995568i | \(-0.470021\pi\) | ||||
0.0940416 | + | 0.995568i | \(0.470021\pi\) | |||||||
\(492\) | −21.5110 | −0.969789 | ||||||||
\(493\) | −5.17353 | −0.233004 | ||||||||
\(494\) | 4.99232 | 0.224615 | ||||||||
\(495\) | 6.63497 | 0.298220 | ||||||||
\(496\) | 2.19270 | 0.0984553 | ||||||||
\(497\) | −7.22761 | −0.324203 | ||||||||
\(498\) | 0.287520 | 0.0128841 | ||||||||
\(499\) | −18.2088 | −0.815137 | −0.407569 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407569 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(500\) | −30.7573 | −1.37551 | ||||||||
\(501\) | 27.7171 | 1.23831 | ||||||||
\(502\) | −24.3601 | −1.08724 | ||||||||
\(503\) | −8.05949 | −0.359355 | −0.179677 | − | 0.983726i | \(-0.557505\pi\) | ||||
−0.179677 | + | 0.983726i | \(0.557505\pi\) | |||||||
\(504\) | −1.69772 | −0.0756226 | ||||||||
\(505\) | 3.98967 | 0.177538 | ||||||||
\(506\) | 19.7934 | 0.879925 | ||||||||
\(507\) | −23.1647 | −1.02878 | ||||||||
\(508\) | −39.8512 | −1.76811 | ||||||||
\(509\) | −21.5490 | −0.955143 | −0.477572 | − | 0.878593i | \(-0.658483\pi\) | ||||
−0.477572 | + | 0.878593i | \(0.658483\pi\) | |||||||
\(510\) | −27.2980 | −1.20877 | ||||||||
\(511\) | 38.6206 | 1.70848 | ||||||||
\(512\) | −25.6137 | −1.13197 | ||||||||
\(513\) | −18.5998 | −0.821199 | ||||||||
\(514\) | −45.3093 | −1.99851 | ||||||||
\(515\) | 21.9783 | 0.968481 | ||||||||
\(516\) | 32.9569 | 1.45085 | ||||||||
\(517\) | −37.5997 | −1.65363 | ||||||||
\(518\) | −7.95192 | −0.349387 | ||||||||
\(519\) | −10.2472 | −0.449802 | ||||||||
\(520\) | −2.78471 | −0.122118 | ||||||||
\(521\) | 35.7218 | 1.56500 | 0.782499 | − | 0.622651i | \(-0.213945\pi\) | ||||
0.782499 | + | 0.622651i | \(0.213945\pi\) | |||||||
\(522\) | −2.10503 | −0.0921347 | ||||||||
\(523\) | 35.0820 | 1.53403 | 0.767015 | − | 0.641629i | \(-0.221741\pi\) | ||||
0.767015 | + | 0.641629i | \(0.221741\pi\) | |||||||
\(524\) | 42.9925 | 1.87813 | ||||||||
\(525\) | 56.2381 | 2.45443 | ||||||||
\(526\) | 11.1460 | 0.485987 | ||||||||
\(527\) | 1.69064 | 0.0736456 | ||||||||
\(528\) | 22.8128 | 0.992798 | ||||||||
\(529\) | −19.6213 | −0.853102 | ||||||||
\(530\) | −4.35104 | −0.188997 | ||||||||
\(531\) | 3.27686 | 0.142204 | ||||||||
\(532\) | 36.9598 | 1.60241 | ||||||||
\(533\) | 2.74571 | 0.118930 | ||||||||
\(534\) | 60.1427 | 2.60263 | ||||||||
\(535\) | 20.3437 | 0.879533 | ||||||||
\(536\) | 8.64691 | 0.373490 | ||||||||
\(537\) | 5.45735 | 0.235502 | ||||||||
\(538\) | 32.9359 | 1.41997 | ||||||||
\(539\) | −34.0770 | −1.46780 | ||||||||
\(540\) | 45.6011 | 1.96236 | ||||||||
\(541\) | 30.0077 | 1.29013 | 0.645067 | − | 0.764126i | \(-0.276830\pi\) | ||||
0.645067 | + | 0.764126i | \(0.276830\pi\) | |||||||
\(542\) | −20.0293 | −0.860330 | ||||||||
\(543\) | 5.91460 | 0.253820 | ||||||||
\(544\) | −14.9331 | −0.640249 | ||||||||
\(545\) | 37.9598 | 1.62602 | ||||||||
\(546\) | 8.83613 | 0.378152 | ||||||||
\(547\) | −8.31544 | −0.355542 | −0.177771 | − | 0.984072i | \(-0.556889\pi\) | ||||
−0.177771 | + | 0.984072i | \(0.556889\pi\) | |||||||
\(548\) | −47.1420 | −2.01381 | ||||||||
\(549\) | 2.42033 | 0.103297 | ||||||||
\(550\) | 88.9695 | 3.79367 | ||||||||
\(551\) | 10.4263 | 0.444176 | ||||||||
\(552\) | −4.25315 | −0.181026 | ||||||||
\(553\) | −44.8019 | −1.90517 | ||||||||
\(554\) | 38.3521 | 1.62942 | ||||||||
\(555\) | −6.67782 | −0.283457 | ||||||||
\(556\) | 26.5822 | 1.12734 | ||||||||
\(557\) | 35.5039 | 1.50435 | 0.752175 | − | 0.658963i | \(-0.229005\pi\) | ||||
0.752175 | + | 0.658963i | \(0.229005\pi\) | |||||||
\(558\) | 0.687897 | 0.0291210 | ||||||||
\(559\) | −4.20670 | −0.177924 | ||||||||
\(560\) | 33.4565 | 1.41379 | ||||||||
\(561\) | 17.5894 | 0.742624 | ||||||||
\(562\) | −67.2825 | −2.83814 | ||||||||
\(563\) | −0.224564 | −0.00946425 | −0.00473212 | − | 0.999989i | \(-0.501506\pi\) | ||||
−0.00473212 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(564\) | 35.5112 | 1.49529 | ||||||||
\(565\) | −2.07438 | −0.0872700 | ||||||||
\(566\) | −44.2111 | −1.85833 | ||||||||
\(567\) | −36.9568 | −1.55204 | ||||||||
\(568\) | 2.45695 | 0.103091 | ||||||||
\(569\) | −35.2108 | −1.47611 | −0.738056 | − | 0.674739i | \(-0.764256\pi\) | ||||
−0.738056 | + | 0.674739i | \(0.764256\pi\) | |||||||
\(570\) | 55.0141 | 2.30429 | ||||||||
\(571\) | −11.3268 | −0.474011 | −0.237005 | − | 0.971508i | \(-0.576166\pi\) | ||||
−0.237005 | + | 0.971508i | \(0.576166\pi\) | |||||||
\(572\) | 7.88660 | 0.329755 | ||||||||
\(573\) | −36.3438 | −1.51829 | ||||||||
\(574\) | 36.0300 | 1.50386 | ||||||||
\(575\) | 15.1867 | 0.633330 | ||||||||
\(576\) | −4.28197 | −0.178415 | ||||||||
\(577\) | −8.81518 | −0.366981 | −0.183490 | − | 0.983022i | \(-0.558740\pi\) | ||||
−0.183490 | + | 0.983022i | \(0.558740\pi\) | |||||||
\(578\) | 28.6169 | 1.19030 | ||||||||
\(579\) | 2.13772 | 0.0888407 | ||||||||
\(580\) | −25.5623 | −1.06141 | ||||||||
\(581\) | −0.271700 | −0.0112720 | ||||||||
\(582\) | −17.0825 | −0.708093 | ||||||||
\(583\) | 2.80358 | 0.116112 | ||||||||
\(584\) | −13.1287 | −0.543267 | ||||||||
\(585\) | 0.799860 | 0.0330701 | ||||||||
\(586\) | −0.403631 | −0.0166738 | ||||||||
\(587\) | −26.0722 | −1.07611 | −0.538057 | − | 0.842909i | \(-0.680841\pi\) | ||||
−0.538057 | + | 0.842909i | \(0.680841\pi\) | |||||||
\(588\) | 32.1841 | 1.32725 | ||||||||
\(589\) | −3.40718 | −0.140391 | ||||||||
\(590\) | 70.5311 | 2.90372 | ||||||||
\(591\) | −26.1001 | −1.07361 | ||||||||
\(592\) | −2.47493 | −0.101719 | ||||||||
\(593\) | 27.7171 | 1.13820 | 0.569102 | − | 0.822267i | \(-0.307291\pi\) | ||||
0.569102 | + | 0.822267i | \(0.307291\pi\) | |||||||
\(594\) | −52.0808 | −2.13690 | ||||||||
\(595\) | 25.7960 | 1.05753 | ||||||||
\(596\) | −21.5311 | −0.881948 | ||||||||
\(597\) | 2.90353 | 0.118834 | ||||||||
\(598\) | 2.38614 | 0.0975764 | ||||||||
\(599\) | −32.3285 | −1.32091 | −0.660454 | − | 0.750866i | \(-0.729636\pi\) | ||||
−0.660454 | + | 0.750866i | \(0.729636\pi\) | |||||||
\(600\) | −19.1175 | −0.780469 | ||||||||
\(601\) | −19.6954 | −0.803393 | −0.401697 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401697 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(602\) | −55.2015 | −2.24984 | ||||||||
\(603\) | −2.48367 | −0.101143 | ||||||||
\(604\) | 6.53748 | 0.266006 | ||||||||
\(605\) | −51.9610 | −2.11251 | ||||||||
\(606\) | 4.30348 | 0.174817 | ||||||||
\(607\) | −23.0743 | −0.936557 | −0.468279 | − | 0.883581i | \(-0.655126\pi\) | ||||
−0.468279 | + | 0.883581i | \(0.655126\pi\) | |||||||
\(608\) | 30.0948 | 1.22051 | ||||||||
\(609\) | 18.4540 | 0.747795 | ||||||||
\(610\) | 52.0952 | 2.10927 | ||||||||
\(611\) | −4.53273 | −0.183375 | ||||||||
\(612\) | −1.79069 | −0.0723842 | ||||||||
\(613\) | 24.6414 | 0.995256 | 0.497628 | − | 0.867391i | \(-0.334205\pi\) | ||||
0.497628 | + | 0.867391i | \(0.334205\pi\) | |||||||
\(614\) | 13.3342 | 0.538126 | ||||||||
\(615\) | 30.2571 | 1.22008 | ||||||||
\(616\) | 23.5456 | 0.948680 | ||||||||
\(617\) | −1.62554 | −0.0654416 | −0.0327208 | − | 0.999465i | \(-0.510417\pi\) | ||||
−0.0327208 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(618\) | 23.7070 | 0.953637 | ||||||||
\(619\) | 20.6595 | 0.830374 | 0.415187 | − | 0.909736i | \(-0.363716\pi\) | ||||
0.415187 | + | 0.909736i | \(0.363716\pi\) | |||||||
\(620\) | 8.35341 | 0.335481 | ||||||||
\(621\) | −8.88998 | −0.356743 | ||||||||
\(622\) | −34.6043 | −1.38751 | ||||||||
\(623\) | −56.8336 | −2.27699 | ||||||||
\(624\) | 2.75013 | 0.110093 | ||||||||
\(625\) | 1.95218 | 0.0780870 | ||||||||
\(626\) | 57.0947 | 2.28196 | ||||||||
\(627\) | −35.4482 | −1.41566 | ||||||||
\(628\) | −27.1178 | −1.08212 | ||||||||
\(629\) | −1.90825 | −0.0760868 | ||||||||
\(630\) | 10.4960 | 0.418170 | ||||||||
\(631\) | −29.2395 | −1.16401 | −0.582004 | − | 0.813186i | \(-0.697731\pi\) | ||||
−0.582004 | + | 0.813186i | \(0.697731\pi\) | |||||||
\(632\) | 15.2299 | 0.605813 | ||||||||
\(633\) | −28.2058 | −1.12108 | ||||||||
\(634\) | 21.9252 | 0.870761 | ||||||||
\(635\) | 56.0541 | 2.22444 | ||||||||
\(636\) | −2.64785 | −0.104994 | ||||||||
\(637\) | −4.10805 | −0.162767 | ||||||||
\(638\) | 29.1945 | 1.15582 | ||||||||
\(639\) | −0.705714 | −0.0279176 | ||||||||
\(640\) | −35.1683 | −1.39015 | ||||||||
\(641\) | 9.88104 | 0.390277 | 0.195139 | − | 0.980776i | \(-0.437484\pi\) | ||||
0.195139 | + | 0.980776i | \(0.437484\pi\) | |||||||
\(642\) | 21.9438 | 0.866052 | ||||||||
\(643\) | −30.8188 | −1.21538 | −0.607688 | − | 0.794176i | \(-0.707903\pi\) | ||||
−0.607688 | + | 0.794176i | \(0.707903\pi\) | |||||||
\(644\) | 17.6654 | 0.696113 | ||||||||
\(645\) | −46.3568 | −1.82530 | ||||||||
\(646\) | 15.7208 | 0.618526 | ||||||||
\(647\) | −38.4563 | −1.51187 | −0.755937 | − | 0.654645i | \(-0.772818\pi\) | ||||
−0.755937 | + | 0.654645i | \(0.772818\pi\) | |||||||
\(648\) | 12.5631 | 0.493523 | ||||||||
\(649\) | −45.4465 | −1.78393 | ||||||||
\(650\) | 10.7255 | 0.420687 | ||||||||
\(651\) | −6.03053 | −0.236355 | ||||||||
\(652\) | 2.58905 | 0.101395 | ||||||||
\(653\) | −27.5722 | −1.07898 | −0.539492 | − | 0.841991i | \(-0.681384\pi\) | ||||
−0.539492 | + | 0.841991i | \(0.681384\pi\) | |||||||
\(654\) | 40.9455 | 1.60109 | ||||||||
\(655\) | −60.4726 | −2.36286 | ||||||||
\(656\) | 11.2139 | 0.437827 | ||||||||
\(657\) | 3.77097 | 0.147120 | ||||||||
\(658\) | −59.4798 | −2.31876 | ||||||||
\(659\) | −9.56340 | −0.372537 | −0.186269 | − | 0.982499i | \(-0.559639\pi\) | ||||
−0.186269 | + | 0.982499i | \(0.559639\pi\) | |||||||
\(660\) | 86.9085 | 3.38291 | ||||||||
\(661\) | 29.5518 | 1.14943 | 0.574717 | − | 0.818352i | \(-0.305112\pi\) | ||||
0.574717 | + | 0.818352i | \(0.305112\pi\) | |||||||
\(662\) | 9.79655 | 0.380754 | ||||||||
\(663\) | 2.12044 | 0.0823509 | ||||||||
\(664\) | 0.0923615 | 0.00358432 | ||||||||
\(665\) | −51.9871 | −2.01597 | ||||||||
\(666\) | −0.776437 | −0.0300863 | ||||||||
\(667\) | 4.98338 | 0.192957 | ||||||||
\(668\) | 39.1345 | 1.51416 | ||||||||
\(669\) | −41.3520 | −1.59876 | ||||||||
\(670\) | −53.4586 | −2.06529 | ||||||||
\(671\) | −33.5674 | −1.29585 | ||||||||
\(672\) | 53.2663 | 2.05479 | ||||||||
\(673\) | 8.34794 | 0.321789 | 0.160895 | − | 0.986972i | \(-0.448562\pi\) | ||||
0.160895 | + | 0.986972i | \(0.448562\pi\) | |||||||
\(674\) | −34.5917 | −1.33242 | ||||||||
\(675\) | −39.9596 | −1.53805 | ||||||||
\(676\) | −32.7069 | −1.25796 | ||||||||
\(677\) | −1.31673 | −0.0506061 | −0.0253031 | − | 0.999680i | \(-0.508055\pi\) | ||||
−0.0253031 | + | 0.999680i | \(0.508055\pi\) | |||||||
\(678\) | −2.23754 | −0.0859324 | ||||||||
\(679\) | 16.1426 | 0.619497 | ||||||||
\(680\) | −8.76906 | −0.336278 | ||||||||
\(681\) | −31.9823 | −1.22556 | ||||||||
\(682\) | −9.54039 | −0.365320 | ||||||||
\(683\) | 26.4013 | 1.01022 | 0.505108 | − | 0.863056i | \(-0.331453\pi\) | ||||
0.505108 | + | 0.863056i | \(0.331453\pi\) | |||||||
\(684\) | 3.60880 | 0.137986 | ||||||||
\(685\) | 66.3093 | 2.53355 | ||||||||
\(686\) | 1.75640 | 0.0670599 | ||||||||
\(687\) | −10.4150 | −0.397358 | ||||||||
\(688\) | −17.1807 | −0.655009 | ||||||||
\(689\) | 0.337978 | 0.0128759 | ||||||||
\(690\) | 26.2947 | 1.00102 | ||||||||
\(691\) | −2.12153 | −0.0807067 | −0.0403534 | − | 0.999185i | \(-0.512848\pi\) | ||||
−0.0403534 | + | 0.999185i | \(0.512848\pi\) | |||||||
\(692\) | −14.4683 | −0.550002 | ||||||||
\(693\) | −6.76306 | −0.256907 | ||||||||
\(694\) | 52.6441 | 1.99834 | ||||||||
\(695\) | −37.3902 | −1.41829 | ||||||||
\(696\) | −6.27324 | −0.237786 | ||||||||
\(697\) | 8.64624 | 0.327500 | ||||||||
\(698\) | −41.4393 | −1.56850 | ||||||||
\(699\) | −38.0033 | −1.43742 | ||||||||
\(700\) | 79.4041 | 3.00119 | ||||||||
\(701\) | 16.8578 | 0.636710 | 0.318355 | − | 0.947972i | \(-0.396870\pi\) | ||||
0.318355 | + | 0.947972i | \(0.396870\pi\) | |||||||
\(702\) | −6.27845 | −0.236965 | ||||||||
\(703\) | 3.84573 | 0.145044 | ||||||||
\(704\) | 59.3863 | 2.23820 | ||||||||
\(705\) | −49.9496 | −1.88121 | ||||||||
\(706\) | 74.5179 | 2.80452 | ||||||||
\(707\) | −4.06669 | −0.152944 | ||||||||
\(708\) | 42.9221 | 1.61311 | ||||||||
\(709\) | −1.39506 | −0.0523924 | −0.0261962 | − | 0.999657i | \(-0.508339\pi\) | ||||
−0.0261962 | + | 0.999657i | \(0.508339\pi\) | |||||||
\(710\) | −15.1898 | −0.570063 | ||||||||
\(711\) | −4.37452 | −0.164057 | ||||||||
\(712\) | 19.3199 | 0.724045 | ||||||||
\(713\) | −1.62850 | −0.0609880 | ||||||||
\(714\) | 27.8250 | 1.04132 | ||||||||
\(715\) | −11.0932 | −0.414862 | ||||||||
\(716\) | 7.70539 | 0.287964 | ||||||||
\(717\) | 10.0656 | 0.375906 | ||||||||
\(718\) | −14.4207 | −0.538175 | ||||||||
\(719\) | 30.1869 | 1.12578 | 0.562891 | − | 0.826531i | \(-0.309689\pi\) | ||||
0.562891 | + | 0.826531i | \(0.309689\pi\) | |||||||
\(720\) | 3.26674 | 0.121744 | ||||||||
\(721\) | −22.4026 | −0.834318 | ||||||||
\(722\) | 9.01954 | 0.335672 | ||||||||
\(723\) | 28.1285 | 1.04611 | ||||||||
\(724\) | 8.35098 | 0.310362 | ||||||||
\(725\) | 22.3998 | 0.831909 | ||||||||
\(726\) | −56.0480 | −2.08013 | ||||||||
\(727\) | −15.3679 | −0.569966 | −0.284983 | − | 0.958533i | \(-0.591988\pi\) | ||||
−0.284983 | + | 0.958533i | \(0.591988\pi\) | |||||||
\(728\) | 2.83847 | 0.105201 | ||||||||
\(729\) | 22.9974 | 0.851755 | ||||||||
\(730\) | 81.1665 | 3.00411 | ||||||||
\(731\) | −13.2469 | −0.489954 | ||||||||
\(732\) | 31.7028 | 1.17177 | ||||||||
\(733\) | −20.2903 | −0.749439 | −0.374720 | − | 0.927138i | \(-0.622261\pi\) | ||||
−0.374720 | + | 0.927138i | \(0.622261\pi\) | |||||||
\(734\) | −23.2176 | −0.856978 | ||||||||
\(735\) | −45.2697 | −1.66980 | ||||||||
\(736\) | 14.3842 | 0.530208 | ||||||||
\(737\) | 34.4459 | 1.26883 | ||||||||
\(738\) | 3.51802 | 0.129500 | ||||||||
\(739\) | −26.5949 | −0.978308 | −0.489154 | − | 0.872197i | \(-0.662694\pi\) | ||||
−0.489154 | + | 0.872197i | \(0.662694\pi\) | |||||||
\(740\) | −9.42859 | −0.346602 | ||||||||
\(741\) | −4.27335 | −0.156985 | ||||||||
\(742\) | 4.43504 | 0.162815 | ||||||||
\(743\) | 7.76515 | 0.284876 | 0.142438 | − | 0.989804i | \(-0.454506\pi\) | ||||
0.142438 | + | 0.989804i | \(0.454506\pi\) | |||||||
\(744\) | 2.05001 | 0.0751571 | ||||||||
\(745\) | 30.2854 | 1.10957 | ||||||||
\(746\) | −42.8115 | −1.56744 | ||||||||
\(747\) | −0.0265292 | −0.000970653 0 | ||||||||
\(748\) | 24.8349 | 0.908054 | ||||||||
\(749\) | −20.7364 | −0.757692 | ||||||||
\(750\) | 46.6657 | 1.70399 | ||||||||
\(751\) | 1.21960 | 0.0445037 | 0.0222518 | − | 0.999752i | \(-0.492916\pi\) | ||||
0.0222518 | + | 0.999752i | \(0.492916\pi\) | |||||||
\(752\) | −18.5123 | −0.675073 | ||||||||
\(753\) | 20.8519 | 0.759884 | ||||||||
\(754\) | 3.51946 | 0.128171 | ||||||||
\(755\) | −9.19554 | −0.334660 | ||||||||
\(756\) | −46.4815 | −1.69051 | ||||||||
\(757\) | 15.6406 | 0.568467 | 0.284233 | − | 0.958755i | \(-0.408261\pi\) | ||||
0.284233 | + | 0.958755i | \(0.408261\pi\) | |||||||
\(758\) | −6.41172 | −0.232884 | ||||||||
\(759\) | −16.9429 | −0.614988 | ||||||||
\(760\) | 17.6724 | 0.641047 | ||||||||
\(761\) | −37.0255 | −1.34217 | −0.671087 | − | 0.741379i | \(-0.734172\pi\) | ||||
−0.671087 | + | 0.741379i | \(0.734172\pi\) | |||||||
\(762\) | 60.4630 | 2.19035 | ||||||||
\(763\) | −38.6926 | −1.40076 | ||||||||
\(764\) | −51.3149 | −1.85651 | ||||||||
\(765\) | 2.51876 | 0.0910658 | ||||||||
\(766\) | 15.7018 | 0.567330 | ||||||||
\(767\) | −5.47867 | −0.197823 | ||||||||
\(768\) | 5.39233 | 0.194579 | ||||||||
\(769\) | 12.3594 | 0.445690 | 0.222845 | − | 0.974854i | \(-0.428466\pi\) | ||||
0.222845 | + | 0.974854i | \(0.428466\pi\) | |||||||
\(770\) | −145.568 | −5.24591 | ||||||||
\(771\) | 38.7841 | 1.39678 | ||||||||
\(772\) | 3.01831 | 0.108631 | ||||||||
\(773\) | 17.9412 | 0.645298 | 0.322649 | − | 0.946519i | \(-0.395427\pi\) | ||||
0.322649 | + | 0.946519i | \(0.395427\pi\) | |||||||
\(774\) | −5.38995 | −0.193738 | ||||||||
\(775\) | −7.31997 | −0.262941 | ||||||||
\(776\) | −5.48750 | −0.196990 | ||||||||
\(777\) | 6.80673 | 0.244190 | ||||||||
\(778\) | 43.5887 | 1.56273 | ||||||||
\(779\) | −17.4249 | −0.624312 | ||||||||
\(780\) | 10.4770 | 0.375137 | ||||||||
\(781\) | 9.78750 | 0.350224 | ||||||||
\(782\) | 7.51394 | 0.268698 | ||||||||
\(783\) | −13.1124 | −0.468598 | ||||||||
\(784\) | −16.7778 | −0.599209 | ||||||||
\(785\) | 38.1436 | 1.36140 | ||||||||
\(786\) | −65.2291 | −2.32664 | ||||||||
\(787\) | −36.8063 | −1.31200 | −0.656001 | − | 0.754760i | \(-0.727753\pi\) | ||||
−0.656001 | + | 0.754760i | \(0.727753\pi\) | |||||||
\(788\) | −36.8514 | −1.31278 | ||||||||
\(789\) | −9.54078 | −0.339661 | ||||||||
\(790\) | −94.1571 | −3.34996 | ||||||||
\(791\) | 2.11443 | 0.0751805 | ||||||||
\(792\) | 2.29903 | 0.0816923 | ||||||||
\(793\) | −4.04662 | −0.143700 | ||||||||
\(794\) | −34.3497 | −1.21903 | ||||||||
\(795\) | 3.72443 | 0.132092 | ||||||||
\(796\) | 4.09957 | 0.145305 | ||||||||
\(797\) | 27.4722 | 0.973117 | 0.486558 | − | 0.873648i | \(-0.338252\pi\) | ||||
0.486558 | + | 0.873648i | \(0.338252\pi\) | |||||||
\(798\) | −56.0761 | −1.98507 | ||||||||
\(799\) | −14.2736 | −0.504962 | ||||||||
\(800\) | 64.6556 | 2.28592 | ||||||||
\(801\) | −5.54931 | −0.196075 | ||||||||
\(802\) | 25.7373 | 0.908816 | ||||||||
\(803\) | −52.2993 | −1.84560 | ||||||||
\(804\) | −32.5325 | −1.14733 | ||||||||
\(805\) | −24.8479 | −0.875773 | ||||||||
\(806\) | −1.15011 | −0.0405110 | ||||||||
\(807\) | −28.1926 | −0.992427 | ||||||||
\(808\) | 1.38243 | 0.0486336 | ||||||||
\(809\) | 27.4470 | 0.964985 | 0.482492 | − | 0.875900i | \(-0.339732\pi\) | ||||
0.482492 | + | 0.875900i | \(0.339732\pi\) | |||||||
\(810\) | −77.6697 | −2.72904 | ||||||||
\(811\) | −27.6991 | −0.972647 | −0.486323 | − | 0.873779i | \(-0.661662\pi\) | ||||
−0.486323 | + | 0.873779i | \(0.661662\pi\) | |||||||
\(812\) | 26.0557 | 0.914377 | ||||||||
\(813\) | 17.1448 | 0.601293 | ||||||||
\(814\) | 10.7683 | 0.377430 | ||||||||
\(815\) | −3.64172 | −0.127564 | ||||||||
\(816\) | 8.66015 | 0.303166 | ||||||||
\(817\) | 26.6967 | 0.933998 | ||||||||
\(818\) | −4.05723 | −0.141858 | ||||||||
\(819\) | −0.815301 | −0.0284889 | ||||||||
\(820\) | 42.7208 | 1.49187 | ||||||||
\(821\) | −44.6775 | −1.55925 | −0.779627 | − | 0.626244i | \(-0.784592\pi\) | ||||
−0.779627 | + | 0.626244i | \(0.784592\pi\) | |||||||
\(822\) | 71.5248 | 2.49471 | ||||||||
\(823\) | 7.11798 | 0.248117 | 0.124059 | − | 0.992275i | \(-0.460409\pi\) | ||||
0.124059 | + | 0.992275i | \(0.460409\pi\) | |||||||
\(824\) | 7.61552 | 0.265299 | ||||||||
\(825\) | −76.1566 | −2.65143 | ||||||||
\(826\) | −71.8927 | −2.50147 | ||||||||
\(827\) | 39.0419 | 1.35762 | 0.678810 | − | 0.734314i | \(-0.262496\pi\) | ||||
0.678810 | + | 0.734314i | \(0.262496\pi\) | |||||||
\(828\) | 1.72487 | 0.0599434 | ||||||||
\(829\) | 22.7626 | 0.790578 | 0.395289 | − | 0.918557i | \(-0.370644\pi\) | ||||
0.395289 | + | 0.918557i | \(0.370644\pi\) | |||||||
\(830\) | −0.571015 | −0.0198202 | ||||||||
\(831\) | −32.8288 | −1.13882 | ||||||||
\(832\) | 7.15914 | 0.248199 | ||||||||
\(833\) | −12.9362 | −0.448214 | ||||||||
\(834\) | −40.3311 | −1.39655 | ||||||||
\(835\) | −55.0460 | −1.90495 | ||||||||
\(836\) | −50.0502 | −1.73102 | ||||||||
\(837\) | 4.28495 | 0.148110 | ||||||||
\(838\) | −25.1774 | −0.869738 | ||||||||
\(839\) | −34.2425 | −1.18218 | −0.591092 | − | 0.806604i | \(-0.701303\pi\) | ||||
−0.591092 | + | 0.806604i | \(0.701303\pi\) | |||||||
\(840\) | 31.2793 | 1.07924 | ||||||||
\(841\) | −21.6497 | −0.746542 | ||||||||
\(842\) | 65.1748 | 2.24607 | ||||||||
\(843\) | 57.5929 | 1.98360 | ||||||||
\(844\) | −39.8245 | −1.37082 | ||||||||
\(845\) | 46.0051 | 1.58262 | ||||||||
\(846\) | −5.80769 | −0.199672 | ||||||||
\(847\) | 52.9641 | 1.81987 | ||||||||
\(848\) | 1.38035 | 0.0474013 | ||||||||
\(849\) | 37.8441 | 1.29880 | ||||||||
\(850\) | 33.7744 | 1.15845 | ||||||||
\(851\) | 1.83811 | 0.0630097 | ||||||||
\(852\) | −9.24383 | −0.316688 | ||||||||
\(853\) | −27.6206 | −0.945710 | −0.472855 | − | 0.881140i | \(-0.656777\pi\) | ||||
−0.472855 | + | 0.881140i | \(0.656777\pi\) | |||||||
\(854\) | −53.1009 | −1.81708 | ||||||||
\(855\) | −5.07609 | −0.173599 | ||||||||
\(856\) | 7.04911 | 0.240934 | ||||||||
\(857\) | 3.73358 | 0.127537 | 0.0637684 | − | 0.997965i | \(-0.479688\pi\) | ||||
0.0637684 | + | 0.997965i | \(0.479688\pi\) | |||||||
\(858\) | −11.9657 | −0.408503 | ||||||||
\(859\) | −58.5685 | −1.99833 | −0.999166 | − | 0.0408277i | \(-0.987001\pi\) | ||||
−0.999166 | + | 0.0408277i | \(0.987001\pi\) | |||||||
\(860\) | −65.4524 | −2.23191 | ||||||||
\(861\) | −30.8412 | −1.05106 | ||||||||
\(862\) | −17.9624 | −0.611802 | ||||||||
\(863\) | −3.35701 | −0.114274 | −0.0571370 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571370 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(864\) | −37.8480 | −1.28761 | ||||||||
\(865\) | 20.3509 | 0.691952 | ||||||||
\(866\) | 35.5931 | 1.20950 | ||||||||
\(867\) | −24.4956 | −0.831915 | ||||||||
\(868\) | −8.51467 | −0.289007 | ||||||||
\(869\) | 60.6698 | 2.05808 | ||||||||
\(870\) | 38.7836 | 1.31489 | ||||||||
\(871\) | 4.15252 | 0.140703 | ||||||||
\(872\) | 13.1531 | 0.445420 | ||||||||
\(873\) | 1.57619 | 0.0533458 | ||||||||
\(874\) | −15.1430 | −0.512219 | ||||||||
\(875\) | −44.0980 | −1.49079 | ||||||||
\(876\) | 49.3942 | 1.66888 | ||||||||
\(877\) | 30.2977 | 1.02308 | 0.511541 | − | 0.859259i | \(-0.329075\pi\) | ||||
0.511541 | + | 0.859259i | \(0.329075\pi\) | |||||||
\(878\) | 85.0958 | 2.87184 | ||||||||
\(879\) | 0.345502 | 0.0116535 | ||||||||
\(880\) | −45.3061 | −1.52727 | ||||||||
\(881\) | −13.7132 | −0.462011 | −0.231005 | − | 0.972952i | \(-0.574201\pi\) | ||||
−0.231005 | + | 0.972952i | \(0.574201\pi\) | |||||||
\(882\) | −5.26356 | −0.177233 | ||||||||
\(883\) | −17.9899 | −0.605407 | −0.302704 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302704 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(884\) | 2.99390 | 0.100696 | ||||||||
\(885\) | −60.3736 | −2.02944 | ||||||||
\(886\) | 35.5793 | 1.19531 | ||||||||
\(887\) | −22.6269 | −0.759738 | −0.379869 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379869 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(888\) | −2.31387 | −0.0776484 | ||||||||
\(889\) | −57.1363 | −1.91629 | ||||||||
\(890\) | −119.443 | −4.00375 | ||||||||
\(891\) | 50.0462 | 1.67661 | ||||||||
\(892\) | −58.3860 | −1.95491 | ||||||||
\(893\) | 28.7657 | 0.962609 | ||||||||
\(894\) | 32.6675 | 1.09256 | ||||||||
\(895\) | −10.8383 | −0.362284 | ||||||||
\(896\) | 35.8472 | 1.19757 | ||||||||
\(897\) | −2.04250 | −0.0681971 | ||||||||
\(898\) | 7.12327 | 0.237707 | ||||||||
\(899\) | −2.40198 | −0.0801106 | ||||||||
\(900\) | 7.75313 | 0.258438 | ||||||||
\(901\) | 1.06429 | 0.0354567 | ||||||||
\(902\) | −48.7912 | −1.62457 | ||||||||
\(903\) | 47.2517 | 1.57244 | ||||||||
\(904\) | −0.718777 | −0.0239062 | ||||||||
\(905\) | −11.7464 | −0.390463 | ||||||||
\(906\) | −9.91881 | −0.329530 | ||||||||
\(907\) | −23.1033 | −0.767132 | −0.383566 | − | 0.923513i | \(-0.625304\pi\) | ||||
−0.383566 | + | 0.923513i | \(0.625304\pi\) | |||||||
\(908\) | −45.1567 | −1.49858 | ||||||||
\(909\) | −0.397078 | −0.0131702 | ||||||||
\(910\) | −17.5485 | −0.581729 | ||||||||
\(911\) | 0.183002 | 0.00606314 | 0.00303157 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303157 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(912\) | −17.4529 | −0.577925 | ||||||||
\(913\) | 0.367932 | 0.0121768 | ||||||||
\(914\) | 21.5002 | 0.711162 | ||||||||
\(915\) | −44.5928 | −1.47419 | ||||||||
\(916\) | −14.7053 | −0.485875 | ||||||||
\(917\) | 61.6401 | 2.03553 | ||||||||
\(918\) | −19.7708 | −0.652535 | ||||||||
\(919\) | −25.1344 | −0.829107 | −0.414553 | − | 0.910025i | \(-0.636062\pi\) | ||||
−0.414553 | + | 0.910025i | \(0.636062\pi\) | |||||||
\(920\) | 8.44676 | 0.278481 | ||||||||
\(921\) | −11.4139 | −0.376101 | ||||||||
\(922\) | −69.6585 | −2.29408 | ||||||||
\(923\) | 1.17990 | 0.0388370 | ||||||||
\(924\) | −88.5862 | −2.91427 | ||||||||
\(925\) | 8.26213 | 0.271657 | ||||||||
\(926\) | 31.3490 | 1.03019 | ||||||||
\(927\) | −2.18742 | −0.0718444 | ||||||||
\(928\) | 21.2161 | 0.696453 | ||||||||
\(929\) | −18.3485 | −0.601994 | −0.300997 | − | 0.953625i | \(-0.597319\pi\) | ||||
−0.300997 | + | 0.953625i | \(0.597319\pi\) | |||||||
\(930\) | −12.6740 | −0.415596 | ||||||||
\(931\) | 26.0706 | 0.854431 | ||||||||
\(932\) | −53.6580 | −1.75762 | ||||||||
\(933\) | 29.6208 | 0.969740 | ||||||||
\(934\) | 29.3172 | 0.959287 | ||||||||
\(935\) | −34.9325 | −1.14241 | ||||||||
\(936\) | 0.277152 | 0.00905901 | ||||||||
\(937\) | −9.74790 | −0.318450 | −0.159225 | − | 0.987242i | \(-0.550900\pi\) | ||||
−0.159225 | + | 0.987242i | \(0.550900\pi\) | |||||||
\(938\) | 54.4906 | 1.77918 | ||||||||
\(939\) | −48.8723 | −1.59489 | ||||||||
\(940\) | −70.5251 | −2.30028 | ||||||||
\(941\) | 14.3744 | 0.468591 | 0.234296 | − | 0.972165i | \(-0.424722\pi\) | ||||
0.234296 | + | 0.972165i | \(0.424722\pi\) | |||||||
\(942\) | 41.1438 | 1.34054 | ||||||||
\(943\) | −8.32845 | −0.271212 | ||||||||
\(944\) | −22.3756 | −0.728265 | ||||||||
\(945\) | 65.3802 | 2.12682 | ||||||||
\(946\) | 74.7528 | 2.43042 | ||||||||
\(947\) | −51.8120 | −1.68367 | −0.841833 | − | 0.539739i | \(-0.818523\pi\) | ||||
−0.841833 | + | 0.539739i | \(0.818523\pi\) | |||||||
\(948\) | −57.2998 | −1.86101 | ||||||||
\(949\) | −6.30480 | −0.204662 | ||||||||
\(950\) | −68.0662 | −2.20836 | ||||||||
\(951\) | −18.7677 | −0.608583 | ||||||||
\(952\) | 8.93834 | 0.289693 | ||||||||
\(953\) | 30.6999 | 0.994466 | 0.497233 | − | 0.867617i | \(-0.334349\pi\) | ||||
0.497233 | + | 0.867617i | \(0.334349\pi\) | |||||||
\(954\) | 0.433043 | 0.0140203 | ||||||||
\(955\) | 72.1788 | 2.33565 | ||||||||
\(956\) | 14.2119 | 0.459645 | ||||||||
\(957\) | −24.9901 | −0.807815 | ||||||||
\(958\) | −73.4600 | −2.37339 | ||||||||
\(959\) | −67.5894 | −2.18258 | ||||||||
\(960\) | 78.8920 | 2.54623 | ||||||||
\(961\) | −30.2151 | −0.974679 | ||||||||
\(962\) | 1.29815 | 0.0418539 | ||||||||
\(963\) | −2.02473 | −0.0652460 | ||||||||
\(964\) | 39.7154 | 1.27915 | ||||||||
\(965\) | −4.24551 | −0.136668 | ||||||||
\(966\) | −26.8023 | −0.862349 | ||||||||
\(967\) | 22.5453 | 0.725007 | 0.362503 | − | 0.931982i | \(-0.381922\pi\) | ||||
0.362503 | + | 0.931982i | \(0.381922\pi\) | |||||||
\(968\) | −18.0046 | −0.578688 | ||||||||
\(969\) | −13.4568 | −0.432294 | ||||||||
\(970\) | 33.9259 | 1.08929 | ||||||||
\(971\) | −6.56473 | −0.210672 | −0.105336 | − | 0.994437i | \(-0.533592\pi\) | ||||
−0.105336 | + | 0.994437i | \(0.533592\pi\) | |||||||
\(972\) | −9.70070 | −0.311150 | ||||||||
\(973\) | 38.1120 | 1.22181 | ||||||||
\(974\) | 39.2512 | 1.25769 | ||||||||
\(975\) | −9.18084 | −0.294022 | ||||||||
\(976\) | −16.5269 | −0.529015 | ||||||||
\(977\) | 13.2751 | 0.424709 | 0.212355 | − | 0.977193i | \(-0.431887\pi\) | ||||
0.212355 | + | 0.977193i | \(0.431887\pi\) | |||||||
\(978\) | −3.92816 | −0.125609 | ||||||||
\(979\) | 76.9630 | 2.45975 | ||||||||
\(980\) | −63.9176 | −2.04177 | ||||||||
\(981\) | −3.77800 | −0.120622 | ||||||||
\(982\) | −8.92795 | −0.284902 | ||||||||
\(983\) | 1.00373 | 0.0320140 | 0.0160070 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160070 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(984\) | 10.4841 | 0.334221 | ||||||||
\(985\) | 51.8347 | 1.65159 | ||||||||
\(986\) | 11.0828 | 0.352947 | ||||||||
\(987\) | 50.9138 | 1.62061 | ||||||||
\(988\) | −6.03366 | −0.191956 | ||||||||
\(989\) | 12.7600 | 0.405744 | ||||||||
\(990\) | −14.2135 | −0.451734 | ||||||||
\(991\) | 25.9342 | 0.823828 | 0.411914 | − | 0.911223i | \(-0.364860\pi\) | ||||
0.411914 | + | 0.911223i | \(0.364860\pi\) | |||||||
\(992\) | −6.93315 | −0.220128 | ||||||||
\(993\) | −8.38571 | −0.266112 | ||||||||
\(994\) | 15.4830 | 0.491092 | ||||||||
\(995\) | −5.76640 | −0.182807 | ||||||||
\(996\) | −0.347494 | −0.0110108 | ||||||||
\(997\) | −12.9841 | −0.411210 | −0.205605 | − | 0.978635i | \(-0.565916\pi\) | ||||
−0.205605 | + | 0.978635i | \(0.565916\pi\) | |||||||
\(998\) | 39.0070 | 1.23474 | ||||||||
\(999\) | −4.83647 | −0.153019 |
(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 | 6031.2.a.b.1.17 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.b.1.17 | ✓ | 109 | 1.1 | even | 1 | trivial |