Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55606 | −1.80741 | −0.903705 | − | 0.428156i | \(-0.859163\pi\) | ||||
−0.903705 | + | 0.428156i | \(0.859163\pi\) | |||||||
\(3\) | −1.84104 | −1.06292 | −0.531462 | − | 0.847082i | \(-0.678357\pi\) | ||||
−0.531462 | + | 0.847082i | \(0.678357\pi\) | |||||||
\(4\) | 4.53346 | 2.26673 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 4.70581 | 1.92114 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.47568 | −2.28950 | ||||||||
\(9\) | 0.389420 | 0.129807 | ||||||||
\(10\) | 2.55606 | 0.808298 | ||||||||
\(11\) | −0.567294 | −0.171046 | −0.0855228 | − | 0.996336i | \(-0.527256\pi\) | ||||
−0.0855228 | + | 0.996336i | \(0.527256\pi\) | |||||||
\(12\) | −8.34627 | −2.40936 | ||||||||
\(13\) | 4.04849 | 1.12285 | 0.561425 | − | 0.827528i | \(-0.310253\pi\) | ||||
0.561425 | + | 0.827528i | \(0.310253\pi\) | |||||||
\(14\) | −2.55606 | −0.683137 | ||||||||
\(15\) | 1.84104 | 0.475354 | ||||||||
\(16\) | 7.48532 | 1.87133 | ||||||||
\(17\) | 1.83930 | 0.446096 | 0.223048 | − | 0.974807i | \(-0.428399\pi\) | ||||
0.223048 | + | 0.974807i | \(0.428399\pi\) | |||||||
\(18\) | −0.995381 | −0.234613 | ||||||||
\(19\) | 0.790478 | 0.181348 | 0.0906741 | − | 0.995881i | \(-0.471098\pi\) | ||||
0.0906741 | + | 0.995881i | \(0.471098\pi\) | |||||||
\(20\) | −4.53346 | −1.01371 | ||||||||
\(21\) | −1.84104 | −0.401747 | ||||||||
\(22\) | 1.45004 | 0.309150 | ||||||||
\(23\) | −7.12445 | −1.48555 | −0.742775 | − | 0.669541i | \(-0.766491\pi\) | ||||
−0.742775 | + | 0.669541i | \(0.766491\pi\) | |||||||
\(24\) | 11.9220 | 2.43356 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −10.3482 | −2.02945 | ||||||||
\(27\) | 4.80618 | 0.924949 | ||||||||
\(28\) | 4.53346 | 0.856743 | ||||||||
\(29\) | −2.27903 | −0.423206 | −0.211603 | − | 0.977356i | \(-0.567868\pi\) | ||||
−0.211603 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(30\) | −4.70581 | −0.859159 | ||||||||
\(31\) | −2.80158 | −0.503179 | −0.251590 | − | 0.967834i | \(-0.580953\pi\) | ||||
−0.251590 | + | 0.967834i | \(0.580953\pi\) | |||||||
\(32\) | −6.18160 | −1.09276 | ||||||||
\(33\) | 1.04441 | 0.181808 | ||||||||
\(34\) | −4.70137 | −0.806278 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.76542 | 0.294236 | ||||||||
\(37\) | 2.22629 | 0.365999 | 0.183000 | − | 0.983113i | \(-0.441419\pi\) | ||||
0.183000 | + | 0.983113i | \(0.441419\pi\) | |||||||
\(38\) | −2.02051 | −0.327770 | ||||||||
\(39\) | −7.45343 | −1.19350 | ||||||||
\(40\) | 6.47568 | 1.02389 | ||||||||
\(41\) | −8.92374 | −1.39365 | −0.696827 | − | 0.717239i | \(-0.745406\pi\) | ||||
−0.696827 | + | 0.717239i | \(0.745406\pi\) | |||||||
\(42\) | 4.70581 | 0.726122 | ||||||||
\(43\) | −0.544936 | −0.0831020 | −0.0415510 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415510 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(44\) | −2.57180 | −0.387714 | ||||||||
\(45\) | −0.389420 | −0.0580512 | ||||||||
\(46\) | 18.2105 | 2.68500 | ||||||||
\(47\) | 9.40998 | 1.37259 | 0.686293 | − | 0.727325i | \(-0.259237\pi\) | ||||
0.686293 | + | 0.727325i | \(0.259237\pi\) | |||||||
\(48\) | −13.7808 | −1.98908 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.55606 | −0.361482 | ||||||||
\(51\) | −3.38622 | −0.474166 | ||||||||
\(52\) | 18.3537 | 2.54520 | ||||||||
\(53\) | 3.72887 | 0.512200 | 0.256100 | − | 0.966650i | \(-0.417562\pi\) | ||||
0.256100 | + | 0.966650i | \(0.417562\pi\) | |||||||
\(54\) | −12.2849 | −1.67176 | ||||||||
\(55\) | 0.567294 | 0.0764939 | ||||||||
\(56\) | −6.47568 | −0.865349 | ||||||||
\(57\) | −1.45530 | −0.192759 | ||||||||
\(58\) | 5.82535 | 0.764906 | ||||||||
\(59\) | 3.90731 | 0.508688 | 0.254344 | − | 0.967114i | \(-0.418140\pi\) | ||||
0.254344 | + | 0.967114i | \(0.418140\pi\) | |||||||
\(60\) | 8.34627 | 1.07750 | ||||||||
\(61\) | 5.06069 | 0.647955 | 0.323978 | − | 0.946065i | \(-0.394980\pi\) | ||||
0.323978 | + | 0.946065i | \(0.394980\pi\) | |||||||
\(62\) | 7.16102 | 0.909451 | ||||||||
\(63\) | 0.389420 | 0.0490622 | ||||||||
\(64\) | 0.829915 | 0.103739 | ||||||||
\(65\) | −4.04849 | −0.502154 | ||||||||
\(66\) | −2.66958 | −0.328602 | ||||||||
\(67\) | 11.6403 | 1.42208 | 0.711042 | − | 0.703150i | \(-0.248224\pi\) | ||||
0.711042 | + | 0.703150i | \(0.248224\pi\) | |||||||
\(68\) | 8.33839 | 1.01118 | ||||||||
\(69\) | 13.1164 | 1.57903 | ||||||||
\(70\) | 2.55606 | 0.305508 | ||||||||
\(71\) | −11.2265 | −1.33234 | −0.666170 | − | 0.745800i | \(-0.732067\pi\) | ||||
−0.666170 | + | 0.745800i | \(0.732067\pi\) | |||||||
\(72\) | −2.52175 | −0.297192 | ||||||||
\(73\) | −0.355823 | −0.0416459 | −0.0208229 | − | 0.999783i | \(-0.506629\pi\) | ||||
−0.0208229 | + | 0.999783i | \(0.506629\pi\) | |||||||
\(74\) | −5.69053 | −0.661510 | ||||||||
\(75\) | −1.84104 | −0.212585 | ||||||||
\(76\) | 3.58360 | 0.411067 | ||||||||
\(77\) | −0.567294 | −0.0646492 | ||||||||
\(78\) | 19.0514 | 2.15715 | ||||||||
\(79\) | −3.57069 | −0.401734 | −0.200867 | − | 0.979619i | \(-0.564376\pi\) | ||||
−0.200867 | + | 0.979619i | \(0.564376\pi\) | |||||||
\(80\) | −7.48532 | −0.836884 | ||||||||
\(81\) | −10.0166 | −1.11296 | ||||||||
\(82\) | 22.8097 | 2.51890 | ||||||||
\(83\) | −4.12676 | −0.452971 | −0.226485 | − | 0.974015i | \(-0.572724\pi\) | ||||
−0.226485 | + | 0.974015i | \(0.572724\pi\) | |||||||
\(84\) | −8.34627 | −0.910652 | ||||||||
\(85\) | −1.83930 | −0.199500 | ||||||||
\(86\) | 1.39289 | 0.150199 | ||||||||
\(87\) | 4.19578 | 0.449835 | ||||||||
\(88\) | 3.67361 | 0.391609 | ||||||||
\(89\) | 1.38911 | 0.147245 | 0.0736225 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736225 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(90\) | 0.995381 | 0.104922 | ||||||||
\(91\) | 4.04849 | 0.424398 | ||||||||
\(92\) | −32.2984 | −3.36734 | ||||||||
\(93\) | 5.15782 | 0.534841 | ||||||||
\(94\) | −24.0525 | −2.48083 | ||||||||
\(95\) | −0.790478 | −0.0811014 | ||||||||
\(96\) | 11.3806 | 1.16152 | ||||||||
\(97\) | −7.76313 | −0.788227 | −0.394113 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394113 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(98\) | −2.55606 | −0.258201 | ||||||||
\(99\) | −0.220915 | −0.0222028 | ||||||||
\(100\) | 4.53346 | 0.453346 | ||||||||
\(101\) | 3.15497 | 0.313931 | 0.156965 | − | 0.987604i | \(-0.449829\pi\) | ||||
0.156965 | + | 0.987604i | \(0.449829\pi\) | |||||||
\(102\) | 8.65539 | 0.857012 | ||||||||
\(103\) | 15.6616 | 1.54318 | 0.771590 | − | 0.636120i | \(-0.219462\pi\) | ||||
0.771590 | + | 0.636120i | \(0.219462\pi\) | |||||||
\(104\) | −26.2167 | −2.57076 | ||||||||
\(105\) | 1.84104 | 0.179667 | ||||||||
\(106\) | −9.53123 | −0.925755 | ||||||||
\(107\) | −18.2898 | −1.76814 | −0.884069 | − | 0.467357i | \(-0.845206\pi\) | ||||
−0.884069 | + | 0.467357i | \(0.845206\pi\) | |||||||
\(108\) | 21.7886 | 2.09661 | ||||||||
\(109\) | 0.854961 | 0.0818905 | 0.0409452 | − | 0.999161i | \(-0.486963\pi\) | ||||
0.0409452 | + | 0.999161i | \(0.486963\pi\) | |||||||
\(110\) | −1.45004 | −0.138256 | ||||||||
\(111\) | −4.09868 | −0.389029 | ||||||||
\(112\) | 7.48532 | 0.707296 | ||||||||
\(113\) | −4.05025 | −0.381015 | −0.190508 | − | 0.981686i | \(-0.561013\pi\) | ||||
−0.190508 | + | 0.981686i | \(0.561013\pi\) | |||||||
\(114\) | 3.71984 | 0.348395 | ||||||||
\(115\) | 7.12445 | 0.664358 | ||||||||
\(116\) | −10.3319 | −0.959292 | ||||||||
\(117\) | 1.57656 | 0.145753 | ||||||||
\(118\) | −9.98733 | −0.919408 | ||||||||
\(119\) | 1.83930 | 0.168608 | ||||||||
\(120\) | −11.9220 | −1.08832 | ||||||||
\(121\) | −10.6782 | −0.970743 | ||||||||
\(122\) | −12.9354 | −1.17112 | ||||||||
\(123\) | 16.4289 | 1.48135 | ||||||||
\(124\) | −12.7009 | −1.14057 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.995381 | −0.0886756 | ||||||||
\(127\) | 14.9741 | 1.32873 | 0.664367 | − | 0.747406i | \(-0.268701\pi\) | ||||
0.664367 | + | 0.747406i | \(0.268701\pi\) | |||||||
\(128\) | 10.2419 | 0.905263 | ||||||||
\(129\) | 1.00325 | 0.0883310 | ||||||||
\(130\) | 10.3482 | 0.907598 | ||||||||
\(131\) | 17.4749 | 1.52679 | 0.763396 | − | 0.645931i | \(-0.223531\pi\) | ||||
0.763396 | + | 0.645931i | \(0.223531\pi\) | |||||||
\(132\) | 4.73479 | 0.412110 | ||||||||
\(133\) | 0.790478 | 0.0685432 | ||||||||
\(134\) | −29.7532 | −2.57029 | ||||||||
\(135\) | −4.80618 | −0.413650 | ||||||||
\(136\) | −11.9107 | −1.02134 | ||||||||
\(137\) | 21.1392 | 1.80605 | 0.903023 | − | 0.429592i | \(-0.141343\pi\) | ||||
0.903023 | + | 0.429592i | \(0.141343\pi\) | |||||||
\(138\) | −33.5263 | −2.85395 | ||||||||
\(139\) | −4.73876 | −0.401936 | −0.200968 | − | 0.979598i | \(-0.564409\pi\) | ||||
−0.200968 | + | 0.979598i | \(0.564409\pi\) | |||||||
\(140\) | −4.53346 | −0.383147 | ||||||||
\(141\) | −17.3241 | −1.45895 | ||||||||
\(142\) | 28.6956 | 2.40808 | ||||||||
\(143\) | −2.29669 | −0.192059 | ||||||||
\(144\) | 2.91493 | 0.242911 | ||||||||
\(145\) | 2.27903 | 0.189263 | ||||||||
\(146\) | 0.909505 | 0.0752712 | ||||||||
\(147\) | −1.84104 | −0.151846 | ||||||||
\(148\) | 10.0928 | 0.829621 | ||||||||
\(149\) | 6.35536 | 0.520651 | 0.260326 | − | 0.965521i | \(-0.416170\pi\) | ||||
0.260326 | + | 0.965521i | \(0.416170\pi\) | |||||||
\(150\) | 4.70581 | 0.384228 | ||||||||
\(151\) | −2.66624 | −0.216975 | −0.108488 | − | 0.994098i | \(-0.534601\pi\) | ||||
−0.108488 | + | 0.994098i | \(0.534601\pi\) | |||||||
\(152\) | −5.11888 | −0.415196 | ||||||||
\(153\) | 0.716259 | 0.0579061 | ||||||||
\(154\) | 1.45004 | 0.116848 | ||||||||
\(155\) | 2.80158 | 0.225029 | ||||||||
\(156\) | −33.7898 | −2.70535 | ||||||||
\(157\) | −9.48698 | −0.757144 | −0.378572 | − | 0.925572i | \(-0.623585\pi\) | ||||
−0.378572 | + | 0.925572i | \(0.623585\pi\) | |||||||
\(158\) | 9.12691 | 0.726098 | ||||||||
\(159\) | −6.86499 | −0.544429 | ||||||||
\(160\) | 6.18160 | 0.488698 | ||||||||
\(161\) | −7.12445 | −0.561485 | ||||||||
\(162\) | 25.6031 | 2.01157 | ||||||||
\(163\) | −1.16073 | −0.0909154 | −0.0454577 | − | 0.998966i | \(-0.514475\pi\) | ||||
−0.0454577 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(164\) | −40.4554 | −3.15904 | ||||||||
\(165\) | −1.04441 | −0.0813072 | ||||||||
\(166\) | 10.5483 | 0.818704 | ||||||||
\(167\) | 2.56334 | 0.198357 | 0.0991786 | − | 0.995070i | \(-0.468378\pi\) | ||||
0.0991786 | + | 0.995070i | \(0.468378\pi\) | |||||||
\(168\) | 11.9220 | 0.919800 | ||||||||
\(169\) | 3.39031 | 0.260793 | ||||||||
\(170\) | 4.70137 | 0.360578 | ||||||||
\(171\) | 0.307828 | 0.0235402 | ||||||||
\(172\) | −2.47044 | −0.188370 | ||||||||
\(173\) | 9.16971 | 0.697160 | 0.348580 | − | 0.937279i | \(-0.386664\pi\) | ||||
0.348580 | + | 0.937279i | \(0.386664\pi\) | |||||||
\(174\) | −10.7247 | −0.813036 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −4.24638 | −0.320083 | ||||||||
\(177\) | −7.19351 | −0.540697 | ||||||||
\(178\) | −3.55064 | −0.266132 | ||||||||
\(179\) | 9.80832 | 0.733108 | 0.366554 | − | 0.930397i | \(-0.380538\pi\) | ||||
0.366554 | + | 0.930397i | \(0.380538\pi\) | |||||||
\(180\) | −1.76542 | −0.131586 | ||||||||
\(181\) | 19.5104 | 1.45020 | 0.725099 | − | 0.688645i | \(-0.241794\pi\) | ||||
0.725099 | + | 0.688645i | \(0.241794\pi\) | |||||||
\(182\) | −10.3482 | −0.767060 | ||||||||
\(183\) | −9.31692 | −0.688727 | ||||||||
\(184\) | 46.1356 | 3.40116 | ||||||||
\(185\) | −2.22629 | −0.163680 | ||||||||
\(186\) | −13.1837 | −0.966676 | ||||||||
\(187\) | −1.04342 | −0.0763028 | ||||||||
\(188\) | 42.6597 | 3.11128 | ||||||||
\(189\) | 4.80618 | 0.349598 | ||||||||
\(190\) | 2.02051 | 0.146583 | ||||||||
\(191\) | −10.1859 | −0.737025 | −0.368512 | − | 0.929623i | \(-0.620133\pi\) | ||||
−0.368512 | + | 0.929623i | \(0.620133\pi\) | |||||||
\(192\) | −1.52790 | −0.110267 | ||||||||
\(193\) | 5.74266 | 0.413366 | 0.206683 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206683 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(194\) | 19.8431 | 1.42465 | ||||||||
\(195\) | 7.45343 | 0.533751 | ||||||||
\(196\) | 4.53346 | 0.323818 | ||||||||
\(197\) | 2.26210 | 0.161168 | 0.0805838 | − | 0.996748i | \(-0.474322\pi\) | ||||
0.0805838 | + | 0.996748i | \(0.474322\pi\) | |||||||
\(198\) | 0.564674 | 0.0401296 | ||||||||
\(199\) | 15.3542 | 1.08843 | 0.544215 | − | 0.838946i | \(-0.316828\pi\) | ||||
0.544215 | + | 0.838946i | \(0.316828\pi\) | |||||||
\(200\) | −6.47568 | −0.457899 | ||||||||
\(201\) | −21.4302 | −1.51157 | ||||||||
\(202\) | −8.06429 | −0.567402 | ||||||||
\(203\) | −2.27903 | −0.159957 | ||||||||
\(204\) | −15.3513 | −1.07481 | ||||||||
\(205\) | 8.92374 | 0.623261 | ||||||||
\(206\) | −40.0319 | −2.78916 | ||||||||
\(207\) | −2.77440 | −0.192834 | ||||||||
\(208\) | 30.3043 | 2.10122 | ||||||||
\(209\) | −0.448434 | −0.0310188 | ||||||||
\(210\) | −4.70581 | −0.324732 | ||||||||
\(211\) | −26.3258 | −1.81234 | −0.906171 | − | 0.422911i | \(-0.861008\pi\) | ||||
−0.906171 | + | 0.422911i | \(0.861008\pi\) | |||||||
\(212\) | 16.9047 | 1.16102 | ||||||||
\(213\) | 20.6684 | 1.41618 | ||||||||
\(214\) | 46.7498 | 3.19575 | ||||||||
\(215\) | 0.544936 | 0.0371643 | ||||||||
\(216\) | −31.1232 | −2.11767 | ||||||||
\(217\) | −2.80158 | −0.190184 | ||||||||
\(218\) | −2.18534 | −0.148010 | ||||||||
\(219\) | 0.655083 | 0.0442664 | ||||||||
\(220\) | 2.57180 | 0.173391 | ||||||||
\(221\) | 7.44640 | 0.500899 | ||||||||
\(222\) | 10.4765 | 0.703135 | ||||||||
\(223\) | −24.3347 | −1.62957 | −0.814786 | − | 0.579762i | \(-0.803146\pi\) | ||||
−0.814786 | + | 0.579762i | \(0.803146\pi\) | |||||||
\(224\) | −6.18160 | −0.413026 | ||||||||
\(225\) | 0.389420 | 0.0259613 | ||||||||
\(226\) | 10.3527 | 0.688651 | ||||||||
\(227\) | −14.5129 | −0.963257 | −0.481628 | − | 0.876376i | \(-0.659954\pi\) | ||||
−0.481628 | + | 0.876376i | \(0.659954\pi\) | |||||||
\(228\) | −6.59754 | −0.436933 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −18.2105 | −1.20077 | ||||||||
\(231\) | 1.04441 | 0.0687171 | ||||||||
\(232\) | 14.7583 | 0.968928 | ||||||||
\(233\) | 3.29021 | 0.215549 | 0.107774 | − | 0.994175i | \(-0.465628\pi\) | ||||
0.107774 | + | 0.994175i | \(0.465628\pi\) | |||||||
\(234\) | −4.02979 | −0.263436 | ||||||||
\(235\) | −9.40998 | −0.613839 | ||||||||
\(236\) | 17.7136 | 1.15306 | ||||||||
\(237\) | 6.57377 | 0.427012 | ||||||||
\(238\) | −4.70137 | −0.304744 | ||||||||
\(239\) | −6.48818 | −0.419685 | −0.209843 | − | 0.977735i | \(-0.567295\pi\) | ||||
−0.209843 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(240\) | 13.7808 | 0.889544 | ||||||||
\(241\) | 18.7577 | 1.20829 | 0.604145 | − | 0.796874i | \(-0.293515\pi\) | ||||
0.604145 | + | 0.796874i | \(0.293515\pi\) | |||||||
\(242\) | 27.2941 | 1.75453 | ||||||||
\(243\) | 4.02243 | 0.258039 | ||||||||
\(244\) | 22.9424 | 1.46874 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −41.9934 | −2.67740 | ||||||||
\(247\) | 3.20025 | 0.203627 | ||||||||
\(248\) | 18.1421 | 1.15203 | ||||||||
\(249\) | 7.59752 | 0.481473 | ||||||||
\(250\) | 2.55606 | 0.161660 | ||||||||
\(251\) | −16.6237 | −1.04928 | −0.524638 | − | 0.851326i | \(-0.675799\pi\) | ||||
−0.524638 | + | 0.851326i | \(0.675799\pi\) | |||||||
\(252\) | 1.76542 | 0.111211 | ||||||||
\(253\) | 4.04166 | 0.254097 | ||||||||
\(254\) | −38.2747 | −2.40157 | ||||||||
\(255\) | 3.38622 | 0.212053 | ||||||||
\(256\) | −27.8387 | −1.73992 | ||||||||
\(257\) | −15.9989 | −0.997982 | −0.498991 | − | 0.866607i | \(-0.666296\pi\) | ||||
−0.498991 | + | 0.866607i | \(0.666296\pi\) | |||||||
\(258\) | −2.56436 | −0.159650 | ||||||||
\(259\) | 2.22629 | 0.138335 | ||||||||
\(260\) | −18.3537 | −1.13825 | ||||||||
\(261\) | −0.887499 | −0.0549348 | ||||||||
\(262\) | −44.6670 | −2.75954 | ||||||||
\(263\) | −4.17169 | −0.257238 | −0.128619 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128619 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(264\) | −6.76326 | −0.416250 | ||||||||
\(265\) | −3.72887 | −0.229063 | ||||||||
\(266\) | −2.02051 | −0.123886 | ||||||||
\(267\) | −2.55740 | −0.156510 | ||||||||
\(268\) | 52.7706 | 3.22348 | ||||||||
\(269\) | −0.916068 | −0.0558537 | −0.0279268 | − | 0.999610i | \(-0.508891\pi\) | ||||
−0.0279268 | + | 0.999610i | \(0.508891\pi\) | |||||||
\(270\) | 12.2849 | 0.747635 | ||||||||
\(271\) | −16.2100 | −0.984689 | −0.492345 | − | 0.870400i | \(-0.663860\pi\) | ||||
−0.492345 | + | 0.870400i | \(0.663860\pi\) | |||||||
\(272\) | 13.7678 | 0.834793 | ||||||||
\(273\) | −7.45343 | −0.451102 | ||||||||
\(274\) | −54.0332 | −3.26426 | ||||||||
\(275\) | −0.567294 | −0.0342091 | ||||||||
\(276\) | 59.4626 | 3.57923 | ||||||||
\(277\) | 27.4953 | 1.65203 | 0.826017 | − | 0.563645i | \(-0.190601\pi\) | ||||
0.826017 | + | 0.563645i | \(0.190601\pi\) | |||||||
\(278\) | 12.1126 | 0.726463 | ||||||||
\(279\) | −1.09099 | −0.0653159 | ||||||||
\(280\) | 6.47568 | 0.386996 | ||||||||
\(281\) | −1.38095 | −0.0823803 | −0.0411901 | − | 0.999151i | \(-0.513115\pi\) | ||||
−0.0411901 | + | 0.999151i | \(0.513115\pi\) | |||||||
\(282\) | 44.2816 | 2.63693 | ||||||||
\(283\) | −19.5361 | −1.16130 | −0.580649 | − | 0.814154i | \(-0.697201\pi\) | ||||
−0.580649 | + | 0.814154i | \(0.697201\pi\) | |||||||
\(284\) | −50.8948 | −3.02005 | ||||||||
\(285\) | 1.45530 | 0.0862045 | ||||||||
\(286\) | 5.87048 | 0.347129 | ||||||||
\(287\) | −8.92374 | −0.526752 | ||||||||
\(288\) | −2.40724 | −0.141848 | ||||||||
\(289\) | −13.6170 | −0.800998 | ||||||||
\(290\) | −5.82535 | −0.342076 | ||||||||
\(291\) | 14.2922 | 0.837825 | ||||||||
\(292\) | −1.61311 | −0.0943999 | ||||||||
\(293\) | 14.9484 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(294\) | 4.70581 | 0.274448 | ||||||||
\(295\) | −3.90731 | −0.227492 | ||||||||
\(296\) | −14.4167 | −0.837954 | ||||||||
\(297\) | −2.72652 | −0.158209 | ||||||||
\(298\) | −16.2447 | −0.941030 | ||||||||
\(299\) | −28.8433 | −1.66805 | ||||||||
\(300\) | −8.34627 | −0.481872 | ||||||||
\(301\) | −0.544936 | −0.0314096 | ||||||||
\(302\) | 6.81507 | 0.392163 | ||||||||
\(303\) | −5.80841 | −0.333685 | ||||||||
\(304\) | 5.91698 | 0.339362 | ||||||||
\(305\) | −5.06069 | −0.289774 | ||||||||
\(306\) | −1.83080 | −0.104660 | ||||||||
\(307\) | −13.8028 | −0.787769 | −0.393884 | − | 0.919160i | \(-0.628869\pi\) | ||||
−0.393884 | + | 0.919160i | \(0.628869\pi\) | |||||||
\(308\) | −2.57180 | −0.146542 | ||||||||
\(309\) | −28.8335 | −1.64028 | ||||||||
\(310\) | −7.16102 | −0.406719 | ||||||||
\(311\) | −6.52286 | −0.369877 | −0.184939 | − | 0.982750i | \(-0.559209\pi\) | ||||
−0.184939 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(312\) | 48.2660 | 2.73252 | ||||||||
\(313\) | 4.05327 | 0.229104 | 0.114552 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114552 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(314\) | 24.2493 | 1.36847 | ||||||||
\(315\) | −0.389420 | −0.0219413 | ||||||||
\(316\) | −16.1876 | −0.910622 | ||||||||
\(317\) | −33.6907 | −1.89226 | −0.946130 | − | 0.323786i | \(-0.895044\pi\) | ||||
−0.946130 | + | 0.323786i | \(0.895044\pi\) | |||||||
\(318\) | 17.5474 | 0.984007 | ||||||||
\(319\) | 1.29288 | 0.0723875 | ||||||||
\(320\) | −0.829915 | −0.0463937 | ||||||||
\(321\) | 33.6721 | 1.87939 | ||||||||
\(322\) | 18.2105 | 1.01483 | ||||||||
\(323\) | 1.45393 | 0.0808987 | ||||||||
\(324\) | −45.4099 | −2.52277 | ||||||||
\(325\) | 4.04849 | 0.224570 | ||||||||
\(326\) | 2.96690 | 0.164321 | ||||||||
\(327\) | −1.57402 | −0.0870433 | ||||||||
\(328\) | 57.7873 | 3.19077 | ||||||||
\(329\) | 9.40998 | 0.518789 | ||||||||
\(330\) | 2.66958 | 0.146955 | ||||||||
\(331\) | −8.29438 | −0.455901 | −0.227950 | − | 0.973673i | \(-0.573202\pi\) | ||||
−0.227950 | + | 0.973673i | \(0.573202\pi\) | |||||||
\(332\) | −18.7085 | −1.02676 | ||||||||
\(333\) | 0.866959 | 0.0475091 | ||||||||
\(334\) | −6.55206 | −0.358513 | ||||||||
\(335\) | −11.6403 | −0.635975 | ||||||||
\(336\) | −13.7808 | −0.751802 | ||||||||
\(337\) | 13.8524 | 0.754589 | 0.377295 | − | 0.926093i | \(-0.376854\pi\) | ||||
0.377295 | + | 0.926093i | \(0.376854\pi\) | |||||||
\(338\) | −8.66583 | −0.471359 | ||||||||
\(339\) | 7.45666 | 0.404990 | ||||||||
\(340\) | −8.33839 | −0.452213 | ||||||||
\(341\) | 1.58932 | 0.0860666 | ||||||||
\(342\) | −0.786827 | −0.0425467 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.52883 | 0.190262 | ||||||||
\(345\) | −13.1164 | −0.706162 | ||||||||
\(346\) | −23.4384 | −1.26005 | ||||||||
\(347\) | −22.8403 | −1.22613 | −0.613065 | − | 0.790033i | \(-0.710064\pi\) | ||||
−0.613065 | + | 0.790033i | \(0.710064\pi\) | |||||||
\(348\) | 19.0214 | 1.01965 | ||||||||
\(349\) | 1.02053 | 0.0546277 | 0.0273139 | − | 0.999627i | \(-0.491305\pi\) | ||||
0.0273139 | + | 0.999627i | \(0.491305\pi\) | |||||||
\(350\) | −2.55606 | −0.136627 | ||||||||
\(351\) | 19.4578 | 1.03858 | ||||||||
\(352\) | 3.50679 | 0.186912 | ||||||||
\(353\) | 18.8129 | 1.00131 | 0.500655 | − | 0.865647i | \(-0.333092\pi\) | ||||
0.500655 | + | 0.865647i | \(0.333092\pi\) | |||||||
\(354\) | 18.3871 | 0.977261 | ||||||||
\(355\) | 11.2265 | 0.595840 | ||||||||
\(356\) | 6.29745 | 0.333764 | ||||||||
\(357\) | −3.38622 | −0.179218 | ||||||||
\(358\) | −25.0707 | −1.32503 | ||||||||
\(359\) | −12.6213 | −0.666128 | −0.333064 | − | 0.942904i | \(-0.608083\pi\) | ||||
−0.333064 | + | 0.942904i | \(0.608083\pi\) | |||||||
\(360\) | 2.52175 | 0.132908 | ||||||||
\(361\) | −18.3751 | −0.967113 | ||||||||
\(362\) | −49.8698 | −2.62110 | ||||||||
\(363\) | 19.6589 | 1.03183 | ||||||||
\(364\) | 18.3537 | 0.961994 | ||||||||
\(365\) | 0.355823 | 0.0186246 | ||||||||
\(366\) | 23.8146 | 1.24481 | ||||||||
\(367\) | 19.8872 | 1.03811 | 0.519053 | − | 0.854742i | \(-0.326285\pi\) | ||||
0.519053 | + | 0.854742i | \(0.326285\pi\) | |||||||
\(368\) | −53.3288 | −2.77996 | ||||||||
\(369\) | −3.47508 | −0.180905 | ||||||||
\(370\) | 5.69053 | 0.295836 | ||||||||
\(371\) | 3.72887 | 0.193593 | ||||||||
\(372\) | 23.3828 | 1.21234 | ||||||||
\(373\) | 25.4873 | 1.31968 | 0.659841 | − | 0.751405i | \(-0.270624\pi\) | ||||
0.659841 | + | 0.751405i | \(0.270624\pi\) | |||||||
\(374\) | 2.66706 | 0.137910 | ||||||||
\(375\) | 1.84104 | 0.0950708 | ||||||||
\(376\) | −60.9360 | −3.14253 | ||||||||
\(377\) | −9.22665 | −0.475196 | ||||||||
\(378\) | −12.2849 | −0.631867 | ||||||||
\(379\) | 22.4839 | 1.15492 | 0.577459 | − | 0.816420i | \(-0.304044\pi\) | ||||
0.577459 | + | 0.816420i | \(0.304044\pi\) | |||||||
\(380\) | −3.58360 | −0.183835 | ||||||||
\(381\) | −27.5678 | −1.41234 | ||||||||
\(382\) | 26.0358 | 1.33211 | ||||||||
\(383\) | −29.9092 | −1.52829 | −0.764143 | − | 0.645047i | \(-0.776838\pi\) | ||||
−0.764143 | + | 0.645047i | \(0.776838\pi\) | |||||||
\(384\) | −18.8557 | −0.962226 | ||||||||
\(385\) | 0.567294 | 0.0289120 | ||||||||
\(386\) | −14.6786 | −0.747122 | ||||||||
\(387\) | −0.212209 | −0.0107872 | ||||||||
\(388\) | −35.1938 | −1.78670 | ||||||||
\(389\) | −2.98528 | −0.151359 | −0.0756797 | − | 0.997132i | \(-0.524113\pi\) | ||||
−0.0756797 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(390\) | −19.0514 | −0.964707 | ||||||||
\(391\) | −13.1040 | −0.662698 | ||||||||
\(392\) | −6.47568 | −0.327071 | ||||||||
\(393\) | −32.1720 | −1.62286 | ||||||||
\(394\) | −5.78206 | −0.291296 | ||||||||
\(395\) | 3.57069 | 0.179661 | ||||||||
\(396\) | −1.00151 | −0.0503278 | ||||||||
\(397\) | −13.2617 | −0.665588 | −0.332794 | − | 0.943000i | \(-0.607991\pi\) | ||||
−0.332794 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(398\) | −39.2463 | −1.96724 | ||||||||
\(399\) | −1.45530 | −0.0728561 | ||||||||
\(400\) | 7.48532 | 0.374266 | ||||||||
\(401\) | 35.8131 | 1.78842 | 0.894210 | − | 0.447648i | \(-0.147738\pi\) | ||||
0.894210 | + | 0.447648i | \(0.147738\pi\) | |||||||
\(402\) | 54.7768 | 2.73202 | ||||||||
\(403\) | −11.3422 | −0.564995 | ||||||||
\(404\) | 14.3029 | 0.711596 | ||||||||
\(405\) | 10.0166 | 0.497729 | ||||||||
\(406\) | 5.82535 | 0.289107 | ||||||||
\(407\) | −1.26296 | −0.0626026 | ||||||||
\(408\) | 21.9281 | 1.08560 | ||||||||
\(409\) | −24.3179 | −1.20244 | −0.601221 | − | 0.799083i | \(-0.705319\pi\) | ||||
−0.601221 | + | 0.799083i | \(0.705319\pi\) | |||||||
\(410\) | −22.8097 | −1.12649 | ||||||||
\(411\) | −38.9181 | −1.91969 | ||||||||
\(412\) | 71.0010 | 3.49797 | ||||||||
\(413\) | 3.90731 | 0.192266 | ||||||||
\(414\) | 7.09154 | 0.348530 | ||||||||
\(415\) | 4.12676 | 0.202575 | ||||||||
\(416\) | −25.0262 | −1.22701 | ||||||||
\(417\) | 8.72423 | 0.427227 | ||||||||
\(418\) | 1.14622 | 0.0560637 | ||||||||
\(419\) | 32.2172 | 1.57391 | 0.786956 | − | 0.617009i | \(-0.211656\pi\) | ||||
0.786956 | + | 0.617009i | \(0.211656\pi\) | |||||||
\(420\) | 8.34627 | 0.407256 | ||||||||
\(421\) | −5.99256 | −0.292059 | −0.146030 | − | 0.989280i | \(-0.546649\pi\) | ||||
−0.146030 | + | 0.989280i | \(0.546649\pi\) | |||||||
\(422\) | 67.2904 | 3.27564 | ||||||||
\(423\) | 3.66443 | 0.178171 | ||||||||
\(424\) | −24.1470 | −1.17268 | ||||||||
\(425\) | 1.83930 | 0.0892192 | ||||||||
\(426\) | −52.8297 | −2.55961 | ||||||||
\(427\) | 5.06069 | 0.244904 | ||||||||
\(428\) | −82.9158 | −4.00789 | ||||||||
\(429\) | 4.22829 | 0.204144 | ||||||||
\(430\) | −1.39289 | −0.0671712 | ||||||||
\(431\) | 21.6186 | 1.04133 | 0.520666 | − | 0.853761i | \(-0.325684\pi\) | ||||
0.520666 | + | 0.853761i | \(0.325684\pi\) | |||||||
\(432\) | 35.9758 | 1.73089 | ||||||||
\(433\) | −0.859051 | −0.0412833 | −0.0206417 | − | 0.999787i | \(-0.506571\pi\) | ||||
−0.0206417 | + | 0.999787i | \(0.506571\pi\) | |||||||
\(434\) | 7.16102 | 0.343740 | ||||||||
\(435\) | −4.19578 | −0.201172 | ||||||||
\(436\) | 3.87593 | 0.185623 | ||||||||
\(437\) | −5.63172 | −0.269402 | ||||||||
\(438\) | −1.67443 | −0.0800075 | ||||||||
\(439\) | −14.4393 | −0.689150 | −0.344575 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344575 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(440\) | −3.67361 | −0.175133 | ||||||||
\(441\) | 0.389420 | 0.0185438 | ||||||||
\(442\) | −19.0335 | −0.905329 | ||||||||
\(443\) | 21.6964 | 1.03083 | 0.515413 | − | 0.856942i | \(-0.327638\pi\) | ||||
0.515413 | + | 0.856942i | \(0.327638\pi\) | |||||||
\(444\) | −18.5812 | −0.881824 | ||||||||
\(445\) | −1.38911 | −0.0658500 | ||||||||
\(446\) | 62.2010 | 2.94530 | ||||||||
\(447\) | −11.7005 | −0.553413 | ||||||||
\(448\) | 0.829915 | 0.0392098 | ||||||||
\(449\) | −32.6633 | −1.54148 | −0.770738 | − | 0.637152i | \(-0.780112\pi\) | ||||
−0.770738 | + | 0.637152i | \(0.780112\pi\) | |||||||
\(450\) | −0.995381 | −0.0469227 | ||||||||
\(451\) | 5.06239 | 0.238379 | ||||||||
\(452\) | −18.3616 | −0.863659 | ||||||||
\(453\) | 4.90864 | 0.230628 | ||||||||
\(454\) | 37.0959 | 1.74100 | ||||||||
\(455\) | −4.04849 | −0.189796 | ||||||||
\(456\) | 9.42405 | 0.441322 | ||||||||
\(457\) | −25.6527 | −1.19998 | −0.599991 | − | 0.800007i | \(-0.704829\pi\) | ||||
−0.599991 | + | 0.800007i | \(0.704829\pi\) | |||||||
\(458\) | 2.55606 | 0.119437 | ||||||||
\(459\) | 8.84000 | 0.412616 | ||||||||
\(460\) | 32.2984 | 1.50592 | ||||||||
\(461\) | −5.55334 | −0.258645 | −0.129323 | − | 0.991603i | \(-0.541280\pi\) | ||||
−0.129323 | + | 0.991603i | \(0.541280\pi\) | |||||||
\(462\) | −2.66958 | −0.124200 | ||||||||
\(463\) | −11.6362 | −0.540779 | −0.270390 | − | 0.962751i | \(-0.587153\pi\) | ||||
−0.270390 | + | 0.962751i | \(0.587153\pi\) | |||||||
\(464\) | −17.0593 | −0.791957 | ||||||||
\(465\) | −5.15782 | −0.239188 | ||||||||
\(466\) | −8.40998 | −0.389585 | ||||||||
\(467\) | −8.08131 | −0.373959 | −0.186979 | − | 0.982364i | \(-0.559870\pi\) | ||||
−0.186979 | + | 0.982364i | \(0.559870\pi\) | |||||||
\(468\) | 7.14728 | 0.330383 | ||||||||
\(469\) | 11.6403 | 0.537497 | ||||||||
\(470\) | 24.0525 | 1.10946 | ||||||||
\(471\) | 17.4659 | 0.804786 | ||||||||
\(472\) | −25.3025 | −1.16464 | ||||||||
\(473\) | 0.309139 | 0.0142142 | ||||||||
\(474\) | −16.8030 | −0.771786 | ||||||||
\(475\) | 0.790478 | 0.0362696 | ||||||||
\(476\) | 8.33839 | 0.382189 | ||||||||
\(477\) | 1.45210 | 0.0664869 | ||||||||
\(478\) | 16.5842 | 0.758543 | ||||||||
\(479\) | −17.6516 | −0.806522 | −0.403261 | − | 0.915085i | \(-0.632123\pi\) | ||||
−0.403261 | + | 0.915085i | \(0.632123\pi\) | |||||||
\(480\) | −11.3806 | −0.519449 | ||||||||
\(481\) | 9.01311 | 0.410962 | ||||||||
\(482\) | −47.9459 | −2.18388 | ||||||||
\(483\) | 13.1164 | 0.596816 | ||||||||
\(484\) | −48.4091 | −2.20041 | ||||||||
\(485\) | 7.76313 | 0.352506 | ||||||||
\(486\) | −10.2816 | −0.466382 | ||||||||
\(487\) | 40.4405 | 1.83253 | 0.916267 | − | 0.400568i | \(-0.131187\pi\) | ||||
0.916267 | + | 0.400568i | \(0.131187\pi\) | |||||||
\(488\) | −32.7714 | −1.48349 | ||||||||
\(489\) | 2.13695 | 0.0966361 | ||||||||
\(490\) | 2.55606 | 0.115471 | ||||||||
\(491\) | −7.24347 | −0.326893 | −0.163447 | − | 0.986552i | \(-0.552261\pi\) | ||||
−0.163447 | + | 0.986552i | \(0.552261\pi\) | |||||||
\(492\) | 74.4799 | 3.35782 | ||||||||
\(493\) | −4.19182 | −0.188790 | ||||||||
\(494\) | −8.18003 | −0.368037 | ||||||||
\(495\) | 0.220915 | 0.00992941 | ||||||||
\(496\) | −20.9707 | −0.941614 | ||||||||
\(497\) | −11.2265 | −0.503577 | ||||||||
\(498\) | −19.4197 | −0.870219 | ||||||||
\(499\) | 20.0545 | 0.897765 | 0.448882 | − | 0.893591i | \(-0.351822\pi\) | ||||
0.448882 | + | 0.893591i | \(0.351822\pi\) | |||||||
\(500\) | −4.53346 | −0.202742 | ||||||||
\(501\) | −4.71921 | −0.210839 | ||||||||
\(502\) | 42.4911 | 1.89647 | ||||||||
\(503\) | −39.8272 | −1.77581 | −0.887903 | − | 0.460031i | \(-0.847838\pi\) | ||||
−0.887903 | + | 0.460031i | \(0.847838\pi\) | |||||||
\(504\) | −2.52175 | −0.112328 | ||||||||
\(505\) | −3.15497 | −0.140394 | ||||||||
\(506\) | −10.3307 | −0.459257 | ||||||||
\(507\) | −6.24168 | −0.277203 | ||||||||
\(508\) | 67.8844 | 3.01188 | ||||||||
\(509\) | −10.0956 | −0.447479 | −0.223740 | − | 0.974649i | \(-0.571827\pi\) | ||||
−0.223740 | + | 0.974649i | \(0.571827\pi\) | |||||||
\(510\) | −8.65539 | −0.383267 | ||||||||
\(511\) | −0.355823 | −0.0157407 | ||||||||
\(512\) | 50.6738 | 2.23949 | ||||||||
\(513\) | 3.79918 | 0.167738 | ||||||||
\(514\) | 40.8941 | 1.80376 | ||||||||
\(515\) | −15.6616 | −0.690131 | ||||||||
\(516\) | 4.54818 | 0.200223 | ||||||||
\(517\) | −5.33823 | −0.234775 | ||||||||
\(518\) | −5.69053 | −0.250027 | ||||||||
\(519\) | −16.8818 | −0.741028 | ||||||||
\(520\) | 26.2167 | 1.14968 | ||||||||
\(521\) | 18.3503 | 0.803940 | 0.401970 | − | 0.915653i | \(-0.368326\pi\) | ||||
0.401970 | + | 0.915653i | \(0.368326\pi\) | |||||||
\(522\) | 2.26850 | 0.0992897 | ||||||||
\(523\) | −3.65062 | −0.159630 | −0.0798152 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798152 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(524\) | 79.2218 | 3.46082 | ||||||||
\(525\) | −1.84104 | −0.0803495 | ||||||||
\(526\) | 10.6631 | 0.464934 | ||||||||
\(527\) | −5.15295 | −0.224466 | ||||||||
\(528\) | 7.81775 | 0.340224 | ||||||||
\(529\) | 27.7578 | 1.20686 | ||||||||
\(530\) | 9.53123 | 0.414010 | ||||||||
\(531\) | 1.52158 | 0.0660311 | ||||||||
\(532\) | 3.58360 | 0.155369 | ||||||||
\(533\) | −36.1277 | −1.56487 | ||||||||
\(534\) | 6.53687 | 0.282878 | ||||||||
\(535\) | 18.2898 | 0.790735 | ||||||||
\(536\) | −75.3785 | −3.25586 | ||||||||
\(537\) | −18.0575 | −0.779238 | ||||||||
\(538\) | 2.34153 | 0.100950 | ||||||||
\(539\) | −0.567294 | −0.0244351 | ||||||||
\(540\) | −21.7886 | −0.937632 | ||||||||
\(541\) | 8.64988 | 0.371888 | 0.185944 | − | 0.982560i | \(-0.440466\pi\) | ||||
0.185944 | + | 0.982560i | \(0.440466\pi\) | |||||||
\(542\) | 41.4339 | 1.77974 | ||||||||
\(543\) | −35.9194 | −1.54145 | ||||||||
\(544\) | −11.3698 | −0.487477 | ||||||||
\(545\) | −0.854961 | −0.0366225 | ||||||||
\(546\) | 19.0514 | 0.815326 | ||||||||
\(547\) | 2.88504 | 0.123355 | 0.0616777 | − | 0.998096i | \(-0.480355\pi\) | ||||
0.0616777 | + | 0.998096i | \(0.480355\pi\) | |||||||
\(548\) | 95.8338 | 4.09382 | ||||||||
\(549\) | 1.97073 | 0.0841088 | ||||||||
\(550\) | 1.45004 | 0.0618299 | ||||||||
\(551\) | −1.80152 | −0.0767475 | ||||||||
\(552\) | −84.9375 | −3.61518 | ||||||||
\(553\) | −3.57069 | −0.151841 | ||||||||
\(554\) | −70.2798 | −2.98590 | ||||||||
\(555\) | 4.09868 | 0.173979 | ||||||||
\(556\) | −21.4830 | −0.911080 | ||||||||
\(557\) | 8.90832 | 0.377458 | 0.188729 | − | 0.982029i | \(-0.439563\pi\) | ||||
0.188729 | + | 0.982029i | \(0.439563\pi\) | |||||||
\(558\) | 2.78864 | 0.118053 | ||||||||
\(559\) | −2.20617 | −0.0933111 | ||||||||
\(560\) | −7.48532 | −0.316313 | ||||||||
\(561\) | 1.92098 | 0.0811040 | ||||||||
\(562\) | 3.52978 | 0.148895 | ||||||||
\(563\) | 46.8421 | 1.97416 | 0.987080 | − | 0.160228i | \(-0.0512229\pi\) | ||||
0.987080 | + | 0.160228i | \(0.0512229\pi\) | |||||||
\(564\) | −78.5382 | −3.30705 | ||||||||
\(565\) | 4.05025 | 0.170395 | ||||||||
\(566\) | 49.9354 | 2.09894 | ||||||||
\(567\) | −10.0166 | −0.420658 | ||||||||
\(568\) | 72.6991 | 3.05039 | ||||||||
\(569\) | −33.9622 | −1.42377 | −0.711884 | − | 0.702297i | \(-0.752158\pi\) | ||||
−0.711884 | + | 0.702297i | \(0.752158\pi\) | |||||||
\(570\) | −3.71984 | −0.155807 | ||||||||
\(571\) | 7.30546 | 0.305724 | 0.152862 | − | 0.988248i | \(-0.451151\pi\) | ||||
0.152862 | + | 0.988248i | \(0.451151\pi\) | |||||||
\(572\) | −10.4119 | −0.435345 | ||||||||
\(573\) | 18.7526 | 0.783401 | ||||||||
\(574\) | 22.8097 | 0.952056 | ||||||||
\(575\) | −7.12445 | −0.297110 | ||||||||
\(576\) | 0.323185 | 0.0134660 | ||||||||
\(577\) | 0.907593 | 0.0377836 | 0.0188918 | − | 0.999822i | \(-0.493986\pi\) | ||||
0.0188918 | + | 0.999822i | \(0.493986\pi\) | |||||||
\(578\) | 34.8058 | 1.44773 | ||||||||
\(579\) | −10.5725 | −0.439376 | ||||||||
\(580\) | 10.3319 | 0.429008 | ||||||||
\(581\) | −4.12676 | −0.171207 | ||||||||
\(582\) | −36.5318 | −1.51429 | ||||||||
\(583\) | −2.11537 | −0.0876096 | ||||||||
\(584\) | 2.30419 | 0.0953482 | ||||||||
\(585\) | −1.57656 | −0.0651828 | ||||||||
\(586\) | −38.2091 | −1.57840 | ||||||||
\(587\) | 13.7166 | 0.566144 | 0.283072 | − | 0.959099i | \(-0.408646\pi\) | ||||
0.283072 | + | 0.959099i | \(0.408646\pi\) | |||||||
\(588\) | −8.34627 | −0.344194 | ||||||||
\(589\) | −2.21459 | −0.0912506 | ||||||||
\(590\) | 9.98733 | 0.411172 | ||||||||
\(591\) | −4.16460 | −0.171309 | ||||||||
\(592\) | 16.6645 | 0.684905 | ||||||||
\(593\) | 14.7906 | 0.607377 | 0.303689 | − | 0.952771i | \(-0.401782\pi\) | ||||
0.303689 | + | 0.952771i | \(0.401782\pi\) | |||||||
\(594\) | 6.96915 | 0.285948 | ||||||||
\(595\) | −1.83930 | −0.0754040 | ||||||||
\(596\) | 28.8118 | 1.18018 | ||||||||
\(597\) | −28.2676 | −1.15692 | ||||||||
\(598\) | 73.7253 | 3.01485 | ||||||||
\(599\) | 23.1794 | 0.947083 | 0.473541 | − | 0.880772i | \(-0.342975\pi\) | ||||
0.473541 | + | 0.880772i | \(0.342975\pi\) | |||||||
\(600\) | 11.9220 | 0.486712 | ||||||||
\(601\) | 26.7457 | 1.09098 | 0.545490 | − | 0.838117i | \(-0.316343\pi\) | ||||
0.545490 | + | 0.838117i | \(0.316343\pi\) | |||||||
\(602\) | 1.39289 | 0.0567700 | ||||||||
\(603\) | 4.53294 | 0.184596 | ||||||||
\(604\) | −12.0873 | −0.491824 | ||||||||
\(605\) | 10.6782 | 0.434130 | ||||||||
\(606\) | 14.8467 | 0.603105 | ||||||||
\(607\) | 18.4141 | 0.747404 | 0.373702 | − | 0.927549i | \(-0.378088\pi\) | ||||
0.373702 | + | 0.927549i | \(0.378088\pi\) | |||||||
\(608\) | −4.88642 | −0.198171 | ||||||||
\(609\) | 4.19578 | 0.170022 | ||||||||
\(610\) | 12.9354 | 0.523741 | ||||||||
\(611\) | 38.0962 | 1.54121 | ||||||||
\(612\) | 3.24713 | 0.131258 | ||||||||
\(613\) | 26.4171 | 1.06698 | 0.533489 | − | 0.845807i | \(-0.320881\pi\) | ||||
0.533489 | + | 0.845807i | \(0.320881\pi\) | |||||||
\(614\) | 35.2809 | 1.42382 | ||||||||
\(615\) | −16.4289 | −0.662479 | ||||||||
\(616\) | 3.67361 | 0.148014 | ||||||||
\(617\) | 22.8313 | 0.919155 | 0.459577 | − | 0.888138i | \(-0.348001\pi\) | ||||
0.459577 | + | 0.888138i | \(0.348001\pi\) | |||||||
\(618\) | 73.7003 | 2.96466 | ||||||||
\(619\) | −10.5590 | −0.424403 | −0.212201 | − | 0.977226i | \(-0.568063\pi\) | ||||
−0.212201 | + | 0.977226i | \(0.568063\pi\) | |||||||
\(620\) | 12.7009 | 0.510079 | ||||||||
\(621\) | −34.2414 | −1.37406 | ||||||||
\(622\) | 16.6728 | 0.668520 | ||||||||
\(623\) | 1.38911 | 0.0556534 | ||||||||
\(624\) | −55.7913 | −2.23344 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.3604 | −0.414085 | ||||||||
\(627\) | 0.825583 | 0.0329706 | ||||||||
\(628\) | −43.0088 | −1.71624 | ||||||||
\(629\) | 4.09481 | 0.163271 | ||||||||
\(630\) | 0.995381 | 0.0396569 | ||||||||
\(631\) | 27.9442 | 1.11244 | 0.556220 | − | 0.831035i | \(-0.312251\pi\) | ||||
0.556220 | + | 0.831035i | \(0.312251\pi\) | |||||||
\(632\) | 23.1226 | 0.919769 | ||||||||
\(633\) | 48.4668 | 1.92638 | ||||||||
\(634\) | 86.1157 | 3.42009 | ||||||||
\(635\) | −14.9741 | −0.594228 | ||||||||
\(636\) | −31.1222 | −1.23407 | ||||||||
\(637\) | 4.04849 | 0.160407 | ||||||||
\(638\) | −3.30469 | −0.130834 | ||||||||
\(639\) | −4.37182 | −0.172946 | ||||||||
\(640\) | −10.2419 | −0.404846 | ||||||||
\(641\) | −39.0484 | −1.54232 | −0.771159 | − | 0.636643i | \(-0.780322\pi\) | ||||
−0.771159 | + | 0.636643i | \(0.780322\pi\) | |||||||
\(642\) | −86.0681 | −3.39684 | ||||||||
\(643\) | −0.604886 | −0.0238544 | −0.0119272 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119272 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(644\) | −32.2984 | −1.27274 | ||||||||
\(645\) | −1.00325 | −0.0395028 | ||||||||
\(646\) | −3.71633 | −0.146217 | ||||||||
\(647\) | 12.3678 | 0.486229 | 0.243115 | − | 0.969998i | \(-0.421831\pi\) | ||||
0.243115 | + | 0.969998i | \(0.421831\pi\) | |||||||
\(648\) | 64.8643 | 2.54811 | ||||||||
\(649\) | −2.21659 | −0.0870089 | ||||||||
\(650\) | −10.3482 | −0.405890 | ||||||||
\(651\) | 5.15782 | 0.202151 | ||||||||
\(652\) | −5.26212 | −0.206081 | ||||||||
\(653\) | 16.8126 | 0.657930 | 0.328965 | − | 0.944342i | \(-0.393300\pi\) | ||||
0.328965 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(654\) | 4.02328 | 0.157323 | ||||||||
\(655\) | −17.4749 | −0.682802 | ||||||||
\(656\) | −66.7971 | −2.60799 | ||||||||
\(657\) | −0.138564 | −0.00540591 | ||||||||
\(658\) | −24.0525 | −0.937664 | ||||||||
\(659\) | 21.4393 | 0.835156 | 0.417578 | − | 0.908641i | \(-0.362879\pi\) | ||||
0.417578 | + | 0.908641i | \(0.362879\pi\) | |||||||
\(660\) | −4.73479 | −0.184301 | ||||||||
\(661\) | −12.2284 | −0.475629 | −0.237814 | − | 0.971311i | \(-0.576431\pi\) | ||||
−0.237814 | + | 0.971311i | \(0.576431\pi\) | |||||||
\(662\) | 21.2010 | 0.823999 | ||||||||
\(663\) | −13.7091 | −0.532417 | ||||||||
\(664\) | 26.7236 | 1.03708 | ||||||||
\(665\) | −0.790478 | −0.0306534 | ||||||||
\(666\) | −2.21600 | −0.0858684 | ||||||||
\(667\) | 16.2368 | 0.628693 | ||||||||
\(668\) | 11.6208 | 0.449622 | ||||||||
\(669\) | 44.8011 | 1.73211 | ||||||||
\(670\) | 29.7532 | 1.14947 | ||||||||
\(671\) | −2.87090 | −0.110830 | ||||||||
\(672\) | 11.3806 | 0.439015 | ||||||||
\(673\) | −28.1622 | −1.08557 | −0.542787 | − | 0.839870i | \(-0.682631\pi\) | ||||
−0.542787 | + | 0.839870i | \(0.682631\pi\) | |||||||
\(674\) | −35.4076 | −1.36385 | ||||||||
\(675\) | 4.80618 | 0.184990 | ||||||||
\(676\) | 15.3698 | 0.591146 | ||||||||
\(677\) | −17.6181 | −0.677118 | −0.338559 | − | 0.940945i | \(-0.609939\pi\) | ||||
−0.338559 | + | 0.940945i | \(0.609939\pi\) | |||||||
\(678\) | −19.0597 | −0.731983 | ||||||||
\(679\) | −7.76313 | −0.297922 | ||||||||
\(680\) | 11.9107 | 0.456755 | ||||||||
\(681\) | 26.7188 | 1.02387 | ||||||||
\(682\) | −4.06241 | −0.155558 | ||||||||
\(683\) | −15.6775 | −0.599884 | −0.299942 | − | 0.953957i | \(-0.596967\pi\) | ||||
−0.299942 | + | 0.953957i | \(0.596967\pi\) | |||||||
\(684\) | 1.39552 | 0.0533592 | ||||||||
\(685\) | −21.1392 | −0.807688 | ||||||||
\(686\) | −2.55606 | −0.0975909 | ||||||||
\(687\) | 1.84104 | 0.0702400 | ||||||||
\(688\) | −4.07902 | −0.155511 | ||||||||
\(689\) | 15.0963 | 0.575124 | ||||||||
\(690\) | 33.5263 | 1.27632 | ||||||||
\(691\) | 12.4553 | 0.473823 | 0.236911 | − | 0.971531i | \(-0.423865\pi\) | ||||
0.236911 | + | 0.971531i | \(0.423865\pi\) | |||||||
\(692\) | 41.5705 | 1.58027 | ||||||||
\(693\) | −0.220915 | −0.00839188 | ||||||||
\(694\) | 58.3811 | 2.21612 | ||||||||
\(695\) | 4.73876 | 0.179751 | ||||||||
\(696\) | −27.1705 | −1.02990 | ||||||||
\(697\) | −16.4134 | −0.621704 | ||||||||
\(698\) | −2.60854 | −0.0987347 | ||||||||
\(699\) | −6.05740 | −0.229112 | ||||||||
\(700\) | 4.53346 | 0.171349 | ||||||||
\(701\) | 35.3135 | 1.33377 | 0.666887 | − | 0.745159i | \(-0.267626\pi\) | ||||
0.666887 | + | 0.745159i | \(0.267626\pi\) | |||||||
\(702\) | −49.7353 | −1.87714 | ||||||||
\(703\) | 1.75983 | 0.0663733 | ||||||||
\(704\) | −0.470806 | −0.0177442 | ||||||||
\(705\) | 17.3241 | 0.652464 | ||||||||
\(706\) | −48.0870 | −1.80978 | ||||||||
\(707\) | 3.15497 | 0.118655 | ||||||||
\(708\) | −32.6114 | −1.22561 | ||||||||
\(709\) | 25.1040 | 0.942802 | 0.471401 | − | 0.881919i | \(-0.343748\pi\) | ||||
0.471401 | + | 0.881919i | \(0.343748\pi\) | |||||||
\(710\) | −28.6956 | −1.07693 | ||||||||
\(711\) | −1.39050 | −0.0521477 | ||||||||
\(712\) | −8.99540 | −0.337117 | ||||||||
\(713\) | 19.9597 | 0.747498 | ||||||||
\(714\) | 8.65539 | 0.323920 | ||||||||
\(715\) | 2.29669 | 0.0858912 | ||||||||
\(716\) | 44.4656 | 1.66176 | ||||||||
\(717\) | 11.9450 | 0.446093 | ||||||||
\(718\) | 32.2609 | 1.20397 | ||||||||
\(719\) | 31.0974 | 1.15974 | 0.579869 | − | 0.814710i | \(-0.303104\pi\) | ||||
0.579869 | + | 0.814710i | \(0.303104\pi\) | |||||||
\(720\) | −2.91493 | −0.108633 | ||||||||
\(721\) | 15.6616 | 0.583267 | ||||||||
\(722\) | 46.9680 | 1.74797 | ||||||||
\(723\) | −34.5336 | −1.28432 | ||||||||
\(724\) | 88.4496 | 3.28720 | ||||||||
\(725\) | −2.27903 | −0.0846411 | ||||||||
\(726\) | −50.2495 | −1.86493 | ||||||||
\(727\) | −1.66818 | −0.0618694 | −0.0309347 | − | 0.999521i | \(-0.509848\pi\) | ||||
−0.0309347 | + | 0.999521i | \(0.509848\pi\) | |||||||
\(728\) | −26.2167 | −0.971657 | ||||||||
\(729\) | 22.6444 | 0.838681 | ||||||||
\(730\) | −0.909505 | −0.0336623 | ||||||||
\(731\) | −1.00230 | −0.0370714 | ||||||||
\(732\) | −42.2379 | −1.56116 | ||||||||
\(733\) | 35.0887 | 1.29603 | 0.648015 | − | 0.761627i | \(-0.275599\pi\) | ||||
0.648015 | + | 0.761627i | \(0.275599\pi\) | |||||||
\(734\) | −50.8330 | −1.87628 | ||||||||
\(735\) | 1.84104 | 0.0679077 | ||||||||
\(736\) | 44.0405 | 1.62335 | ||||||||
\(737\) | −6.60345 | −0.243241 | ||||||||
\(738\) | 8.88252 | 0.326970 | ||||||||
\(739\) | −30.9880 | −1.13991 | −0.569956 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569956 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(740\) | −10.0928 | −0.371018 | ||||||||
\(741\) | −5.89177 | −0.216440 | ||||||||
\(742\) | −9.53123 | −0.349902 | ||||||||
\(743\) | 32.9314 | 1.20813 | 0.604067 | − | 0.796933i | \(-0.293546\pi\) | ||||
0.604067 | + | 0.796933i | \(0.293546\pi\) | |||||||
\(744\) | −33.4004 | −1.22452 | ||||||||
\(745\) | −6.35536 | −0.232842 | ||||||||
\(746\) | −65.1471 | −2.38521 | ||||||||
\(747\) | −1.60704 | −0.0587985 | ||||||||
\(748\) | −4.73032 | −0.172958 | ||||||||
\(749\) | −18.2898 | −0.668293 | ||||||||
\(750\) | −4.70581 | −0.171832 | ||||||||
\(751\) | 7.89382 | 0.288050 | 0.144025 | − | 0.989574i | \(-0.453995\pi\) | ||||
0.144025 | + | 0.989574i | \(0.453995\pi\) | |||||||
\(752\) | 70.4367 | 2.56856 | ||||||||
\(753\) | 30.6048 | 1.11530 | ||||||||
\(754\) | 23.5839 | 0.858874 | ||||||||
\(755\) | 2.66624 | 0.0970343 | ||||||||
\(756\) | 21.7886 | 0.792444 | ||||||||
\(757\) | −19.0952 | −0.694026 | −0.347013 | − | 0.937860i | \(-0.612804\pi\) | ||||
−0.347013 | + | 0.937860i | \(0.612804\pi\) | |||||||
\(758\) | −57.4701 | −2.08741 | ||||||||
\(759\) | −7.44085 | −0.270086 | ||||||||
\(760\) | 5.11888 | 0.185681 | ||||||||
\(761\) | −4.38141 | −0.158826 | −0.0794130 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794130 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(762\) | 70.4652 | 2.55268 | ||||||||
\(763\) | 0.854961 | 0.0309517 | ||||||||
\(764\) | −46.1773 | −1.67064 | ||||||||
\(765\) | −0.716259 | −0.0258964 | ||||||||
\(766\) | 76.4497 | 2.76224 | ||||||||
\(767\) | 15.8187 | 0.571181 | ||||||||
\(768\) | 51.2522 | 1.84940 | ||||||||
\(769\) | −17.2345 | −0.621493 | −0.310747 | − | 0.950493i | \(-0.600579\pi\) | ||||
−0.310747 | + | 0.950493i | \(0.600579\pi\) | |||||||
\(770\) | −1.45004 | −0.0522558 | ||||||||
\(771\) | 29.4545 | 1.06078 | ||||||||
\(772\) | 26.0341 | 0.936989 | ||||||||
\(773\) | 47.8372 | 1.72059 | 0.860293 | − | 0.509800i | \(-0.170281\pi\) | ||||
0.860293 | + | 0.509800i | \(0.170281\pi\) | |||||||
\(774\) | 0.542419 | 0.0194968 | ||||||||
\(775\) | −2.80158 | −0.100636 | ||||||||
\(776\) | 50.2715 | 1.80464 | ||||||||
\(777\) | −4.09868 | −0.147039 | ||||||||
\(778\) | 7.63055 | 0.273569 | ||||||||
\(779\) | −7.05403 | −0.252737 | ||||||||
\(780\) | 33.7898 | 1.20987 | ||||||||
\(781\) | 6.36873 | 0.227891 | ||||||||
\(782\) | 33.4947 | 1.19777 | ||||||||
\(783\) | −10.9534 | −0.391444 | ||||||||
\(784\) | 7.48532 | 0.267333 | ||||||||
\(785\) | 9.48698 | 0.338605 | ||||||||
\(786\) | 82.2337 | 2.93318 | ||||||||
\(787\) | −26.9440 | −0.960451 | −0.480226 | − | 0.877145i | \(-0.659445\pi\) | ||||
−0.480226 | + | 0.877145i | \(0.659445\pi\) | |||||||
\(788\) | 10.2551 | 0.365323 | ||||||||
\(789\) | 7.68024 | 0.273424 | ||||||||
\(790\) | −9.12691 | −0.324721 | ||||||||
\(791\) | −4.05025 | −0.144010 | ||||||||
\(792\) | 1.43058 | 0.0508333 | ||||||||
\(793\) | 20.4882 | 0.727556 | ||||||||
\(794\) | 33.8978 | 1.20299 | ||||||||
\(795\) | 6.86499 | 0.243476 | ||||||||
\(796\) | 69.6075 | 2.46717 | ||||||||
\(797\) | 3.30533 | 0.117081 | 0.0585404 | − | 0.998285i | \(-0.481355\pi\) | ||||
0.0585404 | + | 0.998285i | \(0.481355\pi\) | |||||||
\(798\) | 3.71984 | 0.131681 | ||||||||
\(799\) | 17.3078 | 0.612305 | ||||||||
\(800\) | −6.18160 | −0.218553 | ||||||||
\(801\) | 0.540945 | 0.0191134 | ||||||||
\(802\) | −91.5405 | −3.23241 | ||||||||
\(803\) | 0.201856 | 0.00712335 | ||||||||
\(804\) | −97.1527 | −3.42631 | ||||||||
\(805\) | 7.12445 | 0.251104 | ||||||||
\(806\) | 28.9914 | 1.02118 | ||||||||
\(807\) | 1.68652 | 0.0593682 | ||||||||
\(808\) | −20.4305 | −0.718744 | ||||||||
\(809\) | 26.8689 | 0.944659 | 0.472330 | − | 0.881422i | \(-0.343413\pi\) | ||||
0.472330 | + | 0.881422i | \(0.343413\pi\) | |||||||
\(810\) | −25.6031 | −0.899601 | ||||||||
\(811\) | 44.1809 | 1.55140 | 0.775700 | − | 0.631102i | \(-0.217397\pi\) | ||||
0.775700 | + | 0.631102i | \(0.217397\pi\) | |||||||
\(812\) | −10.3319 | −0.362578 | ||||||||
\(813\) | 29.8433 | 1.04665 | ||||||||
\(814\) | 3.22820 | 0.113148 | ||||||||
\(815\) | 1.16073 | 0.0406586 | ||||||||
\(816\) | −25.3470 | −0.887321 | ||||||||
\(817\) | −0.430760 | −0.0150704 | ||||||||
\(818\) | 62.1580 | 2.17330 | ||||||||
\(819\) | 1.57656 | 0.0550896 | ||||||||
\(820\) | 40.4554 | 1.41276 | ||||||||
\(821\) | 14.9666 | 0.522336 | 0.261168 | − | 0.965293i | \(-0.415892\pi\) | ||||
0.261168 | + | 0.965293i | \(0.415892\pi\) | |||||||
\(822\) | 99.4772 | 3.46966 | ||||||||
\(823\) | 32.1619 | 1.12109 | 0.560547 | − | 0.828123i | \(-0.310591\pi\) | ||||
0.560547 | + | 0.828123i | \(0.310591\pi\) | |||||||
\(824\) | −101.419 | −3.53311 | ||||||||
\(825\) | 1.04441 | 0.0363617 | ||||||||
\(826\) | −9.98733 | −0.347504 | ||||||||
\(827\) | −22.3111 | −0.775833 | −0.387916 | − | 0.921695i | \(-0.626805\pi\) | ||||
−0.387916 | + | 0.921695i | \(0.626805\pi\) | |||||||
\(828\) | −12.5776 | −0.437103 | ||||||||
\(829\) | 36.7607 | 1.27675 | 0.638377 | − | 0.769724i | \(-0.279606\pi\) | ||||
0.638377 | + | 0.769724i | \(0.279606\pi\) | |||||||
\(830\) | −10.5483 | −0.366135 | ||||||||
\(831\) | −50.6200 | −1.75599 | ||||||||
\(832\) | 3.35991 | 0.116484 | ||||||||
\(833\) | 1.83930 | 0.0637280 | ||||||||
\(834\) | −22.2997 | −0.772175 | ||||||||
\(835\) | −2.56334 | −0.0887081 | ||||||||
\(836\) | −2.03296 | −0.0703112 | ||||||||
\(837\) | −13.4649 | −0.465415 | ||||||||
\(838\) | −82.3491 | −2.84470 | ||||||||
\(839\) | −17.4342 | −0.601894 | −0.300947 | − | 0.953641i | \(-0.597303\pi\) | ||||
−0.300947 | + | 0.953641i | \(0.597303\pi\) | |||||||
\(840\) | −11.9220 | −0.411347 | ||||||||
\(841\) | −23.8060 | −0.820897 | ||||||||
\(842\) | 15.3173 | 0.527871 | ||||||||
\(843\) | 2.54237 | 0.0875639 | ||||||||
\(844\) | −119.347 | −4.10809 | ||||||||
\(845\) | −3.39031 | −0.116630 | ||||||||
\(846\) | −9.36651 | −0.322027 | ||||||||
\(847\) | −10.6782 | −0.366907 | ||||||||
\(848\) | 27.9118 | 0.958495 | ||||||||
\(849\) | 35.9666 | 1.23437 | ||||||||
\(850\) | −4.70137 | −0.161256 | ||||||||
\(851\) | −15.8611 | −0.543710 | ||||||||
\(852\) | 93.6993 | 3.21009 | ||||||||
\(853\) | −27.9319 | −0.956369 | −0.478184 | − | 0.878259i | \(-0.658705\pi\) | ||||
−0.478184 | + | 0.878259i | \(0.658705\pi\) | |||||||
\(854\) | −12.9354 | −0.442642 | ||||||||
\(855\) | −0.307828 | −0.0105275 | ||||||||
\(856\) | 118.439 | 4.04815 | ||||||||
\(857\) | 46.8663 | 1.60092 | 0.800461 | − | 0.599385i | \(-0.204588\pi\) | ||||
0.800461 | + | 0.599385i | \(0.204588\pi\) | |||||||
\(858\) | −10.8078 | −0.368971 | ||||||||
\(859\) | 24.7665 | 0.845023 | 0.422512 | − | 0.906358i | \(-0.361149\pi\) | ||||
0.422512 | + | 0.906358i | \(0.361149\pi\) | |||||||
\(860\) | 2.47044 | 0.0842415 | ||||||||
\(861\) | 16.4289 | 0.559897 | ||||||||
\(862\) | −55.2585 | −1.88211 | ||||||||
\(863\) | 58.4302 | 1.98899 | 0.994494 | − | 0.104797i | \(-0.0334191\pi\) | ||||
0.994494 | + | 0.104797i | \(0.0334191\pi\) | |||||||
\(864\) | −29.7099 | −1.01075 | ||||||||
\(865\) | −9.16971 | −0.311780 | ||||||||
\(866\) | 2.19579 | 0.0746159 | ||||||||
\(867\) | 25.0694 | 0.851400 | ||||||||
\(868\) | −12.7009 | −0.431095 | ||||||||
\(869\) | 2.02563 | 0.0687148 | ||||||||
\(870\) | 10.7247 | 0.363601 | ||||||||
\(871\) | 47.1255 | 1.59679 | ||||||||
\(872\) | −5.53645 | −0.187488 | ||||||||
\(873\) | −3.02312 | −0.102317 | ||||||||
\(874\) | 14.3950 | 0.486920 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 2.96979 | 0.100340 | ||||||||
\(877\) | −22.1372 | −0.747519 | −0.373759 | − | 0.927526i | \(-0.621931\pi\) | ||||
−0.373759 | + | 0.927526i | \(0.621931\pi\) | |||||||
\(878\) | 36.9078 | 1.24558 | ||||||||
\(879\) | −27.5206 | −0.928247 | ||||||||
\(880\) | 4.24638 | 0.143145 | ||||||||
\(881\) | 23.5308 | 0.792774 | 0.396387 | − | 0.918083i | \(-0.370264\pi\) | ||||
0.396387 | + | 0.918083i | \(0.370264\pi\) | |||||||
\(882\) | −0.995381 | −0.0335162 | ||||||||
\(883\) | 13.5678 | 0.456592 | 0.228296 | − | 0.973592i | \(-0.426685\pi\) | ||||
0.228296 | + | 0.973592i | \(0.426685\pi\) | |||||||
\(884\) | 33.7579 | 1.13540 | ||||||||
\(885\) | 7.19351 | 0.241807 | ||||||||
\(886\) | −55.4573 | −1.86313 | ||||||||
\(887\) | −20.9871 | −0.704679 | −0.352340 | − | 0.935872i | \(-0.614614\pi\) | ||||
−0.352340 | + | 0.935872i | \(0.614614\pi\) | |||||||
\(888\) | 26.5417 | 0.890681 | ||||||||
\(889\) | 14.9741 | 0.502215 | ||||||||
\(890\) | 3.55064 | 0.119018 | ||||||||
\(891\) | 5.68237 | 0.190366 | ||||||||
\(892\) | −110.320 | −3.69380 | ||||||||
\(893\) | 7.43838 | 0.248916 | ||||||||
\(894\) | 29.9071 | 1.00024 | ||||||||
\(895\) | −9.80832 | −0.327856 | ||||||||
\(896\) | 10.2419 | 0.342157 | ||||||||
\(897\) | 53.1016 | 1.77301 | ||||||||
\(898\) | 83.4894 | 2.78608 | ||||||||
\(899\) | 6.38489 | 0.212948 | ||||||||
\(900\) | 1.76542 | 0.0588472 | ||||||||
\(901\) | 6.85852 | 0.228490 | ||||||||
\(902\) | −12.9398 | −0.430848 | ||||||||
\(903\) | 1.00325 | 0.0333860 | ||||||||
\(904\) | 26.2281 | 0.872334 | ||||||||
\(905\) | −19.5104 | −0.648548 | ||||||||
\(906\) | −12.5468 | −0.416839 | ||||||||
\(907\) | 10.2823 | 0.341420 | 0.170710 | − | 0.985321i | \(-0.445394\pi\) | ||||
0.170710 | + | 0.985321i | \(0.445394\pi\) | |||||||
\(908\) | −65.7937 | −2.18344 | ||||||||
\(909\) | 1.22861 | 0.0407503 | ||||||||
\(910\) | 10.3482 | 0.343040 | ||||||||
\(911\) | 16.8197 | 0.557262 | 0.278631 | − | 0.960398i | \(-0.410119\pi\) | ||||
0.278631 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(912\) | −10.8934 | −0.360716 | ||||||||
\(913\) | 2.34109 | 0.0774787 | ||||||||
\(914\) | 65.5699 | 2.16886 | ||||||||
\(915\) | 9.31692 | 0.308008 | ||||||||
\(916\) | −4.53346 | −0.149790 | ||||||||
\(917\) | 17.4749 | 0.577073 | ||||||||
\(918\) | −22.5956 | −0.745766 | ||||||||
\(919\) | −3.14612 | −0.103781 | −0.0518905 | − | 0.998653i | \(-0.516525\pi\) | ||||
−0.0518905 | + | 0.998653i | \(0.516525\pi\) | |||||||
\(920\) | −46.1356 | −1.52105 | ||||||||
\(921\) | 25.4115 | 0.837338 | ||||||||
\(922\) | 14.1947 | 0.467477 | ||||||||
\(923\) | −45.4504 | −1.49602 | ||||||||
\(924\) | 4.73479 | 0.155763 | ||||||||
\(925\) | 2.22629 | 0.0731998 | ||||||||
\(926\) | 29.7428 | 0.977410 | ||||||||
\(927\) | 6.09892 | 0.200315 | ||||||||
\(928\) | 14.0881 | 0.462463 | ||||||||
\(929\) | −2.88915 | −0.0947901 | −0.0473950 | − | 0.998876i | \(-0.515092\pi\) | ||||
−0.0473950 | + | 0.998876i | \(0.515092\pi\) | |||||||
\(930\) | 13.1837 | 0.432311 | ||||||||
\(931\) | 0.790478 | 0.0259069 | ||||||||
\(932\) | 14.9160 | 0.488591 | ||||||||
\(933\) | 12.0088 | 0.393151 | ||||||||
\(934\) | 20.6563 | 0.675896 | ||||||||
\(935\) | 1.04342 | 0.0341236 | ||||||||
\(936\) | −10.2093 | −0.333702 | ||||||||
\(937\) | 11.0172 | 0.359916 | 0.179958 | − | 0.983674i | \(-0.442404\pi\) | ||||
0.179958 | + | 0.983674i | \(0.442404\pi\) | |||||||
\(938\) | −29.7532 | −0.971477 | ||||||||
\(939\) | −7.46222 | −0.243520 | ||||||||
\(940\) | −42.6597 | −1.39141 | ||||||||
\(941\) | 25.2443 | 0.822941 | 0.411470 | − | 0.911423i | \(-0.365015\pi\) | ||||
0.411470 | + | 0.911423i | \(0.365015\pi\) | |||||||
\(942\) | −44.6439 | −1.45458 | ||||||||
\(943\) | 63.5768 | 2.07034 | ||||||||
\(944\) | 29.2475 | 0.951924 | ||||||||
\(945\) | −4.80618 | −0.156345 | ||||||||
\(946\) | −0.790179 | −0.0256909 | ||||||||
\(947\) | −1.46997 | −0.0477675 | −0.0238838 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238838 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(948\) | 29.8019 | 0.967921 | ||||||||
\(949\) | −1.44055 | −0.0467621 | ||||||||
\(950\) | −2.02051 | −0.0655541 | ||||||||
\(951\) | 62.0259 | 2.01133 | ||||||||
\(952\) | −11.9107 | −0.386028 | ||||||||
\(953\) | 50.3023 | 1.62945 | 0.814726 | − | 0.579846i | \(-0.196887\pi\) | ||||
0.814726 | + | 0.579846i | \(0.196887\pi\) | |||||||
\(954\) | −3.71165 | −0.120169 | ||||||||
\(955\) | 10.1859 | 0.329607 | ||||||||
\(956\) | −29.4139 | −0.951313 | ||||||||
\(957\) | −2.38024 | −0.0769423 | ||||||||
\(958\) | 45.1186 | 1.45772 | ||||||||
\(959\) | 21.1392 | 0.682621 | ||||||||
\(960\) | 1.52790 | 0.0493129 | ||||||||
\(961\) | −23.1511 | −0.746811 | ||||||||
\(962\) | −23.0381 | −0.742777 | ||||||||
\(963\) | −7.12239 | −0.229516 | ||||||||
\(964\) | 85.0373 | 2.73887 | ||||||||
\(965\) | −5.74266 | −0.184863 | ||||||||
\(966\) | −33.5263 | −1.07869 | ||||||||
\(967\) | 17.9790 | 0.578165 | 0.289083 | − | 0.957304i | \(-0.406650\pi\) | ||||
0.289083 | + | 0.957304i | \(0.406650\pi\) | |||||||
\(968\) | 69.1484 | 2.22251 | ||||||||
\(969\) | −2.67673 | −0.0859891 | ||||||||
\(970\) | −19.8431 | −0.637122 | ||||||||
\(971\) | −10.6472 | −0.341685 | −0.170842 | − | 0.985298i | \(-0.554649\pi\) | ||||
−0.170842 | + | 0.985298i | \(0.554649\pi\) | |||||||
\(972\) | 18.2355 | 0.584904 | ||||||||
\(973\) | −4.73876 | −0.151918 | ||||||||
\(974\) | −103.368 | −3.31214 | ||||||||
\(975\) | −7.45343 | −0.238701 | ||||||||
\(976\) | 37.8809 | 1.21254 | ||||||||
\(977\) | −21.0533 | −0.673556 | −0.336778 | − | 0.941584i | \(-0.609337\pi\) | ||||
−0.336778 | + | 0.941584i | \(0.609337\pi\) | |||||||
\(978\) | −5.46217 | −0.174661 | ||||||||
\(979\) | −0.788032 | −0.0251856 | ||||||||
\(980\) | −4.53346 | −0.144816 | ||||||||
\(981\) | 0.332939 | 0.0106299 | ||||||||
\(982\) | 18.5148 | 0.590830 | ||||||||
\(983\) | 40.0100 | 1.27612 | 0.638061 | − | 0.769986i | \(-0.279737\pi\) | ||||
0.638061 | + | 0.769986i | \(0.279737\pi\) | |||||||
\(984\) | −106.389 | −3.39154 | ||||||||
\(985\) | −2.26210 | −0.0720764 | ||||||||
\(986\) | 10.7146 | 0.341221 | ||||||||
\(987\) | −17.3241 | −0.551433 | ||||||||
\(988\) | 14.5082 | 0.461567 | ||||||||
\(989\) | 3.88237 | 0.123452 | ||||||||
\(990\) | −0.564674 | −0.0179465 | ||||||||
\(991\) | −56.1788 | −1.78458 | −0.892288 | − | 0.451466i | \(-0.850901\pi\) | ||||
−0.892288 | + | 0.451466i | \(0.850901\pi\) | |||||||
\(992\) | 17.3183 | 0.549855 | ||||||||
\(993\) | 15.2703 | 0.484587 | ||||||||
\(994\) | 28.6956 | 0.910170 | ||||||||
\(995\) | −15.3542 | −0.486760 | ||||||||
\(996\) | 34.4430 | 1.09137 | ||||||||
\(997\) | 22.0098 | 0.697057 | 0.348528 | − | 0.937298i | \(-0.386682\pi\) | ||||
0.348528 | + | 0.937298i | \(0.386682\pi\) | |||||||
\(998\) | −51.2607 | −1.62263 | ||||||||
\(999\) | 10.6999 | 0.338531 |
(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 | 8015.2.a.n.1.4 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.n.1.4 | ✓ | 68 | 1.1 | even | 1 | trivial |