Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,4,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(13.5704393013\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 68x^{2} - 111x + 342 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.57209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −7.57209 | −1.45725 | −0.728624 | − | 0.684914i | \(-0.759840\pi\) | ||||
−0.728624 | + | 0.684914i | \(0.759840\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 15.1442 | 1.03043 | ||||||||
\(7\) | −35.4229 | −1.91266 | −0.956328 | − | 0.292294i | \(-0.905581\pi\) | ||||
−0.956328 | + | 0.292294i | \(0.905581\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 30.3365 | 1.12357 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | −16.6298 | −0.455826 | −0.227913 | − | 0.973682i | \(-0.573190\pi\) | ||||
−0.227913 | + | 0.973682i | \(0.573190\pi\) | |||||||
\(12\) | −30.2883 | −0.728624 | ||||||||
\(13\) | −79.9132 | −1.70492 | −0.852459 | − | 0.522795i | \(-0.824889\pi\) | ||||
−0.852459 | + | 0.522795i | \(0.824889\pi\) | |||||||
\(14\) | 70.8458 | 1.35245 | ||||||||
\(15\) | 37.8604 | 0.651701 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −46.8219 | −0.667999 | −0.333999 | − | 0.942573i | \(-0.608398\pi\) | ||||
−0.333999 | + | 0.942573i | \(0.608398\pi\) | |||||||
\(18\) | −60.6730 | −0.794486 | ||||||||
\(19\) | −110.653 | −1.33608 | −0.668042 | − | 0.744123i | \(-0.732868\pi\) | ||||
−0.668042 | + | 0.744123i | \(0.732868\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 268.225 | 2.78722 | ||||||||
\(22\) | 33.2597 | 0.322318 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 60.5767 | 0.515215 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 159.826 | 1.20556 | ||||||||
\(27\) | −25.2641 | −0.180077 | ||||||||
\(28\) | −141.692 | −0.956328 | ||||||||
\(29\) | −0.836422 | −0.00535585 | −0.00267793 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267793 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(30\) | −75.7209 | −0.460822 | ||||||||
\(31\) | −119.836 | −0.694295 | −0.347147 | − | 0.937811i | \(-0.612850\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612850\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 125.923 | 0.664252 | ||||||||
\(34\) | 93.6438 | 0.472346 | ||||||||
\(35\) | 177.114 | 0.855366 | ||||||||
\(36\) | 121.346 | 0.561787 | ||||||||
\(37\) | 368.201 | 1.63600 | 0.817998 | − | 0.575221i | \(-0.195084\pi\) | ||||
0.817998 | + | 0.575221i | \(0.195084\pi\) | |||||||
\(38\) | 221.307 | 0.944755 | ||||||||
\(39\) | 605.109 | 2.48449 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −95.7927 | −0.364886 | −0.182443 | − | 0.983216i | \(-0.558400\pi\) | ||||
−0.182443 | + | 0.983216i | \(0.558400\pi\) | |||||||
\(42\) | −536.450 | −1.97086 | ||||||||
\(43\) | 331.961 | 1.17729 | 0.588647 | − | 0.808390i | \(-0.299661\pi\) | ||||
0.588647 | + | 0.808390i | \(0.299661\pi\) | |||||||
\(44\) | −66.5193 | −0.227913 | ||||||||
\(45\) | −151.682 | −0.502477 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −535.037 | −1.66049 | −0.830246 | − | 0.557397i | \(-0.811800\pi\) | ||||
−0.830246 | + | 0.557397i | \(0.811800\pi\) | |||||||
\(48\) | −121.153 | −0.364312 | ||||||||
\(49\) | 911.782 | 2.65826 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 354.539 | 0.973440 | ||||||||
\(52\) | −319.653 | −0.852459 | ||||||||
\(53\) | 409.345 | 1.06090 | 0.530452 | − | 0.847715i | \(-0.322022\pi\) | ||||
0.530452 | + | 0.847715i | \(0.322022\pi\) | |||||||
\(54\) | 50.5282 | 0.127334 | ||||||||
\(55\) | 83.1492 | 0.203852 | ||||||||
\(56\) | 283.383 | 0.676226 | ||||||||
\(57\) | 837.876 | 1.94701 | ||||||||
\(58\) | 1.67284 | 0.00378716 | ||||||||
\(59\) | −352.950 | −0.778817 | −0.389408 | − | 0.921065i | \(-0.627321\pi\) | ||||
−0.389408 | + | 0.921065i | \(0.627321\pi\) | |||||||
\(60\) | 151.442 | 0.325851 | ||||||||
\(61\) | −507.223 | −1.06464 | −0.532322 | − | 0.846542i | \(-0.678680\pi\) | ||||
−0.532322 | + | 0.846542i | \(0.678680\pi\) | |||||||
\(62\) | 239.672 | 0.490941 | ||||||||
\(63\) | −1074.61 | −2.14901 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 399.566 | 0.762462 | ||||||||
\(66\) | −251.845 | −0.469697 | ||||||||
\(67\) | −820.056 | −1.49531 | −0.747655 | − | 0.664087i | \(-0.768820\pi\) | ||||
−0.747655 | + | 0.664087i | \(0.768820\pi\) | |||||||
\(68\) | −187.288 | −0.333999 | ||||||||
\(69\) | 174.158 | 0.303857 | ||||||||
\(70\) | −354.229 | −0.604835 | ||||||||
\(71\) | −733.770 | −1.22651 | −0.613257 | − | 0.789884i | \(-0.710141\pi\) | ||||
−0.613257 | + | 0.789884i | \(0.710141\pi\) | |||||||
\(72\) | −242.692 | −0.397243 | ||||||||
\(73\) | −91.4599 | −0.146638 | −0.0733190 | − | 0.997309i | \(-0.523359\pi\) | ||||
−0.0733190 | + | 0.997309i | \(0.523359\pi\) | |||||||
\(74\) | −736.402 | −1.15682 | ||||||||
\(75\) | −189.302 | −0.291450 | ||||||||
\(76\) | −442.613 | −0.668042 | ||||||||
\(77\) | 589.077 | 0.871838 | ||||||||
\(78\) | −1210.22 | −1.75680 | ||||||||
\(79\) | 329.381 | 0.469092 | 0.234546 | − | 0.972105i | \(-0.424640\pi\) | ||||
0.234546 | + | 0.972105i | \(0.424640\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | −627.783 | −0.861156 | ||||||||
\(82\) | 191.585 | 0.258013 | ||||||||
\(83\) | −753.834 | −0.996916 | −0.498458 | − | 0.866914i | \(-0.666100\pi\) | ||||
−0.498458 | + | 0.866914i | \(0.666100\pi\) | |||||||
\(84\) | 1072.90 | 1.39361 | ||||||||
\(85\) | 234.110 | 0.298738 | ||||||||
\(86\) | −663.922 | −0.832472 | ||||||||
\(87\) | 6.33346 | 0.00780481 | ||||||||
\(88\) | 133.039 | 0.161159 | ||||||||
\(89\) | −1050.14 | −1.25073 | −0.625365 | − | 0.780332i | \(-0.715050\pi\) | ||||
−0.625365 | + | 0.780332i | \(0.715050\pi\) | |||||||
\(90\) | 303.365 | 0.355305 | ||||||||
\(91\) | 2830.76 | 3.26092 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 907.407 | 1.01176 | ||||||||
\(94\) | 1070.07 | 1.17415 | ||||||||
\(95\) | 553.267 | 0.597515 | ||||||||
\(96\) | 242.307 | 0.257608 | ||||||||
\(97\) | −271.928 | −0.284641 | −0.142320 | − | 0.989821i | \(-0.545456\pi\) | ||||
−0.142320 | + | 0.989821i | \(0.545456\pi\) | |||||||
\(98\) | −1823.56 | −1.87967 | ||||||||
\(99\) | −504.491 | −0.512154 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1658.68 | 1.63410 | 0.817052 | − | 0.576563i | \(-0.195607\pi\) | ||||
0.817052 | + | 0.576563i | \(0.195607\pi\) | |||||||
\(102\) | −709.079 | −0.688326 | ||||||||
\(103\) | 1735.52 | 1.66025 | 0.830123 | − | 0.557580i | \(-0.188270\pi\) | ||||
0.830123 | + | 0.557580i | \(0.188270\pi\) | |||||||
\(104\) | 639.305 | 0.602779 | ||||||||
\(105\) | −1341.13 | −1.24648 | ||||||||
\(106\) | −818.691 | −0.750172 | ||||||||
\(107\) | −1629.88 | −1.47258 | −0.736292 | − | 0.676664i | \(-0.763425\pi\) | ||||
−0.736292 | + | 0.676664i | \(0.763425\pi\) | |||||||
\(108\) | −101.056 | −0.0900385 | ||||||||
\(109\) | −432.151 | −0.379748 | −0.189874 | − | 0.981808i | \(-0.560808\pi\) | ||||
−0.189874 | + | 0.981808i | \(0.560808\pi\) | |||||||
\(110\) | −166.298 | −0.144145 | ||||||||
\(111\) | −2788.05 | −2.38405 | ||||||||
\(112\) | −566.766 | −0.478164 | ||||||||
\(113\) | −240.115 | −0.199895 | −0.0999476 | − | 0.994993i | \(-0.531868\pi\) | ||||
−0.0999476 | + | 0.994993i | \(0.531868\pi\) | |||||||
\(114\) | −1675.75 | −1.37674 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | −3.34569 | −0.00267793 | ||||||||
\(117\) | −2424.28 | −1.91560 | ||||||||
\(118\) | 705.900 | 0.550707 | ||||||||
\(119\) | 1658.57 | 1.27765 | ||||||||
\(120\) | −302.883 | −0.230411 | ||||||||
\(121\) | −1054.45 | −0.792223 | ||||||||
\(122\) | 1014.45 | 0.752817 | ||||||||
\(123\) | 725.350 | 0.531729 | ||||||||
\(124\) | −479.343 | −0.347147 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 2149.21 | 1.51958 | ||||||||
\(127\) | −210.993 | −0.147422 | −0.0737110 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737110 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −2513.64 | −1.71561 | ||||||||
\(130\) | −799.132 | −0.539142 | ||||||||
\(131\) | −746.178 | −0.497663 | −0.248832 | − | 0.968547i | \(-0.580047\pi\) | ||||
−0.248832 | + | 0.968547i | \(0.580047\pi\) | |||||||
\(132\) | 503.690 | 0.332126 | ||||||||
\(133\) | 3919.66 | 2.55547 | ||||||||
\(134\) | 1640.11 | 1.05734 | ||||||||
\(135\) | 126.320 | 0.0805329 | ||||||||
\(136\) | 374.575 | 0.236173 | ||||||||
\(137\) | −2420.07 | −1.50920 | −0.754601 | − | 0.656184i | \(-0.772170\pi\) | ||||
−0.754601 | + | 0.656184i | \(0.772170\pi\) | |||||||
\(138\) | −348.316 | −0.214860 | ||||||||
\(139\) | 924.030 | 0.563850 | 0.281925 | − | 0.959436i | \(-0.409027\pi\) | ||||
0.281925 | + | 0.959436i | \(0.409027\pi\) | |||||||
\(140\) | 708.458 | 0.427683 | ||||||||
\(141\) | 4051.34 | 2.41975 | ||||||||
\(142\) | 1467.54 | 0.867276 | ||||||||
\(143\) | 1328.94 | 0.777145 | ||||||||
\(144\) | 485.384 | 0.280893 | ||||||||
\(145\) | 4.18211 | 0.00239521 | ||||||||
\(146\) | 182.920 | 0.103689 | ||||||||
\(147\) | −6904.09 | −3.87374 | ||||||||
\(148\) | 1472.80 | 0.817998 | ||||||||
\(149\) | 430.614 | 0.236760 | 0.118380 | − | 0.992968i | \(-0.462230\pi\) | ||||
0.118380 | + | 0.992968i | \(0.462230\pi\) | |||||||
\(150\) | 378.604 | 0.206086 | ||||||||
\(151\) | −25.4118 | −0.0136953 | −0.00684763 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684763 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(152\) | 885.226 | 0.472377 | ||||||||
\(153\) | −1420.41 | −0.750546 | ||||||||
\(154\) | −1178.15 | −0.616483 | ||||||||
\(155\) | 599.179 | 0.310498 | ||||||||
\(156\) | 2420.44 | 1.24224 | ||||||||
\(157\) | −1580.29 | −0.803317 | −0.401658 | − | 0.915790i | \(-0.631566\pi\) | ||||
−0.401658 | + | 0.915790i | \(0.631566\pi\) | |||||||
\(158\) | −658.762 | −0.331698 | ||||||||
\(159\) | −3099.60 | −1.54600 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 814.727 | 0.398817 | ||||||||
\(162\) | 1255.57 | 0.608930 | ||||||||
\(163\) | 458.739 | 0.220437 | 0.110218 | − | 0.993907i | \(-0.464845\pi\) | ||||
0.110218 | + | 0.993907i | \(0.464845\pi\) | |||||||
\(164\) | −383.171 | −0.182443 | ||||||||
\(165\) | −629.613 | −0.297062 | ||||||||
\(166\) | 1507.67 | 0.704926 | ||||||||
\(167\) | −561.275 | −0.260076 | −0.130038 | − | 0.991509i | \(-0.541510\pi\) | ||||
−0.130038 | + | 0.991509i | \(0.541510\pi\) | |||||||
\(168\) | −2145.80 | −0.985430 | ||||||||
\(169\) | 4189.11 | 1.90674 | ||||||||
\(170\) | −468.219 | −0.211240 | ||||||||
\(171\) | −3356.83 | −1.50119 | ||||||||
\(172\) | 1327.84 | 0.588647 | ||||||||
\(173\) | 1573.95 | 0.691705 | 0.345852 | − | 0.938289i | \(-0.387590\pi\) | ||||
0.345852 | + | 0.938289i | \(0.387590\pi\) | |||||||
\(174\) | −12.6669 | −0.00551883 | ||||||||
\(175\) | −885.572 | −0.382531 | ||||||||
\(176\) | −266.077 | −0.113956 | ||||||||
\(177\) | 2672.57 | 1.13493 | ||||||||
\(178\) | 2100.29 | 0.884400 | ||||||||
\(179\) | 2215.59 | 0.925145 | 0.462572 | − | 0.886581i | \(-0.346927\pi\) | ||||
0.462572 | + | 0.886581i | \(0.346927\pi\) | |||||||
\(180\) | −606.730 | −0.251239 | ||||||||
\(181\) | 873.497 | 0.358710 | 0.179355 | − | 0.983784i | \(-0.442599\pi\) | ||||
0.179355 | + | 0.983784i | \(0.442599\pi\) | |||||||
\(182\) | −5661.51 | −2.30582 | ||||||||
\(183\) | 3840.74 | 1.55145 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −1841.00 | −0.731640 | ||||||||
\(186\) | −1814.81 | −0.715422 | ||||||||
\(187\) | 778.641 | 0.304491 | ||||||||
\(188\) | −2140.15 | −0.830246 | ||||||||
\(189\) | 894.928 | 0.344425 | ||||||||
\(190\) | −1106.53 | −0.422507 | ||||||||
\(191\) | −2497.74 | −0.946230 | −0.473115 | − | 0.881001i | \(-0.656870\pi\) | ||||
−0.473115 | + | 0.881001i | \(0.656870\pi\) | |||||||
\(192\) | −484.613 | −0.182156 | ||||||||
\(193\) | 909.155 | 0.339080 | 0.169540 | − | 0.985523i | \(-0.445772\pi\) | ||||
0.169540 | + | 0.985523i | \(0.445772\pi\) | |||||||
\(194\) | 543.857 | 0.201271 | ||||||||
\(195\) | −3025.55 | −1.11110 | ||||||||
\(196\) | 3647.13 | 1.32913 | ||||||||
\(197\) | 608.627 | 0.220116 | 0.110058 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110058 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(198\) | 1008.98 | 0.362147 | ||||||||
\(199\) | −2304.98 | −0.821083 | −0.410542 | − | 0.911842i | \(-0.634660\pi\) | ||||
−0.410542 | + | 0.911842i | \(0.634660\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 6209.54 | 2.17904 | ||||||||
\(202\) | −3317.36 | −1.15549 | ||||||||
\(203\) | 29.6285 | 0.0102439 | ||||||||
\(204\) | 1418.16 | 0.486720 | ||||||||
\(205\) | 478.963 | 0.163182 | ||||||||
\(206\) | −3471.03 | −1.17397 | ||||||||
\(207\) | −697.739 | −0.234281 | ||||||||
\(208\) | −1278.61 | −0.426229 | ||||||||
\(209\) | 1840.15 | 0.609022 | ||||||||
\(210\) | 2682.25 | 0.881395 | ||||||||
\(211\) | −4373.37 | −1.42690 | −0.713448 | − | 0.700708i | \(-0.752868\pi\) | ||||
−0.713448 | + | 0.700708i | \(0.752868\pi\) | |||||||
\(212\) | 1637.38 | 0.530452 | ||||||||
\(213\) | 5556.17 | 1.78733 | ||||||||
\(214\) | 3259.76 | 1.04127 | ||||||||
\(215\) | −1659.81 | −0.526502 | ||||||||
\(216\) | 202.113 | 0.0636668 | ||||||||
\(217\) | 4244.93 | 1.32795 | ||||||||
\(218\) | 864.303 | 0.268523 | ||||||||
\(219\) | 692.542 | 0.213688 | ||||||||
\(220\) | 332.597 | 0.101926 | ||||||||
\(221\) | 3741.69 | 1.13888 | ||||||||
\(222\) | 5576.10 | 1.68578 | ||||||||
\(223\) | 5439.50 | 1.63343 | 0.816717 | − | 0.577038i | \(-0.195792\pi\) | ||||
0.816717 | + | 0.577038i | \(0.195792\pi\) | |||||||
\(224\) | 1133.53 | 0.338113 | ||||||||
\(225\) | 758.412 | 0.224715 | ||||||||
\(226\) | 480.231 | 0.141347 | ||||||||
\(227\) | 216.498 | 0.0633017 | 0.0316508 | − | 0.999499i | \(-0.489924\pi\) | ||||
0.0316508 | + | 0.999499i | \(0.489924\pi\) | |||||||
\(228\) | 3351.51 | 0.973504 | ||||||||
\(229\) | −924.664 | −0.266828 | −0.133414 | − | 0.991060i | \(-0.542594\pi\) | ||||
−0.133414 | + | 0.991060i | \(0.542594\pi\) | |||||||
\(230\) | −230.000 | −0.0659380 | ||||||||
\(231\) | −4460.54 | −1.27049 | ||||||||
\(232\) | 6.69138 | 0.00189358 | ||||||||
\(233\) | −2369.69 | −0.666280 | −0.333140 | − | 0.942877i | \(-0.608108\pi\) | ||||
−0.333140 | + | 0.942877i | \(0.608108\pi\) | |||||||
\(234\) | 4848.57 | 1.35453 | ||||||||
\(235\) | 2675.18 | 0.742595 | ||||||||
\(236\) | −1411.80 | −0.389408 | ||||||||
\(237\) | −2494.10 | −0.683584 | ||||||||
\(238\) | −3317.14 | −0.903437 | ||||||||
\(239\) | −2769.60 | −0.749583 | −0.374791 | − | 0.927109i | \(-0.622286\pi\) | ||||
−0.374791 | + | 0.927109i | \(0.622286\pi\) | |||||||
\(240\) | 605.767 | 0.162925 | ||||||||
\(241\) | −5334.10 | −1.42572 | −0.712862 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712862 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(242\) | 2108.90 | 0.560186 | ||||||||
\(243\) | 5435.76 | 1.43500 | ||||||||
\(244\) | −2028.89 | −0.532322 | ||||||||
\(245\) | −4558.91 | −1.18881 | ||||||||
\(246\) | −1450.70 | −0.375989 | ||||||||
\(247\) | 8842.66 | 2.27791 | ||||||||
\(248\) | 958.686 | 0.245470 | ||||||||
\(249\) | 5708.10 | 1.45275 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | 4677.13 | 1.17617 | 0.588084 | − | 0.808800i | \(-0.299882\pi\) | ||||
0.588084 | + | 0.808800i | \(0.299882\pi\) | |||||||
\(252\) | −4298.42 | −1.07451 | ||||||||
\(253\) | 382.486 | 0.0950463 | ||||||||
\(254\) | 421.986 | 0.104243 | ||||||||
\(255\) | −1772.70 | −0.435336 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2602.99 | −0.631789 | −0.315895 | − | 0.948794i | \(-0.602305\pi\) | ||||
−0.315895 | + | 0.948794i | \(0.602305\pi\) | |||||||
\(258\) | 5027.28 | 1.21312 | ||||||||
\(259\) | −13042.7 | −3.12910 | ||||||||
\(260\) | 1598.26 | 0.381231 | ||||||||
\(261\) | −25.3741 | −0.00601769 | ||||||||
\(262\) | 1492.36 | 0.351901 | ||||||||
\(263\) | −3411.30 | −0.799809 | −0.399904 | − | 0.916557i | \(-0.630957\pi\) | ||||
−0.399904 | + | 0.916557i | \(0.630957\pi\) | |||||||
\(264\) | −1007.38 | −0.234848 | ||||||||
\(265\) | −2046.73 | −0.474451 | ||||||||
\(266\) | −7839.32 | −1.80699 | ||||||||
\(267\) | 7951.77 | 1.82262 | ||||||||
\(268\) | −3280.22 | −0.747655 | ||||||||
\(269\) | 4366.56 | 0.989718 | 0.494859 | − | 0.868973i | \(-0.335220\pi\) | ||||
0.494859 | + | 0.868973i | \(0.335220\pi\) | |||||||
\(270\) | −252.641 | −0.0569453 | ||||||||
\(271\) | 5682.45 | 1.27374 | 0.636872 | − | 0.770970i | \(-0.280228\pi\) | ||||
0.636872 | + | 0.770970i | \(0.280228\pi\) | |||||||
\(272\) | −749.150 | −0.167000 | ||||||||
\(273\) | −21434.7 | −4.75197 | ||||||||
\(274\) | 4840.14 | 1.06717 | ||||||||
\(275\) | −415.746 | −0.0911652 | ||||||||
\(276\) | 696.632 | 0.151929 | ||||||||
\(277\) | −1884.62 | −0.408794 | −0.204397 | − | 0.978888i | \(-0.565523\pi\) | ||||
−0.204397 | + | 0.978888i | \(0.565523\pi\) | |||||||
\(278\) | −1848.06 | −0.398702 | ||||||||
\(279\) | −3635.39 | −0.780091 | ||||||||
\(280\) | −1416.92 | −0.302418 | ||||||||
\(281\) | −2706.42 | −0.574561 | −0.287281 | − | 0.957846i | \(-0.592751\pi\) | ||||
−0.287281 | + | 0.957846i | \(0.592751\pi\) | |||||||
\(282\) | −8102.69 | −1.71102 | ||||||||
\(283\) | −5963.64 | −1.25266 | −0.626328 | − | 0.779560i | \(-0.715443\pi\) | ||||
−0.626328 | + | 0.779560i | \(0.715443\pi\) | |||||||
\(284\) | −2935.08 | −0.613257 | ||||||||
\(285\) | −4189.38 | −0.870728 | ||||||||
\(286\) | −2657.89 | −0.549525 | ||||||||
\(287\) | 3393.26 | 0.697901 | ||||||||
\(288\) | −970.767 | −0.198622 | ||||||||
\(289\) | −2720.71 | −0.553778 | ||||||||
\(290\) | −8.36422 | −0.00169367 | ||||||||
\(291\) | 2059.06 | 0.414792 | ||||||||
\(292\) | −365.840 | −0.0733190 | ||||||||
\(293\) | −4735.85 | −0.944272 | −0.472136 | − | 0.881526i | \(-0.656517\pi\) | ||||
−0.472136 | + | 0.881526i | \(0.656517\pi\) | |||||||
\(294\) | 13808.2 | 2.73915 | ||||||||
\(295\) | 1764.75 | 0.348297 | ||||||||
\(296\) | −2945.61 | −0.578412 | ||||||||
\(297\) | 420.138 | 0.0820837 | ||||||||
\(298\) | −861.227 | −0.167415 | ||||||||
\(299\) | 1838.00 | 0.355500 | ||||||||
\(300\) | −757.209 | −0.145725 | ||||||||
\(301\) | −11759.0 | −2.25176 | ||||||||
\(302\) | 50.8236 | 0.00968401 | ||||||||
\(303\) | −12559.6 | −2.38130 | ||||||||
\(304\) | −1770.45 | −0.334021 | ||||||||
\(305\) | 2536.12 | 0.476123 | ||||||||
\(306\) | 2840.82 | 0.530716 | ||||||||
\(307\) | −769.241 | −0.143006 | −0.0715031 | − | 0.997440i | \(-0.522780\pi\) | ||||
−0.0715031 | + | 0.997440i | \(0.522780\pi\) | |||||||
\(308\) | 2356.31 | 0.435919 | ||||||||
\(309\) | −13141.5 | −2.41939 | ||||||||
\(310\) | −1198.36 | −0.219555 | ||||||||
\(311\) | −5592.71 | −1.01972 | −0.509861 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509861 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(312\) | −4840.87 | −0.878399 | ||||||||
\(313\) | 9777.19 | 1.76562 | 0.882811 | − | 0.469729i | \(-0.155648\pi\) | ||||
0.882811 | + | 0.469729i | \(0.155648\pi\) | |||||||
\(314\) | 3160.58 | 0.568031 | ||||||||
\(315\) | 5373.03 | 0.961066 | ||||||||
\(316\) | 1317.52 | 0.234546 | ||||||||
\(317\) | 1868.51 | 0.331060 | 0.165530 | − | 0.986205i | \(-0.447066\pi\) | ||||
0.165530 | + | 0.986205i | \(0.447066\pi\) | |||||||
\(318\) | 6199.20 | 1.09319 | ||||||||
\(319\) | 13.9096 | 0.00244134 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 12341.6 | 2.14592 | ||||||||
\(322\) | −1629.45 | −0.282006 | ||||||||
\(323\) | 5181.00 | 0.892503 | ||||||||
\(324\) | −2511.13 | −0.430578 | ||||||||
\(325\) | −1997.83 | −0.340983 | ||||||||
\(326\) | −917.477 | −0.155872 | ||||||||
\(327\) | 3272.29 | 0.553388 | ||||||||
\(328\) | 766.342 | 0.129007 | ||||||||
\(329\) | 18952.6 | 3.17595 | ||||||||
\(330\) | 1259.23 | 0.210055 | ||||||||
\(331\) | 6966.91 | 1.15691 | 0.578454 | − | 0.815715i | \(-0.303656\pi\) | ||||
0.578454 | + | 0.815715i | \(0.303656\pi\) | |||||||
\(332\) | −3015.34 | −0.498458 | ||||||||
\(333\) | 11169.9 | 1.83816 | ||||||||
\(334\) | 1122.55 | 0.183902 | ||||||||
\(335\) | 4100.28 | 0.668723 | ||||||||
\(336\) | 4291.60 | 0.696804 | ||||||||
\(337\) | −17.5487 | −0.00283661 | −0.00141830 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141830 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(338\) | −8378.23 | −1.34827 | ||||||||
\(339\) | 1818.17 | 0.291297 | ||||||||
\(340\) | 936.438 | 0.149369 | ||||||||
\(341\) | 1992.85 | 0.316477 | ||||||||
\(342\) | 6713.66 | 1.06150 | ||||||||
\(343\) | −20147.9 | −3.17167 | ||||||||
\(344\) | −2655.69 | −0.416236 | ||||||||
\(345\) | −870.790 | −0.135889 | ||||||||
\(346\) | −3147.89 | −0.489109 | ||||||||
\(347\) | −9859.30 | −1.52529 | −0.762644 | − | 0.646818i | \(-0.776099\pi\) | ||||
−0.762644 | + | 0.646818i | \(0.776099\pi\) | |||||||
\(348\) | 25.3338 | 0.00390240 | ||||||||
\(349\) | 7200.25 | 1.10436 | 0.552178 | − | 0.833726i | \(-0.313797\pi\) | ||||
0.552178 | + | 0.833726i | \(0.313797\pi\) | |||||||
\(350\) | 1771.14 | 0.270491 | ||||||||
\(351\) | 2018.93 | 0.307016 | ||||||||
\(352\) | 532.155 | 0.0805794 | ||||||||
\(353\) | −6054.58 | −0.912897 | −0.456449 | − | 0.889750i | \(-0.650879\pi\) | ||||
−0.456449 | + | 0.889750i | \(0.650879\pi\) | |||||||
\(354\) | −5345.14 | −0.802516 | ||||||||
\(355\) | 3668.85 | 0.548513 | ||||||||
\(356\) | −4200.57 | −0.625365 | ||||||||
\(357\) | −12558.8 | −1.86186 | ||||||||
\(358\) | −4431.18 | −0.654176 | ||||||||
\(359\) | 2734.26 | 0.401974 | 0.200987 | − | 0.979594i | \(-0.435585\pi\) | ||||
0.200987 | + | 0.979594i | \(0.435585\pi\) | |||||||
\(360\) | 1213.46 | 0.177653 | ||||||||
\(361\) | 5385.16 | 0.785123 | ||||||||
\(362\) | −1746.99 | −0.253646 | ||||||||
\(363\) | 7984.37 | 1.15447 | ||||||||
\(364\) | 11323.0 | 1.63046 | ||||||||
\(365\) | 457.300 | 0.0655785 | ||||||||
\(366\) | −7681.47 | −1.09704 | ||||||||
\(367\) | −2465.50 | −0.350676 | −0.175338 | − | 0.984508i | \(-0.556102\pi\) | ||||
−0.175338 | + | 0.984508i | \(0.556102\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −2906.01 | −0.409976 | ||||||||
\(370\) | 3682.01 | 0.517347 | ||||||||
\(371\) | −14500.2 | −2.02915 | ||||||||
\(372\) | 3629.63 | 0.505880 | ||||||||
\(373\) | 5704.45 | 0.791863 | 0.395932 | − | 0.918280i | \(-0.370422\pi\) | ||||
0.395932 | + | 0.918280i | \(0.370422\pi\) | |||||||
\(374\) | −1557.28 | −0.215308 | ||||||||
\(375\) | 946.511 | 0.130340 | ||||||||
\(376\) | 4280.29 | 0.587073 | ||||||||
\(377\) | 66.8411 | 0.00913128 | ||||||||
\(378\) | −1789.86 | −0.243546 | ||||||||
\(379\) | 10231.9 | 1.38675 | 0.693376 | − | 0.720576i | \(-0.256122\pi\) | ||||
0.693376 | + | 0.720576i | \(0.256122\pi\) | |||||||
\(380\) | 2213.07 | 0.298758 | ||||||||
\(381\) | 1597.66 | 0.214830 | ||||||||
\(382\) | 4995.47 | 0.669086 | ||||||||
\(383\) | 6321.34 | 0.843356 | 0.421678 | − | 0.906746i | \(-0.361441\pi\) | ||||
0.421678 | + | 0.906746i | \(0.361441\pi\) | |||||||
\(384\) | 969.227 | 0.128804 | ||||||||
\(385\) | −2945.38 | −0.389898 | ||||||||
\(386\) | −1818.31 | −0.239766 | ||||||||
\(387\) | 10070.5 | 1.32278 | ||||||||
\(388\) | −1087.71 | −0.142320 | ||||||||
\(389\) | −925.594 | −0.120641 | −0.0603207 | − | 0.998179i | \(-0.519212\pi\) | ||||
−0.0603207 | + | 0.998179i | \(0.519212\pi\) | |||||||
\(390\) | 6051.09 | 0.785664 | ||||||||
\(391\) | 1076.90 | 0.139287 | ||||||||
\(392\) | −7294.25 | −0.939835 | ||||||||
\(393\) | 5650.13 | 0.725219 | ||||||||
\(394\) | −1217.25 | −0.155646 | ||||||||
\(395\) | −1646.91 | −0.209784 | ||||||||
\(396\) | −2017.96 | −0.256077 | ||||||||
\(397\) | −2706.75 | −0.342187 | −0.171093 | − | 0.985255i | \(-0.554730\pi\) | ||||
−0.171093 | + | 0.985255i | \(0.554730\pi\) | |||||||
\(398\) | 4609.96 | 0.580594 | ||||||||
\(399\) | −29680.0 | −3.72396 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −14095.3 | −1.75532 | −0.877661 | − | 0.479281i | \(-0.840897\pi\) | ||||
−0.877661 | + | 0.479281i | \(0.840897\pi\) | |||||||
\(402\) | −12419.1 | −1.54081 | ||||||||
\(403\) | 9576.45 | 1.18372 | ||||||||
\(404\) | 6634.71 | 0.817052 | ||||||||
\(405\) | 3138.92 | 0.385121 | ||||||||
\(406\) | −59.2570 | −0.00724353 | ||||||||
\(407\) | −6123.12 | −0.745729 | ||||||||
\(408\) | −2836.32 | −0.344163 | ||||||||
\(409\) | −10846.0 | −1.31125 | −0.655625 | − | 0.755087i | \(-0.727595\pi\) | ||||
−0.655625 | + | 0.755087i | \(0.727595\pi\) | |||||||
\(410\) | −957.927 | −0.115387 | ||||||||
\(411\) | 18325.0 | 2.19928 | ||||||||
\(412\) | 6942.06 | 0.830123 | ||||||||
\(413\) | 12502.5 | 1.48961 | ||||||||
\(414\) | 1395.48 | 0.165662 | ||||||||
\(415\) | 3769.17 | 0.445834 | ||||||||
\(416\) | 2557.22 | 0.301390 | ||||||||
\(417\) | −6996.84 | −0.821670 | ||||||||
\(418\) | −3680.29 | −0.430644 | ||||||||
\(419\) | −5626.55 | −0.656026 | −0.328013 | − | 0.944673i | \(-0.606379\pi\) | ||||
−0.328013 | + | 0.944673i | \(0.606379\pi\) | |||||||
\(420\) | −5364.50 | −0.623240 | ||||||||
\(421\) | −7109.09 | −0.822983 | −0.411491 | − | 0.911414i | \(-0.634992\pi\) | ||||
−0.411491 | + | 0.911414i | \(0.634992\pi\) | |||||||
\(422\) | 8746.74 | 1.00897 | ||||||||
\(423\) | −16231.1 | −1.86568 | ||||||||
\(424\) | −3274.76 | −0.375086 | ||||||||
\(425\) | −1170.55 | −0.133600 | ||||||||
\(426\) | −11112.3 | −1.26384 | ||||||||
\(427\) | 17967.3 | 2.03630 | ||||||||
\(428\) | −6519.52 | −0.736292 | ||||||||
\(429\) | −10062.9 | −1.13249 | ||||||||
\(430\) | 3319.61 | 0.372293 | ||||||||
\(431\) | 4464.14 | 0.498909 | 0.249455 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249455 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(432\) | −404.226 | −0.0450192 | ||||||||
\(433\) | 11009.4 | 1.22189 | 0.610947 | − | 0.791672i | \(-0.290789\pi\) | ||||
0.610947 | + | 0.791672i | \(0.290789\pi\) | |||||||
\(434\) | −8489.86 | −0.939001 | ||||||||
\(435\) | −31.6673 | −0.00349042 | ||||||||
\(436\) | −1728.61 | −0.189874 | ||||||||
\(437\) | 2545.03 | 0.278593 | ||||||||
\(438\) | −1385.08 | −0.151100 | ||||||||
\(439\) | −3052.70 | −0.331885 | −0.165943 | − | 0.986135i | \(-0.553067\pi\) | ||||
−0.165943 | + | 0.986135i | \(0.553067\pi\) | |||||||
\(440\) | −665.193 | −0.0720724 | ||||||||
\(441\) | 27660.2 | 2.98675 | ||||||||
\(442\) | −7483.37 | −0.805312 | ||||||||
\(443\) | −4465.82 | −0.478956 | −0.239478 | − | 0.970902i | \(-0.576976\pi\) | ||||
−0.239478 | + | 0.970902i | \(0.576976\pi\) | |||||||
\(444\) | −11152.2 | −1.19203 | ||||||||
\(445\) | 5250.72 | 0.559343 | ||||||||
\(446\) | −10879.0 | −1.15501 | ||||||||
\(447\) | −3260.64 | −0.345018 | ||||||||
\(448\) | −2267.07 | −0.239082 | ||||||||
\(449\) | 9040.14 | 0.950179 | 0.475090 | − | 0.879937i | \(-0.342416\pi\) | ||||
0.475090 | + | 0.879937i | \(0.342416\pi\) | |||||||
\(450\) | −1516.82 | −0.158897 | ||||||||
\(451\) | 1593.02 | 0.166324 | ||||||||
\(452\) | −960.462 | −0.0999476 | ||||||||
\(453\) | 192.420 | 0.0199574 | ||||||||
\(454\) | −432.996 | −0.0447610 | ||||||||
\(455\) | −14153.8 | −1.45833 | ||||||||
\(456\) | −6703.01 | −0.688371 | ||||||||
\(457\) | 7756.88 | 0.793986 | 0.396993 | − | 0.917822i | \(-0.370054\pi\) | ||||
0.396993 | + | 0.917822i | \(0.370054\pi\) | |||||||
\(458\) | 1849.33 | 0.188676 | ||||||||
\(459\) | 1182.91 | 0.120291 | ||||||||
\(460\) | 460.000 | 0.0466252 | ||||||||
\(461\) | 7064.19 | 0.713692 | 0.356846 | − | 0.934163i | \(-0.383852\pi\) | ||||
0.356846 | + | 0.934163i | \(0.383852\pi\) | |||||||
\(462\) | 8921.08 | 0.898369 | ||||||||
\(463\) | 12599.7 | 1.26470 | 0.632350 | − | 0.774682i | \(-0.282090\pi\) | ||||
0.632350 | + | 0.774682i | \(0.282090\pi\) | |||||||
\(464\) | −13.3828 | −0.00133896 | ||||||||
\(465\) | −4537.03 | −0.452473 | ||||||||
\(466\) | 4739.37 | 0.471131 | ||||||||
\(467\) | 14746.0 | 1.46117 | 0.730583 | − | 0.682824i | \(-0.239249\pi\) | ||||
0.730583 | + | 0.682824i | \(0.239249\pi\) | |||||||
\(468\) | −9697.14 | −0.957800 | ||||||||
\(469\) | 29048.8 | 2.86002 | ||||||||
\(470\) | −5350.37 | −0.525094 | ||||||||
\(471\) | 11966.1 | 1.17063 | ||||||||
\(472\) | 2823.60 | 0.275353 | ||||||||
\(473\) | −5520.46 | −0.536641 | ||||||||
\(474\) | 4988.20 | 0.483367 | ||||||||
\(475\) | −2766.33 | −0.267217 | ||||||||
\(476\) | 6634.27 | 0.638826 | ||||||||
\(477\) | 12418.1 | 1.19200 | ||||||||
\(478\) | 5539.19 | 0.530035 | ||||||||
\(479\) | −17411.2 | −1.66084 | −0.830418 | − | 0.557141i | \(-0.811898\pi\) | ||||
−0.830418 | + | 0.557141i | \(0.811898\pi\) | |||||||
\(480\) | −1211.53 | −0.115206 | ||||||||
\(481\) | −29424.1 | −2.78924 | ||||||||
\(482\) | 10668.2 | 1.00814 | ||||||||
\(483\) | −6169.18 | −0.581175 | ||||||||
\(484\) | −4217.79 | −0.396111 | ||||||||
\(485\) | 1359.64 | 0.127295 | ||||||||
\(486\) | −10871.5 | −1.01470 | ||||||||
\(487\) | 1320.34 | 0.122855 | 0.0614276 | − | 0.998112i | \(-0.480435\pi\) | ||||
0.0614276 | + | 0.998112i | \(0.480435\pi\) | |||||||
\(488\) | 4057.78 | 0.376408 | ||||||||
\(489\) | −3473.61 | −0.321231 | ||||||||
\(490\) | 9117.82 | 0.840614 | ||||||||
\(491\) | 17115.8 | 1.57317 | 0.786583 | − | 0.617485i | \(-0.211848\pi\) | ||||
0.786583 | + | 0.617485i | \(0.211848\pi\) | |||||||
\(492\) | 2901.40 | 0.265864 | ||||||||
\(493\) | 39.1629 | 0.00357770 | ||||||||
\(494\) | −17685.3 | −1.61073 | ||||||||
\(495\) | 2522.45 | 0.229042 | ||||||||
\(496\) | −1917.37 | −0.173574 | ||||||||
\(497\) | 25992.3 | 2.34590 | ||||||||
\(498\) | −11416.2 | −1.02725 | ||||||||
\(499\) | 17540.6 | 1.57360 | 0.786798 | − | 0.617210i | \(-0.211737\pi\) | ||||
0.786798 | + | 0.617210i | \(0.211737\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 4250.02 | 0.378996 | ||||||||
\(502\) | −9354.27 | −0.831676 | ||||||||
\(503\) | −4934.98 | −0.437455 | −0.218727 | − | 0.975786i | \(-0.570191\pi\) | ||||
−0.218727 | + | 0.975786i | \(0.570191\pi\) | |||||||
\(504\) | 8596.85 | 0.759790 | ||||||||
\(505\) | −8293.39 | −0.730794 | ||||||||
\(506\) | −764.972 | −0.0672079 | ||||||||
\(507\) | −31720.3 | −2.77860 | ||||||||
\(508\) | −843.972 | −0.0737110 | ||||||||
\(509\) | 11927.3 | 1.03865 | 0.519323 | − | 0.854578i | \(-0.326184\pi\) | ||||
0.519323 | + | 0.854578i | \(0.326184\pi\) | |||||||
\(510\) | 3545.39 | 0.307829 | ||||||||
\(511\) | 3239.78 | 0.280468 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2795.56 | 0.240598 | ||||||||
\(514\) | 5205.97 | 0.446743 | ||||||||
\(515\) | −8677.58 | −0.742485 | ||||||||
\(516\) | −10054.6 | −0.857804 | ||||||||
\(517\) | 8897.57 | 0.756895 | ||||||||
\(518\) | 26085.5 | 2.21261 | ||||||||
\(519\) | −11918.1 | −1.00799 | ||||||||
\(520\) | −3196.53 | −0.269571 | ||||||||
\(521\) | −9592.76 | −0.806653 | −0.403327 | − | 0.915056i | \(-0.632146\pi\) | ||||
−0.403327 | + | 0.915056i | \(0.632146\pi\) | |||||||
\(522\) | 50.7482 | 0.00425515 | ||||||||
\(523\) | 6525.20 | 0.545558 | 0.272779 | − | 0.962077i | \(-0.412057\pi\) | ||||
0.272779 | + | 0.962077i | \(0.412057\pi\) | |||||||
\(524\) | −2984.71 | −0.248832 | ||||||||
\(525\) | 6705.63 | 0.557443 | ||||||||
\(526\) | 6822.60 | 0.565550 | ||||||||
\(527\) | 5610.94 | 0.463788 | ||||||||
\(528\) | 2014.76 | 0.166063 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 4093.45 | 0.335487 | ||||||||
\(531\) | −10707.3 | −0.875058 | ||||||||
\(532\) | 15678.6 | 1.27774 | ||||||||
\(533\) | 7655.10 | 0.622100 | ||||||||
\(534\) | −15903.5 | −1.28879 | ||||||||
\(535\) | 8149.40 | 0.658560 | ||||||||
\(536\) | 6560.45 | 0.528672 | ||||||||
\(537\) | −16776.6 | −1.34817 | ||||||||
\(538\) | −8733.13 | −0.699836 | ||||||||
\(539\) | −15162.8 | −1.21170 | ||||||||
\(540\) | 505.282 | 0.0402664 | ||||||||
\(541\) | 5634.05 | 0.447739 | 0.223870 | − | 0.974619i | \(-0.428131\pi\) | ||||
0.223870 | + | 0.974619i | \(0.428131\pi\) | |||||||
\(542\) | −11364.9 | −0.900673 | ||||||||
\(543\) | −6614.19 | −0.522729 | ||||||||
\(544\) | 1498.30 | 0.118087 | ||||||||
\(545\) | 2160.76 | 0.169829 | ||||||||
\(546\) | 42869.5 | 3.36015 | ||||||||
\(547\) | 6093.08 | 0.476273 | 0.238136 | − | 0.971232i | \(-0.423463\pi\) | ||||
0.238136 | + | 0.971232i | \(0.423463\pi\) | |||||||
\(548\) | −9680.29 | −0.754601 | ||||||||
\(549\) | −15387.4 | −1.19620 | ||||||||
\(550\) | 831.492 | 0.0644635 | ||||||||
\(551\) | 92.5529 | 0.00715587 | ||||||||
\(552\) | −1393.26 | −0.107430 | ||||||||
\(553\) | −11667.6 | −0.897212 | ||||||||
\(554\) | 3769.24 | 0.289061 | ||||||||
\(555\) | 13940.2 | 1.06618 | ||||||||
\(556\) | 3696.12 | 0.281925 | ||||||||
\(557\) | 21461.9 | 1.63262 | 0.816311 | − | 0.577612i | \(-0.196015\pi\) | ||||
0.816311 | + | 0.577612i | \(0.196015\pi\) | |||||||
\(558\) | 7270.79 | 0.551608 | ||||||||
\(559\) | −26528.1 | −2.00719 | ||||||||
\(560\) | 2833.83 | 0.213842 | ||||||||
\(561\) | −5895.93 | −0.443719 | ||||||||
\(562\) | 5412.85 | 0.406276 | ||||||||
\(563\) | −11038.5 | −0.826316 | −0.413158 | − | 0.910659i | \(-0.635574\pi\) | ||||
−0.413158 | + | 0.910659i | \(0.635574\pi\) | |||||||
\(564\) | 16205.4 | 1.20988 | ||||||||
\(565\) | 1200.58 | 0.0893959 | ||||||||
\(566\) | 11927.3 | 0.885761 | ||||||||
\(567\) | 22237.9 | 1.64710 | ||||||||
\(568\) | 5870.16 | 0.433638 | ||||||||
\(569\) | −19210.3 | −1.41535 | −0.707677 | − | 0.706536i | \(-0.750257\pi\) | ||||
−0.707677 | + | 0.706536i | \(0.750257\pi\) | |||||||
\(570\) | 8378.76 | 0.615698 | ||||||||
\(571\) | −11967.0 | −0.877066 | −0.438533 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438533 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(572\) | 5315.77 | 0.388573 | ||||||||
\(573\) | 18913.1 | 1.37889 | ||||||||
\(574\) | −6786.51 | −0.493490 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 1941.53 | 0.140447 | ||||||||
\(577\) | −14982.3 | −1.08097 | −0.540487 | − | 0.841352i | \(-0.681760\pi\) | ||||
−0.540487 | + | 0.841352i | \(0.681760\pi\) | |||||||
\(578\) | 5441.42 | 0.391580 | ||||||||
\(579\) | −6884.20 | −0.494124 | ||||||||
\(580\) | 16.7284 | 0.00119760 | ||||||||
\(581\) | 26703.0 | 1.90676 | ||||||||
\(582\) | −4118.13 | −0.293302 | ||||||||
\(583\) | −6807.35 | −0.483587 | ||||||||
\(584\) | 731.679 | 0.0518444 | ||||||||
\(585\) | 12121.4 | 0.856682 | ||||||||
\(586\) | 9471.71 | 0.667701 | ||||||||
\(587\) | 24002.9 | 1.68774 | 0.843871 | − | 0.536547i | \(-0.180271\pi\) | ||||
0.843871 | + | 0.536547i | \(0.180271\pi\) | |||||||
\(588\) | −27616.4 | −1.93687 | ||||||||
\(589\) | 13260.2 | 0.927637 | ||||||||
\(590\) | −3529.50 | −0.246283 | ||||||||
\(591\) | −4608.58 | −0.320764 | ||||||||
\(592\) | 5891.21 | 0.408999 | ||||||||
\(593\) | 5124.67 | 0.354882 | 0.177441 | − | 0.984131i | \(-0.443218\pi\) | ||||
0.177441 | + | 0.984131i | \(0.443218\pi\) | |||||||
\(594\) | −840.276 | −0.0580420 | ||||||||
\(595\) | −8292.84 | −0.571384 | ||||||||
\(596\) | 1722.45 | 0.118380 | ||||||||
\(597\) | 17453.5 | 1.19652 | ||||||||
\(598\) | −3676.01 | −0.251376 | ||||||||
\(599\) | −23776.8 | −1.62186 | −0.810928 | − | 0.585146i | \(-0.801037\pi\) | ||||
−0.810928 | + | 0.585146i | \(0.801037\pi\) | |||||||
\(600\) | 1514.42 | 0.103043 | ||||||||
\(601\) | −25435.3 | −1.72633 | −0.863166 | − | 0.504920i | \(-0.831522\pi\) | ||||
−0.863166 | + | 0.504920i | \(0.831522\pi\) | |||||||
\(602\) | 23518.1 | 1.59223 | ||||||||
\(603\) | −24877.6 | −1.68009 | ||||||||
\(604\) | −101.647 | −0.00684763 | ||||||||
\(605\) | 5272.24 | 0.354293 | ||||||||
\(606\) | 25119.3 | 1.68383 | ||||||||
\(607\) | −7445.94 | −0.497894 | −0.248947 | − | 0.968517i | \(-0.580084\pi\) | ||||
−0.248947 | + | 0.968517i | \(0.580084\pi\) | |||||||
\(608\) | 3540.91 | 0.236189 | ||||||||
\(609\) | −224.349 | −0.0149279 | ||||||||
\(610\) | −5072.23 | −0.336670 | ||||||||
\(611\) | 42756.5 | 2.83100 | ||||||||
\(612\) | −5681.65 | −0.375273 | ||||||||
\(613\) | −12874.4 | −0.848275 | −0.424138 | − | 0.905598i | \(-0.639423\pi\) | ||||
−0.424138 | + | 0.905598i | \(0.639423\pi\) | |||||||
\(614\) | 1538.48 | 0.101121 | ||||||||
\(615\) | −3626.75 | −0.237796 | ||||||||
\(616\) | −4712.62 | −0.308241 | ||||||||
\(617\) | −19247.2 | −1.25585 | −0.627927 | − | 0.778272i | \(-0.716096\pi\) | ||||
−0.627927 | + | 0.778272i | \(0.716096\pi\) | |||||||
\(618\) | 26282.9 | 1.71077 | ||||||||
\(619\) | −14496.4 | −0.941293 | −0.470647 | − | 0.882322i | \(-0.655979\pi\) | ||||
−0.470647 | + | 0.882322i | \(0.655979\pi\) | |||||||
\(620\) | 2396.72 | 0.155249 | ||||||||
\(621\) | 581.074 | 0.0375486 | ||||||||
\(622\) | 11185.4 | 0.721052 | ||||||||
\(623\) | 37199.1 | 2.39222 | ||||||||
\(624\) | 9681.75 | 0.621122 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −19554.4 | −1.24848 | ||||||||
\(627\) | −13933.7 | −0.887496 | ||||||||
\(628\) | −6321.15 | −0.401658 | ||||||||
\(629\) | −17239.9 | −1.09284 | ||||||||
\(630\) | −10746.1 | −0.679577 | ||||||||
\(631\) | −18030.9 | −1.13756 | −0.568779 | − | 0.822490i | \(-0.692584\pi\) | ||||
−0.568779 | + | 0.822490i | \(0.692584\pi\) | |||||||
\(632\) | −2635.05 | −0.165849 | ||||||||
\(633\) | 33115.5 | 2.07934 | ||||||||
\(634\) | −3737.03 | −0.234095 | ||||||||
\(635\) | 1054.96 | 0.0659291 | ||||||||
\(636\) | −12398.4 | −0.773000 | ||||||||
\(637\) | −72863.4 | −4.53211 | ||||||||
\(638\) | −27.8191 | −0.00172628 | ||||||||
\(639\) | −22260.0 | −1.37808 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | 11776.4 | 0.725646 | 0.362823 | − | 0.931858i | \(-0.381813\pi\) | ||||
0.362823 | + | 0.931858i | \(0.381813\pi\) | |||||||
\(642\) | −24683.2 | −1.51740 | ||||||||
\(643\) | 20207.4 | 1.23935 | 0.619676 | − | 0.784858i | \(-0.287264\pi\) | ||||
0.619676 | + | 0.784858i | \(0.287264\pi\) | |||||||
\(644\) | 3258.91 | 0.199408 | ||||||||
\(645\) | 12568.2 | 0.767244 | ||||||||
\(646\) | −10362.0 | −0.631095 | ||||||||
\(647\) | 21452.8 | 1.30355 | 0.651776 | − | 0.758412i | \(-0.274024\pi\) | ||||
0.651776 | + | 0.758412i | \(0.274024\pi\) | |||||||
\(648\) | 5022.26 | 0.304465 | ||||||||
\(649\) | 5869.50 | 0.355005 | ||||||||
\(650\) | 3995.66 | 0.241112 | ||||||||
\(651\) | −32143.0 | −1.93515 | ||||||||
\(652\) | 1834.95 | 0.110218 | ||||||||
\(653\) | −15095.2 | −0.904624 | −0.452312 | − | 0.891860i | \(-0.649401\pi\) | ||||
−0.452312 | + | 0.891860i | \(0.649401\pi\) | |||||||
\(654\) | −6544.57 | −0.391304 | ||||||||
\(655\) | 3730.89 | 0.222562 | ||||||||
\(656\) | −1532.68 | −0.0912214 | ||||||||
\(657\) | −2774.57 | −0.164759 | ||||||||
\(658\) | −37905.1 | −2.24574 | ||||||||
\(659\) | 6964.68 | 0.411693 | 0.205846 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205846 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(660\) | −2518.45 | −0.148531 | ||||||||
\(661\) | −17380.4 | −1.02272 | −0.511361 | − | 0.859366i | \(-0.670858\pi\) | ||||
−0.511361 | + | 0.859366i | \(0.670858\pi\) | |||||||
\(662\) | −13933.8 | −0.818057 | ||||||||
\(663\) | −28332.4 | −1.65964 | ||||||||
\(664\) | 6030.67 | 0.352463 | ||||||||
\(665\) | −19598.3 | −1.14284 | ||||||||
\(666\) | −22339.8 | −1.29978 | ||||||||
\(667\) | 19.2377 | 0.00111677 | ||||||||
\(668\) | −2245.10 | −0.130038 | ||||||||
\(669\) | −41188.3 | −2.38032 | ||||||||
\(670\) | −8200.56 | −0.472859 | ||||||||
\(671\) | 8435.04 | 0.485292 | ||||||||
\(672\) | −8583.21 | −0.492715 | ||||||||
\(673\) | 12383.2 | 0.709271 | 0.354635 | − | 0.935005i | \(-0.384605\pi\) | ||||
0.354635 | + | 0.935005i | \(0.384605\pi\) | |||||||
\(674\) | 35.0973 | 0.00200578 | ||||||||
\(675\) | −631.602 | −0.0360154 | ||||||||
\(676\) | 16756.5 | 0.953371 | ||||||||
\(677\) | −8375.74 | −0.475489 | −0.237744 | − | 0.971328i | \(-0.576408\pi\) | ||||
−0.237744 | + | 0.971328i | \(0.576408\pi\) | |||||||
\(678\) | −3636.35 | −0.205978 | ||||||||
\(679\) | 9632.49 | 0.544420 | ||||||||
\(680\) | −1872.88 | −0.105620 | ||||||||
\(681\) | −1639.34 | −0.0922463 | ||||||||
\(682\) | −3985.70 | −0.223783 | ||||||||
\(683\) | −4434.66 | −0.248444 | −0.124222 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124222 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(684\) | −13427.3 | −0.750595 | ||||||||
\(685\) | 12100.4 | 0.674936 | ||||||||
\(686\) | 40295.8 | 2.24271 | ||||||||
\(687\) | 7001.64 | 0.388834 | ||||||||
\(688\) | 5311.38 | 0.294323 | ||||||||
\(689\) | −32712.1 | −1.80875 | ||||||||
\(690\) | 1741.58 | 0.0960881 | ||||||||
\(691\) | 11032.8 | 0.607389 | 0.303694 | − | 0.952770i | \(-0.401780\pi\) | ||||
0.303694 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(692\) | 6295.79 | 0.345852 | ||||||||
\(693\) | 17870.5 | 0.979574 | ||||||||
\(694\) | 19718.6 | 1.07854 | ||||||||
\(695\) | −4620.15 | −0.252162 | ||||||||
\(696\) | −50.6677 | −0.00275942 | ||||||||
\(697\) | 4485.20 | 0.243743 | ||||||||
\(698\) | −14400.5 | −0.780898 | ||||||||
\(699\) | 17943.5 | 0.970936 | ||||||||
\(700\) | −3542.29 | −0.191266 | ||||||||
\(701\) | 3708.40 | 0.199806 | 0.0999032 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999032 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(702\) | −4037.87 | −0.217093 | ||||||||
\(703\) | −40742.6 | −2.18583 | ||||||||
\(704\) | −1064.31 | −0.0569782 | ||||||||
\(705\) | −20256.7 | −1.08215 | ||||||||
\(706\) | 12109.2 | 0.645516 | ||||||||
\(707\) | −58755.2 | −3.12548 | ||||||||
\(708\) | 10690.3 | 0.567465 | ||||||||
\(709\) | −6315.04 | −0.334508 | −0.167254 | − | 0.985914i | \(-0.553490\pi\) | ||||
−0.167254 | + | 0.985914i | \(0.553490\pi\) | |||||||
\(710\) | −7337.70 | −0.387858 | ||||||||
\(711\) | 9992.26 | 0.527059 | ||||||||
\(712\) | 8401.15 | 0.442200 | ||||||||
\(713\) | 2756.22 | 0.144770 | ||||||||
\(714\) | 25117.6 | 1.31653 | ||||||||
\(715\) | −6644.71 | −0.347550 | ||||||||
\(716\) | 8862.36 | 0.462572 | ||||||||
\(717\) | 20971.6 | 1.09233 | ||||||||
\(718\) | −5468.52 | −0.284239 | ||||||||
\(719\) | 24736.9 | 1.28307 | 0.641536 | − | 0.767093i | \(-0.278297\pi\) | ||||
0.641536 | + | 0.767093i | \(0.278297\pi\) | |||||||
\(720\) | −2426.92 | −0.125619 | ||||||||
\(721\) | −61477.0 | −3.17548 | ||||||||
\(722\) | −10770.3 | −0.555165 | ||||||||
\(723\) | 40390.2 | 2.07763 | ||||||||
\(724\) | 3493.99 | 0.179355 | ||||||||
\(725\) | −20.9106 | −0.00107117 | ||||||||
\(726\) | −15968.7 | −0.816330 | ||||||||
\(727\) | 33283.6 | 1.69797 | 0.848983 | − | 0.528420i | \(-0.177215\pi\) | ||||
0.848983 | + | 0.528420i | \(0.177215\pi\) | |||||||
\(728\) | −22646.0 | −1.15291 | ||||||||
\(729\) | −24209.9 | −1.22999 | ||||||||
\(730\) | −914.599 | −0.0463710 | ||||||||
\(731\) | −15543.1 | −0.786430 | ||||||||
\(732\) | 15362.9 | 0.775725 | ||||||||
\(733\) | −33636.5 | −1.69494 | −0.847471 | − | 0.530841i | \(-0.821876\pi\) | ||||
−0.847471 | + | 0.530841i | \(0.821876\pi\) | |||||||
\(734\) | 4931.00 | 0.247965 | ||||||||
\(735\) | 34520.4 | 1.73239 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 13637.4 | 0.681601 | ||||||||
\(738\) | 5812.03 | 0.289897 | ||||||||
\(739\) | 36575.5 | 1.82064 | 0.910319 | − | 0.413907i | \(-0.135836\pi\) | ||||
0.910319 | + | 0.413907i | \(0.135836\pi\) | |||||||
\(740\) | −7364.02 | −0.365820 | ||||||||
\(741\) | −66957.3 | −3.31949 | ||||||||
\(742\) | 29000.4 | 1.43482 | ||||||||
\(743\) | −17704.7 | −0.874190 | −0.437095 | − | 0.899415i | \(-0.643993\pi\) | ||||
−0.437095 | + | 0.899415i | \(0.643993\pi\) | |||||||
\(744\) | −7259.25 | −0.357711 | ||||||||
\(745\) | −2153.07 | −0.105882 | ||||||||
\(746\) | −11408.9 | −0.559932 | ||||||||
\(747\) | −22868.7 | −1.12011 | ||||||||
\(748\) | 3114.56 | 0.152246 | ||||||||
\(749\) | 57735.1 | 2.81655 | ||||||||
\(750\) | −1893.02 | −0.0921645 | ||||||||
\(751\) | 8858.37 | 0.430421 | 0.215211 | − | 0.976568i | \(-0.430956\pi\) | ||||
0.215211 | + | 0.976568i | \(0.430956\pi\) | |||||||
\(752\) | −8560.59 | −0.415123 | ||||||||
\(753\) | −35415.7 | −1.71397 | ||||||||
\(754\) | −133.682 | −0.00645679 | ||||||||
\(755\) | 127.059 | 0.00612470 | ||||||||
\(756\) | 3579.71 | 0.172213 | ||||||||
\(757\) | 7899.26 | 0.379265 | 0.189633 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189633 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(758\) | −20463.9 | −0.980582 | ||||||||
\(759\) | −2896.22 | −0.138506 | ||||||||
\(760\) | −4426.13 | −0.211254 | ||||||||
\(761\) | 23437.4 | 1.11643 | 0.558216 | − | 0.829696i | \(-0.311486\pi\) | ||||
0.558216 | + | 0.829696i | \(0.311486\pi\) | |||||||
\(762\) | −3195.31 | −0.151908 | ||||||||
\(763\) | 15308.1 | 0.726329 | ||||||||
\(764\) | −9990.95 | −0.473115 | ||||||||
\(765\) | 7102.06 | 0.335654 | ||||||||
\(766\) | −12642.7 | −0.596343 | ||||||||
\(767\) | 28205.4 | 1.32782 | ||||||||
\(768\) | −1938.45 | −0.0910780 | ||||||||
\(769\) | 31447.7 | 1.47468 | 0.737342 | − | 0.675519i | \(-0.236081\pi\) | ||||
0.737342 | + | 0.675519i | \(0.236081\pi\) | |||||||
\(770\) | 5890.77 | 0.275699 | ||||||||
\(771\) | 19710.0 | 0.920674 | ||||||||
\(772\) | 3636.62 | 0.169540 | ||||||||
\(773\) | 2397.42 | 0.111551 | 0.0557756 | − | 0.998443i | \(-0.482237\pi\) | ||||
0.0557756 | + | 0.998443i | \(0.482237\pi\) | |||||||
\(774\) | −20141.1 | −0.935343 | ||||||||
\(775\) | −2995.89 | −0.138859 | ||||||||
\(776\) | 2175.43 | 0.100636 | ||||||||
\(777\) | 98760.8 | 4.55987 | ||||||||
\(778\) | 1851.19 | 0.0853063 | ||||||||
\(779\) | 10599.8 | 0.487518 | ||||||||
\(780\) | −12102.2 | −0.555548 | ||||||||
\(781\) | 12202.5 | 0.559077 | ||||||||
\(782\) | −2153.81 | −0.0984911 | ||||||||
\(783\) | 21.1314 | 0.000964465 0 | ||||||||
\(784\) | 14588.5 | 0.664564 | ||||||||
\(785\) | 7901.44 | 0.359254 | ||||||||
\(786\) | −11300.3 | −0.512807 | ||||||||
\(787\) | −19407.0 | −0.879014 | −0.439507 | − | 0.898239i | \(-0.644847\pi\) | ||||
−0.439507 | + | 0.898239i | \(0.644847\pi\) | |||||||
\(788\) | 2434.51 | 0.110058 | ||||||||
\(789\) | 25830.7 | 1.16552 | ||||||||
\(790\) | 3293.81 | 0.148340 | ||||||||
\(791\) | 8505.58 | 0.382331 | ||||||||
\(792\) | 4035.93 | 0.181074 | ||||||||
\(793\) | 40533.8 | 1.81513 | ||||||||
\(794\) | 5413.51 | 0.241962 | ||||||||
\(795\) | 15498.0 | 0.691393 | ||||||||
\(796\) | −9219.91 | −0.410542 | ||||||||
\(797\) | −28631.1 | −1.27248 | −0.636240 | − | 0.771491i | \(-0.719511\pi\) | ||||
−0.636240 | + | 0.771491i | \(0.719511\pi\) | |||||||
\(798\) | 59360.0 | 2.63324 | ||||||||
\(799\) | 25051.4 | 1.10921 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | −31857.6 | −1.40529 | ||||||||
\(802\) | 28190.6 | 1.24120 | ||||||||
\(803\) | 1520.96 | 0.0668414 | ||||||||
\(804\) | 24838.1 | 1.08952 | ||||||||
\(805\) | −4073.63 | −0.178356 | ||||||||
\(806\) | −19152.9 | −0.837013 | ||||||||
\(807\) | −33064.0 | −1.44227 | ||||||||
\(808\) | −13269.4 | −0.577743 | ||||||||
\(809\) | −9191.25 | −0.399440 | −0.199720 | − | 0.979853i | \(-0.564003\pi\) | ||||
−0.199720 | + | 0.979853i | \(0.564003\pi\) | |||||||
\(810\) | −6277.83 | −0.272322 | ||||||||
\(811\) | −567.477 | −0.0245706 | −0.0122853 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122853 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(812\) | 118.514 | 0.00512195 | ||||||||
\(813\) | −43028.0 | −1.85616 | ||||||||
\(814\) | 12246.2 | 0.527310 | ||||||||
\(815\) | −2293.69 | −0.0985823 | ||||||||
\(816\) | 5672.63 | 0.243360 | ||||||||
\(817\) | −36732.6 | −1.57296 | ||||||||
\(818\) | 21692.0 | 0.927193 | ||||||||
\(819\) | 85875.2 | 3.66388 | ||||||||
\(820\) | 1915.85 | 0.0815909 | ||||||||
\(821\) | −6057.35 | −0.257494 | −0.128747 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128747 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(822\) | −36650.0 | −1.55513 | ||||||||
\(823\) | −21327.0 | −0.903294 | −0.451647 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451647 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(824\) | −13884.1 | −0.586986 | ||||||||
\(825\) | 3148.06 | 0.132850 | ||||||||
\(826\) | −25005.0 | −1.05331 | ||||||||
\(827\) | −27553.8 | −1.15857 | −0.579286 | − | 0.815124i | \(-0.696668\pi\) | ||||
−0.579286 | + | 0.815124i | \(0.696668\pi\) | |||||||
\(828\) | −2790.96 | −0.117141 | ||||||||
\(829\) | 11181.6 | 0.468461 | 0.234231 | − | 0.972181i | \(-0.424743\pi\) | ||||
0.234231 | + | 0.972181i | \(0.424743\pi\) | |||||||
\(830\) | −7538.34 | −0.315253 | ||||||||
\(831\) | 14270.5 | 0.595715 | ||||||||
\(832\) | −5114.44 | −0.213115 | ||||||||
\(833\) | −42691.4 | −1.77571 | ||||||||
\(834\) | 13993.7 | 0.581009 | ||||||||
\(835\) | 2806.37 | 0.116310 | ||||||||
\(836\) | 7360.59 | 0.304511 | ||||||||
\(837\) | 3027.54 | 0.125026 | ||||||||
\(838\) | 11253.1 | 0.463881 | ||||||||
\(839\) | 9811.83 | 0.403745 | 0.201872 | − | 0.979412i | \(-0.435297\pi\) | ||||
0.201872 | + | 0.979412i | \(0.435297\pi\) | |||||||
\(840\) | 10729.0 | 0.440698 | ||||||||
\(841\) | −24388.3 | −0.999971 | ||||||||
\(842\) | 14218.2 | 0.581937 | ||||||||
\(843\) | 20493.3 | 0.837279 | ||||||||
\(844\) | −17493.5 | −0.713448 | ||||||||
\(845\) | −20945.6 | −0.852721 | ||||||||
\(846\) | 32462.3 | 1.31924 | ||||||||
\(847\) | 37351.6 | 1.51525 | ||||||||
\(848\) | 6549.53 | 0.265226 | ||||||||
\(849\) | 45157.2 | 1.82543 | ||||||||
\(850\) | 2341.10 | 0.0944693 | ||||||||
\(851\) | −8468.62 | −0.341129 | ||||||||
\(852\) | 22224.7 | 0.893667 | ||||||||
\(853\) | −24030.8 | −0.964594 | −0.482297 | − | 0.876008i | \(-0.660197\pi\) | ||||
−0.482297 | + | 0.876008i | \(0.660197\pi\) | |||||||
\(854\) | −35934.6 | −1.43988 | ||||||||
\(855\) | 16784.2 | 0.671352 | ||||||||
\(856\) | 13039.0 | 0.520637 | ||||||||
\(857\) | −16934.8 | −0.675008 | −0.337504 | − | 0.941324i | \(-0.609583\pi\) | ||||
−0.337504 | + | 0.941324i | \(0.609583\pi\) | |||||||
\(858\) | 20125.7 | 0.800794 | ||||||||
\(859\) | −31057.0 | −1.23359 | −0.616793 | − | 0.787125i | \(-0.711568\pi\) | ||||
−0.616793 | + | 0.787125i | \(0.711568\pi\) | |||||||
\(860\) | −6639.22 | −0.263251 | ||||||||
\(861\) | −25694.0 | −1.01701 | ||||||||
\(862\) | −8928.27 | −0.352782 | ||||||||
\(863\) | −16157.8 | −0.637332 | −0.318666 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318666 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(864\) | 808.451 | 0.0318334 | ||||||||
\(865\) | −7869.73 | −0.309340 | ||||||||
\(866\) | −22018.9 | −0.864009 | ||||||||
\(867\) | 20601.4 | 0.806992 | ||||||||
\(868\) | 16979.7 | 0.663974 | ||||||||
\(869\) | −5477.55 | −0.213824 | ||||||||
\(870\) | 63.3346 | 0.00246810 | ||||||||
\(871\) | 65533.3 | 2.54938 | ||||||||
\(872\) | 3457.21 | 0.134261 | ||||||||
\(873\) | −8249.35 | −0.319815 | ||||||||
\(874\) | −5090.05 | −0.196995 | ||||||||
\(875\) | 4427.86 | 0.171073 | ||||||||
\(876\) | 2770.17 | 0.106844 | ||||||||
\(877\) | −32473.9 | −1.25036 | −0.625180 | − | 0.780480i | \(-0.714975\pi\) | ||||
−0.625180 | + | 0.780480i | \(0.714975\pi\) | |||||||
\(878\) | 6105.41 | 0.234678 | ||||||||
\(879\) | 35860.3 | 1.37604 | ||||||||
\(880\) | 1330.39 | 0.0509629 | ||||||||
\(881\) | −15703.2 | −0.600517 | −0.300258 | − | 0.953858i | \(-0.597073\pi\) | ||||
−0.300258 | + | 0.953858i | \(0.597073\pi\) | |||||||
\(882\) | −55320.5 | −2.11195 | ||||||||
\(883\) | −14330.4 | −0.546155 | −0.273078 | − | 0.961992i | \(-0.588042\pi\) | ||||
−0.273078 | + | 0.961992i | \(0.588042\pi\) | |||||||
\(884\) | 14966.7 | 0.569441 | ||||||||
\(885\) | −13362.8 | −0.507556 | ||||||||
\(886\) | 8931.65 | 0.338673 | ||||||||
\(887\) | 23238.2 | 0.879664 | 0.439832 | − | 0.898080i | \(-0.355038\pi\) | ||||
0.439832 | + | 0.898080i | \(0.355038\pi\) | |||||||
\(888\) | 22304.4 | 0.842890 | ||||||||
\(889\) | 7473.98 | 0.281968 | ||||||||
\(890\) | −10501.4 | −0.395515 | ||||||||
\(891\) | 10439.9 | 0.392537 | ||||||||
\(892\) | 21758.0 | 0.816717 | ||||||||
\(893\) | 59203.6 | 2.21856 | ||||||||
\(894\) | 6521.29 | 0.243965 | ||||||||
\(895\) | −11077.9 | −0.413737 | ||||||||
\(896\) | 4534.13 | 0.169057 | ||||||||
\(897\) | −13917.5 | −0.518052 | ||||||||
\(898\) | −18080.3 | −0.671878 | ||||||||
\(899\) | 100.233 | 0.00371854 | ||||||||
\(900\) | 3033.65 | 0.112357 | ||||||||
\(901\) | −19166.3 | −0.708683 | ||||||||
\(902\) | −3186.03 | −0.117609 | ||||||||
\(903\) | 89040.4 | 3.28137 | ||||||||
\(904\) | 1920.92 | 0.0706736 | ||||||||
\(905\) | −4367.48 | −0.160420 | ||||||||
\(906\) | −384.841 | −0.0141120 | ||||||||
\(907\) | −3667.46 | −0.134263 | −0.0671313 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671313 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(908\) | 865.992 | 0.0316508 | ||||||||
\(909\) | 50318.4 | 1.83604 | ||||||||
\(910\) | 28307.6 | 1.03119 | ||||||||
\(911\) | 21457.9 | 0.780385 | 0.390192 | − | 0.920733i | \(-0.372409\pi\) | ||||
0.390192 | + | 0.920733i | \(0.372409\pi\) | |||||||
\(912\) | 13406.0 | 0.486752 | ||||||||
\(913\) | 12536.1 | 0.454420 | ||||||||
\(914\) | −15513.8 | −0.561433 | ||||||||
\(915\) | −19203.7 | −0.693830 | ||||||||
\(916\) | −3698.66 | −0.133414 | ||||||||
\(917\) | 26431.8 | 0.951859 | ||||||||
\(918\) | −2365.83 | −0.0850587 | ||||||||
\(919\) | −11109.3 | −0.398762 | −0.199381 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199381 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(920\) | −920.000 | −0.0329690 | ||||||||
\(921\) | 5824.76 | 0.208396 | ||||||||
\(922\) | −14128.4 | −0.504657 | ||||||||
\(923\) | 58637.9 | 2.09110 | ||||||||
\(924\) | −17842.2 | −0.635243 | ||||||||
\(925\) | 9205.02 | 0.327199 | ||||||||
\(926\) | −25199.3 | −0.894279 | ||||||||
\(927\) | 52649.4 | 1.86541 | ||||||||
\(928\) | 26.7655 | 0.000946790 0 | ||||||||
\(929\) | −20804.3 | −0.734732 | −0.367366 | − | 0.930076i | \(-0.619740\pi\) | ||||
−0.367366 | + | 0.930076i | \(0.619740\pi\) | |||||||
\(930\) | 9074.07 | 0.319947 | ||||||||
\(931\) | −100892. | −3.55166 | ||||||||
\(932\) | −9478.75 | −0.333140 | ||||||||
\(933\) | 42348.5 | 1.48599 | ||||||||
\(934\) | −29492.0 | −1.03320 | ||||||||
\(935\) | −3893.20 | −0.136173 | ||||||||
\(936\) | 19394.3 | 0.677267 | ||||||||
\(937\) | −35550.5 | −1.23947 | −0.619735 | − | 0.784811i | \(-0.712760\pi\) | ||||
−0.619735 | + | 0.784811i | \(0.712760\pi\) | |||||||
\(938\) | −58097.5 | −2.02234 | ||||||||
\(939\) | −74033.7 | −2.57295 | ||||||||
\(940\) | 10700.7 | 0.371297 | ||||||||
\(941\) | 49674.4 | 1.72087 | 0.860436 | − | 0.509558i | \(-0.170191\pi\) | ||||
0.860436 | + | 0.509558i | \(0.170191\pi\) | |||||||
\(942\) | −23932.2 | −0.827762 | ||||||||
\(943\) | 2203.23 | 0.0760839 | ||||||||
\(944\) | −5647.20 | −0.194704 | ||||||||
\(945\) | −4474.64 | −0.154032 | ||||||||
\(946\) | 11040.9 | 0.379462 | ||||||||
\(947\) | 33466.2 | 1.14837 | 0.574184 | − | 0.818726i | \(-0.305319\pi\) | ||||
0.574184 | + | 0.818726i | \(0.305319\pi\) | |||||||
\(948\) | −9976.41 | −0.341792 | ||||||||
\(949\) | 7308.85 | 0.250006 | ||||||||
\(950\) | 5532.67 | 0.188951 | ||||||||
\(951\) | −14148.5 | −0.482437 | ||||||||
\(952\) | −13268.5 | −0.451718 | ||||||||
\(953\) | −17298.4 | −0.587984 | −0.293992 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293992 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(954\) | −24836.2 | −0.842874 | ||||||||
\(955\) | 12488.7 | 0.423167 | ||||||||
\(956\) | −11078.4 | −0.374791 | ||||||||
\(957\) | −105.324 | −0.00355763 | ||||||||
\(958\) | 34822.5 | 1.17439 | ||||||||
\(959\) | 85726.0 | 2.88659 | ||||||||
\(960\) | 2423.07 | 0.0814627 | ||||||||
\(961\) | −15430.4 | −0.517955 | ||||||||
\(962\) | 58848.2 | 1.97229 | ||||||||
\(963\) | −49444.8 | −1.65456 | ||||||||
\(964\) | −21336.4 | −0.712862 | ||||||||
\(965\) | −4545.78 | −0.151641 | ||||||||
\(966\) | 12338.4 | 0.410953 | ||||||||
\(967\) | −14869.7 | −0.494495 | −0.247248 | − | 0.968952i | \(-0.579526\pi\) | ||||
−0.247248 | + | 0.968952i | \(0.579526\pi\) | |||||||
\(968\) | 8435.59 | 0.280093 | ||||||||
\(969\) | −39231.0 | −1.30060 | ||||||||
\(970\) | −2719.28 | −0.0900113 | ||||||||
\(971\) | 26634.9 | 0.880283 | 0.440142 | − | 0.897928i | \(-0.354928\pi\) | ||||
0.440142 | + | 0.897928i | \(0.354928\pi\) | |||||||
\(972\) | 21743.0 | 0.717498 | ||||||||
\(973\) | −32731.8 | −1.07845 | ||||||||
\(974\) | −2640.69 | −0.0868717 | ||||||||
\(975\) | 15127.7 | 0.496898 | ||||||||
\(976\) | −8115.57 | −0.266161 | ||||||||
\(977\) | 40803.6 | 1.33615 | 0.668077 | − | 0.744092i | \(-0.267118\pi\) | ||||
0.668077 | + | 0.744092i | \(0.267118\pi\) | |||||||
\(978\) | 6947.22 | 0.227145 | ||||||||
\(979\) | 17463.7 | 0.570115 | ||||||||
\(980\) | −18235.6 | −0.594404 | ||||||||
\(981\) | −13109.9 | −0.426675 | ||||||||
\(982\) | −34231.6 | −1.11240 | ||||||||
\(983\) | −18615.8 | −0.604021 | −0.302011 | − | 0.953305i | \(-0.597658\pi\) | ||||
−0.302011 | + | 0.953305i | \(0.597658\pi\) | |||||||
\(984\) | −5802.80 | −0.187995 | ||||||||
\(985\) | −3043.14 | −0.0984389 | ||||||||
\(986\) | −78.3257 | −0.00252982 | ||||||||
\(987\) | −143510. | −4.62815 | ||||||||
\(988\) | 35370.6 | 1.13896 | ||||||||
\(989\) | −7635.11 | −0.245483 | ||||||||
\(990\) | −5044.91 | −0.161957 | ||||||||
\(991\) | 46185.1 | 1.48044 | 0.740220 | − | 0.672364i | \(-0.234721\pi\) | ||||
0.740220 | + | 0.672364i | \(0.234721\pi\) | |||||||
\(992\) | 3834.74 | 0.122735 | ||||||||
\(993\) | −52754.1 | −1.68590 | ||||||||
\(994\) | −51984.5 | −1.65880 | ||||||||
\(995\) | 11524.9 | 0.367200 | ||||||||
\(996\) | 22832.4 | 0.726377 | ||||||||
\(997\) | 16544.3 | 0.525541 | 0.262771 | − | 0.964858i | \(-0.415364\pi\) | ||||
0.262771 | + | 0.964858i | \(0.415364\pi\) | |||||||
\(998\) | −35081.2 | −1.11270 | ||||||||
\(999\) | −9302.26 | −0.294605 |
(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 | 230.4.a.h.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 2070.4.a.bj.1.1 | 4 | |||
4.3 | odd | 2 | 1840.4.a.m.1.4 | 4 | |||
5.2 | odd | 4 | 1150.4.b.n.599.4 | 8 | |||
5.3 | odd | 4 | 1150.4.b.n.599.5 | 8 | |||
5.4 | even | 2 | 1150.4.a.p.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1150.4.a.p.1.4 | 4 | 5.4 | even | 2 | |||
1150.4.b.n.599.4 | 8 | 5.2 | odd | 4 | |||
1150.4.b.n.599.5 | 8 | 5.3 | odd | 4 | |||
1840.4.a.m.1.4 | 4 | 4.3 | odd | 2 | |||
2070.4.a.bj.1.1 | 4 | 3.2 | odd | 2 |