Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73652 | −1.93501 | −0.967506 | − | 0.252846i | \(-0.918633\pi\) | ||||
−0.967506 | + | 0.252846i | \(0.918633\pi\) | |||||||
\(3\) | −0.570094 | −0.329144 | −0.164572 | − | 0.986365i | \(-0.552624\pi\) | ||||
−0.164572 | + | 0.986365i | \(0.552624\pi\) | |||||||
\(4\) | 5.48855 | 2.74428 | ||||||||
\(5\) | −2.26504 | −1.01296 | −0.506478 | − | 0.862253i | \(-0.669053\pi\) | ||||
−0.506478 | + | 0.862253i | \(0.669053\pi\) | |||||||
\(6\) | 1.56007 | 0.636897 | ||||||||
\(7\) | 4.66290 | 1.76241 | 0.881206 | − | 0.472733i | \(-0.156732\pi\) | ||||
0.881206 | + | 0.472733i | \(0.156732\pi\) | |||||||
\(8\) | −9.54649 | −3.37520 | ||||||||
\(9\) | −2.67499 | −0.891664 | ||||||||
\(10\) | 6.19832 | 1.96008 | ||||||||
\(11\) | 3.99394 | 1.20422 | 0.602110 | − | 0.798413i | \(-0.294327\pi\) | ||||
0.602110 | + | 0.798413i | \(0.294327\pi\) | |||||||
\(12\) | −3.12899 | −0.903261 | ||||||||
\(13\) | 1.10898 | 0.307576 | 0.153788 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153788 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(14\) | −12.7601 | −3.41029 | ||||||||
\(15\) | 1.29128 | 0.333408 | ||||||||
\(16\) | 15.1471 | 3.78677 | ||||||||
\(17\) | −1.14193 | −0.276958 | −0.138479 | − | 0.990365i | \(-0.544221\pi\) | ||||
−0.138479 | + | 0.990365i | \(0.544221\pi\) | |||||||
\(18\) | 7.32018 | 1.72538 | ||||||||
\(19\) | 4.86859 | 1.11693 | 0.558465 | − | 0.829528i | \(-0.311390\pi\) | ||||
0.558465 | + | 0.829528i | \(0.311390\pi\) | |||||||
\(20\) | −12.4318 | −2.77983 | ||||||||
\(21\) | −2.65829 | −0.580087 | ||||||||
\(22\) | −10.9295 | −2.33018 | ||||||||
\(23\) | −3.27795 | −0.683499 | −0.341749 | − | 0.939791i | \(-0.611019\pi\) | ||||
−0.341749 | + | 0.939791i | \(0.611019\pi\) | |||||||
\(24\) | 5.44240 | 1.11092 | ||||||||
\(25\) | 0.130390 | 0.0260780 | ||||||||
\(26\) | −3.03475 | −0.595164 | ||||||||
\(27\) | 3.23528 | 0.622629 | ||||||||
\(28\) | 25.5926 | 4.83654 | ||||||||
\(29\) | 4.88836 | 0.907746 | 0.453873 | − | 0.891066i | \(-0.350042\pi\) | ||||
0.453873 | + | 0.891066i | \(0.350042\pi\) | |||||||
\(30\) | −3.53362 | −0.645148 | ||||||||
\(31\) | −7.53269 | −1.35291 | −0.676456 | − | 0.736483i | \(-0.736485\pi\) | ||||
−0.676456 | + | 0.736483i | \(0.736485\pi\) | |||||||
\(32\) | −22.3573 | −3.95226 | ||||||||
\(33\) | −2.27692 | −0.396361 | ||||||||
\(34\) | 3.12491 | 0.535917 | ||||||||
\(35\) | −10.5616 | −1.78524 | ||||||||
\(36\) | −14.6818 | −2.44697 | ||||||||
\(37\) | 5.56677 | 0.915171 | 0.457585 | − | 0.889166i | \(-0.348714\pi\) | ||||
0.457585 | + | 0.889166i | \(0.348714\pi\) | |||||||
\(38\) | −13.3230 | −2.16128 | ||||||||
\(39\) | −0.632223 | −0.101237 | ||||||||
\(40\) | 21.6232 | 3.41892 | ||||||||
\(41\) | −1.67443 | −0.261502 | −0.130751 | − | 0.991415i | \(-0.541739\pi\) | ||||
−0.130751 | + | 0.991415i | \(0.541739\pi\) | |||||||
\(42\) | 7.27447 | 1.12248 | ||||||||
\(43\) | −8.74394 | −1.33344 | −0.666719 | − | 0.745309i | \(-0.732302\pi\) | ||||
−0.666719 | + | 0.745309i | \(0.732302\pi\) | |||||||
\(44\) | 21.9210 | 3.30471 | ||||||||
\(45\) | 6.05896 | 0.903216 | ||||||||
\(46\) | 8.97017 | 1.32258 | ||||||||
\(47\) | 0.657846 | 0.0959567 | 0.0479784 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479784 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(48\) | −8.63526 | −1.24639 | ||||||||
\(49\) | 14.7427 | 2.10609 | ||||||||
\(50\) | −0.356816 | −0.0504613 | ||||||||
\(51\) | 0.651006 | 0.0911590 | ||||||||
\(52\) | 6.08670 | 0.844074 | ||||||||
\(53\) | −12.2321 | −1.68021 | −0.840105 | − | 0.542424i | \(-0.817507\pi\) | ||||
−0.840105 | + | 0.542424i | \(0.817507\pi\) | |||||||
\(54\) | −8.85341 | −1.20480 | ||||||||
\(55\) | −9.04643 | −1.21982 | ||||||||
\(56\) | −44.5144 | −5.94848 | ||||||||
\(57\) | −2.77555 | −0.367631 | ||||||||
\(58\) | −13.3771 | −1.75650 | ||||||||
\(59\) | 9.39157 | 1.22268 | 0.611339 | − | 0.791369i | \(-0.290631\pi\) | ||||
0.611339 | + | 0.791369i | \(0.290631\pi\) | |||||||
\(60\) | 7.08727 | 0.914963 | ||||||||
\(61\) | −14.8702 | −1.90394 | −0.951970 | − | 0.306191i | \(-0.900945\pi\) | ||||
−0.951970 | + | 0.306191i | \(0.900945\pi\) | |||||||
\(62\) | 20.6134 | 2.61790 | ||||||||
\(63\) | −12.4732 | −1.57148 | ||||||||
\(64\) | 30.8872 | 3.86090 | ||||||||
\(65\) | −2.51188 | −0.311561 | ||||||||
\(66\) | 6.23085 | 0.766964 | ||||||||
\(67\) | −1.48566 | −0.181502 | −0.0907509 | − | 0.995874i | \(-0.528927\pi\) | ||||
−0.0907509 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(68\) | −6.26753 | −0.760049 | ||||||||
\(69\) | 1.86874 | 0.224969 | ||||||||
\(70\) | 28.9022 | 3.45447 | ||||||||
\(71\) | −12.8358 | −1.52333 | −0.761666 | − | 0.647970i | \(-0.775618\pi\) | ||||
−0.761666 | + | 0.647970i | \(0.775618\pi\) | |||||||
\(72\) | 25.5368 | 3.00954 | ||||||||
\(73\) | −5.21937 | −0.610881 | −0.305441 | − | 0.952211i | \(-0.598804\pi\) | ||||
−0.305441 | + | 0.952211i | \(0.598804\pi\) | |||||||
\(74\) | −15.2336 | −1.77087 | ||||||||
\(75\) | −0.0743346 | −0.00858342 | ||||||||
\(76\) | 26.7215 | 3.06516 | ||||||||
\(77\) | 18.6234 | 2.12233 | ||||||||
\(78\) | 1.73009 | 0.195894 | ||||||||
\(79\) | 0.371565 | 0.0418043 | 0.0209022 | − | 0.999782i | \(-0.493346\pi\) | ||||
0.0209022 | + | 0.999782i | \(0.493346\pi\) | |||||||
\(80\) | −34.3087 | −3.83583 | ||||||||
\(81\) | 6.18057 | 0.686730 | ||||||||
\(82\) | 4.58211 | 0.506010 | ||||||||
\(83\) | 6.60968 | 0.725506 | 0.362753 | − | 0.931885i | \(-0.381837\pi\) | ||||
0.362753 | + | 0.931885i | \(0.381837\pi\) | |||||||
\(84\) | −14.5902 | −1.59192 | ||||||||
\(85\) | 2.58651 | 0.280546 | ||||||||
\(86\) | 23.9280 | 2.58022 | ||||||||
\(87\) | −2.78682 | −0.298779 | ||||||||
\(88\) | −38.1282 | −4.06448 | ||||||||
\(89\) | −0.198728 | −0.0210651 | −0.0105326 | − | 0.999945i | \(-0.503353\pi\) | ||||
−0.0105326 | + | 0.999945i | \(0.503353\pi\) | |||||||
\(90\) | −16.5805 | −1.74773 | ||||||||
\(91\) | 5.17107 | 0.542076 | ||||||||
\(92\) | −17.9912 | −1.87571 | ||||||||
\(93\) | 4.29434 | 0.445302 | ||||||||
\(94\) | −1.80021 | −0.185678 | ||||||||
\(95\) | −11.0275 | −1.13140 | ||||||||
\(96\) | 12.7458 | 1.30086 | ||||||||
\(97\) | 5.89498 | 0.598544 | 0.299272 | − | 0.954168i | \(-0.403256\pi\) | ||||
0.299272 | + | 0.954168i | \(0.403256\pi\) | |||||||
\(98\) | −40.3436 | −4.07532 | ||||||||
\(99\) | −10.6838 | −1.07376 | ||||||||
\(100\) | 0.715653 | 0.0715653 | ||||||||
\(101\) | 1.51723 | 0.150970 | 0.0754848 | − | 0.997147i | \(-0.475950\pi\) | ||||
0.0754848 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(102\) | −1.78149 | −0.176394 | ||||||||
\(103\) | −13.2376 | −1.30434 | −0.652169 | − | 0.758073i | \(-0.726141\pi\) | ||||
−0.652169 | + | 0.758073i | \(0.726141\pi\) | |||||||
\(104\) | −10.5869 | −1.03813 | ||||||||
\(105\) | 6.02113 | 0.587602 | ||||||||
\(106\) | 33.4734 | 3.25123 | ||||||||
\(107\) | −7.23165 | −0.699110 | −0.349555 | − | 0.936916i | \(-0.613667\pi\) | ||||
−0.349555 | + | 0.936916i | \(0.613667\pi\) | |||||||
\(108\) | 17.7570 | 1.70867 | ||||||||
\(109\) | 5.16154 | 0.494386 | 0.247193 | − | 0.968966i | \(-0.420492\pi\) | ||||
0.247193 | + | 0.968966i | \(0.420492\pi\) | |||||||
\(110\) | 24.7557 | 2.36037 | ||||||||
\(111\) | −3.17358 | −0.301223 | ||||||||
\(112\) | 70.6294 | 6.67385 | ||||||||
\(113\) | −18.6681 | −1.75615 | −0.878073 | − | 0.478526i | \(-0.841171\pi\) | ||||
−0.878073 | + | 0.478526i | \(0.841171\pi\) | |||||||
\(114\) | 7.59535 | 0.711370 | ||||||||
\(115\) | 7.42467 | 0.692354 | ||||||||
\(116\) | 26.8300 | 2.49110 | ||||||||
\(117\) | −2.96652 | −0.274255 | ||||||||
\(118\) | −25.7002 | −2.36590 | ||||||||
\(119\) | −5.32470 | −0.488114 | ||||||||
\(120\) | −12.3272 | −1.12532 | ||||||||
\(121\) | 4.95158 | 0.450144 | ||||||||
\(122\) | 40.6928 | 3.68415 | ||||||||
\(123\) | 0.954582 | 0.0860717 | ||||||||
\(124\) | −41.3435 | −3.71276 | ||||||||
\(125\) | 11.0298 | 0.986539 | ||||||||
\(126\) | 34.1333 | 3.04083 | ||||||||
\(127\) | 16.5464 | 1.46825 | 0.734127 | − | 0.679012i | \(-0.237592\pi\) | ||||
0.734127 | + | 0.679012i | \(0.237592\pi\) | |||||||
\(128\) | −39.8087 | −3.51863 | ||||||||
\(129\) | 4.98487 | 0.438893 | ||||||||
\(130\) | 6.87383 | 0.602874 | ||||||||
\(131\) | −18.3023 | −1.59908 | −0.799541 | − | 0.600612i | \(-0.794924\pi\) | ||||
−0.799541 | + | 0.600612i | \(0.794924\pi\) | |||||||
\(132\) | −12.4970 | −1.08772 | ||||||||
\(133\) | 22.7017 | 1.96849 | ||||||||
\(134\) | 4.06553 | 0.351208 | ||||||||
\(135\) | −7.32802 | −0.630696 | ||||||||
\(136\) | 10.9014 | 0.934788 | ||||||||
\(137\) | −22.4113 | −1.91472 | −0.957361 | − | 0.288893i | \(-0.906713\pi\) | ||||
−0.957361 | + | 0.288893i | \(0.906713\pi\) | |||||||
\(138\) | −5.11384 | −0.435319 | ||||||||
\(139\) | 6.85597 | 0.581516 | 0.290758 | − | 0.956797i | \(-0.406093\pi\) | ||||
0.290758 | + | 0.956797i | \(0.406093\pi\) | |||||||
\(140\) | −57.9681 | −4.89920 | ||||||||
\(141\) | −0.375034 | −0.0315836 | ||||||||
\(142\) | 35.1255 | 2.94767 | ||||||||
\(143\) | 4.42921 | 0.370389 | ||||||||
\(144\) | −40.5183 | −3.37653 | ||||||||
\(145\) | −11.0723 | −0.919506 | ||||||||
\(146\) | 14.2829 | 1.18206 | ||||||||
\(147\) | −8.40470 | −0.693208 | ||||||||
\(148\) | 30.5535 | 2.51148 | ||||||||
\(149\) | −16.3769 | −1.34165 | −0.670823 | − | 0.741617i | \(-0.734059\pi\) | ||||
−0.670823 | + | 0.741617i | \(0.734059\pi\) | |||||||
\(150\) | 0.203418 | 0.0166090 | ||||||||
\(151\) | 9.00679 | 0.732963 | 0.366481 | − | 0.930425i | \(-0.380562\pi\) | ||||
0.366481 | + | 0.930425i | \(0.380562\pi\) | |||||||
\(152\) | −46.4779 | −3.76986 | ||||||||
\(153\) | 3.05465 | 0.246954 | ||||||||
\(154\) | −50.9632 | −4.10674 | ||||||||
\(155\) | 17.0618 | 1.37044 | ||||||||
\(156\) | −3.46999 | −0.277822 | ||||||||
\(157\) | −11.2499 | −0.897842 | −0.448921 | − | 0.893571i | \(-0.648192\pi\) | ||||
−0.448921 | + | 0.893571i | \(0.648192\pi\) | |||||||
\(158\) | −1.01680 | −0.0808919 | ||||||||
\(159\) | 6.97345 | 0.553030 | ||||||||
\(160\) | 50.6402 | 4.00346 | ||||||||
\(161\) | −15.2847 | −1.20461 | ||||||||
\(162\) | −16.9133 | −1.32883 | ||||||||
\(163\) | 10.5409 | 0.825624 | 0.412812 | − | 0.910816i | \(-0.364547\pi\) | ||||
0.412812 | + | 0.910816i | \(0.364547\pi\) | |||||||
\(164\) | −9.19019 | −0.717633 | ||||||||
\(165\) | 5.15731 | 0.401496 | ||||||||
\(166\) | −18.0875 | −1.40386 | ||||||||
\(167\) | 0.470374 | 0.0363987 | 0.0181993 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181993 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(168\) | 25.3774 | 1.95791 | ||||||||
\(169\) | −11.7702 | −0.905397 | ||||||||
\(170\) | −7.07803 | −0.542860 | ||||||||
\(171\) | −13.0234 | −0.995927 | ||||||||
\(172\) | −47.9916 | −3.65932 | ||||||||
\(173\) | −0.558076 | −0.0424297 | −0.0212149 | − | 0.999775i | \(-0.506753\pi\) | ||||
−0.0212149 | + | 0.999775i | \(0.506753\pi\) | |||||||
\(174\) | 7.62620 | 0.578141 | ||||||||
\(175\) | 0.607997 | 0.0459602 | ||||||||
\(176\) | 60.4966 | 4.56010 | ||||||||
\(177\) | −5.35408 | −0.402437 | ||||||||
\(178\) | 0.543823 | 0.0407613 | ||||||||
\(179\) | −5.04141 | −0.376812 | −0.188406 | − | 0.982091i | \(-0.560332\pi\) | ||||
−0.188406 | + | 0.982091i | \(0.560332\pi\) | |||||||
\(180\) | 33.2549 | 2.47867 | ||||||||
\(181\) | −11.8697 | −0.882271 | −0.441136 | − | 0.897441i | \(-0.645424\pi\) | ||||
−0.441136 | + | 0.897441i | \(0.645424\pi\) | |||||||
\(182\) | −14.1508 | −1.04892 | ||||||||
\(183\) | 8.47743 | 0.626670 | ||||||||
\(184\) | 31.2929 | 2.30694 | ||||||||
\(185\) | −12.6089 | −0.927027 | ||||||||
\(186\) | −11.7516 | −0.861665 | ||||||||
\(187\) | −4.56079 | −0.333518 | ||||||||
\(188\) | 3.61062 | 0.263332 | ||||||||
\(189\) | 15.0858 | 1.09733 | ||||||||
\(190\) | 30.1771 | 2.18927 | ||||||||
\(191\) | 2.82705 | 0.204558 | 0.102279 | − | 0.994756i | \(-0.467387\pi\) | ||||
0.102279 | + | 0.994756i | \(0.467387\pi\) | |||||||
\(192\) | −17.6086 | −1.27079 | ||||||||
\(193\) | −6.08253 | −0.437830 | −0.218915 | − | 0.975744i | \(-0.570252\pi\) | ||||
−0.218915 | + | 0.975744i | \(0.570252\pi\) | |||||||
\(194\) | −16.1317 | −1.15819 | ||||||||
\(195\) | 1.43201 | 0.102548 | ||||||||
\(196\) | 80.9158 | 5.77970 | ||||||||
\(197\) | 11.9295 | 0.849941 | 0.424970 | − | 0.905207i | \(-0.360284\pi\) | ||||
0.424970 | + | 0.905207i | \(0.360284\pi\) | |||||||
\(198\) | 29.2364 | 2.07774 | ||||||||
\(199\) | 1.27930 | 0.0906874 | 0.0453437 | − | 0.998971i | \(-0.485562\pi\) | ||||
0.0453437 | + | 0.998971i | \(0.485562\pi\) | |||||||
\(200\) | −1.24477 | −0.0880185 | ||||||||
\(201\) | 0.846963 | 0.0597402 | ||||||||
\(202\) | −4.15192 | −0.292128 | ||||||||
\(203\) | 22.7940 | 1.59982 | ||||||||
\(204\) | 3.57308 | 0.250165 | ||||||||
\(205\) | 3.79264 | 0.264890 | ||||||||
\(206\) | 36.2250 | 2.52391 | ||||||||
\(207\) | 8.76848 | 0.609452 | ||||||||
\(208\) | 16.7978 | 1.16472 | ||||||||
\(209\) | 19.4449 | 1.34503 | ||||||||
\(210\) | −16.4769 | −1.13702 | ||||||||
\(211\) | 22.6476 | 1.55913 | 0.779563 | − | 0.626324i | \(-0.215441\pi\) | ||||
0.779563 | + | 0.626324i | \(0.215441\pi\) | |||||||
\(212\) | −67.1366 | −4.61096 | ||||||||
\(213\) | 7.31762 | 0.501395 | ||||||||
\(214\) | 19.7896 | 1.35279 | ||||||||
\(215\) | 19.8053 | 1.35071 | ||||||||
\(216\) | −30.8856 | −2.10150 | ||||||||
\(217\) | −35.1242 | −2.38439 | ||||||||
\(218\) | −14.1247 | −0.956644 | ||||||||
\(219\) | 2.97553 | 0.201068 | ||||||||
\(220\) | −49.6518 | −3.34752 | ||||||||
\(221\) | −1.26638 | −0.0851857 | ||||||||
\(222\) | 8.68456 | 0.582870 | ||||||||
\(223\) | 8.00449 | 0.536020 | 0.268010 | − | 0.963416i | \(-0.413634\pi\) | ||||
0.268010 | + | 0.963416i | \(0.413634\pi\) | |||||||
\(224\) | −104.250 | −6.96550 | ||||||||
\(225\) | −0.348793 | −0.0232529 | ||||||||
\(226\) | 51.0856 | 3.39817 | ||||||||
\(227\) | 11.9382 | 0.792365 | 0.396182 | − | 0.918172i | \(-0.370335\pi\) | ||||
0.396182 | + | 0.918172i | \(0.370335\pi\) | |||||||
\(228\) | −15.2337 | −1.00888 | ||||||||
\(229\) | −10.7594 | −0.711001 | −0.355500 | − | 0.934676i | \(-0.615690\pi\) | ||||
−0.355500 | + | 0.934676i | \(0.615690\pi\) | |||||||
\(230\) | −20.3178 | −1.33971 | ||||||||
\(231\) | −10.6171 | −0.698551 | ||||||||
\(232\) | −46.6667 | −3.06382 | ||||||||
\(233\) | −15.4873 | −1.01460 | −0.507302 | − | 0.861768i | \(-0.669357\pi\) | ||||
−0.507302 | + | 0.861768i | \(0.669357\pi\) | |||||||
\(234\) | 8.11794 | 0.530687 | ||||||||
\(235\) | −1.49005 | −0.0971999 | ||||||||
\(236\) | 51.5461 | 3.35537 | ||||||||
\(237\) | −0.211827 | −0.0137596 | ||||||||
\(238\) | 14.5711 | 0.944507 | ||||||||
\(239\) | −0.939021 | −0.0607402 | −0.0303701 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303701 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(240\) | 19.5592 | 1.26254 | ||||||||
\(241\) | −3.34297 | −0.215340 | −0.107670 | − | 0.994187i | \(-0.534339\pi\) | ||||
−0.107670 | + | 0.994187i | \(0.534339\pi\) | |||||||
\(242\) | −13.5501 | −0.871035 | ||||||||
\(243\) | −13.2293 | −0.848662 | ||||||||
\(244\) | −81.6161 | −5.22494 | ||||||||
\(245\) | −33.3927 | −2.13338 | ||||||||
\(246\) | −2.61223 | −0.166550 | ||||||||
\(247\) | 5.39917 | 0.343541 | ||||||||
\(248\) | 71.9108 | 4.56634 | ||||||||
\(249\) | −3.76813 | −0.238796 | ||||||||
\(250\) | −30.1834 | −1.90897 | ||||||||
\(251\) | 26.2692 | 1.65810 | 0.829049 | − | 0.559176i | \(-0.188882\pi\) | ||||
0.829049 | + | 0.559176i | \(0.188882\pi\) | |||||||
\(252\) | −68.4600 | −4.31257 | ||||||||
\(253\) | −13.0919 | −0.823082 | ||||||||
\(254\) | −45.2796 | −2.84109 | ||||||||
\(255\) | −1.47455 | −0.0923400 | ||||||||
\(256\) | 47.1631 | 2.94769 | ||||||||
\(257\) | −11.4111 | −0.711806 | −0.355903 | − | 0.934523i | \(-0.615827\pi\) | ||||
−0.355903 | + | 0.934523i | \(0.615827\pi\) | |||||||
\(258\) | −13.6412 | −0.849264 | ||||||||
\(259\) | 25.9573 | 1.61291 | ||||||||
\(260\) | −13.7866 | −0.855009 | ||||||||
\(261\) | −13.0763 | −0.809405 | ||||||||
\(262\) | 50.0847 | 3.09424 | ||||||||
\(263\) | 21.1481 | 1.30405 | 0.652025 | − | 0.758198i | \(-0.273920\pi\) | ||||
0.652025 | + | 0.758198i | \(0.273920\pi\) | |||||||
\(264\) | 21.7366 | 1.33780 | ||||||||
\(265\) | 27.7062 | 1.70198 | ||||||||
\(266\) | −62.1238 | −3.80906 | ||||||||
\(267\) | 0.113294 | 0.00693345 | ||||||||
\(268\) | −8.15410 | −0.498091 | ||||||||
\(269\) | −6.32645 | −0.385731 | −0.192865 | − | 0.981225i | \(-0.561778\pi\) | ||||
−0.192865 | + | 0.981225i | \(0.561778\pi\) | |||||||
\(270\) | 20.0533 | 1.22040 | ||||||||
\(271\) | 17.9303 | 1.08919 | 0.544593 | − | 0.838701i | \(-0.316684\pi\) | ||||
0.544593 | + | 0.838701i | \(0.316684\pi\) | |||||||
\(272\) | −17.2969 | −1.04878 | ||||||||
\(273\) | −2.94800 | −0.178421 | ||||||||
\(274\) | 61.3289 | 3.70501 | ||||||||
\(275\) | 0.520771 | 0.0314037 | ||||||||
\(276\) | 10.2567 | 0.617378 | ||||||||
\(277\) | 20.5334 | 1.23373 | 0.616865 | − | 0.787069i | \(-0.288402\pi\) | ||||
0.616865 | + | 0.787069i | \(0.288402\pi\) | |||||||
\(278\) | −18.7615 | −1.12524 | ||||||||
\(279\) | 20.1499 | 1.20634 | ||||||||
\(280\) | 100.827 | 6.02555 | ||||||||
\(281\) | 18.7804 | 1.12034 | 0.560172 | − | 0.828377i | \(-0.310735\pi\) | ||||
0.560172 | + | 0.828377i | \(0.310735\pi\) | |||||||
\(282\) | 1.02629 | 0.0611146 | ||||||||
\(283\) | −28.2003 | −1.67634 | −0.838168 | − | 0.545412i | \(-0.816373\pi\) | ||||
−0.838168 | + | 0.545412i | \(0.816373\pi\) | |||||||
\(284\) | −70.4500 | −4.18044 | ||||||||
\(285\) | 6.28672 | 0.372393 | ||||||||
\(286\) | −12.1206 | −0.716708 | ||||||||
\(287\) | −7.80770 | −0.460874 | ||||||||
\(288\) | 59.8057 | 3.52409 | ||||||||
\(289\) | −15.6960 | −0.923294 | ||||||||
\(290\) | 30.2996 | 1.77926 | ||||||||
\(291\) | −3.36069 | −0.197007 | ||||||||
\(292\) | −28.6468 | −1.67643 | ||||||||
\(293\) | 6.16240 | 0.360011 | 0.180006 | − | 0.983666i | \(-0.442388\pi\) | ||||
0.180006 | + | 0.983666i | \(0.442388\pi\) | |||||||
\(294\) | 22.9996 | 1.34137 | ||||||||
\(295\) | −21.2723 | −1.23852 | ||||||||
\(296\) | −53.1431 | −3.08888 | ||||||||
\(297\) | 12.9215 | 0.749782 | ||||||||
\(298\) | 44.8157 | 2.59610 | ||||||||
\(299\) | −3.63518 | −0.210228 | ||||||||
\(300\) | −0.407989 | −0.0235553 | ||||||||
\(301\) | −40.7721 | −2.35007 | ||||||||
\(302\) | −24.6473 | −1.41829 | ||||||||
\(303\) | −0.864961 | −0.0496907 | ||||||||
\(304\) | 73.7449 | 4.22956 | ||||||||
\(305\) | 33.6817 | 1.92861 | ||||||||
\(306\) | −8.35911 | −0.477859 | ||||||||
\(307\) | 13.3326 | 0.760930 | 0.380465 | − | 0.924795i | \(-0.375764\pi\) | ||||
0.380465 | + | 0.924795i | \(0.375764\pi\) | |||||||
\(308\) | 102.215 | 5.82426 | ||||||||
\(309\) | 7.54667 | 0.429315 | ||||||||
\(310\) | −46.6900 | −2.65182 | ||||||||
\(311\) | 10.3884 | 0.589075 | 0.294537 | − | 0.955640i | \(-0.404834\pi\) | ||||
0.294537 | + | 0.955640i | \(0.404834\pi\) | |||||||
\(312\) | 6.03552 | 0.341694 | ||||||||
\(313\) | −22.9733 | −1.29853 | −0.649263 | − | 0.760564i | \(-0.724923\pi\) | ||||
−0.649263 | + | 0.760564i | \(0.724923\pi\) | |||||||
\(314\) | 30.7857 | 1.73734 | ||||||||
\(315\) | 28.2523 | 1.59184 | ||||||||
\(316\) | 2.03935 | 0.114723 | ||||||||
\(317\) | 14.4741 | 0.812947 | 0.406473 | − | 0.913663i | \(-0.366758\pi\) | ||||
0.406473 | + | 0.913663i | \(0.366758\pi\) | |||||||
\(318\) | −19.0830 | −1.07012 | ||||||||
\(319\) | 19.5238 | 1.09313 | ||||||||
\(320\) | −69.9606 | −3.91091 | ||||||||
\(321\) | 4.12272 | 0.230108 | ||||||||
\(322\) | 41.8270 | 2.33093 | ||||||||
\(323\) | −5.55957 | −0.309343 | ||||||||
\(324\) | 33.9224 | 1.88458 | ||||||||
\(325\) | 0.144600 | 0.00802098 | ||||||||
\(326\) | −28.8453 | −1.59759 | ||||||||
\(327\) | −2.94256 | −0.162724 | ||||||||
\(328\) | 15.9849 | 0.882620 | ||||||||
\(329\) | 3.06747 | 0.169115 | ||||||||
\(330\) | −14.1131 | −0.776900 | ||||||||
\(331\) | −1.97181 | −0.108380 | −0.0541902 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541902 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(332\) | 36.2775 | 1.99099 | ||||||||
\(333\) | −14.8911 | −0.816025 | ||||||||
\(334\) | −1.28719 | −0.0704319 | ||||||||
\(335\) | 3.36507 | 0.183853 | ||||||||
\(336\) | −40.2654 | −2.19666 | ||||||||
\(337\) | −8.64558 | −0.470955 | −0.235477 | − | 0.971880i | \(-0.575665\pi\) | ||||
−0.235477 | + | 0.971880i | \(0.575665\pi\) | |||||||
\(338\) | 32.2093 | 1.75195 | ||||||||
\(339\) | 10.6426 | 0.578024 | ||||||||
\(340\) | 14.1962 | 0.769896 | ||||||||
\(341\) | −30.0851 | −1.62920 | ||||||||
\(342\) | 35.6389 | 1.92713 | ||||||||
\(343\) | 36.1033 | 1.94939 | ||||||||
\(344\) | 83.4740 | 4.50062 | ||||||||
\(345\) | −4.23275 | −0.227884 | ||||||||
\(346\) | 1.52719 | 0.0821020 | ||||||||
\(347\) | 30.3428 | 1.62889 | 0.814443 | − | 0.580244i | \(-0.197043\pi\) | ||||
0.814443 | + | 0.580244i | \(0.197043\pi\) | |||||||
\(348\) | −15.2956 | −0.819931 | ||||||||
\(349\) | 23.1148 | 1.23731 | 0.618653 | − | 0.785664i | \(-0.287679\pi\) | ||||
0.618653 | + | 0.785664i | \(0.287679\pi\) | |||||||
\(350\) | −1.66380 | −0.0889336 | ||||||||
\(351\) | 3.58786 | 0.191506 | ||||||||
\(352\) | −89.2939 | −4.75938 | ||||||||
\(353\) | −33.2273 | −1.76851 | −0.884254 | − | 0.467006i | \(-0.845333\pi\) | ||||
−0.884254 | + | 0.467006i | \(0.845333\pi\) | |||||||
\(354\) | 14.6515 | 0.778721 | ||||||||
\(355\) | 29.0736 | 1.54307 | ||||||||
\(356\) | −1.09073 | −0.0578085 | ||||||||
\(357\) | 3.03558 | 0.160660 | ||||||||
\(358\) | 13.7959 | 0.729137 | ||||||||
\(359\) | 23.1646 | 1.22258 | 0.611290 | − | 0.791407i | \(-0.290651\pi\) | ||||
0.611290 | + | 0.791407i | \(0.290651\pi\) | |||||||
\(360\) | −57.8418 | −3.04853 | ||||||||
\(361\) | 4.70314 | 0.247534 | ||||||||
\(362\) | 32.4818 | 1.70721 | ||||||||
\(363\) | −2.82287 | −0.148162 | ||||||||
\(364\) | 28.3817 | 1.48761 | ||||||||
\(365\) | 11.8221 | 0.618795 | ||||||||
\(366\) | −23.1987 | −1.21261 | ||||||||
\(367\) | −32.9042 | −1.71759 | −0.858793 | − | 0.512323i | \(-0.828785\pi\) | ||||
−0.858793 | + | 0.512323i | \(0.828785\pi\) | |||||||
\(368\) | −49.6513 | −2.58825 | ||||||||
\(369\) | 4.47909 | 0.233172 | ||||||||
\(370\) | 34.5046 | 1.79381 | ||||||||
\(371\) | −57.0371 | −2.96122 | ||||||||
\(372\) | 23.5697 | 1.22203 | ||||||||
\(373\) | −13.0324 | −0.674790 | −0.337395 | − | 0.941363i | \(-0.609546\pi\) | ||||
−0.337395 | + | 0.941363i | \(0.609546\pi\) | |||||||
\(374\) | 12.4807 | 0.645362 | ||||||||
\(375\) | −6.28804 | −0.324713 | ||||||||
\(376\) | −6.28012 | −0.323873 | ||||||||
\(377\) | 5.42110 | 0.279201 | ||||||||
\(378\) | −41.2826 | −2.12335 | ||||||||
\(379\) | 16.4968 | 0.847385 | 0.423692 | − | 0.905806i | \(-0.360734\pi\) | ||||
0.423692 | + | 0.905806i | \(0.360734\pi\) | |||||||
\(380\) | −60.5251 | −3.10487 | ||||||||
\(381\) | −9.43299 | −0.483267 | ||||||||
\(382\) | −7.73628 | −0.395822 | ||||||||
\(383\) | −14.9958 | −0.766249 | −0.383125 | − | 0.923697i | \(-0.625152\pi\) | ||||
−0.383125 | + | 0.923697i | \(0.625152\pi\) | |||||||
\(384\) | 22.6947 | 1.15813 | ||||||||
\(385\) | −42.1826 | −2.14982 | ||||||||
\(386\) | 16.6450 | 0.847207 | ||||||||
\(387\) | 23.3900 | 1.18898 | ||||||||
\(388\) | 32.3549 | 1.64257 | ||||||||
\(389\) | 21.4816 | 1.08916 | 0.544581 | − | 0.838708i | \(-0.316689\pi\) | ||||
0.544581 | + | 0.838708i | \(0.316689\pi\) | |||||||
\(390\) | −3.91872 | −0.198432 | ||||||||
\(391\) | 3.74318 | 0.189301 | ||||||||
\(392\) | −140.741 | −7.10848 | ||||||||
\(393\) | 10.4340 | 0.526328 | ||||||||
\(394\) | −32.6453 | −1.64465 | ||||||||
\(395\) | −0.841608 | −0.0423459 | ||||||||
\(396\) | −58.6384 | −2.94669 | ||||||||
\(397\) | 29.9077 | 1.50103 | 0.750513 | − | 0.660856i | \(-0.229806\pi\) | ||||
0.750513 | + | 0.660856i | \(0.229806\pi\) | |||||||
\(398\) | −3.50084 | −0.175481 | ||||||||
\(399\) | −12.9421 | −0.647916 | ||||||||
\(400\) | 1.97503 | 0.0987516 | ||||||||
\(401\) | −7.91642 | −0.395327 | −0.197663 | − | 0.980270i | \(-0.563335\pi\) | ||||
−0.197663 | + | 0.980270i | \(0.563335\pi\) | |||||||
\(402\) | −2.31773 | −0.115598 | ||||||||
\(403\) | −8.35362 | −0.416123 | ||||||||
\(404\) | 8.32737 | 0.414302 | ||||||||
\(405\) | −13.9992 | −0.695627 | ||||||||
\(406\) | −62.3761 | −3.09568 | ||||||||
\(407\) | 22.2334 | 1.10207 | ||||||||
\(408\) | −6.21482 | −0.307679 | ||||||||
\(409\) | −21.3544 | −1.05591 | −0.527954 | − | 0.849273i | \(-0.677041\pi\) | ||||
−0.527954 | + | 0.849273i | \(0.677041\pi\) | |||||||
\(410\) | −10.3787 | −0.512565 | ||||||||
\(411\) | 12.7765 | 0.630219 | ||||||||
\(412\) | −72.6552 | −3.57946 | ||||||||
\(413\) | 43.7920 | 2.15486 | ||||||||
\(414\) | −23.9951 | −1.17930 | ||||||||
\(415\) | −14.9712 | −0.734905 | ||||||||
\(416\) | −24.7939 | −1.21562 | ||||||||
\(417\) | −3.90855 | −0.191402 | ||||||||
\(418\) | −53.2113 | −2.60265 | ||||||||
\(419\) | −10.8263 | −0.528901 | −0.264451 | − | 0.964399i | \(-0.585191\pi\) | ||||
−0.264451 | + | 0.964399i | \(0.585191\pi\) | |||||||
\(420\) | 33.0473 | 1.61254 | ||||||||
\(421\) | −29.4021 | −1.43297 | −0.716486 | − | 0.697601i | \(-0.754251\pi\) | ||||
−0.716486 | + | 0.697601i | \(0.754251\pi\) | |||||||
\(422\) | −61.9757 | −3.01693 | ||||||||
\(423\) | −1.75973 | −0.0855612 | ||||||||
\(424\) | 116.774 | 5.67104 | ||||||||
\(425\) | −0.148896 | −0.00722252 | ||||||||
\(426\) | −20.0248 | −0.970206 | ||||||||
\(427\) | −69.3385 | −3.35553 | ||||||||
\(428\) | −39.6913 | −1.91855 | ||||||||
\(429\) | −2.52506 | −0.121911 | ||||||||
\(430\) | −54.1978 | −2.61365 | ||||||||
\(431\) | −21.6035 | −1.04060 | −0.520302 | − | 0.853983i | \(-0.674181\pi\) | ||||
−0.520302 | + | 0.853983i | \(0.674181\pi\) | |||||||
\(432\) | 49.0050 | 2.35776 | ||||||||
\(433\) | −6.67032 | −0.320555 | −0.160277 | − | 0.987072i | \(-0.551239\pi\) | ||||
−0.160277 | + | 0.987072i | \(0.551239\pi\) | |||||||
\(434\) | 96.1181 | 4.61382 | ||||||||
\(435\) | 6.31226 | 0.302650 | ||||||||
\(436\) | 28.3294 | 1.35673 | ||||||||
\(437\) | −15.9590 | −0.763421 | ||||||||
\(438\) | −8.14261 | −0.389069 | ||||||||
\(439\) | −32.8386 | −1.56730 | −0.783650 | − | 0.621203i | \(-0.786644\pi\) | ||||
−0.783650 | + | 0.621203i | \(0.786644\pi\) | |||||||
\(440\) | 86.3617 | 4.11713 | ||||||||
\(441\) | −39.4365 | −1.87793 | ||||||||
\(442\) | 3.46547 | 0.164835 | ||||||||
\(443\) | −0.761013 | −0.0361568 | −0.0180784 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180784 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(444\) | −17.4183 | −0.826638 | ||||||||
\(445\) | 0.450126 | 0.0213380 | ||||||||
\(446\) | −21.9045 | −1.03721 | ||||||||
\(447\) | 9.33635 | 0.441594 | ||||||||
\(448\) | 144.024 | 6.80449 | ||||||||
\(449\) | 37.9504 | 1.79099 | 0.895494 | − | 0.445073i | \(-0.146822\pi\) | ||||
0.895494 | + | 0.445073i | \(0.146822\pi\) | |||||||
\(450\) | 0.954479 | 0.0449946 | ||||||||
\(451\) | −6.68758 | −0.314906 | ||||||||
\(452\) | −102.461 | −4.81935 | ||||||||
\(453\) | −5.13472 | −0.241250 | ||||||||
\(454\) | −32.6691 | −1.53324 | ||||||||
\(455\) | −11.7127 | −0.549098 | ||||||||
\(456\) | 26.4968 | 1.24083 | ||||||||
\(457\) | −1.85047 | −0.0865615 | −0.0432807 | − | 0.999063i | \(-0.513781\pi\) | ||||
−0.0432807 | + | 0.999063i | \(0.513781\pi\) | |||||||
\(458\) | 29.4433 | 1.37580 | ||||||||
\(459\) | −3.69445 | −0.172442 | ||||||||
\(460\) | 40.7507 | 1.90001 | ||||||||
\(461\) | −5.50219 | −0.256262 | −0.128131 | − | 0.991757i | \(-0.540898\pi\) | ||||
−0.128131 | + | 0.991757i | \(0.540898\pi\) | |||||||
\(462\) | 29.0538 | 1.35171 | ||||||||
\(463\) | −8.90663 | −0.413926 | −0.206963 | − | 0.978349i | \(-0.566358\pi\) | ||||
−0.206963 | + | 0.978349i | \(0.566358\pi\) | |||||||
\(464\) | 74.0444 | 3.43743 | ||||||||
\(465\) | −9.72683 | −0.451071 | ||||||||
\(466\) | 42.3812 | 1.96327 | ||||||||
\(467\) | −10.9198 | −0.505310 | −0.252655 | − | 0.967556i | \(-0.581304\pi\) | ||||
−0.252655 | + | 0.967556i | \(0.581304\pi\) | |||||||
\(468\) | −16.2819 | −0.752631 | ||||||||
\(469\) | −6.92747 | −0.319881 | ||||||||
\(470\) | 4.07754 | 0.188083 | ||||||||
\(471\) | 6.41351 | 0.295519 | ||||||||
\(472\) | −89.6566 | −4.12678 | ||||||||
\(473\) | −34.9228 | −1.60575 | ||||||||
\(474\) | 0.579668 | 0.0266251 | ||||||||
\(475\) | 0.634816 | 0.0291274 | ||||||||
\(476\) | −29.2249 | −1.33952 | ||||||||
\(477\) | 32.7208 | 1.49818 | ||||||||
\(478\) | 2.56965 | 0.117533 | ||||||||
\(479\) | 24.6855 | 1.12791 | 0.563954 | − | 0.825806i | \(-0.309280\pi\) | ||||
0.563954 | + | 0.825806i | \(0.309280\pi\) | |||||||
\(480\) | −28.8696 | −1.31771 | ||||||||
\(481\) | 6.17344 | 0.281485 | ||||||||
\(482\) | 9.14811 | 0.416685 | ||||||||
\(483\) | 8.71373 | 0.396489 | ||||||||
\(484\) | 27.1770 | 1.23532 | ||||||||
\(485\) | −13.3523 | −0.606298 | ||||||||
\(486\) | 36.2024 | 1.64217 | ||||||||
\(487\) | 17.4160 | 0.789195 | 0.394598 | − | 0.918854i | \(-0.370884\pi\) | ||||
0.394598 | + | 0.918854i | \(0.370884\pi\) | |||||||
\(488\) | 141.959 | 6.42617 | ||||||||
\(489\) | −6.00928 | −0.271749 | ||||||||
\(490\) | 91.3797 | 4.12812 | ||||||||
\(491\) | 19.7496 | 0.891287 | 0.445644 | − | 0.895210i | \(-0.352975\pi\) | ||||
0.445644 | + | 0.895210i | \(0.352975\pi\) | |||||||
\(492\) | 5.23927 | 0.236205 | ||||||||
\(493\) | −5.58215 | −0.251408 | ||||||||
\(494\) | −14.7750 | −0.664757 | ||||||||
\(495\) | 24.1991 | 1.08767 | ||||||||
\(496\) | −114.098 | −5.12316 | ||||||||
\(497\) | −59.8522 | −2.68474 | ||||||||
\(498\) | 10.3116 | 0.462073 | ||||||||
\(499\) | 30.9889 | 1.38726 | 0.693628 | − | 0.720334i | \(-0.256011\pi\) | ||||
0.693628 | + | 0.720334i | \(0.256011\pi\) | |||||||
\(500\) | 60.5379 | 2.70734 | ||||||||
\(501\) | −0.268157 | −0.0119804 | ||||||||
\(502\) | −71.8863 | −3.20844 | ||||||||
\(503\) | 0.284066 | 0.0126659 | 0.00633294 | − | 0.999980i | \(-0.497984\pi\) | ||||
0.00633294 | + | 0.999980i | \(0.497984\pi\) | |||||||
\(504\) | 119.076 | 5.30405 | ||||||||
\(505\) | −3.43657 | −0.152925 | ||||||||
\(506\) | 35.8263 | 1.59268 | ||||||||
\(507\) | 6.71009 | 0.298006 | ||||||||
\(508\) | 90.8157 | 4.02929 | ||||||||
\(509\) | 16.1085 | 0.713997 | 0.356999 | − | 0.934105i | \(-0.383800\pi\) | ||||
0.356999 | + | 0.934105i | \(0.383800\pi\) | |||||||
\(510\) | 4.03514 | 0.178679 | ||||||||
\(511\) | −24.3374 | −1.07662 | ||||||||
\(512\) | −49.4454 | −2.18520 | ||||||||
\(513\) | 15.7512 | 0.695434 | ||||||||
\(514\) | 31.2268 | 1.37735 | ||||||||
\(515\) | 29.9836 | 1.32124 | ||||||||
\(516\) | 27.3597 | 1.20444 | ||||||||
\(517\) | 2.62740 | 0.115553 | ||||||||
\(518\) | −71.0327 | −3.12100 | ||||||||
\(519\) | 0.318155 | 0.0139655 | ||||||||
\(520\) | 23.9797 | 1.05158 | ||||||||
\(521\) | 12.9782 | 0.568587 | 0.284293 | − | 0.958737i | \(-0.408241\pi\) | ||||
0.284293 | + | 0.958737i | \(0.408241\pi\) | |||||||
\(522\) | 35.7837 | 1.56621 | ||||||||
\(523\) | 2.41474 | 0.105589 | 0.0527946 | − | 0.998605i | \(-0.483187\pi\) | ||||
0.0527946 | + | 0.998605i | \(0.483187\pi\) | |||||||
\(524\) | −100.453 | −4.38832 | ||||||||
\(525\) | −0.346615 | −0.0151275 | ||||||||
\(526\) | −57.8723 | −2.52335 | ||||||||
\(527\) | 8.60179 | 0.374700 | ||||||||
\(528\) | −34.4887 | −1.50093 | ||||||||
\(529\) | −12.2551 | −0.532829 | ||||||||
\(530\) | −75.8185 | −3.29335 | ||||||||
\(531\) | −25.1224 | −1.09022 | ||||||||
\(532\) | 124.600 | 5.40208 | ||||||||
\(533\) | −1.85691 | −0.0804318 | ||||||||
\(534\) | −0.310030 | −0.0134163 | ||||||||
\(535\) | 16.3800 | 0.708167 | ||||||||
\(536\) | 14.1828 | 0.612604 | ||||||||
\(537\) | 2.87407 | 0.124025 | ||||||||
\(538\) | 17.3125 | 0.746394 | ||||||||
\(539\) | 58.8813 | 2.53620 | ||||||||
\(540\) | −40.2202 | −1.73080 | ||||||||
\(541\) | −0.722846 | −0.0310776 | −0.0155388 | − | 0.999879i | \(-0.504946\pi\) | ||||
−0.0155388 | + | 0.999879i | \(0.504946\pi\) | |||||||
\(542\) | −49.0665 | −2.10759 | ||||||||
\(543\) | 6.76686 | 0.290394 | ||||||||
\(544\) | 25.5305 | 1.09461 | ||||||||
\(545\) | −11.6911 | −0.500791 | ||||||||
\(546\) | 8.06726 | 0.345247 | ||||||||
\(547\) | 7.81021 | 0.333941 | 0.166970 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166970 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(548\) | −123.005 | −5.25453 | ||||||||
\(549\) | 39.7778 | 1.69768 | ||||||||
\(550\) | −1.42510 | −0.0607665 | ||||||||
\(551\) | 23.7994 | 1.01389 | ||||||||
\(552\) | −17.8399 | −0.759315 | ||||||||
\(553\) | 1.73257 | 0.0736764 | ||||||||
\(554\) | −56.1900 | −2.38728 | ||||||||
\(555\) | 7.18827 | 0.305125 | ||||||||
\(556\) | 37.6294 | 1.59584 | ||||||||
\(557\) | −38.5719 | −1.63434 | −0.817172 | − | 0.576394i | \(-0.804459\pi\) | ||||
−0.817172 | + | 0.576394i | \(0.804459\pi\) | |||||||
\(558\) | −55.1406 | −2.33429 | ||||||||
\(559\) | −9.69687 | −0.410134 | ||||||||
\(560\) | −159.978 | −6.76031 | ||||||||
\(561\) | 2.60008 | 0.109775 | ||||||||
\(562\) | −51.3929 | −2.16788 | ||||||||
\(563\) | −34.0066 | −1.43321 | −0.716604 | − | 0.697480i | \(-0.754304\pi\) | ||||
−0.716604 | + | 0.697480i | \(0.754304\pi\) | |||||||
\(564\) | −2.05839 | −0.0866740 | ||||||||
\(565\) | 42.2839 | 1.77890 | ||||||||
\(566\) | 77.1708 | 3.24373 | ||||||||
\(567\) | 28.8194 | 1.21030 | ||||||||
\(568\) | 122.537 | 5.14154 | ||||||||
\(569\) | 13.7389 | 0.575966 | 0.287983 | − | 0.957635i | \(-0.407015\pi\) | ||||
0.287983 | + | 0.957635i | \(0.407015\pi\) | |||||||
\(570\) | −17.2038 | −0.720586 | ||||||||
\(571\) | −17.5097 | −0.732758 | −0.366379 | − | 0.930466i | \(-0.619403\pi\) | ||||
−0.366379 | + | 0.930466i | \(0.619403\pi\) | |||||||
\(572\) | 24.3099 | 1.01645 | ||||||||
\(573\) | −1.61168 | −0.0673290 | ||||||||
\(574\) | 21.3659 | 0.891797 | ||||||||
\(575\) | −0.427412 | −0.0178243 | ||||||||
\(576\) | −82.6230 | −3.44262 | ||||||||
\(577\) | 8.73053 | 0.363457 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(578\) | 42.9524 | 1.78659 | ||||||||
\(579\) | 3.46761 | 0.144109 | ||||||||
\(580\) | −60.7710 | −2.52338 | ||||||||
\(581\) | 30.8203 | 1.27864 | ||||||||
\(582\) | 9.19660 | 0.381211 | ||||||||
\(583\) | −48.8544 | −2.02334 | ||||||||
\(584\) | 49.8267 | 2.06184 | ||||||||
\(585\) | 6.71927 | 0.277808 | ||||||||
\(586\) | −16.8635 | −0.696626 | ||||||||
\(587\) | −36.6607 | −1.51315 | −0.756575 | − | 0.653907i | \(-0.773129\pi\) | ||||
−0.756575 | + | 0.653907i | \(0.773129\pi\) | |||||||
\(588\) | −46.1296 | −1.90235 | ||||||||
\(589\) | −36.6736 | −1.51111 | ||||||||
\(590\) | 58.2120 | 2.39655 | ||||||||
\(591\) | −6.80093 | −0.279753 | ||||||||
\(592\) | 84.3203 | 3.46554 | ||||||||
\(593\) | 36.1801 | 1.48574 | 0.742869 | − | 0.669437i | \(-0.233465\pi\) | ||||
0.742869 | + | 0.669437i | \(0.233465\pi\) | |||||||
\(594\) | −35.3600 | −1.45084 | ||||||||
\(595\) | 12.0606 | 0.494438 | ||||||||
\(596\) | −89.8853 | −3.68185 | ||||||||
\(597\) | −0.729323 | −0.0298492 | ||||||||
\(598\) | 9.94775 | 0.406794 | ||||||||
\(599\) | 12.2345 | 0.499887 | 0.249944 | − | 0.968260i | \(-0.419588\pi\) | ||||
0.249944 | + | 0.968260i | \(0.419588\pi\) | |||||||
\(600\) | 0.709635 | 0.0289707 | ||||||||
\(601\) | −34.6320 | −1.41267 | −0.706335 | − | 0.707878i | \(-0.749653\pi\) | ||||
−0.706335 | + | 0.707878i | \(0.749653\pi\) | |||||||
\(602\) | 111.574 | 4.54741 | ||||||||
\(603\) | 3.97412 | 0.161839 | ||||||||
\(604\) | 49.4342 | 2.01145 | ||||||||
\(605\) | −11.2155 | −0.455976 | ||||||||
\(606\) | 2.36698 | 0.0961521 | ||||||||
\(607\) | −29.3800 | −1.19250 | −0.596249 | − | 0.802800i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802800i | \(0.703343\pi\) | |||||||
\(608\) | −108.849 | −4.41440 | ||||||||
\(609\) | −12.9947 | −0.526571 | ||||||||
\(610\) | −92.1706 | −3.73188 | ||||||||
\(611\) | 0.729539 | 0.0295140 | ||||||||
\(612\) | 16.7656 | 0.677709 | ||||||||
\(613\) | −40.4015 | −1.63180 | −0.815902 | − | 0.578191i | \(-0.803759\pi\) | ||||
−0.815902 | + | 0.578191i | \(0.803759\pi\) | |||||||
\(614\) | −36.4849 | −1.47241 | ||||||||
\(615\) | −2.16216 | −0.0871868 | ||||||||
\(616\) | −177.788 | −7.16328 | ||||||||
\(617\) | −28.6182 | −1.15212 | −0.576062 | − | 0.817406i | \(-0.695411\pi\) | ||||
−0.576062 | + | 0.817406i | \(0.695411\pi\) | |||||||
\(618\) | −20.6516 | −0.830730 | ||||||||
\(619\) | −25.4238 | −1.02187 | −0.510934 | − | 0.859620i | \(-0.670700\pi\) | ||||
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(620\) | 93.6446 | 3.76086 | ||||||||
\(621\) | −10.6051 | −0.425567 | ||||||||
\(622\) | −28.4282 | −1.13987 | ||||||||
\(623\) | −0.926649 | −0.0371254 | ||||||||
\(624\) | −9.57634 | −0.383361 | ||||||||
\(625\) | −25.6349 | −1.02540 | ||||||||
\(626\) | 62.8669 | 2.51267 | ||||||||
\(627\) | −11.0854 | −0.442708 | ||||||||
\(628\) | −61.7458 | −2.46393 | ||||||||
\(629\) | −6.35684 | −0.253464 | ||||||||
\(630\) | −77.3131 | −3.08023 | ||||||||
\(631\) | 37.6747 | 1.49981 | 0.749903 | − | 0.661548i | \(-0.230100\pi\) | ||||
0.749903 | + | 0.661548i | \(0.230100\pi\) | |||||||
\(632\) | −3.54714 | −0.141098 | ||||||||
\(633\) | −12.9113 | −0.513176 | ||||||||
\(634\) | −39.6087 | −1.57306 | ||||||||
\(635\) | −37.4782 | −1.48728 | ||||||||
\(636\) | 38.2741 | 1.51767 | ||||||||
\(637\) | 16.3493 | 0.647784 | ||||||||
\(638\) | −53.4274 | −2.11521 | ||||||||
\(639\) | 34.3357 | 1.35830 | ||||||||
\(640\) | 90.1682 | 3.56421 | ||||||||
\(641\) | −16.2592 | −0.642198 | −0.321099 | − | 0.947046i | \(-0.604052\pi\) | ||||
−0.321099 | + | 0.947046i | \(0.604052\pi\) | |||||||
\(642\) | −11.2819 | −0.445261 | ||||||||
\(643\) | −25.4105 | −1.00209 | −0.501047 | − | 0.865420i | \(-0.667052\pi\) | ||||
−0.501047 | + | 0.865420i | \(0.667052\pi\) | |||||||
\(644\) | −83.8911 | −3.30577 | ||||||||
\(645\) | −11.2909 | −0.444579 | ||||||||
\(646\) | 15.2139 | 0.598583 | ||||||||
\(647\) | 26.4320 | 1.03915 | 0.519574 | − | 0.854426i | \(-0.326091\pi\) | ||||
0.519574 | + | 0.854426i | \(0.326091\pi\) | |||||||
\(648\) | −59.0028 | −2.31785 | ||||||||
\(649\) | 37.5094 | 1.47237 | ||||||||
\(650\) | −0.395702 | −0.0155207 | ||||||||
\(651\) | 20.0241 | 0.784806 | ||||||||
\(652\) | 57.8540 | 2.26574 | ||||||||
\(653\) | −34.3875 | −1.34569 | −0.672843 | − | 0.739785i | \(-0.734927\pi\) | ||||
−0.672843 | + | 0.739785i | \(0.734927\pi\) | |||||||
\(654\) | 8.05239 | 0.314873 | ||||||||
\(655\) | 41.4554 | 1.61980 | ||||||||
\(656\) | −25.3627 | −0.990248 | ||||||||
\(657\) | 13.9618 | 0.544701 | ||||||||
\(658\) | −8.39420 | −0.327240 | ||||||||
\(659\) | −26.0143 | −1.01337 | −0.506687 | − | 0.862130i | \(-0.669130\pi\) | ||||
−0.506687 | + | 0.862130i | \(0.669130\pi\) | |||||||
\(660\) | 28.3062 | 1.10182 | ||||||||
\(661\) | −31.3902 | −1.22094 | −0.610469 | − | 0.792041i | \(-0.709019\pi\) | ||||
−0.610469 | + | 0.792041i | \(0.709019\pi\) | |||||||
\(662\) | 5.39590 | 0.209718 | ||||||||
\(663\) | 0.721953 | 0.0280383 | ||||||||
\(664\) | −63.0992 | −2.44872 | ||||||||
\(665\) | −51.4203 | −1.99399 | ||||||||
\(666\) | 40.7497 | 1.57902 | ||||||||
\(667\) | −16.0238 | −0.620443 | ||||||||
\(668\) | 2.58167 | 0.0998880 | ||||||||
\(669\) | −4.56331 | −0.176428 | ||||||||
\(670\) | −9.20857 | −0.355758 | ||||||||
\(671\) | −59.3909 | −2.29276 | ||||||||
\(672\) | 59.4323 | 2.29265 | ||||||||
\(673\) | 3.97673 | 0.153292 | 0.0766459 | − | 0.997058i | \(-0.475579\pi\) | ||||
0.0766459 | + | 0.997058i | \(0.475579\pi\) | |||||||
\(674\) | 23.6588 | 0.911304 | ||||||||
\(675\) | 0.421848 | 0.0162370 | ||||||||
\(676\) | −64.6011 | −2.48466 | ||||||||
\(677\) | −18.9777 | −0.729372 | −0.364686 | − | 0.931131i | \(-0.618824\pi\) | ||||
−0.364686 | + | 0.931131i | \(0.618824\pi\) | |||||||
\(678\) | −29.1236 | −1.11848 | ||||||||
\(679\) | 27.4877 | 1.05488 | ||||||||
\(680\) | −24.6921 | −0.946898 | ||||||||
\(681\) | −6.80588 | −0.260802 | ||||||||
\(682\) | 82.3286 | 3.15253 | ||||||||
\(683\) | −41.5834 | −1.59115 | −0.795573 | − | 0.605858i | \(-0.792830\pi\) | ||||
−0.795573 | + | 0.605858i | \(0.792830\pi\) | |||||||
\(684\) | −71.4798 | −2.73310 | ||||||||
\(685\) | 50.7623 | 1.93953 | ||||||||
\(686\) | −98.7973 | −3.77210 | ||||||||
\(687\) | 6.13386 | 0.234021 | ||||||||
\(688\) | −132.445 | −5.04943 | ||||||||
\(689\) | −13.5652 | −0.516793 | ||||||||
\(690\) | 11.5830 | 0.440958 | ||||||||
\(691\) | −15.7627 | −0.599643 | −0.299821 | − | 0.953995i | \(-0.596927\pi\) | ||||
−0.299821 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(692\) | −3.06303 | −0.116439 | ||||||||
\(693\) | −49.8174 | −1.89241 | ||||||||
\(694\) | −83.0336 | −3.15191 | ||||||||
\(695\) | −15.5290 | −0.589050 | ||||||||
\(696\) | 26.6044 | 1.00844 | ||||||||
\(697\) | 1.91208 | 0.0724251 | ||||||||
\(698\) | −63.2541 | −2.39420 | ||||||||
\(699\) | 8.82919 | 0.333951 | ||||||||
\(700\) | 3.33702 | 0.126128 | ||||||||
\(701\) | 33.1418 | 1.25175 | 0.625874 | − | 0.779924i | \(-0.284742\pi\) | ||||
0.625874 | + | 0.779924i | \(0.284742\pi\) | |||||||
\(702\) | −9.81827 | −0.370567 | ||||||||
\(703\) | 27.1023 | 1.02218 | ||||||||
\(704\) | 123.362 | 4.64937 | ||||||||
\(705\) | 0.849466 | 0.0319927 | ||||||||
\(706\) | 90.9271 | 3.42209 | ||||||||
\(707\) | 7.07468 | 0.266071 | ||||||||
\(708\) | −29.3861 | −1.10440 | ||||||||
\(709\) | −45.4726 | −1.70776 | −0.853880 | − | 0.520470i | \(-0.825757\pi\) | ||||
−0.853880 | + | 0.520470i | \(0.825757\pi\) | |||||||
\(710\) | −79.5605 | −2.98585 | ||||||||
\(711\) | −0.993933 | −0.0372754 | ||||||||
\(712\) | 1.89716 | 0.0710989 | ||||||||
\(713\) | 24.6917 | 0.924713 | ||||||||
\(714\) | −8.30692 | −0.310879 | ||||||||
\(715\) | −10.0323 | −0.375188 | ||||||||
\(716\) | −27.6700 | −1.03408 | ||||||||
\(717\) | 0.535330 | 0.0199923 | ||||||||
\(718\) | −63.3904 | −2.36571 | ||||||||
\(719\) | −41.2700 | −1.53911 | −0.769555 | − | 0.638580i | \(-0.779522\pi\) | ||||
−0.769555 | + | 0.638580i | \(0.779522\pi\) | |||||||
\(720\) | 91.7755 | 3.42027 | ||||||||
\(721\) | −61.7256 | −2.29878 | ||||||||
\(722\) | −12.8703 | −0.478981 | ||||||||
\(723\) | 1.90581 | 0.0708777 | ||||||||
\(724\) | −65.1477 | −2.42119 | ||||||||
\(725\) | 0.637394 | 0.0236722 | ||||||||
\(726\) | 7.72484 | 0.286696 | ||||||||
\(727\) | −48.5167 | −1.79938 | −0.899692 | − | 0.436525i | \(-0.856209\pi\) | ||||
−0.899692 | + | 0.436525i | \(0.856209\pi\) | |||||||
\(728\) | −49.3656 | −1.82961 | ||||||||
\(729\) | −10.9997 | −0.407398 | ||||||||
\(730\) | −32.3514 | −1.19738 | ||||||||
\(731\) | 9.98495 | 0.369307 | ||||||||
\(732\) | 46.5288 | 1.71975 | ||||||||
\(733\) | −7.90627 | −0.292025 | −0.146012 | − | 0.989283i | \(-0.546644\pi\) | ||||
−0.146012 | + | 0.989283i | \(0.546644\pi\) | |||||||
\(734\) | 90.0431 | 3.32355 | ||||||||
\(735\) | 19.0369 | 0.702188 | ||||||||
\(736\) | 73.2861 | 2.70136 | ||||||||
\(737\) | −5.93363 | −0.218568 | ||||||||
\(738\) | −12.2571 | −0.451191 | ||||||||
\(739\) | −2.15503 | −0.0792740 | −0.0396370 | − | 0.999214i | \(-0.512620\pi\) | ||||
−0.0396370 | + | 0.999214i | \(0.512620\pi\) | |||||||
\(740\) | −69.2047 | −2.54402 | ||||||||
\(741\) | −3.07804 | −0.113074 | ||||||||
\(742\) | 156.083 | 5.73000 | ||||||||
\(743\) | 43.2663 | 1.58729 | 0.793644 | − | 0.608383i | \(-0.208181\pi\) | ||||
0.793644 | + | 0.608383i | \(0.208181\pi\) | |||||||
\(744\) | −40.9959 | −1.50298 | ||||||||
\(745\) | 37.0942 | 1.35903 | ||||||||
\(746\) | 35.6633 | 1.30573 | ||||||||
\(747\) | −17.6808 | −0.646908 | ||||||||
\(748\) | −25.0321 | −0.915266 | ||||||||
\(749\) | −33.7205 | −1.23212 | ||||||||
\(750\) | 17.2074 | 0.628324 | ||||||||
\(751\) | −34.5166 | −1.25953 | −0.629764 | − | 0.776787i | \(-0.716848\pi\) | ||||
−0.629764 | + | 0.776787i | \(0.716848\pi\) | |||||||
\(752\) | 9.96445 | 0.363366 | ||||||||
\(753\) | −14.9759 | −0.545752 | ||||||||
\(754\) | −14.8350 | −0.540258 | ||||||||
\(755\) | −20.4007 | −0.742458 | ||||||||
\(756\) | 82.7991 | 3.01137 | ||||||||
\(757\) | −40.2371 | −1.46244 | −0.731220 | − | 0.682141i | \(-0.761049\pi\) | ||||
−0.731220 | + | 0.682141i | \(0.761049\pi\) | |||||||
\(758\) | −45.1439 | −1.63970 | ||||||||
\(759\) | 7.46362 | 0.270912 | ||||||||
\(760\) | 105.274 | 3.81870 | ||||||||
\(761\) | 12.9575 | 0.469708 | 0.234854 | − | 0.972031i | \(-0.424539\pi\) | ||||
0.234854 | + | 0.972031i | \(0.424539\pi\) | |||||||
\(762\) | 25.8136 | 0.935127 | ||||||||
\(763\) | 24.0678 | 0.871312 | ||||||||
\(764\) | 15.5164 | 0.561363 | ||||||||
\(765\) | −6.91889 | −0.250153 | ||||||||
\(766\) | 41.0363 | 1.48270 | ||||||||
\(767\) | 10.4151 | 0.376067 | ||||||||
\(768\) | −26.8874 | −0.970215 | ||||||||
\(769\) | 26.5850 | 0.958680 | 0.479340 | − | 0.877629i | \(-0.340876\pi\) | ||||
0.479340 | + | 0.877629i | \(0.340876\pi\) | |||||||
\(770\) | 115.434 | 4.15994 | ||||||||
\(771\) | 6.50541 | 0.234286 | ||||||||
\(772\) | −33.3843 | −1.20153 | ||||||||
\(773\) | 19.8923 | 0.715477 | 0.357739 | − | 0.933822i | \(-0.383548\pi\) | ||||
0.357739 | + | 0.933822i | \(0.383548\pi\) | |||||||
\(774\) | −64.0072 | −2.30069 | ||||||||
\(775\) | −0.982189 | −0.0352813 | ||||||||
\(776\) | −56.2764 | −2.02020 | ||||||||
\(777\) | −14.7981 | −0.530878 | ||||||||
\(778\) | −58.7850 | −2.10754 | ||||||||
\(779\) | −8.15211 | −0.292080 | ||||||||
\(780\) | 7.85965 | 0.281421 | ||||||||
\(781\) | −51.2655 | −1.83442 | ||||||||
\(782\) | −10.2433 | −0.366299 | ||||||||
\(783\) | 15.8152 | 0.565189 | ||||||||
\(784\) | 223.308 | 7.97530 | ||||||||
\(785\) | 25.4815 | 0.909474 | ||||||||
\(786\) | −28.5530 | −1.01845 | ||||||||
\(787\) | 29.1242 | 1.03816 | 0.519082 | − | 0.854724i | \(-0.326274\pi\) | ||||
0.519082 | + | 0.854724i | \(0.326274\pi\) | |||||||
\(788\) | 65.4756 | 2.33247 | ||||||||
\(789\) | −12.0564 | −0.429220 | ||||||||
\(790\) | 2.30308 | 0.0819398 | ||||||||
\(791\) | −87.0475 | −3.09505 | ||||||||
\(792\) | 101.993 | 3.62415 | ||||||||
\(793\) | −16.4908 | −0.585607 | ||||||||
\(794\) | −81.8432 | −2.90451 | ||||||||
\(795\) | −15.7951 | −0.560195 | ||||||||
\(796\) | 7.02152 | 0.248871 | ||||||||
\(797\) | −52.2311 | −1.85012 | −0.925060 | − | 0.379821i | \(-0.875985\pi\) | ||||
−0.925060 | + | 0.379821i | \(0.875985\pi\) | |||||||
\(798\) | 35.4164 | 1.25373 | ||||||||
\(799\) | −0.751213 | −0.0265760 | ||||||||
\(800\) | −2.91518 | −0.103067 | ||||||||
\(801\) | 0.531596 | 0.0187830 | ||||||||
\(802\) | 21.6634 | 0.764963 | ||||||||
\(803\) | −20.8459 | −0.735635 | ||||||||
\(804\) | 4.64860 | 0.163943 | ||||||||
\(805\) | 34.6205 | 1.22021 | ||||||||
\(806\) | 22.8599 | 0.805204 | ||||||||
\(807\) | 3.60667 | 0.126961 | ||||||||
\(808\) | −14.4842 | −0.509552 | ||||||||
\(809\) | −19.1441 | −0.673070 | −0.336535 | − | 0.941671i | \(-0.609255\pi\) | ||||
−0.336535 | + | 0.941671i | \(0.609255\pi\) | |||||||
\(810\) | 38.3091 | 1.34605 | ||||||||
\(811\) | 30.1992 | 1.06044 | 0.530218 | − | 0.847861i | \(-0.322110\pi\) | ||||
0.530218 | + | 0.847861i | \(0.322110\pi\) | |||||||
\(812\) | 125.106 | 4.39035 | ||||||||
\(813\) | −10.2219 | −0.358499 | ||||||||
\(814\) | −60.8420 | −2.13251 | ||||||||
\(815\) | −23.8754 | −0.836320 | ||||||||
\(816\) | 9.86084 | 0.345198 | ||||||||
\(817\) | −42.5706 | −1.48936 | ||||||||
\(818\) | 58.4369 | 2.04320 | ||||||||
\(819\) | −13.8326 | −0.483350 | ||||||||
\(820\) | 20.8161 | 0.726930 | ||||||||
\(821\) | −6.17622 | −0.215551 | −0.107776 | − | 0.994175i | \(-0.534373\pi\) | ||||
−0.107776 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(822\) | −34.9632 | −1.21948 | ||||||||
\(823\) | 20.5679 | 0.716953 | 0.358476 | − | 0.933539i | \(-0.383296\pi\) | ||||
0.358476 | + | 0.933539i | \(0.383296\pi\) | |||||||
\(824\) | 126.373 | 4.40240 | ||||||||
\(825\) | −0.296888 | −0.0103363 | ||||||||
\(826\) | −119.838 | −4.16969 | ||||||||
\(827\) | −42.4866 | −1.47740 | −0.738702 | − | 0.674032i | \(-0.764561\pi\) | ||||
−0.738702 | + | 0.674032i | \(0.764561\pi\) | |||||||
\(828\) | 48.1263 | 1.67250 | ||||||||
\(829\) | −5.82469 | −0.202300 | −0.101150 | − | 0.994871i | \(-0.532252\pi\) | ||||
−0.101150 | + | 0.994871i | \(0.532252\pi\) | |||||||
\(830\) | 40.9689 | 1.42205 | ||||||||
\(831\) | −11.7059 | −0.406075 | ||||||||
\(832\) | 34.2533 | 1.18752 | ||||||||
\(833\) | −16.8350 | −0.583300 | ||||||||
\(834\) | 10.6958 | 0.370366 | ||||||||
\(835\) | −1.06542 | −0.0368702 | ||||||||
\(836\) | 106.724 | 3.69113 | ||||||||
\(837\) | −24.3703 | −0.842362 | ||||||||
\(838\) | 29.6265 | 1.02343 | ||||||||
\(839\) | 18.5192 | 0.639353 | 0.319677 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319677 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(840\) | −57.4806 | −1.98327 | ||||||||
\(841\) | −5.10392 | −0.175997 | ||||||||
\(842\) | 80.4596 | 2.77282 | ||||||||
\(843\) | −10.7066 | −0.368754 | ||||||||
\(844\) | 124.303 | 4.27867 | ||||||||
\(845\) | 26.6598 | 0.917126 | ||||||||
\(846\) | 4.81555 | 0.165562 | ||||||||
\(847\) | 23.0888 | 0.793339 | ||||||||
\(848\) | −185.281 | −6.36257 | ||||||||
\(849\) | 16.0768 | 0.551755 | ||||||||
\(850\) | 0.407457 | 0.0139757 | ||||||||
\(851\) | −18.2476 | −0.625518 | ||||||||
\(852\) | 40.1631 | 1.37597 | ||||||||
\(853\) | −14.8095 | −0.507067 | −0.253534 | − | 0.967327i | \(-0.581593\pi\) | ||||
−0.253534 | + | 0.967327i | \(0.581593\pi\) | |||||||
\(854\) | 189.746 | 6.49299 | ||||||||
\(855\) | 29.4986 | 1.00883 | ||||||||
\(856\) | 69.0369 | 2.35963 | ||||||||
\(857\) | 4.18096 | 0.142819 | 0.0714095 | − | 0.997447i | \(-0.477250\pi\) | ||||
0.0714095 | + | 0.997447i | \(0.477250\pi\) | |||||||
\(858\) | 6.90989 | 0.235900 | ||||||||
\(859\) | −55.5340 | −1.89479 | −0.947397 | − | 0.320060i | \(-0.896297\pi\) | ||||
−0.947397 | + | 0.320060i | \(0.896297\pi\) | |||||||
\(860\) | 108.703 | 3.70673 | ||||||||
\(861\) | 4.45112 | 0.151694 | ||||||||
\(862\) | 59.1184 | 2.01358 | ||||||||
\(863\) | 10.9966 | 0.374328 | 0.187164 | − | 0.982329i | \(-0.440070\pi\) | ||||
0.187164 | + | 0.982329i | \(0.440070\pi\) | |||||||
\(864\) | −72.3322 | −2.46079 | ||||||||
\(865\) | 1.26406 | 0.0429794 | ||||||||
\(866\) | 18.2535 | 0.620278 | ||||||||
\(867\) | 8.94819 | 0.303896 | ||||||||
\(868\) | −192.781 | −6.54341 | ||||||||
\(869\) | 1.48401 | 0.0503416 | ||||||||
\(870\) | −17.2736 | −0.585631 | ||||||||
\(871\) | −1.64757 | −0.0558256 | ||||||||
\(872\) | −49.2746 | −1.66865 | ||||||||
\(873\) | −15.7690 | −0.533701 | ||||||||
\(874\) | 43.6720 | 1.47723 | ||||||||
\(875\) | 51.4311 | 1.73869 | ||||||||
\(876\) | 16.3314 | 0.551785 | ||||||||
\(877\) | −30.5762 | −1.03248 | −0.516242 | − | 0.856443i | \(-0.672670\pi\) | ||||
−0.516242 | + | 0.856443i | \(0.672670\pi\) | |||||||
\(878\) | 89.8634 | 3.03274 | ||||||||
\(879\) | −3.51314 | −0.118495 | ||||||||
\(880\) | −137.027 | −4.61918 | ||||||||
\(881\) | 11.5721 | 0.389874 | 0.194937 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194937 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(882\) | 107.919 | 3.63382 | ||||||||
\(883\) | 7.27647 | 0.244873 | 0.122436 | − | 0.992476i | \(-0.460929\pi\) | ||||
0.122436 | + | 0.992476i | \(0.460929\pi\) | |||||||
\(884\) | −6.95057 | −0.233773 | ||||||||
\(885\) | 12.1272 | 0.407651 | ||||||||
\(886\) | 2.08253 | 0.0699639 | ||||||||
\(887\) | 24.6195 | 0.826642 | 0.413321 | − | 0.910585i | \(-0.364369\pi\) | ||||
0.413321 | + | 0.910585i | \(0.364369\pi\) | |||||||
\(888\) | 30.2965 | 1.01669 | ||||||||
\(889\) | 77.1542 | 2.58767 | ||||||||
\(890\) | −1.23178 | −0.0412894 | ||||||||
\(891\) | 24.6848 | 0.826973 | ||||||||
\(892\) | 43.9330 | 1.47099 | ||||||||
\(893\) | 3.20278 | 0.107177 | ||||||||
\(894\) | −25.5491 | −0.854491 | ||||||||
\(895\) | 11.4190 | 0.381694 | ||||||||
\(896\) | −185.624 | −6.20127 | ||||||||
\(897\) | 2.07239 | 0.0691952 | ||||||||
\(898\) | −103.852 | −3.46559 | ||||||||
\(899\) | −36.8225 | −1.22810 | ||||||||
\(900\) | −1.91437 | −0.0638122 | ||||||||
\(901\) | 13.9682 | 0.465348 | ||||||||
\(902\) | 18.3007 | 0.609347 | ||||||||
\(903\) | 23.2439 | 0.773510 | ||||||||
\(904\) | 178.215 | 5.92734 | ||||||||
\(905\) | 26.8854 | 0.893701 | ||||||||
\(906\) | 14.0513 | 0.466822 | ||||||||
\(907\) | 9.52432 | 0.316250 | 0.158125 | − | 0.987419i | \(-0.449455\pi\) | ||||
0.158125 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(908\) | 65.5233 | 2.17447 | ||||||||
\(909\) | −4.05857 | −0.134614 | ||||||||
\(910\) | 32.0520 | 1.06251 | ||||||||
\(911\) | 24.4041 | 0.808542 | 0.404271 | − | 0.914639i | \(-0.367525\pi\) | ||||
0.404271 | + | 0.914639i | \(0.367525\pi\) | |||||||
\(912\) | −42.0415 | −1.39213 | ||||||||
\(913\) | 26.3987 | 0.873668 | ||||||||
\(914\) | 5.06386 | 0.167498 | ||||||||
\(915\) | −19.2017 | −0.634789 | ||||||||
\(916\) | −59.0535 | −1.95118 | ||||||||
\(917\) | −85.3419 | −2.81824 | ||||||||
\(918\) | 10.1099 | 0.333678 | ||||||||
\(919\) | 37.8082 | 1.24718 | 0.623589 | − | 0.781753i | \(-0.285674\pi\) | ||||
0.623589 | + | 0.781753i | \(0.285674\pi\) | |||||||
\(920\) | −70.8795 | −2.33683 | ||||||||
\(921\) | −7.60081 | −0.250455 | ||||||||
\(922\) | 15.0568 | 0.495871 | ||||||||
\(923\) | −14.2347 | −0.468540 | ||||||||
\(924\) | −58.2723 | −1.91702 | ||||||||
\(925\) | 0.725852 | 0.0238659 | ||||||||
\(926\) | 24.3732 | 0.800952 | ||||||||
\(927\) | 35.4105 | 1.16303 | ||||||||
\(928\) | −109.291 | −3.58764 | ||||||||
\(929\) | −41.3478 | −1.35658 | −0.678288 | − | 0.734796i | \(-0.737278\pi\) | ||||
−0.678288 | + | 0.734796i | \(0.737278\pi\) | |||||||
\(930\) | 26.6177 | 0.872828 | ||||||||
\(931\) | 71.7759 | 2.35236 | ||||||||
\(932\) | −85.0026 | −2.78435 | ||||||||
\(933\) | −5.92238 | −0.193890 | ||||||||
\(934\) | 29.8824 | 0.977782 | ||||||||
\(935\) | 10.3304 | 0.337839 | ||||||||
\(936\) | 28.3199 | 0.925663 | ||||||||
\(937\) | −36.1228 | −1.18008 | −0.590039 | − | 0.807374i | \(-0.700888\pi\) | ||||
−0.590039 | + | 0.807374i | \(0.700888\pi\) | |||||||
\(938\) | 18.9572 | 0.618974 | ||||||||
\(939\) | 13.0969 | 0.427402 | ||||||||
\(940\) | −8.17819 | −0.266743 | ||||||||
\(941\) | 19.6689 | 0.641188 | 0.320594 | − | 0.947217i | \(-0.396118\pi\) | ||||
0.320594 | + | 0.947217i | \(0.396118\pi\) | |||||||
\(942\) | −17.5507 | −0.571833 | ||||||||
\(943\) | 5.48869 | 0.178736 | ||||||||
\(944\) | 142.255 | 4.63000 | ||||||||
\(945\) | −34.1698 | −1.11155 | ||||||||
\(946\) | 95.5670 | 3.10715 | ||||||||
\(947\) | −44.3838 | −1.44228 | −0.721140 | − | 0.692790i | \(-0.756381\pi\) | ||||
−0.721140 | + | 0.692790i | \(0.756381\pi\) | |||||||
\(948\) | −1.16262 | −0.0377602 | ||||||||
\(949\) | −5.78819 | −0.187893 | ||||||||
\(950\) | −1.73719 | −0.0563618 | ||||||||
\(951\) | −8.25159 | −0.267576 | ||||||||
\(952\) | 50.8322 | 1.64748 | ||||||||
\(953\) | −4.56764 | −0.147960 | −0.0739802 | − | 0.997260i | \(-0.523570\pi\) | ||||
−0.0739802 | + | 0.997260i | \(0.523570\pi\) | |||||||
\(954\) | −89.5412 | −2.89900 | ||||||||
\(955\) | −6.40337 | −0.207208 | ||||||||
\(956\) | −5.15386 | −0.166688 | ||||||||
\(957\) | −11.1304 | −0.359795 | ||||||||
\(958\) | −67.5523 | −2.18252 | ||||||||
\(959\) | −104.502 | −3.37453 | ||||||||
\(960\) | 39.8841 | 1.28725 | ||||||||
\(961\) | 25.7414 | 0.830368 | ||||||||
\(962\) | −16.8938 | −0.544677 | ||||||||
\(963\) | 19.3446 | 0.623371 | ||||||||
\(964\) | −18.3481 | −0.590951 | ||||||||
\(965\) | 13.7771 | 0.443502 | ||||||||
\(966\) | −23.8453 | −0.767210 | ||||||||
\(967\) | −49.8239 | −1.60223 | −0.801115 | − | 0.598511i | \(-0.795759\pi\) | ||||
−0.801115 | + | 0.598511i | \(0.795759\pi\) | |||||||
\(968\) | −47.2703 | −1.51932 | ||||||||
\(969\) | 3.16948 | 0.101818 | ||||||||
\(970\) | 36.5390 | 1.17320 | ||||||||
\(971\) | −6.28595 | −0.201726 | −0.100863 | − | 0.994900i | \(-0.532160\pi\) | ||||
−0.100863 | + | 0.994900i | \(0.532160\pi\) | |||||||
\(972\) | −72.6099 | −2.32896 | ||||||||
\(973\) | 31.9687 | 1.02487 | ||||||||
\(974\) | −47.6593 | −1.52710 | ||||||||
\(975\) | −0.0824357 | −0.00264006 | ||||||||
\(976\) | −225.241 | −7.20979 | ||||||||
\(977\) | −30.0439 | −0.961188 | −0.480594 | − | 0.876943i | \(-0.659579\pi\) | ||||
−0.480594 | + | 0.876943i | \(0.659579\pi\) | |||||||
\(978\) | 16.4445 | 0.525838 | ||||||||
\(979\) | −0.793708 | −0.0253670 | ||||||||
\(980\) | −183.277 | −5.85458 | ||||||||
\(981\) | −13.8071 | −0.440827 | ||||||||
\(982\) | −54.0452 | −1.72465 | ||||||||
\(983\) | 17.7807 | 0.567116 | 0.283558 | − | 0.958955i | \(-0.408485\pi\) | ||||
0.283558 | + | 0.958955i | \(0.408485\pi\) | |||||||
\(984\) | −9.11291 | −0.290509 | ||||||||
\(985\) | −27.0207 | −0.860952 | ||||||||
\(986\) | 15.2757 | 0.486477 | ||||||||
\(987\) | −1.74875 | −0.0556632 | ||||||||
\(988\) | 29.6336 | 0.942772 | ||||||||
\(989\) | 28.6622 | 0.911404 | ||||||||
\(990\) | −66.2214 | −2.10466 | ||||||||
\(991\) | −12.4615 | −0.395854 | −0.197927 | − | 0.980217i | \(-0.563421\pi\) | ||||
−0.197927 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(992\) | 168.411 | 5.34705 | ||||||||
\(993\) | 1.12412 | 0.0356727 | ||||||||
\(994\) | 163.787 | 5.19500 | ||||||||
\(995\) | −2.89767 | −0.0918623 | ||||||||
\(996\) | −20.6816 | −0.655321 | ||||||||
\(997\) | −2.10260 | −0.0665900 | −0.0332950 | − | 0.999446i | \(-0.510600\pi\) | ||||
−0.0332950 | + | 0.999446i | \(0.510600\pi\) | |||||||
\(998\) | −84.8019 | −2.68436 | ||||||||
\(999\) | 18.0100 | 0.569812 |
(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 | 6037.2.a.a.1.8 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.8 | ✓ | 243 | 1.1 | even | 1 | trivial |