Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.60614 | −1.27496 | −0.637482 | − | 0.770465i | \(-0.720024\pi\) | ||||
−0.637482 | + | 0.770465i | \(0.720024\pi\) | |||||||
\(3\) | 0.812227 | 0.156313 | 0.0781566 | − | 0.996941i | \(-0.475097\pi\) | ||||
0.0781566 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(4\) | 5.00427 | 0.625534 | ||||||||
\(5\) | −5.99647 | −0.536341 | −0.268170 | − | 0.963371i | \(-0.586419\pi\) | ||||
−0.268170 | + | 0.963371i | \(0.586419\pi\) | |||||||
\(6\) | −2.92901 | −0.199294 | ||||||||
\(7\) | 26.3629 | 1.42346 | 0.711732 | − | 0.702451i | \(-0.247911\pi\) | ||||
0.711732 | + | 0.702451i | \(0.247911\pi\) | |||||||
\(8\) | 10.8030 | 0.477431 | ||||||||
\(9\) | −26.3403 | −0.975566 | ||||||||
\(10\) | 21.6241 | 0.683815 | ||||||||
\(11\) | −27.0936 | −0.742639 | −0.371319 | − | 0.928505i | \(-0.621095\pi\) | ||||
−0.371319 | + | 0.928505i | \(0.621095\pi\) | |||||||
\(12\) | 4.06461 | 0.0977792 | ||||||||
\(13\) | 83.2869 | 1.77689 | 0.888447 | − | 0.458979i | \(-0.151785\pi\) | ||||
0.888447 | + | 0.458979i | \(0.151785\pi\) | |||||||
\(14\) | −95.0685 | −1.81487 | ||||||||
\(15\) | −4.87050 | −0.0838371 | ||||||||
\(16\) | −78.9914 | −1.23424 | ||||||||
\(17\) | 19.3669 | 0.276304 | 0.138152 | − | 0.990411i | \(-0.455884\pi\) | ||||
0.138152 | + | 0.990411i | \(0.455884\pi\) | |||||||
\(18\) | 94.9869 | 1.24381 | ||||||||
\(19\) | 1.45555 | 0.0175751 | 0.00878754 | − | 0.999961i | \(-0.497203\pi\) | ||||
0.00878754 | + | 0.999961i | \(0.497203\pi\) | |||||||
\(20\) | −30.0080 | −0.335499 | ||||||||
\(21\) | 21.4127 | 0.222506 | ||||||||
\(22\) | 97.7034 | 0.946838 | ||||||||
\(23\) | 56.8171 | 0.515095 | 0.257548 | − | 0.966266i | \(-0.417086\pi\) | ||||
0.257548 | + | 0.966266i | \(0.417086\pi\) | |||||||
\(24\) | 8.77451 | 0.0746287 | ||||||||
\(25\) | −89.0423 | −0.712339 | ||||||||
\(26\) | −300.344 | −2.26548 | ||||||||
\(27\) | −43.3244 | −0.308807 | ||||||||
\(28\) | 131.927 | 0.890425 | ||||||||
\(29\) | −187.383 | −1.19987 | −0.599933 | − | 0.800050i | \(-0.704806\pi\) | ||||
−0.599933 | + | 0.800050i | \(0.704806\pi\) | |||||||
\(30\) | 17.5637 | 0.106889 | ||||||||
\(31\) | 65.8760 | 0.381667 | 0.190834 | − | 0.981622i | \(-0.438881\pi\) | ||||
0.190834 | + | 0.981622i | \(0.438881\pi\) | |||||||
\(32\) | 198.430 | 1.09618 | ||||||||
\(33\) | −22.0062 | −0.116084 | ||||||||
\(34\) | −69.8398 | −0.352277 | ||||||||
\(35\) | −158.085 | −0.763462 | ||||||||
\(36\) | −131.814 | −0.610250 | ||||||||
\(37\) | 164.226 | 0.729691 | 0.364845 | − | 0.931068i | \(-0.381122\pi\) | ||||
0.364845 | + | 0.931068i | \(0.381122\pi\) | |||||||
\(38\) | −5.24893 | −0.0224076 | ||||||||
\(39\) | 67.6479 | 0.277752 | ||||||||
\(40\) | −64.7800 | −0.256066 | ||||||||
\(41\) | −273.507 | −1.04182 | −0.520910 | − | 0.853612i | \(-0.674407\pi\) | ||||
−0.520910 | + | 0.853612i | \(0.674407\pi\) | |||||||
\(42\) | −77.2172 | −0.283687 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −135.584 | −0.464546 | ||||||||
\(45\) | 157.949 | 0.523236 | ||||||||
\(46\) | −204.891 | −0.656728 | ||||||||
\(47\) | 111.518 | 0.346096 | 0.173048 | − | 0.984913i | \(-0.444638\pi\) | ||||
0.173048 | + | 0.984913i | \(0.444638\pi\) | |||||||
\(48\) | −64.1590 | −0.192928 | ||||||||
\(49\) | 352.003 | 1.02625 | ||||||||
\(50\) | 321.099 | 0.908206 | ||||||||
\(51\) | 15.7303 | 0.0431899 | ||||||||
\(52\) | 416.790 | 1.11151 | ||||||||
\(53\) | −637.668 | −1.65265 | −0.826324 | − | 0.563194i | \(-0.809572\pi\) | ||||
−0.826324 | + | 0.563194i | \(0.809572\pi\) | |||||||
\(54\) | 156.234 | 0.393718 | ||||||||
\(55\) | 162.466 | 0.398308 | ||||||||
\(56\) | 284.799 | 0.679605 | ||||||||
\(57\) | 1.18224 | 0.00274722 | ||||||||
\(58\) | 675.729 | 1.52979 | ||||||||
\(59\) | 810.839 | 1.78919 | 0.894596 | − | 0.446876i | \(-0.147464\pi\) | ||||
0.894596 | + | 0.446876i | \(0.147464\pi\) | |||||||
\(60\) | −24.3733 | −0.0524430 | ||||||||
\(61\) | −789.470 | −1.65707 | −0.828535 | − | 0.559938i | \(-0.810825\pi\) | ||||
−0.828535 | + | 0.559938i | \(0.810825\pi\) | |||||||
\(62\) | −237.558 | −0.486612 | ||||||||
\(63\) | −694.407 | −1.38868 | ||||||||
\(64\) | −83.6366 | −0.163353 | ||||||||
\(65\) | −499.427 | −0.953021 | ||||||||
\(66\) | 79.3573 | 0.148003 | ||||||||
\(67\) | 125.028 | 0.227979 | 0.113990 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113990 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(68\) | 96.9172 | 0.172837 | ||||||||
\(69\) | 46.1484 | 0.0805162 | ||||||||
\(70\) | 570.075 | 0.973386 | ||||||||
\(71\) | −731.846 | −1.22330 | −0.611649 | − | 0.791130i | \(-0.709493\pi\) | ||||
−0.611649 | + | 0.791130i | \(0.709493\pi\) | |||||||
\(72\) | −284.555 | −0.465765 | ||||||||
\(73\) | −432.763 | −0.693850 | −0.346925 | − | 0.937893i | \(-0.612774\pi\) | ||||
−0.346925 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(74\) | −592.222 | −0.930330 | ||||||||
\(75\) | −72.3226 | −0.111348 | ||||||||
\(76\) | 7.28398 | 0.0109938 | ||||||||
\(77\) | −714.266 | −1.05712 | ||||||||
\(78\) | −243.948 | −0.354124 | ||||||||
\(79\) | 119.998 | 0.170896 | 0.0854482 | − | 0.996343i | \(-0.472768\pi\) | ||||
0.0854482 | + | 0.996343i | \(0.472768\pi\) | |||||||
\(80\) | 473.670 | 0.661974 | ||||||||
\(81\) | 675.998 | 0.927296 | ||||||||
\(82\) | 986.305 | 1.32828 | ||||||||
\(83\) | −45.8667 | −0.0606570 | −0.0303285 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303285 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(84\) | 107.155 | 0.139185 | ||||||||
\(85\) | −116.133 | −0.148193 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −152.197 | −0.187555 | ||||||||
\(88\) | −292.693 | −0.354559 | ||||||||
\(89\) | −942.217 | −1.12219 | −0.561094 | − | 0.827752i | \(-0.689619\pi\) | ||||
−0.561094 | + | 0.827752i | \(0.689619\pi\) | |||||||
\(90\) | −569.586 | −0.667107 | ||||||||
\(91\) | 2195.68 | 2.52934 | ||||||||
\(92\) | 284.328 | 0.322210 | ||||||||
\(93\) | 53.5063 | 0.0596596 | ||||||||
\(94\) | −402.148 | −0.441260 | ||||||||
\(95\) | −8.72818 | −0.00942624 | ||||||||
\(96\) | 161.170 | 0.171348 | ||||||||
\(97\) | 355.167 | 0.371770 | 0.185885 | − | 0.982571i | \(-0.440485\pi\) | ||||
0.185885 | + | 0.982571i | \(0.440485\pi\) | |||||||
\(98\) | −1269.37 | −1.30843 | ||||||||
\(99\) | 713.653 | 0.724493 | ||||||||
\(100\) | −445.592 | −0.445592 | ||||||||
\(101\) | −217.765 | −0.214539 | −0.107270 | − | 0.994230i | \(-0.534211\pi\) | ||||
−0.107270 | + | 0.994230i | \(0.534211\pi\) | |||||||
\(102\) | −56.7258 | −0.0550656 | ||||||||
\(103\) | 1538.74 | 1.47201 | 0.736005 | − | 0.676976i | \(-0.236710\pi\) | ||||
0.736005 | + | 0.676976i | \(0.236710\pi\) | |||||||
\(104\) | 899.750 | 0.848344 | ||||||||
\(105\) | −128.401 | −0.119339 | ||||||||
\(106\) | 2299.52 | 2.10707 | ||||||||
\(107\) | 932.741 | 0.842724 | 0.421362 | − | 0.906893i | \(-0.361552\pi\) | ||||
0.421362 | + | 0.906893i | \(0.361552\pi\) | |||||||
\(108\) | −216.807 | −0.193169 | ||||||||
\(109\) | 1859.77 | 1.63426 | 0.817129 | − | 0.576455i | \(-0.195564\pi\) | ||||
0.817129 | + | 0.576455i | \(0.195564\pi\) | |||||||
\(110\) | −585.876 | −0.507828 | ||||||||
\(111\) | 133.389 | 0.114060 | ||||||||
\(112\) | −2082.44 | −1.75690 | ||||||||
\(113\) | 1298.13 | 1.08069 | 0.540344 | − | 0.841444i | \(-0.318294\pi\) | ||||
0.540344 | + | 0.841444i | \(0.318294\pi\) | |||||||
\(114\) | −4.26332 | −0.00350260 | ||||||||
\(115\) | −340.702 | −0.276267 | ||||||||
\(116\) | −937.714 | −0.750557 | ||||||||
\(117\) | −2193.80 | −1.73348 | ||||||||
\(118\) | −2924.00 | −2.28116 | ||||||||
\(119\) | 510.568 | 0.393308 | ||||||||
\(120\) | −52.6161 | −0.0400264 | ||||||||
\(121\) | −596.937 | −0.448488 | ||||||||
\(122\) | 2846.94 | 2.11270 | ||||||||
\(123\) | −222.150 | −0.162850 | ||||||||
\(124\) | 329.661 | 0.238746 | ||||||||
\(125\) | 1283.50 | 0.918397 | ||||||||
\(126\) | 2504.13 | 1.77052 | ||||||||
\(127\) | −444.380 | −0.310491 | −0.155245 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155245 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(128\) | −1285.84 | −0.887914 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1801.01 | 1.21507 | ||||||||
\(131\) | −800.630 | −0.533980 | −0.266990 | − | 0.963699i | \(-0.586029\pi\) | ||||
−0.266990 | + | 0.963699i | \(0.586029\pi\) | |||||||
\(132\) | −110.125 | −0.0726146 | ||||||||
\(133\) | 38.3726 | 0.0250175 | ||||||||
\(134\) | −450.869 | −0.290665 | ||||||||
\(135\) | 259.794 | 0.165626 | ||||||||
\(136\) | 209.221 | 0.131916 | ||||||||
\(137\) | −1117.24 | −0.696735 | −0.348367 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348367 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(138\) | −166.418 | −0.102655 | ||||||||
\(139\) | −2130.76 | −1.30021 | −0.650105 | − | 0.759845i | \(-0.725275\pi\) | ||||
−0.650105 | + | 0.759845i | \(0.725275\pi\) | |||||||
\(140\) | −791.098 | −0.477571 | ||||||||
\(141\) | 90.5776 | 0.0540994 | ||||||||
\(142\) | 2639.14 | 1.55966 | ||||||||
\(143\) | −2256.54 | −1.31959 | ||||||||
\(144\) | 2080.66 | 1.20408 | ||||||||
\(145\) | 1123.64 | 0.643537 | ||||||||
\(146\) | 1560.60 | 0.884634 | ||||||||
\(147\) | 285.907 | 0.160416 | ||||||||
\(148\) | 821.831 | 0.456446 | ||||||||
\(149\) | 307.578 | 0.169113 | 0.0845563 | − | 0.996419i | \(-0.473053\pi\) | ||||
0.0845563 | + | 0.996419i | \(0.473053\pi\) | |||||||
\(150\) | 260.806 | 0.141965 | ||||||||
\(151\) | −2633.15 | −1.41909 | −0.709545 | − | 0.704661i | \(-0.751099\pi\) | ||||
−0.709545 | + | 0.704661i | \(0.751099\pi\) | |||||||
\(152\) | 15.7244 | 0.00839089 | ||||||||
\(153\) | −510.130 | −0.269553 | ||||||||
\(154\) | 2575.75 | 1.34779 | ||||||||
\(155\) | −395.024 | −0.204704 | ||||||||
\(156\) | 338.528 | 0.173743 | ||||||||
\(157\) | 918.529 | 0.466921 | 0.233461 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233461 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(158\) | −432.729 | −0.217887 | ||||||||
\(159\) | −517.931 | −0.258331 | ||||||||
\(160\) | −1189.88 | −0.587928 | ||||||||
\(161\) | 1497.87 | 0.733219 | ||||||||
\(162\) | −2437.75 | −1.18227 | ||||||||
\(163\) | 823.215 | 0.395578 | 0.197789 | − | 0.980245i | \(-0.436624\pi\) | ||||
0.197789 | + | 0.980245i | \(0.436624\pi\) | |||||||
\(164\) | −1368.70 | −0.651694 | ||||||||
\(165\) | 131.959 | 0.0622607 | ||||||||
\(166\) | 165.402 | 0.0773355 | ||||||||
\(167\) | 1814.13 | 0.840607 | 0.420304 | − | 0.907384i | \(-0.361924\pi\) | ||||
0.420304 | + | 0.907384i | \(0.361924\pi\) | |||||||
\(168\) | 231.322 | 0.106231 | ||||||||
\(169\) | 4739.70 | 2.15735 | ||||||||
\(170\) | 418.793 | 0.188941 | ||||||||
\(171\) | −38.3397 | −0.0171457 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4328.67 | −1.90233 | −0.951163 | − | 0.308690i | \(-0.900110\pi\) | ||||
−0.951163 | + | 0.308690i | \(0.900110\pi\) | |||||||
\(174\) | 548.845 | 0.239126 | ||||||||
\(175\) | −2347.41 | −1.01399 | ||||||||
\(176\) | 2140.16 | 0.916595 | ||||||||
\(177\) | 658.586 | 0.279674 | ||||||||
\(178\) | 3397.77 | 1.43075 | ||||||||
\(179\) | −2571.96 | −1.07395 | −0.536976 | − | 0.843598i | \(-0.680433\pi\) | ||||
−0.536976 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(180\) | 790.419 | 0.327302 | ||||||||
\(181\) | 4230.81 | 1.73742 | 0.868712 | − | 0.495317i | \(-0.164948\pi\) | ||||
0.868712 | + | 0.495317i | \(0.164948\pi\) | |||||||
\(182\) | −7917.95 | −3.22482 | ||||||||
\(183\) | −641.229 | −0.259022 | ||||||||
\(184\) | 613.797 | 0.245922 | ||||||||
\(185\) | −984.776 | −0.391363 | ||||||||
\(186\) | −192.951 | −0.0760639 | ||||||||
\(187\) | −524.719 | −0.205194 | ||||||||
\(188\) | 558.064 | 0.216495 | ||||||||
\(189\) | −1142.16 | −0.439576 | ||||||||
\(190\) | 31.4751 | 0.0120181 | ||||||||
\(191\) | 1341.08 | 0.508048 | 0.254024 | − | 0.967198i | \(-0.418246\pi\) | ||||
0.254024 | + | 0.967198i | \(0.418246\pi\) | |||||||
\(192\) | −67.9319 | −0.0255342 | ||||||||
\(193\) | −2927.70 | −1.09192 | −0.545959 | − | 0.837812i | \(-0.683835\pi\) | ||||
−0.545959 | + | 0.837812i | \(0.683835\pi\) | |||||||
\(194\) | −1280.78 | −0.473994 | ||||||||
\(195\) | −405.648 | −0.148970 | ||||||||
\(196\) | 1761.52 | 0.641953 | ||||||||
\(197\) | 429.316 | 0.155266 | 0.0776332 | − | 0.996982i | \(-0.475264\pi\) | ||||
0.0776332 | + | 0.996982i | \(0.475264\pi\) | |||||||
\(198\) | −2573.54 | −0.923703 | ||||||||
\(199\) | 2549.43 | 0.908164 | 0.454082 | − | 0.890960i | \(-0.349967\pi\) | ||||
0.454082 | + | 0.890960i | \(0.349967\pi\) | |||||||
\(200\) | −961.926 | −0.340092 | ||||||||
\(201\) | 101.551 | 0.0356361 | ||||||||
\(202\) | 785.293 | 0.273530 | ||||||||
\(203\) | −4939.96 | −1.70796 | ||||||||
\(204\) | 78.7188 | 0.0270168 | ||||||||
\(205\) | 1640.08 | 0.558770 | ||||||||
\(206\) | −5548.93 | −1.87676 | ||||||||
\(207\) | −1496.58 | −0.502510 | ||||||||
\(208\) | −6578.95 | −2.19312 | ||||||||
\(209\) | −39.4362 | −0.0130519 | ||||||||
\(210\) | 463.031 | 0.152153 | ||||||||
\(211\) | 3496.49 | 1.14080 | 0.570398 | − | 0.821368i | \(-0.306789\pi\) | ||||
0.570398 | + | 0.821368i | \(0.306789\pi\) | |||||||
\(212\) | −3191.06 | −1.03379 | ||||||||
\(213\) | −594.425 | −0.191217 | ||||||||
\(214\) | −3363.60 | −1.07444 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −468.035 | −0.147434 | ||||||||
\(217\) | 1736.68 | 0.543289 | ||||||||
\(218\) | −6706.62 | −2.08362 | ||||||||
\(219\) | −351.502 | −0.108458 | ||||||||
\(220\) | 813.024 | 0.249155 | ||||||||
\(221\) | 1613.01 | 0.490962 | ||||||||
\(222\) | −481.019 | −0.145423 | ||||||||
\(223\) | 5415.25 | 1.62615 | 0.813076 | − | 0.582158i | \(-0.197792\pi\) | ||||
0.813076 | + | 0.582158i | \(0.197792\pi\) | |||||||
\(224\) | 5231.20 | 1.56038 | ||||||||
\(225\) | 2345.40 | 0.694933 | ||||||||
\(226\) | −4681.24 | −1.37784 | ||||||||
\(227\) | −3228.62 | −0.944014 | −0.472007 | − | 0.881595i | \(-0.656470\pi\) | ||||
−0.472007 | + | 0.881595i | \(0.656470\pi\) | |||||||
\(228\) | 5.91625 | 0.00171848 | ||||||||
\(229\) | −4595.18 | −1.32602 | −0.663010 | − | 0.748611i | \(-0.730721\pi\) | ||||
−0.663010 | + | 0.748611i | \(0.730721\pi\) | |||||||
\(230\) | 1228.62 | 0.352230 | ||||||||
\(231\) | −580.146 | −0.165242 | ||||||||
\(232\) | −2024.30 | −0.572853 | ||||||||
\(233\) | −248.763 | −0.0699442 | −0.0349721 | − | 0.999388i | \(-0.511134\pi\) | ||||
−0.0349721 | + | 0.999388i | \(0.511134\pi\) | |||||||
\(234\) | 7911.16 | 2.21012 | ||||||||
\(235\) | −668.712 | −0.185625 | ||||||||
\(236\) | 4057.66 | 1.11920 | ||||||||
\(237\) | 97.4655 | 0.0267133 | ||||||||
\(238\) | −1841.18 | −0.501454 | ||||||||
\(239\) | 4503.78 | 1.21893 | 0.609467 | − | 0.792811i | \(-0.291383\pi\) | ||||
0.609467 | + | 0.792811i | \(0.291383\pi\) | |||||||
\(240\) | 384.728 | 0.103475 | ||||||||
\(241\) | −508.539 | −0.135925 | −0.0679625 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679625 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(242\) | 2152.64 | 0.571806 | ||||||||
\(243\) | 1718.82 | 0.453756 | ||||||||
\(244\) | −3950.72 | −1.03655 | ||||||||
\(245\) | −2110.78 | −0.550419 | ||||||||
\(246\) | 801.104 | 0.207628 | ||||||||
\(247\) | 121.228 | 0.0312291 | ||||||||
\(248\) | 711.660 | 0.182220 | ||||||||
\(249\) | −37.2542 | −0.00948148 | ||||||||
\(250\) | −4628.48 | −1.17092 | ||||||||
\(251\) | 4760.66 | 1.19717 | 0.598586 | − | 0.801059i | \(-0.295730\pi\) | ||||
0.598586 | + | 0.801059i | \(0.295730\pi\) | |||||||
\(252\) | −3475.00 | −0.868669 | ||||||||
\(253\) | −1539.38 | −0.382530 | ||||||||
\(254\) | 1602.50 | 0.395865 | ||||||||
\(255\) | −94.3264 | −0.0231645 | ||||||||
\(256\) | 5306.00 | 1.29541 | ||||||||
\(257\) | 2086.48 | 0.506423 | 0.253212 | − | 0.967411i | \(-0.418513\pi\) | ||||
0.253212 | + | 0.967411i | \(0.418513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4329.47 | 1.03869 | ||||||||
\(260\) | −2499.27 | −0.596147 | ||||||||
\(261\) | 4935.72 | 1.17055 | ||||||||
\(262\) | 2887.19 | 0.680806 | ||||||||
\(263\) | −7112.50 | −1.66759 | −0.833793 | − | 0.552077i | \(-0.813835\pi\) | ||||
−0.833793 | + | 0.552077i | \(0.813835\pi\) | |||||||
\(264\) | −237.733 | −0.0554222 | ||||||||
\(265\) | 3823.76 | 0.886383 | ||||||||
\(266\) | −138.377 | −0.0318964 | ||||||||
\(267\) | −765.294 | −0.175413 | ||||||||
\(268\) | 625.674 | 0.142609 | ||||||||
\(269\) | −5421.57 | −1.22884 | −0.614422 | − | 0.788977i | \(-0.710611\pi\) | ||||
−0.614422 | + | 0.788977i | \(0.710611\pi\) | |||||||
\(270\) | −936.854 | −0.211167 | ||||||||
\(271\) | 6809.33 | 1.52634 | 0.763169 | − | 0.646199i | \(-0.223643\pi\) | ||||
0.763169 | + | 0.646199i | \(0.223643\pi\) | |||||||
\(272\) | −1529.82 | −0.341025 | ||||||||
\(273\) | 1783.39 | 0.395370 | ||||||||
\(274\) | 4028.95 | 0.888312 | ||||||||
\(275\) | 2412.48 | 0.529010 | ||||||||
\(276\) | 230.939 | 0.0503656 | ||||||||
\(277\) | −6687.15 | −1.45051 | −0.725256 | − | 0.688480i | \(-0.758278\pi\) | ||||
−0.725256 | + | 0.688480i | \(0.758278\pi\) | |||||||
\(278\) | 7683.84 | 1.65772 | ||||||||
\(279\) | −1735.19 | −0.372342 | ||||||||
\(280\) | −1707.79 | −0.364500 | ||||||||
\(281\) | −6052.56 | −1.28493 | −0.642465 | − | 0.766315i | \(-0.722088\pi\) | ||||
−0.642465 | + | 0.766315i | \(0.722088\pi\) | |||||||
\(282\) | −326.636 | −0.0689747 | ||||||||
\(283\) | −3810.80 | −0.800453 | −0.400227 | − | 0.916416i | \(-0.631069\pi\) | ||||
−0.400227 | + | 0.916416i | \(0.631069\pi\) | |||||||
\(284\) | −3662.35 | −0.765214 | ||||||||
\(285\) | −7.08926 | −0.00147344 | ||||||||
\(286\) | 8137.41 | 1.68243 | ||||||||
\(287\) | −7210.44 | −1.48299 | ||||||||
\(288\) | −5226.71 | −1.06940 | ||||||||
\(289\) | −4537.92 | −0.923656 | ||||||||
\(290\) | −4051.99 | −0.820487 | ||||||||
\(291\) | 288.476 | 0.0581126 | ||||||||
\(292\) | −2165.66 | −0.434027 | ||||||||
\(293\) | −1344.32 | −0.268041 | −0.134020 | − | 0.990979i | \(-0.542789\pi\) | ||||
−0.134020 | + | 0.990979i | \(0.542789\pi\) | |||||||
\(294\) | −1031.02 | −0.204525 | ||||||||
\(295\) | −4862.18 | −0.959616 | ||||||||
\(296\) | 1774.14 | 0.348377 | ||||||||
\(297\) | 1173.81 | 0.229332 | ||||||||
\(298\) | −1109.17 | −0.215613 | ||||||||
\(299\) | 4732.12 | 0.915270 | ||||||||
\(300\) | −361.922 | −0.0696519 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9495.51 | 1.80929 | ||||||||
\(303\) | −176.875 | −0.0335353 | ||||||||
\(304\) | −114.976 | −0.0216919 | ||||||||
\(305\) | 4734.03 | 0.888754 | ||||||||
\(306\) | 1839.60 | 0.343670 | ||||||||
\(307\) | −8180.21 | −1.52075 | −0.760374 | − | 0.649486i | \(-0.774984\pi\) | ||||
−0.760374 | + | 0.649486i | \(0.774984\pi\) | |||||||
\(308\) | −3574.38 | −0.661264 | ||||||||
\(309\) | 1249.81 | 0.230095 | ||||||||
\(310\) | 1424.51 | 0.260990 | ||||||||
\(311\) | 198.784 | 0.0362445 | 0.0181222 | − | 0.999836i | \(-0.494231\pi\) | ||||
0.0181222 | + | 0.999836i | \(0.494231\pi\) | |||||||
\(312\) | 730.801 | 0.132607 | ||||||||
\(313\) | 326.674 | 0.0589926 | 0.0294963 | − | 0.999565i | \(-0.490610\pi\) | ||||
0.0294963 | + | 0.999565i | \(0.490610\pi\) | |||||||
\(314\) | −3312.35 | −0.595308 | ||||||||
\(315\) | 4163.99 | 0.744807 | ||||||||
\(316\) | 600.502 | 0.106901 | ||||||||
\(317\) | −2068.44 | −0.366484 | −0.183242 | − | 0.983068i | \(-0.558659\pi\) | ||||
−0.183242 | + | 0.983068i | \(0.558659\pi\) | |||||||
\(318\) | 1867.73 | 0.329363 | ||||||||
\(319\) | 5076.87 | 0.891067 | ||||||||
\(320\) | 501.525 | 0.0876128 | ||||||||
\(321\) | 757.597 | 0.131729 | ||||||||
\(322\) | −5401.52 | −0.934829 | ||||||||
\(323\) | 28.1895 | 0.00485606 | ||||||||
\(324\) | 3382.88 | 0.580055 | ||||||||
\(325\) | −7416.06 | −1.26575 | ||||||||
\(326\) | −2968.63 | −0.504348 | ||||||||
\(327\) | 1510.56 | 0.255456 | ||||||||
\(328\) | −2954.70 | −0.497397 | ||||||||
\(329\) | 2939.93 | 0.492655 | ||||||||
\(330\) | −475.864 | −0.0793802 | ||||||||
\(331\) | −3764.18 | −0.625069 | −0.312535 | − | 0.949906i | \(-0.601178\pi\) | ||||
−0.312535 | + | 0.949906i | \(0.601178\pi\) | |||||||
\(332\) | −229.530 | −0.0379430 | ||||||||
\(333\) | −4325.76 | −0.711862 | ||||||||
\(334\) | −6542.01 | −1.07174 | ||||||||
\(335\) | −749.727 | −0.122274 | ||||||||
\(336\) | −1691.42 | −0.274626 | ||||||||
\(337\) | −5712.02 | −0.923305 | −0.461653 | − | 0.887061i | \(-0.652743\pi\) | ||||
−0.461653 | + | 0.887061i | \(0.652743\pi\) | |||||||
\(338\) | −17092.1 | −2.75055 | ||||||||
\(339\) | 1054.38 | 0.168926 | ||||||||
\(340\) | −581.162 | −0.0926997 | ||||||||
\(341\) | −1784.82 | −0.283441 | ||||||||
\(342\) | 138.258 | 0.0218601 | ||||||||
\(343\) | 237.353 | 0.0373640 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −276.728 | −0.0431841 | ||||||||
\(346\) | 15609.8 | 2.42540 | ||||||||
\(347\) | −12550.3 | −1.94160 | −0.970802 | − | 0.239881i | \(-0.922892\pi\) | ||||
−0.970802 | + | 0.239881i | \(0.922892\pi\) | |||||||
\(348\) | −761.637 | −0.117322 | ||||||||
\(349\) | −5215.06 | −0.799874 | −0.399937 | − | 0.916543i | \(-0.630968\pi\) | ||||
−0.399937 | + | 0.916543i | \(0.630968\pi\) | |||||||
\(350\) | 8465.12 | 1.29280 | ||||||||
\(351\) | −3608.36 | −0.548717 | ||||||||
\(352\) | −5376.19 | −0.814068 | ||||||||
\(353\) | −2092.54 | −0.315509 | −0.157754 | − | 0.987478i | \(-0.550425\pi\) | ||||
−0.157754 | + | 0.987478i | \(0.550425\pi\) | |||||||
\(354\) | −2374.95 | −0.356575 | ||||||||
\(355\) | 4388.49 | 0.656104 | ||||||||
\(356\) | −4715.11 | −0.701967 | ||||||||
\(357\) | 414.697 | 0.0614792 | ||||||||
\(358\) | 9274.86 | 1.36925 | ||||||||
\(359\) | −10088.2 | −1.48310 | −0.741549 | − | 0.670898i | \(-0.765909\pi\) | ||||
−0.741549 | + | 0.670898i | \(0.765909\pi\) | |||||||
\(360\) | 1706.32 | 0.249809 | ||||||||
\(361\) | −6856.88 | −0.999691 | ||||||||
\(362\) | −15256.9 | −2.21515 | ||||||||
\(363\) | −484.848 | −0.0701045 | ||||||||
\(364\) | 10987.8 | 1.58219 | ||||||||
\(365\) | 2595.05 | 0.372140 | ||||||||
\(366\) | 2312.36 | 0.330244 | ||||||||
\(367\) | −2565.33 | −0.364876 | −0.182438 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182438 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(368\) | −4488.07 | −0.635752 | ||||||||
\(369\) | 7204.25 | 1.01636 | ||||||||
\(370\) | 3551.24 | 0.498974 | ||||||||
\(371\) | −16810.8 | −2.35249 | ||||||||
\(372\) | 267.760 | 0.0373191 | ||||||||
\(373\) | 907.539 | 0.125980 | 0.0629900 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629900 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(374\) | 1892.21 | 0.261615 | ||||||||
\(375\) | 1042.49 | 0.143558 | ||||||||
\(376\) | 1204.73 | 0.165237 | ||||||||
\(377\) | −15606.5 | −2.13203 | ||||||||
\(378\) | 4118.79 | 0.560443 | ||||||||
\(379\) | 9411.80 | 1.27560 | 0.637799 | − | 0.770203i | \(-0.279845\pi\) | ||||
0.637799 | + | 0.770203i | \(0.279845\pi\) | |||||||
\(380\) | −43.6782 | −0.00589643 | ||||||||
\(381\) | −360.937 | −0.0485338 | ||||||||
\(382\) | −4836.12 | −0.647743 | ||||||||
\(383\) | −10469.6 | −1.39680 | −0.698398 | − | 0.715710i | \(-0.746103\pi\) | ||||
−0.698398 | + | 0.715710i | \(0.746103\pi\) | |||||||
\(384\) | −1044.39 | −0.138793 | ||||||||
\(385\) | 4283.08 | 0.566976 | ||||||||
\(386\) | 10557.7 | 1.39216 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1777.35 | 0.232555 | ||||||||
\(389\) | 6173.88 | 0.804700 | 0.402350 | − | 0.915486i | \(-0.368194\pi\) | ||||
0.402350 | + | 0.915486i | \(0.368194\pi\) | |||||||
\(390\) | 1462.83 | 0.189931 | ||||||||
\(391\) | 1100.37 | 0.142323 | ||||||||
\(392\) | 3802.70 | 0.489963 | ||||||||
\(393\) | −650.294 | −0.0834681 | ||||||||
\(394\) | −1548.17 | −0.197959 | ||||||||
\(395\) | −719.564 | −0.0916587 | ||||||||
\(396\) | 3571.31 | 0.453195 | ||||||||
\(397\) | −3847.68 | −0.486422 | −0.243211 | − | 0.969973i | \(-0.578201\pi\) | ||||
−0.243211 | + | 0.969973i | \(0.578201\pi\) | |||||||
\(398\) | −9193.63 | −1.15788 | ||||||||
\(399\) | 31.1673 | 0.00391056 | ||||||||
\(400\) | 7033.58 | 0.879198 | ||||||||
\(401\) | −2160.31 | −0.269029 | −0.134515 | − | 0.990912i | \(-0.542948\pi\) | ||||
−0.134515 | + | 0.990912i | \(0.542948\pi\) | |||||||
\(402\) | −366.208 | −0.0454348 | ||||||||
\(403\) | 5486.61 | 0.678182 | ||||||||
\(404\) | −1089.76 | −0.134202 | ||||||||
\(405\) | −4053.61 | −0.497346 | ||||||||
\(406\) | 17814.2 | 2.17759 | ||||||||
\(407\) | −4449.47 | −0.541897 | ||||||||
\(408\) | 169.935 | 0.0206202 | ||||||||
\(409\) | −4818.22 | −0.582508 | −0.291254 | − | 0.956646i | \(-0.594073\pi\) | ||||
−0.291254 | + | 0.956646i | \(0.594073\pi\) | |||||||
\(410\) | −5914.35 | −0.712412 | ||||||||
\(411\) | −907.457 | −0.108909 | ||||||||
\(412\) | 7700.30 | 0.920792 | ||||||||
\(413\) | 21376.1 | 2.54685 | ||||||||
\(414\) | 5396.88 | 0.640682 | ||||||||
\(415\) | 275.039 | 0.0325328 | ||||||||
\(416\) | 16526.6 | 1.94780 | ||||||||
\(417\) | −1730.66 | −0.203240 | ||||||||
\(418\) | 142.212 | 0.0166408 | ||||||||
\(419\) | −924.481 | −0.107790 | −0.0538948 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538948 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(420\) | −642.551 | −0.0746507 | ||||||||
\(421\) | −14389.0 | −1.66574 | −0.832870 | − | 0.553468i | \(-0.813304\pi\) | ||||
−0.832870 | + | 0.553468i | \(0.813304\pi\) | |||||||
\(422\) | −12608.8 | −1.45448 | ||||||||
\(423\) | −2937.40 | −0.337640 | ||||||||
\(424\) | −6888.74 | −0.789025 | ||||||||
\(425\) | −1724.47 | −0.196822 | ||||||||
\(426\) | 2143.58 | 0.243795 | ||||||||
\(427\) | −20812.7 | −2.35878 | ||||||||
\(428\) | 4667.69 | 0.527153 | ||||||||
\(429\) | −1832.82 | −0.206269 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2076.77 | 0.232098 | 0.116049 | − | 0.993243i | \(-0.462977\pi\) | ||||
0.116049 | + | 0.993243i | \(0.462977\pi\) | |||||||
\(432\) | 3422.26 | 0.381142 | ||||||||
\(433\) | 1585.85 | 0.176007 | 0.0880033 | − | 0.996120i | \(-0.471951\pi\) | ||||
0.0880033 | + | 0.996120i | \(0.471951\pi\) | |||||||
\(434\) | −6262.73 | −0.692674 | ||||||||
\(435\) | 912.647 | 0.100593 | ||||||||
\(436\) | 9306.82 | 1.02228 | ||||||||
\(437\) | 82.7003 | 0.00905284 | ||||||||
\(438\) | 1267.57 | 0.138280 | ||||||||
\(439\) | −278.813 | −0.0303121 | −0.0151561 | − | 0.999885i | \(-0.504825\pi\) | ||||
−0.0151561 | + | 0.999885i | \(0.504825\pi\) | |||||||
\(440\) | 1755.12 | 0.190164 | ||||||||
\(441\) | −9271.87 | −1.00117 | ||||||||
\(442\) | −5816.74 | −0.625959 | ||||||||
\(443\) | 4961.81 | 0.532151 | 0.266075 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266075 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(444\) | 667.513 | 0.0713486 | ||||||||
\(445\) | 5649.98 | 0.601875 | ||||||||
\(446\) | −19528.2 | −2.07328 | ||||||||
\(447\) | 249.823 | 0.0264345 | ||||||||
\(448\) | −2204.91 | −0.232527 | ||||||||
\(449\) | −12048.2 | −1.26634 | −0.633171 | − | 0.774012i | \(-0.718247\pi\) | ||||
−0.633171 | + | 0.774012i | \(0.718247\pi\) | |||||||
\(450\) | −8457.85 | −0.886015 | ||||||||
\(451\) | 7410.29 | 0.773696 | ||||||||
\(452\) | 6496.19 | 0.676007 | ||||||||
\(453\) | −2138.71 | −0.221822 | ||||||||
\(454\) | 11642.9 | 1.20358 | ||||||||
\(455\) | −13166.4 | −1.35659 | ||||||||
\(456\) | 12.7718 | 0.00131161 | ||||||||
\(457\) | −12738.5 | −1.30390 | −0.651948 | − | 0.758263i | \(-0.726048\pi\) | ||||
−0.651948 | + | 0.758263i | \(0.726048\pi\) | |||||||
\(458\) | 16570.9 | 1.69063 | ||||||||
\(459\) | −839.060 | −0.0853245 | ||||||||
\(460\) | −1704.97 | −0.172814 | ||||||||
\(461\) | 4651.57 | 0.469947 | 0.234973 | − | 0.972002i | \(-0.424500\pi\) | ||||
0.234973 | + | 0.972002i | \(0.424500\pi\) | |||||||
\(462\) | 2092.09 | 0.210677 | ||||||||
\(463\) | −217.350 | −0.0218166 | −0.0109083 | − | 0.999941i | \(-0.503472\pi\) | ||||
−0.0109083 | + | 0.999941i | \(0.503472\pi\) | |||||||
\(464\) | 14801.6 | 1.48092 | ||||||||
\(465\) | −320.849 | −0.0319979 | ||||||||
\(466\) | 897.075 | 0.0891764 | ||||||||
\(467\) | 1915.22 | 0.189777 | 0.0948887 | − | 0.995488i | \(-0.469750\pi\) | ||||
0.0948887 | + | 0.995488i | \(0.469750\pi\) | |||||||
\(468\) | −10978.4 | −1.08435 | ||||||||
\(469\) | 3296.10 | 0.324520 | ||||||||
\(470\) | 2411.47 | 0.236666 | ||||||||
\(471\) | 746.054 | 0.0729859 | ||||||||
\(472\) | 8759.52 | 0.854215 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −351.474 | −0.0340586 | ||||||||
\(475\) | −129.606 | −0.0125194 | ||||||||
\(476\) | 2555.02 | 0.246028 | ||||||||
\(477\) | 16796.3 | 1.61227 | ||||||||
\(478\) | −16241.3 | −1.55410 | ||||||||
\(479\) | −11167.6 | −1.06526 | −0.532630 | − | 0.846348i | \(-0.678796\pi\) | ||||
−0.532630 | + | 0.846348i | \(0.678796\pi\) | |||||||
\(480\) | −966.454 | −0.0919008 | ||||||||
\(481\) | 13677.9 | 1.29658 | ||||||||
\(482\) | 1833.87 | 0.173299 | ||||||||
\(483\) | 1216.61 | 0.114612 | ||||||||
\(484\) | −2987.24 | −0.280544 | ||||||||
\(485\) | −2129.75 | −0.199396 | ||||||||
\(486\) | −6198.33 | −0.578522 | ||||||||
\(487\) | 18058.4 | 1.68030 | 0.840150 | − | 0.542354i | \(-0.182467\pi\) | ||||
0.840150 | + | 0.542354i | \(0.182467\pi\) | |||||||
\(488\) | −8528.66 | −0.791136 | ||||||||
\(489\) | 668.638 | 0.0618340 | ||||||||
\(490\) | 7611.77 | 0.701765 | ||||||||
\(491\) | 19234.3 | 1.76789 | 0.883945 | − | 0.467592i | \(-0.154878\pi\) | ||||
0.883945 | + | 0.467592i | \(0.154878\pi\) | |||||||
\(492\) | −1111.70 | −0.101868 | ||||||||
\(493\) | −3629.02 | −0.331527 | ||||||||
\(494\) | −437.167 | −0.0398160 | ||||||||
\(495\) | −4279.40 | −0.388575 | ||||||||
\(496\) | −5203.64 | −0.471069 | ||||||||
\(497\) | −19293.6 | −1.74132 | ||||||||
\(498\) | 134.344 | 0.0120886 | ||||||||
\(499\) | −9828.54 | −0.881735 | −0.440868 | − | 0.897572i | \(-0.645329\pi\) | ||||
−0.440868 | + | 0.897572i | \(0.645329\pi\) | |||||||
\(500\) | 6422.98 | 0.574489 | ||||||||
\(501\) | 1473.48 | 0.131398 | ||||||||
\(502\) | −17167.6 | −1.52635 | ||||||||
\(503\) | 11481.5 | 1.01776 | 0.508880 | − | 0.860838i | \(-0.330060\pi\) | ||||
0.508880 | + | 0.860838i | \(0.330060\pi\) | |||||||
\(504\) | −7501.69 | −0.663000 | ||||||||
\(505\) | 1305.82 | 0.115066 | ||||||||
\(506\) | 5551.23 | 0.487712 | ||||||||
\(507\) | 3849.72 | 0.337223 | ||||||||
\(508\) | −2223.80 | −0.194223 | ||||||||
\(509\) | −3994.60 | −0.347854 | −0.173927 | − | 0.984759i | \(-0.555646\pi\) | ||||
−0.173927 | + | 0.984759i | \(0.555646\pi\) | |||||||
\(510\) | 340.155 | 0.0295339 | ||||||||
\(511\) | −11408.9 | −0.987670 | ||||||||
\(512\) | −8847.52 | −0.763689 | ||||||||
\(513\) | −63.0610 | −0.00542731 | ||||||||
\(514\) | −7524.13 | −0.645672 | ||||||||
\(515\) | −9227.04 | −0.789499 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3021.41 | −0.257024 | ||||||||
\(518\) | −15612.7 | −1.32429 | ||||||||
\(519\) | −3515.86 | −0.297359 | ||||||||
\(520\) | −5395.33 | −0.455001 | ||||||||
\(521\) | −6982.25 | −0.587136 | −0.293568 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293568 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(522\) | −17798.9 | −1.49241 | ||||||||
\(523\) | −8757.64 | −0.732208 | −0.366104 | − | 0.930574i | \(-0.619309\pi\) | ||||
−0.366104 | + | 0.930574i | \(0.619309\pi\) | |||||||
\(524\) | −4006.57 | −0.334023 | ||||||||
\(525\) | −1906.63 | −0.158500 | ||||||||
\(526\) | 25648.7 | 2.12611 | ||||||||
\(527\) | 1275.81 | 0.105456 | ||||||||
\(528\) | 1738.30 | 0.143276 | ||||||||
\(529\) | −8938.81 | −0.734677 | ||||||||
\(530\) | −13789.0 | −1.13011 | ||||||||
\(531\) | −21357.7 | −1.74547 | ||||||||
\(532\) | 192.027 | 0.0156493 | ||||||||
\(533\) | −22779.5 | −1.85120 | ||||||||
\(534\) | 2759.76 | 0.223645 | ||||||||
\(535\) | −5593.16 | −0.451987 | ||||||||
\(536\) | 1350.68 | 0.108844 | ||||||||
\(537\) | −2089.02 | −0.167873 | ||||||||
\(538\) | 19551.0 | 1.56673 | ||||||||
\(539\) | −9537.04 | −0.762132 | ||||||||
\(540\) | 1300.08 | 0.103605 | ||||||||
\(541\) | −3230.72 | −0.256746 | −0.128373 | − | 0.991726i | \(-0.540976\pi\) | ||||
−0.128373 | + | 0.991726i | \(0.540976\pi\) | |||||||
\(542\) | −24555.4 | −1.94603 | ||||||||
\(543\) | 3436.38 | 0.271582 | ||||||||
\(544\) | 3842.98 | 0.302879 | ||||||||
\(545\) | −11152.1 | −0.876519 | ||||||||
\(546\) | −6431.18 | −0.504082 | ||||||||
\(547\) | −441.868 | −0.0345391 | −0.0172696 | − | 0.999851i | \(-0.505497\pi\) | ||||
−0.0172696 | + | 0.999851i | \(0.505497\pi\) | |||||||
\(548\) | −5591.00 | −0.435831 | ||||||||
\(549\) | 20794.9 | 1.61658 | ||||||||
\(550\) | −8699.74 | −0.674469 | ||||||||
\(551\) | −272.745 | −0.0210877 | ||||||||
\(552\) | 498.542 | 0.0384409 | ||||||||
\(553\) | 3163.49 | 0.243265 | ||||||||
\(554\) | 24114.8 | 1.84935 | ||||||||
\(555\) | −799.861 | −0.0611752 | ||||||||
\(556\) | −10662.9 | −0.813325 | ||||||||
\(557\) | −12443.5 | −0.946586 | −0.473293 | − | 0.880905i | \(-0.656935\pi\) | ||||
−0.473293 | + | 0.880905i | \(0.656935\pi\) | |||||||
\(558\) | 6257.36 | 0.474722 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 12487.3 | 0.942296 | ||||||||
\(561\) | −426.191 | −0.0320745 | ||||||||
\(562\) | 21826.4 | 1.63824 | ||||||||
\(563\) | 12004.7 | 0.898647 | 0.449324 | − | 0.893369i | \(-0.351665\pi\) | ||||
0.449324 | + | 0.893369i | \(0.351665\pi\) | |||||||
\(564\) | 453.275 | 0.0338410 | ||||||||
\(565\) | −7784.20 | −0.579617 | ||||||||
\(566\) | 13742.3 | 1.02055 | ||||||||
\(567\) | 17821.3 | 1.31997 | ||||||||
\(568\) | −7906.14 | −0.584040 | ||||||||
\(569\) | −17399.4 | −1.28194 | −0.640969 | − | 0.767567i | \(-0.721467\pi\) | ||||
−0.640969 | + | 0.767567i | \(0.721467\pi\) | |||||||
\(570\) | 25.5649 | 0.00187859 | ||||||||
\(571\) | 187.663 | 0.0137539 | 0.00687694 | − | 0.999976i | \(-0.497811\pi\) | ||||
0.00687694 | + | 0.999976i | \(0.497811\pi\) | |||||||
\(572\) | −11292.3 | −0.825449 | ||||||||
\(573\) | 1089.26 | 0.0794145 | ||||||||
\(574\) | 26001.9 | 1.89076 | ||||||||
\(575\) | −5059.13 | −0.366922 | ||||||||
\(576\) | 2203.01 | 0.159361 | ||||||||
\(577\) | −15258.1 | −1.10087 | −0.550437 | − | 0.834877i | \(-0.685539\pi\) | ||||
−0.550437 | + | 0.834877i | \(0.685539\pi\) | |||||||
\(578\) | 16364.4 | 1.17763 | ||||||||
\(579\) | −2377.96 | −0.170681 | ||||||||
\(580\) | 5622.98 | 0.402554 | ||||||||
\(581\) | −1209.18 | −0.0863430 | ||||||||
\(582\) | −1040.29 | −0.0740915 | ||||||||
\(583\) | 17276.7 | 1.22732 | ||||||||
\(584\) | −4675.15 | −0.331265 | ||||||||
\(585\) | 13155.1 | 0.929735 | ||||||||
\(586\) | 4847.81 | 0.341743 | ||||||||
\(587\) | −20653.7 | −1.45225 | −0.726124 | − | 0.687563i | \(-0.758680\pi\) | ||||
−0.726124 | + | 0.687563i | \(0.758680\pi\) | |||||||
\(588\) | 1430.75 | 0.100346 | ||||||||
\(589\) | 95.8860 | 0.00670783 | ||||||||
\(590\) | 17533.7 | 1.22348 | ||||||||
\(591\) | 348.702 | 0.0242702 | ||||||||
\(592\) | −12972.4 | −0.900614 | ||||||||
\(593\) | 2747.81 | 0.190285 | 0.0951426 | − | 0.995464i | \(-0.469669\pi\) | ||||
0.0951426 | + | 0.995464i | \(0.469669\pi\) | |||||||
\(594\) | −4232.94 | −0.292390 | ||||||||
\(595\) | −3061.61 | −0.210947 | ||||||||
\(596\) | 1539.20 | 0.105786 | ||||||||
\(597\) | 2070.72 | 0.141958 | ||||||||
\(598\) | −17064.7 | −1.16694 | ||||||||
\(599\) | 23896.4 | 1.63002 | 0.815008 | − | 0.579450i | \(-0.196733\pi\) | ||||
0.815008 | + | 0.579450i | \(0.196733\pi\) | |||||||
\(600\) | −781.302 | −0.0531609 | ||||||||
\(601\) | −15868.2 | −1.07700 | −0.538501 | − | 0.842625i | \(-0.681009\pi\) | ||||
−0.538501 | + | 0.842625i | \(0.681009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3293.27 | −0.222409 | ||||||||
\(604\) | −13177.0 | −0.887689 | ||||||||
\(605\) | 3579.52 | 0.240542 | ||||||||
\(606\) | 637.837 | 0.0427563 | ||||||||
\(607\) | −8394.74 | −0.561338 | −0.280669 | − | 0.959805i | \(-0.590556\pi\) | ||||
−0.280669 | + | 0.959805i | \(0.590556\pi\) | |||||||
\(608\) | 288.826 | 0.0192655 | ||||||||
\(609\) | −4012.37 | −0.266977 | ||||||||
\(610\) | −17071.6 | −1.13313 | ||||||||
\(611\) | 9287.95 | 0.614976 | ||||||||
\(612\) | −2552.83 | −0.168614 | ||||||||
\(613\) | −1487.66 | −0.0980197 | −0.0490099 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490099 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(614\) | 29499.0 | 1.93890 | ||||||||
\(615\) | 1332.11 | 0.0873432 | ||||||||
\(616\) | −7716.23 | −0.504701 | ||||||||
\(617\) | 7581.38 | 0.494676 | 0.247338 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247338 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(618\) | −4506.99 | −0.293362 | ||||||||
\(619\) | −328.731 | −0.0213454 | −0.0106727 | − | 0.999943i | \(-0.503397\pi\) | ||||
−0.0106727 | + | 0.999943i | \(0.503397\pi\) | |||||||
\(620\) | −1976.81 | −0.128049 | ||||||||
\(621\) | −2461.57 | −0.159065 | ||||||||
\(622\) | −716.845 | −0.0462104 | ||||||||
\(623\) | −24839.6 | −1.59739 | ||||||||
\(624\) | −5343.60 | −0.342813 | ||||||||
\(625\) | 3433.82 | 0.219765 | ||||||||
\(626\) | −1178.03 | −0.0752135 | ||||||||
\(627\) | −32.0311 | −0.00204019 | ||||||||
\(628\) | 4596.57 | 0.292075 | ||||||||
\(629\) | 3180.54 | 0.201616 | ||||||||
\(630\) | −15016.0 | −0.949603 | ||||||||
\(631\) | 20258.2 | 1.27807 | 0.639037 | − | 0.769176i | \(-0.279333\pi\) | ||||
0.639037 | + | 0.769176i | \(0.279333\pi\) | |||||||
\(632\) | 1296.34 | 0.0815911 | ||||||||
\(633\) | 2839.94 | 0.178322 | ||||||||
\(634\) | 7459.10 | 0.467253 | ||||||||
\(635\) | 2664.71 | 0.166529 | ||||||||
\(636\) | −2591.87 | −0.161595 | ||||||||
\(637\) | 29317.3 | 1.82354 | ||||||||
\(638\) | −18307.9 | −1.13608 | ||||||||
\(639\) | 19277.0 | 1.19341 | ||||||||
\(640\) | 7710.48 | 0.476224 | ||||||||
\(641\) | 7317.96 | 0.450924 | 0.225462 | − | 0.974252i | \(-0.427611\pi\) | ||||
0.225462 | + | 0.974252i | \(0.427611\pi\) | |||||||
\(642\) | −2732.00 | −0.167950 | ||||||||
\(643\) | 14629.6 | 0.897253 | 0.448627 | − | 0.893719i | \(-0.351913\pi\) | ||||
0.448627 | + | 0.893719i | \(0.351913\pi\) | |||||||
\(644\) | 7495.73 | 0.458654 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −101.656 | −0.00619130 | ||||||||
\(647\) | 6446.09 | 0.391688 | 0.195844 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195844 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(648\) | 7302.83 | 0.442719 | ||||||||
\(649\) | −21968.6 | −1.32872 | ||||||||
\(650\) | 26743.4 | 1.61379 | ||||||||
\(651\) | 1410.58 | 0.0849233 | ||||||||
\(652\) | 4119.59 | 0.247447 | ||||||||
\(653\) | −15267.7 | −0.914961 | −0.457480 | − | 0.889220i | \(-0.651248\pi\) | ||||
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(654\) | −5447.29 | −0.325697 | ||||||||
\(655\) | 4800.96 | 0.286395 | ||||||||
\(656\) | 21604.7 | 1.28586 | ||||||||
\(657\) | 11399.1 | 0.676897 | ||||||||
\(658\) | −10601.8 | −0.628118 | ||||||||
\(659\) | −13991.4 | −0.827055 | −0.413527 | − | 0.910492i | \(-0.635703\pi\) | ||||
−0.413527 | + | 0.910492i | \(0.635703\pi\) | |||||||
\(660\) | 660.360 | 0.0389462 | ||||||||
\(661\) | 17096.8 | 1.00603 | 0.503016 | − | 0.864277i | \(-0.332224\pi\) | ||||
0.503016 | + | 0.864277i | \(0.332224\pi\) | |||||||
\(662\) | 13574.2 | 0.796941 | ||||||||
\(663\) | 1310.13 | 0.0767439 | ||||||||
\(664\) | −495.499 | −0.0289595 | ||||||||
\(665\) | −230.100 | −0.0134179 | ||||||||
\(666\) | 15599.3 | 0.907598 | ||||||||
\(667\) | −10646.6 | −0.618045 | ||||||||
\(668\) | 9078.39 | 0.525829 | ||||||||
\(669\) | 4398.41 | 0.254189 | ||||||||
\(670\) | 2703.62 | 0.155896 | ||||||||
\(671\) | 21389.6 | 1.23060 | ||||||||
\(672\) | 4248.92 | 0.243907 | ||||||||
\(673\) | −9239.00 | −0.529179 | −0.264589 | − | 0.964361i | \(-0.585236\pi\) | ||||
−0.264589 | + | 0.964361i | \(0.585236\pi\) | |||||||
\(674\) | 20598.4 | 1.17718 | ||||||||
\(675\) | 3857.71 | 0.219975 | ||||||||
\(676\) | 23718.8 | 1.34950 | ||||||||
\(677\) | 4341.97 | 0.246493 | 0.123246 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123246 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(678\) | −3802.23 | −0.215374 | ||||||||
\(679\) | 9363.23 | 0.529202 | ||||||||
\(680\) | −1254.59 | −0.0707519 | ||||||||
\(681\) | −2622.37 | −0.147562 | ||||||||
\(682\) | 6436.31 | 0.361377 | ||||||||
\(683\) | 935.126 | 0.0523889 | 0.0261944 | − | 0.999657i | \(-0.491661\pi\) | ||||
0.0261944 | + | 0.999657i | \(0.491661\pi\) | |||||||
\(684\) | −191.862 | −0.0107252 | ||||||||
\(685\) | 6699.53 | 0.373687 | ||||||||
\(686\) | −855.928 | −0.0476377 | ||||||||
\(687\) | −3732.33 | −0.207274 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53109.3 | −2.93658 | ||||||||
\(690\) | 997.920 | 0.0550582 | ||||||||
\(691\) | −14883.7 | −0.819398 | −0.409699 | − | 0.912221i | \(-0.634366\pi\) | ||||
−0.409699 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(692\) | −21661.8 | −1.18997 | ||||||||
\(693\) | 18814.0 | 1.03129 | ||||||||
\(694\) | 45258.3 | 2.47548 | ||||||||
\(695\) | 12777.1 | 0.697355 | ||||||||
\(696\) | −1644.19 | −0.0895444 | ||||||||
\(697\) | −5296.98 | −0.287859 | ||||||||
\(698\) | 18806.3 | 1.01981 | ||||||||
\(699\) | −202.052 | −0.0109332 | ||||||||
\(700\) | −11747.1 | −0.634284 | ||||||||
\(701\) | −6934.09 | −0.373605 | −0.186802 | − | 0.982398i | \(-0.559812\pi\) | ||||
−0.186802 | + | 0.982398i | \(0.559812\pi\) | |||||||
\(702\) | 13012.2 | 0.699595 | ||||||||
\(703\) | 239.039 | 0.0128244 | ||||||||
\(704\) | 2266.02 | 0.121312 | ||||||||
\(705\) | −543.146 | −0.0290157 | ||||||||
\(706\) | 7545.99 | 0.402262 | ||||||||
\(707\) | −5740.93 | −0.305389 | ||||||||
\(708\) | 3295.74 | 0.174946 | ||||||||
\(709\) | 904.231 | 0.0478972 | 0.0239486 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239486 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(710\) | −15825.5 | −0.836509 | ||||||||
\(711\) | −3160.78 | −0.166721 | ||||||||
\(712\) | −10178.8 | −0.535767 | ||||||||
\(713\) | 3742.89 | 0.196595 | ||||||||
\(714\) | −1495.46 | −0.0783838 | ||||||||
\(715\) | 13531.3 | 0.707750 | ||||||||
\(716\) | −12870.8 | −0.671793 | ||||||||
\(717\) | 3658.09 | 0.190535 | ||||||||
\(718\) | 36379.3 | 1.89090 | ||||||||
\(719\) | −23525.7 | −1.22025 | −0.610125 | − | 0.792306i | \(-0.708881\pi\) | ||||
−0.610125 | + | 0.792306i | \(0.708881\pi\) | |||||||
\(720\) | −12476.6 | −0.645799 | ||||||||
\(721\) | 40565.8 | 2.09535 | ||||||||
\(722\) | 24726.9 | 1.27457 | ||||||||
\(723\) | −413.049 | −0.0212469 | ||||||||
\(724\) | 21172.1 | 1.08682 | ||||||||
\(725\) | 16685.0 | 0.854710 | ||||||||
\(726\) | 1748.43 | 0.0893808 | ||||||||
\(727\) | 33029.9 | 1.68502 | 0.842512 | − | 0.538678i | \(-0.181076\pi\) | ||||
0.842512 | + | 0.538678i | \(0.181076\pi\) | |||||||
\(728\) | 23720.0 | 1.20759 | ||||||||
\(729\) | −16855.9 | −0.856368 | ||||||||
\(730\) | −9358.12 | −0.474465 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3208.88 | −0.162027 | ||||||||
\(733\) | 4063.29 | 0.204749 | 0.102375 | − | 0.994746i | \(-0.467356\pi\) | ||||
0.102375 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(734\) | 9250.96 | 0.465203 | ||||||||
\(735\) | −1714.43 | −0.0860377 | ||||||||
\(736\) | 11274.2 | 0.564639 | ||||||||
\(737\) | −3387.46 | −0.169306 | ||||||||
\(738\) | −25979.6 | −1.29583 | ||||||||
\(739\) | −9373.56 | −0.466593 | −0.233296 | − | 0.972406i | \(-0.574951\pi\) | ||||
−0.233296 | + | 0.972406i | \(0.574951\pi\) | |||||||
\(740\) | −4928.09 | −0.244811 | ||||||||
\(741\) | 98.4650 | 0.00488151 | ||||||||
\(742\) | 60622.1 | 2.99934 | ||||||||
\(743\) | −21092.5 | −1.04147 | −0.520734 | − | 0.853719i | \(-0.674341\pi\) | ||||
−0.520734 | + | 0.853719i | \(0.674341\pi\) | |||||||
\(744\) | 578.030 | 0.0284833 | ||||||||
\(745\) | −1844.38 | −0.0907020 | ||||||||
\(746\) | −3272.71 | −0.160620 | ||||||||
\(747\) | 1208.14 | 0.0591749 | ||||||||
\(748\) | −2625.84 | −0.128356 | ||||||||
\(749\) | 24589.8 | 1.19959 | ||||||||
\(750\) | −3759.38 | −0.183031 | ||||||||
\(751\) | −15261.7 | −0.741555 | −0.370777 | − | 0.928722i | \(-0.620909\pi\) | ||||
−0.370777 | + | 0.928722i | \(0.620909\pi\) | |||||||
\(752\) | −8808.93 | −0.427166 | ||||||||
\(753\) | 3866.73 | 0.187134 | ||||||||
\(754\) | 56279.4 | 2.71827 | ||||||||
\(755\) | 15789.6 | 0.761115 | ||||||||
\(756\) | −5715.67 | −0.274969 | ||||||||
\(757\) | −6955.07 | −0.333932 | −0.166966 | − | 0.985963i | \(-0.553397\pi\) | ||||
−0.166966 | + | 0.985963i | \(0.553397\pi\) | |||||||
\(758\) | −33940.3 | −1.62634 | ||||||||
\(759\) | −1250.33 | −0.0597944 | ||||||||
\(760\) | −94.2908 | −0.00450038 | ||||||||
\(761\) | 3295.92 | 0.157000 | 0.0785000 | − | 0.996914i | \(-0.474987\pi\) | ||||
0.0785000 | + | 0.996914i | \(0.474987\pi\) | |||||||
\(762\) | 1301.59 | 0.0618789 | ||||||||
\(763\) | 49029.1 | 2.32631 | ||||||||
\(764\) | 6711.13 | 0.317801 | ||||||||
\(765\) | 3058.98 | 0.144572 | ||||||||
\(766\) | 37755.0 | 1.78086 | ||||||||
\(767\) | 67532.3 | 3.17920 | ||||||||
\(768\) | 4309.68 | 0.202490 | ||||||||
\(769\) | −5722.67 | −0.268355 | −0.134177 | − | 0.990957i | \(-0.542839\pi\) | ||||
−0.134177 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(770\) | −15445.4 | −0.722875 | ||||||||
\(771\) | 1694.69 | 0.0791606 | ||||||||
\(772\) | −14651.0 | −0.683032 | ||||||||
\(773\) | 17526.3 | 0.815494 | 0.407747 | − | 0.913095i | \(-0.366315\pi\) | ||||
0.407747 | + | 0.913095i | \(0.366315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5865.75 | −0.271876 | ||||||||
\(776\) | 3836.88 | 0.177495 | ||||||||
\(777\) | 3516.51 | 0.162361 | ||||||||
\(778\) | −22263.9 | −1.02596 | ||||||||
\(779\) | −398.104 | −0.0183101 | ||||||||
\(780\) | −2029.98 | −0.0931856 | ||||||||
\(781\) | 19828.3 | 0.908468 | ||||||||
\(782\) | −3968.10 | −0.181456 | ||||||||
\(783\) | 8118.25 | 0.370527 | ||||||||
\(784\) | −27805.2 | −1.26664 | ||||||||
\(785\) | −5507.94 | −0.250429 | ||||||||
\(786\) | 2345.05 | 0.106419 | ||||||||
\(787\) | 35884.3 | 1.62533 | 0.812667 | − | 0.582729i | \(-0.198015\pi\) | ||||
0.812667 | + | 0.582729i | \(0.198015\pi\) | |||||||
\(788\) | 2148.41 | 0.0971244 | ||||||||
\(789\) | −5776.96 | −0.260666 | ||||||||
\(790\) | 2594.85 | 0.116862 | ||||||||
\(791\) | 34222.5 | 1.53832 | ||||||||
\(792\) | 7709.61 | 0.345895 | ||||||||
\(793\) | −65752.5 | −2.94444 | ||||||||
\(794\) | 13875.3 | 0.620171 | ||||||||
\(795\) | 3105.76 | 0.138553 | ||||||||
\(796\) | 12758.1 | 0.568088 | ||||||||
\(797\) | 26874.0 | 1.19439 | 0.597194 | − | 0.802097i | \(-0.296282\pi\) | ||||
0.597194 | + | 0.802097i | \(0.296282\pi\) | |||||||
\(798\) | −112.394 | −0.00498583 | ||||||||
\(799\) | 2159.75 | 0.0956276 | ||||||||
\(800\) | −17668.7 | −0.780853 | ||||||||
\(801\) | 24818.3 | 1.09477 | ||||||||
\(802\) | 7790.38 | 0.343003 | ||||||||
\(803\) | 11725.1 | 0.515280 | ||||||||
\(804\) | 508.189 | 0.0222916 | ||||||||
\(805\) | −8981.91 | −0.393255 | ||||||||
\(806\) | −19785.5 | −0.864658 | ||||||||
\(807\) | −4403.55 | −0.192085 | ||||||||
\(808\) | −2352.53 | −0.102428 | ||||||||
\(809\) | 16365.2 | 0.711212 | 0.355606 | − | 0.934636i | \(-0.384274\pi\) | ||||
0.355606 | + | 0.934636i | \(0.384274\pi\) | |||||||
\(810\) | 14617.9 | 0.634099 | ||||||||
\(811\) | 9500.55 | 0.411356 | 0.205678 | − | 0.978620i | \(-0.434060\pi\) | ||||
0.205678 | + | 0.978620i | \(0.434060\pi\) | |||||||
\(812\) | −24720.9 | −1.06839 | ||||||||
\(813\) | 5530.72 | 0.238587 | ||||||||
\(814\) | 16045.4 | 0.690899 | ||||||||
\(815\) | −4936.39 | −0.212165 | ||||||||
\(816\) | −1242.56 | −0.0533068 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17375.2 | 0.742677 | ||||||||
\(819\) | −57835.0 | −2.46754 | ||||||||
\(820\) | 8207.39 | 0.349530 | ||||||||
\(821\) | −10038.9 | −0.426748 | −0.213374 | − | 0.976971i | \(-0.568445\pi\) | ||||
−0.213374 | + | 0.976971i | \(0.568445\pi\) | |||||||
\(822\) | 3272.42 | 0.138855 | ||||||||
\(823\) | −23596.1 | −0.999403 | −0.499702 | − | 0.866198i | \(-0.666557\pi\) | ||||
−0.499702 | + | 0.866198i | \(0.666557\pi\) | |||||||
\(824\) | 16623.1 | 0.702783 | ||||||||
\(825\) | 1959.48 | 0.0826913 | ||||||||
\(826\) | −77085.3 | −3.24714 | ||||||||
\(827\) | 29302.6 | 1.23211 | 0.616053 | − | 0.787705i | \(-0.288731\pi\) | ||||
0.616053 | + | 0.787705i | \(0.288731\pi\) | |||||||
\(828\) | −7489.29 | −0.314337 | ||||||||
\(829\) | 16593.4 | 0.695190 | 0.347595 | − | 0.937645i | \(-0.386998\pi\) | ||||
0.347595 | + | 0.937645i | \(0.386998\pi\) | |||||||
\(830\) | −991.829 | −0.0414782 | ||||||||
\(831\) | −5431.48 | −0.226734 | ||||||||
\(832\) | −6965.83 | −0.290261 | ||||||||
\(833\) | 6817.21 | 0.283556 | ||||||||
\(834\) | 6241.02 | 0.259123 | ||||||||
\(835\) | −10878.4 | −0.450852 | ||||||||
\(836\) | −197.349 | −0.00816443 | ||||||||
\(837\) | −2854.04 | −0.117861 | ||||||||
\(838\) | 3333.81 | 0.137428 | ||||||||
\(839\) | 16106.7 | 0.662772 | 0.331386 | − | 0.943495i | \(-0.392484\pi\) | ||||
0.331386 | + | 0.943495i | \(0.392484\pi\) | |||||||
\(840\) | −1387.11 | −0.0569762 | ||||||||
\(841\) | 10723.3 | 0.439677 | ||||||||
\(842\) | 51888.8 | 2.12376 | ||||||||
\(843\) | −4916.05 | −0.200852 | ||||||||
\(844\) | 17497.4 | 0.713607 | ||||||||
\(845\) | −28421.5 | −1.15708 | ||||||||
\(846\) | 10592.7 | 0.430478 | ||||||||
\(847\) | −15737.0 | −0.638406 | ||||||||
\(848\) | 50370.3 | 2.03977 | ||||||||
\(849\) | −3095.23 | −0.125121 | ||||||||
\(850\) | 6218.70 | 0.250941 | ||||||||
\(851\) | 9330.84 | 0.375860 | ||||||||
\(852\) | −2974.66 | −0.119613 | ||||||||
\(853\) | 16973.0 | 0.681293 | 0.340647 | − | 0.940191i | \(-0.389354\pi\) | ||||
0.340647 | + | 0.940191i | \(0.389354\pi\) | |||||||
\(854\) | 75053.7 | 3.00736 | ||||||||
\(855\) | 229.903 | 0.00919592 | ||||||||
\(856\) | 10076.4 | 0.402342 | ||||||||
\(857\) | −10313.8 | −0.411101 | −0.205551 | − | 0.978647i | \(-0.565898\pi\) | ||||
−0.205551 | + | 0.978647i | \(0.565898\pi\) | |||||||
\(858\) | 6609.43 | 0.262986 | ||||||||
\(859\) | −22942.2 | −0.911267 | −0.455634 | − | 0.890167i | \(-0.650587\pi\) | ||||
−0.455634 | + | 0.890167i | \(0.650587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5856.51 | −0.231811 | ||||||||
\(862\) | −7489.11 | −0.295917 | ||||||||
\(863\) | 19747.4 | 0.778920 | 0.389460 | − | 0.921043i | \(-0.372662\pi\) | ||||
0.389460 | + | 0.921043i | \(0.372662\pi\) | |||||||
\(864\) | −8596.88 | −0.338509 | ||||||||
\(865\) | 25956.7 | 1.02029 | ||||||||
\(866\) | −5718.79 | −0.224402 | ||||||||
\(867\) | −3685.82 | −0.144380 | ||||||||
\(868\) | 8690.84 | 0.339846 | ||||||||
\(869\) | −3251.17 | −0.126914 | ||||||||
\(870\) | −3291.14 | −0.128253 | ||||||||
\(871\) | 10413.2 | 0.405095 | ||||||||
\(872\) | 20091.2 | 0.780245 | ||||||||
\(873\) | −9355.20 | −0.362687 | ||||||||
\(874\) | −298.229 | −0.0115421 | ||||||||
\(875\) | 33836.8 | 1.30730 | ||||||||
\(876\) | −1759.01 | −0.0678441 | ||||||||
\(877\) | 9726.70 | 0.374512 | 0.187256 | − | 0.982311i | \(-0.440041\pi\) | ||||
0.187256 | + | 0.982311i | \(0.440041\pi\) | |||||||
\(878\) | 1005.44 | 0.0386469 | ||||||||
\(879\) | −1091.89 | −0.0418983 | ||||||||
\(880\) | −12833.4 | −0.491608 | ||||||||
\(881\) | 16960.9 | 0.648613 | 0.324306 | − | 0.945952i | \(-0.394869\pi\) | ||||
0.324306 | + | 0.945952i | \(0.394869\pi\) | |||||||
\(882\) | 33435.7 | 1.27646 | ||||||||
\(883\) | 23172.9 | 0.883159 | 0.441579 | − | 0.897222i | \(-0.354418\pi\) | ||||
0.441579 | + | 0.897222i | \(0.354418\pi\) | |||||||
\(884\) | 8071.93 | 0.307114 | ||||||||
\(885\) | −3949.19 | −0.150001 | ||||||||
\(886\) | −17893.0 | −0.678473 | ||||||||
\(887\) | 38740.7 | 1.46650 | 0.733250 | − | 0.679959i | \(-0.238002\pi\) | ||||
0.733250 | + | 0.679959i | \(0.238002\pi\) | |||||||
\(888\) | 1441.00 | 0.0544559 | ||||||||
\(889\) | −11715.2 | −0.441972 | ||||||||
\(890\) | −20374.6 | −0.767370 | ||||||||
\(891\) | −18315.2 | −0.688646 | ||||||||
\(892\) | 27099.4 | 1.01721 | ||||||||
\(893\) | 162.320 | 0.00608267 | ||||||||
\(894\) | −900.898 | −0.0337031 | ||||||||
\(895\) | 15422.7 | 0.576004 | ||||||||
\(896\) | −33898.4 | −1.26391 | ||||||||
\(897\) | 3843.56 | 0.143069 | ||||||||
\(898\) | 43447.4 | 1.61454 | ||||||||
\(899\) | −12344.0 | −0.457949 | ||||||||
\(900\) | 11737.0 | 0.434705 | ||||||||
\(901\) | −12349.6 | −0.456633 | ||||||||
\(902\) | −26722.6 | −0.986434 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14023.7 | 0.515954 | ||||||||
\(905\) | −25370.0 | −0.931852 | ||||||||
\(906\) | 7712.51 | 0.282816 | ||||||||
\(907\) | 11304.7 | 0.413855 | 0.206928 | − | 0.978356i | \(-0.433654\pi\) | ||||
0.206928 | + | 0.978356i | \(0.433654\pi\) | |||||||
\(908\) | −16156.9 | −0.590513 | ||||||||
\(909\) | 5736.00 | 0.209297 | ||||||||
\(910\) | 47479.8 | 1.72960 | ||||||||
\(911\) | −15797.8 | −0.574537 | −0.287269 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287269 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(912\) | −93.3868 | −0.00339073 | ||||||||
\(913\) | 1242.69 | 0.0450462 | ||||||||
\(914\) | 45936.8 | 1.66242 | ||||||||
\(915\) | 3845.11 | 0.138924 | ||||||||
\(916\) | −22995.6 | −0.829470 | ||||||||
\(917\) | −21107.0 | −0.760101 | ||||||||
\(918\) | 3025.77 | 0.108786 | ||||||||
\(919\) | 38867.9 | 1.39514 | 0.697570 | − | 0.716517i | \(-0.254265\pi\) | ||||
0.697570 | + | 0.716517i | \(0.254265\pi\) | |||||||
\(920\) | −3680.62 | −0.131898 | ||||||||
\(921\) | −6644.19 | −0.237713 | ||||||||
\(922\) | −16774.2 | −0.599165 | ||||||||
\(923\) | −60953.1 | −2.17367 | ||||||||
\(924\) | −2903.21 | −0.103364 | ||||||||
\(925\) | −14623.0 | −0.519787 | ||||||||
\(926\) | 783.795 | 0.0278154 | ||||||||
\(927\) | −40531.0 | −1.43604 | ||||||||
\(928\) | −37182.4 | −1.31527 | ||||||||
\(929\) | −13829.3 | −0.488400 | −0.244200 | − | 0.969725i | \(-0.578525\pi\) | ||||
−0.244200 | + | 0.969725i | \(0.578525\pi\) | |||||||
\(930\) | 1157.03 | 0.0407961 | ||||||||
\(931\) | 512.359 | 0.0180364 | ||||||||
\(932\) | −1244.88 | −0.0437525 | ||||||||
\(933\) | 161.458 | 0.00566549 | ||||||||
\(934\) | −6906.58 | −0.241959 | ||||||||
\(935\) | 3146.46 | 0.110054 | ||||||||
\(936\) | −23699.7 | −0.827616 | ||||||||
\(937\) | −40293.0 | −1.40482 | −0.702410 | − | 0.711773i | \(-0.747893\pi\) | ||||
−0.702410 | + | 0.711773i | \(0.747893\pi\) | |||||||
\(938\) | −11886.2 | −0.413751 | ||||||||
\(939\) | 265.333 | 0.00922132 | ||||||||
\(940\) | −3346.42 | −0.116115 | ||||||||
\(941\) | −18141.7 | −0.628482 | −0.314241 | − | 0.949343i | \(-0.601750\pi\) | ||||
−0.314241 | + | 0.949343i | \(0.601750\pi\) | |||||||
\(942\) | −2690.38 | −0.0930544 | ||||||||
\(943\) | −15539.9 | −0.536636 | ||||||||
\(944\) | −64049.4 | −2.20829 | ||||||||
\(945\) | 6848.92 | 0.235762 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42305.7 | −1.45169 | −0.725845 | − | 0.687858i | \(-0.758551\pi\) | ||||
−0.725845 | + | 0.687858i | \(0.758551\pi\) | |||||||
\(948\) | 487.744 | 0.0167101 | ||||||||
\(949\) | −36043.5 | −1.23290 | ||||||||
\(950\) | 467.377 | 0.0159618 | ||||||||
\(951\) | −1680.04 | −0.0572862 | ||||||||
\(952\) | 5515.68 | 0.187777 | ||||||||
\(953\) | −34528.2 | −1.17364 | −0.586819 | − | 0.809718i | \(-0.699620\pi\) | ||||
−0.586819 | + | 0.809718i | \(0.699620\pi\) | |||||||
\(954\) | −60570.0 | −2.05558 | ||||||||
\(955\) | −8041.75 | −0.272487 | ||||||||
\(956\) | 22538.1 | 0.762485 | ||||||||
\(957\) | 4123.57 | 0.139285 | ||||||||
\(958\) | 40271.9 | 1.35817 | ||||||||
\(959\) | −29453.8 | −0.991777 | ||||||||
\(960\) | 407.352 | 0.0136950 | ||||||||
\(961\) | −25451.4 | −0.854330 | ||||||||
\(962\) | −49324.3 | −1.65310 | ||||||||
\(963\) | −24568.7 | −0.822133 | ||||||||
\(964\) | −2544.87 | −0.0850257 | ||||||||
\(965\) | 17555.9 | 0.585641 | ||||||||
\(966\) | −4387.26 | −0.146126 | ||||||||
\(967\) | −29151.9 | −0.969454 | −0.484727 | − | 0.874666i | \(-0.661081\pi\) | ||||
−0.484727 | + | 0.874666i | \(0.661081\pi\) | |||||||
\(968\) | −6448.72 | −0.214122 | ||||||||
\(969\) | 22.8963 | 0.000759066 0 | ||||||||
\(970\) | 7680.18 | 0.254222 | ||||||||
\(971\) | 4560.27 | 0.150717 | 0.0753584 | − | 0.997157i | \(-0.475990\pi\) | ||||
0.0753584 | + | 0.997157i | \(0.475990\pi\) | |||||||
\(972\) | 8601.46 | 0.283840 | ||||||||
\(973\) | −56173.2 | −1.85080 | ||||||||
\(974\) | −65121.3 | −2.14232 | ||||||||
\(975\) | −6023.52 | −0.197853 | ||||||||
\(976\) | 62361.3 | 2.04522 | ||||||||
\(977\) | 23774.7 | 0.778526 | 0.389263 | − | 0.921127i | \(-0.372730\pi\) | ||||
0.389263 | + | 0.921127i | \(0.372730\pi\) | |||||||
\(978\) | −2411.20 | −0.0788362 | ||||||||
\(979\) | 25528.0 | 0.833381 | ||||||||
\(980\) | −10562.9 | −0.344306 | ||||||||
\(981\) | −48987.0 | −1.59433 | ||||||||
\(982\) | −69361.8 | −2.25400 | ||||||||
\(983\) | 53606.1 | 1.73934 | 0.869669 | − | 0.493636i | \(-0.164333\pi\) | ||||
0.869669 | + | 0.493636i | \(0.164333\pi\) | |||||||
\(984\) | −2399.89 | −0.0777496 | ||||||||
\(985\) | −2574.38 | −0.0832757 | ||||||||
\(986\) | 13086.8 | 0.422685 | ||||||||
\(987\) | 2387.89 | 0.0770085 | ||||||||
\(988\) | 606.660 | 0.0195348 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 15432.1 | 0.495420 | ||||||||
\(991\) | 33076.1 | 1.06024 | 0.530119 | − | 0.847923i | \(-0.322147\pi\) | ||||
0.530119 | + | 0.847923i | \(0.322147\pi\) | |||||||
\(992\) | 13071.8 | 0.418377 | ||||||||
\(993\) | −3057.37 | −0.0977065 | ||||||||
\(994\) | 69575.4 | 2.22012 | ||||||||
\(995\) | −15287.6 | −0.487085 | ||||||||
\(996\) | −186.430 | −0.00593099 | ||||||||
\(997\) | 31969.9 | 1.01554 | 0.507772 | − | 0.861491i | \(-0.330469\pi\) | ||||
0.507772 | + | 0.861491i | \(0.330469\pi\) | |||||||
\(998\) | 35443.1 | 1.12418 | ||||||||
\(999\) | −7114.99 | −0.225334 |
(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 | 1849.4.a.g.1.7 | 30 | ||
43.8 | odd | 14 | 43.4.e.a.21.3 | ✓ | 60 | ||
43.27 | odd | 14 | 43.4.e.a.41.3 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.24 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.21.3 | ✓ | 60 | 43.8 | odd | 14 | ||
43.4.e.a.41.3 | yes | 60 | 43.27 | odd | 14 | ||
1849.4.a.g.1.7 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.24 | 30 | 43.42 | odd | 2 |