Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, 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("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69755 | −1.90746 | −0.953729 | − | 0.300667i | \(-0.902791\pi\) | ||||
−0.953729 | + | 0.300667i | \(0.902791\pi\) | |||||||
\(3\) | 3.18040 | 1.83620 | 0.918102 | − | 0.396345i | \(-0.129722\pi\) | ||||
0.918102 | + | 0.396345i | \(0.129722\pi\) | |||||||
\(4\) | 5.27679 | 2.63840 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −8.57929 | −3.50248 | ||||||||
\(7\) | 2.84577 | 1.07560 | 0.537800 | − | 0.843072i | \(-0.319255\pi\) | ||||
0.537800 | + | 0.843072i | \(0.319255\pi\) | |||||||
\(8\) | −8.83933 | −3.12517 | ||||||||
\(9\) | 7.11493 | 2.37164 | ||||||||
\(10\) | 2.69755 | 0.853041 | ||||||||
\(11\) | 0.275530 | 0.0830753 | 0.0415377 | − | 0.999137i | \(-0.486774\pi\) | ||||
0.0415377 | + | 0.999137i | \(0.486774\pi\) | |||||||
\(12\) | 16.7823 | 4.84463 | ||||||||
\(13\) | −4.71319 | −1.30720 | −0.653602 | − | 0.756838i | \(-0.726743\pi\) | ||||
−0.653602 | + | 0.756838i | \(0.726743\pi\) | |||||||
\(14\) | −7.67662 | −2.05166 | ||||||||
\(15\) | −3.18040 | −0.821175 | ||||||||
\(16\) | 13.2910 | 3.32274 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −19.1929 | −4.52381 | ||||||||
\(19\) | 0.349365 | 0.0801498 | 0.0400749 | − | 0.999197i | \(-0.487240\pi\) | ||||
0.0400749 | + | 0.999197i | \(0.487240\pi\) | |||||||
\(20\) | −5.27679 | −1.17993 | ||||||||
\(21\) | 9.05069 | 1.97502 | ||||||||
\(22\) | −0.743256 | −0.158463 | ||||||||
\(23\) | −0.891742 | −0.185941 | −0.0929706 | − | 0.995669i | \(-0.529636\pi\) | ||||
−0.0929706 | + | 0.995669i | \(0.529636\pi\) | |||||||
\(24\) | −28.1126 | −5.73846 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 12.7141 | 2.49344 | ||||||||
\(27\) | 13.0871 | 2.51862 | ||||||||
\(28\) | 15.0166 | 2.83786 | ||||||||
\(29\) | −5.91246 | −1.09792 | −0.548959 | − | 0.835850i | \(-0.684976\pi\) | ||||
−0.548959 | + | 0.835850i | \(0.684976\pi\) | |||||||
\(30\) | 8.57929 | 1.56636 | ||||||||
\(31\) | 4.83127 | 0.867722 | 0.433861 | − | 0.900980i | \(-0.357151\pi\) | ||||
0.433861 | + | 0.900980i | \(0.357151\pi\) | |||||||
\(32\) | −18.1744 | −3.21282 | ||||||||
\(33\) | 0.876294 | 0.152543 | ||||||||
\(34\) | −2.69755 | −0.462627 | ||||||||
\(35\) | −2.84577 | −0.481023 | ||||||||
\(36\) | 37.5440 | 6.25734 | ||||||||
\(37\) | 6.79832 | 1.11764 | 0.558819 | − | 0.829290i | \(-0.311255\pi\) | ||||
0.558819 | + | 0.829290i | \(0.311255\pi\) | |||||||
\(38\) | −0.942430 | −0.152882 | ||||||||
\(39\) | −14.9898 | −2.40029 | ||||||||
\(40\) | 8.83933 | 1.39762 | ||||||||
\(41\) | −6.30778 | −0.985110 | −0.492555 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492555 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(42\) | −24.4147 | −3.76727 | ||||||||
\(43\) | −1.15455 | −0.176067 | −0.0880333 | − | 0.996118i | \(-0.528058\pi\) | ||||
−0.0880333 | + | 0.996118i | \(0.528058\pi\) | |||||||
\(44\) | 1.45391 | 0.219186 | ||||||||
\(45\) | −7.11493 | −1.06063 | ||||||||
\(46\) | 2.40552 | 0.354675 | ||||||||
\(47\) | 3.91305 | 0.570776 | 0.285388 | − | 0.958412i | \(-0.407877\pi\) | ||||
0.285388 | + | 0.958412i | \(0.407877\pi\) | |||||||
\(48\) | 42.2706 | 6.10123 | ||||||||
\(49\) | 1.09842 | 0.156917 | ||||||||
\(50\) | −2.69755 | −0.381492 | ||||||||
\(51\) | 3.18040 | 0.445345 | ||||||||
\(52\) | −24.8705 | −3.44892 | ||||||||
\(53\) | 11.4633 | 1.57461 | 0.787305 | − | 0.616563i | \(-0.211475\pi\) | ||||
0.787305 | + | 0.616563i | \(0.211475\pi\) | |||||||
\(54\) | −35.3032 | −4.80415 | ||||||||
\(55\) | −0.275530 | −0.0371524 | ||||||||
\(56\) | −25.1547 | −3.36144 | ||||||||
\(57\) | 1.11112 | 0.147171 | ||||||||
\(58\) | 15.9492 | 2.09423 | ||||||||
\(59\) | −2.92255 | −0.380483 | −0.190242 | − | 0.981737i | \(-0.560927\pi\) | ||||
−0.190242 | + | 0.981737i | \(0.560927\pi\) | |||||||
\(60\) | −16.7823 | −2.16659 | ||||||||
\(61\) | 7.18124 | 0.919464 | 0.459732 | − | 0.888058i | \(-0.347946\pi\) | ||||
0.459732 | + | 0.888058i | \(0.347946\pi\) | |||||||
\(62\) | −13.0326 | −1.65514 | ||||||||
\(63\) | 20.2475 | 2.55094 | ||||||||
\(64\) | 22.4446 | 2.80557 | ||||||||
\(65\) | 4.71319 | 0.584600 | ||||||||
\(66\) | −2.36385 | −0.290970 | ||||||||
\(67\) | 8.62627 | 1.05387 | 0.526933 | − | 0.849907i | \(-0.323342\pi\) | ||||
0.526933 | + | 0.849907i | \(0.323342\pi\) | |||||||
\(68\) | 5.27679 | 0.639905 | ||||||||
\(69\) | −2.83610 | −0.341426 | ||||||||
\(70\) | 7.67662 | 0.917532 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −62.8912 | −7.41180 | ||||||||
\(73\) | 4.10662 | 0.480644 | 0.240322 | − | 0.970693i | \(-0.422747\pi\) | ||||
0.240322 | + | 0.970693i | \(0.422747\pi\) | |||||||
\(74\) | −18.3388 | −2.13185 | ||||||||
\(75\) | 3.18040 | 0.367241 | ||||||||
\(76\) | 1.84353 | 0.211467 | ||||||||
\(77\) | 0.784095 | 0.0893559 | ||||||||
\(78\) | 40.4359 | 4.57846 | ||||||||
\(79\) | 6.59513 | 0.742010 | 0.371005 | − | 0.928631i | \(-0.379013\pi\) | ||||
0.371005 | + | 0.928631i | \(0.379013\pi\) | |||||||
\(80\) | −13.2910 | −1.48598 | ||||||||
\(81\) | 20.2774 | 2.25305 | ||||||||
\(82\) | 17.0156 | 1.87906 | ||||||||
\(83\) | −4.36368 | −0.478976 | −0.239488 | − | 0.970899i | \(-0.576980\pi\) | ||||
−0.239488 | + | 0.970899i | \(0.576980\pi\) | |||||||
\(84\) | 47.7586 | 5.21089 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 3.11445 | 0.335840 | ||||||||
\(87\) | −18.8040 | −2.01600 | ||||||||
\(88\) | −2.43550 | −0.259625 | ||||||||
\(89\) | 8.64674 | 0.916553 | 0.458276 | − | 0.888810i | \(-0.348467\pi\) | ||||
0.458276 | + | 0.888810i | \(0.348467\pi\) | |||||||
\(90\) | 19.1929 | 2.02311 | ||||||||
\(91\) | −13.4127 | −1.40603 | ||||||||
\(92\) | −4.70554 | −0.490587 | ||||||||
\(93\) | 15.3654 | 1.59331 | ||||||||
\(94\) | −10.5556 | −1.08873 | ||||||||
\(95\) | −0.349365 | −0.0358441 | ||||||||
\(96\) | −57.8020 | −5.89939 | ||||||||
\(97\) | 7.93741 | 0.805922 | 0.402961 | − | 0.915217i | \(-0.367981\pi\) | ||||
0.402961 | + | 0.915217i | \(0.367981\pi\) | |||||||
\(98\) | −2.96304 | −0.299313 | ||||||||
\(99\) | 1.96037 | 0.197025 | ||||||||
\(100\) | 5.27679 | 0.527679 | ||||||||
\(101\) | 9.09860 | 0.905345 | 0.452672 | − | 0.891677i | \(-0.350471\pi\) | ||||
0.452672 | + | 0.891677i | \(0.350471\pi\) | |||||||
\(102\) | −8.57929 | −0.849477 | ||||||||
\(103\) | 1.80476 | 0.177828 | 0.0889141 | − | 0.996039i | \(-0.471660\pi\) | ||||
0.0889141 | + | 0.996039i | \(0.471660\pi\) | |||||||
\(104\) | 41.6615 | 4.08524 | ||||||||
\(105\) | −9.05069 | −0.883257 | ||||||||
\(106\) | −30.9230 | −3.00350 | ||||||||
\(107\) | 10.3112 | 0.996824 | 0.498412 | − | 0.866940i | \(-0.333917\pi\) | ||||
0.498412 | + | 0.866940i | \(0.333917\pi\) | |||||||
\(108\) | 69.0580 | 6.64511 | ||||||||
\(109\) | 3.33893 | 0.319811 | 0.159906 | − | 0.987132i | \(-0.448881\pi\) | ||||
0.159906 | + | 0.987132i | \(0.448881\pi\) | |||||||
\(110\) | 0.743256 | 0.0708667 | ||||||||
\(111\) | 21.6214 | 2.05221 | ||||||||
\(112\) | 37.8231 | 3.57394 | ||||||||
\(113\) | −9.35353 | −0.879906 | −0.439953 | − | 0.898021i | \(-0.645005\pi\) | ||||
−0.439953 | + | 0.898021i | \(0.645005\pi\) | |||||||
\(114\) | −2.99730 | −0.280723 | ||||||||
\(115\) | 0.891742 | 0.0831554 | ||||||||
\(116\) | −31.1989 | −2.89674 | ||||||||
\(117\) | −33.5340 | −3.10022 | ||||||||
\(118\) | 7.88373 | 0.725756 | ||||||||
\(119\) | 2.84577 | 0.260872 | ||||||||
\(120\) | 28.1126 | 2.56632 | ||||||||
\(121\) | −10.9241 | −0.993098 | ||||||||
\(122\) | −19.3718 | −1.75384 | ||||||||
\(123\) | −20.0613 | −1.80886 | ||||||||
\(124\) | 25.4936 | 2.28939 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −54.6186 | −4.86581 | ||||||||
\(127\) | 13.7774 | 1.22255 | 0.611274 | − | 0.791419i | \(-0.290657\pi\) | ||||
0.611274 | + | 0.791419i | \(0.290657\pi\) | |||||||
\(128\) | −24.1966 | −2.13870 | ||||||||
\(129\) | −3.67192 | −0.323294 | ||||||||
\(130\) | −12.7141 | −1.11510 | ||||||||
\(131\) | −10.4835 | −0.915949 | −0.457974 | − | 0.888965i | \(-0.651425\pi\) | ||||
−0.457974 | + | 0.888965i | \(0.651425\pi\) | |||||||
\(132\) | 4.62402 | 0.402469 | ||||||||
\(133\) | 0.994213 | 0.0862092 | ||||||||
\(134\) | −23.2698 | −2.01021 | ||||||||
\(135\) | −13.0871 | −1.12636 | ||||||||
\(136\) | −8.83933 | −0.757966 | ||||||||
\(137\) | 7.23089 | 0.617776 | 0.308888 | − | 0.951098i | \(-0.400043\pi\) | ||||
0.308888 | + | 0.951098i | \(0.400043\pi\) | |||||||
\(138\) | 7.65052 | 0.651255 | ||||||||
\(139\) | 10.0191 | 0.849809 | 0.424904 | − | 0.905238i | \(-0.360308\pi\) | ||||
0.424904 | + | 0.905238i | \(0.360308\pi\) | |||||||
\(140\) | −15.0166 | −1.26913 | ||||||||
\(141\) | 12.4450 | 1.04806 | ||||||||
\(142\) | 2.69755 | 0.226374 | ||||||||
\(143\) | −1.29862 | −0.108596 | ||||||||
\(144\) | 94.5643 | 7.88036 | ||||||||
\(145\) | 5.91246 | 0.491003 | ||||||||
\(146\) | −11.0778 | −0.916808 | ||||||||
\(147\) | 3.49341 | 0.288132 | ||||||||
\(148\) | 35.8734 | 2.94877 | ||||||||
\(149\) | −12.1565 | −0.995897 | −0.497949 | − | 0.867207i | \(-0.665913\pi\) | ||||
−0.497949 | + | 0.867207i | \(0.665913\pi\) | |||||||
\(150\) | −8.57929 | −0.700496 | ||||||||
\(151\) | −14.6494 | −1.19215 | −0.596074 | − | 0.802929i | \(-0.703274\pi\) | ||||
−0.596074 | + | 0.802929i | \(0.703274\pi\) | |||||||
\(152\) | −3.08815 | −0.250482 | ||||||||
\(153\) | 7.11493 | 0.575208 | ||||||||
\(154\) | −2.11514 | −0.170443 | ||||||||
\(155\) | −4.83127 | −0.388057 | ||||||||
\(156\) | −79.0982 | −6.33293 | ||||||||
\(157\) | 5.57332 | 0.444799 | 0.222400 | − | 0.974956i | \(-0.428611\pi\) | ||||
0.222400 | + | 0.974956i | \(0.428611\pi\) | |||||||
\(158\) | −17.7907 | −1.41535 | ||||||||
\(159\) | 36.4580 | 2.89131 | ||||||||
\(160\) | 18.1744 | 1.43682 | ||||||||
\(161\) | −2.53770 | −0.199998 | ||||||||
\(162\) | −54.6994 | −4.29759 | ||||||||
\(163\) | −0.683516 | −0.0535371 | −0.0267685 | − | 0.999642i | \(-0.508522\pi\) | ||||
−0.0267685 | + | 0.999642i | \(0.508522\pi\) | |||||||
\(164\) | −33.2849 | −2.59911 | ||||||||
\(165\) | −0.876294 | −0.0682194 | ||||||||
\(166\) | 11.7713 | 0.913627 | ||||||||
\(167\) | −19.9279 | −1.54207 | −0.771035 | − | 0.636793i | \(-0.780260\pi\) | ||||
−0.771035 | + | 0.636793i | \(0.780260\pi\) | |||||||
\(168\) | −80.0020 | −6.17229 | ||||||||
\(169\) | 9.21419 | 0.708784 | ||||||||
\(170\) | 2.69755 | 0.206893 | ||||||||
\(171\) | 2.48571 | 0.190087 | ||||||||
\(172\) | −6.09230 | −0.464534 | ||||||||
\(173\) | 23.4532 | 1.78311 | 0.891556 | − | 0.452910i | \(-0.149614\pi\) | ||||
0.891556 | + | 0.452910i | \(0.149614\pi\) | |||||||
\(174\) | 50.7248 | 3.84543 | ||||||||
\(175\) | 2.84577 | 0.215120 | ||||||||
\(176\) | 3.66206 | 0.276038 | ||||||||
\(177\) | −9.29487 | −0.698645 | ||||||||
\(178\) | −23.3250 | −1.74829 | ||||||||
\(179\) | 22.3842 | 1.67308 | 0.836538 | − | 0.547909i | \(-0.184576\pi\) | ||||
0.836538 | + | 0.547909i | \(0.184576\pi\) | |||||||
\(180\) | −37.5440 | −2.79837 | ||||||||
\(181\) | −1.07690 | −0.0800455 | −0.0400228 | − | 0.999199i | \(-0.512743\pi\) | ||||
−0.0400228 | + | 0.999199i | \(0.512743\pi\) | |||||||
\(182\) | 36.1814 | 2.68194 | ||||||||
\(183\) | 22.8392 | 1.68832 | ||||||||
\(184\) | 7.88240 | 0.581098 | ||||||||
\(185\) | −6.79832 | −0.499823 | ||||||||
\(186\) | −41.4489 | −3.03918 | ||||||||
\(187\) | 0.275530 | 0.0201487 | ||||||||
\(188\) | 20.6483 | 1.50593 | ||||||||
\(189\) | 37.2429 | 2.70902 | ||||||||
\(190\) | 0.942430 | 0.0683711 | ||||||||
\(191\) | 22.6457 | 1.63858 | 0.819291 | − | 0.573378i | \(-0.194367\pi\) | ||||
0.819291 | + | 0.573378i | \(0.194367\pi\) | |||||||
\(192\) | 71.3827 | 5.15160 | ||||||||
\(193\) | −15.8763 | −1.14280 | −0.571401 | − | 0.820671i | \(-0.693600\pi\) | ||||
−0.571401 | + | 0.820671i | \(0.693600\pi\) | |||||||
\(194\) | −21.4116 | −1.53726 | ||||||||
\(195\) | 14.9898 | 1.07344 | ||||||||
\(196\) | 5.79613 | 0.414009 | ||||||||
\(197\) | 22.4421 | 1.59893 | 0.799466 | − | 0.600712i | \(-0.205116\pi\) | ||||
0.799466 | + | 0.600712i | \(0.205116\pi\) | |||||||
\(198\) | −5.28821 | −0.375817 | ||||||||
\(199\) | −13.1416 | −0.931584 | −0.465792 | − | 0.884894i | \(-0.654231\pi\) | ||||
−0.465792 | + | 0.884894i | \(0.654231\pi\) | |||||||
\(200\) | −8.83933 | −0.625035 | ||||||||
\(201\) | 27.4350 | 1.93511 | ||||||||
\(202\) | −24.5440 | −1.72691 | ||||||||
\(203\) | −16.8255 | −1.18092 | ||||||||
\(204\) | 16.7823 | 1.17500 | ||||||||
\(205\) | 6.30778 | 0.440555 | ||||||||
\(206\) | −4.86844 | −0.339200 | ||||||||
\(207\) | −6.34468 | −0.440986 | ||||||||
\(208\) | −62.6429 | −4.34350 | ||||||||
\(209\) | 0.0962604 | 0.00665847 | ||||||||
\(210\) | 24.4147 | 1.68478 | ||||||||
\(211\) | 24.0232 | 1.65382 | 0.826912 | − | 0.562331i | \(-0.190095\pi\) | ||||
0.826912 | + | 0.562331i | \(0.190095\pi\) | |||||||
\(212\) | 60.4897 | 4.15445 | ||||||||
\(213\) | −3.18040 | −0.217917 | ||||||||
\(214\) | −27.8151 | −1.90140 | ||||||||
\(215\) | 1.15455 | 0.0787394 | ||||||||
\(216\) | −115.681 | −7.87111 | ||||||||
\(217\) | 13.7487 | 0.933322 | ||||||||
\(218\) | −9.00693 | −0.610026 | ||||||||
\(219\) | 13.0607 | 0.882560 | ||||||||
\(220\) | −1.45391 | −0.0980228 | ||||||||
\(221\) | −4.71319 | −0.317044 | ||||||||
\(222\) | −58.3248 | −3.91450 | ||||||||
\(223\) | 27.0459 | 1.81113 | 0.905563 | − | 0.424212i | \(-0.139449\pi\) | ||||
0.905563 | + | 0.424212i | \(0.139449\pi\) | |||||||
\(224\) | −51.7203 | −3.45571 | ||||||||
\(225\) | 7.11493 | 0.474329 | ||||||||
\(226\) | 25.2317 | 1.67838 | ||||||||
\(227\) | −12.5839 | −0.835224 | −0.417612 | − | 0.908625i | \(-0.637133\pi\) | ||||
−0.417612 | + | 0.908625i | \(0.637133\pi\) | |||||||
\(228\) | 5.86315 | 0.388296 | ||||||||
\(229\) | −17.5124 | −1.15725 | −0.578626 | − | 0.815593i | \(-0.696411\pi\) | ||||
−0.578626 | + | 0.815593i | \(0.696411\pi\) | |||||||
\(230\) | −2.40552 | −0.158615 | ||||||||
\(231\) | 2.49373 | 0.164076 | ||||||||
\(232\) | 52.2622 | 3.43118 | ||||||||
\(233\) | 25.6469 | 1.68019 | 0.840093 | − | 0.542443i | \(-0.182501\pi\) | ||||
0.840093 | + | 0.542443i | \(0.182501\pi\) | |||||||
\(234\) | 90.4598 | 5.91354 | ||||||||
\(235\) | −3.91305 | −0.255259 | ||||||||
\(236\) | −15.4217 | −1.00387 | ||||||||
\(237\) | 20.9751 | 1.36248 | ||||||||
\(238\) | −7.67662 | −0.497602 | ||||||||
\(239\) | 24.5864 | 1.59036 | 0.795182 | − | 0.606370i | \(-0.207375\pi\) | ||||
0.795182 | + | 0.606370i | \(0.207375\pi\) | |||||||
\(240\) | −42.2706 | −2.72855 | ||||||||
\(241\) | −1.04985 | −0.0676267 | −0.0338134 | − | 0.999428i | \(-0.510765\pi\) | ||||
−0.0338134 | + | 0.999428i | \(0.510765\pi\) | |||||||
\(242\) | 29.4683 | 1.89429 | ||||||||
\(243\) | 25.2289 | 1.61844 | ||||||||
\(244\) | 37.8939 | 2.42591 | ||||||||
\(245\) | −1.09842 | −0.0701754 | ||||||||
\(246\) | 54.1163 | 3.45033 | ||||||||
\(247\) | −1.64662 | −0.104772 | ||||||||
\(248\) | −42.7052 | −2.71178 | ||||||||
\(249\) | −13.8782 | −0.879498 | ||||||||
\(250\) | 2.69755 | 0.170608 | ||||||||
\(251\) | 12.2072 | 0.770512 | 0.385256 | − | 0.922810i | \(-0.374113\pi\) | ||||
0.385256 | + | 0.922810i | \(0.374113\pi\) | |||||||
\(252\) | 106.842 | 6.73040 | ||||||||
\(253\) | −0.245701 | −0.0154471 | ||||||||
\(254\) | −37.1653 | −2.33196 | ||||||||
\(255\) | −3.18040 | −0.199164 | ||||||||
\(256\) | 20.3824 | 1.27390 | ||||||||
\(257\) | −15.0162 | −0.936688 | −0.468344 | − | 0.883546i | \(-0.655149\pi\) | ||||
−0.468344 | + | 0.883546i | \(0.655149\pi\) | |||||||
\(258\) | 9.90519 | 0.616670 | ||||||||
\(259\) | 19.3465 | 1.20213 | ||||||||
\(260\) | 24.8705 | 1.54241 | ||||||||
\(261\) | −42.0668 | −2.60387 | ||||||||
\(262\) | 28.2798 | 1.74713 | ||||||||
\(263\) | −26.7620 | −1.65022 | −0.825109 | − | 0.564974i | \(-0.808886\pi\) | ||||
−0.825109 | + | 0.564974i | \(0.808886\pi\) | |||||||
\(264\) | −7.74585 | −0.476724 | ||||||||
\(265\) | −11.4633 | −0.704187 | ||||||||
\(266\) | −2.68194 | −0.164440 | ||||||||
\(267\) | 27.5001 | 1.68298 | ||||||||
\(268\) | 45.5191 | 2.78052 | ||||||||
\(269\) | 8.86467 | 0.540489 | 0.270244 | − | 0.962792i | \(-0.412896\pi\) | ||||
0.270244 | + | 0.962792i | \(0.412896\pi\) | |||||||
\(270\) | 35.3032 | 2.14848 | ||||||||
\(271\) | 8.80664 | 0.534965 | 0.267483 | − | 0.963563i | \(-0.413808\pi\) | ||||
0.267483 | + | 0.963563i | \(0.413808\pi\) | |||||||
\(272\) | 13.2910 | 0.805883 | ||||||||
\(273\) | −42.6576 | −2.58176 | ||||||||
\(274\) | −19.5057 | −1.17838 | ||||||||
\(275\) | 0.275530 | 0.0166151 | ||||||||
\(276\) | −14.9655 | −0.900817 | ||||||||
\(277\) | 28.8769 | 1.73505 | 0.867523 | − | 0.497397i | \(-0.165711\pi\) | ||||
0.867523 | + | 0.497397i | \(0.165711\pi\) | |||||||
\(278\) | −27.0271 | −1.62097 | ||||||||
\(279\) | 34.3741 | 2.05793 | ||||||||
\(280\) | 25.1547 | 1.50328 | ||||||||
\(281\) | −28.1362 | −1.67847 | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||||
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(282\) | −33.5712 | −1.99913 | ||||||||
\(283\) | −2.24734 | −0.133590 | −0.0667951 | − | 0.997767i | \(-0.521277\pi\) | ||||
−0.0667951 | + | 0.997767i | \(0.521277\pi\) | |||||||
\(284\) | −5.27679 | −0.313120 | ||||||||
\(285\) | −1.11112 | −0.0658170 | ||||||||
\(286\) | 3.50311 | 0.207143 | ||||||||
\(287\) | −17.9505 | −1.05958 | ||||||||
\(288\) | −129.310 | −7.61966 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −15.9492 | −0.936569 | ||||||||
\(291\) | 25.2441 | 1.47984 | ||||||||
\(292\) | 21.6698 | 1.26813 | ||||||||
\(293\) | −21.9119 | −1.28011 | −0.640055 | − | 0.768329i | \(-0.721088\pi\) | ||||
−0.640055 | + | 0.768329i | \(0.721088\pi\) | |||||||
\(294\) | −9.42366 | −0.549599 | ||||||||
\(295\) | 2.92255 | 0.170157 | ||||||||
\(296\) | −60.0926 | −3.49281 | ||||||||
\(297\) | 3.60589 | 0.209235 | ||||||||
\(298\) | 32.7927 | 1.89963 | ||||||||
\(299\) | 4.20295 | 0.243063 | ||||||||
\(300\) | 16.7823 | 0.968927 | ||||||||
\(301\) | −3.28557 | −0.189377 | ||||||||
\(302\) | 39.5175 | 2.27397 | ||||||||
\(303\) | 28.9372 | 1.66240 | ||||||||
\(304\) | 4.64340 | 0.266317 | ||||||||
\(305\) | −7.18124 | −0.411197 | ||||||||
\(306\) | −19.1929 | −1.09719 | ||||||||
\(307\) | −13.6355 | −0.778220 | −0.389110 | − | 0.921191i | \(-0.627217\pi\) | ||||
−0.389110 | + | 0.921191i | \(0.627217\pi\) | |||||||
\(308\) | 4.13751 | 0.235756 | ||||||||
\(309\) | 5.73985 | 0.326529 | ||||||||
\(310\) | 13.0326 | 0.740202 | ||||||||
\(311\) | −18.9255 | −1.07317 | −0.536584 | − | 0.843847i | \(-0.680286\pi\) | ||||
−0.536584 | + | 0.843847i | \(0.680286\pi\) | |||||||
\(312\) | 132.500 | 7.50133 | ||||||||
\(313\) | 13.1890 | 0.745487 | 0.372744 | − | 0.927934i | \(-0.378417\pi\) | ||||
0.372744 | + | 0.927934i | \(0.378417\pi\) | |||||||
\(314\) | −15.0343 | −0.848436 | ||||||||
\(315\) | −20.2475 | −1.14082 | ||||||||
\(316\) | 34.8011 | 1.95772 | ||||||||
\(317\) | −26.2470 | −1.47418 | −0.737089 | − | 0.675796i | \(-0.763800\pi\) | ||||
−0.737089 | + | 0.675796i | \(0.763800\pi\) | |||||||
\(318\) | −98.3473 | −5.51505 | ||||||||
\(319\) | −1.62906 | −0.0912098 | ||||||||
\(320\) | −22.4446 | −1.25469 | ||||||||
\(321\) | 32.7938 | 1.83037 | ||||||||
\(322\) | 6.84557 | 0.381489 | ||||||||
\(323\) | 0.349365 | 0.0194392 | ||||||||
\(324\) | 107.000 | 5.94443 | ||||||||
\(325\) | −4.71319 | −0.261441 | ||||||||
\(326\) | 1.84382 | 0.102120 | ||||||||
\(327\) | 10.6191 | 0.587238 | ||||||||
\(328\) | 55.7565 | 3.07864 | ||||||||
\(329\) | 11.1356 | 0.613927 | ||||||||
\(330\) | 2.36385 | 0.130126 | ||||||||
\(331\) | −23.7360 | −1.30465 | −0.652323 | − | 0.757941i | \(-0.726206\pi\) | ||||
−0.652323 | + | 0.757941i | \(0.726206\pi\) | |||||||
\(332\) | −23.0262 | −1.26373 | ||||||||
\(333\) | 48.3696 | 2.65064 | ||||||||
\(334\) | 53.7566 | 2.94143 | ||||||||
\(335\) | −8.62627 | −0.471304 | ||||||||
\(336\) | 120.292 | 6.56249 | ||||||||
\(337\) | 23.8976 | 1.30178 | 0.650892 | − | 0.759170i | \(-0.274395\pi\) | ||||
0.650892 | + | 0.759170i | \(0.274395\pi\) | |||||||
\(338\) | −24.8558 | −1.35198 | ||||||||
\(339\) | −29.7480 | −1.61569 | ||||||||
\(340\) | −5.27679 | −0.286174 | ||||||||
\(341\) | 1.33116 | 0.0720862 | ||||||||
\(342\) | −6.70532 | −0.362582 | ||||||||
\(343\) | −16.7946 | −0.906821 | ||||||||
\(344\) | 10.2054 | 0.550239 | ||||||||
\(345\) | 2.83610 | 0.152690 | ||||||||
\(346\) | −63.2662 | −3.40121 | ||||||||
\(347\) | −10.5200 | −0.564743 | −0.282372 | − | 0.959305i | \(-0.591121\pi\) | ||||
−0.282372 | + | 0.959305i | \(0.591121\pi\) | |||||||
\(348\) | −99.2248 | −5.31901 | ||||||||
\(349\) | −2.16415 | −0.115845 | −0.0579223 | − | 0.998321i | \(-0.518448\pi\) | ||||
−0.0579223 | + | 0.998321i | \(0.518448\pi\) | |||||||
\(350\) | −7.67662 | −0.410333 | ||||||||
\(351\) | −61.6821 | −3.29235 | ||||||||
\(352\) | −5.00760 | −0.266906 | ||||||||
\(353\) | 16.6761 | 0.887581 | 0.443791 | − | 0.896130i | \(-0.353633\pi\) | ||||
0.443791 | + | 0.896130i | \(0.353633\pi\) | |||||||
\(354\) | 25.0734 | 1.33264 | ||||||||
\(355\) | 1.00000 | 0.0530745 | ||||||||
\(356\) | 45.6271 | 2.41823 | ||||||||
\(357\) | 9.05069 | 0.479013 | ||||||||
\(358\) | −60.3826 | −3.19132 | ||||||||
\(359\) | −3.71358 | −0.195996 | −0.0979978 | − | 0.995187i | \(-0.531244\pi\) | ||||
−0.0979978 | + | 0.995187i | \(0.531244\pi\) | |||||||
\(360\) | 62.8912 | 3.31466 | ||||||||
\(361\) | −18.8779 | −0.993576 | ||||||||
\(362\) | 2.90500 | 0.152684 | ||||||||
\(363\) | −34.7429 | −1.82353 | ||||||||
\(364\) | −70.7759 | −3.70967 | ||||||||
\(365\) | −4.10662 | −0.214950 | ||||||||
\(366\) | −61.6100 | −3.22040 | ||||||||
\(367\) | −21.6802 | −1.13170 | −0.565849 | − | 0.824509i | \(-0.691452\pi\) | ||||
−0.565849 | + | 0.824509i | \(0.691452\pi\) | |||||||
\(368\) | −11.8521 | −0.617834 | ||||||||
\(369\) | −44.8794 | −2.33633 | ||||||||
\(370\) | 18.3388 | 0.953391 | ||||||||
\(371\) | 32.6221 | 1.69365 | ||||||||
\(372\) | 81.0798 | 4.20379 | ||||||||
\(373\) | −29.5737 | −1.53127 | −0.765635 | − | 0.643276i | \(-0.777575\pi\) | ||||
−0.765635 | + | 0.643276i | \(0.777575\pi\) | |||||||
\(374\) | −0.743256 | −0.0384328 | ||||||||
\(375\) | −3.18040 | −0.164235 | ||||||||
\(376\) | −34.5887 | −1.78378 | ||||||||
\(377\) | 27.8666 | 1.43520 | ||||||||
\(378\) | −100.465 | −5.16735 | ||||||||
\(379\) | −0.690475 | −0.0354673 | −0.0177337 | − | 0.999843i | \(-0.505645\pi\) | ||||
−0.0177337 | + | 0.999843i | \(0.505645\pi\) | |||||||
\(380\) | −1.84353 | −0.0945709 | ||||||||
\(381\) | 43.8176 | 2.24485 | ||||||||
\(382\) | −61.0879 | −3.12553 | ||||||||
\(383\) | 16.2407 | 0.829863 | 0.414931 | − | 0.909853i | \(-0.363806\pi\) | ||||
0.414931 | + | 0.909853i | \(0.363806\pi\) | |||||||
\(384\) | −76.9548 | −3.92708 | ||||||||
\(385\) | −0.784095 | −0.0399612 | ||||||||
\(386\) | 42.8272 | 2.17985 | ||||||||
\(387\) | −8.21451 | −0.417567 | ||||||||
\(388\) | 41.8841 | 2.12634 | ||||||||
\(389\) | 15.0464 | 0.762883 | 0.381442 | − | 0.924393i | \(-0.375428\pi\) | ||||
0.381442 | + | 0.924393i | \(0.375428\pi\) | |||||||
\(390\) | −40.4359 | −2.04755 | ||||||||
\(391\) | −0.891742 | −0.0450973 | ||||||||
\(392\) | −9.70929 | −0.490393 | ||||||||
\(393\) | −33.3417 | −1.68187 | ||||||||
\(394\) | −60.5387 | −3.04990 | ||||||||
\(395\) | −6.59513 | −0.331837 | ||||||||
\(396\) | 10.3445 | 0.519830 | ||||||||
\(397\) | 4.08645 | 0.205093 | 0.102547 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102547 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(398\) | 35.4502 | 1.77696 | ||||||||
\(399\) | 3.16199 | 0.158298 | ||||||||
\(400\) | 13.2910 | 0.664548 | ||||||||
\(401\) | −28.4296 | −1.41971 | −0.709853 | − | 0.704350i | \(-0.751239\pi\) | ||||
−0.709853 | + | 0.704350i | \(0.751239\pi\) | |||||||
\(402\) | −74.0073 | −3.69115 | ||||||||
\(403\) | −22.7707 | −1.13429 | ||||||||
\(404\) | 48.0114 | 2.38866 | ||||||||
\(405\) | −20.2774 | −1.00759 | ||||||||
\(406\) | 45.3878 | 2.25256 | ||||||||
\(407\) | 1.87314 | 0.0928481 | ||||||||
\(408\) | −28.1126 | −1.39178 | ||||||||
\(409\) | 21.8152 | 1.07869 | 0.539345 | − | 0.842085i | \(-0.318672\pi\) | ||||
0.539345 | + | 0.842085i | \(0.318672\pi\) | |||||||
\(410\) | −17.0156 | −0.840339 | ||||||||
\(411\) | 22.9971 | 1.13436 | ||||||||
\(412\) | 9.52335 | 0.469182 | ||||||||
\(413\) | −8.31691 | −0.409248 | ||||||||
\(414\) | 17.1151 | 0.841162 | ||||||||
\(415\) | 4.36368 | 0.214205 | ||||||||
\(416\) | 85.6597 | 4.19981 | ||||||||
\(417\) | 31.8647 | 1.56042 | ||||||||
\(418\) | −0.259667 | −0.0127008 | ||||||||
\(419\) | −6.93235 | −0.338667 | −0.169334 | − | 0.985559i | \(-0.554162\pi\) | ||||
−0.169334 | + | 0.985559i | \(0.554162\pi\) | |||||||
\(420\) | −47.7586 | −2.33038 | ||||||||
\(421\) | −12.6176 | −0.614943 | −0.307471 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307471 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(422\) | −64.8038 | −3.15460 | ||||||||
\(423\) | 27.8410 | 1.35368 | ||||||||
\(424\) | −101.328 | −4.92093 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 8.57929 | 0.415668 | ||||||||
\(427\) | 20.4362 | 0.988976 | ||||||||
\(428\) | 54.4102 | 2.63002 | ||||||||
\(429\) | −4.13014 | −0.199405 | ||||||||
\(430\) | −3.11445 | −0.150192 | ||||||||
\(431\) | −37.1830 | −1.79104 | −0.895522 | − | 0.445018i | \(-0.853197\pi\) | ||||
−0.895522 | + | 0.445018i | \(0.853197\pi\) | |||||||
\(432\) | 173.940 | 8.36871 | ||||||||
\(433\) | 15.9716 | 0.767548 | 0.383774 | − | 0.923427i | \(-0.374624\pi\) | ||||
0.383774 | + | 0.923427i | \(0.374624\pi\) | |||||||
\(434\) | −37.0878 | −1.78027 | ||||||||
\(435\) | 18.8040 | 0.901582 | ||||||||
\(436\) | 17.6188 | 0.843789 | ||||||||
\(437\) | −0.311543 | −0.0149031 | ||||||||
\(438\) | −35.2319 | −1.68345 | ||||||||
\(439\) | 21.9530 | 1.04776 | 0.523879 | − | 0.851792i | \(-0.324484\pi\) | ||||
0.523879 | + | 0.851792i | \(0.324484\pi\) | |||||||
\(440\) | 2.43550 | 0.116108 | ||||||||
\(441\) | 7.81518 | 0.372151 | ||||||||
\(442\) | 12.7141 | 0.604748 | ||||||||
\(443\) | −28.2099 | −1.34029 | −0.670147 | − | 0.742228i | \(-0.733769\pi\) | ||||
−0.670147 | + | 0.742228i | \(0.733769\pi\) | |||||||
\(444\) | 114.092 | 5.41454 | ||||||||
\(445\) | −8.64674 | −0.409895 | ||||||||
\(446\) | −72.9577 | −3.45465 | ||||||||
\(447\) | −38.6624 | −1.82867 | ||||||||
\(448\) | 63.8722 | 3.01768 | ||||||||
\(449\) | −33.6137 | −1.58633 | −0.793164 | − | 0.609008i | \(-0.791568\pi\) | ||||
−0.793164 | + | 0.609008i | \(0.791568\pi\) | |||||||
\(450\) | −19.1929 | −0.904762 | ||||||||
\(451\) | −1.73798 | −0.0818383 | ||||||||
\(452\) | −49.3567 | −2.32154 | ||||||||
\(453\) | −46.5908 | −2.18903 | ||||||||
\(454\) | 33.9458 | 1.59315 | ||||||||
\(455\) | 13.4127 | 0.628796 | ||||||||
\(456\) | −9.82155 | −0.459936 | ||||||||
\(457\) | −26.9946 | −1.26276 | −0.631378 | − | 0.775475i | \(-0.717510\pi\) | ||||
−0.631378 | + | 0.775475i | \(0.717510\pi\) | |||||||
\(458\) | 47.2406 | 2.20741 | ||||||||
\(459\) | 13.0871 | 0.610854 | ||||||||
\(460\) | 4.70554 | 0.219397 | ||||||||
\(461\) | −19.7885 | −0.921644 | −0.460822 | − | 0.887493i | \(-0.652445\pi\) | ||||
−0.460822 | + | 0.887493i | \(0.652445\pi\) | |||||||
\(462\) | −6.72698 | −0.312967 | ||||||||
\(463\) | 14.3452 | 0.666677 | 0.333339 | − | 0.942807i | \(-0.391825\pi\) | ||||
0.333339 | + | 0.942807i | \(0.391825\pi\) | |||||||
\(464\) | −78.5824 | −3.64810 | ||||||||
\(465\) | −15.3654 | −0.712551 | ||||||||
\(466\) | −69.1839 | −3.20488 | ||||||||
\(467\) | −6.76080 | −0.312853 | −0.156426 | − | 0.987690i | \(-0.549997\pi\) | ||||
−0.156426 | + | 0.987690i | \(0.549997\pi\) | |||||||
\(468\) | −176.952 | −8.17962 | ||||||||
\(469\) | 24.5484 | 1.13354 | ||||||||
\(470\) | 10.5556 | 0.486896 | ||||||||
\(471\) | 17.7254 | 0.816742 | ||||||||
\(472\) | 25.8334 | 1.18908 | ||||||||
\(473\) | −0.318112 | −0.0146268 | ||||||||
\(474\) | −56.5815 | −2.59887 | ||||||||
\(475\) | 0.349365 | 0.0160300 | ||||||||
\(476\) | 15.0166 | 0.688283 | ||||||||
\(477\) | 81.5609 | 3.73441 | ||||||||
\(478\) | −66.3232 | −3.03355 | ||||||||
\(479\) | −16.9620 | −0.775015 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(480\) | 57.8020 | 2.63829 | ||||||||
\(481\) | −32.0418 | −1.46098 | ||||||||
\(482\) | 2.83202 | 0.128995 | ||||||||
\(483\) | −8.07088 | −0.367238 | ||||||||
\(484\) | −57.6441 | −2.62019 | ||||||||
\(485\) | −7.93741 | −0.360419 | ||||||||
\(486\) | −68.0564 | −3.08710 | ||||||||
\(487\) | −14.8598 | −0.673362 | −0.336681 | − | 0.941619i | \(-0.609304\pi\) | ||||
−0.336681 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(488\) | −63.4773 | −2.87348 | ||||||||
\(489\) | −2.17385 | −0.0983050 | ||||||||
\(490\) | 2.96304 | 0.133857 | ||||||||
\(491\) | −35.8231 | −1.61667 | −0.808337 | − | 0.588720i | \(-0.799632\pi\) | ||||
−0.808337 | + | 0.588720i | \(0.799632\pi\) | |||||||
\(492\) | −105.859 | −4.77250 | ||||||||
\(493\) | −5.91246 | −0.266284 | ||||||||
\(494\) | 4.44186 | 0.199849 | ||||||||
\(495\) | −1.96037 | −0.0881122 | ||||||||
\(496\) | 64.2122 | 2.88321 | ||||||||
\(497\) | −2.84577 | −0.127650 | ||||||||
\(498\) | 37.4373 | 1.67760 | ||||||||
\(499\) | −18.9121 | −0.846620 | −0.423310 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423310 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(500\) | −5.27679 | −0.235985 | ||||||||
\(501\) | −63.3787 | −2.83155 | ||||||||
\(502\) | −32.9296 | −1.46972 | ||||||||
\(503\) | 21.5673 | 0.961637 | 0.480818 | − | 0.876820i | \(-0.340340\pi\) | ||||
0.480818 | + | 0.876820i | \(0.340340\pi\) | |||||||
\(504\) | −178.974 | −7.97213 | ||||||||
\(505\) | −9.09860 | −0.404882 | ||||||||
\(506\) | 0.662793 | 0.0294647 | ||||||||
\(507\) | 29.3048 | 1.30147 | ||||||||
\(508\) | 72.7006 | 3.22557 | ||||||||
\(509\) | −31.0862 | −1.37787 | −0.688935 | − | 0.724823i | \(-0.741922\pi\) | ||||
−0.688935 | + | 0.724823i | \(0.741922\pi\) | |||||||
\(510\) | 8.57929 | 0.379897 | ||||||||
\(511\) | 11.6865 | 0.516981 | ||||||||
\(512\) | −6.58950 | −0.291218 | ||||||||
\(513\) | 4.57218 | 0.201867 | ||||||||
\(514\) | 40.5071 | 1.78669 | ||||||||
\(515\) | −1.80476 | −0.0795272 | ||||||||
\(516\) | −19.3759 | −0.852978 | ||||||||
\(517\) | 1.07816 | 0.0474174 | ||||||||
\(518\) | −52.1882 | −2.29302 | ||||||||
\(519\) | 74.5904 | 3.27416 | ||||||||
\(520\) | −41.6615 | −1.82698 | ||||||||
\(521\) | −6.12307 | −0.268256 | −0.134128 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134128 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(522\) | 113.477 | 4.96677 | ||||||||
\(523\) | −9.45477 | −0.413428 | −0.206714 | − | 0.978401i | \(-0.566277\pi\) | ||||
−0.206714 | + | 0.978401i | \(0.566277\pi\) | |||||||
\(524\) | −55.3193 | −2.41664 | ||||||||
\(525\) | 9.05069 | 0.395004 | ||||||||
\(526\) | 72.1920 | 3.14772 | ||||||||
\(527\) | 4.83127 | 0.210453 | ||||||||
\(528\) | 11.6468 | 0.506862 | ||||||||
\(529\) | −22.2048 | −0.965426 | ||||||||
\(530\) | 30.9230 | 1.34321 | ||||||||
\(531\) | −20.7937 | −0.902371 | ||||||||
\(532\) | 5.24626 | 0.227454 | ||||||||
\(533\) | 29.7298 | 1.28774 | ||||||||
\(534\) | −74.1829 | −3.21021 | ||||||||
\(535\) | −10.3112 | −0.445793 | ||||||||
\(536\) | −76.2504 | −3.29352 | ||||||||
\(537\) | 71.1907 | 3.07211 | ||||||||
\(538\) | −23.9129 | −1.03096 | ||||||||
\(539\) | 0.302647 | 0.0130359 | ||||||||
\(540\) | −69.0580 | −2.97178 | ||||||||
\(541\) | 16.2666 | 0.699354 | 0.349677 | − | 0.936870i | \(-0.386291\pi\) | ||||
0.349677 | + | 0.936870i | \(0.386291\pi\) | |||||||
\(542\) | −23.7564 | −1.02042 | ||||||||
\(543\) | −3.42498 | −0.146980 | ||||||||
\(544\) | −18.1744 | −0.779223 | ||||||||
\(545\) | −3.33893 | −0.143024 | ||||||||
\(546\) | 115.071 | 4.92459 | ||||||||
\(547\) | 26.6935 | 1.14133 | 0.570665 | − | 0.821183i | \(-0.306685\pi\) | ||||
0.570665 | + | 0.821183i | \(0.306685\pi\) | |||||||
\(548\) | 38.1559 | 1.62994 | ||||||||
\(549\) | 51.0940 | 2.18064 | ||||||||
\(550\) | −0.743256 | −0.0316925 | ||||||||
\(551\) | −2.06561 | −0.0879978 | ||||||||
\(552\) | 25.0692 | 1.06701 | ||||||||
\(553\) | 18.7682 | 0.798106 | ||||||||
\(554\) | −77.8970 | −3.30953 | ||||||||
\(555\) | −21.6214 | −0.917776 | ||||||||
\(556\) | 52.8687 | 2.24213 | ||||||||
\(557\) | 28.4151 | 1.20399 | 0.601994 | − | 0.798501i | \(-0.294373\pi\) | ||||
0.601994 | + | 0.798501i | \(0.294373\pi\) | |||||||
\(558\) | −92.7261 | −3.92541 | ||||||||
\(559\) | 5.44160 | 0.230155 | ||||||||
\(560\) | −37.8231 | −1.59832 | ||||||||
\(561\) | 0.876294 | 0.0369972 | ||||||||
\(562\) | 75.8989 | 3.20160 | ||||||||
\(563\) | 34.1107 | 1.43759 | 0.718797 | − | 0.695220i | \(-0.244693\pi\) | ||||
0.718797 | + | 0.695220i | \(0.244693\pi\) | |||||||
\(564\) | 65.6699 | 2.76520 | ||||||||
\(565\) | 9.35353 | 0.393506 | ||||||||
\(566\) | 6.06231 | 0.254818 | ||||||||
\(567\) | 57.7049 | 2.42338 | ||||||||
\(568\) | 8.83933 | 0.370890 | ||||||||
\(569\) | 1.18662 | 0.0497457 | 0.0248729 | − | 0.999691i | \(-0.492082\pi\) | ||||
0.0248729 | + | 0.999691i | \(0.492082\pi\) | |||||||
\(570\) | 2.99730 | 0.125543 | ||||||||
\(571\) | 23.0551 | 0.964824 | 0.482412 | − | 0.875944i | \(-0.339761\pi\) | ||||
0.482412 | + | 0.875944i | \(0.339761\pi\) | |||||||
\(572\) | −6.85257 | −0.286520 | ||||||||
\(573\) | 72.0222 | 3.00877 | ||||||||
\(574\) | 48.4225 | 2.02111 | ||||||||
\(575\) | −0.891742 | −0.0371882 | ||||||||
\(576\) | 159.692 | 6.65382 | ||||||||
\(577\) | −45.5096 | −1.89459 | −0.947295 | − | 0.320363i | \(-0.896195\pi\) | ||||
−0.947295 | + | 0.320363i | \(0.896195\pi\) | |||||||
\(578\) | −2.69755 | −0.112203 | ||||||||
\(579\) | −50.4930 | −2.09842 | ||||||||
\(580\) | 31.1989 | 1.29546 | ||||||||
\(581\) | −12.4180 | −0.515187 | ||||||||
\(582\) | −68.0974 | −2.82273 | ||||||||
\(583\) | 3.15849 | 0.130811 | ||||||||
\(584\) | −36.2998 | −1.50210 | ||||||||
\(585\) | 33.5340 | 1.38646 | ||||||||
\(586\) | 59.1086 | 2.44175 | ||||||||
\(587\) | −10.3440 | −0.426943 | −0.213471 | − | 0.976949i | \(-0.568477\pi\) | ||||
−0.213471 | + | 0.976949i | \(0.568477\pi\) | |||||||
\(588\) | 18.4340 | 0.760206 | ||||||||
\(589\) | 1.68788 | 0.0695477 | ||||||||
\(590\) | −7.88373 | −0.324568 | ||||||||
\(591\) | 71.3747 | 2.93596 | ||||||||
\(592\) | 90.3563 | 3.71362 | ||||||||
\(593\) | 13.6977 | 0.562499 | 0.281249 | − | 0.959635i | \(-0.409251\pi\) | ||||
0.281249 | + | 0.959635i | \(0.409251\pi\) | |||||||
\(594\) | −9.72707 | −0.399107 | ||||||||
\(595\) | −2.84577 | −0.116665 | ||||||||
\(596\) | −64.1472 | −2.62757 | ||||||||
\(597\) | −41.7956 | −1.71058 | ||||||||
\(598\) | −11.3377 | −0.463633 | ||||||||
\(599\) | 7.43921 | 0.303958 | 0.151979 | − | 0.988384i | \(-0.451435\pi\) | ||||
0.151979 | + | 0.988384i | \(0.451435\pi\) | |||||||
\(600\) | −28.1126 | −1.14769 | ||||||||
\(601\) | −9.77905 | −0.398896 | −0.199448 | − | 0.979908i | \(-0.563915\pi\) | ||||
−0.199448 | + | 0.979908i | \(0.563915\pi\) | |||||||
\(602\) | 8.86301 | 0.361229 | ||||||||
\(603\) | 61.3753 | 2.49940 | ||||||||
\(604\) | −77.3017 | −3.14536 | ||||||||
\(605\) | 10.9241 | 0.444127 | ||||||||
\(606\) | −78.0596 | −3.17095 | ||||||||
\(607\) | 32.1885 | 1.30649 | 0.653246 | − | 0.757146i | \(-0.273407\pi\) | ||||
0.653246 | + | 0.757146i | \(0.273407\pi\) | |||||||
\(608\) | −6.34951 | −0.257507 | ||||||||
\(609\) | −53.5119 | −2.16841 | ||||||||
\(610\) | 19.3718 | 0.784341 | ||||||||
\(611\) | −18.4429 | −0.746121 | ||||||||
\(612\) | 37.5440 | 1.51763 | ||||||||
\(613\) | 25.4165 | 1.02656 | 0.513282 | − | 0.858220i | \(-0.328429\pi\) | ||||
0.513282 | + | 0.858220i | \(0.328429\pi\) | |||||||
\(614\) | 36.7825 | 1.48442 | ||||||||
\(615\) | 20.0613 | 0.808948 | ||||||||
\(616\) | −6.93087 | −0.279253 | ||||||||
\(617\) | 37.2621 | 1.50012 | 0.750058 | − | 0.661372i | \(-0.230025\pi\) | ||||
0.750058 | + | 0.661372i | \(0.230025\pi\) | |||||||
\(618\) | −15.4836 | −0.622840 | ||||||||
\(619\) | −2.65749 | −0.106813 | −0.0534067 | − | 0.998573i | \(-0.517008\pi\) | ||||
−0.0534067 | + | 0.998573i | \(0.517008\pi\) | |||||||
\(620\) | −25.4936 | −1.02385 | ||||||||
\(621\) | −11.6703 | −0.468314 | ||||||||
\(622\) | 51.0526 | 2.04702 | ||||||||
\(623\) | 24.6067 | 0.985845 | ||||||||
\(624\) | −199.229 | −7.97556 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.5781 | −1.42199 | ||||||||
\(627\) | 0.306146 | 0.0122263 | ||||||||
\(628\) | 29.4093 | 1.17356 | ||||||||
\(629\) | 6.79832 | 0.271067 | ||||||||
\(630\) | 54.6186 | 2.17606 | ||||||||
\(631\) | −8.12025 | −0.323262 | −0.161631 | − | 0.986851i | \(-0.551675\pi\) | ||||
−0.161631 | + | 0.986851i | \(0.551675\pi\) | |||||||
\(632\) | −58.2965 | −2.31891 | ||||||||
\(633\) | 76.4033 | 3.03676 | ||||||||
\(634\) | 70.8027 | 2.81193 | ||||||||
\(635\) | −13.7774 | −0.546740 | ||||||||
\(636\) | 192.381 | 7.62841 | ||||||||
\(637\) | −5.17706 | −0.205123 | ||||||||
\(638\) | 4.39447 | 0.173979 | ||||||||
\(639\) | −7.11493 | −0.281462 | ||||||||
\(640\) | 24.1966 | 0.956455 | ||||||||
\(641\) | −12.7338 | −0.502955 | −0.251477 | − | 0.967863i | \(-0.580916\pi\) | ||||
−0.251477 | + | 0.967863i | \(0.580916\pi\) | |||||||
\(642\) | −88.4630 | −3.49136 | ||||||||
\(643\) | −43.5384 | −1.71699 | −0.858494 | − | 0.512824i | \(-0.828600\pi\) | ||||
−0.858494 | + | 0.512824i | \(0.828600\pi\) | |||||||
\(644\) | −13.3909 | −0.527675 | ||||||||
\(645\) | 3.67192 | 0.144582 | ||||||||
\(646\) | −0.942430 | −0.0370794 | ||||||||
\(647\) | 41.1993 | 1.61971 | 0.809856 | − | 0.586628i | \(-0.199545\pi\) | ||||
0.809856 | + | 0.586628i | \(0.199545\pi\) | |||||||
\(648\) | −179.239 | −7.04116 | ||||||||
\(649\) | −0.805249 | −0.0316088 | ||||||||
\(650\) | 12.7141 | 0.498688 | ||||||||
\(651\) | 43.7263 | 1.71377 | ||||||||
\(652\) | −3.60677 | −0.141252 | ||||||||
\(653\) | 10.4815 | 0.410172 | 0.205086 | − | 0.978744i | \(-0.434253\pi\) | ||||
0.205086 | + | 0.978744i | \(0.434253\pi\) | |||||||
\(654\) | −28.6456 | −1.12013 | ||||||||
\(655\) | 10.4835 | 0.409625 | ||||||||
\(656\) | −83.8365 | −3.27327 | ||||||||
\(657\) | 29.2183 | 1.13992 | ||||||||
\(658\) | −30.0390 | −1.17104 | ||||||||
\(659\) | −27.4712 | −1.07013 | −0.535063 | − | 0.844812i | \(-0.679712\pi\) | ||||
−0.535063 | + | 0.844812i | \(0.679712\pi\) | |||||||
\(660\) | −4.62402 | −0.179990 | ||||||||
\(661\) | −10.7306 | −0.417373 | −0.208686 | − | 0.977983i | \(-0.566919\pi\) | ||||
−0.208686 | + | 0.977983i | \(0.566919\pi\) | |||||||
\(662\) | 64.0290 | 2.48856 | ||||||||
\(663\) | −14.9898 | −0.582157 | ||||||||
\(664\) | 38.5720 | 1.49688 | ||||||||
\(665\) | −0.994213 | −0.0385539 | ||||||||
\(666\) | −130.480 | −5.05598 | ||||||||
\(667\) | 5.27240 | 0.204148 | ||||||||
\(668\) | −105.156 | −4.06859 | ||||||||
\(669\) | 86.0166 | 3.32560 | ||||||||
\(670\) | 23.2698 | 0.898992 | ||||||||
\(671\) | 1.97864 | 0.0763847 | ||||||||
\(672\) | −164.491 | −6.34539 | ||||||||
\(673\) | −30.2186 | −1.16484 | −0.582420 | − | 0.812888i | \(-0.697894\pi\) | ||||
−0.582420 | + | 0.812888i | \(0.697894\pi\) | |||||||
\(674\) | −64.4650 | −2.48310 | ||||||||
\(675\) | 13.0871 | 0.503723 | ||||||||
\(676\) | 48.6214 | 1.87005 | ||||||||
\(677\) | −30.7449 | −1.18162 | −0.590811 | − | 0.806810i | \(-0.701192\pi\) | ||||
−0.590811 | + | 0.806810i | \(0.701192\pi\) | |||||||
\(678\) | 80.2467 | 3.08186 | ||||||||
\(679\) | 22.5881 | 0.866851 | ||||||||
\(680\) | 8.83933 | 0.338973 | ||||||||
\(681\) | −40.0219 | −1.53364 | ||||||||
\(682\) | −3.59087 | −0.137501 | ||||||||
\(683\) | 2.68269 | 0.102650 | 0.0513251 | − | 0.998682i | \(-0.483656\pi\) | ||||
0.0513251 | + | 0.998682i | \(0.483656\pi\) | |||||||
\(684\) | 13.1166 | 0.501524 | ||||||||
\(685\) | −7.23089 | −0.276278 | ||||||||
\(686\) | 45.3042 | 1.72972 | ||||||||
\(687\) | −55.6964 | −2.12495 | ||||||||
\(688\) | −15.3450 | −0.585024 | ||||||||
\(689\) | −54.0289 | −2.05834 | ||||||||
\(690\) | −7.65052 | −0.291250 | ||||||||
\(691\) | 25.0297 | 0.952175 | 0.476087 | − | 0.879398i | \(-0.342055\pi\) | ||||
0.476087 | + | 0.879398i | \(0.342055\pi\) | |||||||
\(692\) | 123.758 | 4.70456 | ||||||||
\(693\) | 5.57878 | 0.211920 | ||||||||
\(694\) | 28.3783 | 1.07722 | ||||||||
\(695\) | −10.0191 | −0.380046 | ||||||||
\(696\) | 166.215 | 6.30035 | ||||||||
\(697\) | −6.30778 | −0.238924 | ||||||||
\(698\) | 5.83792 | 0.220969 | ||||||||
\(699\) | 81.5674 | 3.08516 | ||||||||
\(700\) | 15.0166 | 0.567572 | ||||||||
\(701\) | 28.3282 | 1.06994 | 0.534971 | − | 0.844871i | \(-0.320323\pi\) | ||||
0.534971 | + | 0.844871i | \(0.320323\pi\) | |||||||
\(702\) | 166.391 | 6.28001 | ||||||||
\(703\) | 2.37510 | 0.0895784 | ||||||||
\(704\) | 6.18415 | 0.233074 | ||||||||
\(705\) | −12.4450 | −0.468707 | ||||||||
\(706\) | −44.9848 | −1.69302 | ||||||||
\(707\) | 25.8925 | 0.973789 | ||||||||
\(708\) | −49.0471 | −1.84330 | ||||||||
\(709\) | −18.0703 | −0.678645 | −0.339323 | − | 0.940670i | \(-0.610198\pi\) | ||||
−0.339323 | + | 0.940670i | \(0.610198\pi\) | |||||||
\(710\) | −2.69755 | −0.101237 | ||||||||
\(711\) | 46.9239 | 1.75978 | ||||||||
\(712\) | −76.4314 | −2.86439 | ||||||||
\(713\) | −4.30825 | −0.161345 | ||||||||
\(714\) | −24.4147 | −0.913698 | ||||||||
\(715\) | 1.29862 | 0.0485658 | ||||||||
\(716\) | 118.117 | 4.41424 | ||||||||
\(717\) | 78.1947 | 2.92023 | ||||||||
\(718\) | 10.0176 | 0.373853 | ||||||||
\(719\) | 19.8558 | 0.740497 | 0.370249 | − | 0.928933i | \(-0.379272\pi\) | ||||
0.370249 | + | 0.928933i | \(0.379272\pi\) | |||||||
\(720\) | −94.5643 | −3.52420 | ||||||||
\(721\) | 5.13594 | 0.191272 | ||||||||
\(722\) | 50.9243 | 1.89520 | ||||||||
\(723\) | −3.33894 | −0.124176 | ||||||||
\(724\) | −5.68259 | −0.211192 | ||||||||
\(725\) | −5.91246 | −0.219583 | ||||||||
\(726\) | 93.7209 | 3.47831 | ||||||||
\(727\) | 27.0586 | 1.00355 | 0.501774 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501774 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(728\) | 118.559 | 4.39409 | ||||||||
\(729\) | 19.4058 | 0.718733 | ||||||||
\(730\) | 11.0778 | 0.410009 | ||||||||
\(731\) | −1.15455 | −0.0427024 | ||||||||
\(732\) | 120.518 | 4.45447 | ||||||||
\(733\) | 44.5826 | 1.64669 | 0.823347 | − | 0.567538i | \(-0.192104\pi\) | ||||
0.823347 | + | 0.567538i | \(0.192104\pi\) | |||||||
\(734\) | 58.4836 | 2.15867 | ||||||||
\(735\) | −3.49341 | −0.128856 | ||||||||
\(736\) | 16.2069 | 0.597395 | ||||||||
\(737\) | 2.37679 | 0.0875503 | ||||||||
\(738\) | 121.065 | 4.45645 | ||||||||
\(739\) | −53.4844 | −1.96746 | −0.983728 | − | 0.179666i | \(-0.942498\pi\) | ||||
−0.983728 | + | 0.179666i | \(0.942498\pi\) | |||||||
\(740\) | −35.8734 | −1.31873 | ||||||||
\(741\) | −5.23692 | −0.192383 | ||||||||
\(742\) | −87.9997 | −3.23057 | ||||||||
\(743\) | 26.1739 | 0.960228 | 0.480114 | − | 0.877206i | \(-0.340595\pi\) | ||||
0.480114 | + | 0.877206i | \(0.340595\pi\) | |||||||
\(744\) | −135.819 | −4.97938 | ||||||||
\(745\) | 12.1565 | 0.445379 | ||||||||
\(746\) | 79.7767 | 2.92083 | ||||||||
\(747\) | −31.0473 | −1.13596 | ||||||||
\(748\) | 1.45391 | 0.0531603 | ||||||||
\(749\) | 29.3434 | 1.07218 | ||||||||
\(750\) | 8.57929 | 0.313271 | ||||||||
\(751\) | −1.81809 | −0.0663432 | −0.0331716 | − | 0.999450i | \(-0.510561\pi\) | ||||
−0.0331716 | + | 0.999450i | \(0.510561\pi\) | |||||||
\(752\) | 52.0082 | 1.89654 | ||||||||
\(753\) | 38.8238 | 1.41482 | ||||||||
\(754\) | −75.1716 | −2.73759 | ||||||||
\(755\) | 14.6494 | 0.533145 | ||||||||
\(756\) | 196.523 | 7.14748 | ||||||||
\(757\) | −29.1732 | −1.06032 | −0.530158 | − | 0.847899i | \(-0.677868\pi\) | ||||
−0.530158 | + | 0.847899i | \(0.677868\pi\) | |||||||
\(758\) | 1.86259 | 0.0676524 | ||||||||
\(759\) | −0.781428 | −0.0283641 | ||||||||
\(760\) | 3.08815 | 0.112019 | ||||||||
\(761\) | −4.63249 | −0.167928 | −0.0839638 | − | 0.996469i | \(-0.526758\pi\) | ||||
−0.0839638 | + | 0.996469i | \(0.526758\pi\) | |||||||
\(762\) | −118.200 | −4.28195 | ||||||||
\(763\) | 9.50182 | 0.343989 | ||||||||
\(764\) | 119.496 | 4.32323 | ||||||||
\(765\) | −7.11493 | −0.257241 | ||||||||
\(766\) | −43.8102 | −1.58293 | ||||||||
\(767\) | 13.7745 | 0.497370 | ||||||||
\(768\) | 64.8242 | 2.33914 | ||||||||
\(769\) | 41.7295 | 1.50480 | 0.752402 | − | 0.658704i | \(-0.228895\pi\) | ||||
0.752402 | + | 0.658704i | \(0.228895\pi\) | |||||||
\(770\) | 2.11514 | 0.0762242 | ||||||||
\(771\) | −47.7576 | −1.71995 | ||||||||
\(772\) | −83.7760 | −3.01516 | ||||||||
\(773\) | −8.42708 | −0.303101 | −0.151550 | − | 0.988450i | \(-0.548427\pi\) | ||||
−0.151550 | + | 0.988450i | \(0.548427\pi\) | |||||||
\(774\) | 22.1591 | 0.796492 | ||||||||
\(775\) | 4.83127 | 0.173544 | ||||||||
\(776\) | −70.1614 | −2.51865 | ||||||||
\(777\) | 61.5295 | 2.20736 | ||||||||
\(778\) | −40.5885 | −1.45517 | ||||||||
\(779\) | −2.20372 | −0.0789564 | ||||||||
\(780\) | 79.0982 | 2.83217 | ||||||||
\(781\) | −0.275530 | −0.00985923 | ||||||||
\(782\) | 2.40552 | 0.0860213 | ||||||||
\(783\) | −77.3771 | −2.76523 | ||||||||
\(784\) | 14.5991 | 0.521395 | ||||||||
\(785\) | −5.57332 | −0.198920 | ||||||||
\(786\) | 89.9411 | 3.20809 | ||||||||
\(787\) | 33.9509 | 1.21022 | 0.605110 | − | 0.796142i | \(-0.293129\pi\) | ||||
0.605110 | + | 0.796142i | \(0.293129\pi\) | |||||||
\(788\) | 118.422 | 4.21862 | ||||||||
\(789\) | −85.1139 | −3.03013 | ||||||||
\(790\) | 17.7907 | 0.632965 | ||||||||
\(791\) | −26.6180 | −0.946428 | ||||||||
\(792\) | −17.3284 | −0.615737 | ||||||||
\(793\) | −33.8466 | −1.20193 | ||||||||
\(794\) | −11.0234 | −0.391207 | ||||||||
\(795\) | −36.4580 | −1.29303 | ||||||||
\(796\) | −69.3456 | −2.45789 | ||||||||
\(797\) | −25.9801 | −0.920263 | −0.460132 | − | 0.887851i | \(-0.652198\pi\) | ||||
−0.460132 | + | 0.887851i | \(0.652198\pi\) | |||||||
\(798\) | −8.52964 | −0.301946 | ||||||||
\(799\) | 3.91305 | 0.138434 | ||||||||
\(800\) | −18.1744 | −0.642564 | ||||||||
\(801\) | 61.5210 | 2.17374 | ||||||||
\(802\) | 76.6904 | 2.70803 | ||||||||
\(803\) | 1.13150 | 0.0399296 | ||||||||
\(804\) | 144.769 | 5.10560 | ||||||||
\(805\) | 2.53770 | 0.0894420 | ||||||||
\(806\) | 61.4252 | 2.16361 | ||||||||
\(807\) | 28.1932 | 0.992447 | ||||||||
\(808\) | −80.4255 | −2.82936 | ||||||||
\(809\) | −0.983893 | −0.0345919 | −0.0172959 | − | 0.999850i | \(-0.505506\pi\) | ||||
−0.0172959 | + | 0.999850i | \(0.505506\pi\) | |||||||
\(810\) | 54.6994 | 1.92194 | ||||||||
\(811\) | −11.3003 | −0.396808 | −0.198404 | − | 0.980120i | \(-0.563576\pi\) | ||||
−0.198404 | + | 0.980120i | \(0.563576\pi\) | |||||||
\(812\) | −88.7848 | −3.11574 | ||||||||
\(813\) | 28.0086 | 0.982305 | ||||||||
\(814\) | −5.05289 | −0.177104 | ||||||||
\(815\) | 0.683516 | 0.0239425 | ||||||||
\(816\) | 42.2706 | 1.47977 | ||||||||
\(817\) | −0.403358 | −0.0141117 | ||||||||
\(818\) | −58.8476 | −2.05756 | ||||||||
\(819\) | −95.4302 | −3.33460 | ||||||||
\(820\) | 33.2849 | 1.16236 | ||||||||
\(821\) | 3.89470 | 0.135926 | 0.0679631 | − | 0.997688i | \(-0.478350\pi\) | ||||
0.0679631 | + | 0.997688i | \(0.478350\pi\) | |||||||
\(822\) | −62.0359 | −2.16375 | ||||||||
\(823\) | −46.1921 | −1.61016 | −0.805079 | − | 0.593168i | \(-0.797877\pi\) | ||||
−0.805079 | + | 0.593168i | \(0.797877\pi\) | |||||||
\(824\) | −15.9529 | −0.555744 | ||||||||
\(825\) | 0.876294 | 0.0305086 | ||||||||
\(826\) | 22.4353 | 0.780624 | ||||||||
\(827\) | −39.4933 | −1.37332 | −0.686658 | − | 0.726981i | \(-0.740923\pi\) | ||||
−0.686658 | + | 0.726981i | \(0.740923\pi\) | |||||||
\(828\) | −33.4796 | −1.16350 | ||||||||
\(829\) | −2.83430 | −0.0984392 | −0.0492196 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492196 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(830\) | −11.7713 | −0.408586 | ||||||||
\(831\) | 91.8401 | 3.18590 | ||||||||
\(832\) | −105.786 | −3.66746 | ||||||||
\(833\) | 1.09842 | 0.0380580 | ||||||||
\(834\) | −85.9568 | −2.97644 | ||||||||
\(835\) | 19.9279 | 0.689634 | ||||||||
\(836\) | 0.507946 | 0.0175677 | ||||||||
\(837\) | 63.2273 | 2.18546 | ||||||||
\(838\) | 18.7004 | 0.645994 | ||||||||
\(839\) | 27.9202 | 0.963912 | 0.481956 | − | 0.876195i | \(-0.339926\pi\) | ||||
0.481956 | + | 0.876195i | \(0.339926\pi\) | |||||||
\(840\) | 80.0020 | 2.76033 | ||||||||
\(841\) | 5.95724 | 0.205422 | ||||||||
\(842\) | 34.0366 | 1.17298 | ||||||||
\(843\) | −89.4843 | −3.08200 | ||||||||
\(844\) | 126.765 | 4.36345 | ||||||||
\(845\) | −9.21419 | −0.316978 | ||||||||
\(846\) | −75.1027 | −2.58208 | ||||||||
\(847\) | −31.0875 | −1.06818 | ||||||||
\(848\) | 152.359 | 5.23203 | ||||||||
\(849\) | −7.14742 | −0.245299 | ||||||||
\(850\) | −2.69755 | −0.0925253 | ||||||||
\(851\) | −6.06235 | −0.207815 | ||||||||
\(852\) | −16.7823 | −0.574952 | ||||||||
\(853\) | 5.08937 | 0.174257 | 0.0871284 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871284 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(854\) | −55.1277 | −1.88643 | ||||||||
\(855\) | −2.48571 | −0.0850094 | ||||||||
\(856\) | −91.1443 | −3.11525 | ||||||||
\(857\) | −24.7556 | −0.845635 | −0.422818 | − | 0.906215i | \(-0.638959\pi\) | ||||
−0.422818 | + | 0.906215i | \(0.638959\pi\) | |||||||
\(858\) | 11.1413 | 0.380357 | ||||||||
\(859\) | −18.0133 | −0.614607 | −0.307304 | − | 0.951612i | \(-0.599427\pi\) | ||||
−0.307304 | + | 0.951612i | \(0.599427\pi\) | |||||||
\(860\) | 6.09230 | 0.207746 | ||||||||
\(861\) | −57.0898 | −1.94561 | ||||||||
\(862\) | 100.303 | 3.41634 | ||||||||
\(863\) | 37.0240 | 1.26031 | 0.630156 | − | 0.776468i | \(-0.282991\pi\) | ||||
0.630156 | + | 0.776468i | \(0.282991\pi\) | |||||||
\(864\) | −237.851 | −8.09185 | ||||||||
\(865\) | −23.4532 | −0.797432 | ||||||||
\(866\) | −43.0843 | −1.46407 | ||||||||
\(867\) | 3.18040 | 0.108012 | ||||||||
\(868\) | 72.5490 | 2.46247 | ||||||||
\(869\) | 1.81715 | 0.0616427 | ||||||||
\(870\) | −50.7248 | −1.71973 | ||||||||
\(871\) | −40.6573 | −1.37762 | ||||||||
\(872\) | −29.5139 | −0.999465 | ||||||||
\(873\) | 56.4741 | 1.91136 | ||||||||
\(874\) | 0.840405 | 0.0284271 | ||||||||
\(875\) | −2.84577 | −0.0962047 | ||||||||
\(876\) | 68.9186 | 2.32854 | ||||||||
\(877\) | 28.7289 | 0.970107 | 0.485054 | − | 0.874484i | \(-0.338800\pi\) | ||||
0.485054 | + | 0.874484i | \(0.338800\pi\) | |||||||
\(878\) | −59.2193 | −1.99856 | ||||||||
\(879\) | −69.6887 | −2.35054 | ||||||||
\(880\) | −3.66206 | −0.123448 | ||||||||
\(881\) | 2.30441 | 0.0776375 | 0.0388188 | − | 0.999246i | \(-0.487640\pi\) | ||||
0.0388188 | + | 0.999246i | \(0.487640\pi\) | |||||||
\(882\) | −21.0819 | −0.709863 | ||||||||
\(883\) | 36.0110 | 1.21187 | 0.605933 | − | 0.795516i | \(-0.292800\pi\) | ||||
0.605933 | + | 0.795516i | \(0.292800\pi\) | |||||||
\(884\) | −24.8705 | −0.836487 | ||||||||
\(885\) | 9.29487 | 0.312444 | ||||||||
\(886\) | 76.0978 | 2.55656 | ||||||||
\(887\) | −58.6613 | −1.96965 | −0.984826 | − | 0.173542i | \(-0.944479\pi\) | ||||
−0.984826 | + | 0.173542i | \(0.944479\pi\) | |||||||
\(888\) | −191.118 | −6.41351 | ||||||||
\(889\) | 39.2074 | 1.31497 | ||||||||
\(890\) | 23.3250 | 0.781857 | ||||||||
\(891\) | 5.58703 | 0.187173 | ||||||||
\(892\) | 142.716 | 4.77847 | ||||||||
\(893\) | 1.36708 | 0.0457476 | ||||||||
\(894\) | 104.294 | 3.48811 | ||||||||
\(895\) | −22.3842 | −0.748222 | ||||||||
\(896\) | −68.8580 | −2.30038 | ||||||||
\(897\) | 13.3671 | 0.446313 | ||||||||
\(898\) | 90.6747 | 3.02585 | ||||||||
\(899\) | −28.5647 | −0.952686 | ||||||||
\(900\) | 37.5440 | 1.25147 | ||||||||
\(901\) | 11.4633 | 0.381899 | ||||||||
\(902\) | 4.68830 | 0.156103 | ||||||||
\(903\) | −10.4494 | −0.347735 | ||||||||
\(904\) | 82.6789 | 2.74986 | ||||||||
\(905\) | 1.07690 | 0.0357975 | ||||||||
\(906\) | 125.681 | 4.17548 | ||||||||
\(907\) | −15.8605 | −0.526638 | −0.263319 | − | 0.964709i | \(-0.584817\pi\) | ||||
−0.263319 | + | 0.964709i | \(0.584817\pi\) | |||||||
\(908\) | −66.4027 | −2.20365 | ||||||||
\(909\) | 64.7359 | 2.14715 | ||||||||
\(910\) | −36.1814 | −1.19940 | ||||||||
\(911\) | 39.1938 | 1.29855 | 0.649274 | − | 0.760555i | \(-0.275073\pi\) | ||||
0.649274 | + | 0.760555i | \(0.275073\pi\) | |||||||
\(912\) | 14.7678 | 0.489012 | ||||||||
\(913\) | −1.20232 | −0.0397911 | ||||||||
\(914\) | 72.8195 | 2.40865 | ||||||||
\(915\) | −22.8392 | −0.755041 | ||||||||
\(916\) | −92.4093 | −3.05329 | ||||||||
\(917\) | −29.8337 | −0.985195 | ||||||||
\(918\) | −35.3032 | −1.16518 | ||||||||
\(919\) | 46.5033 | 1.53400 | 0.767001 | − | 0.641646i | \(-0.221748\pi\) | ||||
0.767001 | + | 0.641646i | \(0.221748\pi\) | |||||||
\(920\) | −7.88240 | −0.259875 | ||||||||
\(921\) | −43.3664 | −1.42897 | ||||||||
\(922\) | 53.3806 | 1.75800 | ||||||||
\(923\) | 4.71319 | 0.155137 | ||||||||
\(924\) | 13.1589 | 0.432896 | ||||||||
\(925\) | 6.79832 | 0.223528 | ||||||||
\(926\) | −38.6969 | −1.27166 | ||||||||
\(927\) | 12.8407 | 0.421745 | ||||||||
\(928\) | 107.456 | 3.52741 | ||||||||
\(929\) | −0.460171 | −0.0150977 | −0.00754886 | − | 0.999972i | \(-0.502403\pi\) | ||||
−0.00754886 | + | 0.999972i | \(0.502403\pi\) | |||||||
\(930\) | 41.4489 | 1.35916 | ||||||||
\(931\) | 0.383749 | 0.0125769 | ||||||||
\(932\) | 135.333 | 4.43300 | ||||||||
\(933\) | −60.1907 | −1.97056 | ||||||||
\(934\) | 18.2376 | 0.596753 | ||||||||
\(935\) | −0.275530 | −0.00901078 | ||||||||
\(936\) | 296.418 | 9.68873 | ||||||||
\(937\) | −58.7929 | −1.92068 | −0.960339 | − | 0.278834i | \(-0.910052\pi\) | ||||
−0.960339 | + | 0.278834i | \(0.910052\pi\) | |||||||
\(938\) | −66.2206 | −2.16218 | ||||||||
\(939\) | 41.9463 | 1.36887 | ||||||||
\(940\) | −20.6483 | −0.673474 | ||||||||
\(941\) | −49.2885 | −1.60676 | −0.803379 | − | 0.595468i | \(-0.796967\pi\) | ||||
−0.803379 | + | 0.595468i | \(0.796967\pi\) | |||||||
\(942\) | −47.8151 | −1.55790 | ||||||||
\(943\) | 5.62492 | 0.183172 | ||||||||
\(944\) | −38.8435 | −1.26425 | ||||||||
\(945\) | −37.2429 | −1.21151 | ||||||||
\(946\) | 0.858123 | 0.0279000 | ||||||||
\(947\) | 25.3430 | 0.823537 | 0.411768 | − | 0.911289i | \(-0.364911\pi\) | ||||
0.411768 | + | 0.911289i | \(0.364911\pi\) | |||||||
\(948\) | 110.681 | 3.59476 | ||||||||
\(949\) | −19.3553 | −0.628300 | ||||||||
\(950\) | −0.942430 | −0.0305765 | ||||||||
\(951\) | −83.4759 | −2.70689 | ||||||||
\(952\) | −25.1547 | −0.815269 | ||||||||
\(953\) | −8.93054 | −0.289288 | −0.144644 | − | 0.989484i | \(-0.546204\pi\) | ||||
−0.144644 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(954\) | −220.015 | −7.12324 | ||||||||
\(955\) | −22.6457 | −0.732796 | ||||||||
\(956\) | 129.738 | 4.19601 | ||||||||
\(957\) | −5.18106 | −0.167480 | ||||||||
\(958\) | 45.7560 | 1.47831 | ||||||||
\(959\) | 20.5775 | 0.664481 | ||||||||
\(960\) | −71.3827 | −2.30387 | ||||||||
\(961\) | −7.65884 | −0.247059 | ||||||||
\(962\) | 86.4345 | 2.78676 | ||||||||
\(963\) | 73.3637 | 2.36411 | ||||||||
\(964\) | −5.53984 | −0.178426 | ||||||||
\(965\) | 15.8763 | 0.511076 | ||||||||
\(966\) | 21.7716 | 0.700491 | ||||||||
\(967\) | 11.3677 | 0.365559 | 0.182779 | − | 0.983154i | \(-0.441491\pi\) | ||||
0.182779 | + | 0.983154i | \(0.441491\pi\) | |||||||
\(968\) | 96.5615 | 3.10361 | ||||||||
\(969\) | 1.11112 | 0.0356943 | ||||||||
\(970\) | 21.4116 | 0.687485 | ||||||||
\(971\) | 40.0192 | 1.28428 | 0.642139 | − | 0.766588i | \(-0.278047\pi\) | ||||
0.642139 | + | 0.766588i | \(0.278047\pi\) | |||||||
\(972\) | 133.128 | 4.27008 | ||||||||
\(973\) | 28.5121 | 0.914055 | ||||||||
\(974\) | 40.0851 | 1.28441 | ||||||||
\(975\) | −14.9898 | −0.480059 | ||||||||
\(976\) | 95.4457 | 3.05514 | ||||||||
\(977\) | 35.0625 | 1.12175 | 0.560874 | − | 0.827901i | \(-0.310465\pi\) | ||||
0.560874 | + | 0.827901i | \(0.310465\pi\) | |||||||
\(978\) | 5.86408 | 0.187513 | ||||||||
\(979\) | 2.38243 | 0.0761429 | ||||||||
\(980\) | −5.79613 | −0.185151 | ||||||||
\(981\) | 23.7562 | 0.758478 | ||||||||
\(982\) | 96.6347 | 3.08374 | ||||||||
\(983\) | 19.3763 | 0.618008 | 0.309004 | − | 0.951061i | \(-0.400004\pi\) | ||||
0.309004 | + | 0.951061i | \(0.400004\pi\) | |||||||
\(984\) | 177.328 | 5.65301 | ||||||||
\(985\) | −22.4421 | −0.715064 | ||||||||
\(986\) | 15.9492 | 0.507926 | ||||||||
\(987\) | 35.4157 | 1.12730 | ||||||||
\(988\) | −8.68890 | −0.276431 | ||||||||
\(989\) | 1.02956 | 0.0327380 | ||||||||
\(990\) | 5.28821 | 0.168070 | ||||||||
\(991\) | −43.0845 | −1.36863 | −0.684313 | − | 0.729189i | \(-0.739898\pi\) | ||||
−0.684313 | + | 0.729189i | \(0.739898\pi\) | |||||||
\(992\) | −87.8056 | −2.78783 | ||||||||
\(993\) | −75.4898 | −2.39560 | ||||||||
\(994\) | 7.67662 | 0.243488 | ||||||||
\(995\) | 13.1416 | 0.416617 | ||||||||
\(996\) | −73.2326 | −2.32046 | ||||||||
\(997\) | −21.0303 | −0.666035 | −0.333018 | − | 0.942921i | \(-0.608067\pi\) | ||||
−0.333018 | + | 0.942921i | \(0.608067\pi\) | |||||||
\(998\) | 51.0163 | 1.61489 | ||||||||
\(999\) | 88.9704 | 2.81490 |
(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 | 6035.2.a.e.1.2 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6035.2.a.e.1.2 | ✓ | 49 | 1.1 | even | 1 | trivial |