Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(15.0684\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −17.0684 | −1.52665 | −0.763324 | − | 0.646016i | \(-0.776434\pi\) | ||||
−0.763324 | + | 0.646016i | \(0.776434\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −34.1369 | −1.07950 | ||||||||
\(11\) | −63.2891 | −1.73476 | −0.867381 | − | 0.497644i | \(-0.834198\pi\) | ||||
−0.867381 | + | 0.497644i | \(0.834198\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 22.2563 | 0.474829 | 0.237415 | − | 0.971408i | \(-0.423700\pi\) | ||||
0.237415 | + | 0.971408i | \(0.423700\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | −51.2053 | −0.881411 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 53.5635 | 0.764181 | 0.382090 | − | 0.924125i | \(-0.375204\pi\) | ||||
0.382090 | + | 0.924125i | \(0.375204\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 40.5028 | 0.489051 | 0.244526 | − | 0.969643i | \(-0.421368\pi\) | ||||
0.244526 | + | 0.969643i | \(0.421368\pi\) | |||||||
\(20\) | −68.2738 | −0.763324 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −126.578 | −1.22666 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 166.332 | 1.33065 | ||||||||
\(26\) | 44.5126 | 0.335755 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 151.616 | 0.970841 | 0.485420 | − | 0.874281i | \(-0.338667\pi\) | ||||
0.485420 | + | 0.874281i | \(0.338667\pi\) | |||||||
\(30\) | −102.411 | −0.623251 | ||||||||
\(31\) | 181.258 | 1.05016 | 0.525078 | − | 0.851054i | \(-0.324036\pi\) | ||||
0.525078 | + | 0.851054i | \(0.324036\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −189.867 | −1.00157 | ||||||||
\(34\) | 107.127 | 0.540357 | ||||||||
\(35\) | 119.479 | 0.577019 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 346.839 | 1.54108 | 0.770541 | − | 0.637390i | \(-0.219986\pi\) | ||||
0.770541 | + | 0.637390i | \(0.219986\pi\) | |||||||
\(38\) | 81.0056 | 0.345812 | ||||||||
\(39\) | 66.7688 | 0.274143 | ||||||||
\(40\) | −136.548 | −0.539752 | ||||||||
\(41\) | −83.1893 | −0.316878 | −0.158439 | − | 0.987369i | \(-0.550646\pi\) | ||||
−0.158439 | + | 0.987369i | \(0.550646\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 61.9979 | 0.219874 | 0.109937 | − | 0.993939i | \(-0.464935\pi\) | ||||
0.109937 | + | 0.993939i | \(0.464935\pi\) | |||||||
\(44\) | −253.156 | −0.867381 | ||||||||
\(45\) | −153.616 | −0.508883 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 401.068 | 1.24472 | 0.622360 | − | 0.782731i | \(-0.286174\pi\) | ||||
0.622360 | + | 0.782731i | \(0.286174\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 332.663 | 0.940914 | ||||||||
\(51\) | 160.691 | 0.441200 | ||||||||
\(52\) | 89.0251 | 0.237415 | ||||||||
\(53\) | −354.475 | −0.918696 | −0.459348 | − | 0.888256i | \(-0.651917\pi\) | ||||
−0.459348 | + | 0.888256i | \(0.651917\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 1080.25 | 2.64837 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 121.508 | 0.282354 | ||||||||
\(58\) | 303.232 | 0.686488 | ||||||||
\(59\) | 159.553 | 0.352068 | 0.176034 | − | 0.984384i | \(-0.443673\pi\) | ||||
0.176034 | + | 0.984384i | \(0.443673\pi\) | |||||||
\(60\) | −204.821 | −0.440705 | ||||||||
\(61\) | −438.025 | −0.919398 | −0.459699 | − | 0.888075i | \(-0.652043\pi\) | ||||
−0.459699 | + | 0.888075i | \(0.652043\pi\) | |||||||
\(62\) | 362.515 | 0.742573 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −379.880 | −0.724897 | ||||||||
\(66\) | −379.735 | −0.708214 | ||||||||
\(67\) | 41.8010 | 0.0762210 | 0.0381105 | − | 0.999274i | \(-0.487866\pi\) | ||||
0.0381105 | + | 0.999274i | \(0.487866\pi\) | |||||||
\(68\) | 214.254 | 0.382090 | ||||||||
\(69\) | −69.0000 | −0.120386 | ||||||||
\(70\) | 238.958 | 0.408014 | ||||||||
\(71\) | 479.166 | 0.800938 | 0.400469 | − | 0.916310i | \(-0.368847\pi\) | ||||
0.400469 | + | 0.916310i | \(0.368847\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 584.054 | 0.936416 | 0.468208 | − | 0.883618i | \(-0.344900\pi\) | ||||
0.468208 | + | 0.883618i | \(0.344900\pi\) | |||||||
\(74\) | 693.679 | 1.08971 | ||||||||
\(75\) | 498.995 | 0.768253 | ||||||||
\(76\) | 162.011 | 0.244526 | ||||||||
\(77\) | 443.024 | 0.655679 | ||||||||
\(78\) | 133.538 | 0.193848 | ||||||||
\(79\) | 555.934 | 0.791740 | 0.395870 | − | 0.918307i | \(-0.370443\pi\) | ||||
0.395870 | + | 0.918307i | \(0.370443\pi\) | |||||||
\(80\) | −273.095 | −0.381662 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −166.379 | −0.224066 | ||||||||
\(83\) | −815.363 | −1.07829 | −0.539143 | − | 0.842215i | \(-0.681252\pi\) | ||||
−0.539143 | + | 0.842215i | \(0.681252\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −914.246 | −1.16663 | ||||||||
\(86\) | 123.996 | 0.155475 | ||||||||
\(87\) | 454.848 | 0.560515 | ||||||||
\(88\) | −506.313 | −0.613331 | ||||||||
\(89\) | −422.496 | −0.503196 | −0.251598 | − | 0.967832i | \(-0.580956\pi\) | ||||
−0.251598 | + | 0.967832i | \(0.580956\pi\) | |||||||
\(90\) | −307.232 | −0.359834 | ||||||||
\(91\) | −155.794 | −0.179469 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 543.773 | 0.606308 | ||||||||
\(94\) | 802.137 | 0.880150 | ||||||||
\(95\) | −691.320 | −0.746609 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −124.121 | −0.129924 | −0.0649620 | − | 0.997888i | \(-0.520693\pi\) | ||||
−0.0649620 | + | 0.997888i | \(0.520693\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −569.602 | −0.578254 | ||||||||
\(100\) | 665.327 | 0.665327 | ||||||||
\(101\) | −544.113 | −0.536052 | −0.268026 | − | 0.963412i | \(-0.586371\pi\) | ||||
−0.268026 | + | 0.963412i | \(0.586371\pi\) | |||||||
\(102\) | 321.381 | 0.311975 | ||||||||
\(103\) | 924.598 | 0.884498 | 0.442249 | − | 0.896892i | \(-0.354181\pi\) | ||||
0.442249 | + | 0.896892i | \(0.354181\pi\) | |||||||
\(104\) | 178.050 | 0.167878 | ||||||||
\(105\) | 358.437 | 0.333142 | ||||||||
\(106\) | −708.950 | −0.649616 | ||||||||
\(107\) | 1931.47 | 1.74506 | 0.872532 | − | 0.488557i | \(-0.162477\pi\) | ||||
0.872532 | + | 0.488557i | \(0.162477\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 604.510 | 0.531207 | 0.265603 | − | 0.964082i | \(-0.414429\pi\) | ||||
0.265603 | + | 0.964082i | \(0.414429\pi\) | |||||||
\(110\) | 2160.49 | 1.87268 | ||||||||
\(111\) | 1040.52 | 0.889744 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −770.432 | −0.641382 | −0.320691 | − | 0.947184i | \(-0.603915\pi\) | ||||
−0.320691 | + | 0.947184i | \(0.603915\pi\) | |||||||
\(114\) | 243.017 | 0.199654 | ||||||||
\(115\) | 392.574 | 0.318328 | ||||||||
\(116\) | 606.464 | 0.485420 | ||||||||
\(117\) | 200.306 | 0.158276 | ||||||||
\(118\) | 319.106 | 0.248950 | ||||||||
\(119\) | −374.945 | −0.288833 | ||||||||
\(120\) | −409.643 | −0.311626 | ||||||||
\(121\) | 2674.51 | 2.00940 | ||||||||
\(122\) | −876.049 | −0.650113 | ||||||||
\(123\) | −249.568 | −0.182949 | ||||||||
\(124\) | 725.031 | 0.525078 | ||||||||
\(125\) | −705.468 | −0.504792 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | −205.742 | −0.143753 | −0.0718764 | − | 0.997414i | \(-0.522899\pi\) | ||||
−0.0718764 | + | 0.997414i | \(0.522899\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 185.994 | 0.126944 | ||||||||
\(130\) | −759.760 | −0.512580 | ||||||||
\(131\) | −338.187 | −0.225554 | −0.112777 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112777 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(132\) | −759.469 | −0.500783 | ||||||||
\(133\) | −283.520 | −0.184844 | ||||||||
\(134\) | 83.6021 | 0.0538964 | ||||||||
\(135\) | −460.848 | −0.293804 | ||||||||
\(136\) | 428.508 | 0.270179 | ||||||||
\(137\) | 303.650 | 0.189362 | 0.0946810 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946810 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | −1159.68 | −0.707644 | −0.353822 | − | 0.935313i | \(-0.615118\pi\) | ||||
−0.353822 | + | 0.935313i | \(0.615118\pi\) | |||||||
\(140\) | 477.916 | 0.288509 | ||||||||
\(141\) | 1203.21 | 0.718639 | ||||||||
\(142\) | 958.333 | 0.566348 | ||||||||
\(143\) | −1408.58 | −0.823716 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −2587.85 | −1.48213 | ||||||||
\(146\) | 1168.11 | 0.662146 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 1387.36 | 0.770541 | ||||||||
\(149\) | 1537.19 | 0.845178 | 0.422589 | − | 0.906322i | \(-0.361121\pi\) | ||||
0.422589 | + | 0.906322i | \(0.361121\pi\) | |||||||
\(150\) | 997.990 | 0.543237 | ||||||||
\(151\) | −392.585 | −0.211577 | −0.105789 | − | 0.994389i | \(-0.533737\pi\) | ||||
−0.105789 | + | 0.994389i | \(0.533737\pi\) | |||||||
\(152\) | 324.022 | 0.172906 | ||||||||
\(153\) | 482.072 | 0.254727 | ||||||||
\(154\) | 886.048 | 0.463635 | ||||||||
\(155\) | −3093.79 | −1.60322 | ||||||||
\(156\) | 267.075 | 0.137071 | ||||||||
\(157\) | 1364.03 | 0.693387 | 0.346694 | − | 0.937978i | \(-0.387304\pi\) | ||||
0.346694 | + | 0.937978i | \(0.387304\pi\) | |||||||
\(158\) | 1111.87 | 0.559845 | ||||||||
\(159\) | −1063.42 | −0.530409 | ||||||||
\(160\) | −546.190 | −0.269876 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1131.18 | 0.543566 | 0.271783 | − | 0.962359i | \(-0.412387\pi\) | ||||
0.271783 | + | 0.962359i | \(0.412387\pi\) | |||||||
\(164\) | −332.757 | −0.158439 | ||||||||
\(165\) | 3240.74 | 1.52904 | ||||||||
\(166\) | −1630.73 | −0.762463 | ||||||||
\(167\) | −1753.41 | −0.812473 | −0.406236 | − | 0.913768i | \(-0.633159\pi\) | ||||
−0.406236 | + | 0.913768i | \(0.633159\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | −1701.66 | −0.774537 | ||||||||
\(170\) | −1828.49 | −0.824935 | ||||||||
\(171\) | 364.525 | 0.163017 | ||||||||
\(172\) | 247.992 | 0.109937 | ||||||||
\(173\) | −3851.07 | −1.69244 | −0.846218 | − | 0.532837i | \(-0.821126\pi\) | ||||
−0.846218 | + | 0.532837i | \(0.821126\pi\) | |||||||
\(174\) | 909.696 | 0.396344 | ||||||||
\(175\) | −1164.32 | −0.502940 | ||||||||
\(176\) | −1012.63 | −0.433691 | ||||||||
\(177\) | 478.659 | 0.203267 | ||||||||
\(178\) | −844.992 | −0.355814 | ||||||||
\(179\) | 2028.12 | 0.846865 | 0.423433 | − | 0.905928i | \(-0.360825\pi\) | ||||
0.423433 | + | 0.905928i | \(0.360825\pi\) | |||||||
\(180\) | −614.464 | −0.254441 | ||||||||
\(181\) | −3136.57 | −1.28806 | −0.644031 | − | 0.764999i | \(-0.722739\pi\) | ||||
−0.644031 | + | 0.764999i | \(0.722739\pi\) | |||||||
\(182\) | −311.588 | −0.126903 | ||||||||
\(183\) | −1314.07 | −0.530815 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −5920.01 | −2.35269 | ||||||||
\(186\) | 1087.55 | 0.428725 | ||||||||
\(187\) | −3389.99 | −1.32567 | ||||||||
\(188\) | 1604.27 | 0.622360 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −1382.64 | −0.527933 | ||||||||
\(191\) | −995.461 | −0.377115 | −0.188558 | − | 0.982062i | \(-0.560381\pi\) | ||||
−0.188558 | + | 0.982062i | \(0.560381\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 3334.74 | 1.24373 | 0.621864 | − | 0.783125i | \(-0.286376\pi\) | ||||
0.621864 | + | 0.783125i | \(0.286376\pi\) | |||||||
\(194\) | −248.243 | −0.0918701 | ||||||||
\(195\) | −1139.64 | −0.418520 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 801.347 | 0.289815 | 0.144908 | − | 0.989445i | \(-0.453712\pi\) | ||||
0.144908 | + | 0.989445i | \(0.453712\pi\) | |||||||
\(198\) | −1139.20 | −0.408887 | ||||||||
\(199\) | 2231.55 | 0.794926 | 0.397463 | − | 0.917618i | \(-0.369891\pi\) | ||||
0.397463 | + | 0.917618i | \(0.369891\pi\) | |||||||
\(200\) | 1330.65 | 0.470457 | ||||||||
\(201\) | 125.403 | 0.0440062 | ||||||||
\(202\) | −1088.23 | −0.379046 | ||||||||
\(203\) | −1061.31 | −0.366943 | ||||||||
\(204\) | 642.763 | 0.220600 | ||||||||
\(205\) | 1419.91 | 0.483761 | ||||||||
\(206\) | 1849.20 | 0.625435 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 356.100 | 0.118707 | ||||||||
\(209\) | −2563.39 | −0.848388 | ||||||||
\(210\) | 716.875 | 0.235567 | ||||||||
\(211\) | 4649.81 | 1.51709 | 0.758546 | − | 0.651620i | \(-0.225910\pi\) | ||||
0.758546 | + | 0.651620i | \(0.225910\pi\) | |||||||
\(212\) | −1417.90 | −0.459348 | ||||||||
\(213\) | 1437.50 | 0.462422 | ||||||||
\(214\) | 3862.93 | 1.23395 | ||||||||
\(215\) | −1058.21 | −0.335671 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1268.80 | −0.396922 | ||||||||
\(218\) | 1209.02 | 0.375620 | ||||||||
\(219\) | 1752.16 | 0.540640 | ||||||||
\(220\) | 4320.99 | 1.32419 | ||||||||
\(221\) | 1192.13 | 0.362855 | ||||||||
\(222\) | 2081.04 | 0.629144 | ||||||||
\(223\) | −3620.90 | −1.08732 | −0.543662 | − | 0.839304i | \(-0.682963\pi\) | ||||
−0.543662 | + | 0.839304i | \(0.682963\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 1496.99 | 0.443551 | ||||||||
\(226\) | −1540.86 | −0.453525 | ||||||||
\(227\) | 2189.52 | 0.640192 | 0.320096 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320096 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(228\) | 486.033 | 0.141177 | ||||||||
\(229\) | −5748.77 | −1.65891 | −0.829453 | − | 0.558577i | \(-0.811348\pi\) | ||||
−0.829453 | + | 0.558577i | \(0.811348\pi\) | |||||||
\(230\) | 785.148 | 0.225092 | ||||||||
\(231\) | 1329.07 | 0.378556 | ||||||||
\(232\) | 1212.93 | 0.343244 | ||||||||
\(233\) | 5231.77 | 1.47101 | 0.735504 | − | 0.677521i | \(-0.236946\pi\) | ||||
0.735504 | + | 0.677521i | \(0.236946\pi\) | |||||||
\(234\) | 400.613 | 0.111918 | ||||||||
\(235\) | −6845.61 | −1.90025 | ||||||||
\(236\) | 638.212 | 0.176034 | ||||||||
\(237\) | 1667.80 | 0.457111 | ||||||||
\(238\) | −749.890 | −0.204236 | ||||||||
\(239\) | −3242.68 | −0.877620 | −0.438810 | − | 0.898580i | \(-0.644600\pi\) | ||||
−0.438810 | + | 0.898580i | \(0.644600\pi\) | |||||||
\(240\) | −819.285 | −0.220353 | ||||||||
\(241\) | 6571.09 | 1.75635 | 0.878177 | − | 0.478336i | \(-0.158760\pi\) | ||||
0.878177 | + | 0.478336i | \(0.158760\pi\) | |||||||
\(242\) | 5349.02 | 1.42086 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1752.10 | −0.459699 | ||||||||
\(245\) | −836.354 | −0.218093 | ||||||||
\(246\) | −499.136 | −0.129365 | ||||||||
\(247\) | 901.441 | 0.232216 | ||||||||
\(248\) | 1450.06 | 0.371286 | ||||||||
\(249\) | −2446.09 | −0.622548 | ||||||||
\(250\) | −1410.94 | −0.356942 | ||||||||
\(251\) | 5874.34 | 1.47723 | 0.738616 | − | 0.674127i | \(-0.235480\pi\) | ||||
0.738616 | + | 0.674127i | \(0.235480\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | 1455.65 | 0.361723 | ||||||||
\(254\) | −411.483 | −0.101649 | ||||||||
\(255\) | −2742.74 | −0.673557 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2618.66 | 0.635593 | 0.317797 | − | 0.948159i | \(-0.397057\pi\) | ||||
0.317797 | + | 0.948159i | \(0.397057\pi\) | |||||||
\(258\) | 371.988 | 0.0897633 | ||||||||
\(259\) | −2427.88 | −0.582474 | ||||||||
\(260\) | −1519.52 | −0.362449 | ||||||||
\(261\) | 1364.54 | 0.323614 | ||||||||
\(262\) | −676.375 | −0.159491 | ||||||||
\(263\) | 3280.34 | 0.769105 | 0.384553 | − | 0.923103i | \(-0.374356\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(264\) | −1518.94 | −0.354107 | ||||||||
\(265\) | 6050.33 | 1.40252 | ||||||||
\(266\) | −567.039 | −0.130704 | ||||||||
\(267\) | −1267.49 | −0.290521 | ||||||||
\(268\) | 167.204 | 0.0381105 | ||||||||
\(269\) | 2482.84 | 0.562755 | 0.281378 | − | 0.959597i | \(-0.409209\pi\) | ||||
0.281378 | + | 0.959597i | \(0.409209\pi\) | |||||||
\(270\) | −921.696 | −0.207750 | ||||||||
\(271\) | −4847.56 | −1.08660 | −0.543299 | − | 0.839539i | \(-0.682825\pi\) | ||||
−0.543299 | + | 0.839539i | \(0.682825\pi\) | |||||||
\(272\) | 857.017 | 0.191045 | ||||||||
\(273\) | −467.382 | −0.103616 | ||||||||
\(274\) | 607.301 | 0.133899 | ||||||||
\(275\) | −10527.0 | −2.30837 | ||||||||
\(276\) | −276.000 | −0.0601929 | ||||||||
\(277\) | 3012.01 | 0.653336 | 0.326668 | − | 0.945139i | \(-0.394074\pi\) | ||||
0.326668 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(278\) | −2319.36 | −0.500380 | ||||||||
\(279\) | 1631.32 | 0.350052 | ||||||||
\(280\) | 955.833 | 0.204007 | ||||||||
\(281\) | 5944.23 | 1.26193 | 0.630966 | − | 0.775810i | \(-0.282659\pi\) | ||||
0.630966 | + | 0.775810i | \(0.282659\pi\) | |||||||
\(282\) | 2406.41 | 0.508155 | ||||||||
\(283\) | −50.5291 | −0.0106136 | −0.00530679 | − | 0.999986i | \(-0.501689\pi\) | ||||
−0.00530679 | + | 0.999986i | \(0.501689\pi\) | |||||||
\(284\) | 1916.67 | 0.400469 | ||||||||
\(285\) | −2073.96 | −0.431055 | ||||||||
\(286\) | −2817.16 | −0.582455 | ||||||||
\(287\) | 582.325 | 0.119768 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −2043.95 | −0.416028 | ||||||||
\(290\) | −5175.70 | −1.04803 | ||||||||
\(291\) | −372.364 | −0.0750116 | ||||||||
\(292\) | 2336.22 | 0.468208 | ||||||||
\(293\) | −8282.29 | −1.65139 | −0.825694 | − | 0.564118i | \(-0.809216\pi\) | ||||
−0.825694 | + | 0.564118i | \(0.809216\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | −2723.32 | −0.537484 | ||||||||
\(296\) | 2774.72 | 0.544855 | ||||||||
\(297\) | −1708.81 | −0.333855 | ||||||||
\(298\) | 3074.38 | 0.597631 | ||||||||
\(299\) | −511.894 | −0.0990087 | ||||||||
\(300\) | 1995.98 | 0.384127 | ||||||||
\(301\) | −433.985 | −0.0831047 | ||||||||
\(302\) | −785.171 | −0.149608 | ||||||||
\(303\) | −1632.34 | −0.309490 | ||||||||
\(304\) | 648.045 | 0.122263 | ||||||||
\(305\) | 7476.40 | 1.40360 | ||||||||
\(306\) | 964.144 | 0.180119 | ||||||||
\(307\) | 6900.46 | 1.28283 | 0.641417 | − | 0.767193i | \(-0.278347\pi\) | ||||
0.641417 | + | 0.767193i | \(0.278347\pi\) | |||||||
\(308\) | 1772.10 | 0.327839 | ||||||||
\(309\) | 2773.79 | 0.510665 | ||||||||
\(310\) | −6187.57 | −1.13365 | ||||||||
\(311\) | 4412.27 | 0.804492 | 0.402246 | − | 0.915532i | \(-0.368230\pi\) | ||||
0.402246 | + | 0.915532i | \(0.368230\pi\) | |||||||
\(312\) | 534.151 | 0.0969241 | ||||||||
\(313\) | 246.414 | 0.0444989 | 0.0222495 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222495 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(314\) | 2728.07 | 0.490299 | ||||||||
\(315\) | 1075.31 | 0.192340 | ||||||||
\(316\) | 2223.74 | 0.395870 | ||||||||
\(317\) | 7944.22 | 1.40754 | 0.703772 | − | 0.710426i | \(-0.251498\pi\) | ||||
0.703772 | + | 0.710426i | \(0.251498\pi\) | |||||||
\(318\) | −2126.85 | −0.375056 | ||||||||
\(319\) | −9595.64 | −1.68418 | ||||||||
\(320\) | −1092.38 | −0.190831 | ||||||||
\(321\) | 5794.40 | 1.00751 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 2169.47 | 0.373724 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 3701.93 | 0.631833 | ||||||||
\(326\) | 2262.37 | 0.384359 | ||||||||
\(327\) | 1813.53 | 0.306693 | ||||||||
\(328\) | −665.514 | −0.112033 | ||||||||
\(329\) | −2807.48 | −0.470460 | ||||||||
\(330\) | 6481.48 | 1.08119 | ||||||||
\(331\) | −2485.12 | −0.412673 | −0.206336 | − | 0.978481i | \(-0.566154\pi\) | ||||
−0.206336 | + | 0.978481i | \(0.566154\pi\) | |||||||
\(332\) | −3261.45 | −0.539143 | ||||||||
\(333\) | 3121.55 | 0.513694 | ||||||||
\(334\) | −3506.82 | −0.574505 | ||||||||
\(335\) | −713.479 | −0.116363 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 4701.99 | 0.760041 | 0.380021 | − | 0.924978i | \(-0.375917\pi\) | ||||
0.380021 | + | 0.924978i | \(0.375917\pi\) | |||||||
\(338\) | −3403.32 | −0.547680 | ||||||||
\(339\) | −2311.30 | −0.370302 | ||||||||
\(340\) | −3656.99 | −0.583317 | ||||||||
\(341\) | −11471.6 | −1.82177 | ||||||||
\(342\) | 729.050 | 0.115271 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 495.983 | 0.0777373 | ||||||||
\(345\) | 1177.72 | 0.183787 | ||||||||
\(346\) | −7702.14 | −1.19673 | ||||||||
\(347\) | −1405.56 | −0.217448 | −0.108724 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108724 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(348\) | 1819.39 | 0.280258 | ||||||||
\(349\) | 252.056 | 0.0386598 | 0.0193299 | − | 0.999813i | \(-0.493847\pi\) | ||||
0.0193299 | + | 0.999813i | \(0.493847\pi\) | |||||||
\(350\) | −2328.64 | −0.355632 | ||||||||
\(351\) | 600.919 | 0.0913809 | ||||||||
\(352\) | −2025.25 | −0.306666 | ||||||||
\(353\) | −1075.60 | −0.162177 | −0.0810886 | − | 0.996707i | \(-0.525840\pi\) | ||||
−0.0810886 | + | 0.996707i | \(0.525840\pi\) | |||||||
\(354\) | 957.318 | 0.143731 | ||||||||
\(355\) | −8178.62 | −1.22275 | ||||||||
\(356\) | −1689.98 | −0.251598 | ||||||||
\(357\) | −1124.83 | −0.166758 | ||||||||
\(358\) | 4056.24 | 0.598824 | ||||||||
\(359\) | −7098.48 | −1.04357 | −0.521787 | − | 0.853076i | \(-0.674735\pi\) | ||||
−0.521787 | + | 0.853076i | \(0.674735\pi\) | |||||||
\(360\) | −1228.93 | −0.179917 | ||||||||
\(361\) | −5218.52 | −0.760829 | ||||||||
\(362\) | −6273.13 | −0.910797 | ||||||||
\(363\) | 8023.54 | 1.16013 | ||||||||
\(364\) | −623.176 | −0.0897343 | ||||||||
\(365\) | −9968.89 | −1.42958 | ||||||||
\(366\) | −2628.15 | −0.375343 | ||||||||
\(367\) | 4081.79 | 0.580566 | 0.290283 | − | 0.956941i | \(-0.406251\pi\) | ||||
0.290283 | + | 0.956941i | \(0.406251\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −748.703 | −0.105626 | ||||||||
\(370\) | −11840.0 | −1.66360 | ||||||||
\(371\) | 2481.32 | 0.347234 | ||||||||
\(372\) | 2175.09 | 0.303154 | ||||||||
\(373\) | −2285.49 | −0.317260 | −0.158630 | − | 0.987338i | \(-0.550708\pi\) | ||||
−0.158630 | + | 0.987338i | \(0.550708\pi\) | |||||||
\(374\) | −6779.98 | −0.937391 | ||||||||
\(375\) | −2116.41 | −0.291442 | ||||||||
\(376\) | 3208.55 | 0.440075 | ||||||||
\(377\) | 3374.41 | 0.460984 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | −9978.10 | −1.35235 | −0.676175 | − | 0.736741i | \(-0.736364\pi\) | ||||
−0.676175 | + | 0.736741i | \(0.736364\pi\) | |||||||
\(380\) | −2765.28 | −0.373305 | ||||||||
\(381\) | −617.225 | −0.0829958 | ||||||||
\(382\) | −1990.92 | −0.266661 | ||||||||
\(383\) | 2054.78 | 0.274136 | 0.137068 | − | 0.990562i | \(-0.456232\pi\) | ||||
0.137068 | + | 0.990562i | \(0.456232\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −7561.73 | −1.00099 | ||||||||
\(386\) | 6669.47 | 0.879449 | ||||||||
\(387\) | 557.981 | 0.0732914 | ||||||||
\(388\) | −496.486 | −0.0649620 | ||||||||
\(389\) | 7183.55 | 0.936300 | 0.468150 | − | 0.883649i | \(-0.344921\pi\) | ||||
0.468150 | + | 0.883649i | \(0.344921\pi\) | |||||||
\(390\) | −2279.28 | −0.295938 | ||||||||
\(391\) | −1231.96 | −0.159343 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −1014.56 | −0.130224 | ||||||||
\(394\) | 1602.69 | 0.204930 | ||||||||
\(395\) | −9488.92 | −1.20871 | ||||||||
\(396\) | −2278.41 | −0.289127 | ||||||||
\(397\) | −9361.01 | −1.18341 | −0.591707 | − | 0.806153i | \(-0.701546\pi\) | ||||
−0.591707 | + | 0.806153i | \(0.701546\pi\) | |||||||
\(398\) | 4463.10 | 0.562097 | ||||||||
\(399\) | −850.559 | −0.106720 | ||||||||
\(400\) | 2661.31 | 0.332663 | ||||||||
\(401\) | 908.583 | 0.113148 | 0.0565741 | − | 0.998398i | \(-0.481982\pi\) | ||||
0.0565741 | + | 0.998398i | \(0.481982\pi\) | |||||||
\(402\) | 250.806 | 0.0311171 | ||||||||
\(403\) | 4034.12 | 0.498645 | ||||||||
\(404\) | −2176.45 | −0.268026 | ||||||||
\(405\) | −1382.54 | −0.169628 | ||||||||
\(406\) | −2122.62 | −0.259468 | ||||||||
\(407\) | −21951.2 | −2.67341 | ||||||||
\(408\) | 1285.53 | 0.155988 | ||||||||
\(409\) | 6063.62 | 0.733073 | 0.366536 | − | 0.930404i | \(-0.380544\pi\) | ||||
0.366536 | + | 0.930404i | \(0.380544\pi\) | |||||||
\(410\) | 2839.82 | 0.342070 | ||||||||
\(411\) | 910.951 | 0.109328 | ||||||||
\(412\) | 3698.39 | 0.442249 | ||||||||
\(413\) | −1116.87 | −0.133069 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | 13917.0 | 1.64616 | ||||||||
\(416\) | 712.201 | 0.0839388 | ||||||||
\(417\) | −3479.03 | −0.408559 | ||||||||
\(418\) | −5126.77 | −0.599901 | ||||||||
\(419\) | −11669.9 | −1.36064 | −0.680322 | − | 0.732913i | \(-0.738160\pi\) | ||||
−0.680322 | + | 0.732913i | \(0.738160\pi\) | |||||||
\(420\) | 1433.75 | 0.166571 | ||||||||
\(421\) | −14906.4 | −1.72564 | −0.862821 | − | 0.505509i | \(-0.831305\pi\) | ||||
−0.862821 | + | 0.505509i | \(0.831305\pi\) | |||||||
\(422\) | 9299.63 | 1.07275 | ||||||||
\(423\) | 3609.62 | 0.414907 | ||||||||
\(424\) | −2835.80 | −0.324808 | ||||||||
\(425\) | 8909.32 | 1.01686 | ||||||||
\(426\) | 2875.00 | 0.326981 | ||||||||
\(427\) | 3066.17 | 0.347500 | ||||||||
\(428\) | 7725.86 | 0.872532 | ||||||||
\(429\) | −4225.74 | −0.475573 | ||||||||
\(430\) | −2116.42 | −0.237355 | ||||||||
\(431\) | −9659.56 | −1.07955 | −0.539773 | − | 0.841811i | \(-0.681490\pi\) | ||||
−0.539773 | + | 0.841811i | \(0.681490\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 1441.23 | 0.159956 | 0.0799782 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799782 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(434\) | −2537.61 | −0.280666 | ||||||||
\(435\) | −7763.55 | −0.855709 | ||||||||
\(436\) | 2418.04 | 0.265603 | ||||||||
\(437\) | −931.564 | −0.101974 | ||||||||
\(438\) | 3504.32 | 0.382290 | ||||||||
\(439\) | 14116.1 | 1.53468 | 0.767339 | − | 0.641242i | \(-0.221581\pi\) | ||||
0.767339 | + | 0.641242i | \(0.221581\pi\) | |||||||
\(440\) | 8641.97 | 0.936341 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 2384.25 | 0.256577 | ||||||||
\(443\) | −2529.67 | −0.271306 | −0.135653 | − | 0.990756i | \(-0.543313\pi\) | ||||
−0.135653 | + | 0.990756i | \(0.543313\pi\) | |||||||
\(444\) | 4162.07 | 0.444872 | ||||||||
\(445\) | 7211.35 | 0.768204 | ||||||||
\(446\) | −7241.79 | −0.768854 | ||||||||
\(447\) | 4611.57 | 0.487964 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −13297.6 | −1.39767 | −0.698833 | − | 0.715285i | \(-0.746297\pi\) | ||||
−0.698833 | + | 0.715285i | \(0.746297\pi\) | |||||||
\(450\) | 2993.97 | 0.313638 | ||||||||
\(451\) | 5264.98 | 0.549707 | ||||||||
\(452\) | −3081.73 | −0.320691 | ||||||||
\(453\) | −1177.76 | −0.122154 | ||||||||
\(454\) | 4379.04 | 0.452684 | ||||||||
\(455\) | 2659.16 | 0.273985 | ||||||||
\(456\) | 972.067 | 0.0998272 | ||||||||
\(457\) | 12384.0 | 1.26762 | 0.633808 | − | 0.773490i | \(-0.281491\pi\) | ||||
0.633808 | + | 0.773490i | \(0.281491\pi\) | |||||||
\(458\) | −11497.5 | −1.17302 | ||||||||
\(459\) | 1446.22 | 0.147067 | ||||||||
\(460\) | 1570.30 | 0.159164 | ||||||||
\(461\) | −15167.2 | −1.53234 | −0.766168 | − | 0.642641i | \(-0.777839\pi\) | ||||
−0.766168 | + | 0.642641i | \(0.777839\pi\) | |||||||
\(462\) | 2658.14 | 0.267680 | ||||||||
\(463\) | 2425.65 | 0.243477 | 0.121738 | − | 0.992562i | \(-0.461153\pi\) | ||||
0.121738 | + | 0.992562i | \(0.461153\pi\) | |||||||
\(464\) | 2425.86 | 0.242710 | ||||||||
\(465\) | −9281.36 | −0.925619 | ||||||||
\(466\) | 10463.5 | 1.04016 | ||||||||
\(467\) | −2348.70 | −0.232730 | −0.116365 | − | 0.993207i | \(-0.537124\pi\) | ||||
−0.116365 | + | 0.993207i | \(0.537124\pi\) | |||||||
\(468\) | 801.226 | 0.0791382 | ||||||||
\(469\) | −292.607 | −0.0288088 | ||||||||
\(470\) | −13691.2 | −1.34368 | ||||||||
\(471\) | 4092.10 | 0.400327 | ||||||||
\(472\) | 1276.42 | 0.124475 | ||||||||
\(473\) | −3923.79 | −0.381430 | ||||||||
\(474\) | 3335.60 | 0.323226 | ||||||||
\(475\) | 6736.90 | 0.650758 | ||||||||
\(476\) | −1499.78 | −0.144417 | ||||||||
\(477\) | −3190.27 | −0.306232 | ||||||||
\(478\) | −6485.35 | −0.620571 | ||||||||
\(479\) | −10710.7 | −1.02168 | −0.510838 | − | 0.859677i | \(-0.670665\pi\) | ||||
−0.510838 | + | 0.859677i | \(0.670665\pi\) | |||||||
\(480\) | −1638.57 | −0.155813 | ||||||||
\(481\) | 7719.35 | 0.731751 | ||||||||
\(482\) | 13142.2 | 1.24193 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | 10698.0 | 1.00470 | ||||||||
\(485\) | 2118.56 | 0.198348 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 14462.9 | 1.34574 | 0.672871 | − | 0.739760i | \(-0.265061\pi\) | ||||
0.672871 | + | 0.739760i | \(0.265061\pi\) | |||||||
\(488\) | −3504.20 | −0.325056 | ||||||||
\(489\) | 3393.55 | 0.313828 | ||||||||
\(490\) | −1672.71 | −0.154215 | ||||||||
\(491\) | −5583.57 | −0.513204 | −0.256602 | − | 0.966517i | \(-0.582603\pi\) | ||||
−0.256602 | + | 0.966517i | \(0.582603\pi\) | |||||||
\(492\) | −998.271 | −0.0914747 | ||||||||
\(493\) | 8121.09 | 0.741897 | ||||||||
\(494\) | 1802.88 | 0.164201 | ||||||||
\(495\) | 9722.22 | 0.882790 | ||||||||
\(496\) | 2900.12 | 0.262539 | ||||||||
\(497\) | −3354.16 | −0.302726 | ||||||||
\(498\) | −4892.18 | −0.440208 | ||||||||
\(499\) | 1670.76 | 0.149887 | 0.0749434 | − | 0.997188i | \(-0.476122\pi\) | ||||
0.0749434 | + | 0.997188i | \(0.476122\pi\) | |||||||
\(500\) | −2821.87 | −0.252396 | ||||||||
\(501\) | −5260.23 | −0.469081 | ||||||||
\(502\) | 11748.7 | 1.04456 | ||||||||
\(503\) | 105.819 | 0.00938020 | 0.00469010 | − | 0.999989i | \(-0.498507\pi\) | ||||
0.00469010 | + | 0.999989i | \(0.498507\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | 9287.16 | 0.818363 | ||||||||
\(506\) | 2911.30 | 0.255777 | ||||||||
\(507\) | −5104.97 | −0.447179 | ||||||||
\(508\) | −822.966 | −0.0718764 | ||||||||
\(509\) | −4456.71 | −0.388095 | −0.194048 | − | 0.980992i | \(-0.562162\pi\) | ||||
−0.194048 | + | 0.980992i | \(0.562162\pi\) | |||||||
\(510\) | −5485.48 | −0.476277 | ||||||||
\(511\) | −4088.38 | −0.353932 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1093.58 | 0.0941180 | ||||||||
\(514\) | 5237.32 | 0.449432 | ||||||||
\(515\) | −15781.4 | −1.35032 | ||||||||
\(516\) | 743.975 | 0.0634722 | ||||||||
\(517\) | −25383.3 | −2.15929 | ||||||||
\(518\) | −4855.75 | −0.411872 | ||||||||
\(519\) | −11553.2 | −0.977129 | ||||||||
\(520\) | −3039.04 | −0.256290 | ||||||||
\(521\) | 12970.8 | 1.09071 | 0.545355 | − | 0.838205i | \(-0.316395\pi\) | ||||
0.545355 | + | 0.838205i | \(0.316395\pi\) | |||||||
\(522\) | 2729.09 | 0.228829 | ||||||||
\(523\) | 20645.8 | 1.72615 | 0.863076 | − | 0.505074i | \(-0.168535\pi\) | ||||
0.863076 | + | 0.505074i | \(0.168535\pi\) | |||||||
\(524\) | −1352.75 | −0.112777 | ||||||||
\(525\) | −3492.97 | −0.290372 | ||||||||
\(526\) | 6560.69 | 0.543839 | ||||||||
\(527\) | 9708.81 | 0.802509 | ||||||||
\(528\) | −3037.88 | −0.250391 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 12100.7 | 0.991735 | ||||||||
\(531\) | 1435.98 | 0.117356 | ||||||||
\(532\) | −1134.08 | −0.0924220 | ||||||||
\(533\) | −1851.48 | −0.150463 | ||||||||
\(534\) | −2534.98 | −0.205429 | ||||||||
\(535\) | −32967.1 | −2.66410 | ||||||||
\(536\) | 334.408 | 0.0269482 | ||||||||
\(537\) | 6084.36 | 0.488938 | ||||||||
\(538\) | 4965.67 | 0.397928 | ||||||||
\(539\) | −3101.17 | −0.247823 | ||||||||
\(540\) | −1843.39 | −0.146902 | ||||||||
\(541\) | −16727.0 | −1.32930 | −0.664650 | − | 0.747155i | \(-0.731419\pi\) | ||||
−0.664650 | + | 0.747155i | \(0.731419\pi\) | |||||||
\(542\) | −9695.12 | −0.768341 | ||||||||
\(543\) | −9409.70 | −0.743663 | ||||||||
\(544\) | 1714.03 | 0.135089 | ||||||||
\(545\) | −10318.0 | −0.810966 | ||||||||
\(546\) | −934.764 | −0.0732677 | ||||||||
\(547\) | 19711.6 | 1.54078 | 0.770392 | − | 0.637570i | \(-0.220061\pi\) | ||||
0.770392 | + | 0.637570i | \(0.220061\pi\) | |||||||
\(548\) | 1214.60 | 0.0946810 | ||||||||
\(549\) | −3942.22 | −0.306466 | ||||||||
\(550\) | −21054.0 | −1.63226 | ||||||||
\(551\) | 6140.87 | 0.474791 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | −3891.54 | −0.299249 | ||||||||
\(554\) | 6024.02 | 0.461978 | ||||||||
\(555\) | −17760.0 | −1.35833 | ||||||||
\(556\) | −4638.71 | −0.353822 | ||||||||
\(557\) | −21814.7 | −1.65946 | −0.829728 | − | 0.558168i | \(-0.811504\pi\) | ||||
−0.829728 | + | 0.558168i | \(0.811504\pi\) | |||||||
\(558\) | 3262.64 | 0.247524 | ||||||||
\(559\) | 1379.84 | 0.104403 | ||||||||
\(560\) | 1911.67 | 0.144255 | ||||||||
\(561\) | −10170.0 | −0.765377 | ||||||||
\(562\) | 11888.5 | 0.892321 | ||||||||
\(563\) | −20280.8 | −1.51818 | −0.759090 | − | 0.650986i | \(-0.774356\pi\) | ||||
−0.759090 | + | 0.650986i | \(0.774356\pi\) | |||||||
\(564\) | 4812.82 | 0.359320 | ||||||||
\(565\) | 13150.1 | 0.979164 | ||||||||
\(566\) | −101.058 | −0.00750494 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 3833.33 | 0.283174 | ||||||||
\(569\) | −21214.3 | −1.56300 | −0.781502 | − | 0.623902i | \(-0.785546\pi\) | ||||
−0.781502 | + | 0.623902i | \(0.785546\pi\) | |||||||
\(570\) | −4147.92 | −0.304802 | ||||||||
\(571\) | 23364.1 | 1.71236 | 0.856179 | − | 0.516680i | \(-0.172832\pi\) | ||||
0.856179 | + | 0.516680i | \(0.172832\pi\) | |||||||
\(572\) | −5634.32 | −0.411858 | ||||||||
\(573\) | −2986.38 | −0.217728 | ||||||||
\(574\) | 1164.65 | 0.0846891 | ||||||||
\(575\) | −3825.63 | −0.277461 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 2069.97 | 0.149348 | 0.0746741 | − | 0.997208i | \(-0.476208\pi\) | ||||
0.0746741 | + | 0.997208i | \(0.476208\pi\) | |||||||
\(578\) | −4087.89 | −0.294176 | ||||||||
\(579\) | 10004.2 | 0.718067 | ||||||||
\(580\) | −10351.4 | −0.741066 | ||||||||
\(581\) | 5707.54 | 0.407553 | ||||||||
\(582\) | −744.729 | −0.0530412 | ||||||||
\(583\) | 22434.4 | 1.59372 | ||||||||
\(584\) | 4672.43 | 0.331073 | ||||||||
\(585\) | −3418.92 | −0.241632 | ||||||||
\(586\) | −16564.6 | −1.16771 | ||||||||
\(587\) | −14726.0 | −1.03545 | −0.517724 | − | 0.855547i | \(-0.673221\pi\) | ||||
−0.517724 | + | 0.855547i | \(0.673221\pi\) | |||||||
\(588\) | 588.000 | 0.0412393 | ||||||||
\(589\) | 7341.44 | 0.513580 | ||||||||
\(590\) | −5446.64 | −0.380059 | ||||||||
\(591\) | 2404.04 | 0.167325 | ||||||||
\(592\) | 5549.43 | 0.385271 | ||||||||
\(593\) | 10601.6 | 0.734157 | 0.367079 | − | 0.930190i | \(-0.380358\pi\) | ||||
0.367079 | + | 0.930190i | \(0.380358\pi\) | |||||||
\(594\) | −3417.61 | −0.236071 | ||||||||
\(595\) | 6399.72 | 0.440946 | ||||||||
\(596\) | 6148.76 | 0.422589 | ||||||||
\(597\) | 6694.64 | 0.458951 | ||||||||
\(598\) | −1023.79 | −0.0700098 | ||||||||
\(599\) | 18715.5 | 1.27662 | 0.638310 | − | 0.769779i | \(-0.279634\pi\) | ||||
0.638310 | + | 0.769779i | \(0.279634\pi\) | |||||||
\(600\) | 3991.96 | 0.271619 | ||||||||
\(601\) | −23578.4 | −1.60031 | −0.800154 | − | 0.599795i | \(-0.795249\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(602\) | −867.971 | −0.0587639 | ||||||||
\(603\) | 376.209 | 0.0254070 | ||||||||
\(604\) | −1570.34 | −0.105789 | ||||||||
\(605\) | −45649.8 | −3.06765 | ||||||||
\(606\) | −3264.68 | −0.218842 | ||||||||
\(607\) | 18198.4 | 1.21688 | 0.608442 | − | 0.793598i | \(-0.291795\pi\) | ||||
0.608442 | + | 0.793598i | \(0.291795\pi\) | |||||||
\(608\) | 1296.09 | 0.0864529 | ||||||||
\(609\) | −3183.94 | −0.211855 | ||||||||
\(610\) | 14952.8 | 0.992493 | ||||||||
\(611\) | 8926.29 | 0.591030 | ||||||||
\(612\) | 1928.29 | 0.127363 | ||||||||
\(613\) | 24455.2 | 1.61131 | 0.805657 | − | 0.592383i | \(-0.201813\pi\) | ||||
0.805657 | + | 0.592383i | \(0.201813\pi\) | |||||||
\(614\) | 13800.9 | 0.907100 | ||||||||
\(615\) | 4259.73 | 0.279299 | ||||||||
\(616\) | 3544.19 | 0.231817 | ||||||||
\(617\) | 11449.5 | 0.747069 | 0.373534 | − | 0.927616i | \(-0.378146\pi\) | ||||
0.373534 | + | 0.927616i | \(0.378146\pi\) | |||||||
\(618\) | 5547.59 | 0.361095 | ||||||||
\(619\) | −8695.71 | −0.564637 | −0.282318 | − | 0.959321i | \(-0.591103\pi\) | ||||
−0.282318 | + | 0.959321i | \(0.591103\pi\) | |||||||
\(620\) | −12375.1 | −0.801610 | ||||||||
\(621\) | −621.000 | −0.0401286 | ||||||||
\(622\) | 8824.55 | 0.568862 | ||||||||
\(623\) | 2957.47 | 0.190190 | ||||||||
\(624\) | 1068.30 | 0.0685357 | ||||||||
\(625\) | −8750.22 | −0.560014 | ||||||||
\(626\) | 492.829 | 0.0314655 | ||||||||
\(627\) | −7690.16 | −0.489817 | ||||||||
\(628\) | 5456.14 | 0.346694 | ||||||||
\(629\) | 18578.0 | 1.17767 | ||||||||
\(630\) | 2150.62 | 0.136005 | ||||||||
\(631\) | 4645.27 | 0.293067 | 0.146534 | − | 0.989206i | \(-0.453188\pi\) | ||||
0.146534 | + | 0.989206i | \(0.453188\pi\) | |||||||
\(632\) | 4447.47 | 0.279922 | ||||||||
\(633\) | 13949.4 | 0.875893 | ||||||||
\(634\) | 15888.4 | 0.995284 | ||||||||
\(635\) | 3511.69 | 0.219460 | ||||||||
\(636\) | −4253.70 | −0.265205 | ||||||||
\(637\) | 1090.56 | 0.0678328 | ||||||||
\(638\) | −19191.3 | −1.19089 | ||||||||
\(639\) | 4312.50 | 0.266979 | ||||||||
\(640\) | −2184.76 | −0.134938 | ||||||||
\(641\) | 11438.8 | 0.704847 | 0.352424 | − | 0.935841i | \(-0.385358\pi\) | ||||
0.352424 | + | 0.935841i | \(0.385358\pi\) | |||||||
\(642\) | 11588.8 | 0.712419 | ||||||||
\(643\) | 17370.6 | 1.06536 | 0.532681 | − | 0.846316i | \(-0.321184\pi\) | ||||
0.532681 | + | 0.846316i | \(0.321184\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | −3174.62 | −0.193800 | ||||||||
\(646\) | 4338.95 | 0.264262 | ||||||||
\(647\) | −7601.36 | −0.461886 | −0.230943 | − | 0.972967i | \(-0.574181\pi\) | ||||
−0.230943 | + | 0.972967i | \(0.574181\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −10098.0 | −0.610755 | ||||||||
\(650\) | 7403.85 | 0.446774 | ||||||||
\(651\) | −3806.41 | −0.229163 | ||||||||
\(652\) | 4524.74 | 0.271783 | ||||||||
\(653\) | −9187.39 | −0.550582 | −0.275291 | − | 0.961361i | \(-0.588774\pi\) | ||||
−0.275291 | + | 0.961361i | \(0.588774\pi\) | |||||||
\(654\) | 3627.06 | 0.216864 | ||||||||
\(655\) | 5772.33 | 0.344341 | ||||||||
\(656\) | −1331.03 | −0.0792194 | ||||||||
\(657\) | 5256.49 | 0.312139 | ||||||||
\(658\) | −5614.96 | −0.332665 | ||||||||
\(659\) | 28617.3 | 1.69161 | 0.845804 | − | 0.533493i | \(-0.179121\pi\) | ||||
0.845804 | + | 0.533493i | \(0.179121\pi\) | |||||||
\(660\) | 12963.0 | 0.764519 | ||||||||
\(661\) | 6987.83 | 0.411188 | 0.205594 | − | 0.978637i | \(-0.434087\pi\) | ||||
0.205594 | + | 0.978637i | \(0.434087\pi\) | |||||||
\(662\) | −4970.24 | −0.291804 | ||||||||
\(663\) | 3576.38 | 0.209495 | ||||||||
\(664\) | −6522.90 | −0.381231 | ||||||||
\(665\) | 4839.24 | 0.282192 | ||||||||
\(666\) | 6243.11 | 0.363237 | ||||||||
\(667\) | −3487.17 | −0.202434 | ||||||||
\(668\) | −7013.64 | −0.406236 | ||||||||
\(669\) | −10862.7 | −0.627767 | ||||||||
\(670\) | −1426.96 | −0.0822808 | ||||||||
\(671\) | 27722.2 | 1.59494 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | −16988.1 | −0.973020 | −0.486510 | − | 0.873675i | \(-0.661730\pi\) | ||||
−0.486510 | + | 0.873675i | \(0.661730\pi\) | |||||||
\(674\) | 9403.99 | 0.537430 | ||||||||
\(675\) | 4490.96 | 0.256084 | ||||||||
\(676\) | −6806.63 | −0.387269 | ||||||||
\(677\) | −17446.1 | −0.990412 | −0.495206 | − | 0.868776i | \(-0.664907\pi\) | ||||
−0.495206 | + | 0.868776i | \(0.664907\pi\) | |||||||
\(678\) | −4622.59 | −0.261843 | ||||||||
\(679\) | 868.850 | 0.0491066 | ||||||||
\(680\) | −7313.97 | −0.412468 | ||||||||
\(681\) | 6568.56 | 0.369615 | ||||||||
\(682\) | −22943.3 | −1.28819 | ||||||||
\(683\) | −15659.5 | −0.877296 | −0.438648 | − | 0.898659i | \(-0.644543\pi\) | ||||
−0.438648 | + | 0.898659i | \(0.644543\pi\) | |||||||
\(684\) | 1458.10 | 0.0815086 | ||||||||
\(685\) | −5182.84 | −0.289089 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | −17246.3 | −0.957770 | ||||||||
\(688\) | 991.967 | 0.0549686 | ||||||||
\(689\) | −7889.29 | −0.436224 | ||||||||
\(690\) | 2355.45 | 0.129957 | ||||||||
\(691\) | 9537.41 | 0.525066 | 0.262533 | − | 0.964923i | \(-0.415442\pi\) | ||||
0.262533 | + | 0.964923i | \(0.415442\pi\) | |||||||
\(692\) | −15404.3 | −0.846218 | ||||||||
\(693\) | 3987.21 | 0.218560 | ||||||||
\(694\) | −2811.12 | −0.153759 | ||||||||
\(695\) | 19793.9 | 1.08032 | ||||||||
\(696\) | 3638.78 | 0.198172 | ||||||||
\(697\) | −4455.91 | −0.242152 | ||||||||
\(698\) | 504.112 | 0.0273366 | ||||||||
\(699\) | 15695.3 | 0.849287 | ||||||||
\(700\) | −4657.29 | −0.251470 | ||||||||
\(701\) | 10884.0 | 0.586424 | 0.293212 | − | 0.956048i | \(-0.405276\pi\) | ||||
0.293212 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(702\) | 1201.84 | 0.0646161 | ||||||||
\(703\) | 14048.0 | 0.753669 | ||||||||
\(704\) | −4050.50 | −0.216845 | ||||||||
\(705\) | −20536.8 | −1.09711 | ||||||||
\(706\) | −2151.20 | −0.114677 | ||||||||
\(707\) | 3808.79 | 0.202609 | ||||||||
\(708\) | 1914.64 | 0.101633 | ||||||||
\(709\) | 31200.7 | 1.65270 | 0.826352 | − | 0.563154i | \(-0.190412\pi\) | ||||
0.826352 | + | 0.563154i | \(0.190412\pi\) | |||||||
\(710\) | −16357.2 | −0.864615 | ||||||||
\(711\) | 5003.40 | 0.263913 | ||||||||
\(712\) | −3379.97 | −0.177907 | ||||||||
\(713\) | −4168.93 | −0.218973 | ||||||||
\(714\) | −2249.67 | −0.117916 | ||||||||
\(715\) | 24042.3 | 1.25752 | ||||||||
\(716\) | 8112.48 | 0.423433 | ||||||||
\(717\) | −9728.03 | −0.506694 | ||||||||
\(718\) | −14197.0 | −0.737919 | ||||||||
\(719\) | 13774.6 | 0.714473 | 0.357236 | − | 0.934014i | \(-0.383719\pi\) | ||||
0.357236 | + | 0.934014i | \(0.383719\pi\) | |||||||
\(720\) | −2457.86 | −0.127221 | ||||||||
\(721\) | −6472.18 | −0.334309 | ||||||||
\(722\) | −10437.0 | −0.537987 | ||||||||
\(723\) | 19713.3 | 1.01403 | ||||||||
\(724\) | −12546.3 | −0.644031 | ||||||||
\(725\) | 25218.5 | 1.29185 | ||||||||
\(726\) | 16047.1 | 0.820334 | ||||||||
\(727\) | −14858.9 | −0.758027 | −0.379014 | − | 0.925391i | \(-0.623737\pi\) | ||||
−0.379014 | + | 0.925391i | \(0.623737\pi\) | |||||||
\(728\) | −1246.35 | −0.0634517 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −19937.8 | −1.01086 | ||||||||
\(731\) | 3320.83 | 0.168024 | ||||||||
\(732\) | −5256.29 | −0.265407 | ||||||||
\(733\) | −35179.1 | −1.77267 | −0.886336 | − | 0.463043i | \(-0.846757\pi\) | ||||
−0.886336 | + | 0.463043i | \(0.846757\pi\) | |||||||
\(734\) | 8163.57 | 0.410522 | ||||||||
\(735\) | −2509.06 | −0.125916 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −2645.55 | −0.132225 | ||||||||
\(738\) | −1497.41 | −0.0746888 | ||||||||
\(739\) | 5814.21 | 0.289417 | 0.144708 | − | 0.989474i | \(-0.453776\pi\) | ||||
0.144708 | + | 0.989474i | \(0.453776\pi\) | |||||||
\(740\) | −23680.0 | −1.17635 | ||||||||
\(741\) | 2704.32 | 0.134070 | ||||||||
\(742\) | 4962.65 | 0.245532 | ||||||||
\(743\) | −32551.6 | −1.60727 | −0.803637 | − | 0.595120i | \(-0.797104\pi\) | ||||
−0.803637 | + | 0.595120i | \(0.797104\pi\) | |||||||
\(744\) | 4350.19 | 0.214362 | ||||||||
\(745\) | −26237.4 | −1.29029 | ||||||||
\(746\) | −4570.97 | −0.224337 | ||||||||
\(747\) | −7338.26 | −0.359428 | ||||||||
\(748\) | −13560.0 | −0.662836 | ||||||||
\(749\) | −13520.3 | −0.659572 | ||||||||
\(750\) | −4232.81 | −0.206081 | ||||||||
\(751\) | 24224.1 | 1.17703 | 0.588515 | − | 0.808486i | \(-0.299713\pi\) | ||||
0.588515 | + | 0.808486i | \(0.299713\pi\) | |||||||
\(752\) | 6417.10 | 0.311180 | ||||||||
\(753\) | 17623.0 | 0.852880 | ||||||||
\(754\) | 6748.81 | 0.325965 | ||||||||
\(755\) | 6700.82 | 0.323004 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | −22180.9 | −1.06497 | −0.532483 | − | 0.846441i | \(-0.678741\pi\) | ||||
−0.532483 | + | 0.846441i | \(0.678741\pi\) | |||||||
\(758\) | −19956.2 | −0.956256 | ||||||||
\(759\) | 4366.95 | 0.208841 | ||||||||
\(760\) | −5530.56 | −0.263966 | ||||||||
\(761\) | 34512.3 | 1.64398 | 0.821990 | − | 0.569502i | \(-0.192864\pi\) | ||||
0.821990 | + | 0.569502i | \(0.192864\pi\) | |||||||
\(762\) | −1234.45 | −0.0586869 | ||||||||
\(763\) | −4231.57 | −0.200777 | ||||||||
\(764\) | −3981.84 | −0.188558 | ||||||||
\(765\) | −8228.22 | −0.388878 | ||||||||
\(766\) | 4109.55 | 0.193844 | ||||||||
\(767\) | 3551.06 | 0.167172 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −30867.8 | −1.44749 | −0.723746 | − | 0.690067i | \(-0.757581\pi\) | ||||
−0.723746 | + | 0.690067i | \(0.757581\pi\) | |||||||
\(770\) | −15123.5 | −0.707807 | ||||||||
\(771\) | 7855.98 | 0.366960 | ||||||||
\(772\) | 13338.9 | 0.621864 | ||||||||
\(773\) | 25543.7 | 1.18854 | 0.594271 | − | 0.804265i | \(-0.297441\pi\) | ||||
0.594271 | + | 0.804265i | \(0.297441\pi\) | |||||||
\(774\) | 1115.96 | 0.0518249 | ||||||||
\(775\) | 30148.9 | 1.39739 | ||||||||
\(776\) | −992.971 | −0.0459350 | ||||||||
\(777\) | −7283.63 | −0.336292 | ||||||||
\(778\) | 14367.1 | 0.662064 | ||||||||
\(779\) | −3369.40 | −0.154969 | ||||||||
\(780\) | −4558.56 | −0.209260 | ||||||||
\(781\) | −30326.0 | −1.38944 | ||||||||
\(782\) | −2463.92 | −0.112672 | ||||||||
\(783\) | 4093.63 | 0.186838 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −23281.9 | −1.05856 | ||||||||
\(786\) | −2029.12 | −0.0920820 | ||||||||
\(787\) | −26008.6 | −1.17803 | −0.589013 | − | 0.808123i | \(-0.700483\pi\) | ||||
−0.589013 | + | 0.808123i | \(0.700483\pi\) | |||||||
\(788\) | 3205.39 | 0.144908 | ||||||||
\(789\) | 9841.03 | 0.444043 | ||||||||
\(790\) | −18977.8 | −0.854685 | ||||||||
\(791\) | 5393.02 | 0.242419 | ||||||||
\(792\) | −4556.82 | −0.204444 | ||||||||
\(793\) | −9748.80 | −0.436557 | ||||||||
\(794\) | −18722.0 | −0.836801 | ||||||||
\(795\) | 18151.0 | 0.809748 | ||||||||
\(796\) | 8926.19 | 0.397463 | ||||||||
\(797\) | 40066.1 | 1.78070 | 0.890348 | − | 0.455281i | \(-0.150461\pi\) | ||||
0.890348 | + | 0.455281i | \(0.150461\pi\) | |||||||
\(798\) | −1701.12 | −0.0754623 | ||||||||
\(799\) | 21482.6 | 0.951191 | ||||||||
\(800\) | 5322.62 | 0.235229 | ||||||||
\(801\) | −3802.46 | −0.167732 | ||||||||
\(802\) | 1817.17 | 0.0800079 | ||||||||
\(803\) | −36964.3 | −1.62446 | ||||||||
\(804\) | 501.612 | 0.0220031 | ||||||||
\(805\) | −2748.02 | −0.120317 | ||||||||
\(806\) | 8068.24 | 0.352595 | ||||||||
\(807\) | 7448.51 | 0.324907 | ||||||||
\(808\) | −4352.90 | −0.189523 | ||||||||
\(809\) | 31655.4 | 1.37570 | 0.687851 | − | 0.725852i | \(-0.258554\pi\) | ||||
0.687851 | + | 0.725852i | \(0.258554\pi\) | |||||||
\(810\) | −2765.09 | −0.119945 | ||||||||
\(811\) | −18907.1 | −0.818640 | −0.409320 | − | 0.912391i | \(-0.634234\pi\) | ||||
−0.409320 | + | 0.912391i | \(0.634234\pi\) | |||||||
\(812\) | −4245.25 | −0.183472 | ||||||||
\(813\) | −14542.7 | −0.627348 | ||||||||
\(814\) | −43902.3 | −1.89039 | ||||||||
\(815\) | −19307.6 | −0.829833 | ||||||||
\(816\) | 2571.05 | 0.110300 | ||||||||
\(817\) | 2511.09 | 0.107530 | ||||||||
\(818\) | 12127.2 | 0.518361 | ||||||||
\(819\) | −1402.15 | −0.0598229 | ||||||||
\(820\) | 5679.65 | 0.241880 | ||||||||
\(821\) | −1227.03 | −0.0521604 | −0.0260802 | − | 0.999660i | \(-0.508303\pi\) | ||||
−0.0260802 | + | 0.999660i | \(0.508303\pi\) | |||||||
\(822\) | 1821.90 | 0.0773067 | ||||||||
\(823\) | 13362.2 | 0.565951 | 0.282976 | − | 0.959127i | \(-0.408678\pi\) | ||||
0.282976 | + | 0.959127i | \(0.408678\pi\) | |||||||
\(824\) | 7396.78 | 0.312717 | ||||||||
\(825\) | −31581.0 | −1.33274 | ||||||||
\(826\) | −2233.74 | −0.0940942 | ||||||||
\(827\) | 30313.1 | 1.27459 | 0.637297 | − | 0.770618i | \(-0.280053\pi\) | ||||
0.637297 | + | 0.770618i | \(0.280053\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | −6416.41 | −0.268819 | −0.134410 | − | 0.990926i | \(-0.542914\pi\) | ||||
−0.134410 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(830\) | 27833.9 | 1.16401 | ||||||||
\(831\) | 9036.03 | 0.377204 | ||||||||
\(832\) | 1424.40 | 0.0593537 | ||||||||
\(833\) | 2624.61 | 0.109169 | ||||||||
\(834\) | −6958.07 | −0.288895 | ||||||||
\(835\) | 29928.0 | 1.24036 | ||||||||
\(836\) | −10253.5 | −0.424194 | ||||||||
\(837\) | 4893.96 | 0.202103 | ||||||||
\(838\) | −23339.7 | −0.962121 | ||||||||
\(839\) | −21333.8 | −0.877858 | −0.438929 | − | 0.898522i | \(-0.644642\pi\) | ||||
−0.438929 | + | 0.898522i | \(0.644642\pi\) | |||||||
\(840\) | 2867.50 | 0.117783 | ||||||||
\(841\) | −1401.60 | −0.0574685 | ||||||||
\(842\) | −29812.9 | −1.22021 | ||||||||
\(843\) | 17832.7 | 0.728577 | ||||||||
\(844\) | 18599.3 | 0.758546 | ||||||||
\(845\) | 29044.7 | 1.18245 | ||||||||
\(846\) | 7219.23 | 0.293383 | ||||||||
\(847\) | −18721.6 | −0.759482 | ||||||||
\(848\) | −5671.60 | −0.229674 | ||||||||
\(849\) | −151.587 | −0.00612776 | ||||||||
\(850\) | 17818.6 | 0.719028 | ||||||||
\(851\) | −7977.31 | −0.321338 | ||||||||
\(852\) | 5750.00 | 0.231211 | ||||||||
\(853\) | 44204.3 | 1.77436 | 0.887178 | − | 0.461428i | \(-0.152663\pi\) | ||||
0.887178 | + | 0.461428i | \(0.152663\pi\) | |||||||
\(854\) | 6132.34 | 0.245720 | ||||||||
\(855\) | −6221.88 | −0.248870 | ||||||||
\(856\) | 15451.7 | 0.616973 | ||||||||
\(857\) | −24525.9 | −0.977585 | −0.488792 | − | 0.872400i | \(-0.662562\pi\) | ||||
−0.488792 | + | 0.872400i | \(0.662562\pi\) | |||||||
\(858\) | −8451.48 | −0.336281 | ||||||||
\(859\) | 23934.9 | 0.950695 | 0.475348 | − | 0.879798i | \(-0.342322\pi\) | ||||
0.475348 | + | 0.879798i | \(0.342322\pi\) | |||||||
\(860\) | −4232.83 | −0.167835 | ||||||||
\(861\) | 1746.97 | 0.0691484 | ||||||||
\(862\) | −19319.1 | −0.763354 | ||||||||
\(863\) | −27472.0 | −1.08361 | −0.541807 | − | 0.840503i | \(-0.682260\pi\) | ||||
−0.541807 | + | 0.840503i | \(0.682260\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 65731.8 | 2.58375 | ||||||||
\(866\) | 2882.46 | 0.113106 | ||||||||
\(867\) | −6131.84 | −0.240194 | ||||||||
\(868\) | −5075.22 | −0.198461 | ||||||||
\(869\) | −35184.6 | −1.37348 | ||||||||
\(870\) | −15527.1 | −0.605078 | ||||||||
\(871\) | 930.335 | 0.0361920 | ||||||||
\(872\) | 4836.08 | 0.187810 | ||||||||
\(873\) | −1117.09 | −0.0433080 | ||||||||
\(874\) | −1863.13 | −0.0721067 | ||||||||
\(875\) | 4938.28 | 0.190793 | ||||||||
\(876\) | 7008.65 | 0.270320 | ||||||||
\(877\) | 14503.1 | 0.558420 | 0.279210 | − | 0.960230i | \(-0.409927\pi\) | ||||
0.279210 | + | 0.960230i | \(0.409927\pi\) | |||||||
\(878\) | 28232.1 | 1.08518 | ||||||||
\(879\) | −24846.9 | −0.953429 | ||||||||
\(880\) | 17283.9 | 0.662093 | ||||||||
\(881\) | −10198.5 | −0.390008 | −0.195004 | − | 0.980802i | \(-0.562472\pi\) | ||||
−0.195004 | + | 0.980802i | \(0.562472\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 366.578 | 0.0139709 | 0.00698546 | − | 0.999976i | \(-0.497776\pi\) | ||||
0.00698546 | + | 0.999976i | \(0.497776\pi\) | |||||||
\(884\) | 4768.50 | 0.181428 | ||||||||
\(885\) | −8169.97 | −0.310317 | ||||||||
\(886\) | −5059.35 | −0.191842 | ||||||||
\(887\) | 26509.7 | 1.00350 | 0.501752 | − | 0.865012i | \(-0.332689\pi\) | ||||
0.501752 | + | 0.865012i | \(0.332689\pi\) | |||||||
\(888\) | 8324.15 | 0.314572 | ||||||||
\(889\) | 1440.19 | 0.0543335 | ||||||||
\(890\) | 14422.7 | 0.543202 | ||||||||
\(891\) | −5126.42 | −0.192751 | ||||||||
\(892\) | −14483.6 | −0.543662 | ||||||||
\(893\) | 16244.4 | 0.608732 | ||||||||
\(894\) | 9223.14 | 0.345042 | ||||||||
\(895\) | −34616.9 | −1.29286 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | −1535.68 | −0.0571627 | ||||||||
\(898\) | −26595.2 | −0.988299 | ||||||||
\(899\) | 27481.6 | 1.01953 | ||||||||
\(900\) | 5987.94 | 0.221776 | ||||||||
\(901\) | −18986.9 | −0.702049 | ||||||||
\(902\) | 10530.0 | 0.388702 | ||||||||
\(903\) | −1301.96 | −0.0479805 | ||||||||
\(904\) | −6163.45 | −0.226763 | ||||||||
\(905\) | 53536.3 | 1.96642 | ||||||||
\(906\) | −2355.51 | −0.0863760 | ||||||||
\(907\) | −3179.92 | −0.116414 | −0.0582071 | − | 0.998305i | \(-0.518538\pi\) | ||||
−0.0582071 | + | 0.998305i | \(0.518538\pi\) | |||||||
\(908\) | 8758.08 | 0.320096 | ||||||||
\(909\) | −4897.02 | −0.178684 | ||||||||
\(910\) | 5318.32 | 0.193737 | ||||||||
\(911\) | −7517.86 | −0.273411 | −0.136706 | − | 0.990612i | \(-0.543651\pi\) | ||||
−0.136706 | + | 0.990612i | \(0.543651\pi\) | |||||||
\(912\) | 1944.13 | 0.0705885 | ||||||||
\(913\) | 51603.6 | 1.87057 | ||||||||
\(914\) | 24768.1 | 0.896340 | ||||||||
\(915\) | 22429.2 | 0.810367 | ||||||||
\(916\) | −22995.1 | −0.829453 | ||||||||
\(917\) | 2367.31 | 0.0852514 | ||||||||
\(918\) | 2892.43 | 0.103992 | ||||||||
\(919\) | 20848.6 | 0.748347 | 0.374173 | − | 0.927359i | \(-0.377926\pi\) | ||||
0.374173 | + | 0.927359i | \(0.377926\pi\) | |||||||
\(920\) | 3140.59 | 0.112546 | ||||||||
\(921\) | 20701.4 | 0.740644 | ||||||||
\(922\) | −30334.4 | −1.08352 | ||||||||
\(923\) | 10664.5 | 0.380309 | ||||||||
\(924\) | 5316.29 | 0.189278 | ||||||||
\(925\) | 57690.4 | 2.05065 | ||||||||
\(926\) | 4851.31 | 0.172164 | ||||||||
\(927\) | 8321.38 | 0.294833 | ||||||||
\(928\) | 4851.71 | 0.171622 | ||||||||
\(929\) | −5293.99 | −0.186965 | −0.0934824 | − | 0.995621i | \(-0.529800\pi\) | ||||
−0.0934824 | + | 0.995621i | \(0.529800\pi\) | |||||||
\(930\) | −18562.7 | −0.654511 | ||||||||
\(931\) | 1984.64 | 0.0698645 | ||||||||
\(932\) | 20927.1 | 0.735504 | ||||||||
\(933\) | 13236.8 | 0.464474 | ||||||||
\(934\) | −4697.40 | −0.164565 | ||||||||
\(935\) | 57861.8 | 2.02383 | ||||||||
\(936\) | 1602.45 | 0.0559592 | ||||||||
\(937\) | 32372.2 | 1.12866 | 0.564329 | − | 0.825550i | \(-0.309135\pi\) | ||||
0.564329 | + | 0.825550i | \(0.309135\pi\) | |||||||
\(938\) | −585.215 | −0.0203709 | ||||||||
\(939\) | 739.243 | 0.0256915 | ||||||||
\(940\) | −27382.5 | −0.950125 | ||||||||
\(941\) | 14785.0 | 0.512196 | 0.256098 | − | 0.966651i | \(-0.417563\pi\) | ||||
0.256098 | + | 0.966651i | \(0.417563\pi\) | |||||||
\(942\) | 8184.21 | 0.283074 | ||||||||
\(943\) | 1913.35 | 0.0660736 | ||||||||
\(944\) | 2552.85 | 0.0880171 | ||||||||
\(945\) | 3225.94 | 0.111047 | ||||||||
\(946\) | −7847.59 | −0.269711 | ||||||||
\(947\) | 29711.4 | 1.01952 | 0.509762 | − | 0.860315i | \(-0.329733\pi\) | ||||
0.509762 | + | 0.860315i | \(0.329733\pi\) | |||||||
\(948\) | 6671.21 | 0.228556 | ||||||||
\(949\) | 12998.9 | 0.444638 | ||||||||
\(950\) | 13473.8 | 0.460156 | ||||||||
\(951\) | 23832.6 | 0.812646 | ||||||||
\(952\) | −2999.56 | −0.102118 | ||||||||
\(953\) | 10740.6 | 0.365082 | 0.182541 | − | 0.983198i | \(-0.441568\pi\) | ||||
0.182541 | + | 0.983198i | \(0.441568\pi\) | |||||||
\(954\) | −6380.55 | −0.216539 | ||||||||
\(955\) | 16991.0 | 0.575722 | ||||||||
\(956\) | −12970.7 | −0.438810 | ||||||||
\(957\) | −28786.9 | −0.972360 | ||||||||
\(958\) | −21421.3 | −0.722433 | ||||||||
\(959\) | −2125.55 | −0.0715721 | ||||||||
\(960\) | −3277.14 | −0.110176 | ||||||||
\(961\) | 3063.36 | 0.102828 | ||||||||
\(962\) | 15438.7 | 0.517426 | ||||||||
\(963\) | 17383.2 | 0.581688 | ||||||||
\(964\) | 26284.4 | 0.878177 | ||||||||
\(965\) | −56918.8 | −1.89874 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | 24542.7 | 0.816175 | 0.408087 | − | 0.912943i | \(-0.366196\pi\) | ||||
0.408087 | + | 0.912943i | \(0.366196\pi\) | |||||||
\(968\) | 21396.1 | 0.710430 | ||||||||
\(969\) | 6508.42 | 0.215769 | ||||||||
\(970\) | 4237.12 | 0.140253 | ||||||||
\(971\) | 45866.8 | 1.51590 | 0.757948 | − | 0.652315i | \(-0.226202\pi\) | ||||
0.757948 | + | 0.652315i | \(0.226202\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 8117.74 | 0.267464 | ||||||||
\(974\) | 28925.8 | 0.951583 | ||||||||
\(975\) | 11105.8 | 0.364789 | ||||||||
\(976\) | −7008.39 | −0.229850 | ||||||||
\(977\) | 11048.0 | 0.361779 | 0.180890 | − | 0.983503i | \(-0.442102\pi\) | ||||
0.180890 | + | 0.983503i | \(0.442102\pi\) | |||||||
\(978\) | 6787.11 | 0.221910 | ||||||||
\(979\) | 26739.4 | 0.872926 | ||||||||
\(980\) | −3345.41 | −0.109046 | ||||||||
\(981\) | 5440.59 | 0.177069 | ||||||||
\(982\) | −11167.1 | −0.362890 | ||||||||
\(983\) | 44742.5 | 1.45174 | 0.725872 | − | 0.687830i | \(-0.241437\pi\) | ||||
0.725872 | + | 0.687830i | \(0.241437\pi\) | |||||||
\(984\) | −1996.54 | −0.0646824 | ||||||||
\(985\) | −13677.7 | −0.442446 | ||||||||
\(986\) | 16242.2 | 0.524601 | ||||||||
\(987\) | −8422.44 | −0.271620 | ||||||||
\(988\) | 3605.77 | 0.116108 | ||||||||
\(989\) | −1425.95 | −0.0458470 | ||||||||
\(990\) | 19444.4 | 0.624227 | ||||||||
\(991\) | 53711.0 | 1.72168 | 0.860841 | − | 0.508874i | \(-0.169938\pi\) | ||||
0.860841 | + | 0.508874i | \(0.169938\pi\) | |||||||
\(992\) | 5800.25 | 0.185643 | ||||||||
\(993\) | −7455.37 | −0.238257 | ||||||||
\(994\) | −6708.33 | −0.214060 | ||||||||
\(995\) | −38089.0 | −1.21357 | ||||||||
\(996\) | −9784.35 | −0.311274 | ||||||||
\(997\) | −60393.5 | −1.91844 | −0.959218 | − | 0.282667i | \(-0.908781\pi\) | ||||
−0.959218 | + | 0.282667i | \(0.908781\pi\) | |||||||
\(998\) | 3341.52 | 0.105986 | ||||||||
\(999\) | 9364.66 | 0.296581 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 966.4.a.q.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.q.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial |