Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
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: | \( x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.84623\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.84623 | 1.35985 | 0.679923 | − | 0.733284i | \(-0.262013\pi\) | ||||
0.679923 | + | 0.733284i | \(0.262013\pi\) | |||||||
\(3\) | 8.96795 | 1.72588 | 0.862941 | − | 0.505304i | \(-0.168620\pi\) | ||||
0.862941 | + | 0.505304i | \(0.168620\pi\) | |||||||
\(4\) | 6.79345 | 0.849181 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 34.4927 | 2.34693 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.64067 | −0.205090 | ||||||||
\(9\) | 53.4241 | 1.97867 | ||||||||
\(10\) | 19.2311 | 0.608142 | ||||||||
\(11\) | 23.1120 | 0.633501 | 0.316751 | − | 0.948509i | \(-0.397408\pi\) | ||||
0.316751 | + | 0.948509i | \(0.397408\pi\) | |||||||
\(12\) | 60.9233 | 1.46559 | ||||||||
\(13\) | −61.0473 | −1.30242 | −0.651211 | − | 0.758897i | \(-0.725739\pi\) | ||||
−0.651211 | + | 0.758897i | \(0.725739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.8397 | 0.771838 | ||||||||
\(16\) | −72.1966 | −1.12807 | ||||||||
\(17\) | −0.688309 | −0.00981996 | −0.00490998 | − | 0.999988i | \(-0.501563\pi\) | ||||
−0.00490998 | + | 0.999988i | \(0.501563\pi\) | |||||||
\(18\) | 205.481 | 2.69069 | ||||||||
\(19\) | −63.2247 | −0.763407 | −0.381704 | − | 0.924285i | \(-0.624663\pi\) | ||||
−0.381704 | + | 0.924285i | \(0.624663\pi\) | |||||||
\(20\) | 33.9672 | 0.379765 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 88.8938 | 0.861464 | ||||||||
\(23\) | 124.502 | 1.12871 | 0.564356 | − | 0.825531i | \(-0.309125\pi\) | ||||
0.564356 | + | 0.825531i | \(0.309125\pi\) | |||||||
\(24\) | −41.6172 | −0.353962 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −234.802 | −1.77109 | ||||||||
\(27\) | 236.970 | 1.68907 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 104.167 | 0.667011 | 0.333506 | − | 0.942748i | \(-0.391768\pi\) | ||||
0.333506 | + | 0.942748i | \(0.391768\pi\) | |||||||
\(30\) | 172.464 | 1.04958 | ||||||||
\(31\) | −280.022 | −1.62237 | −0.811185 | − | 0.584790i | \(-0.801177\pi\) | ||||
−0.811185 | + | 0.584790i | \(0.801177\pi\) | |||||||
\(32\) | −240.559 | −1.32891 | ||||||||
\(33\) | 207.267 | 1.09335 | ||||||||
\(34\) | −2.64739 | −0.0133536 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 362.934 | 1.68025 | ||||||||
\(37\) | −263.871 | −1.17244 | −0.586219 | − | 0.810153i | \(-0.699384\pi\) | ||||
−0.586219 | + | 0.810153i | \(0.699384\pi\) | |||||||
\(38\) | −243.176 | −1.03812 | ||||||||
\(39\) | −547.469 | −2.24783 | ||||||||
\(40\) | −23.2033 | −0.0917192 | ||||||||
\(41\) | 243.366 | 0.927009 | 0.463505 | − | 0.886095i | \(-0.346592\pi\) | ||||
0.463505 | + | 0.886095i | \(0.346592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 172.541 | 0.611913 | 0.305956 | − | 0.952046i | \(-0.401024\pi\) | ||||
0.305956 | + | 0.952046i | \(0.401024\pi\) | |||||||
\(44\) | 157.010 | 0.537957 | ||||||||
\(45\) | 267.120 | 0.884888 | ||||||||
\(46\) | 478.861 | 1.53487 | ||||||||
\(47\) | 107.381 | 0.333260 | 0.166630 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166630 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(48\) | −647.456 | −1.94692 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 96.1556 | 0.271969 | ||||||||
\(51\) | −6.17272 | −0.0169481 | ||||||||
\(52\) | −414.722 | −1.10599 | ||||||||
\(53\) | 44.8086 | 0.116131 | 0.0580654 | − | 0.998313i | \(-0.481507\pi\) | ||||
0.0580654 | + | 0.998313i | \(0.481507\pi\) | |||||||
\(54\) | 911.440 | 2.29687 | ||||||||
\(55\) | 115.560 | 0.283310 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −566.996 | −1.31755 | ||||||||
\(58\) | 400.650 | 0.907033 | ||||||||
\(59\) | −457.246 | −1.00895 | −0.504477 | − | 0.863425i | \(-0.668315\pi\) | ||||
−0.504477 | + | 0.863425i | \(0.668315\pi\) | |||||||
\(60\) | 304.617 | 0.655430 | ||||||||
\(61\) | −473.802 | −0.994493 | −0.497247 | − | 0.867609i | \(-0.665656\pi\) | ||||
−0.497247 | + | 0.867609i | \(0.665656\pi\) | |||||||
\(62\) | −1077.03 | −2.20617 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −347.672 | −0.679047 | ||||||||
\(65\) | −305.237 | −0.582461 | ||||||||
\(66\) | 797.195 | 1.48679 | ||||||||
\(67\) | −229.454 | −0.418392 | −0.209196 | − | 0.977874i | \(-0.567085\pi\) | ||||
−0.209196 | + | 0.977874i | \(0.567085\pi\) | |||||||
\(68\) | −4.67599 | −0.00833893 | ||||||||
\(69\) | 1116.52 | 1.94802 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 407.688 | 0.681460 | 0.340730 | − | 0.940161i | \(-0.389326\pi\) | ||||
0.340730 | + | 0.940161i | \(0.389326\pi\) | |||||||
\(72\) | −247.923 | −0.405806 | ||||||||
\(73\) | 348.475 | 0.558712 | 0.279356 | − | 0.960188i | \(-0.409879\pi\) | ||||
0.279356 | + | 0.960188i | \(0.409879\pi\) | |||||||
\(74\) | −1014.91 | −1.59433 | ||||||||
\(75\) | 224.199 | 0.345176 | ||||||||
\(76\) | −429.514 | −0.648271 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2105.69 | −3.05670 | ||||||||
\(79\) | 840.135 | 1.19649 | 0.598244 | − | 0.801314i | \(-0.295865\pi\) | ||||
0.598244 | + | 0.801314i | \(0.295865\pi\) | |||||||
\(80\) | −360.983 | −0.504489 | ||||||||
\(81\) | 682.683 | 0.936465 | ||||||||
\(82\) | 936.040 | 1.26059 | ||||||||
\(83\) | 885.652 | 1.17124 | 0.585620 | − | 0.810586i | \(-0.300851\pi\) | ||||
0.585620 | + | 0.810586i | \(0.300851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44154 | −0.00439162 | ||||||||
\(86\) | 663.632 | 0.832107 | ||||||||
\(87\) | 934.164 | 1.15118 | ||||||||
\(88\) | −107.255 | −0.129925 | ||||||||
\(89\) | 856.096 | 1.01962 | 0.509809 | − | 0.860288i | \(-0.329716\pi\) | ||||
0.509809 | + | 0.860288i | \(0.329716\pi\) | |||||||
\(90\) | 1027.41 | 1.20331 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 845.795 | 0.958481 | ||||||||
\(93\) | −2511.22 | −2.80002 | ||||||||
\(94\) | 413.013 | 0.453182 | ||||||||
\(95\) | −316.124 | −0.341406 | ||||||||
\(96\) | −2157.32 | −2.29355 | ||||||||
\(97\) | −189.436 | −0.198292 | −0.0991459 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991459 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1234.74 | 1.25349 | ||||||||
\(100\) | 169.836 | 0.169836 | ||||||||
\(101\) | −795.803 | −0.784013 | −0.392007 | − | 0.919962i | \(-0.628219\pi\) | ||||
−0.392007 | + | 0.919962i | \(0.628219\pi\) | |||||||
\(102\) | −23.7417 | −0.0230468 | ||||||||
\(103\) | −1940.71 | −1.85654 | −0.928269 | − | 0.371909i | \(-0.878703\pi\) | ||||
−0.928269 | + | 0.371909i | \(0.878703\pi\) | |||||||
\(104\) | 283.300 | 0.267114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 172.344 | 0.157920 | ||||||||
\(107\) | 488.688 | 0.441526 | 0.220763 | − | 0.975327i | \(-0.429145\pi\) | ||||
0.220763 | + | 0.975327i | \(0.429145\pi\) | |||||||
\(108\) | 1609.84 | 1.43433 | ||||||||
\(109\) | 1630.05 | 1.43239 | 0.716197 | − | 0.697899i | \(-0.245881\pi\) | ||||
0.716197 | + | 0.697899i | \(0.245881\pi\) | |||||||
\(110\) | 444.469 | 0.385259 | ||||||||
\(111\) | −2366.38 | −2.02349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 345.925 | 0.287981 | 0.143991 | − | 0.989579i | \(-0.454007\pi\) | ||||
0.143991 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(114\) | −2180.79 | −1.79167 | ||||||||
\(115\) | 622.508 | 0.504775 | ||||||||
\(116\) | 707.653 | 0.566414 | ||||||||
\(117\) | −3261.40 | −2.57706 | ||||||||
\(118\) | −1758.67 | −1.37202 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −208.086 | −0.158297 | ||||||||
\(121\) | −796.838 | −0.598676 | ||||||||
\(122\) | −1822.35 | −1.35236 | ||||||||
\(123\) | 2182.49 | 1.59991 | ||||||||
\(124\) | −1902.32 | −1.37769 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1665.24 | −1.16351 | −0.581757 | − | 0.813362i | \(-0.697635\pi\) | ||||
−0.581757 | + | 0.813362i | \(0.697635\pi\) | |||||||
\(128\) | 587.249 | 0.405516 | ||||||||
\(129\) | 1547.34 | 1.05609 | ||||||||
\(130\) | −1174.01 | −0.792057 | ||||||||
\(131\) | −676.747 | −0.451356 | −0.225678 | − | 0.974202i | \(-0.572460\pi\) | ||||
−0.225678 | + | 0.974202i | \(0.572460\pi\) | |||||||
\(132\) | 1408.06 | 0.928451 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −882.531 | −0.568948 | ||||||||
\(135\) | 1184.85 | 0.755375 | ||||||||
\(136\) | 3.19421 | 0.00201398 | ||||||||
\(137\) | −1034.23 | −0.644967 | −0.322484 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322484 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(138\) | 4294.40 | 2.64901 | ||||||||
\(139\) | −435.826 | −0.265944 | −0.132972 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132972 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 962.992 | 0.575167 | ||||||||
\(142\) | 1568.06 | 0.926681 | ||||||||
\(143\) | −1410.92 | −0.825086 | ||||||||
\(144\) | −3857.04 | −2.23208 | ||||||||
\(145\) | 520.835 | 0.298297 | ||||||||
\(146\) | 1340.31 | 0.759762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1792.60 | −0.995612 | ||||||||
\(149\) | 2119.95 | 1.16559 | 0.582795 | − | 0.812619i | \(-0.301959\pi\) | ||||
0.582795 | + | 0.812619i | \(0.301959\pi\) | |||||||
\(150\) | 862.319 | 0.469387 | ||||||||
\(151\) | −2400.40 | −1.29365 | −0.646827 | − | 0.762637i | \(-0.723904\pi\) | ||||
−0.646827 | + | 0.762637i | \(0.723904\pi\) | |||||||
\(152\) | 293.405 | 0.156568 | ||||||||
\(153\) | −36.7723 | −0.0194305 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1400.11 | −0.725546 | ||||||||
\(156\) | −3719.21 | −1.90881 | ||||||||
\(157\) | 506.188 | 0.257313 | 0.128657 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128657 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(158\) | 3231.35 | 1.62704 | ||||||||
\(159\) | 401.841 | 0.200428 | ||||||||
\(160\) | −1202.80 | −0.594309 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2625.75 | 1.27345 | ||||||||
\(163\) | 2600.95 | 1.24983 | 0.624913 | − | 0.780694i | \(-0.285134\pi\) | ||||
0.624913 | + | 0.780694i | \(0.285134\pi\) | |||||||
\(164\) | 1653.29 | 0.787199 | ||||||||
\(165\) | 1036.33 | 0.488961 | ||||||||
\(166\) | 3406.42 | 1.59271 | ||||||||
\(167\) | −546.077 | −0.253034 | −0.126517 | − | 0.991964i | \(-0.540380\pi\) | ||||
−0.126517 | + | 0.991964i | \(0.540380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1529.78 | 0.696303 | ||||||||
\(170\) | −13.2370 | −0.00597193 | ||||||||
\(171\) | −3377.72 | −1.51053 | ||||||||
\(172\) | 1172.15 | 0.519625 | ||||||||
\(173\) | 3020.32 | 1.32735 | 0.663673 | − | 0.748023i | \(-0.268997\pi\) | ||||
0.663673 | + | 0.748023i | \(0.268997\pi\) | |||||||
\(174\) | 3593.01 | 1.56543 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1668.61 | −0.714636 | ||||||||
\(177\) | −4100.55 | −1.74134 | ||||||||
\(178\) | 3292.74 | 1.38652 | ||||||||
\(179\) | 1999.17 | 0.834775 | 0.417387 | − | 0.908729i | \(-0.362946\pi\) | ||||
0.417387 | + | 0.908729i | \(0.362946\pi\) | |||||||
\(180\) | 1814.67 | 0.751430 | ||||||||
\(181\) | 681.145 | 0.279719 | 0.139859 | − | 0.990171i | \(-0.455335\pi\) | ||||
0.139859 | + | 0.990171i | \(0.455335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4249.03 | −1.71638 | ||||||||
\(184\) | −577.770 | −0.231488 | ||||||||
\(185\) | −1319.36 | −0.524330 | ||||||||
\(186\) | −9658.73 | −3.80759 | ||||||||
\(187\) | −15.9082 | −0.00622096 | ||||||||
\(188\) | 729.491 | 0.282998 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1215.88 | −0.464260 | ||||||||
\(191\) | −1612.76 | −0.610970 | −0.305485 | − | 0.952197i | \(-0.598819\pi\) | ||||
−0.305485 | + | 0.952197i | \(0.598819\pi\) | |||||||
\(192\) | −3117.90 | −1.17195 | ||||||||
\(193\) | 808.921 | 0.301697 | 0.150848 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150848 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(194\) | −728.613 | −0.269646 | ||||||||
\(195\) | −2737.35 | −1.00526 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3704.23 | 1.33967 | 0.669836 | − | 0.742509i | \(-0.266364\pi\) | ||||
0.669836 | + | 0.742509i | \(0.266364\pi\) | |||||||
\(198\) | 4749.07 | 1.70455 | ||||||||
\(199\) | 367.928 | 0.131064 | 0.0655319 | − | 0.997850i | \(-0.479126\pi\) | ||||
0.0655319 | + | 0.997850i | \(0.479126\pi\) | |||||||
\(200\) | −116.017 | −0.0410181 | ||||||||
\(201\) | −2057.73 | −0.722095 | ||||||||
\(202\) | −3060.84 | −1.06614 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −41.9340 | −0.0143920 | ||||||||
\(205\) | 1216.83 | 0.414571 | ||||||||
\(206\) | −7464.39 | −2.52461 | ||||||||
\(207\) | 6651.39 | 2.23335 | ||||||||
\(208\) | 4407.41 | 1.46923 | ||||||||
\(209\) | −1461.25 | −0.483620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1073.36 | −0.350205 | −0.175102 | − | 0.984550i | \(-0.556026\pi\) | ||||
−0.175102 | + | 0.984550i | \(0.556026\pi\) | |||||||
\(212\) | 304.405 | 0.0986161 | ||||||||
\(213\) | 3656.13 | 1.17612 | ||||||||
\(214\) | 1879.61 | 0.600407 | ||||||||
\(215\) | 862.705 | 0.273656 | ||||||||
\(216\) | −1099.70 | −0.346412 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6269.55 | 1.94783 | ||||||||
\(219\) | 3125.11 | 0.964271 | ||||||||
\(220\) | 785.049 | 0.240582 | ||||||||
\(221\) | 42.0194 | 0.0127897 | ||||||||
\(222\) | −9101.65 | −2.75163 | ||||||||
\(223\) | 1725.16 | 0.518050 | 0.259025 | − | 0.965871i | \(-0.416599\pi\) | ||||
0.259025 | + | 0.965871i | \(0.416599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1335.60 | 0.395734 | ||||||||
\(226\) | 1330.50 | 0.391610 | ||||||||
\(227\) | 3616.99 | 1.05757 | 0.528784 | − | 0.848757i | \(-0.322648\pi\) | ||||
0.528784 | + | 0.848757i | \(0.322648\pi\) | |||||||
\(228\) | −3851.86 | −1.11884 | ||||||||
\(229\) | −1461.79 | −0.421823 | −0.210912 | − | 0.977505i | \(-0.567643\pi\) | ||||
−0.210912 | + | 0.977505i | \(0.567643\pi\) | |||||||
\(230\) | 2394.31 | 0.686417 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −483.404 | −0.136798 | ||||||||
\(233\) | 2135.32 | 0.600383 | 0.300192 | − | 0.953879i | \(-0.402949\pi\) | ||||
0.300192 | + | 0.953879i | \(0.402949\pi\) | |||||||
\(234\) | −12544.1 | −3.50441 | ||||||||
\(235\) | 536.907 | 0.149038 | ||||||||
\(236\) | −3106.27 | −0.856785 | ||||||||
\(237\) | 7534.29 | 2.06500 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5952.35 | 1.61099 | 0.805493 | − | 0.592605i | \(-0.201900\pi\) | ||||
0.805493 | + | 0.592605i | \(0.201900\pi\) | |||||||
\(240\) | −3237.28 | −0.870689 | ||||||||
\(241\) | 3847.56 | 1.02839 | 0.514197 | − | 0.857672i | \(-0.328090\pi\) | ||||
0.514197 | + | 0.857672i | \(0.328090\pi\) | |||||||
\(242\) | −3064.82 | −0.814107 | ||||||||
\(243\) | −275.920 | −0.0728407 | ||||||||
\(244\) | −3218.75 | −0.844505 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8394.36 | 2.17563 | ||||||||
\(247\) | 3859.70 | 0.994279 | ||||||||
\(248\) | 1299.49 | 0.332732 | ||||||||
\(249\) | 7942.48 | 2.02142 | ||||||||
\(250\) | 480.778 | 0.121628 | ||||||||
\(251\) | 1731.69 | 0.435470 | 0.217735 | − | 0.976008i | \(-0.430133\pi\) | ||||
0.217735 | + | 0.976008i | \(0.430133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2877.47 | 0.715041 | ||||||||
\(254\) | −6404.90 | −1.58220 | ||||||||
\(255\) | −30.8636 | −0.00757942 | ||||||||
\(256\) | 5040.07 | 1.23049 | ||||||||
\(257\) | 4054.43 | 0.984078 | 0.492039 | − | 0.870573i | \(-0.336252\pi\) | ||||
0.492039 | + | 0.870573i | \(0.336252\pi\) | |||||||
\(258\) | 5951.41 | 1.43612 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2073.61 | −0.494615 | ||||||||
\(261\) | 5565.03 | 1.31980 | ||||||||
\(262\) | −2602.92 | −0.613775 | ||||||||
\(263\) | −6335.82 | −1.48549 | −0.742744 | − | 0.669576i | \(-0.766476\pi\) | ||||
−0.742744 | + | 0.669576i | \(0.766476\pi\) | |||||||
\(264\) | −961.856 | −0.224235 | ||||||||
\(265\) | 224.043 | 0.0519353 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7677.42 | 1.75974 | ||||||||
\(268\) | −1558.78 | −0.355290 | ||||||||
\(269\) | 1321.63 | 0.299559 | 0.149780 | − | 0.988719i | \(-0.452144\pi\) | ||||
0.149780 | + | 0.988719i | \(0.452144\pi\) | |||||||
\(270\) | 4557.20 | 1.02719 | ||||||||
\(271\) | 2336.00 | 0.523624 | 0.261812 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261812 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(272\) | 49.6936 | 0.0110776 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3977.90 | −0.877056 | ||||||||
\(275\) | 577.799 | 0.126700 | ||||||||
\(276\) | 7585.05 | 1.65423 | ||||||||
\(277\) | −7085.23 | −1.53686 | −0.768430 | − | 0.639934i | \(-0.778962\pi\) | ||||
−0.768430 | + | 0.639934i | \(0.778962\pi\) | |||||||
\(278\) | −1676.28 | −0.361643 | ||||||||
\(279\) | −14959.9 | −3.21013 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2123.17 | 0.450738 | 0.225369 | − | 0.974273i | \(-0.427641\pi\) | ||||
0.225369 | + | 0.974273i | \(0.427641\pi\) | |||||||
\(282\) | 3703.88 | 0.782138 | ||||||||
\(283\) | −5891.63 | −1.23753 | −0.618765 | − | 0.785576i | \(-0.712367\pi\) | ||||
−0.618765 | + | 0.785576i | \(0.712367\pi\) | |||||||
\(284\) | 2769.61 | 0.578683 | ||||||||
\(285\) | −2834.98 | −0.589227 | ||||||||
\(286\) | −5426.73 | −1.12199 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12851.7 | −2.62948 | ||||||||
\(289\) | −4912.53 | −0.999904 | ||||||||
\(290\) | 2003.25 | 0.405637 | ||||||||
\(291\) | −1698.85 | −0.342228 | ||||||||
\(292\) | 2367.35 | 0.474448 | ||||||||
\(293\) | 8137.75 | 1.62257 | 0.811284 | − | 0.584652i | \(-0.198769\pi\) | ||||
0.811284 | + | 0.584652i | \(0.198769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2286.23 | −0.451218 | ||||||||
\(296\) | 1224.54 | 0.240456 | ||||||||
\(297\) | 5476.84 | 1.07003 | ||||||||
\(298\) | 8153.80 | 1.58502 | ||||||||
\(299\) | −7600.49 | −1.47006 | ||||||||
\(300\) | 1523.08 | 0.293117 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9232.47 | −1.75917 | ||||||||
\(303\) | −7136.72 | −1.35312 | ||||||||
\(304\) | 4564.61 | 0.861179 | ||||||||
\(305\) | −2369.01 | −0.444751 | ||||||||
\(306\) | −141.434 | −0.0264224 | ||||||||
\(307\) | 4797.24 | 0.891833 | 0.445917 | − | 0.895075i | \(-0.352878\pi\) | ||||
0.445917 | + | 0.895075i | \(0.352878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17404.1 | −3.20417 | ||||||||
\(310\) | −5385.14 | −0.986631 | ||||||||
\(311\) | −5189.53 | −0.946210 | −0.473105 | − | 0.881006i | \(-0.656867\pi\) | ||||
−0.473105 | + | 0.881006i | \(0.656867\pi\) | |||||||
\(312\) | 2540.62 | 0.461008 | ||||||||
\(313\) | 2245.24 | 0.405459 | 0.202729 | − | 0.979235i | \(-0.435019\pi\) | ||||
0.202729 | + | 0.979235i | \(0.435019\pi\) | |||||||
\(314\) | 1946.91 | 0.349907 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5707.42 | 1.01604 | ||||||||
\(317\) | −9742.27 | −1.72612 | −0.863060 | − | 0.505101i | \(-0.831455\pi\) | ||||
−0.863060 | + | 0.505101i | \(0.831455\pi\) | |||||||
\(318\) | 1545.57 | 0.272551 | ||||||||
\(319\) | 2407.50 | 0.422553 | ||||||||
\(320\) | −1738.36 | −0.303679 | ||||||||
\(321\) | 4382.53 | 0.762022 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.5181 | 0.00749663 | ||||||||
\(324\) | 4637.77 | 0.795229 | ||||||||
\(325\) | −1526.18 | −0.260484 | ||||||||
\(326\) | 10003.8 | 1.69957 | ||||||||
\(327\) | 14618.2 | 2.47214 | ||||||||
\(328\) | −1129.38 | −0.190121 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3985.97 | 0.664911 | ||||||||
\(331\) | 11330.8 | 1.88156 | 0.940778 | − | 0.339023i | \(-0.110096\pi\) | ||||
0.940778 | + | 0.339023i | \(0.110096\pi\) | |||||||
\(332\) | 6016.63 | 0.994595 | ||||||||
\(333\) | −14097.1 | −2.31987 | ||||||||
\(334\) | −2100.33 | −0.344087 | ||||||||
\(335\) | −1147.27 | −0.187110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3637.35 | 0.587950 | 0.293975 | − | 0.955813i | \(-0.405022\pi\) | ||||
0.293975 | + | 0.955813i | \(0.405022\pi\) | |||||||
\(338\) | 5883.87 | 0.946865 | ||||||||
\(339\) | 3102.23 | 0.497021 | ||||||||
\(340\) | −23.3800 | −0.00372928 | ||||||||
\(341\) | −6471.86 | −1.02777 | ||||||||
\(342\) | −12991.5 | −2.05409 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −800.705 | −0.125497 | ||||||||
\(345\) | 5582.62 | 0.871183 | ||||||||
\(346\) | 11616.8 | 1.80498 | ||||||||
\(347\) | −4030.12 | −0.623482 | −0.311741 | − | 0.950167i | \(-0.600912\pi\) | ||||
−0.311741 | + | 0.950167i | \(0.600912\pi\) | |||||||
\(348\) | 6346.20 | 0.977563 | ||||||||
\(349\) | −2887.69 | −0.442906 | −0.221453 | − | 0.975171i | \(-0.571080\pi\) | ||||
−0.221453 | + | 0.975171i | \(0.571080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14466.4 | −2.19988 | ||||||||
\(352\) | −5559.79 | −0.841869 | ||||||||
\(353\) | 524.918 | 0.0791461 | 0.0395731 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395731 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(354\) | −15771.7 | −2.36795 | ||||||||
\(355\) | 2038.44 | 0.304758 | ||||||||
\(356\) | 5815.84 | 0.865840 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7689.25 | 1.13517 | ||||||||
\(359\) | −3285.31 | −0.482987 | −0.241493 | − | 0.970402i | \(-0.577637\pi\) | ||||
−0.241493 | + | 0.970402i | \(0.577637\pi\) | |||||||
\(360\) | −1239.62 | −0.181482 | ||||||||
\(361\) | −2861.64 | −0.417209 | ||||||||
\(362\) | 2619.84 | 0.380374 | ||||||||
\(363\) | −7146.00 | −1.03324 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1742.38 | 0.249864 | ||||||||
\(366\) | −16342.7 | −2.33401 | ||||||||
\(367\) | −9053.95 | −1.28777 | −0.643886 | − | 0.765121i | \(-0.722679\pi\) | ||||
−0.643886 | + | 0.765121i | \(0.722679\pi\) | |||||||
\(368\) | −8988.60 | −1.27327 | ||||||||
\(369\) | 13001.6 | 1.83424 | ||||||||
\(370\) | −5074.54 | −0.713008 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17059.9 | −2.37772 | ||||||||
\(373\) | −5209.10 | −0.723102 | −0.361551 | − | 0.932352i | \(-0.617753\pi\) | ||||
−0.361551 | + | 0.932352i | \(0.617753\pi\) | |||||||
\(374\) | −61.1864 | −0.00845955 | ||||||||
\(375\) | 1120.99 | 0.154368 | ||||||||
\(376\) | −498.322 | −0.0683483 | ||||||||
\(377\) | −6359.12 | −0.868730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3200.68 | 0.433794 | 0.216897 | − | 0.976194i | \(-0.430406\pi\) | ||||
0.216897 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(380\) | −2147.57 | −0.289916 | ||||||||
\(381\) | −14933.8 | −2.00809 | ||||||||
\(382\) | −6203.04 | −0.830825 | ||||||||
\(383\) | 2202.81 | 0.293886 | 0.146943 | − | 0.989145i | \(-0.453057\pi\) | ||||
0.146943 | + | 0.989145i | \(0.453057\pi\) | |||||||
\(384\) | 5266.42 | 0.699872 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3111.29 | 0.410261 | ||||||||
\(387\) | 9217.85 | 1.21077 | ||||||||
\(388\) | −1286.92 | −0.168386 | ||||||||
\(389\) | −6241.59 | −0.813525 | −0.406762 | − | 0.913534i | \(-0.633342\pi\) | ||||
−0.406762 | + | 0.913534i | \(0.633342\pi\) | |||||||
\(390\) | −10528.5 | −1.36700 | ||||||||
\(391\) | −85.6955 | −0.0110839 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6069.04 | −0.778988 | ||||||||
\(394\) | 14247.3 | 1.82175 | ||||||||
\(395\) | 4200.68 | 0.535086 | ||||||||
\(396\) | 8388.11 | 1.06444 | ||||||||
\(397\) | −10407.2 | −1.31567 | −0.657834 | − | 0.753163i | \(-0.728527\pi\) | ||||
−0.657834 | + | 0.753163i | \(0.728527\pi\) | |||||||
\(398\) | 1415.13 | 0.178227 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1804.92 | −0.225615 | ||||||||
\(401\) | −14973.3 | −1.86466 | −0.932330 | − | 0.361608i | \(-0.882228\pi\) | ||||
−0.932330 | + | 0.361608i | \(0.882228\pi\) | |||||||
\(402\) | −7914.49 | −0.981938 | ||||||||
\(403\) | 17094.6 | 2.11301 | ||||||||
\(404\) | −5406.25 | −0.665769 | ||||||||
\(405\) | 3413.42 | 0.418800 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6098.58 | −0.742741 | ||||||||
\(408\) | 28.6455 | 0.00347589 | ||||||||
\(409\) | 7059.10 | 0.853422 | 0.426711 | − | 0.904388i | \(-0.359672\pi\) | ||||
0.426711 | + | 0.904388i | \(0.359672\pi\) | |||||||
\(410\) | 4680.20 | 0.563753 | ||||||||
\(411\) | −9274.95 | −1.11314 | ||||||||
\(412\) | −13184.1 | −1.57654 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 25582.7 | 3.03701 | ||||||||
\(415\) | 4428.26 | 0.523795 | ||||||||
\(416\) | 14685.5 | 1.73081 | ||||||||
\(417\) | −3908.46 | −0.458989 | ||||||||
\(418\) | −5620.28 | −0.657648 | ||||||||
\(419\) | −928.543 | −0.108263 | −0.0541316 | − | 0.998534i | \(-0.517239\pi\) | ||||
−0.0541316 | + | 0.998534i | \(0.517239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7105.06 | 0.822517 | 0.411258 | − | 0.911519i | \(-0.365089\pi\) | ||||
0.411258 | + | 0.911519i | \(0.365089\pi\) | |||||||
\(422\) | −4128.39 | −0.476225 | ||||||||
\(423\) | 5736.76 | 0.659411 | ||||||||
\(424\) | −207.942 | −0.0238173 | ||||||||
\(425\) | −17.2077 | −0.00196399 | ||||||||
\(426\) | 14062.3 | 1.59934 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3319.88 | 0.374936 | ||||||||
\(429\) | −12653.1 | −1.42400 | ||||||||
\(430\) | 3318.16 | 0.372130 | ||||||||
\(431\) | −4319.27 | −0.482719 | −0.241360 | − | 0.970436i | \(-0.577593\pi\) | ||||
−0.241360 | + | 0.970436i | \(0.577593\pi\) | |||||||
\(432\) | −17108.4 | −1.90539 | ||||||||
\(433\) | −4600.60 | −0.510602 | −0.255301 | − | 0.966862i | \(-0.582175\pi\) | ||||
−0.255301 | + | 0.966862i | \(0.582175\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4670.82 | 0.514825 | ||||||||
\(436\) | 11073.7 | 1.21636 | ||||||||
\(437\) | −7871.58 | −0.861667 | ||||||||
\(438\) | 12019.9 | 1.31126 | ||||||||
\(439\) | −1923.74 | −0.209146 | −0.104573 | − | 0.994517i | \(-0.533348\pi\) | ||||
−0.104573 | + | 0.994517i | \(0.533348\pi\) | |||||||
\(440\) | −536.274 | −0.0581042 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 161.616 | 0.0173921 | ||||||||
\(443\) | −4534.87 | −0.486362 | −0.243181 | − | 0.969981i | \(-0.578191\pi\) | ||||
−0.243181 | + | 0.969981i | \(0.578191\pi\) | |||||||
\(444\) | −16075.9 | −1.71831 | ||||||||
\(445\) | 4280.48 | 0.455987 | ||||||||
\(446\) | 6635.35 | 0.704468 | ||||||||
\(447\) | 19011.6 | 2.01167 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17431.9 | −1.83221 | −0.916105 | − | 0.400937i | \(-0.868684\pi\) | ||||
−0.916105 | + | 0.400937i | \(0.868684\pi\) | |||||||
\(450\) | 5137.03 | 0.538137 | ||||||||
\(451\) | 5624.66 | 0.587262 | ||||||||
\(452\) | 2350.02 | 0.244548 | ||||||||
\(453\) | −21526.6 | −2.23269 | ||||||||
\(454\) | 13911.7 | 1.43813 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2631.24 | 0.270217 | ||||||||
\(457\) | −1962.32 | −0.200861 | −0.100431 | − | 0.994944i | \(-0.532022\pi\) | ||||
−0.100431 | + | 0.994944i | \(0.532022\pi\) | |||||||
\(458\) | −5622.36 | −0.573614 | ||||||||
\(459\) | −163.108 | −0.0165866 | ||||||||
\(460\) | 4228.98 | 0.428646 | ||||||||
\(461\) | −14344.4 | −1.44920 | −0.724602 | − | 0.689167i | \(-0.757976\pi\) | ||||
−0.724602 | + | 0.689167i | \(0.757976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11657.8 | 1.17016 | 0.585081 | − | 0.810975i | \(-0.301063\pi\) | ||||
0.585081 | + | 0.810975i | \(0.301063\pi\) | |||||||
\(464\) | −7520.51 | −0.752437 | ||||||||
\(465\) | −12556.1 | −1.25221 | ||||||||
\(466\) | 8212.91 | 0.816429 | ||||||||
\(467\) | 16513.8 | 1.63633 | 0.818164 | − | 0.574985i | \(-0.194992\pi\) | ||||
0.818164 | + | 0.574985i | \(0.194992\pi\) | |||||||
\(468\) | −22156.1 | −2.18839 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2065.07 | 0.202669 | ||||||||
\(471\) | 4539.47 | 0.444093 | ||||||||
\(472\) | 2121.92 | 0.206927 | ||||||||
\(473\) | 3987.76 | 0.387648 | ||||||||
\(474\) | 28978.6 | 2.80808 | ||||||||
\(475\) | −1580.62 | −0.152681 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2393.86 | 0.229785 | ||||||||
\(478\) | 22894.1 | 2.19069 | ||||||||
\(479\) | 15620.1 | 1.48998 | 0.744988 | − | 0.667077i | \(-0.232455\pi\) | ||||
0.744988 | + | 0.667077i | \(0.232455\pi\) | |||||||
\(480\) | −10786.6 | −1.02571 | ||||||||
\(481\) | 16108.6 | 1.52701 | ||||||||
\(482\) | 14798.6 | 1.39846 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5413.28 | −0.508384 | ||||||||
\(485\) | −947.180 | −0.0886788 | ||||||||
\(486\) | −1061.25 | −0.0990521 | ||||||||
\(487\) | 1901.38 | 0.176920 | 0.0884598 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884598 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(488\) | 2198.76 | 0.203961 | ||||||||
\(489\) | 23325.1 | 2.15705 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15964.1 | −1.46731 | −0.733654 | − | 0.679524i | \(-0.762186\pi\) | ||||
−0.733654 | + | 0.679524i | \(0.762186\pi\) | |||||||
\(492\) | 14826.7 | 1.35861 | ||||||||
\(493\) | −71.6991 | −0.00655003 | ||||||||
\(494\) | 14845.3 | 1.35207 | ||||||||
\(495\) | 6173.68 | 0.560578 | ||||||||
\(496\) | 20216.7 | 1.83015 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 30548.6 | 2.74882 | ||||||||
\(499\) | −6849.18 | −0.614451 | −0.307226 | − | 0.951637i | \(-0.599401\pi\) | ||||
−0.307226 | + | 0.951637i | \(0.599401\pi\) | |||||||
\(500\) | 849.181 | 0.0759531 | ||||||||
\(501\) | −4897.19 | −0.436707 | ||||||||
\(502\) | 6660.45 | 0.592173 | ||||||||
\(503\) | 766.190 | 0.0679179 | 0.0339590 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339590 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3979.02 | −0.350621 | ||||||||
\(506\) | 11067.4 | 0.972345 | ||||||||
\(507\) | 13719.0 | 1.20174 | ||||||||
\(508\) | −11312.7 | −0.988035 | ||||||||
\(509\) | −13604.7 | −1.18471 | −0.592356 | − | 0.805676i | \(-0.701802\pi\) | ||||
−0.592356 | + | 0.805676i | \(0.701802\pi\) | |||||||
\(510\) | −118.708 | −0.0103068 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14687.2 | 1.26776 | ||||||||
\(513\) | −14982.4 | −1.28945 | ||||||||
\(514\) | 15594.2 | 1.33820 | ||||||||
\(515\) | −9703.53 | −0.830269 | ||||||||
\(516\) | 10511.8 | 0.896812 | ||||||||
\(517\) | 2481.80 | 0.211120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27086.1 | 2.29084 | ||||||||
\(520\) | 1416.50 | 0.119457 | ||||||||
\(521\) | −18428.3 | −1.54963 | −0.774817 | − | 0.632185i | \(-0.782158\pi\) | ||||
−0.774817 | + | 0.632185i | \(0.782158\pi\) | |||||||
\(522\) | 21404.4 | 1.79472 | ||||||||
\(523\) | −4340.13 | −0.362869 | −0.181435 | − | 0.983403i | \(-0.558074\pi\) | ||||
−0.181435 | + | 0.983403i | \(0.558074\pi\) | |||||||
\(524\) | −4597.45 | −0.383283 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24369.0 | −2.02003 | ||||||||
\(527\) | 192.742 | 0.0159316 | ||||||||
\(528\) | −14964.0 | −1.23338 | ||||||||
\(529\) | 3333.65 | 0.273991 | ||||||||
\(530\) | 861.720 | 0.0706240 | ||||||||
\(531\) | −24427.9 | −1.99639 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14856.8 | −1.20736 | ||||||||
\(534\) | 29529.1 | 2.39298 | ||||||||
\(535\) | 2443.44 | 0.197456 | ||||||||
\(536\) | 1064.82 | 0.0858081 | ||||||||
\(537\) | 17928.4 | 1.44072 | ||||||||
\(538\) | 5083.30 | 0.407354 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8049.21 | 0.641450 | ||||||||
\(541\) | 12616.2 | 1.00262 | 0.501308 | − | 0.865269i | \(-0.332852\pi\) | ||||
0.501308 | + | 0.865269i | \(0.332852\pi\) | |||||||
\(542\) | 8984.79 | 0.712047 | ||||||||
\(543\) | 6108.47 | 0.482762 | ||||||||
\(544\) | 165.579 | 0.0130499 | ||||||||
\(545\) | 8150.27 | 0.640586 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20677.8 | 1.61630 | 0.808151 | − | 0.588975i | \(-0.200468\pi\) | ||||
0.808151 | + | 0.588975i | \(0.200468\pi\) | |||||||
\(548\) | −7026.01 | −0.547694 | ||||||||
\(549\) | −25312.4 | −1.96777 | ||||||||
\(550\) | 2222.34 | 0.172293 | ||||||||
\(551\) | −6585.93 | −0.509201 | ||||||||
\(552\) | −5181.41 | −0.399521 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27251.4 | −2.08989 | ||||||||
\(555\) | −11831.9 | −0.904932 | ||||||||
\(556\) | −2960.76 | −0.225835 | ||||||||
\(557\) | −1015.17 | −0.0772248 | −0.0386124 | − | 0.999254i | \(-0.512294\pi\) | ||||
−0.0386124 | + | 0.999254i | \(0.512294\pi\) | |||||||
\(558\) | −57539.3 | −4.36529 | ||||||||
\(559\) | −10533.2 | −0.796969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −142.664 | −0.0107366 | ||||||||
\(562\) | 8166.17 | 0.612935 | ||||||||
\(563\) | −5296.64 | −0.396495 | −0.198248 | − | 0.980152i | \(-0.563525\pi\) | ||||
−0.198248 | + | 0.980152i | \(0.563525\pi\) | |||||||
\(564\) | 6542.04 | 0.488421 | ||||||||
\(565\) | 1729.62 | 0.128789 | ||||||||
\(566\) | −22660.5 | −1.68285 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1891.94 | −0.139761 | ||||||||
\(569\) | 14741.2 | 1.08609 | 0.543044 | − | 0.839704i | \(-0.317272\pi\) | ||||
0.543044 | + | 0.839704i | \(0.317272\pi\) | |||||||
\(570\) | −10904.0 | −0.801258 | ||||||||
\(571\) | 13661.4 | 1.00125 | 0.500624 | − | 0.865665i | \(-0.333104\pi\) | ||||
0.500624 | + | 0.865665i | \(0.333104\pi\) | |||||||
\(572\) | −9585.04 | −0.700648 | ||||||||
\(573\) | −14463.2 | −1.05446 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3112.54 | 0.225742 | ||||||||
\(576\) | −18574.1 | −1.34361 | ||||||||
\(577\) | −1078.61 | −0.0778220 | −0.0389110 | − | 0.999243i | \(-0.512389\pi\) | ||||
−0.0389110 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(578\) | −18894.7 | −1.35971 | ||||||||
\(579\) | 7254.37 | 0.520693 | ||||||||
\(580\) | 3538.27 | 0.253308 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6534.17 | −0.465378 | ||||||||
\(583\) | 1035.61 | 0.0735690 | ||||||||
\(584\) | −1617.16 | −0.114586 | ||||||||
\(585\) | −16307.0 | −1.15250 | ||||||||
\(586\) | 31299.6 | 2.20644 | ||||||||
\(587\) | −3863.36 | −0.271649 | −0.135824 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135824 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17704.3 | 1.23853 | ||||||||
\(590\) | −8793.35 | −0.613587 | ||||||||
\(591\) | 33219.3 | 2.31212 | ||||||||
\(592\) | 19050.6 | 1.32259 | ||||||||
\(593\) | 9440.81 | 0.653774 | 0.326887 | − | 0.945063i | \(-0.394000\pi\) | ||||
0.326887 | + | 0.945063i | \(0.394000\pi\) | |||||||
\(594\) | 21065.1 | 1.45507 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14401.8 | 0.989797 | ||||||||
\(597\) | 3299.56 | 0.226201 | ||||||||
\(598\) | −29233.2 | −1.99905 | ||||||||
\(599\) | −21368.9 | −1.45761 | −0.728807 | − | 0.684719i | \(-0.759925\pi\) | ||||
−0.728807 | + | 0.684719i | \(0.759925\pi\) | |||||||
\(600\) | −1040.43 | −0.0707924 | ||||||||
\(601\) | −5801.37 | −0.393748 | −0.196874 | − | 0.980429i | \(-0.563079\pi\) | ||||
−0.196874 | + | 0.980429i | \(0.563079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12258.4 | −0.827859 | ||||||||
\(604\) | −16307.0 | −1.09855 | ||||||||
\(605\) | −3984.19 | −0.267736 | ||||||||
\(606\) | −27449.4 | −1.84003 | ||||||||
\(607\) | −26740.0 | −1.78805 | −0.894023 | − | 0.448021i | \(-0.852129\pi\) | ||||
−0.894023 | + | 0.448021i | \(0.852129\pi\) | |||||||
\(608\) | 15209.3 | 1.01450 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9111.74 | −0.604793 | ||||||||
\(611\) | −6555.36 | −0.434045 | ||||||||
\(612\) | −249.811 | −0.0165000 | ||||||||
\(613\) | −8339.75 | −0.549493 | −0.274746 | − | 0.961517i | \(-0.588594\pi\) | ||||
−0.274746 | + | 0.961517i | \(0.588594\pi\) | |||||||
\(614\) | 18451.3 | 1.21276 | ||||||||
\(615\) | 10912.5 | 0.715501 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26639.2 | −1.73818 | −0.869088 | − | 0.494658i | \(-0.835293\pi\) | ||||
−0.869088 | + | 0.494658i | \(0.835293\pi\) | |||||||
\(618\) | −66940.3 | −4.35717 | ||||||||
\(619\) | −27860.3 | −1.80905 | −0.904523 | − | 0.426424i | \(-0.859773\pi\) | ||||
−0.904523 | + | 0.426424i | \(0.859773\pi\) | |||||||
\(620\) | −9511.58 | −0.616120 | ||||||||
\(621\) | 29503.1 | 1.90647 | ||||||||
\(622\) | −19960.1 | −1.28670 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 39525.5 | 2.53571 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 8635.71 | 0.551361 | ||||||||
\(627\) | −13104.4 | −0.834671 | ||||||||
\(628\) | 3438.76 | 0.218506 | ||||||||
\(629\) | 181.625 | 0.0115133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10886.7 | −0.686833 | −0.343417 | − | 0.939183i | \(-0.611584\pi\) | ||||
−0.343417 | + | 0.939183i | \(0.611584\pi\) | |||||||
\(632\) | −3898.79 | −0.245388 | ||||||||
\(633\) | −9625.85 | −0.604413 | ||||||||
\(634\) | −37470.9 | −2.34726 | ||||||||
\(635\) | −8326.21 | −0.520340 | ||||||||
\(636\) | 2729.89 | 0.170200 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9259.80 | 0.574607 | ||||||||
\(639\) | 21780.4 | 1.34839 | ||||||||
\(640\) | 2936.25 | 0.181352 | ||||||||
\(641\) | −16851.5 | −1.03837 | −0.519183 | − | 0.854663i | \(-0.673764\pi\) | ||||
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(642\) | 16856.2 | 1.03623 | ||||||||
\(643\) | −4793.72 | −0.294006 | −0.147003 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147003 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7736.69 | 0.472298 | ||||||||
\(646\) | 167.380 | 0.0101943 | ||||||||
\(647\) | 26684.5 | 1.62145 | 0.810725 | − | 0.585428i | \(-0.199073\pi\) | ||||
0.810725 | + | 0.585428i | \(0.199073\pi\) | |||||||
\(648\) | −3168.10 | −0.192060 | ||||||||
\(649\) | −10567.8 | −0.639174 | ||||||||
\(650\) | −5870.05 | −0.354219 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17669.4 | 1.06133 | ||||||||
\(653\) | 17541.9 | 1.05125 | 0.525625 | − | 0.850716i | \(-0.323831\pi\) | ||||
0.525625 | + | 0.850716i | \(0.323831\pi\) | |||||||
\(654\) | 56225.0 | 3.36173 | ||||||||
\(655\) | −3383.74 | −0.201853 | ||||||||
\(656\) | −17570.2 | −1.04573 | ||||||||
\(657\) | 18617.0 | 1.10551 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26285.3 | −1.55377 | −0.776883 | − | 0.629645i | \(-0.783200\pi\) | ||||
−0.776883 | + | 0.629645i | \(0.783200\pi\) | |||||||
\(660\) | 7040.28 | 0.415216 | ||||||||
\(661\) | −25044.3 | −1.47369 | −0.736845 | − | 0.676062i | \(-0.763685\pi\) | ||||
−0.736845 | + | 0.676062i | \(0.763685\pi\) | |||||||
\(662\) | 43580.7 | 2.55863 | ||||||||
\(663\) | 376.828 | 0.0220736 | ||||||||
\(664\) | −4110.02 | −0.240210 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −54220.6 | −3.15466 | ||||||||
\(667\) | 12969.0 | 0.752864 | ||||||||
\(668\) | −3709.75 | −0.214872 | ||||||||
\(669\) | 15471.1 | 0.894094 | ||||||||
\(670\) | −4412.66 | −0.254441 | ||||||||
\(671\) | −10950.5 | −0.630013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20799.4 | 1.19132 | 0.595658 | − | 0.803238i | \(-0.296891\pi\) | ||||
0.595658 | + | 0.803238i | \(0.296891\pi\) | |||||||
\(674\) | 13990.1 | 0.799521 | ||||||||
\(675\) | 5924.25 | 0.337814 | ||||||||
\(676\) | 10392.5 | 0.591288 | ||||||||
\(677\) | −29772.5 | −1.69018 | −0.845089 | − | 0.534625i | \(-0.820453\pi\) | ||||
−0.845089 | + | 0.534625i | \(0.820453\pi\) | |||||||
\(678\) | 11931.9 | 0.675873 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.9711 | 0.000900679 0 | ||||||||
\(681\) | 32437.0 | 1.82524 | ||||||||
\(682\) | −24892.2 | −1.39761 | ||||||||
\(683\) | 23890.3 | 1.33842 | 0.669208 | − | 0.743075i | \(-0.266633\pi\) | ||||
0.669208 | + | 0.743075i | \(0.266633\pi\) | |||||||
\(684\) | −22946.4 | −1.28271 | ||||||||
\(685\) | −5171.17 | −0.288438 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13109.2 | −0.728017 | ||||||||
\(688\) | −12456.9 | −0.690282 | ||||||||
\(689\) | −2735.45 | −0.151251 | ||||||||
\(690\) | 21472.0 | 1.18467 | ||||||||
\(691\) | 25297.6 | 1.39271 | 0.696356 | − | 0.717696i | \(-0.254803\pi\) | ||||
0.696356 | + | 0.717696i | \(0.254803\pi\) | |||||||
\(692\) | 20518.4 | 1.12716 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15500.8 | −0.847839 | ||||||||
\(695\) | −2179.13 | −0.118934 | ||||||||
\(696\) | −4335.14 | −0.236097 | ||||||||
\(697\) | −167.511 | −0.00910320 | ||||||||
\(698\) | −11106.7 | −0.602284 | ||||||||
\(699\) | 19149.4 | 1.03619 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18659.1 | 1.00534 | 0.502670 | − | 0.864478i | \(-0.332351\pi\) | ||||
0.502670 | + | 0.864478i | \(0.332351\pi\) | |||||||
\(702\) | −55641.0 | −2.99150 | ||||||||
\(703\) | 16683.2 | 0.895047 | ||||||||
\(704\) | −8035.38 | −0.430177 | ||||||||
\(705\) | 4814.96 | 0.257222 | ||||||||
\(706\) | 2018.95 | 0.107627 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −27856.9 | −1.47871 | ||||||||
\(709\) | −25694.8 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738249\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738249\pi\) | |||||||
\(710\) | 7840.30 | 0.414424 | ||||||||
\(711\) | 44883.5 | 2.36746 | ||||||||
\(712\) | −3972.85 | −0.209114 | ||||||||
\(713\) | −34863.2 | −1.83119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7054.62 | −0.368990 | ||||||||
\(716\) | 13581.2 | 0.708875 | ||||||||
\(717\) | 53380.4 | 2.78037 | ||||||||
\(718\) | −12636.1 | −0.656788 | ||||||||
\(719\) | 27254.7 | 1.41367 | 0.706834 | − | 0.707379i | \(-0.250123\pi\) | ||||
0.706834 | + | 0.707379i | \(0.250123\pi\) | |||||||
\(720\) | −19285.2 | −0.998218 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11006.5 | −0.567340 | ||||||||
\(723\) | 34504.7 | 1.77489 | ||||||||
\(724\) | 4627.32 | 0.237532 | ||||||||
\(725\) | 2604.18 | 0.133402 | ||||||||
\(726\) | −27485.1 | −1.40505 | ||||||||
\(727\) | 13194.3 | 0.673110 | 0.336555 | − | 0.941664i | \(-0.390738\pi\) | ||||
0.336555 | + | 0.941664i | \(0.390738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20906.9 | −1.06218 | ||||||||
\(730\) | 6701.57 | 0.339776 | ||||||||
\(731\) | −118.761 | −0.00600896 | ||||||||
\(732\) | −28865.6 | −1.45752 | ||||||||
\(733\) | −5808.95 | −0.292713 | −0.146356 | − | 0.989232i | \(-0.546755\pi\) | ||||
−0.146356 | + | 0.989232i | \(0.546755\pi\) | |||||||
\(734\) | −34823.5 | −1.75117 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29950.0 | −1.49996 | ||||||||
\(737\) | −5303.13 | −0.265052 | ||||||||
\(738\) | 50007.1 | 2.49429 | ||||||||
\(739\) | 13936.7 | 0.693734 | 0.346867 | − | 0.937914i | \(-0.387246\pi\) | ||||
0.346867 | + | 0.937914i | \(0.387246\pi\) | |||||||
\(740\) | −8962.98 | −0.445251 | ||||||||
\(741\) | 34613.6 | 1.71601 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32424.2 | 1.60098 | 0.800489 | − | 0.599347i | \(-0.204573\pi\) | ||||
0.800489 | + | 0.599347i | \(0.204573\pi\) | |||||||
\(744\) | 11653.7 | 0.574257 | ||||||||
\(745\) | 10599.7 | 0.521268 | ||||||||
\(746\) | −20035.4 | −0.983308 | ||||||||
\(747\) | 47315.2 | 2.31750 | ||||||||
\(748\) | −108.071 | −0.00528272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4311.59 | 0.209916 | ||||||||
\(751\) | −35288.3 | −1.71463 | −0.857316 | − | 0.514791i | \(-0.827870\pi\) | ||||
−0.857316 | + | 0.514791i | \(0.827870\pi\) | |||||||
\(752\) | −7752.58 | −0.375941 | ||||||||
\(753\) | 15529.7 | 0.751571 | ||||||||
\(754\) | −24458.6 | −1.18134 | ||||||||
\(755\) | −12002.0 | −0.578539 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2079.86 | 0.0998595 | 0.0499298 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499298 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(758\) | 12310.5 | 0.589893 | ||||||||
\(759\) | 25805.0 | 1.23408 | ||||||||
\(760\) | 1467.02 | 0.0700191 | ||||||||
\(761\) | −12251.4 | −0.583593 | −0.291797 | − | 0.956480i | \(-0.594253\pi\) | ||||
−0.291797 | + | 0.956480i | \(0.594253\pi\) | |||||||
\(762\) | −57438.8 | −2.73069 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10956.2 | −0.518824 | ||||||||
\(765\) | −183.861 | −0.00868957 | ||||||||
\(766\) | 8472.50 | 0.399639 | ||||||||
\(767\) | 27913.6 | 1.31408 | ||||||||
\(768\) | 45199.1 | 2.12367 | ||||||||
\(769\) | −4335.87 | −0.203323 | −0.101661 | − | 0.994819i | \(-0.532416\pi\) | ||||
−0.101661 | + | 0.994819i | \(0.532416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36359.9 | 1.69840 | ||||||||
\(772\) | 5495.37 | 0.256195 | ||||||||
\(773\) | −30399.5 | −1.41448 | −0.707240 | − | 0.706973i | \(-0.750060\pi\) | ||||
−0.707240 | + | 0.706973i | \(0.750060\pi\) | |||||||
\(774\) | 35453.9 | 1.64647 | ||||||||
\(775\) | −7000.55 | −0.324474 | ||||||||
\(776\) | 879.109 | 0.0406677 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24006.6 | −1.10627 | ||||||||
\(779\) | −15386.7 | −0.707686 | ||||||||
\(780\) | −18596.0 | −0.853647 | ||||||||
\(781\) | 9422.47 | 0.431706 | ||||||||
\(782\) | −329.604 | −0.0150724 | ||||||||
\(783\) | 24684.4 | 1.12663 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2530.94 | 0.115074 | ||||||||
\(786\) | −23342.9 | −1.05930 | ||||||||
\(787\) | −35274.2 | −1.59770 | −0.798850 | − | 0.601530i | \(-0.794558\pi\) | ||||
−0.798850 | + | 0.601530i | \(0.794558\pi\) | |||||||
\(788\) | 25164.5 | 1.13762 | ||||||||
\(789\) | −56819.3 | −2.56378 | ||||||||
\(790\) | 16156.8 | 0.727635 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5729.99 | −0.257079 | ||||||||
\(793\) | 28924.3 | 1.29525 | ||||||||
\(794\) | −40028.3 | −1.78911 | ||||||||
\(795\) | 2009.21 | 0.0896342 | ||||||||
\(796\) | 2499.50 | 0.111297 | ||||||||
\(797\) | 27524.0 | 1.22328 | 0.611638 | − | 0.791138i | \(-0.290511\pi\) | ||||
0.611638 | + | 0.791138i | \(0.290511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −73.9116 | −0.00327260 | ||||||||
\(800\) | −6013.98 | −0.265783 | ||||||||
\(801\) | 45736.1 | 2.01749 | ||||||||
\(802\) | −57590.5 | −2.53565 | ||||||||
\(803\) | 8053.95 | 0.353945 | ||||||||
\(804\) | −13979.1 | −0.613189 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 65749.7 | 2.87337 | ||||||||
\(807\) | 11852.3 | 0.517004 | ||||||||
\(808\) | 3693.06 | 0.160794 | ||||||||
\(809\) | −7067.35 | −0.307138 | −0.153569 | − | 0.988138i | \(-0.549077\pi\) | ||||
−0.153569 | + | 0.988138i | \(0.549077\pi\) | |||||||
\(810\) | 13128.8 | 0.569503 | ||||||||
\(811\) | 37757.5 | 1.63483 | 0.817413 | − | 0.576052i | \(-0.195407\pi\) | ||||
0.817413 | + | 0.576052i | \(0.195407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20949.1 | 0.903713 | ||||||||
\(814\) | −23456.5 | −1.01001 | ||||||||
\(815\) | 13004.7 | 0.558940 | ||||||||
\(816\) | 445.649 | 0.0191187 | ||||||||
\(817\) | −10908.9 | −0.467139 | ||||||||
\(818\) | 27150.9 | 1.16052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8266.47 | 0.352046 | ||||||||
\(821\) | −25307.4 | −1.07580 | −0.537902 | − | 0.843008i | \(-0.680783\pi\) | ||||
−0.537902 | + | 0.843008i | \(0.680783\pi\) | |||||||
\(822\) | −35673.6 | −1.51370 | ||||||||
\(823\) | −25484.8 | −1.07940 | −0.539699 | − | 0.841858i | \(-0.681462\pi\) | ||||
−0.539699 | + | 0.841858i | \(0.681462\pi\) | |||||||
\(824\) | 9006.17 | 0.380758 | ||||||||
\(825\) | 5181.67 | 0.218670 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34985.7 | 1.47107 | 0.735534 | − | 0.677488i | \(-0.236931\pi\) | ||||
0.735534 | + | 0.677488i | \(0.236931\pi\) | |||||||
\(828\) | 45185.8 | 1.89652 | ||||||||
\(829\) | −3898.09 | −0.163313 | −0.0816564 | − | 0.996661i | \(-0.526021\pi\) | ||||
−0.0816564 | + | 0.996661i | \(0.526021\pi\) | |||||||
\(830\) | 17032.1 | 0.712280 | ||||||||
\(831\) | −63540.0 | −2.65244 | ||||||||
\(832\) | 21224.4 | 0.884405 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15032.8 | −0.624154 | ||||||||
\(835\) | −2730.38 | −0.113160 | ||||||||
\(836\) | −9926.90 | −0.410681 | ||||||||
\(837\) | −66356.8 | −2.74030 | ||||||||
\(838\) | −3571.38 | −0.147221 | ||||||||
\(839\) | −22118.8 | −0.910161 | −0.455081 | − | 0.890450i | \(-0.650390\pi\) | ||||
−0.455081 | + | 0.890450i | \(0.650390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13538.2 | −0.555096 | ||||||||
\(842\) | 27327.7 | 1.11850 | ||||||||
\(843\) | 19040.4 | 0.777921 | ||||||||
\(844\) | −7291.83 | −0.297387 | ||||||||
\(845\) | 7648.89 | 0.311396 | ||||||||
\(846\) | 22064.9 | 0.896697 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3235.03 | −0.131004 | ||||||||
\(849\) | −52835.8 | −2.13583 | ||||||||
\(850\) | −66.1848 | −0.00267073 | ||||||||
\(851\) | −32852.4 | −1.32334 | ||||||||
\(852\) | 24837.7 | 0.998739 | ||||||||
\(853\) | −33152.4 | −1.33074 | −0.665368 | − | 0.746516i | \(-0.731725\pi\) | ||||
−0.665368 | + | 0.746516i | \(0.731725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16888.6 | −0.675530 | ||||||||
\(856\) | −2267.84 | −0.0905527 | ||||||||
\(857\) | 10346.2 | 0.412393 | 0.206197 | − | 0.978511i | \(-0.433891\pi\) | ||||
0.206197 | + | 0.978511i | \(0.433891\pi\) | |||||||
\(858\) | −48666.6 | −1.93642 | ||||||||
\(859\) | 11905.6 | 0.472893 | 0.236447 | − | 0.971644i | \(-0.424017\pi\) | ||||
0.236447 | + | 0.971644i | \(0.424017\pi\) | |||||||
\(860\) | 5860.74 | 0.232383 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16612.9 | −0.656424 | ||||||||
\(863\) | 30802.3 | 1.21497 | 0.607487 | − | 0.794329i | \(-0.292177\pi\) | ||||
0.607487 | + | 0.794329i | \(0.292177\pi\) | |||||||
\(864\) | −57005.3 | −2.24463 | ||||||||
\(865\) | 15101.6 | 0.593607 | ||||||||
\(866\) | −17694.9 | −0.694340 | ||||||||
\(867\) | −44055.3 | −1.72572 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19417.2 | 0.757977 | ||||||||
\(870\) | 17965.0 | 0.700082 | ||||||||
\(871\) | 14007.5 | 0.544923 | ||||||||
\(872\) | −7564.53 | −0.293770 | ||||||||
\(873\) | −10120.4 | −0.392354 | ||||||||
\(874\) | −30275.9 | −1.17173 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21230.3 | 0.818841 | ||||||||
\(877\) | −21693.3 | −0.835268 | −0.417634 | − | 0.908615i | \(-0.637141\pi\) | ||||
−0.417634 | + | 0.908615i | \(0.637141\pi\) | |||||||
\(878\) | −7399.13 | −0.284406 | ||||||||
\(879\) | 72978.9 | 2.80036 | ||||||||
\(880\) | −8343.03 | −0.319595 | ||||||||
\(881\) | 29963.1 | 1.14584 | 0.572918 | − | 0.819612i | \(-0.305811\pi\) | ||||
0.572918 | + | 0.819612i | \(0.305811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4090.61 | −0.155900 | −0.0779501 | − | 0.996957i | \(-0.524837\pi\) | ||||
−0.0779501 | + | 0.996957i | \(0.524837\pi\) | |||||||
\(884\) | 285.457 | 0.0108608 | ||||||||
\(885\) | −20502.8 | −0.778749 | ||||||||
\(886\) | −17442.1 | −0.661377 | ||||||||
\(887\) | 28819.4 | 1.09094 | 0.545468 | − | 0.838132i | \(-0.316352\pi\) | ||||
0.545468 | + | 0.838132i | \(0.316352\pi\) | |||||||
\(888\) | 10981.6 | 0.414998 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16463.7 | 0.620072 | ||||||||
\(891\) | 15778.1 | 0.593252 | ||||||||
\(892\) | 11719.8 | 0.439918 | ||||||||
\(893\) | −6789.16 | −0.254413 | ||||||||
\(894\) | 73122.8 | 2.73556 | ||||||||
\(895\) | 9995.83 | 0.373323 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −68160.8 | −2.53715 | ||||||||
\(898\) | −67047.1 | −2.49152 | ||||||||
\(899\) | −29169.1 | −1.08214 | ||||||||
\(900\) | 9073.35 | 0.336050 | ||||||||
\(901\) | −30.8421 | −0.00114040 | ||||||||
\(902\) | 21633.7 | 0.798585 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1605.32 | −0.0590621 | ||||||||
\(905\) | 3405.72 | 0.125094 | ||||||||
\(906\) | −82796.3 | −3.03612 | ||||||||
\(907\) | −20638.8 | −0.755567 | −0.377784 | − | 0.925894i | \(-0.623314\pi\) | ||||
−0.377784 | + | 0.925894i | \(0.623314\pi\) | |||||||
\(908\) | 24571.8 | 0.898067 | ||||||||
\(909\) | −42515.1 | −1.55130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15080.1 | −0.548435 | −0.274218 | − | 0.961668i | \(-0.588419\pi\) | ||||
−0.274218 | + | 0.961668i | \(0.588419\pi\) | |||||||
\(912\) | 40935.2 | 1.48629 | ||||||||
\(913\) | 20469.1 | 0.741982 | ||||||||
\(914\) | −7547.54 | −0.273141 | ||||||||
\(915\) | −21245.1 | −0.767588 | ||||||||
\(916\) | −9930.56 | −0.358204 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −627.352 | −0.0225552 | ||||||||
\(919\) | −2164.29 | −0.0776858 | −0.0388429 | − | 0.999245i | \(-0.512367\pi\) | ||||
−0.0388429 | + | 0.999245i | \(0.512367\pi\) | |||||||
\(920\) | −2888.85 | −0.103525 | ||||||||
\(921\) | 43021.4 | 1.53920 | ||||||||
\(922\) | −55171.6 | −1.97069 | ||||||||
\(923\) | −24888.3 | −0.887549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6596.78 | −0.234487 | ||||||||
\(926\) | 44838.6 | 1.59124 | ||||||||
\(927\) | −103680. | −3.67348 | ||||||||
\(928\) | −25058.3 | −0.886401 | ||||||||
\(929\) | −13639.1 | −0.481684 | −0.240842 | − | 0.970564i | \(-0.577424\pi\) | ||||
−0.240842 | + | 0.970564i | \(0.577424\pi\) | |||||||
\(930\) | −48293.7 | −1.70281 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14506.2 | 0.509834 | ||||||||
\(933\) | −46539.4 | −1.63305 | ||||||||
\(934\) | 63515.6 | 2.22515 | ||||||||
\(935\) | −79.5408 | −0.00278210 | ||||||||
\(936\) | 15135.1 | 0.528531 | ||||||||
\(937\) | −6568.49 | −0.229011 | −0.114505 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114505 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20135.2 | 0.699774 | ||||||||
\(940\) | 3647.45 | 0.126560 | ||||||||
\(941\) | −9454.51 | −0.327533 | −0.163766 | − | 0.986499i | \(-0.552364\pi\) | ||||
−0.163766 | + | 0.986499i | \(0.552364\pi\) | |||||||
\(942\) | 17459.8 | 0.603898 | ||||||||
\(943\) | 30299.4 | 1.04633 | ||||||||
\(944\) | 33011.6 | 1.13817 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15337.8 | 0.527141 | ||||||||
\(947\) | 34076.7 | 1.16932 | 0.584660 | − | 0.811279i | \(-0.301228\pi\) | ||||
0.584660 | + | 0.811279i | \(0.301228\pi\) | |||||||
\(948\) | 51183.8 | 1.75356 | ||||||||
\(949\) | −21273.5 | −0.727679 | ||||||||
\(950\) | −6079.41 | −0.207623 | ||||||||
\(951\) | −87368.1 | −2.97908 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32862.3 | −1.11702 | −0.558508 | − | 0.829499i | \(-0.688626\pi\) | ||||
−0.558508 | + | 0.829499i | \(0.688626\pi\) | |||||||
\(954\) | 9207.32 | 0.312472 | ||||||||
\(955\) | −8063.81 | −0.273234 | ||||||||
\(956\) | 40437.0 | 1.36802 | ||||||||
\(957\) | 21590.4 | 0.729276 | ||||||||
\(958\) | 60078.3 | 2.02614 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15589.5 | −0.524114 | ||||||||
\(961\) | 48621.4 | 1.63208 | ||||||||
\(962\) | 61957.5 | 2.07650 | ||||||||
\(963\) | 26107.7 | 0.873634 | ||||||||
\(964\) | 26138.2 | 0.873292 | ||||||||
\(965\) | 4044.61 | 0.134923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57597.8 | 1.91543 | 0.957715 | − | 0.287720i | \(-0.0928972\pi\) | ||||
0.957715 | + | 0.287720i | \(0.0928972\pi\) | |||||||
\(968\) | 3697.86 | 0.122783 | ||||||||
\(969\) | 390.268 | 0.0129383 | ||||||||
\(970\) | −3643.07 | −0.120590 | ||||||||
\(971\) | 28185.7 | 0.931536 | 0.465768 | − | 0.884907i | \(-0.345778\pi\) | ||||
0.465768 | + | 0.884907i | \(0.345778\pi\) | |||||||
\(972\) | −1874.45 | −0.0618549 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7313.15 | 0.240583 | ||||||||
\(975\) | −13686.7 | −0.449565 | ||||||||
\(976\) | 34206.9 | 1.12186 | ||||||||
\(977\) | 44263.6 | 1.44945 | 0.724727 | − | 0.689036i | \(-0.241966\pi\) | ||||
0.724727 | + | 0.689036i | \(0.241966\pi\) | |||||||
\(978\) | 89713.8 | 2.93326 | ||||||||
\(979\) | 19786.0 | 0.645929 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 87084.1 | 2.83423 | ||||||||
\(982\) | −61401.4 | −1.99531 | ||||||||
\(983\) | −147.400 | −0.00478262 | −0.00239131 | − | 0.999997i | \(-0.500761\pi\) | ||||
−0.00239131 | + | 0.999997i | \(0.500761\pi\) | |||||||
\(984\) | −10128.2 | −0.328126 | ||||||||
\(985\) | 18521.1 | 0.599119 | ||||||||
\(986\) | −275.771 | −0.00890703 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26220.7 | 0.844323 | ||||||||
\(989\) | 21481.6 | 0.690674 | ||||||||
\(990\) | 23745.3 | 0.762300 | ||||||||
\(991\) | 12486.8 | 0.400260 | 0.200130 | − | 0.979769i | \(-0.435864\pi\) | ||||
0.200130 | + | 0.979769i | \(0.435864\pi\) | |||||||
\(992\) | 67361.9 | 2.15599 | ||||||||
\(993\) | 101614. | 3.24734 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1839.64 | 0.0586135 | ||||||||
\(996\) | 53956.9 | 1.71655 | ||||||||
\(997\) | 6621.15 | 0.210325 | 0.105162 | − | 0.994455i | \(-0.466464\pi\) | ||||
0.105162 | + | 0.994455i | \(0.466464\pi\) | |||||||
\(998\) | −26343.5 | −0.835559 | ||||||||
\(999\) | −62529.6 | −1.98033 |
(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 | 245.4.a.n.1.4 | 5 | ||
3.2 | odd | 2 | 2205.4.a.bt.1.2 | 5 | |||
5.4 | even | 2 | 1225.4.a.bf.1.2 | 5 | |||
7.2 | even | 3 | 245.4.e.o.116.2 | 10 | |||
7.3 | odd | 6 | 35.4.e.c.16.2 | yes | 10 | ||
7.4 | even | 3 | 245.4.e.o.226.2 | 10 | |||
7.5 | odd | 6 | 35.4.e.c.11.2 | ✓ | 10 | ||
7.6 | odd | 2 | 245.4.a.m.1.4 | 5 | |||
21.5 | even | 6 | 315.4.j.g.46.4 | 10 | |||
21.17 | even | 6 | 315.4.j.g.226.4 | 10 | |||
21.20 | even | 2 | 2205.4.a.bu.1.2 | 5 | |||
28.3 | even | 6 | 560.4.q.n.401.1 | 10 | |||
28.19 | even | 6 | 560.4.q.n.81.1 | 10 | |||
35.3 | even | 12 | 175.4.k.d.149.8 | 20 | |||
35.12 | even | 12 | 175.4.k.d.74.8 | 20 | |||
35.17 | even | 12 | 175.4.k.d.149.3 | 20 | |||
35.19 | odd | 6 | 175.4.e.d.151.4 | 10 | |||
35.24 | odd | 6 | 175.4.e.d.51.4 | 10 | |||
35.33 | even | 12 | 175.4.k.d.74.3 | 20 | |||
35.34 | odd | 2 | 1225.4.a.bg.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.2 | ✓ | 10 | 7.5 | odd | 6 | ||
35.4.e.c.16.2 | yes | 10 | 7.3 | odd | 6 | ||
175.4.e.d.51.4 | 10 | 35.24 | odd | 6 | |||
175.4.e.d.151.4 | 10 | 35.19 | odd | 6 | |||
175.4.k.d.74.3 | 20 | 35.33 | even | 12 | |||
175.4.k.d.74.8 | 20 | 35.12 | even | 12 | |||
175.4.k.d.149.3 | 20 | 35.17 | even | 12 | |||
175.4.k.d.149.8 | 20 | 35.3 | even | 12 | |||
245.4.a.m.1.4 | 5 | 7.6 | odd | 2 | |||
245.4.a.n.1.4 | 5 | 1.1 | even | 1 | trivial | ||
245.4.e.o.116.2 | 10 | 7.2 | even | 3 | |||
245.4.e.o.226.2 | 10 | 7.4 | even | 3 | |||
315.4.j.g.46.4 | 10 | 21.5 | even | 6 | |||
315.4.j.g.226.4 | 10 | 21.17 | even | 6 | |||
560.4.q.n.81.1 | 10 | 28.19 | even | 6 | |||
560.4.q.n.401.1 | 10 | 28.3 | even | 6 | |||
1225.4.a.bf.1.2 | 5 | 5.4 | even | 2 | |||
1225.4.a.bg.1.2 | 5 | 35.34 | odd | 2 | |||
2205.4.a.bt.1.2 | 5 | 3.2 | odd | 2 | |||
2205.4.a.bu.1.2 | 5 | 21.20 | even | 2 |