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: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.31 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29424 | 0.457582 | 0.228791 | − | 0.973476i | \(-0.426523\pi\) | ||||
0.228791 | + | 0.973476i | \(0.426523\pi\) | |||||||
\(3\) | −3.36009 | −0.646650 | −0.323325 | − | 0.946288i | \(-0.604801\pi\) | ||||
−0.323325 | + | 0.946288i | \(0.604801\pi\) | |||||||
\(4\) | −6.32495 | −0.790618 | ||||||||
\(5\) | 1.78174 | 0.159363 | 0.0796817 | − | 0.996820i | \(-0.474610\pi\) | ||||
0.0796817 | + | 0.996820i | \(0.474610\pi\) | |||||||
\(6\) | −4.34876 | −0.295896 | ||||||||
\(7\) | −27.5745 | −1.48888 | −0.744440 | − | 0.667689i | \(-0.767284\pi\) | ||||
−0.744440 | + | 0.667689i | \(0.767284\pi\) | |||||||
\(8\) | −18.5399 | −0.819355 | ||||||||
\(9\) | −15.7098 | −0.581843 | ||||||||
\(10\) | 2.30599 | 0.0729218 | ||||||||
\(11\) | 9.45755 | 0.259233 | 0.129616 | − | 0.991564i | \(-0.458625\pi\) | ||||
0.129616 | + | 0.991564i | \(0.458625\pi\) | |||||||
\(12\) | 21.2524 | 0.511254 | ||||||||
\(13\) | 38.4667 | 0.820672 | 0.410336 | − | 0.911934i | \(-0.365411\pi\) | ||||
0.410336 | + | 0.911934i | \(0.365411\pi\) | |||||||
\(14\) | −35.6879 | −0.681285 | ||||||||
\(15\) | −5.98680 | −0.103052 | ||||||||
\(16\) | 26.6046 | 0.415696 | ||||||||
\(17\) | 54.0990 | 0.771820 | 0.385910 | − | 0.922536i | \(-0.373888\pi\) | ||||
0.385910 | + | 0.922536i | \(0.373888\pi\) | |||||||
\(18\) | −20.3322 | −0.266241 | ||||||||
\(19\) | 37.3489 | 0.450970 | 0.225485 | − | 0.974247i | \(-0.427603\pi\) | ||||
0.225485 | + | 0.974247i | \(0.427603\pi\) | |||||||
\(20\) | −11.2694 | −0.125996 | ||||||||
\(21\) | 92.6528 | 0.962786 | ||||||||
\(22\) | 12.2403 | 0.118620 | ||||||||
\(23\) | −100.967 | −0.915351 | −0.457675 | − | 0.889119i | \(-0.651318\pi\) | ||||
−0.457675 | + | 0.889119i | \(0.651318\pi\) | |||||||
\(24\) | 62.2958 | 0.529836 | ||||||||
\(25\) | −121.825 | −0.974603 | ||||||||
\(26\) | 49.7850 | 0.375525 | ||||||||
\(27\) | 143.509 | 1.02290 | ||||||||
\(28\) | 174.407 | 1.17714 | ||||||||
\(29\) | 175.001 | 1.12058 | 0.560292 | − | 0.828295i | \(-0.310689\pi\) | ||||
0.560292 | + | 0.828295i | \(0.310689\pi\) | |||||||
\(30\) | −7.74835 | −0.0471549 | ||||||||
\(31\) | −247.586 | −1.43445 | −0.717223 | − | 0.696844i | \(-0.754587\pi\) | ||||
−0.717223 | + | 0.696844i | \(0.754587\pi\) | |||||||
\(32\) | 182.752 | 1.00957 | ||||||||
\(33\) | −31.7783 | −0.167633 | ||||||||
\(34\) | 70.0170 | 0.353171 | ||||||||
\(35\) | −49.1304 | −0.237273 | ||||||||
\(36\) | 99.3634 | 0.460016 | ||||||||
\(37\) | 234.362 | 1.04132 | 0.520660 | − | 0.853764i | \(-0.325686\pi\) | ||||
0.520660 | + | 0.853764i | \(0.325686\pi\) | |||||||
\(38\) | 48.3384 | 0.206356 | ||||||||
\(39\) | −129.252 | −0.530688 | ||||||||
\(40\) | −33.0332 | −0.130575 | ||||||||
\(41\) | 325.321 | 1.23919 | 0.619593 | − | 0.784923i | \(-0.287298\pi\) | ||||
0.619593 | + | 0.784923i | \(0.287298\pi\) | |||||||
\(42\) | 119.915 | 0.440554 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −59.8185 | −0.204954 | ||||||||
\(45\) | −27.9907 | −0.0927245 | ||||||||
\(46\) | −130.675 | −0.418848 | ||||||||
\(47\) | 148.643 | 0.461315 | 0.230657 | − | 0.973035i | \(-0.425912\pi\) | ||||
0.230657 | + | 0.973035i | \(0.425912\pi\) | |||||||
\(48\) | −89.3938 | −0.268810 | ||||||||
\(49\) | 417.351 | 1.21677 | ||||||||
\(50\) | −157.671 | −0.445961 | ||||||||
\(51\) | −181.778 | −0.499098 | ||||||||
\(52\) | −243.300 | −0.648838 | ||||||||
\(53\) | 735.610 | 1.90649 | 0.953244 | − | 0.302202i | \(-0.0977216\pi\) | ||||
0.953244 | + | 0.302202i | \(0.0977216\pi\) | |||||||
\(54\) | 185.735 | 0.468061 | ||||||||
\(55\) | 16.8509 | 0.0413122 | ||||||||
\(56\) | 511.228 | 1.21992 | ||||||||
\(57\) | −125.496 | −0.291620 | ||||||||
\(58\) | 226.493 | 0.512760 | ||||||||
\(59\) | −275.860 | −0.608710 | −0.304355 | − | 0.952559i | \(-0.598441\pi\) | ||||
−0.304355 | + | 0.952559i | \(0.598441\pi\) | |||||||
\(60\) | 37.8662 | 0.0814751 | ||||||||
\(61\) | 30.9134 | 0.0648861 | 0.0324431 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324431 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(62\) | −320.436 | −0.656377 | ||||||||
\(63\) | 433.188 | 0.866295 | ||||||||
\(64\) | 23.6879 | 0.0462654 | ||||||||
\(65\) | 68.5375 | 0.130785 | ||||||||
\(66\) | −41.1286 | −0.0767058 | ||||||||
\(67\) | −27.3051 | −0.0497888 | −0.0248944 | − | 0.999690i | \(-0.507925\pi\) | ||||
−0.0248944 | + | 0.999690i | \(0.507925\pi\) | |||||||
\(68\) | −342.173 | −0.610215 | ||||||||
\(69\) | 339.259 | 0.591912 | ||||||||
\(70\) | −63.5864 | −0.108572 | ||||||||
\(71\) | −66.0822 | −0.110458 | −0.0552290 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552290 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(72\) | 291.257 | 0.476736 | ||||||||
\(73\) | −511.898 | −0.820728 | −0.410364 | − | 0.911922i | \(-0.634598\pi\) | ||||
−0.410364 | + | 0.911922i | \(0.634598\pi\) | |||||||
\(74\) | 303.320 | 0.476490 | ||||||||
\(75\) | 409.345 | 0.630228 | ||||||||
\(76\) | −236.230 | −0.356545 | ||||||||
\(77\) | −260.787 | −0.385967 | ||||||||
\(78\) | −167.282 | −0.242833 | ||||||||
\(79\) | −1190.03 | −1.69479 | −0.847397 | − | 0.530959i | \(-0.821832\pi\) | ||||
−0.847397 | + | 0.530959i | \(0.821832\pi\) | |||||||
\(80\) | 47.4023 | 0.0662467 | ||||||||
\(81\) | −58.0396 | −0.0796154 | ||||||||
\(82\) | 421.043 | 0.567030 | ||||||||
\(83\) | −144.868 | −0.191582 | −0.0957909 | − | 0.995401i | \(-0.530538\pi\) | ||||
−0.0957909 | + | 0.995401i | \(0.530538\pi\) | |||||||
\(84\) | −586.024 | −0.761196 | ||||||||
\(85\) | 96.3902 | 0.123000 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −588.021 | −0.724626 | ||||||||
\(88\) | −175.342 | −0.212404 | ||||||||
\(89\) | 769.313 | 0.916258 | 0.458129 | − | 0.888886i | \(-0.348520\pi\) | ||||
0.458129 | + | 0.888886i | \(0.348520\pi\) | |||||||
\(90\) | −36.2266 | −0.0424291 | ||||||||
\(91\) | −1060.70 | −1.22188 | ||||||||
\(92\) | 638.611 | 0.723693 | ||||||||
\(93\) | 831.914 | 0.927585 | ||||||||
\(94\) | 192.379 | 0.211090 | ||||||||
\(95\) | 66.5460 | 0.0718681 | ||||||||
\(96\) | −614.063 | −0.652839 | ||||||||
\(97\) | 1881.67 | 1.96964 | 0.984820 | − | 0.173577i | \(-0.0555325\pi\) | ||||
0.984820 | + | 0.173577i | \(0.0555325\pi\) | |||||||
\(98\) | 540.151 | 0.556771 | ||||||||
\(99\) | −148.576 | −0.150833 | ||||||||
\(100\) | 770.539 | 0.770539 | ||||||||
\(101\) | −664.679 | −0.654832 | −0.327416 | − | 0.944880i | \(-0.606178\pi\) | ||||
−0.327416 | + | 0.944880i | \(0.606178\pi\) | |||||||
\(102\) | −235.264 | −0.228378 | ||||||||
\(103\) | −757.340 | −0.724495 | −0.362247 | − | 0.932082i | \(-0.617990\pi\) | ||||
−0.362247 | + | 0.932082i | \(0.617990\pi\) | |||||||
\(104\) | −713.168 | −0.672422 | ||||||||
\(105\) | 165.083 | 0.153433 | ||||||||
\(106\) | 952.055 | 0.872375 | ||||||||
\(107\) | −1312.68 | −1.18599 | −0.592996 | − | 0.805205i | \(-0.702055\pi\) | ||||
−0.592996 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(108\) | −907.686 | −0.808723 | ||||||||
\(109\) | 314.072 | 0.275988 | 0.137994 | − | 0.990433i | \(-0.455935\pi\) | ||||
0.137994 | + | 0.990433i | \(0.455935\pi\) | |||||||
\(110\) | 21.8090 | 0.0189037 | ||||||||
\(111\) | −787.478 | −0.673370 | ||||||||
\(112\) | −733.606 | −0.618922 | ||||||||
\(113\) | −2100.85 | −1.74895 | −0.874477 | − | 0.485068i | \(-0.838795\pi\) | ||||
−0.874477 | + | 0.485068i | \(0.838795\pi\) | |||||||
\(114\) | −162.422 | −0.133440 | ||||||||
\(115\) | −179.896 | −0.145873 | ||||||||
\(116\) | −1106.87 | −0.885955 | ||||||||
\(117\) | −604.302 | −0.477502 | ||||||||
\(118\) | −357.028 | −0.278535 | ||||||||
\(119\) | −1491.75 | −1.14915 | ||||||||
\(120\) | 110.995 | 0.0844365 | ||||||||
\(121\) | −1241.55 | −0.932798 | ||||||||
\(122\) | 40.0093 | 0.0296907 | ||||||||
\(123\) | −1093.11 | −0.801321 | ||||||||
\(124\) | 1565.97 | 1.13410 | ||||||||
\(125\) | −439.778 | −0.314679 | ||||||||
\(126\) | 560.649 | 0.396401 | ||||||||
\(127\) | −1771.00 | −1.23741 | −0.618703 | − | 0.785625i | \(-0.712342\pi\) | ||||
−0.618703 | + | 0.785625i | \(0.712342\pi\) | |||||||
\(128\) | −1431.36 | −0.988400 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 88.7038 | 0.0598449 | ||||||||
\(131\) | 2833.28 | 1.88966 | 0.944828 | − | 0.327567i | \(-0.106229\pi\) | ||||
0.944828 | + | 0.327567i | \(0.106229\pi\) | |||||||
\(132\) | 200.996 | 0.132534 | ||||||||
\(133\) | −1029.88 | −0.671441 | ||||||||
\(134\) | −35.3393 | −0.0227825 | ||||||||
\(135\) | 255.695 | 0.163013 | ||||||||
\(136\) | −1002.99 | −0.632395 | ||||||||
\(137\) | 384.344 | 0.239684 | 0.119842 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119842 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(138\) | 439.081 | 0.270848 | ||||||||
\(139\) | 1099.42 | 0.670872 | 0.335436 | − | 0.942063i | \(-0.391116\pi\) | ||||
0.335436 | + | 0.942063i | \(0.391116\pi\) | |||||||
\(140\) | 310.747 | 0.187592 | ||||||||
\(141\) | −499.454 | −0.298310 | ||||||||
\(142\) | −85.5261 | −0.0505436 | ||||||||
\(143\) | 363.800 | 0.212745 | ||||||||
\(144\) | −417.951 | −0.241870 | ||||||||
\(145\) | 311.806 | 0.178580 | ||||||||
\(146\) | −662.518 | −0.375550 | ||||||||
\(147\) | −1402.34 | −0.786823 | ||||||||
\(148\) | −1482.33 | −0.823287 | ||||||||
\(149\) | 2307.28 | 1.26859 | 0.634294 | − | 0.773092i | \(-0.281291\pi\) | ||||
0.634294 | + | 0.773092i | \(0.281291\pi\) | |||||||
\(150\) | 529.790 | 0.288381 | ||||||||
\(151\) | 2158.29 | 1.16317 | 0.581586 | − | 0.813485i | \(-0.302432\pi\) | ||||
0.581586 | + | 0.813485i | \(0.302432\pi\) | |||||||
\(152\) | −692.445 | −0.369505 | ||||||||
\(153\) | −849.883 | −0.449078 | ||||||||
\(154\) | −337.520 | −0.176611 | ||||||||
\(155\) | −441.134 | −0.228598 | ||||||||
\(156\) | 817.510 | 0.419572 | ||||||||
\(157\) | −2032.88 | −1.03338 | −0.516692 | − | 0.856171i | \(-0.672837\pi\) | ||||
−0.516692 | + | 0.856171i | \(0.672837\pi\) | |||||||
\(158\) | −1540.18 | −0.775508 | ||||||||
\(159\) | −2471.72 | −1.23283 | ||||||||
\(160\) | 325.615 | 0.160888 | ||||||||
\(161\) | 2784.11 | 1.36285 | ||||||||
\(162\) | −75.1171 | −0.0364306 | ||||||||
\(163\) | 41.5668 | 0.0199740 | 0.00998701 | − | 0.999950i | \(-0.496821\pi\) | ||||
0.00998701 | + | 0.999950i | \(0.496821\pi\) | |||||||
\(164\) | −2057.64 | −0.979724 | ||||||||
\(165\) | −56.6205 | −0.0267145 | ||||||||
\(166\) | −187.493 | −0.0876644 | ||||||||
\(167\) | −3405.82 | −1.57814 | −0.789072 | − | 0.614301i | \(-0.789438\pi\) | ||||
−0.789072 | + | 0.614301i | \(0.789438\pi\) | |||||||
\(168\) | −1717.77 | −0.788863 | ||||||||
\(169\) | −717.315 | −0.326498 | ||||||||
\(170\) | 124.752 | 0.0562825 | ||||||||
\(171\) | −586.743 | −0.262394 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 841.476 | 0.369805 | 0.184902 | − | 0.982757i | \(-0.440803\pi\) | ||||
0.184902 | + | 0.982757i | \(0.440803\pi\) | |||||||
\(174\) | −761.040 | −0.331576 | ||||||||
\(175\) | 3359.27 | 1.45107 | ||||||||
\(176\) | 251.614 | 0.107762 | ||||||||
\(177\) | 926.915 | 0.393622 | ||||||||
\(178\) | 995.674 | 0.419263 | ||||||||
\(179\) | 757.562 | 0.316329 | 0.158164 | − | 0.987413i | \(-0.449442\pi\) | ||||
0.158164 | + | 0.987413i | \(0.449442\pi\) | |||||||
\(180\) | 177.039 | 0.0733097 | ||||||||
\(181\) | −2451.87 | −1.00688 | −0.503442 | − | 0.864029i | \(-0.667933\pi\) | ||||
−0.503442 | + | 0.864029i | \(0.667933\pi\) | |||||||
\(182\) | −1372.80 | −0.559112 | ||||||||
\(183\) | −103.872 | −0.0419586 | ||||||||
\(184\) | 1871.92 | 0.749997 | ||||||||
\(185\) | 417.571 | 0.165948 | ||||||||
\(186\) | 1076.69 | 0.424446 | ||||||||
\(187\) | 511.644 | 0.200081 | ||||||||
\(188\) | −940.159 | −0.364724 | ||||||||
\(189\) | −3957.18 | −1.52298 | ||||||||
\(190\) | 86.1263 | 0.0328856 | ||||||||
\(191\) | 957.463 | 0.362720 | 0.181360 | − | 0.983417i | \(-0.441950\pi\) | ||||
0.181360 | + | 0.983417i | \(0.441950\pi\) | |||||||
\(192\) | −79.5935 | −0.0299175 | ||||||||
\(193\) | 4925.30 | 1.83695 | 0.918474 | − | 0.395481i | \(-0.129422\pi\) | ||||
0.918474 | + | 0.395481i | \(0.129422\pi\) | |||||||
\(194\) | 2435.34 | 0.901273 | ||||||||
\(195\) | −230.292 | −0.0845722 | ||||||||
\(196\) | −2639.72 | −0.961998 | ||||||||
\(197\) | −1146.48 | −0.414636 | −0.207318 | − | 0.978274i | \(-0.566474\pi\) | ||||
−0.207318 | + | 0.978274i | \(0.566474\pi\) | |||||||
\(198\) | −192.293 | −0.0690184 | ||||||||
\(199\) | 3188.35 | 1.13576 | 0.567880 | − | 0.823111i | \(-0.307764\pi\) | ||||
0.567880 | + | 0.823111i | \(0.307764\pi\) | |||||||
\(200\) | 2258.63 | 0.798546 | ||||||||
\(201\) | 91.7478 | 0.0321960 | ||||||||
\(202\) | −860.253 | −0.299640 | ||||||||
\(203\) | −4825.57 | −1.66842 | ||||||||
\(204\) | 1149.74 | 0.394596 | ||||||||
\(205\) | 579.637 | 0.197481 | ||||||||
\(206\) | −980.179 | −0.331516 | ||||||||
\(207\) | 1586.17 | 0.532591 | ||||||||
\(208\) | 1023.39 | 0.341150 | ||||||||
\(209\) | 353.230 | 0.116906 | ||||||||
\(210\) | 213.656 | 0.0702081 | ||||||||
\(211\) | −5892.40 | −1.92251 | −0.961256 | − | 0.275659i | \(-0.911104\pi\) | ||||
−0.961256 | + | 0.275659i | \(0.911104\pi\) | |||||||
\(212\) | −4652.70 | −1.50730 | ||||||||
\(213\) | 222.042 | 0.0714277 | ||||||||
\(214\) | −1698.92 | −0.542689 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2660.64 | −0.838118 | ||||||||
\(217\) | 6827.06 | 2.13572 | ||||||||
\(218\) | 406.484 | 0.126287 | ||||||||
\(219\) | 1720.03 | 0.530724 | ||||||||
\(220\) | −106.581 | −0.0326622 | ||||||||
\(221\) | 2081.01 | 0.633411 | ||||||||
\(222\) | −1019.18 | −0.308122 | ||||||||
\(223\) | −1185.81 | −0.356088 | −0.178044 | − | 0.984023i | \(-0.556977\pi\) | ||||
−0.178044 | + | 0.984023i | \(0.556977\pi\) | |||||||
\(224\) | −5039.28 | −1.50313 | ||||||||
\(225\) | 1913.85 | 0.567066 | ||||||||
\(226\) | −2719.01 | −0.800290 | ||||||||
\(227\) | 4647.73 | 1.35895 | 0.679473 | − | 0.733700i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733700i | \(0.262208\pi\) | |||||||
\(228\) | 793.756 | 0.230560 | ||||||||
\(229\) | −1956.95 | −0.564711 | −0.282355 | − | 0.959310i | \(-0.591116\pi\) | ||||
−0.282355 | + | 0.959310i | \(0.591116\pi\) | |||||||
\(230\) | −232.829 | −0.0667490 | ||||||||
\(231\) | 876.269 | 0.249585 | ||||||||
\(232\) | −3244.51 | −0.918157 | ||||||||
\(233\) | −2211.01 | −0.621665 | −0.310832 | − | 0.950465i | \(-0.600608\pi\) | ||||
−0.310832 | + | 0.950465i | \(0.600608\pi\) | |||||||
\(234\) | −782.111 | −0.218497 | ||||||||
\(235\) | 264.842 | 0.0735167 | ||||||||
\(236\) | 1744.80 | 0.481257 | ||||||||
\(237\) | 3998.61 | 1.09594 | ||||||||
\(238\) | −1930.68 | −0.525830 | ||||||||
\(239\) | 808.463 | 0.218808 | 0.109404 | − | 0.993997i | \(-0.465106\pi\) | ||||
0.109404 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(240\) | −159.276 | −0.0428385 | ||||||||
\(241\) | −3816.46 | −1.02008 | −0.510041 | − | 0.860150i | \(-0.670370\pi\) | ||||
−0.510041 | + | 0.860150i | \(0.670370\pi\) | |||||||
\(242\) | −1606.87 | −0.426832 | ||||||||
\(243\) | −3679.72 | −0.971416 | ||||||||
\(244\) | −195.526 | −0.0513002 | ||||||||
\(245\) | 743.609 | 0.193908 | ||||||||
\(246\) | −1414.74 | −0.366670 | ||||||||
\(247\) | 1436.69 | 0.370099 | ||||||||
\(248\) | 4590.22 | 1.17532 | ||||||||
\(249\) | 486.769 | 0.123886 | ||||||||
\(250\) | −569.177 | −0.143992 | ||||||||
\(251\) | 4999.26 | 1.25717 | 0.628586 | − | 0.777740i | \(-0.283634\pi\) | ||||
0.628586 | + | 0.777740i | \(0.283634\pi\) | |||||||
\(252\) | −2739.89 | −0.684909 | ||||||||
\(253\) | −954.900 | −0.237289 | ||||||||
\(254\) | −2292.09 | −0.566215 | ||||||||
\(255\) | −323.880 | −0.0795379 | ||||||||
\(256\) | −2042.02 | −0.498540 | ||||||||
\(257\) | −2878.94 | −0.698767 | −0.349383 | − | 0.936980i | \(-0.613609\pi\) | ||||
−0.349383 | + | 0.936980i | \(0.613609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6462.40 | −1.55040 | ||||||||
\(260\) | −433.496 | −0.103401 | ||||||||
\(261\) | −2749.23 | −0.652004 | ||||||||
\(262\) | 3666.94 | 0.864673 | ||||||||
\(263\) | 7196.10 | 1.68719 | 0.843594 | − | 0.536982i | \(-0.180436\pi\) | ||||
0.843594 | + | 0.536982i | \(0.180436\pi\) | |||||||
\(264\) | 589.166 | 0.137351 | ||||||||
\(265\) | 1310.66 | 0.303824 | ||||||||
\(266\) | −1332.91 | −0.307239 | ||||||||
\(267\) | −2584.96 | −0.592499 | ||||||||
\(268\) | 172.703 | 0.0393640 | ||||||||
\(269\) | 8400.53 | 1.90405 | 0.952025 | − | 0.306019i | \(-0.0989972\pi\) | ||||
0.952025 | + | 0.306019i | \(0.0989972\pi\) | |||||||
\(270\) | 330.930 | 0.0745917 | ||||||||
\(271\) | −692.143 | −0.155147 | −0.0775733 | − | 0.996987i | \(-0.524717\pi\) | ||||
−0.0775733 | + | 0.996987i | \(0.524717\pi\) | |||||||
\(272\) | 1439.28 | 0.320843 | ||||||||
\(273\) | 3564.04 | 0.790131 | ||||||||
\(274\) | 497.432 | 0.109675 | ||||||||
\(275\) | −1152.17 | −0.252649 | ||||||||
\(276\) | −2145.79 | −0.467977 | ||||||||
\(277\) | −2581.54 | −0.559963 | −0.279981 | − | 0.960005i | \(-0.590328\pi\) | ||||
−0.279981 | + | 0.960005i | \(0.590328\pi\) | |||||||
\(278\) | 1422.91 | 0.306979 | ||||||||
\(279\) | 3889.52 | 0.834623 | ||||||||
\(280\) | 910.873 | 0.194411 | ||||||||
\(281\) | −5866.29 | −1.24539 | −0.622693 | − | 0.782466i | \(-0.713961\pi\) | ||||
−0.622693 | + | 0.782466i | \(0.713961\pi\) | |||||||
\(282\) | −646.413 | −0.136501 | ||||||||
\(283\) | −7501.69 | −1.57572 | −0.787861 | − | 0.615854i | \(-0.788811\pi\) | ||||
−0.787861 | + | 0.615854i | \(0.788811\pi\) | |||||||
\(284\) | 417.966 | 0.0873301 | ||||||||
\(285\) | −223.601 | −0.0464736 | ||||||||
\(286\) | 470.844 | 0.0973483 | ||||||||
\(287\) | −8970.56 | −1.84500 | ||||||||
\(288\) | −2870.99 | −0.587412 | ||||||||
\(289\) | −1986.30 | −0.404294 | ||||||||
\(290\) | 403.552 | 0.0817151 | ||||||||
\(291\) | −6322.61 | −1.27367 | ||||||||
\(292\) | 3237.73 | 0.648883 | ||||||||
\(293\) | −4809.72 | −0.958999 | −0.479500 | − | 0.877542i | \(-0.659182\pi\) | ||||
−0.479500 | + | 0.877542i | \(0.659182\pi\) | |||||||
\(294\) | −1814.96 | −0.360036 | ||||||||
\(295\) | −491.509 | −0.0970060 | ||||||||
\(296\) | −4345.04 | −0.853211 | ||||||||
\(297\) | 1357.24 | 0.265169 | ||||||||
\(298\) | 2986.17 | 0.580483 | ||||||||
\(299\) | −3883.86 | −0.751203 | ||||||||
\(300\) | −2589.09 | −0.498270 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2793.34 | 0.532247 | ||||||||
\(303\) | 2233.39 | 0.423448 | ||||||||
\(304\) | 993.652 | 0.187467 | ||||||||
\(305\) | 55.0795 | 0.0103405 | ||||||||
\(306\) | −1099.95 | −0.205490 | ||||||||
\(307\) | −2532.95 | −0.470890 | −0.235445 | − | 0.971888i | \(-0.575655\pi\) | ||||
−0.235445 | + | 0.971888i | \(0.575655\pi\) | |||||||
\(308\) | 1649.46 | 0.305152 | ||||||||
\(309\) | 2544.73 | 0.468495 | ||||||||
\(310\) | −570.932 | −0.104602 | ||||||||
\(311\) | −9641.95 | −1.75802 | −0.879011 | − | 0.476802i | \(-0.841796\pi\) | ||||
−0.879011 | + | 0.476802i | \(0.841796\pi\) | |||||||
\(312\) | 2396.31 | 0.434822 | ||||||||
\(313\) | 7799.67 | 1.40851 | 0.704254 | − | 0.709948i | \(-0.251281\pi\) | ||||
0.704254 | + | 0.709948i | \(0.251281\pi\) | |||||||
\(314\) | −2631.03 | −0.472858 | ||||||||
\(315\) | 771.827 | 0.138056 | ||||||||
\(316\) | 7526.87 | 1.33994 | ||||||||
\(317\) | −8558.52 | −1.51639 | −0.758193 | − | 0.652031i | \(-0.773917\pi\) | ||||
−0.758193 | + | 0.652031i | \(0.773917\pi\) | |||||||
\(318\) | −3198.99 | −0.564122 | ||||||||
\(319\) | 1655.08 | 0.290492 | ||||||||
\(320\) | 42.2055 | 0.00737300 | ||||||||
\(321\) | 4410.72 | 0.766923 | ||||||||
\(322\) | 3603.30 | 0.623615 | ||||||||
\(323\) | 2020.54 | 0.348068 | ||||||||
\(324\) | 367.098 | 0.0629454 | ||||||||
\(325\) | −4686.22 | −0.799830 | ||||||||
\(326\) | 53.7974 | 0.00913976 | ||||||||
\(327\) | −1055.31 | −0.178468 | ||||||||
\(328\) | −6031.42 | −1.01533 | ||||||||
\(329\) | −4098.75 | −0.686843 | ||||||||
\(330\) | −73.2804 | −0.0122241 | ||||||||
\(331\) | −3134.43 | −0.520495 | −0.260247 | − | 0.965542i | \(-0.583804\pi\) | ||||
−0.260247 | + | 0.965542i | \(0.583804\pi\) | |||||||
\(332\) | 916.280 | 0.151468 | ||||||||
\(333\) | −3681.77 | −0.605885 | ||||||||
\(334\) | −4407.94 | −0.722131 | ||||||||
\(335\) | −48.6505 | −0.00793451 | ||||||||
\(336\) | 2464.99 | 0.400226 | ||||||||
\(337\) | −192.133 | −0.0310569 | −0.0155284 | − | 0.999879i | \(-0.504943\pi\) | ||||
−0.0155284 | + | 0.999879i | \(0.504943\pi\) | |||||||
\(338\) | −928.377 | −0.149400 | ||||||||
\(339\) | 7059.07 | 1.13096 | ||||||||
\(340\) | −609.663 | −0.0972459 | ||||||||
\(341\) | −2341.56 | −0.371855 | ||||||||
\(342\) | −759.385 | −0.120067 | ||||||||
\(343\) | −2050.19 | −0.322740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 604.469 | 0.0943291 | ||||||||
\(346\) | 1089.07 | 0.169216 | ||||||||
\(347\) | 4066.72 | 0.629144 | 0.314572 | − | 0.949234i | \(-0.398139\pi\) | ||||
0.314572 | + | 0.949234i | \(0.398139\pi\) | |||||||
\(348\) | 3719.20 | 0.572903 | ||||||||
\(349\) | −9154.26 | −1.40406 | −0.702029 | − | 0.712148i | \(-0.747723\pi\) | ||||
−0.702029 | + | 0.712148i | \(0.747723\pi\) | |||||||
\(350\) | 4347.70 | 0.663983 | ||||||||
\(351\) | 5520.31 | 0.839465 | ||||||||
\(352\) | 1728.38 | 0.261714 | ||||||||
\(353\) | 854.088 | 0.128778 | 0.0643888 | − | 0.997925i | \(-0.479490\pi\) | ||||
0.0643888 | + | 0.997925i | \(0.479490\pi\) | |||||||
\(354\) | 1199.65 | 0.180115 | ||||||||
\(355\) | −117.741 | −0.0176029 | ||||||||
\(356\) | −4865.86 | −0.724411 | ||||||||
\(357\) | 5012.42 | 0.743097 | ||||||||
\(358\) | 980.465 | 0.144746 | ||||||||
\(359\) | 3079.71 | 0.452761 | 0.226380 | − | 0.974039i | \(-0.427311\pi\) | ||||
0.226380 | + | 0.974039i | \(0.427311\pi\) | |||||||
\(360\) | 518.944 | 0.0759743 | ||||||||
\(361\) | −5464.06 | −0.796626 | ||||||||
\(362\) | −3173.30 | −0.460732 | ||||||||
\(363\) | 4171.74 | 0.603195 | ||||||||
\(364\) | 6708.86 | 0.966043 | ||||||||
\(365\) | −912.067 | −0.130794 | ||||||||
\(366\) | −134.435 | −0.0191995 | ||||||||
\(367\) | 1288.57 | 0.183277 | 0.0916384 | − | 0.995792i | \(-0.470790\pi\) | ||||
0.0916384 | + | 0.995792i | \(0.470790\pi\) | |||||||
\(368\) | −2686.18 | −0.380508 | ||||||||
\(369\) | −5110.72 | −0.721012 | ||||||||
\(370\) | 540.436 | 0.0759350 | ||||||||
\(371\) | −20284.1 | −2.83853 | ||||||||
\(372\) | −5261.81 | −0.733366 | ||||||||
\(373\) | −9257.47 | −1.28508 | −0.642538 | − | 0.766254i | \(-0.722119\pi\) | ||||
−0.642538 | + | 0.766254i | \(0.722119\pi\) | |||||||
\(374\) | 662.189 | 0.0915535 | ||||||||
\(375\) | 1477.69 | 0.203488 | ||||||||
\(376\) | −2755.82 | −0.377981 | ||||||||
\(377\) | 6731.72 | 0.919632 | ||||||||
\(378\) | −5121.53 | −0.696887 | ||||||||
\(379\) | −7746.53 | −1.04990 | −0.524951 | − | 0.851133i | \(-0.675916\pi\) | ||||
−0.524951 | + | 0.851133i | \(0.675916\pi\) | |||||||
\(380\) | −420.900 | −0.0568203 | ||||||||
\(381\) | 5950.72 | 0.800169 | ||||||||
\(382\) | 1239.19 | 0.165974 | ||||||||
\(383\) | 247.436 | 0.0330114 | 0.0165057 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165057 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(384\) | 4809.49 | 0.639149 | ||||||||
\(385\) | −464.653 | −0.0615089 | ||||||||
\(386\) | 6374.51 | 0.840555 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11901.5 | −1.55723 | ||||||||
\(389\) | 10078.8 | 1.31366 | 0.656831 | − | 0.754038i | \(-0.271896\pi\) | ||||
0.656831 | + | 0.754038i | \(0.271896\pi\) | |||||||
\(390\) | −298.053 | −0.0386987 | ||||||||
\(391\) | −5462.21 | −0.706486 | ||||||||
\(392\) | −7737.64 | −0.996964 | ||||||||
\(393\) | −9520.09 | −1.22195 | ||||||||
\(394\) | −1483.82 | −0.189730 | ||||||||
\(395\) | −2120.32 | −0.270088 | ||||||||
\(396\) | 939.735 | 0.119251 | ||||||||
\(397\) | −58.9880 | −0.00745723 | −0.00372862 | − | 0.999993i | \(-0.501187\pi\) | ||||
−0.00372862 | + | 0.999993i | \(0.501187\pi\) | |||||||
\(398\) | 4126.49 | 0.519704 | ||||||||
\(399\) | 3460.48 | 0.434188 | ||||||||
\(400\) | −3241.11 | −0.405139 | ||||||||
\(401\) | 7494.39 | 0.933297 | 0.466648 | − | 0.884443i | \(-0.345461\pi\) | ||||
0.466648 | + | 0.884443i | \(0.345461\pi\) | |||||||
\(402\) | 118.743 | 0.0147323 | ||||||||
\(403\) | −9523.82 | −1.17721 | ||||||||
\(404\) | 4204.06 | 0.517723 | ||||||||
\(405\) | −103.411 | −0.0126878 | ||||||||
\(406\) | −6245.44 | −0.763438 | ||||||||
\(407\) | 2216.49 | 0.269944 | ||||||||
\(408\) | 3370.14 | 0.408938 | ||||||||
\(409\) | −9345.06 | −1.12979 | −0.564894 | − | 0.825163i | \(-0.691083\pi\) | ||||
−0.564894 | + | 0.825163i | \(0.691083\pi\) | |||||||
\(410\) | 750.188 | 0.0903637 | ||||||||
\(411\) | −1291.43 | −0.154992 | ||||||||
\(412\) | 4790.14 | 0.572799 | ||||||||
\(413\) | 7606.68 | 0.906296 | ||||||||
\(414\) | 2052.88 | 0.243704 | ||||||||
\(415\) | −258.116 | −0.0305311 | ||||||||
\(416\) | 7029.85 | 0.828526 | ||||||||
\(417\) | −3694.14 | −0.433820 | ||||||||
\(418\) | 457.163 | 0.0534942 | ||||||||
\(419\) | 11194.4 | 1.30521 | 0.652607 | − | 0.757697i | \(-0.273675\pi\) | ||||
0.652607 | + | 0.757697i | \(0.273675\pi\) | |||||||
\(420\) | −1044.14 | −0.121307 | ||||||||
\(421\) | 4066.28 | 0.470732 | 0.235366 | − | 0.971907i | \(-0.424371\pi\) | ||||
0.235366 | + | 0.971907i | \(0.424371\pi\) | |||||||
\(422\) | −7626.17 | −0.879707 | ||||||||
\(423\) | −2335.15 | −0.268413 | ||||||||
\(424\) | −13638.1 | −1.56209 | ||||||||
\(425\) | −6590.63 | −0.752218 | ||||||||
\(426\) | 287.376 | 0.0326840 | ||||||||
\(427\) | −852.420 | −0.0966077 | ||||||||
\(428\) | 8302.61 | 0.937668 | ||||||||
\(429\) | −1222.40 | −0.137572 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8136.58 | −0.909340 | −0.454670 | − | 0.890660i | \(-0.650243\pi\) | ||||
−0.454670 | + | 0.890660i | \(0.650243\pi\) | |||||||
\(432\) | 3817.99 | 0.425215 | ||||||||
\(433\) | −7039.42 | −0.781277 | −0.390638 | − | 0.920544i | \(-0.627746\pi\) | ||||
−0.390638 | + | 0.920544i | \(0.627746\pi\) | |||||||
\(434\) | 8835.84 | 0.977267 | ||||||||
\(435\) | −1047.70 | −0.115479 | ||||||||
\(436\) | −1986.49 | −0.218201 | ||||||||
\(437\) | −3771.01 | −0.412796 | ||||||||
\(438\) | 2226.12 | 0.242850 | ||||||||
\(439\) | 12596.3 | 1.36945 | 0.684727 | − | 0.728800i | \(-0.259922\pi\) | ||||
0.684727 | + | 0.728800i | \(0.259922\pi\) | |||||||
\(440\) | −312.413 | −0.0338493 | ||||||||
\(441\) | −6556.49 | −0.707967 | ||||||||
\(442\) | 2693.32 | 0.289838 | ||||||||
\(443\) | 17582.4 | 1.88570 | 0.942851 | − | 0.333216i | \(-0.108134\pi\) | ||||
0.942851 | + | 0.333216i | \(0.108134\pi\) | |||||||
\(444\) | 4980.76 | 0.532379 | ||||||||
\(445\) | 1370.71 | 0.146018 | ||||||||
\(446\) | −1534.72 | −0.162939 | ||||||||
\(447\) | −7752.67 | −0.820333 | ||||||||
\(448\) | −653.180 | −0.0688836 | ||||||||
\(449\) | 1356.00 | 0.142524 | 0.0712621 | − | 0.997458i | \(-0.477297\pi\) | ||||
0.0712621 | + | 0.997458i | \(0.477297\pi\) | |||||||
\(450\) | 2476.98 | 0.259479 | ||||||||
\(451\) | 3076.74 | 0.321238 | ||||||||
\(452\) | 13287.8 | 1.38275 | ||||||||
\(453\) | −7252.05 | −0.752166 | ||||||||
\(454\) | 6015.27 | 0.621830 | ||||||||
\(455\) | −1889.88 | −0.194723 | ||||||||
\(456\) | 2326.68 | 0.238940 | ||||||||
\(457\) | 9380.12 | 0.960139 | 0.480069 | − | 0.877230i | \(-0.340611\pi\) | ||||
0.480069 | + | 0.877230i | \(0.340611\pi\) | |||||||
\(458\) | −2532.76 | −0.258402 | ||||||||
\(459\) | 7763.69 | 0.789494 | ||||||||
\(460\) | 1137.84 | 0.115330 | ||||||||
\(461\) | 8627.66 | 0.871649 | 0.435825 | − | 0.900032i | \(-0.356457\pi\) | ||||
0.435825 | + | 0.900032i | \(0.356457\pi\) | |||||||
\(462\) | 1134.10 | 0.114206 | ||||||||
\(463\) | −2501.34 | −0.251073 | −0.125537 | − | 0.992089i | \(-0.540065\pi\) | ||||
−0.125537 | + | 0.992089i | \(0.540065\pi\) | |||||||
\(464\) | 4655.83 | 0.465823 | ||||||||
\(465\) | 1482.25 | 0.147823 | ||||||||
\(466\) | −2861.57 | −0.284463 | ||||||||
\(467\) | 10147.1 | 1.00546 | 0.502731 | − | 0.864443i | \(-0.332329\pi\) | ||||
0.502731 | + | 0.864443i | \(0.332329\pi\) | |||||||
\(468\) | 3822.18 | 0.377522 | ||||||||
\(469\) | 752.924 | 0.0741296 | ||||||||
\(470\) | 342.769 | 0.0336399 | ||||||||
\(471\) | 6830.66 | 0.668238 | ||||||||
\(472\) | 5114.41 | 0.498749 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5175.15 | 0.501483 | ||||||||
\(475\) | −4550.05 | −0.439517 | ||||||||
\(476\) | 9435.25 | 0.908538 | ||||||||
\(477\) | −11556.3 | −1.10928 | ||||||||
\(478\) | 1046.34 | 0.100123 | ||||||||
\(479\) | 20100.3 | 1.91735 | 0.958673 | − | 0.284511i | \(-0.0918313\pi\) | ||||
0.958673 | + | 0.284511i | \(0.0918313\pi\) | |||||||
\(480\) | −1094.10 | −0.104039 | ||||||||
\(481\) | 9015.12 | 0.854582 | ||||||||
\(482\) | −4939.41 | −0.466772 | ||||||||
\(483\) | −9354.87 | −0.881287 | ||||||||
\(484\) | 7852.77 | 0.737488 | ||||||||
\(485\) | 3352.65 | 0.313888 | ||||||||
\(486\) | −4762.43 | −0.444503 | ||||||||
\(487\) | −8302.85 | −0.772563 | −0.386281 | − | 0.922381i | \(-0.626241\pi\) | ||||
−0.386281 | + | 0.922381i | \(0.626241\pi\) | |||||||
\(488\) | −573.131 | −0.0531648 | ||||||||
\(489\) | −139.669 | −0.0129162 | ||||||||
\(490\) | 962.407 | 0.0887288 | ||||||||
\(491\) | 988.707 | 0.0908752 | 0.0454376 | − | 0.998967i | \(-0.485532\pi\) | ||||
0.0454376 | + | 0.998967i | \(0.485532\pi\) | |||||||
\(492\) | 6913.87 | 0.633539 | ||||||||
\(493\) | 9467.40 | 0.864889 | ||||||||
\(494\) | 1859.42 | 0.169351 | ||||||||
\(495\) | −264.723 | −0.0240372 | ||||||||
\(496\) | −6586.92 | −0.596294 | ||||||||
\(497\) | 1822.18 | 0.164459 | ||||||||
\(498\) | 629.995 | 0.0566882 | ||||||||
\(499\) | −1586.04 | −0.142286 | −0.0711430 | − | 0.997466i | \(-0.522665\pi\) | ||||
−0.0711430 | + | 0.997466i | \(0.522665\pi\) | |||||||
\(500\) | 2781.57 | 0.248791 | ||||||||
\(501\) | 11443.9 | 1.02051 | ||||||||
\(502\) | 6470.23 | 0.575260 | ||||||||
\(503\) | 9056.14 | 0.802770 | 0.401385 | − | 0.915909i | \(-0.368529\pi\) | ||||
0.401385 | + | 0.915909i | \(0.368529\pi\) | |||||||
\(504\) | −8031.26 | −0.709803 | ||||||||
\(505\) | −1184.28 | −0.104356 | ||||||||
\(506\) | −1235.87 | −0.108579 | ||||||||
\(507\) | 2410.25 | 0.211130 | ||||||||
\(508\) | 11201.5 | 0.978316 | ||||||||
\(509\) | 10268.3 | 0.894170 | 0.447085 | − | 0.894491i | \(-0.352462\pi\) | ||||
0.447085 | + | 0.894491i | \(0.352462\pi\) | |||||||
\(510\) | −419.178 | −0.0363951 | ||||||||
\(511\) | 14115.3 | 1.22197 | ||||||||
\(512\) | 8807.99 | 0.760277 | ||||||||
\(513\) | 5359.90 | 0.461297 | ||||||||
\(514\) | −3726.03 | −0.319743 | ||||||||
\(515\) | −1349.38 | −0.115458 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1405.80 | 0.119588 | ||||||||
\(518\) | −8363.88 | −0.709436 | ||||||||
\(519\) | −2827.44 | −0.239134 | ||||||||
\(520\) | −1270.68 | −0.107159 | ||||||||
\(521\) | 8690.28 | 0.730764 | 0.365382 | − | 0.930858i | \(-0.380938\pi\) | ||||
0.365382 | + | 0.930858i | \(0.380938\pi\) | |||||||
\(522\) | −3558.16 | −0.298346 | ||||||||
\(523\) | −11938.1 | −0.998124 | −0.499062 | − | 0.866566i | \(-0.666322\pi\) | ||||
−0.499062 | + | 0.866566i | \(0.666322\pi\) | |||||||
\(524\) | −17920.4 | −1.49400 | ||||||||
\(525\) | −11287.5 | −0.938334 | ||||||||
\(526\) | 9313.46 | 0.772027 | ||||||||
\(527\) | −13394.2 | −1.10713 | ||||||||
\(528\) | −845.446 | −0.0696843 | ||||||||
\(529\) | −1972.67 | −0.162133 | ||||||||
\(530\) | 1696.31 | 0.139025 | ||||||||
\(531\) | 4333.69 | 0.354174 | ||||||||
\(532\) | 6513.92 | 0.530854 | ||||||||
\(533\) | 12514.0 | 1.01697 | ||||||||
\(534\) | −3345.56 | −0.271117 | ||||||||
\(535\) | −2338.84 | −0.189004 | ||||||||
\(536\) | 506.234 | 0.0407947 | ||||||||
\(537\) | −2545.48 | −0.204554 | ||||||||
\(538\) | 10872.3 | 0.871260 | ||||||||
\(539\) | 3947.12 | 0.315426 | ||||||||
\(540\) | −1617.26 | −0.128881 | ||||||||
\(541\) | −11644.8 | −0.925413 | −0.462707 | − | 0.886511i | \(-0.653122\pi\) | ||||
−0.462707 | + | 0.886511i | \(0.653122\pi\) | |||||||
\(542\) | −895.798 | −0.0709923 | ||||||||
\(543\) | 8238.51 | 0.651102 | ||||||||
\(544\) | 9886.69 | 0.779206 | ||||||||
\(545\) | 559.594 | 0.0439823 | ||||||||
\(546\) | 4612.72 | 0.361550 | ||||||||
\(547\) | −16635.8 | −1.30035 | −0.650177 | − | 0.759783i | \(-0.725305\pi\) | ||||
−0.650177 | + | 0.759783i | \(0.725305\pi\) | |||||||
\(548\) | −2430.95 | −0.189498 | ||||||||
\(549\) | −485.642 | −0.0377536 | ||||||||
\(550\) | −1491.18 | −0.115608 | ||||||||
\(551\) | 6536.12 | 0.505350 | ||||||||
\(552\) | −6289.82 | −0.484986 | ||||||||
\(553\) | 32814.4 | 2.52335 | ||||||||
\(554\) | −3341.13 | −0.256229 | ||||||||
\(555\) | −1403.08 | −0.107310 | ||||||||
\(556\) | −6953.75 | −0.530404 | ||||||||
\(557\) | 310.333 | 0.0236073 | 0.0118036 | − | 0.999930i | \(-0.496243\pi\) | ||||
0.0118036 | + | 0.999930i | \(0.496243\pi\) | |||||||
\(558\) | 5033.97 | 0.381908 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1307.09 | −0.0986335 | ||||||||
\(561\) | −1719.17 | −0.129382 | ||||||||
\(562\) | −7592.37 | −0.569866 | ||||||||
\(563\) | −5029.04 | −0.376463 | −0.188232 | − | 0.982125i | \(-0.560276\pi\) | ||||
−0.188232 | + | 0.982125i | \(0.560276\pi\) | |||||||
\(564\) | 3159.02 | 0.235849 | ||||||||
\(565\) | −3743.17 | −0.278719 | ||||||||
\(566\) | −9708.97 | −0.721022 | ||||||||
\(567\) | 1600.41 | 0.118538 | ||||||||
\(568\) | 1225.16 | 0.0905043 | ||||||||
\(569\) | 11414.7 | 0.841001 | 0.420500 | − | 0.907292i | \(-0.361855\pi\) | ||||
0.420500 | + | 0.907292i | \(0.361855\pi\) | |||||||
\(570\) | −289.393 | −0.0212655 | ||||||||
\(571\) | −5046.78 | −0.369879 | −0.184940 | − | 0.982750i | \(-0.559209\pi\) | ||||
−0.184940 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(572\) | −2301.02 | −0.168200 | ||||||||
\(573\) | −3217.17 | −0.234553 | ||||||||
\(574\) | −11610.0 | −0.844240 | ||||||||
\(575\) | 12300.3 | 0.892104 | ||||||||
\(576\) | −372.131 | −0.0269192 | ||||||||
\(577\) | −1338.61 | −0.0965807 | −0.0482904 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482904 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(578\) | −2570.74 | −0.184998 | ||||||||
\(579\) | −16549.5 | −1.18786 | ||||||||
\(580\) | −1972.16 | −0.141189 | ||||||||
\(581\) | 3994.65 | 0.285243 | ||||||||
\(582\) | −8182.96 | −0.582808 | ||||||||
\(583\) | 6957.07 | 0.494224 | ||||||||
\(584\) | 9490.53 | 0.672468 | ||||||||
\(585\) | −1076.71 | −0.0760964 | ||||||||
\(586\) | −6224.92 | −0.438821 | ||||||||
\(587\) | −8253.72 | −0.580354 | −0.290177 | − | 0.956973i | \(-0.593714\pi\) | ||||
−0.290177 | + | 0.956973i | \(0.593714\pi\) | |||||||
\(588\) | 8869.72 | 0.622077 | ||||||||
\(589\) | −9247.09 | −0.646892 | ||||||||
\(590\) | −636.130 | −0.0443882 | ||||||||
\(591\) | 3852.28 | 0.268125 | ||||||||
\(592\) | 6235.09 | 0.432873 | ||||||||
\(593\) | 17646.3 | 1.22200 | 0.610999 | − | 0.791631i | \(-0.290768\pi\) | ||||
0.610999 | + | 0.791631i | \(0.290768\pi\) | |||||||
\(594\) | 1756.59 | 0.121337 | ||||||||
\(595\) | −2657.91 | −0.183132 | ||||||||
\(596\) | −14593.4 | −1.00297 | ||||||||
\(597\) | −10713.2 | −0.734440 | ||||||||
\(598\) | −5026.64 | −0.343737 | ||||||||
\(599\) | −19407.0 | −1.32379 | −0.661894 | − | 0.749598i | \(-0.730247\pi\) | ||||
−0.661894 | + | 0.749598i | \(0.730247\pi\) | |||||||
\(600\) | −7589.21 | −0.516380 | ||||||||
\(601\) | 2556.29 | 0.173500 | 0.0867499 | − | 0.996230i | \(-0.472352\pi\) | ||||
0.0867499 | + | 0.996230i | \(0.472352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 428.957 | 0.0289693 | ||||||||
\(604\) | −13651.1 | −0.919625 | ||||||||
\(605\) | −2212.12 | −0.148654 | ||||||||
\(606\) | 2890.53 | 0.193762 | ||||||||
\(607\) | 14431.3 | 0.964988 | 0.482494 | − | 0.875899i | \(-0.339731\pi\) | ||||
0.482494 | + | 0.875899i | \(0.339731\pi\) | |||||||
\(608\) | 6825.58 | 0.455286 | ||||||||
\(609\) | 16214.4 | 1.07888 | ||||||||
\(610\) | 71.2860 | 0.00473162 | ||||||||
\(611\) | 5717.80 | 0.378588 | ||||||||
\(612\) | 5375.46 | 0.355049 | ||||||||
\(613\) | −10358.6 | −0.682512 | −0.341256 | − | 0.939970i | \(-0.610852\pi\) | ||||
−0.341256 | + | 0.939970i | \(0.610852\pi\) | |||||||
\(614\) | −3278.25 | −0.215471 | ||||||||
\(615\) | −1947.63 | −0.127701 | ||||||||
\(616\) | 4834.96 | 0.316244 | ||||||||
\(617\) | −25620.7 | −1.67172 | −0.835860 | − | 0.548942i | \(-0.815031\pi\) | ||||
−0.835860 | + | 0.548942i | \(0.815031\pi\) | |||||||
\(618\) | 3293.49 | 0.214375 | ||||||||
\(619\) | 7346.23 | 0.477011 | 0.238505 | − | 0.971141i | \(-0.423343\pi\) | ||||
0.238505 | + | 0.971141i | \(0.423343\pi\) | |||||||
\(620\) | 2790.15 | 0.180734 | ||||||||
\(621\) | −14489.7 | −0.936312 | ||||||||
\(622\) | −12479.0 | −0.804440 | ||||||||
\(623\) | −21213.4 | −1.36420 | ||||||||
\(624\) | −3438.68 | −0.220605 | ||||||||
\(625\) | 14444.6 | 0.924455 | ||||||||
\(626\) | 10094.6 | 0.644509 | ||||||||
\(627\) | −1186.88 | −0.0755975 | ||||||||
\(628\) | 12857.8 | 0.817012 | ||||||||
\(629\) | 12678.7 | 0.803711 | ||||||||
\(630\) | 998.928 | 0.0631718 | ||||||||
\(631\) | −10677.3 | −0.673626 | −0.336813 | − | 0.941572i | \(-0.609349\pi\) | ||||
−0.336813 | + | 0.941572i | \(0.609349\pi\) | |||||||
\(632\) | 22063.0 | 1.38864 | ||||||||
\(633\) | 19799.0 | 1.24319 | ||||||||
\(634\) | −11076.8 | −0.693871 | ||||||||
\(635\) | −3155.45 | −0.197197 | ||||||||
\(636\) | 15633.5 | 0.974699 | ||||||||
\(637\) | 16054.1 | 0.998566 | ||||||||
\(638\) | 2142.07 | 0.132924 | ||||||||
\(639\) | 1038.14 | 0.0642692 | ||||||||
\(640\) | −2550.30 | −0.157515 | ||||||||
\(641\) | 1114.95 | 0.0687018 | 0.0343509 | − | 0.999410i | \(-0.489064\pi\) | ||||
0.0343509 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(642\) | 5708.52 | 0.350930 | ||||||||
\(643\) | 9253.91 | 0.567556 | 0.283778 | − | 0.958890i | \(-0.408412\pi\) | ||||
0.283778 | + | 0.958890i | \(0.408412\pi\) | |||||||
\(644\) | −17609.3 | −1.07749 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2615.06 | 0.159270 | ||||||||
\(647\) | −18799.8 | −1.14234 | −0.571172 | − | 0.820831i | \(-0.693511\pi\) | ||||
−0.571172 | + | 0.820831i | \(0.693511\pi\) | |||||||
\(648\) | 1076.05 | 0.0652333 | ||||||||
\(649\) | −2608.96 | −0.157797 | ||||||||
\(650\) | −6065.08 | −0.365988 | ||||||||
\(651\) | −22939.6 | −1.38106 | ||||||||
\(652\) | −262.908 | −0.0157918 | ||||||||
\(653\) | 24082.8 | 1.44324 | 0.721618 | − | 0.692291i | \(-0.243399\pi\) | ||||
0.721618 | + | 0.692291i | \(0.243399\pi\) | |||||||
\(654\) | −1365.82 | −0.0816636 | ||||||||
\(655\) | 5048.16 | 0.301142 | ||||||||
\(656\) | 8655.03 | 0.515125 | ||||||||
\(657\) | 8041.80 | 0.477535 | ||||||||
\(658\) | −5304.76 | −0.314287 | ||||||||
\(659\) | −23306.6 | −1.37769 | −0.688843 | − | 0.724911i | \(-0.741881\pi\) | ||||
−0.688843 | + | 0.724911i | \(0.741881\pi\) | |||||||
\(660\) | 358.122 | 0.0211210 | ||||||||
\(661\) | 8490.11 | 0.499587 | 0.249793 | − | 0.968299i | \(-0.419637\pi\) | ||||
0.249793 | + | 0.968299i | \(0.419637\pi\) | |||||||
\(662\) | −4056.69 | −0.238169 | ||||||||
\(663\) | −6992.39 | −0.409595 | ||||||||
\(664\) | 2685.83 | 0.156974 | ||||||||
\(665\) | −1834.97 | −0.107003 | ||||||||
\(666\) | −4765.09 | −0.277242 | ||||||||
\(667\) | −17669.4 | −1.02573 | ||||||||
\(668\) | 21541.6 | 1.24771 | ||||||||
\(669\) | 3984.43 | 0.230264 | ||||||||
\(670\) | −62.9654 | −0.00363069 | ||||||||
\(671\) | 292.365 | 0.0168206 | ||||||||
\(672\) | 16932.5 | 0.972000 | ||||||||
\(673\) | 6648.43 | 0.380800 | 0.190400 | − | 0.981707i | \(-0.439022\pi\) | ||||
0.190400 | + | 0.981707i | \(0.439022\pi\) | |||||||
\(674\) | −248.666 | −0.0142111 | ||||||||
\(675\) | −17483.0 | −0.996921 | ||||||||
\(676\) | 4536.98 | 0.258135 | ||||||||
\(677\) | −18154.8 | −1.03064 | −0.515320 | − | 0.856998i | \(-0.672327\pi\) | ||||
−0.515320 | + | 0.856998i | \(0.672327\pi\) | |||||||
\(678\) | 9136.11 | 0.517508 | ||||||||
\(679\) | −51886.2 | −2.93256 | ||||||||
\(680\) | −1787.06 | −0.100781 | ||||||||
\(681\) | −15616.8 | −0.878763 | ||||||||
\(682\) | −3030.54 | −0.170154 | ||||||||
\(683\) | 1949.71 | 0.109229 | 0.0546147 | − | 0.998508i | \(-0.482607\pi\) | ||||
0.0546147 | + | 0.998508i | \(0.482607\pi\) | |||||||
\(684\) | 3711.12 | 0.207454 | ||||||||
\(685\) | 684.799 | 0.0381968 | ||||||||
\(686\) | −2653.43 | −0.147680 | ||||||||
\(687\) | 6575.53 | 0.365170 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28296.5 | 1.56460 | ||||||||
\(690\) | 782.327 | 0.0431633 | ||||||||
\(691\) | 6988.90 | 0.384762 | 0.192381 | − | 0.981320i | \(-0.438379\pi\) | ||||
0.192381 | + | 0.981320i | \(0.438379\pi\) | |||||||
\(692\) | −5322.29 | −0.292374 | ||||||||
\(693\) | 4096.90 | 0.224572 | ||||||||
\(694\) | 5263.31 | 0.287885 | ||||||||
\(695\) | 1958.87 | 0.106912 | ||||||||
\(696\) | 10901.9 | 0.593726 | ||||||||
\(697\) | 17599.6 | 0.956429 | ||||||||
\(698\) | −11847.8 | −0.642472 | ||||||||
\(699\) | 7429.19 | 0.402000 | ||||||||
\(700\) | −21247.2 | −1.14724 | ||||||||
\(701\) | −6698.64 | −0.360919 | −0.180459 | − | 0.983582i | \(-0.557758\pi\) | ||||
−0.180459 | + | 0.983582i | \(0.557758\pi\) | |||||||
\(702\) | 7144.59 | 0.384124 | ||||||||
\(703\) | 8753.17 | 0.469604 | ||||||||
\(704\) | 224.029 | 0.0119935 | ||||||||
\(705\) | −889.896 | −0.0475396 | ||||||||
\(706\) | 1105.39 | 0.0589263 | ||||||||
\(707\) | 18328.2 | 0.974968 | ||||||||
\(708\) | −5862.69 | −0.311205 | ||||||||
\(709\) | −33993.1 | −1.80062 | −0.900309 | − | 0.435251i | \(-0.856659\pi\) | ||||
−0.900309 | + | 0.435251i | \(0.856659\pi\) | |||||||
\(710\) | −152.385 | −0.00805479 | ||||||||
\(711\) | 18695.1 | 0.986105 | ||||||||
\(712\) | −14263.0 | −0.750741 | ||||||||
\(713\) | 24998.0 | 1.31302 | ||||||||
\(714\) | 6487.27 | 0.340028 | ||||||||
\(715\) | 648.196 | 0.0339037 | ||||||||
\(716\) | −4791.54 | −0.250095 | ||||||||
\(717\) | −2716.51 | −0.141492 | ||||||||
\(718\) | 3985.88 | 0.207175 | ||||||||
\(719\) | 6671.11 | 0.346023 | 0.173011 | − | 0.984920i | \(-0.444650\pi\) | ||||
0.173011 | + | 0.984920i | \(0.444650\pi\) | |||||||
\(720\) | −744.679 | −0.0385452 | ||||||||
\(721\) | 20883.3 | 1.07869 | ||||||||
\(722\) | −7071.79 | −0.364522 | ||||||||
\(723\) | 12823.7 | 0.659637 | ||||||||
\(724\) | 15507.9 | 0.796061 | ||||||||
\(725\) | −21319.6 | −1.09213 | ||||||||
\(726\) | 5399.23 | 0.276011 | ||||||||
\(727\) | 20828.5 | 1.06257 | 0.531285 | − | 0.847193i | \(-0.321710\pi\) | ||||
0.531285 | + | 0.847193i | \(0.321710\pi\) | |||||||
\(728\) | 19665.2 | 1.00116 | ||||||||
\(729\) | 13931.3 | 0.707782 | ||||||||
\(730\) | −1180.43 | −0.0598490 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 656.984 | 0.0331733 | ||||||||
\(733\) | 19082.3 | 0.961556 | 0.480778 | − | 0.876842i | \(-0.340354\pi\) | ||||
0.480778 | + | 0.876842i | \(0.340354\pi\) | |||||||
\(734\) | 1667.71 | 0.0838642 | ||||||||
\(735\) | −2498.60 | −0.125391 | ||||||||
\(736\) | −18451.9 | −0.924111 | ||||||||
\(737\) | −258.240 | −0.0129069 | ||||||||
\(738\) | −6614.49 | −0.329922 | ||||||||
\(739\) | −21641.2 | −1.07725 | −0.538623 | − | 0.842547i | \(-0.681055\pi\) | ||||
−0.538623 | + | 0.842547i | \(0.681055\pi\) | |||||||
\(740\) | −2641.11 | −0.131202 | ||||||||
\(741\) | −4827.41 | −0.239324 | ||||||||
\(742\) | −26252.4 | −1.29886 | ||||||||
\(743\) | −22127.2 | −1.09255 | −0.546277 | − | 0.837605i | \(-0.683955\pi\) | ||||
−0.546277 | + | 0.837605i | \(0.683955\pi\) | |||||||
\(744\) | −15423.6 | −0.760022 | ||||||||
\(745\) | 4110.96 | 0.202166 | ||||||||
\(746\) | −11981.4 | −0.588028 | ||||||||
\(747\) | 2275.84 | 0.111471 | ||||||||
\(748\) | −3236.12 | −0.158188 | ||||||||
\(749\) | 36196.3 | 1.76580 | ||||||||
\(750\) | 1912.49 | 0.0931123 | ||||||||
\(751\) | −18774.4 | −0.912234 | −0.456117 | − | 0.889920i | \(-0.650760\pi\) | ||||
−0.456117 | + | 0.889920i | \(0.650760\pi\) | |||||||
\(752\) | 3954.58 | 0.191767 | ||||||||
\(753\) | −16798.0 | −0.812952 | ||||||||
\(754\) | 8712.45 | 0.420807 | ||||||||
\(755\) | 3845.50 | 0.185367 | ||||||||
\(756\) | 25029.0 | 1.20409 | ||||||||
\(757\) | −39416.8 | −1.89251 | −0.946253 | − | 0.323429i | \(-0.895164\pi\) | ||||
−0.946253 | + | 0.323429i | \(0.895164\pi\) | |||||||
\(758\) | −10025.9 | −0.480416 | ||||||||
\(759\) | 3208.55 | 0.153443 | ||||||||
\(760\) | −1233.75 | −0.0588855 | ||||||||
\(761\) | −562.546 | −0.0267967 | −0.0133983 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133983 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(762\) | 7701.64 | 0.366143 | ||||||||
\(763\) | −8660.37 | −0.410913 | ||||||||
\(764\) | −6055.91 | −0.286774 | ||||||||
\(765\) | −1514.27 | −0.0715666 | ||||||||
\(766\) | 320.241 | 0.0151054 | ||||||||
\(767\) | −10611.4 | −0.499551 | ||||||||
\(768\) | 6861.38 | 0.322381 | ||||||||
\(769\) | −25134.3 | −1.17863 | −0.589315 | − | 0.807903i | \(-0.700602\pi\) | ||||
−0.589315 | + | 0.807903i | \(0.700602\pi\) | |||||||
\(770\) | −601.372 | −0.0281454 | ||||||||
\(771\) | 9673.49 | 0.451858 | ||||||||
\(772\) | −31152.3 | −1.45233 | ||||||||
\(773\) | 22440.0 | 1.04413 | 0.522063 | − | 0.852907i | \(-0.325163\pi\) | ||||
0.522063 | + | 0.852907i | \(0.325163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30162.3 | 1.39802 | ||||||||
\(776\) | −34886.1 | −1.61384 | ||||||||
\(777\) | 21714.3 | 1.00257 | ||||||||
\(778\) | 13044.3 | 0.601108 | ||||||||
\(779\) | 12150.4 | 0.558836 | ||||||||
\(780\) | 1456.59 | 0.0668643 | ||||||||
\(781\) | −624.976 | −0.0286343 | ||||||||
\(782\) | −7069.40 | −0.323275 | ||||||||
\(783\) | 25114.3 | 1.14625 | ||||||||
\(784\) | 11103.4 | 0.505805 | ||||||||
\(785\) | −3622.05 | −0.164683 | ||||||||
\(786\) | −12321.3 | −0.559141 | ||||||||
\(787\) | 12520.6 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(788\) | 7251.43 | 0.327819 | ||||||||
\(789\) | −24179.6 | −1.09102 | ||||||||
\(790\) | −2744.20 | −0.123588 | ||||||||
\(791\) | 57929.9 | 2.60398 | ||||||||
\(792\) | 2754.58 | 0.123586 | ||||||||
\(793\) | 1189.14 | 0.0532502 | ||||||||
\(794\) | −76.3445 | −0.00341230 | ||||||||
\(795\) | −4403.95 | −0.196468 | ||||||||
\(796\) | −20166.2 | −0.897954 | ||||||||
\(797\) | −682.158 | −0.0303178 | −0.0151589 | − | 0.999885i | \(-0.504825\pi\) | ||||
−0.0151589 | + | 0.999885i | \(0.504825\pi\) | |||||||
\(798\) | 4478.69 | 0.198677 | ||||||||
\(799\) | 8041.44 | 0.356052 | ||||||||
\(800\) | −22263.8 | −0.983931 | ||||||||
\(801\) | −12085.7 | −0.533118 | ||||||||
\(802\) | 9699.52 | 0.427060 | ||||||||
\(803\) | −4841.30 | −0.212759 | ||||||||
\(804\) | −580.300 | −0.0254547 | ||||||||
\(805\) | 4960.55 | 0.217188 | ||||||||
\(806\) | −12326.1 | −0.538670 | ||||||||
\(807\) | −28226.6 | −1.23126 | ||||||||
\(808\) | 12323.1 | 0.536540 | ||||||||
\(809\) | −20230.9 | −0.879211 | −0.439605 | − | 0.898191i | \(-0.644882\pi\) | ||||
−0.439605 | + | 0.898191i | \(0.644882\pi\) | |||||||
\(810\) | −133.839 | −0.00580570 | ||||||||
\(811\) | −30575.2 | −1.32385 | −0.661924 | − | 0.749571i | \(-0.730260\pi\) | ||||
−0.661924 | + | 0.749571i | \(0.730260\pi\) | |||||||
\(812\) | 30521.5 | 1.31908 | ||||||||
\(813\) | 2325.67 | 0.100326 | ||||||||
\(814\) | 2868.66 | 0.123522 | ||||||||
\(815\) | 74.0611 | 0.00318313 | ||||||||
\(816\) | −4836.12 | −0.207473 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −12094.7 | −0.516971 | ||||||||
\(819\) | 16663.3 | 0.710944 | ||||||||
\(820\) | −3666.17 | −0.156132 | ||||||||
\(821\) | −24080.7 | −1.02365 | −0.511827 | − | 0.859088i | \(-0.671031\pi\) | ||||
−0.511827 | + | 0.859088i | \(0.671031\pi\) | |||||||
\(822\) | −1671.42 | −0.0709214 | ||||||||
\(823\) | −37732.6 | −1.59815 | −0.799073 | − | 0.601234i | \(-0.794676\pi\) | ||||
−0.799073 | + | 0.601234i | \(0.794676\pi\) | |||||||
\(824\) | 14041.0 | 0.593619 | ||||||||
\(825\) | 3871.40 | 0.163376 | ||||||||
\(826\) | 9844.86 | 0.414705 | ||||||||
\(827\) | −4683.21 | −0.196918 | −0.0984590 | − | 0.995141i | \(-0.531391\pi\) | ||||
−0.0984590 | + | 0.995141i | \(0.531391\pi\) | |||||||
\(828\) | −10032.4 | −0.421076 | ||||||||
\(829\) | −32363.7 | −1.35590 | −0.677948 | − | 0.735110i | \(-0.737130\pi\) | ||||
−0.677948 | + | 0.735110i | \(0.737130\pi\) | |||||||
\(830\) | −334.063 | −0.0139705 | ||||||||
\(831\) | 8674.22 | 0.362100 | ||||||||
\(832\) | 911.193 | 0.0379687 | ||||||||
\(833\) | 22578.3 | 0.939125 | ||||||||
\(834\) | −4781.10 | −0.198508 | ||||||||
\(835\) | −6068.27 | −0.251498 | ||||||||
\(836\) | −2234.16 | −0.0924282 | ||||||||
\(837\) | −35530.8 | −1.46729 | ||||||||
\(838\) | 14488.3 | 0.597243 | ||||||||
\(839\) | −41429.4 | −1.70477 | −0.852385 | − | 0.522915i | \(-0.824845\pi\) | ||||
−0.852385 | + | 0.522915i | \(0.824845\pi\) | |||||||
\(840\) | −3060.62 | −0.125716 | ||||||||
\(841\) | 6236.50 | 0.255710 | ||||||||
\(842\) | 5262.73 | 0.215399 | ||||||||
\(843\) | 19711.3 | 0.805329 | ||||||||
\(844\) | 37269.2 | 1.51997 | ||||||||
\(845\) | −1278.07 | −0.0520317 | ||||||||
\(846\) | −3022.23 | −0.122821 | ||||||||
\(847\) | 34235.2 | 1.38883 | ||||||||
\(848\) | 19570.6 | 0.792520 | ||||||||
\(849\) | 25206.4 | 1.01894 | ||||||||
\(850\) | −8529.85 | −0.344202 | ||||||||
\(851\) | −23662.8 | −0.953173 | ||||||||
\(852\) | −1404.41 | −0.0564720 | ||||||||
\(853\) | 3138.27 | 0.125970 | 0.0629849 | − | 0.998014i | \(-0.479938\pi\) | ||||
0.0629849 | + | 0.998014i | \(0.479938\pi\) | |||||||
\(854\) | −1103.23 | −0.0442060 | ||||||||
\(855\) | −1045.42 | −0.0418160 | ||||||||
\(856\) | 24336.9 | 0.971749 | ||||||||
\(857\) | 28519.2 | 1.13675 | 0.568376 | − | 0.822769i | \(-0.307572\pi\) | ||||
0.568376 | + | 0.822769i | \(0.307572\pi\) | |||||||
\(858\) | −1582.08 | −0.0629503 | ||||||||
\(859\) | 11047.9 | 0.438823 | 0.219411 | − | 0.975632i | \(-0.429586\pi\) | ||||
0.219411 | + | 0.975632i | \(0.429586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30141.9 | 1.19307 | ||||||||
\(862\) | −10530.7 | −0.416098 | ||||||||
\(863\) | −38205.6 | −1.50699 | −0.753496 | − | 0.657452i | \(-0.771634\pi\) | ||||
−0.753496 | + | 0.657452i | \(0.771634\pi\) | |||||||
\(864\) | 26226.5 | 1.03269 | ||||||||
\(865\) | 1499.29 | 0.0589333 | ||||||||
\(866\) | −9110.68 | −0.357498 | ||||||||
\(867\) | 6674.15 | 0.261437 | ||||||||
\(868\) | −43180.8 | −1.68854 | ||||||||
\(869\) | −11254.8 | −0.439346 | ||||||||
\(870\) | −1355.97 | −0.0528411 | ||||||||
\(871\) | −1050.34 | −0.0408603 | ||||||||
\(872\) | −5822.86 | −0.226132 | ||||||||
\(873\) | −29560.7 | −1.14602 | ||||||||
\(874\) | −4880.58 | −0.188888 | ||||||||
\(875\) | 12126.6 | 0.468520 | ||||||||
\(876\) | −10879.1 | −0.419600 | ||||||||
\(877\) | 17849.2 | 0.687258 | 0.343629 | − | 0.939106i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(878\) | 16302.6 | 0.626637 | ||||||||
\(879\) | 16161.1 | 0.620137 | ||||||||
\(880\) | 448.310 | 0.0171733 | ||||||||
\(881\) | −3455.04 | −0.132126 | −0.0660632 | − | 0.997815i | \(-0.521044\pi\) | ||||
−0.0660632 | + | 0.997815i | \(0.521044\pi\) | |||||||
\(882\) | −8485.65 | −0.323953 | ||||||||
\(883\) | −2949.64 | −0.112416 | −0.0562081 | − | 0.998419i | \(-0.517901\pi\) | ||||
−0.0562081 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(884\) | −13162.3 | −0.500786 | ||||||||
\(885\) | 1651.52 | 0.0627290 | ||||||||
\(886\) | 22755.8 | 0.862863 | ||||||||
\(887\) | 16846.9 | 0.637728 | 0.318864 | − | 0.947800i | \(-0.396699\pi\) | ||||
0.318864 | + | 0.947800i | \(0.396699\pi\) | |||||||
\(888\) | 14599.8 | 0.551729 | ||||||||
\(889\) | 48834.3 | 1.84235 | ||||||||
\(890\) | 1774.03 | 0.0668152 | ||||||||
\(891\) | −548.913 | −0.0206389 | ||||||||
\(892\) | 7500.17 | 0.281530 | ||||||||
\(893\) | 5551.66 | 0.208039 | ||||||||
\(894\) | −10033.8 | −0.375370 | ||||||||
\(895\) | 1349.78 | 0.0504112 | ||||||||
\(896\) | 39468.9 | 1.47161 | ||||||||
\(897\) | 13050.1 | 0.485766 | ||||||||
\(898\) | 1754.98 | 0.0652165 | ||||||||
\(899\) | −43328.0 | −1.60742 | ||||||||
\(900\) | −12105.0 | −0.448333 | ||||||||
\(901\) | 39795.8 | 1.47147 | ||||||||
\(902\) | 3982.04 | 0.146993 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38949.6 | 1.43301 | ||||||||
\(905\) | −4368.58 | −0.160460 | ||||||||
\(906\) | −9385.88 | −0.344178 | ||||||||
\(907\) | −12483.3 | −0.457004 | −0.228502 | − | 0.973543i | \(-0.573383\pi\) | ||||
−0.228502 | + | 0.973543i | \(0.573383\pi\) | |||||||
\(908\) | −29396.7 | −1.07441 | ||||||||
\(909\) | 10442.0 | 0.381010 | ||||||||
\(910\) | −2445.96 | −0.0891019 | ||||||||
\(911\) | 30326.7 | 1.10293 | 0.551465 | − | 0.834198i | \(-0.314069\pi\) | ||||
0.551465 | + | 0.834198i | \(0.314069\pi\) | |||||||
\(912\) | −3338.76 | −0.121225 | ||||||||
\(913\) | −1370.09 | −0.0496643 | ||||||||
\(914\) | 12140.1 | 0.439343 | ||||||||
\(915\) | −185.072 | −0.00668667 | ||||||||
\(916\) | 12377.6 | 0.446471 | ||||||||
\(917\) | −78126.2 | −2.81347 | ||||||||
\(918\) | 10048.1 | 0.361259 | ||||||||
\(919\) | 23434.7 | 0.841175 | 0.420587 | − | 0.907252i | \(-0.361824\pi\) | ||||
0.420587 | + | 0.907252i | \(0.361824\pi\) | |||||||
\(920\) | 3335.26 | 0.119522 | ||||||||
\(921\) | 8510.96 | 0.304501 | ||||||||
\(922\) | 11166.2 | 0.398851 | ||||||||
\(923\) | −2541.96 | −0.0906497 | ||||||||
\(924\) | −5542.35 | −0.197327 | ||||||||
\(925\) | −28551.2 | −1.01487 | ||||||||
\(926\) | −3237.32 | −0.114887 | ||||||||
\(927\) | 11897.6 | 0.421542 | ||||||||
\(928\) | 31981.8 | 1.13131 | ||||||||
\(929\) | −8192.13 | −0.289317 | −0.144658 | − | 0.989482i | \(-0.546208\pi\) | ||||
−0.144658 | + | 0.989482i | \(0.546208\pi\) | |||||||
\(930\) | 1918.38 | 0.0676412 | ||||||||
\(931\) | 15587.6 | 0.548726 | ||||||||
\(932\) | 13984.5 | 0.491500 | ||||||||
\(933\) | 32397.9 | 1.13683 | ||||||||
\(934\) | 13132.7 | 0.460082 | ||||||||
\(935\) | 911.615 | 0.0318856 | ||||||||
\(936\) | 11203.7 | 0.391244 | ||||||||
\(937\) | 12436.4 | 0.433596 | 0.216798 | − | 0.976216i | \(-0.430439\pi\) | ||||
0.216798 | + | 0.976216i | \(0.430439\pi\) | |||||||
\(938\) | 974.463 | 0.0339204 | ||||||||
\(939\) | −26207.6 | −0.910813 | ||||||||
\(940\) | −1675.11 | −0.0581236 | ||||||||
\(941\) | −15625.9 | −0.541327 | −0.270664 | − | 0.962674i | \(-0.587243\pi\) | ||||
−0.270664 | + | 0.962674i | \(0.587243\pi\) | |||||||
\(942\) | 8840.50 | 0.305774 | ||||||||
\(943\) | −32846.7 | −1.13429 | ||||||||
\(944\) | −7339.12 | −0.253038 | ||||||||
\(945\) | −7050.65 | −0.242706 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9888.65 | −0.339322 | −0.169661 | − | 0.985502i | \(-0.554267\pi\) | ||||
−0.169661 | + | 0.985502i | \(0.554267\pi\) | |||||||
\(948\) | −25291.0 | −0.866470 | ||||||||
\(949\) | −19691.0 | −0.673548 | ||||||||
\(950\) | −5888.85 | −0.201115 | ||||||||
\(951\) | 28757.4 | 0.980571 | ||||||||
\(952\) | 27656.9 | 0.941560 | ||||||||
\(953\) | 7170.55 | 0.243732 | 0.121866 | − | 0.992547i | \(-0.461112\pi\) | ||||
0.121866 | + | 0.992547i | \(0.461112\pi\) | |||||||
\(954\) | −14956.6 | −0.507585 | ||||||||
\(955\) | 1705.95 | 0.0578043 | ||||||||
\(956\) | −5113.48 | −0.172994 | ||||||||
\(957\) | −5561.24 | −0.187847 | ||||||||
\(958\) | 26014.6 | 0.877343 | ||||||||
\(959\) | −10598.1 | −0.356861 | ||||||||
\(960\) | −141.815 | −0.00476775 | ||||||||
\(961\) | 31508.0 | 1.05764 | ||||||||
\(962\) | 11667.7 | 0.391042 | ||||||||
\(963\) | 20621.8 | 0.690062 | ||||||||
\(964\) | 24138.9 | 0.806496 | ||||||||
\(965\) | 8775.59 | 0.292742 | ||||||||
\(966\) | −12107.4 | −0.403261 | ||||||||
\(967\) | 314.417 | 0.0104560 | 0.00522801 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522801 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(968\) | 23018.3 | 0.764293 | ||||||||
\(969\) | −6789.21 | −0.225078 | ||||||||
\(970\) | 4339.12 | 0.143630 | ||||||||
\(971\) | 4278.97 | 0.141420 | 0.0707100 | − | 0.997497i | \(-0.477474\pi\) | ||||
0.0707100 | + | 0.997497i | \(0.477474\pi\) | |||||||
\(972\) | 23274.0 | 0.768020 | ||||||||
\(973\) | −30315.8 | −0.998849 | ||||||||
\(974\) | −10745.9 | −0.353511 | ||||||||
\(975\) | 15746.1 | 0.517210 | ||||||||
\(976\) | 822.437 | 0.0269729 | ||||||||
\(977\) | −23808.5 | −0.779634 | −0.389817 | − | 0.920892i | \(-0.627462\pi\) | ||||
−0.389817 | + | 0.920892i | \(0.627462\pi\) | |||||||
\(978\) | −180.764 | −0.00591023 | ||||||||
\(979\) | 7275.81 | 0.237524 | ||||||||
\(980\) | −4703.29 | −0.153307 | ||||||||
\(981\) | −4934.00 | −0.160582 | ||||||||
\(982\) | 1279.62 | 0.0415829 | ||||||||
\(983\) | 26887.8 | 0.872418 | 0.436209 | − | 0.899845i | \(-0.356321\pi\) | ||||
0.436209 | + | 0.899845i | \(0.356321\pi\) | |||||||
\(984\) | 20266.1 | 0.656566 | ||||||||
\(985\) | −2042.73 | −0.0660778 | ||||||||
\(986\) | 12253.1 | 0.395758 | ||||||||
\(987\) | 13772.2 | 0.444147 | ||||||||
\(988\) | −9086.99 | −0.292607 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −342.615 | −0.0109990 | ||||||||
\(991\) | −17203.2 | −0.551441 | −0.275720 | − | 0.961238i | \(-0.588916\pi\) | ||||
−0.275720 | + | 0.961238i | \(0.588916\pi\) | |||||||
\(992\) | −45246.8 | −1.44817 | ||||||||
\(993\) | 10532.0 | 0.336578 | ||||||||
\(994\) | 2358.34 | 0.0752534 | ||||||||
\(995\) | 5680.81 | 0.180999 | ||||||||
\(996\) | −3078.79 | −0.0979469 | ||||||||
\(997\) | −41515.7 | −1.31877 | −0.659385 | − | 0.751805i | \(-0.729183\pi\) | ||||
−0.659385 | + | 0.751805i | \(0.729183\pi\) | |||||||
\(998\) | −2052.71 | −0.0651076 | ||||||||
\(999\) | 33633.0 | 1.06517 |
(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.i.1.31 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.20 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.31 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.20 | yes | 50 | 43.42 | odd | 2 |