Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.94452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 2.94452 | 0.263366 | 0.131683 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131683 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 5.88904 | 0.186228 | ||||||||
\(11\) | 33.3030 | 0.912839 | 0.456420 | − | 0.889765i | \(-0.349132\pi\) | ||||
0.456420 | + | 0.889765i | \(0.349132\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 71.9263 | 1.53452 | 0.767261 | − | 0.641335i | \(-0.221619\pi\) | ||||
0.767261 | + | 0.641335i | \(0.221619\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 8.83356 | 0.152054 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 53.4542 | 0.762620 | 0.381310 | − | 0.924447i | \(-0.375473\pi\) | ||||
0.381310 | + | 0.924447i | \(0.375473\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −75.3776 | −0.910148 | −0.455074 | − | 0.890454i | \(-0.650387\pi\) | ||||
−0.455074 | + | 0.890454i | \(0.650387\pi\) | |||||||
\(20\) | 11.7781 | 0.131683 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 66.6060 | 0.645475 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −116.330 | −0.930638 | ||||||||
\(26\) | 143.853 | 1.08507 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 76.0785 | 0.487153 | 0.243576 | − | 0.969882i | \(-0.421679\pi\) | ||||
0.243576 | + | 0.969882i | \(0.421679\pi\) | |||||||
\(30\) | 17.6671 | 0.107519 | ||||||||
\(31\) | 150.370 | 0.871201 | 0.435601 | − | 0.900140i | \(-0.356536\pi\) | ||||
0.435601 | + | 0.900140i | \(0.356536\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 99.9090 | 0.527028 | ||||||||
\(34\) | 106.908 | 0.539254 | ||||||||
\(35\) | −20.6116 | −0.0995430 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −54.5216 | −0.242251 | −0.121126 | − | 0.992637i | \(-0.538650\pi\) | ||||
−0.121126 | + | 0.992637i | \(0.538650\pi\) | |||||||
\(38\) | −150.755 | −0.643572 | ||||||||
\(39\) | 215.779 | 0.885956 | ||||||||
\(40\) | 23.5562 | 0.0931139 | ||||||||
\(41\) | −222.763 | −0.848530 | −0.424265 | − | 0.905538i | \(-0.639468\pi\) | ||||
−0.424265 | + | 0.905538i | \(0.639468\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | −289.007 | −1.02496 | −0.512478 | − | 0.858700i | \(-0.671272\pi\) | ||||
−0.512478 | + | 0.858700i | \(0.671272\pi\) | |||||||
\(44\) | 133.212 | 0.456420 | ||||||||
\(45\) | 26.5007 | 0.0877887 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −36.1212 | −0.112102 | −0.0560512 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560512 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −232.660 | −0.658061 | ||||||||
\(51\) | 160.363 | 0.440299 | ||||||||
\(52\) | 287.705 | 0.767261 | ||||||||
\(53\) | 200.898 | 0.520669 | 0.260334 | − | 0.965519i | \(-0.416167\pi\) | ||||
0.260334 | + | 0.965519i | \(0.416167\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 98.0614 | 0.240411 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | −226.133 | −0.525474 | ||||||||
\(58\) | 152.157 | 0.344469 | ||||||||
\(59\) | 904.079 | 1.99493 | 0.997467 | − | 0.0711347i | \(-0.0226620\pi\) | ||||
0.997467 | + | 0.0711347i | \(0.0226620\pi\) | |||||||
\(60\) | 35.3343 | 0.0760272 | ||||||||
\(61\) | 630.351 | 1.32308 | 0.661542 | − | 0.749908i | \(-0.269902\pi\) | ||||
0.661542 | + | 0.749908i | \(0.269902\pi\) | |||||||
\(62\) | 300.740 | 0.616032 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 211.789 | 0.404141 | ||||||||
\(66\) | 199.818 | 0.372665 | ||||||||
\(67\) | 898.686 | 1.63869 | 0.819343 | − | 0.573304i | \(-0.194339\pi\) | ||||
0.819343 | + | 0.573304i | \(0.194339\pi\) | |||||||
\(68\) | 213.817 | 0.381310 | ||||||||
\(69\) | −69.0000 | −0.120386 | ||||||||
\(70\) | −41.2233 | −0.0703875 | ||||||||
\(71\) | 516.037 | 0.862567 | 0.431284 | − | 0.902216i | \(-0.358061\pi\) | ||||
0.431284 | + | 0.902216i | \(0.358061\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −662.453 | −1.06211 | −0.531057 | − | 0.847336i | \(-0.678205\pi\) | ||||
−0.531057 | + | 0.847336i | \(0.678205\pi\) | |||||||
\(74\) | −109.043 | −0.171298 | ||||||||
\(75\) | −348.989 | −0.537304 | ||||||||
\(76\) | −301.510 | −0.455074 | ||||||||
\(77\) | −233.121 | −0.345021 | ||||||||
\(78\) | 431.558 | 0.626466 | ||||||||
\(79\) | 1346.54 | 1.91769 | 0.958843 | − | 0.283938i | \(-0.0916409\pi\) | ||||
0.958843 | + | 0.283938i | \(0.0916409\pi\) | |||||||
\(80\) | 47.1123 | 0.0658415 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −445.526 | −0.600001 | ||||||||
\(83\) | −100.162 | −0.132461 | −0.0662304 | − | 0.997804i | \(-0.521097\pi\) | ||||
−0.0662304 | + | 0.997804i | \(0.521097\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | 157.397 | 0.200848 | ||||||||
\(86\) | −578.013 | −0.724753 | ||||||||
\(87\) | 228.236 | 0.281258 | ||||||||
\(88\) | 266.424 | 0.322737 | ||||||||
\(89\) | 82.5612 | 0.0983311 | 0.0491656 | − | 0.998791i | \(-0.484344\pi\) | ||||
0.0491656 | + | 0.998791i | \(0.484344\pi\) | |||||||
\(90\) | 53.0014 | 0.0620760 | ||||||||
\(91\) | −503.484 | −0.579995 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 451.110 | 0.502988 | ||||||||
\(94\) | −72.2423 | −0.0792684 | ||||||||
\(95\) | −221.951 | −0.239702 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −295.624 | −0.309444 | −0.154722 | − | 0.987958i | \(-0.549448\pi\) | ||||
−0.154722 | + | 0.987958i | \(0.549448\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 299.727 | 0.304280 | ||||||||
\(100\) | −465.319 | −0.465319 | ||||||||
\(101\) | 1762.47 | 1.73636 | 0.868181 | − | 0.496247i | \(-0.165289\pi\) | ||||
0.868181 | + | 0.496247i | \(0.165289\pi\) | |||||||
\(102\) | 320.725 | 0.311339 | ||||||||
\(103\) | −1391.82 | −1.33146 | −0.665731 | − | 0.746192i | \(-0.731880\pi\) | ||||
−0.665731 | + | 0.746192i | \(0.731880\pi\) | |||||||
\(104\) | 575.411 | 0.542535 | ||||||||
\(105\) | −61.8349 | −0.0574712 | ||||||||
\(106\) | 401.796 | 0.368168 | ||||||||
\(107\) | 31.8292 | 0.0287574 | 0.0143787 | − | 0.999897i | \(-0.495423\pi\) | ||||
0.0143787 | + | 0.999897i | \(0.495423\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −1391.24 | −1.22254 | −0.611268 | − | 0.791424i | \(-0.709340\pi\) | ||||
−0.611268 | + | 0.791424i | \(0.709340\pi\) | |||||||
\(110\) | 196.123 | 0.169996 | ||||||||
\(111\) | −163.565 | −0.139864 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −524.351 | −0.436520 | −0.218260 | − | 0.975891i | \(-0.570038\pi\) | ||||
−0.218260 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(114\) | −452.266 | −0.371566 | ||||||||
\(115\) | −67.7240 | −0.0549156 | ||||||||
\(116\) | 304.314 | 0.243576 | ||||||||
\(117\) | 647.337 | 0.511507 | ||||||||
\(118\) | 1808.16 | 1.41063 | ||||||||
\(119\) | −374.179 | −0.288243 | ||||||||
\(120\) | 70.6685 | 0.0537594 | ||||||||
\(121\) | −221.910 | −0.166724 | ||||||||
\(122\) | 1260.70 | 0.935562 | ||||||||
\(123\) | −668.289 | −0.489899 | ||||||||
\(124\) | 601.480 | 0.435601 | ||||||||
\(125\) | −710.601 | −0.508464 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | 46.9541 | 0.0328071 | 0.0164036 | − | 0.999865i | \(-0.494778\pi\) | ||||
0.0164036 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −867.020 | −0.591758 | ||||||||
\(130\) | 423.577 | 0.285771 | ||||||||
\(131\) | −1398.47 | −0.932712 | −0.466356 | − | 0.884597i | \(-0.654433\pi\) | ||||
−0.466356 | + | 0.884597i | \(0.654433\pi\) | |||||||
\(132\) | 399.636 | 0.263514 | ||||||||
\(133\) | 527.643 | 0.344004 | ||||||||
\(134\) | 1797.37 | 1.15873 | ||||||||
\(135\) | 79.5021 | 0.0506848 | ||||||||
\(136\) | 427.634 | 0.269627 | ||||||||
\(137\) | −1970.59 | −1.22890 | −0.614449 | − | 0.788957i | \(-0.710622\pi\) | ||||
−0.614449 | + | 0.788957i | \(0.710622\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | 574.110 | 0.350326 | 0.175163 | − | 0.984539i | \(-0.443955\pi\) | ||||
0.175163 | + | 0.984539i | \(0.443955\pi\) | |||||||
\(140\) | −82.4466 | −0.0497715 | ||||||||
\(141\) | −108.363 | −0.0647223 | ||||||||
\(142\) | 1032.07 | 0.609927 | ||||||||
\(143\) | 2395.36 | 1.40077 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 224.015 | 0.128299 | ||||||||
\(146\) | −1324.91 | −0.751028 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | −218.087 | −0.121126 | ||||||||
\(149\) | −1934.41 | −1.06358 | −0.531788 | − | 0.846877i | \(-0.678480\pi\) | ||||
−0.531788 | + | 0.846877i | \(0.678480\pi\) | |||||||
\(150\) | −697.979 | −0.379932 | ||||||||
\(151\) | 1244.37 | 0.670631 | 0.335316 | − | 0.942106i | \(-0.391157\pi\) | ||||
0.335316 | + | 0.942106i | \(0.391157\pi\) | |||||||
\(152\) | −603.021 | −0.321786 | ||||||||
\(153\) | 481.088 | 0.254207 | ||||||||
\(154\) | −466.242 | −0.243967 | ||||||||
\(155\) | 442.767 | 0.229445 | ||||||||
\(156\) | 863.116 | 0.442978 | ||||||||
\(157\) | −2599.68 | −1.32151 | −0.660754 | − | 0.750603i | \(-0.729763\pi\) | ||||
−0.660754 | + | 0.750603i | \(0.729763\pi\) | |||||||
\(158\) | 2693.07 | 1.35601 | ||||||||
\(159\) | 602.694 | 0.300608 | ||||||||
\(160\) | 94.2247 | 0.0465570 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1146.93 | 0.551130 | 0.275565 | − | 0.961282i | \(-0.411135\pi\) | ||||
0.275565 | + | 0.961282i | \(0.411135\pi\) | |||||||
\(164\) | −891.052 | −0.424265 | ||||||||
\(165\) | 294.184 | 0.138801 | ||||||||
\(166\) | −200.325 | −0.0936639 | ||||||||
\(167\) | −2287.66 | −1.06003 | −0.530013 | − | 0.847989i | \(-0.677813\pi\) | ||||
−0.530013 | + | 0.847989i | \(0.677813\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | 2976.40 | 1.35476 | ||||||||
\(170\) | 314.794 | 0.142021 | ||||||||
\(171\) | −678.398 | −0.303383 | ||||||||
\(172\) | −1156.03 | −0.512478 | ||||||||
\(173\) | 1127.23 | 0.495388 | 0.247694 | − | 0.968838i | \(-0.420327\pi\) | ||||
0.247694 | + | 0.968838i | \(0.420327\pi\) | |||||||
\(174\) | 456.471 | 0.198879 | ||||||||
\(175\) | 814.309 | 0.351748 | ||||||||
\(176\) | 532.848 | 0.228210 | ||||||||
\(177\) | 2712.24 | 1.15178 | ||||||||
\(178\) | 165.122 | 0.0695306 | ||||||||
\(179\) | −137.792 | −0.0575366 | −0.0287683 | − | 0.999586i | \(-0.509158\pi\) | ||||
−0.0287683 | + | 0.999586i | \(0.509158\pi\) | |||||||
\(180\) | 106.003 | 0.0438943 | ||||||||
\(181\) | −1012.20 | −0.415671 | −0.207835 | − | 0.978164i | \(-0.566642\pi\) | ||||
−0.207835 | + | 0.978164i | \(0.566642\pi\) | |||||||
\(182\) | −1006.97 | −0.410118 | ||||||||
\(183\) | 1891.05 | 0.763883 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −160.540 | −0.0638008 | ||||||||
\(186\) | 902.220 | 0.355666 | ||||||||
\(187\) | 1780.19 | 0.696150 | ||||||||
\(188\) | −144.485 | −0.0560512 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −443.902 | −0.169495 | ||||||||
\(191\) | −2051.91 | −0.777335 | −0.388667 | − | 0.921378i | \(-0.627064\pi\) | ||||
−0.388667 | + | 0.921378i | \(0.627064\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 1127.02 | 0.420333 | 0.210167 | − | 0.977666i | \(-0.432599\pi\) | ||||
0.210167 | + | 0.977666i | \(0.432599\pi\) | |||||||
\(194\) | −591.248 | −0.218810 | ||||||||
\(195\) | 635.366 | 0.233331 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 103.638 | 0.0374817 | 0.0187409 | − | 0.999824i | \(-0.494034\pi\) | ||||
0.0187409 | + | 0.999824i | \(0.494034\pi\) | |||||||
\(198\) | 599.454 | 0.215158 | ||||||||
\(199\) | −569.184 | −0.202756 | −0.101378 | − | 0.994848i | \(-0.532325\pi\) | ||||
−0.101378 | + | 0.994848i | \(0.532325\pi\) | |||||||
\(200\) | −930.638 | −0.329030 | ||||||||
\(201\) | 2696.06 | 0.946095 | ||||||||
\(202\) | 3524.95 | 1.22779 | ||||||||
\(203\) | −532.550 | −0.184126 | ||||||||
\(204\) | 641.450 | 0.220150 | ||||||||
\(205\) | −655.930 | −0.223474 | ||||||||
\(206\) | −2783.65 | −0.941486 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 1150.82 | 0.383630 | ||||||||
\(209\) | −2510.30 | −0.830819 | ||||||||
\(210\) | −123.670 | −0.0406383 | ||||||||
\(211\) | −4048.85 | −1.32102 | −0.660509 | − | 0.750819i | \(-0.729659\pi\) | ||||
−0.660509 | + | 0.750819i | \(0.729659\pi\) | |||||||
\(212\) | 803.592 | 0.260334 | ||||||||
\(213\) | 1548.11 | 0.498003 | ||||||||
\(214\) | 63.6584 | 0.0203346 | ||||||||
\(215\) | −850.986 | −0.269938 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1052.59 | −0.329283 | ||||||||
\(218\) | −2782.47 | −0.864463 | ||||||||
\(219\) | −1987.36 | −0.613212 | ||||||||
\(220\) | 392.246 | 0.120205 | ||||||||
\(221\) | 3844.76 | 1.17026 | ||||||||
\(222\) | −327.130 | −0.0988987 | ||||||||
\(223\) | 965.710 | 0.289994 | 0.144997 | − | 0.989432i | \(-0.453683\pi\) | ||||
0.144997 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −1046.97 | −0.310213 | ||||||||
\(226\) | −1048.70 | −0.308666 | ||||||||
\(227\) | −2823.71 | −0.825623 | −0.412811 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412811 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(228\) | −904.531 | −0.262737 | ||||||||
\(229\) | 2103.54 | 0.607012 | 0.303506 | − | 0.952829i | \(-0.401843\pi\) | ||||
0.303506 | + | 0.952829i | \(0.401843\pi\) | |||||||
\(230\) | −135.448 | −0.0388312 | ||||||||
\(231\) | −699.363 | −0.199198 | ||||||||
\(232\) | 608.628 | 0.172234 | ||||||||
\(233\) | 2434.86 | 0.684604 | 0.342302 | − | 0.939590i | \(-0.388793\pi\) | ||||
0.342302 | + | 0.939590i | \(0.388793\pi\) | |||||||
\(234\) | 1294.67 | 0.361690 | ||||||||
\(235\) | −106.359 | −0.0295240 | ||||||||
\(236\) | 3616.32 | 0.997467 | ||||||||
\(237\) | 4039.61 | 1.10718 | ||||||||
\(238\) | −748.359 | −0.203819 | ||||||||
\(239\) | 2452.42 | 0.663739 | 0.331870 | − | 0.943325i | \(-0.392321\pi\) | ||||
0.331870 | + | 0.943325i | \(0.392321\pi\) | |||||||
\(240\) | 141.337 | 0.0380136 | ||||||||
\(241\) | −2085.36 | −0.557384 | −0.278692 | − | 0.960381i | \(-0.589901\pi\) | ||||
−0.278692 | + | 0.960381i | \(0.589901\pi\) | |||||||
\(242\) | −443.820 | −0.117892 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2521.40 | 0.661542 | ||||||||
\(245\) | 144.282 | 0.0376237 | ||||||||
\(246\) | −1336.58 | −0.346411 | ||||||||
\(247\) | −5421.64 | −1.39664 | ||||||||
\(248\) | 1202.96 | 0.308016 | ||||||||
\(249\) | −300.487 | −0.0764763 | ||||||||
\(250\) | −1421.20 | −0.359539 | ||||||||
\(251\) | 783.617 | 0.197058 | 0.0985289 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985289 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | −765.969 | −0.190340 | ||||||||
\(254\) | 93.9083 | 0.0231981 | ||||||||
\(255\) | 472.191 | 0.115960 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2932.94 | −0.711875 | −0.355937 | − | 0.934510i | \(-0.615838\pi\) | ||||
−0.355937 | + | 0.934510i | \(0.615838\pi\) | |||||||
\(258\) | −1734.04 | −0.418436 | ||||||||
\(259\) | 381.651 | 0.0915624 | ||||||||
\(260\) | 847.154 | 0.202070 | ||||||||
\(261\) | 684.707 | 0.162384 | ||||||||
\(262\) | −2796.95 | −0.659527 | ||||||||
\(263\) | 2494.46 | 0.584848 | 0.292424 | − | 0.956289i | \(-0.405538\pi\) | ||||
0.292424 | + | 0.956289i | \(0.405538\pi\) | |||||||
\(264\) | 799.272 | 0.186333 | ||||||||
\(265\) | 591.548 | 0.137126 | ||||||||
\(266\) | 1055.29 | 0.243247 | ||||||||
\(267\) | 247.684 | 0.0567715 | ||||||||
\(268\) | 3594.74 | 0.819343 | ||||||||
\(269\) | −3438.38 | −0.779337 | −0.389669 | − | 0.920955i | \(-0.627410\pi\) | ||||
−0.389669 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(270\) | 159.004 | 0.0358396 | ||||||||
\(271\) | −6653.18 | −1.49134 | −0.745668 | − | 0.666318i | \(-0.767869\pi\) | ||||
−0.745668 | + | 0.666318i | \(0.767869\pi\) | |||||||
\(272\) | 855.267 | 0.190655 | ||||||||
\(273\) | −1510.45 | −0.334860 | ||||||||
\(274\) | −3941.18 | −0.868962 | ||||||||
\(275\) | −3874.13 | −0.849523 | ||||||||
\(276\) | −276.000 | −0.0601929 | ||||||||
\(277\) | 556.075 | 0.120618 | 0.0603092 | − | 0.998180i | \(-0.480791\pi\) | ||||
0.0603092 | + | 0.998180i | \(0.480791\pi\) | |||||||
\(278\) | 1148.22 | 0.247718 | ||||||||
\(279\) | 1353.33 | 0.290400 | ||||||||
\(280\) | −164.893 | −0.0351938 | ||||||||
\(281\) | −6620.16 | −1.40543 | −0.702714 | − | 0.711472i | \(-0.748029\pi\) | ||||
−0.702714 | + | 0.711472i | \(0.748029\pi\) | |||||||
\(282\) | −216.727 | −0.0457656 | ||||||||
\(283\) | 8294.89 | 1.74233 | 0.871167 | − | 0.490988i | \(-0.163364\pi\) | ||||
0.871167 | + | 0.490988i | \(0.163364\pi\) | |||||||
\(284\) | 2064.15 | 0.431284 | ||||||||
\(285\) | −665.853 | −0.138392 | ||||||||
\(286\) | 4790.73 | 0.990495 | ||||||||
\(287\) | 1559.34 | 0.320714 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −2055.65 | −0.418410 | ||||||||
\(290\) | 448.029 | 0.0907214 | ||||||||
\(291\) | −886.873 | −0.178658 | ||||||||
\(292\) | −2649.81 | −0.531057 | ||||||||
\(293\) | 5145.52 | 1.02595 | 0.512977 | − | 0.858402i | \(-0.328543\pi\) | ||||
0.512977 | + | 0.858402i | \(0.328543\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 2662.08 | 0.525398 | ||||||||
\(296\) | −436.173 | −0.0856488 | ||||||||
\(297\) | 899.181 | 0.175676 | ||||||||
\(298\) | −3868.82 | −0.752062 | ||||||||
\(299\) | −1654.31 | −0.319970 | ||||||||
\(300\) | −1395.96 | −0.268652 | ||||||||
\(301\) | 2023.05 | 0.387397 | ||||||||
\(302\) | 2488.74 | 0.474208 | ||||||||
\(303\) | 5287.42 | 1.00249 | ||||||||
\(304\) | −1206.04 | −0.227537 | ||||||||
\(305\) | 1856.08 | 0.348456 | ||||||||
\(306\) | 962.176 | 0.179751 | ||||||||
\(307\) | −1701.99 | −0.316409 | −0.158205 | − | 0.987406i | \(-0.550571\pi\) | ||||
−0.158205 | + | 0.987406i | \(0.550571\pi\) | |||||||
\(308\) | −932.484 | −0.172510 | ||||||||
\(309\) | −4175.47 | −0.768720 | ||||||||
\(310\) | 885.535 | 0.162242 | ||||||||
\(311\) | −9623.56 | −1.75467 | −0.877334 | − | 0.479880i | \(-0.840680\pi\) | ||||
−0.877334 | + | 0.479880i | \(0.840680\pi\) | |||||||
\(312\) | 1726.23 | 0.313233 | ||||||||
\(313\) | −4845.60 | −0.875047 | −0.437524 | − | 0.899207i | \(-0.644144\pi\) | ||||
−0.437524 | + | 0.899207i | \(0.644144\pi\) | |||||||
\(314\) | −5199.35 | −0.934447 | ||||||||
\(315\) | −185.505 | −0.0331810 | ||||||||
\(316\) | 5386.14 | 0.958843 | ||||||||
\(317\) | −290.347 | −0.0514433 | −0.0257216 | − | 0.999669i | \(-0.508188\pi\) | ||||
−0.0257216 | + | 0.999669i | \(0.508188\pi\) | |||||||
\(318\) | 1205.39 | 0.212562 | ||||||||
\(319\) | 2533.64 | 0.444692 | ||||||||
\(320\) | 188.449 | 0.0329207 | ||||||||
\(321\) | 95.4876 | 0.0166031 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | −4029.25 | −0.694097 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −8367.18 | −1.42808 | ||||||||
\(326\) | 2293.85 | 0.389708 | ||||||||
\(327\) | −4173.71 | −0.705831 | ||||||||
\(328\) | −1782.10 | −0.300001 | ||||||||
\(329\) | 252.848 | 0.0423707 | ||||||||
\(330\) | 588.368 | 0.0981473 | ||||||||
\(331\) | 8780.35 | 1.45804 | 0.729021 | − | 0.684491i | \(-0.239976\pi\) | ||||
0.729021 | + | 0.684491i | \(0.239976\pi\) | |||||||
\(332\) | −400.649 | −0.0662304 | ||||||||
\(333\) | −490.695 | −0.0807505 | ||||||||
\(334\) | −4575.32 | −0.749552 | ||||||||
\(335\) | 2646.20 | 0.431574 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 4249.59 | 0.686913 | 0.343457 | − | 0.939169i | \(-0.388402\pi\) | ||||
0.343457 | + | 0.939169i | \(0.388402\pi\) | |||||||
\(338\) | 5952.80 | 0.957957 | ||||||||
\(339\) | −1573.05 | −0.252025 | ||||||||
\(340\) | 629.588 | 0.100424 | ||||||||
\(341\) | 5007.77 | 0.795267 | ||||||||
\(342\) | −1356.80 | −0.214524 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −2312.05 | −0.362377 | ||||||||
\(345\) | −203.172 | −0.0317055 | ||||||||
\(346\) | 2254.47 | 0.350292 | ||||||||
\(347\) | −1210.90 | −0.187333 | −0.0936666 | − | 0.995604i | \(-0.529859\pi\) | ||||
−0.0936666 | + | 0.995604i | \(0.529859\pi\) | |||||||
\(348\) | 912.942 | 0.140629 | ||||||||
\(349\) | −12420.0 | −1.90495 | −0.952476 | − | 0.304613i | \(-0.901473\pi\) | ||||
−0.952476 | + | 0.304613i | \(0.901473\pi\) | |||||||
\(350\) | 1628.62 | 0.248724 | ||||||||
\(351\) | 1942.01 | 0.295319 | ||||||||
\(352\) | 1065.70 | 0.161369 | ||||||||
\(353\) | 2920.86 | 0.440401 | 0.220201 | − | 0.975455i | \(-0.429329\pi\) | ||||
0.220201 | + | 0.975455i | \(0.429329\pi\) | |||||||
\(354\) | 5424.47 | 0.814428 | ||||||||
\(355\) | 1519.48 | 0.227171 | ||||||||
\(356\) | 330.245 | 0.0491656 | ||||||||
\(357\) | −1122.54 | −0.166417 | ||||||||
\(358\) | −275.584 | −0.0406845 | ||||||||
\(359\) | −8083.24 | −1.18835 | −0.594174 | − | 0.804336i | \(-0.702521\pi\) | ||||
−0.594174 | + | 0.804336i | \(0.702521\pi\) | |||||||
\(360\) | 212.006 | 0.0310380 | ||||||||
\(361\) | −1177.22 | −0.171631 | ||||||||
\(362\) | −2024.40 | −0.293923 | ||||||||
\(363\) | −665.729 | −0.0962582 | ||||||||
\(364\) | −2013.94 | −0.289997 | ||||||||
\(365\) | −1950.61 | −0.279725 | ||||||||
\(366\) | 3782.11 | 0.540147 | ||||||||
\(367\) | −2067.09 | −0.294009 | −0.147005 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147005 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −2004.87 | −0.282843 | ||||||||
\(370\) | −321.080 | −0.0451140 | ||||||||
\(371\) | −1406.29 | −0.196794 | ||||||||
\(372\) | 1804.44 | 0.251494 | ||||||||
\(373\) | 1597.92 | 0.221815 | 0.110908 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110908 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(374\) | 3560.37 | 0.492252 | ||||||||
\(375\) | −2131.80 | −0.293562 | ||||||||
\(376\) | −288.969 | −0.0396342 | ||||||||
\(377\) | 5472.05 | 0.747546 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | 10840.4 | 1.46922 | 0.734610 | − | 0.678490i | \(-0.237365\pi\) | ||||
0.734610 | + | 0.678490i | \(0.237365\pi\) | |||||||
\(380\) | −887.804 | −0.119851 | ||||||||
\(381\) | 140.862 | 0.0189412 | ||||||||
\(382\) | −4103.82 | −0.549659 | ||||||||
\(383\) | −12198.6 | −1.62747 | −0.813733 | − | 0.581239i | \(-0.802568\pi\) | ||||
−0.813733 | + | 0.581239i | \(0.802568\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −686.430 | −0.0908668 | ||||||||
\(386\) | 2254.03 | 0.297221 | ||||||||
\(387\) | −2601.06 | −0.341652 | ||||||||
\(388\) | −1182.50 | −0.154722 | ||||||||
\(389\) | −3120.09 | −0.406671 | −0.203335 | − | 0.979109i | \(-0.565178\pi\) | ||||
−0.203335 | + | 0.979109i | \(0.565178\pi\) | |||||||
\(390\) | 1270.73 | 0.164990 | ||||||||
\(391\) | −1229.45 | −0.159017 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −4195.42 | −0.538502 | ||||||||
\(394\) | 207.276 | 0.0265036 | ||||||||
\(395\) | 3964.90 | 0.505053 | ||||||||
\(396\) | 1198.91 | 0.152140 | ||||||||
\(397\) | −307.495 | −0.0388734 | −0.0194367 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194367 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(398\) | −1138.37 | −0.143370 | ||||||||
\(399\) | 1582.93 | 0.198611 | ||||||||
\(400\) | −1861.28 | −0.232660 | ||||||||
\(401\) | −8087.81 | −1.00720 | −0.503598 | − | 0.863938i | \(-0.667991\pi\) | ||||
−0.503598 | + | 0.863938i | \(0.667991\pi\) | |||||||
\(402\) | 5392.11 | 0.668990 | ||||||||
\(403\) | 10815.6 | 1.33688 | ||||||||
\(404\) | 7049.89 | 0.868181 | ||||||||
\(405\) | 238.506 | 0.0292629 | ||||||||
\(406\) | −1065.10 | −0.130197 | ||||||||
\(407\) | −1815.73 | −0.221137 | ||||||||
\(408\) | 1282.90 | 0.155669 | ||||||||
\(409\) | −2563.65 | −0.309937 | −0.154968 | − | 0.987919i | \(-0.549528\pi\) | ||||
−0.154968 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(410\) | −1311.86 | −0.158020 | ||||||||
\(411\) | −5911.77 | −0.709504 | ||||||||
\(412\) | −5567.30 | −0.665731 | ||||||||
\(413\) | −6328.55 | −0.754014 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | −294.930 | −0.0348857 | ||||||||
\(416\) | 2301.64 | 0.271268 | ||||||||
\(417\) | 1722.33 | 0.202261 | ||||||||
\(418\) | −5020.60 | −0.587478 | ||||||||
\(419\) | −4312.73 | −0.502842 | −0.251421 | − | 0.967878i | \(-0.580898\pi\) | ||||
−0.251421 | + | 0.967878i | \(0.580898\pi\) | |||||||
\(420\) | −247.340 | −0.0287356 | ||||||||
\(421\) | −9798.57 | −1.13433 | −0.567165 | − | 0.823604i | \(-0.691960\pi\) | ||||
−0.567165 | + | 0.823604i | \(0.691960\pi\) | |||||||
\(422\) | −8097.71 | −0.934100 | ||||||||
\(423\) | −325.090 | −0.0373675 | ||||||||
\(424\) | 1607.18 | 0.184084 | ||||||||
\(425\) | −6218.32 | −0.709724 | ||||||||
\(426\) | 3096.22 | 0.352142 | ||||||||
\(427\) | −4412.46 | −0.500079 | ||||||||
\(428\) | 127.317 | 0.0143787 | ||||||||
\(429\) | 7186.09 | 0.808736 | ||||||||
\(430\) | −1701.97 | −0.190875 | ||||||||
\(431\) | 295.391 | 0.0330127 | 0.0165064 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165064 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 12791.4 | 1.41966 | 0.709831 | − | 0.704372i | \(-0.248771\pi\) | ||||
0.709831 | + | 0.704372i | \(0.248771\pi\) | |||||||
\(434\) | −2105.18 | −0.232838 | ||||||||
\(435\) | 672.044 | 0.0740737 | ||||||||
\(436\) | −5564.95 | −0.611268 | ||||||||
\(437\) | 1733.68 | 0.189779 | ||||||||
\(438\) | −3974.72 | −0.433606 | ||||||||
\(439\) | 17695.4 | 1.92382 | 0.961910 | − | 0.273365i | \(-0.0881367\pi\) | ||||
0.961910 | + | 0.273365i | \(0.0881367\pi\) | |||||||
\(440\) | 784.491 | 0.0849981 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 7689.53 | 0.827497 | ||||||||
\(443\) | 3077.45 | 0.330054 | 0.165027 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165027 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(444\) | −654.260 | −0.0699320 | ||||||||
\(445\) | 243.103 | 0.0258971 | ||||||||
\(446\) | 1931.42 | 0.205057 | ||||||||
\(447\) | −5803.23 | −0.614056 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −15712.1 | −1.65145 | −0.825726 | − | 0.564072i | \(-0.809234\pi\) | ||||
−0.825726 | + | 0.564072i | \(0.809234\pi\) | |||||||
\(450\) | −2093.94 | −0.219354 | ||||||||
\(451\) | −7418.68 | −0.774572 | ||||||||
\(452\) | −2097.40 | −0.218260 | ||||||||
\(453\) | 3733.11 | 0.387189 | ||||||||
\(454\) | −5647.42 | −0.583803 | ||||||||
\(455\) | −1482.52 | −0.152751 | ||||||||
\(456\) | −1809.06 | −0.185783 | ||||||||
\(457\) | 3434.37 | 0.351539 | 0.175769 | − | 0.984431i | \(-0.443759\pi\) | ||||
0.175769 | + | 0.984431i | \(0.443759\pi\) | |||||||
\(458\) | 4207.08 | 0.429222 | ||||||||
\(459\) | 1443.26 | 0.146766 | ||||||||
\(460\) | −270.896 | −0.0274578 | ||||||||
\(461\) | 14522.0 | 1.46715 | 0.733577 | − | 0.679606i | \(-0.237849\pi\) | ||||
0.733577 | + | 0.679606i | \(0.237849\pi\) | |||||||
\(462\) | −1398.73 | −0.140854 | ||||||||
\(463\) | −12851.4 | −1.28997 | −0.644985 | − | 0.764196i | \(-0.723136\pi\) | ||||
−0.644985 | + | 0.764196i | \(0.723136\pi\) | |||||||
\(464\) | 1217.26 | 0.121788 | ||||||||
\(465\) | 1328.30 | 0.132470 | ||||||||
\(466\) | 4869.71 | 0.484088 | ||||||||
\(467\) | −13061.3 | −1.29423 | −0.647116 | − | 0.762392i | \(-0.724025\pi\) | ||||
−0.647116 | + | 0.762392i | \(0.724025\pi\) | |||||||
\(468\) | 2589.35 | 0.255754 | ||||||||
\(469\) | −6290.80 | −0.619365 | ||||||||
\(470\) | −212.719 | −0.0208766 | ||||||||
\(471\) | −7799.03 | −0.762973 | ||||||||
\(472\) | 7232.63 | 0.705315 | ||||||||
\(473\) | −9624.79 | −0.935620 | ||||||||
\(474\) | 8079.22 | 0.782892 | ||||||||
\(475\) | 8768.66 | 0.847018 | ||||||||
\(476\) | −1496.72 | −0.144122 | ||||||||
\(477\) | 1808.08 | 0.173556 | ||||||||
\(478\) | 4904.83 | 0.469334 | ||||||||
\(479\) | −17584.0 | −1.67732 | −0.838659 | − | 0.544657i | \(-0.816660\pi\) | ||||
−0.838659 | + | 0.544657i | \(0.816660\pi\) | |||||||
\(480\) | 282.674 | 0.0268797 | ||||||||
\(481\) | −3921.54 | −0.371740 | ||||||||
\(482\) | −4170.71 | −0.394130 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −887.639 | −0.0833620 | ||||||||
\(485\) | −870.472 | −0.0814971 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 10252.0 | 0.953923 | 0.476962 | − | 0.878924i | \(-0.341738\pi\) | ||||
0.476962 | + | 0.878924i | \(0.341738\pi\) | |||||||
\(488\) | 5042.81 | 0.467781 | ||||||||
\(489\) | 3440.78 | 0.318195 | ||||||||
\(490\) | 288.563 | 0.0266040 | ||||||||
\(491\) | 15948.2 | 1.46585 | 0.732926 | − | 0.680309i | \(-0.238154\pi\) | ||||
0.732926 | + | 0.680309i | \(0.238154\pi\) | |||||||
\(492\) | −2673.16 | −0.244950 | ||||||||
\(493\) | 4066.72 | 0.371512 | ||||||||
\(494\) | −10843.3 | −0.987574 | ||||||||
\(495\) | 882.553 | 0.0801370 | ||||||||
\(496\) | 2405.92 | 0.217800 | ||||||||
\(497\) | −3612.26 | −0.326020 | ||||||||
\(498\) | −600.974 | −0.0540769 | ||||||||
\(499\) | 19414.2 | 1.74169 | 0.870843 | − | 0.491562i | \(-0.163574\pi\) | ||||
0.870843 | + | 0.491562i | \(0.163574\pi\) | |||||||
\(500\) | −2842.40 | −0.254232 | ||||||||
\(501\) | −6862.98 | −0.612007 | ||||||||
\(502\) | 1567.23 | 0.139341 | ||||||||
\(503\) | −14362.5 | −1.27315 | −0.636575 | − | 0.771215i | \(-0.719649\pi\) | ||||
−0.636575 | + | 0.771215i | \(0.719649\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | 5189.64 | 0.457299 | ||||||||
\(506\) | −1531.94 | −0.134591 | ||||||||
\(507\) | 8929.20 | 0.782169 | ||||||||
\(508\) | 187.817 | 0.0164036 | ||||||||
\(509\) | −7843.00 | −0.682976 | −0.341488 | − | 0.939886i | \(-0.610931\pi\) | ||||
−0.341488 | + | 0.939886i | \(0.610931\pi\) | |||||||
\(510\) | 944.382 | 0.0819960 | ||||||||
\(511\) | 4637.17 | 0.401441 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −2035.20 | −0.175158 | ||||||||
\(514\) | −5865.88 | −0.503371 | ||||||||
\(515\) | −4098.26 | −0.350662 | ||||||||
\(516\) | −3468.08 | −0.295879 | ||||||||
\(517\) | −1202.94 | −0.102331 | ||||||||
\(518\) | 763.303 | 0.0647444 | ||||||||
\(519\) | 3381.70 | 0.286012 | ||||||||
\(520\) | 1694.31 | 0.142885 | ||||||||
\(521\) | −14344.2 | −1.20620 | −0.603099 | − | 0.797666i | \(-0.706068\pi\) | ||||
−0.603099 | + | 0.797666i | \(0.706068\pi\) | |||||||
\(522\) | 1369.41 | 0.114823 | ||||||||
\(523\) | 7691.98 | 0.643110 | 0.321555 | − | 0.946891i | \(-0.395794\pi\) | ||||
0.321555 | + | 0.946891i | \(0.395794\pi\) | |||||||
\(524\) | −5593.90 | −0.466356 | ||||||||
\(525\) | 2442.93 | 0.203082 | ||||||||
\(526\) | 4988.92 | 0.413550 | ||||||||
\(527\) | 8037.90 | 0.664396 | ||||||||
\(528\) | 1598.54 | 0.131757 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 1183.10 | 0.0969630 | ||||||||
\(531\) | 8136.71 | 0.664978 | ||||||||
\(532\) | 2110.57 | 0.172002 | ||||||||
\(533\) | −16022.5 | −1.30209 | ||||||||
\(534\) | 495.367 | 0.0401435 | ||||||||
\(535\) | 93.7217 | 0.00757373 | ||||||||
\(536\) | 7189.48 | 0.579363 | ||||||||
\(537\) | −413.376 | −0.0332188 | ||||||||
\(538\) | −6876.76 | −0.551074 | ||||||||
\(539\) | 1631.85 | 0.130406 | ||||||||
\(540\) | 318.008 | 0.0253424 | ||||||||
\(541\) | 21129.9 | 1.67920 | 0.839599 | − | 0.543207i | \(-0.182790\pi\) | ||||
0.839599 | + | 0.543207i | \(0.182790\pi\) | |||||||
\(542\) | −13306.4 | −1.05453 | ||||||||
\(543\) | −3036.61 | −0.239987 | ||||||||
\(544\) | 1710.53 | 0.134814 | ||||||||
\(545\) | −4096.53 | −0.321974 | ||||||||
\(546\) | −3020.91 | −0.236782 | ||||||||
\(547\) | −24249.4 | −1.89549 | −0.947744 | − | 0.319033i | \(-0.896642\pi\) | ||||
−0.947744 | + | 0.319033i | \(0.896642\pi\) | |||||||
\(548\) | −7882.36 | −0.614449 | ||||||||
\(549\) | 5673.16 | 0.441028 | ||||||||
\(550\) | −7748.26 | −0.600704 | ||||||||
\(551\) | −5734.62 | −0.443381 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | −9425.75 | −0.724817 | ||||||||
\(554\) | 1112.15 | 0.0852901 | ||||||||
\(555\) | −481.620 | −0.0368354 | ||||||||
\(556\) | 2296.44 | 0.175163 | ||||||||
\(557\) | 6400.10 | 0.486860 | 0.243430 | − | 0.969918i | \(-0.421727\pi\) | ||||
0.243430 | + | 0.969918i | \(0.421727\pi\) | |||||||
\(558\) | 2706.66 | 0.205344 | ||||||||
\(559\) | −20787.2 | −1.57282 | ||||||||
\(560\) | −329.786 | −0.0248857 | ||||||||
\(561\) | 5340.56 | 0.401922 | ||||||||
\(562\) | −13240.3 | −0.993788 | ||||||||
\(563\) | −19067.7 | −1.42737 | −0.713685 | − | 0.700467i | \(-0.752975\pi\) | ||||
−0.713685 | + | 0.700467i | \(0.752975\pi\) | |||||||
\(564\) | −433.454 | −0.0323612 | ||||||||
\(565\) | −1543.96 | −0.114964 | ||||||||
\(566\) | 16589.8 | 1.23202 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 4128.29 | 0.304964 | ||||||||
\(569\) | −378.905 | −0.0279165 | −0.0139583 | − | 0.999903i | \(-0.504443\pi\) | ||||
−0.0139583 | + | 0.999903i | \(0.504443\pi\) | |||||||
\(570\) | −1331.71 | −0.0978579 | ||||||||
\(571\) | 20250.2 | 1.48414 | 0.742071 | − | 0.670321i | \(-0.233844\pi\) | ||||
0.742071 | + | 0.670321i | \(0.233844\pi\) | |||||||
\(572\) | 9581.45 | 0.700386 | ||||||||
\(573\) | −6155.73 | −0.448794 | ||||||||
\(574\) | 3118.68 | 0.226779 | ||||||||
\(575\) | 2675.59 | 0.194052 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −11763.4 | −0.848730 | −0.424365 | − | 0.905491i | \(-0.639503\pi\) | ||||
−0.424365 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(578\) | −4111.30 | −0.295861 | ||||||||
\(579\) | 3381.05 | 0.242680 | ||||||||
\(580\) | 896.059 | 0.0641497 | ||||||||
\(581\) | 701.136 | 0.0500655 | ||||||||
\(582\) | −1773.75 | −0.126330 | ||||||||
\(583\) | 6690.50 | 0.475287 | ||||||||
\(584\) | −5299.63 | −0.375514 | ||||||||
\(585\) | 1906.10 | 0.134714 | ||||||||
\(586\) | 10291.0 | 0.725459 | ||||||||
\(587\) | 4307.93 | 0.302909 | 0.151454 | − | 0.988464i | \(-0.451604\pi\) | ||||
0.151454 | + | 0.988464i | \(0.451604\pi\) | |||||||
\(588\) | 588.000 | 0.0412393 | ||||||||
\(589\) | −11334.5 | −0.792922 | ||||||||
\(590\) | 5324.16 | 0.371512 | ||||||||
\(591\) | 310.914 | 0.0216401 | ||||||||
\(592\) | −872.346 | −0.0605628 | ||||||||
\(593\) | −3726.45 | −0.258055 | −0.129028 | − | 0.991641i | \(-0.541186\pi\) | ||||
−0.129028 | + | 0.991641i | \(0.541186\pi\) | |||||||
\(594\) | 1798.36 | 0.124222 | ||||||||
\(595\) | −1101.78 | −0.0759135 | ||||||||
\(596\) | −7737.63 | −0.531788 | ||||||||
\(597\) | −1707.55 | −0.117061 | ||||||||
\(598\) | −3308.61 | −0.226253 | ||||||||
\(599\) | −1077.77 | −0.0735163 | −0.0367582 | − | 0.999324i | \(-0.511703\pi\) | ||||
−0.0367582 | + | 0.999324i | \(0.511703\pi\) | |||||||
\(600\) | −2791.92 | −0.189966 | ||||||||
\(601\) | 9085.00 | 0.616614 | 0.308307 | − | 0.951287i | \(-0.400238\pi\) | ||||
0.308307 | + | 0.951287i | \(0.400238\pi\) | |||||||
\(602\) | 4046.09 | 0.273931 | ||||||||
\(603\) | 8088.17 | 0.546228 | ||||||||
\(604\) | 4977.47 | 0.335316 | ||||||||
\(605\) | −653.418 | −0.0439094 | ||||||||
\(606\) | 10574.8 | 0.708867 | ||||||||
\(607\) | −21094.5 | −1.41055 | −0.705273 | − | 0.708936i | \(-0.749176\pi\) | ||||
−0.705273 | + | 0.708936i | \(0.749176\pi\) | |||||||
\(608\) | −2412.08 | −0.160893 | ||||||||
\(609\) | −1597.65 | −0.106305 | ||||||||
\(610\) | 3712.16 | 0.246395 | ||||||||
\(611\) | −2598.06 | −0.172023 | ||||||||
\(612\) | 1924.35 | 0.127103 | ||||||||
\(613\) | 11427.4 | 0.752931 | 0.376465 | − | 0.926431i | \(-0.377139\pi\) | ||||
0.376465 | + | 0.926431i | \(0.377139\pi\) | |||||||
\(614\) | −3403.98 | −0.223735 | ||||||||
\(615\) | −1967.79 | −0.129023 | ||||||||
\(616\) | −1864.97 | −0.121983 | ||||||||
\(617\) | 10113.8 | 0.659911 | 0.329955 | − | 0.943997i | \(-0.392966\pi\) | ||||
0.329955 | + | 0.943997i | \(0.392966\pi\) | |||||||
\(618\) | −8350.95 | −0.543567 | ||||||||
\(619\) | −13563.4 | −0.880706 | −0.440353 | − | 0.897825i | \(-0.645147\pi\) | ||||
−0.440353 | + | 0.897825i | \(0.645147\pi\) | |||||||
\(620\) | 1771.07 | 0.114722 | ||||||||
\(621\) | −621.000 | −0.0401286 | ||||||||
\(622\) | −19247.1 | −1.24074 | ||||||||
\(623\) | −577.928 | −0.0371657 | ||||||||
\(624\) | 3452.46 | 0.221489 | ||||||||
\(625\) | 12448.8 | 0.796726 | ||||||||
\(626\) | −9691.21 | −0.618752 | ||||||||
\(627\) | −7530.90 | −0.479673 | ||||||||
\(628\) | −10398.7 | −0.660754 | ||||||||
\(629\) | −2914.41 | −0.184746 | ||||||||
\(630\) | −371.010 | −0.0234625 | ||||||||
\(631\) | −2862.30 | −0.180580 | −0.0902902 | − | 0.995915i | \(-0.528779\pi\) | ||||
−0.0902902 | + | 0.995915i | \(0.528779\pi\) | |||||||
\(632\) | 10772.3 | 0.678004 | ||||||||
\(633\) | −12146.6 | −0.762690 | ||||||||
\(634\) | −580.694 | −0.0363759 | ||||||||
\(635\) | 138.257 | 0.00864028 | ||||||||
\(636\) | 2410.77 | 0.150304 | ||||||||
\(637\) | 3524.39 | 0.219217 | ||||||||
\(638\) | 5067.29 | 0.314445 | ||||||||
\(639\) | 4644.33 | 0.287522 | ||||||||
\(640\) | 376.899 | 0.0232785 | ||||||||
\(641\) | 1986.61 | 0.122413 | 0.0612064 | − | 0.998125i | \(-0.480505\pi\) | ||||
0.0612064 | + | 0.998125i | \(0.480505\pi\) | |||||||
\(642\) | 190.975 | 0.0117402 | ||||||||
\(643\) | −6395.67 | −0.392256 | −0.196128 | − | 0.980578i | \(-0.562837\pi\) | ||||
−0.196128 | + | 0.980578i | \(0.562837\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | −2552.96 | −0.155849 | ||||||||
\(646\) | −8058.50 | −0.490801 | ||||||||
\(647\) | −9918.22 | −0.602667 | −0.301333 | − | 0.953519i | \(-0.597432\pi\) | ||||
−0.301333 | + | 0.953519i | \(0.597432\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 30108.6 | 1.82105 | ||||||||
\(650\) | −16734.4 | −1.00981 | ||||||||
\(651\) | −3157.77 | −0.190112 | ||||||||
\(652\) | 4587.71 | 0.275565 | ||||||||
\(653\) | 2677.52 | 0.160459 | 0.0802294 | − | 0.996776i | \(-0.474435\pi\) | ||||
0.0802294 | + | 0.996776i | \(0.474435\pi\) | |||||||
\(654\) | −8347.42 | −0.499098 | ||||||||
\(655\) | −4117.84 | −0.245645 | ||||||||
\(656\) | −3564.21 | −0.212133 | ||||||||
\(657\) | −5962.08 | −0.354038 | ||||||||
\(658\) | 505.696 | 0.0299606 | ||||||||
\(659\) | 17641.4 | 1.04281 | 0.521405 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521405 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(660\) | 1176.74 | 0.0694006 | ||||||||
\(661\) | 18089.5 | 1.06445 | 0.532224 | − | 0.846604i | \(-0.321356\pi\) | ||||
0.532224 | + | 0.846604i | \(0.321356\pi\) | |||||||
\(662\) | 17560.7 | 1.03099 | ||||||||
\(663\) | 11534.3 | 0.675648 | ||||||||
\(664\) | −801.299 | −0.0468320 | ||||||||
\(665\) | 1553.66 | 0.0905988 | ||||||||
\(666\) | −981.389 | −0.0570992 | ||||||||
\(667\) | −1749.81 | −0.101578 | ||||||||
\(668\) | −9150.64 | −0.530013 | ||||||||
\(669\) | 2897.13 | 0.167428 | ||||||||
\(670\) | 5292.40 | 0.305169 | ||||||||
\(671\) | 20992.6 | 1.20776 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 7886.75 | 0.451727 | 0.225863 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225863 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(674\) | 8499.18 | 0.485721 | ||||||||
\(675\) | −3140.90 | −0.179101 | ||||||||
\(676\) | 11905.6 | 0.677378 | ||||||||
\(677\) | 3790.70 | 0.215197 | 0.107599 | − | 0.994194i | \(-0.465684\pi\) | ||||
0.107599 | + | 0.994194i | \(0.465684\pi\) | |||||||
\(678\) | −3146.10 | −0.178209 | ||||||||
\(679\) | 2069.37 | 0.116959 | ||||||||
\(680\) | 1259.18 | 0.0710106 | ||||||||
\(681\) | −8471.14 | −0.476674 | ||||||||
\(682\) | 10015.5 | 0.562339 | ||||||||
\(683\) | 25479.3 | 1.42743 | 0.713717 | − | 0.700435i | \(-0.247010\pi\) | ||||
0.713717 | + | 0.700435i | \(0.247010\pi\) | |||||||
\(684\) | −2713.59 | −0.151691 | ||||||||
\(685\) | −5802.45 | −0.323650 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 6310.62 | 0.350459 | ||||||||
\(688\) | −4624.11 | −0.256239 | ||||||||
\(689\) | 14449.8 | 0.798977 | ||||||||
\(690\) | −406.344 | −0.0224192 | ||||||||
\(691\) | 25749.2 | 1.41758 | 0.708790 | − | 0.705420i | \(-0.249242\pi\) | ||||
0.708790 | + | 0.705420i | \(0.249242\pi\) | |||||||
\(692\) | 4508.94 | 0.247694 | ||||||||
\(693\) | −2098.09 | −0.115007 | ||||||||
\(694\) | −2421.80 | −0.132465 | ||||||||
\(695\) | 1690.48 | 0.0922640 | ||||||||
\(696\) | 1825.88 | 0.0994396 | ||||||||
\(697\) | −11907.6 | −0.647106 | ||||||||
\(698\) | −24840.0 | −1.34700 | ||||||||
\(699\) | 7304.57 | 0.395256 | ||||||||
\(700\) | 3257.23 | 0.175874 | ||||||||
\(701\) | −30576.6 | −1.64745 | −0.823726 | − | 0.566988i | \(-0.808108\pi\) | ||||
−0.823726 | + | 0.566988i | \(0.808108\pi\) | |||||||
\(702\) | 3884.02 | 0.208822 | ||||||||
\(703\) | 4109.71 | 0.220485 | ||||||||
\(704\) | 2131.39 | 0.114105 | ||||||||
\(705\) | −319.078 | −0.0170457 | ||||||||
\(706\) | 5841.72 | 0.311411 | ||||||||
\(707\) | −12337.3 | −0.656283 | ||||||||
\(708\) | 10848.9 | 0.575888 | ||||||||
\(709\) | 3594.18 | 0.190384 | 0.0951921 | − | 0.995459i | \(-0.469653\pi\) | ||||
0.0951921 | + | 0.995459i | \(0.469653\pi\) | |||||||
\(710\) | 3038.96 | 0.160634 | ||||||||
\(711\) | 12118.8 | 0.639228 | ||||||||
\(712\) | 660.490 | 0.0347653 | ||||||||
\(713\) | −3458.51 | −0.181658 | ||||||||
\(714\) | −2245.08 | −0.117675 | ||||||||
\(715\) | 7053.20 | 0.368916 | ||||||||
\(716\) | −551.167 | −0.0287683 | ||||||||
\(717\) | 7357.25 | 0.383210 | ||||||||
\(718\) | −16166.5 | −0.840290 | ||||||||
\(719\) | −18314.9 | −0.949974 | −0.474987 | − | 0.879993i | \(-0.657547\pi\) | ||||
−0.474987 | + | 0.879993i | \(0.657547\pi\) | |||||||
\(720\) | 424.011 | 0.0219472 | ||||||||
\(721\) | 9742.77 | 0.503245 | ||||||||
\(722\) | −2354.43 | −0.121361 | ||||||||
\(723\) | −6256.07 | −0.321806 | ||||||||
\(724\) | −4048.81 | −0.207835 | ||||||||
\(725\) | −8850.20 | −0.453363 | ||||||||
\(726\) | −1331.46 | −0.0680648 | ||||||||
\(727\) | 12672.9 | 0.646511 | 0.323255 | − | 0.946312i | \(-0.395223\pi\) | ||||
0.323255 | + | 0.946312i | \(0.395223\pi\) | |||||||
\(728\) | −4027.88 | −0.205059 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3901.21 | −0.197795 | ||||||||
\(731\) | −15448.6 | −0.781652 | ||||||||
\(732\) | 7564.21 | 0.381942 | ||||||||
\(733\) | 18048.3 | 0.909454 | 0.454727 | − | 0.890631i | \(-0.349737\pi\) | ||||
0.454727 | + | 0.890631i | \(0.349737\pi\) | |||||||
\(734\) | −4134.18 | −0.207896 | ||||||||
\(735\) | 432.845 | 0.0217221 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 29928.9 | 1.49586 | ||||||||
\(738\) | −4009.73 | −0.200000 | ||||||||
\(739\) | 31405.8 | 1.56330 | 0.781652 | − | 0.623715i | \(-0.214377\pi\) | ||||
0.781652 | + | 0.623715i | \(0.214377\pi\) | |||||||
\(740\) | −642.160 | −0.0319004 | ||||||||
\(741\) | −16264.9 | −0.806351 | ||||||||
\(742\) | −2812.57 | −0.139155 | ||||||||
\(743\) | −23718.8 | −1.17114 | −0.585571 | − | 0.810621i | \(-0.699129\pi\) | ||||
−0.585571 | + | 0.810621i | \(0.699129\pi\) | |||||||
\(744\) | 3608.88 | 0.177833 | ||||||||
\(745\) | −5695.91 | −0.280110 | ||||||||
\(746\) | 3195.84 | 0.156847 | ||||||||
\(747\) | −901.461 | −0.0441536 | ||||||||
\(748\) | 7120.74 | 0.348075 | ||||||||
\(749\) | −222.804 | −0.0108693 | ||||||||
\(750\) | −4263.60 | −0.207580 | ||||||||
\(751\) | 4139.21 | 0.201121 | 0.100561 | − | 0.994931i | \(-0.467936\pi\) | ||||
0.100561 | + | 0.994931i | \(0.467936\pi\) | |||||||
\(752\) | −577.938 | −0.0280256 | ||||||||
\(753\) | 2350.85 | 0.113771 | ||||||||
\(754\) | 10944.1 | 0.528595 | ||||||||
\(755\) | 3664.07 | 0.176621 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | −7001.52 | −0.336162 | −0.168081 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168081 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(758\) | 21680.8 | 1.03890 | ||||||||
\(759\) | −2297.91 | −0.109893 | ||||||||
\(760\) | −1775.61 | −0.0847474 | ||||||||
\(761\) | −36988.0 | −1.76191 | −0.880955 | − | 0.473200i | \(-0.843099\pi\) | ||||
−0.880955 | + | 0.473200i | \(0.843099\pi\) | |||||||
\(762\) | 281.725 | 0.0133935 | ||||||||
\(763\) | 9738.66 | 0.462075 | ||||||||
\(764\) | −8207.63 | −0.388667 | ||||||||
\(765\) | 1416.57 | 0.0669494 | ||||||||
\(766\) | −24397.2 | −1.15079 | ||||||||
\(767\) | 65027.1 | 3.06127 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 2125.31 | 0.0996626 | 0.0498313 | − | 0.998758i | \(-0.484132\pi\) | ||||
0.0498313 | + | 0.998758i | \(0.484132\pi\) | |||||||
\(770\) | −1372.86 | −0.0642525 | ||||||||
\(771\) | −8798.82 | −0.411001 | ||||||||
\(772\) | 4508.06 | 0.210167 | ||||||||
\(773\) | −19747.6 | −0.918851 | −0.459425 | − | 0.888216i | \(-0.651945\pi\) | ||||
−0.459425 | + | 0.888216i | \(0.651945\pi\) | |||||||
\(774\) | −5202.12 | −0.241584 | ||||||||
\(775\) | −17492.5 | −0.810773 | ||||||||
\(776\) | −2364.99 | −0.109405 | ||||||||
\(777\) | 1144.95 | 0.0528636 | ||||||||
\(778\) | −6240.18 | −0.287560 | ||||||||
\(779\) | 16791.3 | 0.772288 | ||||||||
\(780\) | 2541.46 | 0.116665 | ||||||||
\(781\) | 17185.6 | 0.787385 | ||||||||
\(782\) | −2458.89 | −0.112442 | ||||||||
\(783\) | 2054.12 | 0.0937525 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −7654.80 | −0.348040 | ||||||||
\(786\) | −8390.85 | −0.380778 | ||||||||
\(787\) | −25946.4 | −1.17521 | −0.587604 | − | 0.809149i | \(-0.699929\pi\) | ||||
−0.587604 | + | 0.809149i | \(0.699929\pi\) | |||||||
\(788\) | 414.552 | 0.0187409 | ||||||||
\(789\) | 7483.38 | 0.337662 | ||||||||
\(790\) | 7929.81 | 0.357126 | ||||||||
\(791\) | 3670.45 | 0.164989 | ||||||||
\(792\) | 2397.82 | 0.107579 | ||||||||
\(793\) | 45338.8 | 2.03030 | ||||||||
\(794\) | −614.990 | −0.0274876 | ||||||||
\(795\) | 1774.64 | 0.0791700 | ||||||||
\(796\) | −2276.74 | −0.101378 | ||||||||
\(797\) | −25491.1 | −1.13293 | −0.566463 | − | 0.824087i | \(-0.691689\pi\) | ||||
−0.566463 | + | 0.824087i | \(0.691689\pi\) | |||||||
\(798\) | 3165.86 | 0.140439 | ||||||||
\(799\) | −1930.83 | −0.0854916 | ||||||||
\(800\) | −3722.55 | −0.164515 | ||||||||
\(801\) | 743.051 | 0.0327770 | ||||||||
\(802\) | −16175.6 | −0.712196 | ||||||||
\(803\) | −22061.7 | −0.969539 | ||||||||
\(804\) | 10784.2 | 0.473048 | ||||||||
\(805\) | 474.068 | 0.0207561 | ||||||||
\(806\) | 21631.1 | 0.945315 | ||||||||
\(807\) | −10315.1 | −0.449950 | ||||||||
\(808\) | 14099.8 | 0.613897 | ||||||||
\(809\) | 2372.35 | 0.103100 | 0.0515498 | − | 0.998670i | \(-0.483584\pi\) | ||||
0.0515498 | + | 0.998670i | \(0.483584\pi\) | |||||||
\(810\) | 477.012 | 0.0206920 | ||||||||
\(811\) | −16891.1 | −0.731350 | −0.365675 | − | 0.930743i | \(-0.619162\pi\) | ||||
−0.365675 | + | 0.930743i | \(0.619162\pi\) | |||||||
\(812\) | −2130.20 | −0.0920632 | ||||||||
\(813\) | −19959.5 | −0.861023 | ||||||||
\(814\) | −3631.47 | −0.156367 | ||||||||
\(815\) | 3377.15 | 0.145149 | ||||||||
\(816\) | 2565.80 | 0.110075 | ||||||||
\(817\) | 21784.6 | 0.932861 | ||||||||
\(818\) | −5127.29 | −0.219158 | ||||||||
\(819\) | −4531.36 | −0.193332 | ||||||||
\(820\) | −2623.72 | −0.111737 | ||||||||
\(821\) | −1307.96 | −0.0556006 | −0.0278003 | − | 0.999613i | \(-0.508850\pi\) | ||||
−0.0278003 | + | 0.999613i | \(0.508850\pi\) | |||||||
\(822\) | −11823.5 | −0.501695 | ||||||||
\(823\) | 20512.2 | 0.868784 | 0.434392 | − | 0.900724i | \(-0.356963\pi\) | ||||
0.434392 | + | 0.900724i | \(0.356963\pi\) | |||||||
\(824\) | −11134.6 | −0.470743 | ||||||||
\(825\) | −11622.4 | −0.490473 | ||||||||
\(826\) | −12657.1 | −0.533168 | ||||||||
\(827\) | −39485.2 | −1.66026 | −0.830129 | − | 0.557571i | \(-0.811733\pi\) | ||||
−0.830129 | + | 0.557571i | \(0.811733\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | 9471.20 | 0.396801 | 0.198401 | − | 0.980121i | \(-0.436425\pi\) | ||||
0.198401 | + | 0.980121i | \(0.436425\pi\) | |||||||
\(830\) | −589.860 | −0.0246679 | ||||||||
\(831\) | 1668.22 | 0.0696391 | ||||||||
\(832\) | 4603.29 | 0.191815 | ||||||||
\(833\) | 2619.26 | 0.108946 | ||||||||
\(834\) | 3444.66 | 0.143020 | ||||||||
\(835\) | −6736.07 | −0.279175 | ||||||||
\(836\) | −10041.2 | −0.415409 | ||||||||
\(837\) | 4059.99 | 0.167663 | ||||||||
\(838\) | −8625.46 | −0.355563 | ||||||||
\(839\) | 2416.73 | 0.0994455 | 0.0497228 | − | 0.998763i | \(-0.484166\pi\) | ||||
0.0497228 | + | 0.998763i | \(0.484166\pi\) | |||||||
\(840\) | −494.680 | −0.0203191 | ||||||||
\(841\) | −18601.1 | −0.762682 | ||||||||
\(842\) | −19597.1 | −0.802093 | ||||||||
\(843\) | −19860.5 | −0.811425 | ||||||||
\(844\) | −16195.4 | −0.660509 | ||||||||
\(845\) | 8764.07 | 0.356797 | ||||||||
\(846\) | −650.181 | −0.0264228 | ||||||||
\(847\) | 1553.37 | 0.0630158 | ||||||||
\(848\) | 3214.37 | 0.130167 | ||||||||
\(849\) | 24884.7 | 1.00594 | ||||||||
\(850\) | −12436.6 | −0.501851 | ||||||||
\(851\) | 1254.00 | 0.0505129 | ||||||||
\(852\) | 6192.44 | 0.249002 | ||||||||
\(853\) | −12555.6 | −0.503980 | −0.251990 | − | 0.967730i | \(-0.581085\pi\) | ||||
−0.251990 | + | 0.967730i | \(0.581085\pi\) | |||||||
\(854\) | −8824.91 | −0.353609 | ||||||||
\(855\) | −1997.56 | −0.0799007 | ||||||||
\(856\) | 254.634 | 0.0101673 | ||||||||
\(857\) | −38397.6 | −1.53050 | −0.765250 | − | 0.643734i | \(-0.777385\pi\) | ||||
−0.765250 | + | 0.643734i | \(0.777385\pi\) | |||||||
\(858\) | 14372.2 | 0.571863 | ||||||||
\(859\) | 48766.2 | 1.93700 | 0.968498 | − | 0.249021i | \(-0.0801088\pi\) | ||||
0.968498 | + | 0.249021i | \(0.0801088\pi\) | |||||||
\(860\) | −3403.94 | −0.134969 | ||||||||
\(861\) | 4678.02 | 0.185164 | ||||||||
\(862\) | 590.782 | 0.0233435 | ||||||||
\(863\) | 40228.1 | 1.58677 | 0.793383 | − | 0.608722i | \(-0.208318\pi\) | ||||
0.793383 | + | 0.608722i | \(0.208318\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 3319.17 | 0.130468 | ||||||||
\(866\) | 25582.7 | 1.00385 | ||||||||
\(867\) | −6166.95 | −0.241569 | ||||||||
\(868\) | −4210.36 | −0.164642 | ||||||||
\(869\) | 44843.7 | 1.75054 | ||||||||
\(870\) | 1344.09 | 0.0523780 | ||||||||
\(871\) | 64639.2 | 2.51460 | ||||||||
\(872\) | −11129.9 | −0.432231 | ||||||||
\(873\) | −2660.62 | −0.103148 | ||||||||
\(874\) | 3467.37 | 0.134194 | ||||||||
\(875\) | 4974.20 | 0.192181 | ||||||||
\(876\) | −7949.44 | −0.306606 | ||||||||
\(877\) | 15873.3 | 0.611179 | 0.305589 | − | 0.952163i | \(-0.401147\pi\) | ||||
0.305589 | + | 0.952163i | \(0.401147\pi\) | |||||||
\(878\) | 35390.9 | 1.36035 | ||||||||
\(879\) | 15436.6 | 0.592335 | ||||||||
\(880\) | 1568.98 | 0.0601027 | ||||||||
\(881\) | 367.109 | 0.0140388 | 0.00701942 | − | 0.999975i | \(-0.497766\pi\) | ||||
0.00701942 | + | 0.999975i | \(0.497766\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 40251.3 | 1.53405 | 0.767024 | − | 0.641618i | \(-0.221737\pi\) | ||||
0.767024 | + | 0.641618i | \(0.221737\pi\) | |||||||
\(884\) | 15379.1 | 0.585129 | ||||||||
\(885\) | 7986.24 | 0.303338 | ||||||||
\(886\) | 6154.90 | 0.233384 | ||||||||
\(887\) | 16530.2 | 0.625739 | 0.312870 | − | 0.949796i | \(-0.398710\pi\) | ||||
0.312870 | + | 0.949796i | \(0.398710\pi\) | |||||||
\(888\) | −1308.52 | −0.0494494 | ||||||||
\(889\) | −328.679 | −0.0123999 | ||||||||
\(890\) | 486.206 | 0.0183120 | ||||||||
\(891\) | 2697.54 | 0.101427 | ||||||||
\(892\) | 3862.84 | 0.144997 | ||||||||
\(893\) | 2722.73 | 0.102030 | ||||||||
\(894\) | −11606.5 | −0.434203 | ||||||||
\(895\) | −405.731 | −0.0151532 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | −4962.92 | −0.184735 | ||||||||
\(898\) | −31424.3 | −1.16775 | ||||||||
\(899\) | 11439.9 | 0.424408 | ||||||||
\(900\) | −4187.87 | −0.155106 | ||||||||
\(901\) | 10738.8 | 0.397073 | ||||||||
\(902\) | −14837.4 | −0.547705 | ||||||||
\(903\) | 6069.14 | 0.223664 | ||||||||
\(904\) | −4194.80 | −0.154333 | ||||||||
\(905\) | −2980.45 | −0.109473 | ||||||||
\(906\) | 7466.21 | 0.273784 | ||||||||
\(907\) | 12082.3 | 0.442322 | 0.221161 | − | 0.975237i | \(-0.429015\pi\) | ||||
0.221161 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(908\) | −11294.8 | −0.412811 | ||||||||
\(909\) | 15862.3 | 0.578788 | ||||||||
\(910\) | −2965.04 | −0.108011 | ||||||||
\(911\) | 30313.0 | 1.10243 | 0.551216 | − | 0.834362i | \(-0.314164\pi\) | ||||
0.551216 | + | 0.834362i | \(0.314164\pi\) | |||||||
\(912\) | −3618.12 | −0.131369 | ||||||||
\(913\) | −3335.71 | −0.120915 | ||||||||
\(914\) | 6868.75 | 0.248575 | ||||||||
\(915\) | 5568.25 | 0.201181 | ||||||||
\(916\) | 8414.16 | 0.303506 | ||||||||
\(917\) | 9789.32 | 0.352532 | ||||||||
\(918\) | 2886.53 | 0.103780 | ||||||||
\(919\) | 17257.0 | 0.619430 | 0.309715 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309715 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(920\) | −541.792 | −0.0194156 | ||||||||
\(921\) | −5105.97 | −0.182679 | ||||||||
\(922\) | 29044.1 | 1.03743 | ||||||||
\(923\) | 37116.6 | 1.32363 | ||||||||
\(924\) | −2797.45 | −0.0995990 | ||||||||
\(925\) | 6342.49 | 0.225448 | ||||||||
\(926\) | −25702.8 | −0.912146 | ||||||||
\(927\) | −12526.4 | −0.443821 | ||||||||
\(928\) | 2434.51 | 0.0861172 | ||||||||
\(929\) | 11354.5 | 0.401002 | 0.200501 | − | 0.979694i | \(-0.435743\pi\) | ||||
0.200501 | + | 0.979694i | \(0.435743\pi\) | |||||||
\(930\) | 2656.60 | 0.0936704 | ||||||||
\(931\) | −3693.50 | −0.130021 | ||||||||
\(932\) | 9739.42 | 0.342302 | ||||||||
\(933\) | −28870.7 | −1.01306 | ||||||||
\(934\) | −26122.7 | −0.915160 | ||||||||
\(935\) | 5241.79 | 0.183342 | ||||||||
\(936\) | 5178.70 | 0.180845 | ||||||||
\(937\) | 12607.4 | 0.439558 | 0.219779 | − | 0.975550i | \(-0.429466\pi\) | ||||
0.219779 | + | 0.975550i | \(0.429466\pi\) | |||||||
\(938\) | −12581.6 | −0.437957 | ||||||||
\(939\) | −14536.8 | −0.505209 | ||||||||
\(940\) | −425.438 | −0.0147620 | ||||||||
\(941\) | −39798.4 | −1.37873 | −0.689367 | − | 0.724412i | \(-0.742111\pi\) | ||||
−0.689367 | + | 0.724412i | \(0.742111\pi\) | |||||||
\(942\) | −15598.1 | −0.539503 | ||||||||
\(943\) | 5123.55 | 0.176931 | ||||||||
\(944\) | 14465.3 | 0.498733 | ||||||||
\(945\) | −556.514 | −0.0191571 | ||||||||
\(946\) | −19249.6 | −0.661583 | ||||||||
\(947\) | 36620.0 | 1.25659 | 0.628296 | − | 0.777975i | \(-0.283753\pi\) | ||||
0.628296 | + | 0.777975i | \(0.283753\pi\) | |||||||
\(948\) | 16158.4 | 0.553588 | ||||||||
\(949\) | −47647.8 | −1.62984 | ||||||||
\(950\) | 17537.3 | 0.598932 | ||||||||
\(951\) | −871.041 | −0.0297008 | ||||||||
\(952\) | −2993.44 | −0.101909 | ||||||||
\(953\) | −39926.4 | −1.35713 | −0.678565 | − | 0.734541i | \(-0.737398\pi\) | ||||
−0.678565 | + | 0.734541i | \(0.737398\pi\) | |||||||
\(954\) | 3616.16 | 0.122723 | ||||||||
\(955\) | −6041.89 | −0.204723 | ||||||||
\(956\) | 9809.67 | 0.331870 | ||||||||
\(957\) | 7600.93 | 0.256743 | ||||||||
\(958\) | −35168.1 | −1.18604 | ||||||||
\(959\) | 13794.1 | 0.464480 | ||||||||
\(960\) | 565.348 | 0.0190068 | ||||||||
\(961\) | −7179.88 | −0.241008 | ||||||||
\(962\) | −7843.08 | −0.262860 | ||||||||
\(963\) | 286.463 | 0.00958581 | ||||||||
\(964\) | −8341.42 | −0.278692 | ||||||||
\(965\) | 3318.52 | 0.110702 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | −37120.0 | −1.23444 | −0.617218 | − | 0.786792i | \(-0.711740\pi\) | ||||
−0.617218 | + | 0.786792i | \(0.711740\pi\) | |||||||
\(968\) | −1775.28 | −0.0589459 | ||||||||
\(969\) | −12087.7 | −0.400737 | ||||||||
\(970\) | −1740.94 | −0.0576271 | ||||||||
\(971\) | 58985.1 | 1.94946 | 0.974729 | − | 0.223392i | \(-0.0717128\pi\) | ||||
0.974729 | + | 0.223392i | \(0.0717128\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −4018.77 | −0.132411 | ||||||||
\(974\) | 20503.9 | 0.674526 | ||||||||
\(975\) | −25101.5 | −0.824505 | ||||||||
\(976\) | 10085.6 | 0.330771 | ||||||||
\(977\) | 53661.1 | 1.75719 | 0.878593 | − | 0.477572i | \(-0.158483\pi\) | ||||
0.878593 | + | 0.477572i | \(0.158483\pi\) | |||||||
\(978\) | 6881.56 | 0.224998 | ||||||||
\(979\) | 2749.54 | 0.0897605 | ||||||||
\(980\) | 577.126 | 0.0188119 | ||||||||
\(981\) | −12521.1 | −0.407512 | ||||||||
\(982\) | 31896.4 | 1.03651 | ||||||||
\(983\) | 28944.6 | 0.939155 | 0.469578 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469578 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(984\) | −5346.31 | −0.173205 | ||||||||
\(985\) | 305.164 | 0.00987141 | ||||||||
\(986\) | 8133.43 | 0.262699 | ||||||||
\(987\) | 758.544 | 0.0244627 | ||||||||
\(988\) | −21686.5 | −0.698321 | ||||||||
\(989\) | 6647.15 | 0.213718 | ||||||||
\(990\) | 1765.11 | 0.0566654 | ||||||||
\(991\) | −44674.1 | −1.43201 | −0.716003 | − | 0.698097i | \(-0.754030\pi\) | ||||
−0.716003 | + | 0.698097i | \(0.754030\pi\) | |||||||
\(992\) | 4811.84 | 0.154008 | ||||||||
\(993\) | 26341.1 | 0.841801 | ||||||||
\(994\) | −7224.51 | −0.230531 | ||||||||
\(995\) | −1675.97 | −0.0533990 | ||||||||
\(996\) | −1201.95 | −0.0382381 | ||||||||
\(997\) | −33719.5 | −1.07112 | −0.535561 | − | 0.844497i | \(-0.679900\pi\) | ||||
−0.535561 | + | 0.844497i | \(0.679900\pi\) | |||||||
\(998\) | 38828.5 | 1.23156 | ||||||||
\(999\) | −1472.08 | −0.0466213 |
(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 | 966.4.a.q.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.q.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial |