Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.158900 | −0.0561798 | −0.0280899 | − | 0.999605i | \(-0.508942\pi\) | ||||
−0.0280899 | + | 0.999605i | \(0.508942\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.97475 | −0.996844 | ||||||||
\(5\) | 7.59417 | 0.679244 | 0.339622 | − | 0.940562i | \(-0.389701\pi\) | ||||
0.339622 | + | 0.940562i | \(0.389701\pi\) | |||||||
\(6\) | 0.476701 | 0.0324354 | ||||||||
\(7\) | −16.2139 | −0.875470 | −0.437735 | − | 0.899104i | \(-0.644219\pi\) | ||||
−0.437735 | + | 0.899104i | \(0.644219\pi\) | |||||||
\(8\) | 2.53840 | 0.112182 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −1.20672 | −0.0381598 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 23.9243 | 0.575528 | ||||||||
\(13\) | 56.3754 | 1.20275 | 0.601374 | − | 0.798967i | \(-0.294620\pi\) | ||||
0.601374 | + | 0.798967i | \(0.294620\pi\) | |||||||
\(14\) | 2.57640 | 0.0491837 | ||||||||
\(15\) | −22.7825 | −0.392161 | ||||||||
\(16\) | 63.3947 | 0.990541 | ||||||||
\(17\) | 54.6452 | 0.779613 | 0.389806 | − | 0.920897i | \(-0.372542\pi\) | ||||
0.389806 | + | 0.920897i | \(0.372542\pi\) | |||||||
\(18\) | −1.43010 | −0.0187266 | ||||||||
\(19\) | −148.362 | −1.79140 | −0.895700 | − | 0.444660i | \(-0.853325\pi\) | ||||
−0.895700 | + | 0.444660i | \(0.853325\pi\) | |||||||
\(20\) | −60.5616 | −0.677100 | ||||||||
\(21\) | 48.6418 | 0.505453 | ||||||||
\(22\) | 1.74791 | 0.0169388 | ||||||||
\(23\) | −148.655 | −1.34769 | −0.673843 | − | 0.738875i | \(-0.735358\pi\) | ||||
−0.673843 | + | 0.738875i | \(0.735358\pi\) | |||||||
\(24\) | −7.61519 | −0.0647685 | ||||||||
\(25\) | −67.3285 | −0.538628 | ||||||||
\(26\) | −8.95808 | −0.0675702 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 129.302 | 0.872707 | ||||||||
\(29\) | 125.987 | 0.806728 | 0.403364 | − | 0.915040i | \(-0.367841\pi\) | ||||
0.403364 | + | 0.915040i | \(0.367841\pi\) | |||||||
\(30\) | 3.62015 | 0.0220316 | ||||||||
\(31\) | 7.15680 | 0.0414645 | 0.0207322 | − | 0.999785i | \(-0.493400\pi\) | ||||
0.0207322 | + | 0.999785i | \(0.493400\pi\) | |||||||
\(32\) | −30.3806 | −0.167831 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −8.68315 | −0.0437985 | ||||||||
\(35\) | −123.131 | −0.594658 | ||||||||
\(36\) | −71.7728 | −0.332281 | ||||||||
\(37\) | 175.991 | 0.781968 | 0.390984 | − | 0.920398i | \(-0.372135\pi\) | ||||
0.390984 | + | 0.920398i | \(0.372135\pi\) | |||||||
\(38\) | 23.5748 | 0.100640 | ||||||||
\(39\) | −169.126 | −0.694407 | ||||||||
\(40\) | 19.2770 | 0.0761991 | ||||||||
\(41\) | 247.068 | 0.941110 | 0.470555 | − | 0.882371i | \(-0.344054\pi\) | ||||
0.470555 | + | 0.882371i | \(0.344054\pi\) | |||||||
\(42\) | −7.72921 | −0.0283963 | ||||||||
\(43\) | 31.0284 | 0.110042 | 0.0550208 | − | 0.998485i | \(-0.482477\pi\) | ||||
0.0550208 | + | 0.998485i | \(0.482477\pi\) | |||||||
\(44\) | 87.7223 | 0.300560 | ||||||||
\(45\) | 68.3476 | 0.226415 | ||||||||
\(46\) | 23.6214 | 0.0757127 | ||||||||
\(47\) | 129.677 | 0.402455 | 0.201228 | − | 0.979544i | \(-0.435507\pi\) | ||||
0.201228 | + | 0.979544i | \(0.435507\pi\) | |||||||
\(48\) | −190.184 | −0.571889 | ||||||||
\(49\) | −80.1082 | −0.233552 | ||||||||
\(50\) | 10.6985 | 0.0302600 | ||||||||
\(51\) | −163.936 | −0.450110 | ||||||||
\(52\) | −449.580 | −1.19895 | ||||||||
\(53\) | −16.4698 | −0.0426850 | −0.0213425 | − | 0.999772i | \(-0.506794\pi\) | ||||
−0.0213425 | + | 0.999772i | \(0.506794\pi\) | |||||||
\(54\) | 4.29031 | 0.0108118 | ||||||||
\(55\) | −83.5359 | −0.204800 | ||||||||
\(56\) | −41.1574 | −0.0982123 | ||||||||
\(57\) | 445.086 | 1.03426 | ||||||||
\(58\) | −20.0193 | −0.0453218 | ||||||||
\(59\) | 371.300 | 0.819308 | 0.409654 | − | 0.912241i | \(-0.365649\pi\) | ||||
0.409654 | + | 0.912241i | \(0.365649\pi\) | |||||||
\(60\) | 181.685 | 0.390924 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | −1.13722 | −0.00232947 | ||||||||
\(63\) | −145.925 | −0.291823 | ||||||||
\(64\) | −502.330 | −0.981113 | ||||||||
\(65\) | 428.125 | 0.816959 | ||||||||
\(66\) | −5.24372 | −0.00977965 | ||||||||
\(67\) | 68.0398 | 0.124065 | 0.0620327 | − | 0.998074i | \(-0.480242\pi\) | ||||
0.0620327 | + | 0.998074i | \(0.480242\pi\) | |||||||
\(68\) | −435.782 | −0.777152 | ||||||||
\(69\) | 445.966 | 0.778087 | ||||||||
\(70\) | 19.5656 | 0.0334077 | ||||||||
\(71\) | 329.123 | 0.550138 | 0.275069 | − | 0.961425i | \(-0.411299\pi\) | ||||
0.275069 | + | 0.961425i | \(0.411299\pi\) | |||||||
\(72\) | 22.8456 | 0.0373941 | ||||||||
\(73\) | 788.527 | 1.26425 | 0.632124 | − | 0.774868i | \(-0.282183\pi\) | ||||
0.632124 | + | 0.774868i | \(0.282183\pi\) | |||||||
\(74\) | −27.9651 | −0.0439308 | ||||||||
\(75\) | 201.986 | 0.310977 | ||||||||
\(76\) | 1183.15 | 1.78575 | ||||||||
\(77\) | 178.353 | 0.263964 | ||||||||
\(78\) | 26.8742 | 0.0390117 | ||||||||
\(79\) | 1249.99 | 1.78018 | 0.890092 | − | 0.455781i | \(-0.150640\pi\) | ||||
0.890092 | + | 0.455781i | \(0.150640\pi\) | |||||||
\(80\) | 481.430 | 0.672819 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −39.2592 | −0.0528714 | ||||||||
\(83\) | −903.772 | −1.19520 | −0.597602 | − | 0.801793i | \(-0.703880\pi\) | ||||
−0.597602 | + | 0.801793i | \(0.703880\pi\) | |||||||
\(84\) | −387.906 | −0.503858 | ||||||||
\(85\) | 414.985 | 0.529547 | ||||||||
\(86\) | −4.93043 | −0.00618212 | ||||||||
\(87\) | −377.960 | −0.465765 | ||||||||
\(88\) | −27.9223 | −0.0338242 | ||||||||
\(89\) | 630.261 | 0.750647 | 0.375324 | − | 0.926894i | \(-0.377532\pi\) | ||||
0.375324 | + | 0.926894i | \(0.377532\pi\) | |||||||
\(90\) | −10.8605 | −0.0127199 | ||||||||
\(91\) | −914.068 | −1.05297 | ||||||||
\(92\) | 1185.49 | 1.34343 | ||||||||
\(93\) | −21.4704 | −0.0239395 | ||||||||
\(94\) | −20.6058 | −0.0226099 | ||||||||
\(95\) | −1126.69 | −1.21680 | ||||||||
\(96\) | 91.1418 | 0.0968971 | ||||||||
\(97\) | 611.113 | 0.639682 | 0.319841 | − | 0.947471i | \(-0.396371\pi\) | ||||
0.319841 | + | 0.947471i | \(0.396371\pi\) | |||||||
\(98\) | 12.7292 | 0.0131209 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 536.928 | 0.536928 | ||||||||
\(101\) | −1783.57 | −1.75715 | −0.878574 | − | 0.477606i | \(-0.841505\pi\) | ||||
−0.878574 | + | 0.477606i | \(0.841505\pi\) | |||||||
\(102\) | 26.0495 | 0.0252871 | ||||||||
\(103\) | 942.273 | 0.901407 | 0.450704 | − | 0.892674i | \(-0.351173\pi\) | ||||
0.450704 | + | 0.892674i | \(0.351173\pi\) | |||||||
\(104\) | 143.103 | 0.134927 | ||||||||
\(105\) | 369.394 | 0.343326 | ||||||||
\(106\) | 2.61707 | 0.00239804 | ||||||||
\(107\) | −1443.28 | −1.30399 | −0.651996 | − | 0.758222i | \(-0.726068\pi\) | ||||
−0.651996 | + | 0.758222i | \(0.726068\pi\) | |||||||
\(108\) | 215.318 | 0.191843 | ||||||||
\(109\) | −184.596 | −0.162212 | −0.0811058 | − | 0.996705i | \(-0.525845\pi\) | ||||
−0.0811058 | + | 0.996705i | \(0.525845\pi\) | |||||||
\(110\) | 13.2739 | 0.0115056 | ||||||||
\(111\) | −527.974 | −0.451469 | ||||||||
\(112\) | −1027.88 | −0.867190 | ||||||||
\(113\) | 1635.68 | 1.36170 | 0.680848 | − | 0.732425i | \(-0.261611\pi\) | ||||
0.680848 | + | 0.732425i | \(0.261611\pi\) | |||||||
\(114\) | −70.7244 | −0.0581048 | ||||||||
\(115\) | −1128.91 | −0.915407 | ||||||||
\(116\) | −1004.71 | −0.804182 | ||||||||
\(117\) | 507.379 | 0.400916 | ||||||||
\(118\) | −58.9998 | −0.0460286 | ||||||||
\(119\) | −886.014 | −0.682528 | ||||||||
\(120\) | −57.8310 | −0.0439936 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −9.69293 | −0.00719309 | ||||||||
\(123\) | −741.204 | −0.543350 | ||||||||
\(124\) | −57.0737 | −0.0413336 | ||||||||
\(125\) | −1460.58 | −1.04510 | ||||||||
\(126\) | 23.1876 | 0.0163946 | ||||||||
\(127\) | 570.566 | 0.398658 | 0.199329 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199329 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(128\) | 322.865 | 0.222949 | ||||||||
\(129\) | −93.0853 | −0.0635326 | ||||||||
\(130\) | −68.0292 | −0.0458966 | ||||||||
\(131\) | 171.536 | 0.114406 | 0.0572029 | − | 0.998363i | \(-0.481782\pi\) | ||||
0.0572029 | + | 0.998363i | \(0.481782\pi\) | |||||||
\(132\) | −263.167 | −0.173528 | ||||||||
\(133\) | 2405.53 | 1.56832 | ||||||||
\(134\) | −10.8116 | −0.00696997 | ||||||||
\(135\) | −205.043 | −0.130720 | ||||||||
\(136\) | 138.711 | 0.0874587 | ||||||||
\(137\) | −2658.78 | −1.65807 | −0.829033 | − | 0.559200i | \(-0.811108\pi\) | ||||
−0.829033 | + | 0.559200i | \(0.811108\pi\) | |||||||
\(138\) | −70.8642 | −0.0437127 | ||||||||
\(139\) | −1643.72 | −1.00301 | −0.501506 | − | 0.865154i | \(-0.667220\pi\) | ||||
−0.501506 | + | 0.865154i | \(0.667220\pi\) | |||||||
\(140\) | 981.943 | 0.592781 | ||||||||
\(141\) | −389.032 | −0.232358 | ||||||||
\(142\) | −52.2979 | −0.0309066 | ||||||||
\(143\) | −620.130 | −0.362642 | ||||||||
\(144\) | 570.552 | 0.330180 | ||||||||
\(145\) | 956.764 | 0.547965 | ||||||||
\(146\) | −125.297 | −0.0710252 | ||||||||
\(147\) | 240.325 | 0.134841 | ||||||||
\(148\) | −1403.49 | −0.779500 | ||||||||
\(149\) | −1619.05 | −0.890185 | −0.445093 | − | 0.895484i | \(-0.646829\pi\) | ||||
−0.445093 | + | 0.895484i | \(0.646829\pi\) | |||||||
\(150\) | −32.0956 | −0.0174706 | ||||||||
\(151\) | −2216.61 | −1.19460 | −0.597301 | − | 0.802017i | \(-0.703760\pi\) | ||||
−0.597301 | + | 0.802017i | \(0.703760\pi\) | |||||||
\(152\) | −376.601 | −0.200963 | ||||||||
\(153\) | 491.807 | 0.259871 | ||||||||
\(154\) | −28.3404 | −0.0148295 | ||||||||
\(155\) | 54.3500 | 0.0281645 | ||||||||
\(156\) | 1348.74 | 0.692216 | ||||||||
\(157\) | −1702.98 | −0.865685 | −0.432842 | − | 0.901470i | \(-0.642489\pi\) | ||||
−0.432842 | + | 0.901470i | \(0.642489\pi\) | |||||||
\(158\) | −198.623 | −0.100010 | ||||||||
\(159\) | 49.4095 | 0.0246442 | ||||||||
\(160\) | −230.716 | −0.113998 | ||||||||
\(161\) | 2410.29 | 1.17986 | ||||||||
\(162\) | −12.8709 | −0.00624220 | ||||||||
\(163\) | −1426.06 | −0.685260 | −0.342630 | − | 0.939470i | \(-0.611318\pi\) | ||||
−0.342630 | + | 0.939470i | \(0.611318\pi\) | |||||||
\(164\) | −1970.30 | −0.938140 | ||||||||
\(165\) | 250.608 | 0.118241 | ||||||||
\(166\) | 143.610 | 0.0671463 | ||||||||
\(167\) | −417.430 | −0.193423 | −0.0967116 | − | 0.995312i | \(-0.530832\pi\) | ||||
−0.0967116 | + | 0.995312i | \(0.530832\pi\) | |||||||
\(168\) | 123.472 | 0.0567029 | ||||||||
\(169\) | 981.190 | 0.446604 | ||||||||
\(170\) | −65.9414 | −0.0297498 | ||||||||
\(171\) | −1335.26 | −0.597133 | ||||||||
\(172\) | −247.444 | −0.109694 | ||||||||
\(173\) | 1836.60 | 0.807131 | 0.403566 | − | 0.914951i | \(-0.367771\pi\) | ||||
0.403566 | + | 0.914951i | \(0.367771\pi\) | |||||||
\(174\) | 60.0580 | 0.0261666 | ||||||||
\(175\) | 1091.66 | 0.471553 | ||||||||
\(176\) | −697.341 | −0.298659 | ||||||||
\(177\) | −1113.90 | −0.473028 | ||||||||
\(178\) | −100.149 | −0.0421712 | ||||||||
\(179\) | −774.926 | −0.323579 | −0.161790 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161790 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(180\) | −545.055 | −0.225700 | ||||||||
\(181\) | 2076.69 | 0.852814 | 0.426407 | − | 0.904532i | \(-0.359779\pi\) | ||||
0.426407 | + | 0.904532i | \(0.359779\pi\) | |||||||
\(182\) | 145.246 | 0.0591557 | ||||||||
\(183\) | −183.000 | −0.0739221 | ||||||||
\(184\) | −377.346 | −0.151186 | ||||||||
\(185\) | 1336.51 | 0.531147 | ||||||||
\(186\) | 3.41166 | 0.00134492 | ||||||||
\(187\) | −601.098 | −0.235062 | ||||||||
\(188\) | −1034.15 | −0.401185 | ||||||||
\(189\) | 437.776 | 0.168484 | ||||||||
\(190\) | 179.031 | 0.0683594 | ||||||||
\(191\) | −1027.55 | −0.389273 | −0.194636 | − | 0.980875i | \(-0.562353\pi\) | ||||
−0.194636 | + | 0.980875i | \(0.562353\pi\) | |||||||
\(192\) | 1506.99 | 0.566446 | ||||||||
\(193\) | −1139.83 | −0.425111 | −0.212556 | − | 0.977149i | \(-0.568179\pi\) | ||||
−0.212556 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(194\) | −97.1061 | −0.0359372 | ||||||||
\(195\) | −1284.37 | −0.471672 | ||||||||
\(196\) | 638.843 | 0.232814 | ||||||||
\(197\) | 515.497 | 0.186435 | 0.0932173 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932173 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(198\) | 15.7311 | 0.00564628 | ||||||||
\(199\) | 721.842 | 0.257136 | 0.128568 | − | 0.991701i | \(-0.458962\pi\) | ||||
0.128568 | + | 0.991701i | \(0.458962\pi\) | |||||||
\(200\) | −170.906 | −0.0604245 | ||||||||
\(201\) | −204.119 | −0.0716292 | ||||||||
\(202\) | 283.410 | 0.0987162 | ||||||||
\(203\) | −2042.74 | −0.706266 | ||||||||
\(204\) | 1307.35 | 0.448689 | ||||||||
\(205\) | 1876.28 | 0.639243 | ||||||||
\(206\) | −149.728 | −0.0506409 | ||||||||
\(207\) | −1337.90 | −0.449229 | ||||||||
\(208\) | 3573.90 | 1.19137 | ||||||||
\(209\) | 1631.98 | 0.540127 | ||||||||
\(210\) | −58.6969 | −0.0192880 | ||||||||
\(211\) | 5042.49 | 1.64521 | 0.822606 | − | 0.568612i | \(-0.192519\pi\) | ||||
0.822606 | + | 0.568612i | \(0.192519\pi\) | |||||||
\(212\) | 131.343 | 0.0425503 | ||||||||
\(213\) | −987.370 | −0.317622 | ||||||||
\(214\) | 229.338 | 0.0732580 | ||||||||
\(215\) | 235.635 | 0.0747451 | ||||||||
\(216\) | −68.5367 | −0.0215895 | ||||||||
\(217\) | −116.040 | −0.0363009 | ||||||||
\(218\) | 29.3324 | 0.00911302 | ||||||||
\(219\) | −2365.58 | −0.729913 | ||||||||
\(220\) | 666.178 | 0.204153 | ||||||||
\(221\) | 3080.65 | 0.937678 | ||||||||
\(222\) | 83.8953 | 0.0253635 | ||||||||
\(223\) | −800.257 | −0.240310 | −0.120155 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120155 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(224\) | 492.589 | 0.146931 | ||||||||
\(225\) | −605.957 | −0.179543 | ||||||||
\(226\) | −259.910 | −0.0764998 | ||||||||
\(227\) | −4702.17 | −1.37486 | −0.687432 | − | 0.726249i | \(-0.741262\pi\) | ||||
−0.687432 | + | 0.726249i | \(0.741262\pi\) | |||||||
\(228\) | −3549.45 | −1.03100 | ||||||||
\(229\) | 993.610 | 0.286723 | 0.143362 | − | 0.989670i | \(-0.454209\pi\) | ||||
0.143362 | + | 0.989670i | \(0.454209\pi\) | |||||||
\(230\) | 179.385 | 0.0514274 | ||||||||
\(231\) | −535.060 | −0.152400 | ||||||||
\(232\) | 319.804 | 0.0905006 | ||||||||
\(233\) | −3670.09 | −1.03191 | −0.515956 | − | 0.856615i | \(-0.672563\pi\) | ||||
−0.515956 | + | 0.856615i | \(0.672563\pi\) | |||||||
\(234\) | −80.6227 | −0.0225234 | ||||||||
\(235\) | 984.793 | 0.273365 | ||||||||
\(236\) | −2961.03 | −0.816723 | ||||||||
\(237\) | −3749.96 | −1.02779 | ||||||||
\(238\) | 140.788 | 0.0383443 | ||||||||
\(239\) | −4046.34 | −1.09513 | −0.547565 | − | 0.836763i | \(-0.684445\pi\) | ||||
−0.547565 | + | 0.836763i | \(0.684445\pi\) | |||||||
\(240\) | −1444.29 | −0.388452 | ||||||||
\(241\) | 5851.00 | 1.56388 | 0.781942 | − | 0.623351i | \(-0.214229\pi\) | ||||
0.781942 | + | 0.623351i | \(0.214229\pi\) | |||||||
\(242\) | −19.2270 | −0.00510725 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −486.460 | −0.127633 | ||||||||
\(245\) | −608.356 | −0.158638 | ||||||||
\(246\) | 117.778 | 0.0305253 | ||||||||
\(247\) | −8363.97 | −2.15460 | ||||||||
\(248\) | 18.1668 | 0.00465158 | ||||||||
\(249\) | 2711.32 | 0.690051 | ||||||||
\(250\) | 232.086 | 0.0587137 | ||||||||
\(251\) | −536.741 | −0.134975 | −0.0674877 | − | 0.997720i | \(-0.521498\pi\) | ||||
−0.0674877 | + | 0.997720i | \(0.521498\pi\) | |||||||
\(252\) | 1163.72 | 0.290902 | ||||||||
\(253\) | 1635.21 | 0.406342 | ||||||||
\(254\) | −90.6633 | −0.0223965 | ||||||||
\(255\) | −1244.96 | −0.305734 | ||||||||
\(256\) | 3967.33 | 0.968588 | ||||||||
\(257\) | −713.229 | −0.173113 | −0.0865564 | − | 0.996247i | \(-0.527586\pi\) | ||||
−0.0865564 | + | 0.996247i | \(0.527586\pi\) | |||||||
\(258\) | 14.7913 | 0.00356925 | ||||||||
\(259\) | −2853.51 | −0.684590 | ||||||||
\(260\) | −3414.19 | −0.814381 | ||||||||
\(261\) | 1133.88 | 0.268909 | ||||||||
\(262\) | −27.2571 | −0.00642730 | ||||||||
\(263\) | 5480.26 | 1.28489 | 0.642447 | − | 0.766330i | \(-0.277919\pi\) | ||||
0.642447 | + | 0.766330i | \(0.277919\pi\) | |||||||
\(264\) | 83.7670 | 0.0195284 | ||||||||
\(265\) | −125.075 | −0.0289935 | ||||||||
\(266\) | −382.240 | −0.0881077 | ||||||||
\(267\) | −1890.78 | −0.433386 | ||||||||
\(268\) | −542.600 | −0.123674 | ||||||||
\(269\) | −6249.32 | −1.41646 | −0.708230 | − | 0.705982i | \(-0.750506\pi\) | ||||
−0.708230 | + | 0.705982i | \(0.750506\pi\) | |||||||
\(270\) | 32.5814 | 0.00734385 | ||||||||
\(271\) | −7855.98 | −1.76095 | −0.880473 | − | 0.474096i | \(-0.842775\pi\) | ||||
−0.880473 | + | 0.474096i | \(0.842775\pi\) | |||||||
\(272\) | 3464.22 | 0.772239 | ||||||||
\(273\) | 2742.20 | 0.607933 | ||||||||
\(274\) | 422.482 | 0.0931498 | ||||||||
\(275\) | 740.614 | 0.162403 | ||||||||
\(276\) | −3556.47 | −0.775631 | ||||||||
\(277\) | −81.7755 | −0.0177380 | −0.00886898 | − | 0.999961i | \(-0.502823\pi\) | ||||
−0.00886898 | + | 0.999961i | \(0.502823\pi\) | |||||||
\(278\) | 261.188 | 0.0563490 | ||||||||
\(279\) | 64.4112 | 0.0138215 | ||||||||
\(280\) | −312.556 | −0.0667100 | ||||||||
\(281\) | −5856.93 | −1.24340 | −0.621699 | − | 0.783256i | \(-0.713557\pi\) | ||||
−0.621699 | + | 0.783256i | \(0.713557\pi\) | |||||||
\(282\) | 61.8174 | 0.0130538 | ||||||||
\(283\) | −5144.26 | −1.08055 | −0.540273 | − | 0.841490i | \(-0.681679\pi\) | ||||
−0.540273 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(284\) | −2624.68 | −0.548401 | ||||||||
\(285\) | 3380.06 | 0.702518 | ||||||||
\(286\) | 98.5389 | 0.0203732 | ||||||||
\(287\) | −4005.94 | −0.823914 | ||||||||
\(288\) | −273.425 | −0.0559436 | ||||||||
\(289\) | −1926.90 | −0.392204 | ||||||||
\(290\) | −152.030 | −0.0307846 | ||||||||
\(291\) | −1833.34 | −0.369320 | ||||||||
\(292\) | −6288.30 | −1.26026 | ||||||||
\(293\) | −70.3266 | −0.0140223 | −0.00701114 | − | 0.999975i | \(-0.502232\pi\) | ||||
−0.00701114 | + | 0.999975i | \(0.502232\pi\) | |||||||
\(294\) | −38.1877 | −0.00757535 | ||||||||
\(295\) | 2819.72 | 0.556510 | ||||||||
\(296\) | 446.736 | 0.0877229 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | 257.268 | 0.0500104 | ||||||||
\(299\) | −8380.51 | −1.62093 | ||||||||
\(300\) | −1610.78 | −0.309996 | ||||||||
\(301\) | −503.093 | −0.0963382 | ||||||||
\(302\) | 352.220 | 0.0671125 | ||||||||
\(303\) | 5350.71 | 1.01449 | ||||||||
\(304\) | −9405.36 | −1.77445 | ||||||||
\(305\) | 463.245 | 0.0869682 | ||||||||
\(306\) | −78.1484 | −0.0145995 | ||||||||
\(307\) | −2205.88 | −0.410085 | −0.205043 | − | 0.978753i | \(-0.565733\pi\) | ||||
−0.205043 | + | 0.978753i | \(0.565733\pi\) | |||||||
\(308\) | −1422.32 | −0.263131 | ||||||||
\(309\) | −2826.82 | −0.520428 | ||||||||
\(310\) | −8.63624 | −0.00158228 | ||||||||
\(311\) | −2188.69 | −0.399066 | −0.199533 | − | 0.979891i | \(-0.563942\pi\) | ||||
−0.199533 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(312\) | −429.309 | −0.0779002 | ||||||||
\(313\) | 5172.12 | 0.934011 | 0.467005 | − | 0.884254i | \(-0.345333\pi\) | ||||
0.467005 | + | 0.884254i | \(0.345333\pi\) | |||||||
\(314\) | 270.604 | 0.0486340 | ||||||||
\(315\) | −1108.18 | −0.198219 | ||||||||
\(316\) | −9968.33 | −1.77457 | ||||||||
\(317\) | 9532.28 | 1.68892 | 0.844458 | − | 0.535622i | \(-0.179923\pi\) | ||||
0.844458 | + | 0.535622i | \(0.179923\pi\) | |||||||
\(318\) | −7.85120 | −0.00138451 | ||||||||
\(319\) | −1385.85 | −0.243238 | ||||||||
\(320\) | −3814.78 | −0.666415 | ||||||||
\(321\) | 4329.84 | 0.752860 | ||||||||
\(322\) | −382.996 | −0.0662842 | ||||||||
\(323\) | −8107.28 | −1.39660 | ||||||||
\(324\) | −645.955 | −0.110760 | ||||||||
\(325\) | −3795.67 | −0.647834 | ||||||||
\(326\) | 226.601 | 0.0384978 | ||||||||
\(327\) | 553.787 | 0.0936529 | ||||||||
\(328\) | 627.156 | 0.105576 | ||||||||
\(329\) | −2102.58 | −0.352338 | ||||||||
\(330\) | −39.8217 | −0.00664276 | ||||||||
\(331\) | −2277.85 | −0.378254 | −0.189127 | − | 0.981953i | \(-0.560566\pi\) | ||||
−0.189127 | + | 0.981953i | \(0.560566\pi\) | |||||||
\(332\) | 7207.36 | 1.19143 | ||||||||
\(333\) | 1583.92 | 0.260656 | ||||||||
\(334\) | 66.3298 | 0.0108665 | ||||||||
\(335\) | 516.706 | 0.0842706 | ||||||||
\(336\) | 3083.63 | 0.500672 | ||||||||
\(337\) | −142.077 | −0.0229657 | −0.0114829 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114829 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(338\) | −155.912 | −0.0250901 | ||||||||
\(339\) | −4907.03 | −0.786175 | ||||||||
\(340\) | −3309.40 | −0.527876 | ||||||||
\(341\) | −78.7248 | −0.0125020 | ||||||||
\(342\) | 212.173 | 0.0335468 | ||||||||
\(343\) | 6860.25 | 1.07994 | ||||||||
\(344\) | 78.7624 | 0.0123447 | ||||||||
\(345\) | 3386.74 | 0.528510 | ||||||||
\(346\) | −291.836 | −0.0453445 | ||||||||
\(347\) | 7853.16 | 1.21493 | 0.607463 | − | 0.794348i | \(-0.292187\pi\) | ||||
0.607463 | + | 0.794348i | \(0.292187\pi\) | |||||||
\(348\) | 3014.13 | 0.464295 | ||||||||
\(349\) | −10420.0 | −1.59820 | −0.799098 | − | 0.601201i | \(-0.794689\pi\) | ||||
−0.799098 | + | 0.601201i | \(0.794689\pi\) | |||||||
\(350\) | −173.465 | −0.0264918 | ||||||||
\(351\) | −1522.14 | −0.231469 | ||||||||
\(352\) | 334.187 | 0.0506029 | ||||||||
\(353\) | 2915.86 | 0.439648 | 0.219824 | − | 0.975540i | \(-0.429452\pi\) | ||||
0.219824 | + | 0.975540i | \(0.429452\pi\) | |||||||
\(354\) | 176.999 | 0.0265746 | ||||||||
\(355\) | 2499.42 | 0.373677 | ||||||||
\(356\) | −5026.18 | −0.748278 | ||||||||
\(357\) | 2658.04 | 0.394058 | ||||||||
\(358\) | 123.136 | 0.0181786 | ||||||||
\(359\) | 2333.29 | 0.343026 | 0.171513 | − | 0.985182i | \(-0.445134\pi\) | ||||
0.171513 | + | 0.985182i | \(0.445134\pi\) | |||||||
\(360\) | 173.493 | 0.0253997 | ||||||||
\(361\) | 15152.3 | 2.20911 | ||||||||
\(362\) | −329.987 | −0.0479109 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 7289.46 | 1.04965 | ||||||||
\(365\) | 5988.21 | 0.858732 | ||||||||
\(366\) | 29.0788 | 0.00415293 | ||||||||
\(367\) | −1464.31 | −0.208274 | −0.104137 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104137 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(368\) | −9423.95 | −1.33494 | ||||||||
\(369\) | 2223.61 | 0.313703 | ||||||||
\(370\) | −212.372 | −0.0298397 | ||||||||
\(371\) | 267.041 | 0.0373695 | ||||||||
\(372\) | 171.221 | 0.0238640 | ||||||||
\(373\) | −8778.48 | −1.21859 | −0.609293 | − | 0.792945i | \(-0.708547\pi\) | ||||
−0.609293 | + | 0.792945i | \(0.708547\pi\) | |||||||
\(374\) | 95.5147 | 0.0132057 | ||||||||
\(375\) | 4381.73 | 0.603391 | ||||||||
\(376\) | 329.173 | 0.0451484 | ||||||||
\(377\) | 7102.55 | 0.970291 | ||||||||
\(378\) | −69.5629 | −0.00946542 | ||||||||
\(379\) | −13243.3 | −1.79488 | −0.897441 | − | 0.441134i | \(-0.854576\pi\) | ||||
−0.897441 | + | 0.441134i | \(0.854576\pi\) | |||||||
\(380\) | 8985.05 | 1.21296 | ||||||||
\(381\) | −1711.70 | −0.230165 | ||||||||
\(382\) | 163.279 | 0.0218693 | ||||||||
\(383\) | −3271.85 | −0.436511 | −0.218255 | − | 0.975892i | \(-0.570037\pi\) | ||||
−0.218255 | + | 0.975892i | \(0.570037\pi\) | |||||||
\(384\) | −968.596 | −0.128720 | ||||||||
\(385\) | 1354.45 | 0.179296 | ||||||||
\(386\) | 181.119 | 0.0238827 | ||||||||
\(387\) | 279.256 | 0.0366805 | ||||||||
\(388\) | −4873.47 | −0.637663 | ||||||||
\(389\) | −8212.76 | −1.07045 | −0.535223 | − | 0.844711i | \(-0.679772\pi\) | ||||
−0.535223 | + | 0.844711i | \(0.679772\pi\) | |||||||
\(390\) | 204.088 | 0.0264984 | ||||||||
\(391\) | −8123.30 | −1.05067 | ||||||||
\(392\) | −203.346 | −0.0262004 | ||||||||
\(393\) | −514.608 | −0.0660522 | ||||||||
\(394\) | −81.9127 | −0.0104739 | ||||||||
\(395\) | 9492.62 | 1.20918 | ||||||||
\(396\) | 789.500 | 0.100187 | ||||||||
\(397\) | −1768.51 | −0.223574 | −0.111787 | − | 0.993732i | \(-0.535657\pi\) | ||||
−0.111787 | + | 0.993732i | \(0.535657\pi\) | |||||||
\(398\) | −114.701 | −0.0144458 | ||||||||
\(399\) | −7216.60 | −0.905468 | ||||||||
\(400\) | −4268.27 | −0.533534 | ||||||||
\(401\) | −15785.8 | −1.96585 | −0.982924 | − | 0.184010i | \(-0.941092\pi\) | ||||
−0.982924 | + | 0.184010i | \(0.941092\pi\) | |||||||
\(402\) | 32.4347 | 0.00402411 | ||||||||
\(403\) | 403.468 | 0.0498714 | ||||||||
\(404\) | 14223.5 | 1.75160 | ||||||||
\(405\) | 615.128 | 0.0754715 | ||||||||
\(406\) | 324.592 | 0.0396779 | ||||||||
\(407\) | −1935.91 | −0.235772 | ||||||||
\(408\) | −416.134 | −0.0504943 | ||||||||
\(409\) | −6829.39 | −0.825652 | −0.412826 | − | 0.910810i | \(-0.635458\pi\) | ||||
−0.412826 | + | 0.910810i | \(0.635458\pi\) | |||||||
\(410\) | −298.141 | −0.0359125 | ||||||||
\(411\) | 7976.34 | 0.957285 | ||||||||
\(412\) | −7514.40 | −0.898562 | ||||||||
\(413\) | −6020.24 | −0.717280 | ||||||||
\(414\) | 212.593 | 0.0252376 | ||||||||
\(415\) | −6863.40 | −0.811834 | ||||||||
\(416\) | −1712.72 | −0.201858 | ||||||||
\(417\) | 4931.16 | 0.579089 | ||||||||
\(418\) | −259.323 | −0.0303442 | ||||||||
\(419\) | −8553.85 | −0.997334 | −0.498667 | − | 0.866794i | \(-0.666177\pi\) | ||||
−0.498667 | + | 0.866794i | \(0.666177\pi\) | |||||||
\(420\) | −2945.83 | −0.342242 | ||||||||
\(421\) | −1437.53 | −0.166416 | −0.0832079 | − | 0.996532i | \(-0.526517\pi\) | ||||
−0.0832079 | + | 0.996532i | \(0.526517\pi\) | |||||||
\(422\) | −801.255 | −0.0924277 | ||||||||
\(423\) | 1167.10 | 0.134152 | ||||||||
\(424\) | −41.8070 | −0.00478851 | ||||||||
\(425\) | −3679.18 | −0.419921 | ||||||||
\(426\) | 156.894 | 0.0178439 | ||||||||
\(427\) | −989.050 | −0.112092 | ||||||||
\(428\) | 11509.8 | 1.29988 | ||||||||
\(429\) | 1860.39 | 0.209372 | ||||||||
\(430\) | −37.4425 | −0.00419916 | ||||||||
\(431\) | −5831.09 | −0.651679 | −0.325840 | − | 0.945425i | \(-0.605647\pi\) | ||||
−0.325840 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(432\) | −1711.66 | −0.190630 | ||||||||
\(433\) | −10183.1 | −1.13018 | −0.565089 | − | 0.825030i | \(-0.691158\pi\) | ||||
−0.565089 | + | 0.825030i | \(0.691158\pi\) | |||||||
\(434\) | 18.4388 | 0.00203938 | ||||||||
\(435\) | −2870.29 | −0.316368 | ||||||||
\(436\) | 1472.11 | 0.161700 | ||||||||
\(437\) | 22054.8 | 2.41424 | ||||||||
\(438\) | 375.892 | 0.0410064 | ||||||||
\(439\) | −10005.8 | −1.08782 | −0.543909 | − | 0.839144i | \(-0.683056\pi\) | ||||
−0.543909 | + | 0.839144i | \(0.683056\pi\) | |||||||
\(440\) | −212.047 | −0.0229749 | ||||||||
\(441\) | −720.974 | −0.0778505 | ||||||||
\(442\) | −489.517 | −0.0526786 | ||||||||
\(443\) | −14141.0 | −1.51661 | −0.758305 | − | 0.651899i | \(-0.773972\pi\) | ||||
−0.758305 | + | 0.651899i | \(0.773972\pi\) | |||||||
\(444\) | 4210.46 | 0.450044 | ||||||||
\(445\) | 4786.32 | 0.509872 | ||||||||
\(446\) | 127.161 | 0.0135006 | ||||||||
\(447\) | 4857.15 | 0.513949 | ||||||||
\(448\) | 8144.74 | 0.858935 | ||||||||
\(449\) | 6345.25 | 0.666929 | 0.333464 | − | 0.942763i | \(-0.391782\pi\) | ||||
0.333464 | + | 0.942763i | \(0.391782\pi\) | |||||||
\(450\) | 96.2868 | 0.0100867 | ||||||||
\(451\) | −2717.75 | −0.283755 | ||||||||
\(452\) | −13044.1 | −1.35740 | ||||||||
\(453\) | 6649.82 | 0.689704 | ||||||||
\(454\) | 747.177 | 0.0772396 | ||||||||
\(455\) | −6941.59 | −0.715224 | ||||||||
\(456\) | 1129.80 | 0.116026 | ||||||||
\(457\) | −16600.2 | −1.69918 | −0.849588 | − | 0.527447i | \(-0.823149\pi\) | ||||
−0.849588 | + | 0.527447i | \(0.823149\pi\) | |||||||
\(458\) | −157.885 | −0.0161080 | ||||||||
\(459\) | −1475.42 | −0.150037 | ||||||||
\(460\) | 9002.81 | 0.912518 | ||||||||
\(461\) | 2278.07 | 0.230153 | 0.115076 | − | 0.993357i | \(-0.463289\pi\) | ||||
0.115076 | + | 0.993357i | \(0.463289\pi\) | |||||||
\(462\) | 85.0213 | 0.00856179 | ||||||||
\(463\) | −167.261 | −0.0167889 | −0.00839447 | − | 0.999965i | \(-0.502672\pi\) | ||||
−0.00839447 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(464\) | 7986.87 | 0.799097 | ||||||||
\(465\) | −163.050 | −0.0162608 | ||||||||
\(466\) | 583.179 | 0.0579726 | ||||||||
\(467\) | 13178.8 | 1.30587 | 0.652934 | − | 0.757415i | \(-0.273538\pi\) | ||||
0.652934 | + | 0.757415i | \(0.273538\pi\) | |||||||
\(468\) | −4046.22 | −0.399651 | ||||||||
\(469\) | −1103.19 | −0.108616 | ||||||||
\(470\) | −156.484 | −0.0153576 | ||||||||
\(471\) | 5108.94 | 0.499803 | ||||||||
\(472\) | 942.507 | 0.0919119 | ||||||||
\(473\) | −341.313 | −0.0331788 | ||||||||
\(474\) | 595.870 | 0.0577410 | ||||||||
\(475\) | 9989.00 | 0.964898 | ||||||||
\(476\) | 7065.74 | 0.680374 | ||||||||
\(477\) | −148.229 | −0.0142283 | ||||||||
\(478\) | 642.966 | 0.0615242 | ||||||||
\(479\) | 13097.7 | 1.24938 | 0.624688 | − | 0.780874i | \(-0.285226\pi\) | ||||
0.624688 | + | 0.780874i | \(0.285226\pi\) | |||||||
\(480\) | 692.147 | 0.0658167 | ||||||||
\(481\) | 9921.59 | 0.940511 | ||||||||
\(482\) | −929.727 | −0.0878587 | ||||||||
\(483\) | −7230.86 | −0.681192 | ||||||||
\(484\) | −964.945 | −0.0906222 | ||||||||
\(485\) | 4640.90 | 0.434500 | ||||||||
\(486\) | 38.6128 | 0.00360394 | ||||||||
\(487\) | −20142.6 | −1.87422 | −0.937112 | − | 0.349028i | \(-0.886512\pi\) | ||||
−0.937112 | + | 0.349028i | \(0.886512\pi\) | |||||||
\(488\) | 154.842 | 0.0143635 | ||||||||
\(489\) | 4278.17 | 0.395635 | ||||||||
\(490\) | 96.6680 | 0.00891228 | ||||||||
\(491\) | 17184.9 | 1.57952 | 0.789758 | − | 0.613418i | \(-0.210206\pi\) | ||||
0.789758 | + | 0.613418i | \(0.210206\pi\) | |||||||
\(492\) | 5910.91 | 0.541635 | ||||||||
\(493\) | 6884.56 | 0.628935 | ||||||||
\(494\) | 1329.04 | 0.121045 | ||||||||
\(495\) | −751.823 | −0.0682665 | ||||||||
\(496\) | 453.703 | 0.0410723 | ||||||||
\(497\) | −5336.39 | −0.481629 | ||||||||
\(498\) | −430.830 | −0.0387669 | ||||||||
\(499\) | −1854.10 | −0.166335 | −0.0831674 | − | 0.996536i | \(-0.526504\pi\) | ||||
−0.0831674 | + | 0.996536i | \(0.526504\pi\) | |||||||
\(500\) | 11647.7 | 1.04180 | ||||||||
\(501\) | 1252.29 | 0.111673 | ||||||||
\(502\) | 85.2885 | 0.00758289 | ||||||||
\(503\) | 19551.2 | 1.73309 | 0.866547 | − | 0.499095i | \(-0.166334\pi\) | ||||
0.866547 | + | 0.499095i | \(0.166334\pi\) | |||||||
\(504\) | −370.416 | −0.0327374 | ||||||||
\(505\) | −13544.8 | −1.19353 | ||||||||
\(506\) | −259.835 | −0.0228282 | ||||||||
\(507\) | −2943.57 | −0.257847 | ||||||||
\(508\) | −4550.12 | −0.397400 | ||||||||
\(509\) | −794.442 | −0.0691808 | −0.0345904 | − | 0.999402i | \(-0.511013\pi\) | ||||
−0.0345904 | + | 0.999402i | \(0.511013\pi\) | |||||||
\(510\) | 197.824 | 0.0171761 | ||||||||
\(511\) | −12785.1 | −1.10681 | ||||||||
\(512\) | −3213.33 | −0.277364 | ||||||||
\(513\) | 4005.77 | 0.344755 | ||||||||
\(514\) | 113.332 | 0.00972545 | ||||||||
\(515\) | 7155.79 | 0.612275 | ||||||||
\(516\) | 742.332 | 0.0633320 | ||||||||
\(517\) | −1426.45 | −0.121345 | ||||||||
\(518\) | 453.425 | 0.0384601 | ||||||||
\(519\) | −5509.79 | −0.465998 | ||||||||
\(520\) | 1086.75 | 0.0916484 | ||||||||
\(521\) | −9926.01 | −0.834676 | −0.417338 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417338 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(522\) | −180.174 | −0.0151073 | ||||||||
\(523\) | 10642.5 | 0.889796 | 0.444898 | − | 0.895581i | \(-0.353240\pi\) | ||||
0.444898 | + | 0.895581i | \(0.353240\pi\) | |||||||
\(524\) | −1367.96 | −0.114045 | ||||||||
\(525\) | −3274.98 | −0.272251 | ||||||||
\(526\) | −870.816 | −0.0721851 | ||||||||
\(527\) | 391.085 | 0.0323262 | ||||||||
\(528\) | 2092.02 | 0.172431 | ||||||||
\(529\) | 9931.39 | 0.816256 | ||||||||
\(530\) | 19.8745 | 0.00162885 | ||||||||
\(531\) | 3341.70 | 0.273103 | ||||||||
\(532\) | −19183.5 | −1.56337 | ||||||||
\(533\) | 13928.6 | 1.13192 | ||||||||
\(534\) | 300.447 | 0.0243476 | ||||||||
\(535\) | −10960.5 | −0.885728 | ||||||||
\(536\) | 172.712 | 0.0139179 | ||||||||
\(537\) | 2324.78 | 0.186819 | ||||||||
\(538\) | 993.020 | 0.0795764 | ||||||||
\(539\) | 881.190 | 0.0704185 | ||||||||
\(540\) | 1635.16 | 0.130308 | ||||||||
\(541\) | −20526.6 | −1.63125 | −0.815625 | − | 0.578581i | \(-0.803607\pi\) | ||||
−0.815625 | + | 0.578581i | \(0.803607\pi\) | |||||||
\(542\) | 1248.32 | 0.0989296 | ||||||||
\(543\) | −6230.07 | −0.492372 | ||||||||
\(544\) | −1660.15 | −0.130843 | ||||||||
\(545\) | −1401.85 | −0.110181 | ||||||||
\(546\) | −435.737 | −0.0341536 | ||||||||
\(547\) | 3413.70 | 0.266836 | 0.133418 | − | 0.991060i | \(-0.457405\pi\) | ||||
0.133418 | + | 0.991060i | \(0.457405\pi\) | |||||||
\(548\) | 21203.1 | 1.65283 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | −117.684 | −0.00912374 | ||||||||
\(551\) | −18691.6 | −1.44517 | ||||||||
\(552\) | 1132.04 | 0.0872875 | ||||||||
\(553\) | −20267.2 | −1.55850 | ||||||||
\(554\) | 12.9942 | 0.000996515 0 | ||||||||
\(555\) | −4009.53 | −0.306658 | ||||||||
\(556\) | 13108.3 | 0.999846 | ||||||||
\(557\) | −8914.40 | −0.678125 | −0.339062 | − | 0.940764i | \(-0.610110\pi\) | ||||
−0.339062 | + | 0.940764i | \(0.610110\pi\) | |||||||
\(558\) | −10.2350 | −0.000776489 0 | ||||||||
\(559\) | 1749.24 | 0.132352 | ||||||||
\(560\) | −7805.88 | −0.589033 | ||||||||
\(561\) | 1803.29 | 0.135713 | ||||||||
\(562\) | 930.668 | 0.0698539 | ||||||||
\(563\) | −2690.90 | −0.201435 | −0.100718 | − | 0.994915i | \(-0.532114\pi\) | ||||
−0.100718 | + | 0.994915i | \(0.532114\pi\) | |||||||
\(564\) | 3102.44 | 0.231624 | ||||||||
\(565\) | 12421.6 | 0.924923 | ||||||||
\(566\) | 817.425 | 0.0607048 | ||||||||
\(567\) | −1313.33 | −0.0972745 | ||||||||
\(568\) | 835.445 | 0.0617157 | ||||||||
\(569\) | 474.580 | 0.0349656 | 0.0174828 | − | 0.999847i | \(-0.494435\pi\) | ||||
0.0174828 | + | 0.999847i | \(0.494435\pi\) | |||||||
\(570\) | −537.093 | −0.0394673 | ||||||||
\(571\) | 24472.2 | 1.79357 | 0.896785 | − | 0.442467i | \(-0.145897\pi\) | ||||
0.896785 | + | 0.442467i | \(0.145897\pi\) | |||||||
\(572\) | 4945.38 | 0.361498 | ||||||||
\(573\) | 3082.66 | 0.224747 | ||||||||
\(574\) | 636.546 | 0.0462873 | ||||||||
\(575\) | 10008.7 | 0.725901 | ||||||||
\(576\) | −4520.97 | −0.327038 | ||||||||
\(577\) | 6572.85 | 0.474231 | 0.237116 | − | 0.971481i | \(-0.423798\pi\) | ||||
0.237116 | + | 0.971481i | \(0.423798\pi\) | |||||||
\(578\) | 306.185 | 0.0220340 | ||||||||
\(579\) | 3419.48 | 0.245438 | ||||||||
\(580\) | −7629.95 | −0.546235 | ||||||||
\(581\) | 14653.7 | 1.04637 | ||||||||
\(582\) | 291.318 | 0.0207483 | ||||||||
\(583\) | 181.168 | 0.0128700 | ||||||||
\(584\) | 2001.59 | 0.141826 | ||||||||
\(585\) | 3853.12 | 0.272320 | ||||||||
\(586\) | 11.1749 | 0.000787768 0 | ||||||||
\(587\) | 3223.80 | 0.226679 | 0.113339 | − | 0.993556i | \(-0.463845\pi\) | ||||
0.113339 | + | 0.993556i | \(0.463845\pi\) | |||||||
\(588\) | −1916.53 | −0.134416 | ||||||||
\(589\) | −1061.80 | −0.0742794 | ||||||||
\(590\) | −448.055 | −0.0312646 | ||||||||
\(591\) | −1546.49 | −0.107638 | ||||||||
\(592\) | 11156.9 | 0.774572 | ||||||||
\(593\) | −19688.6 | −1.36343 | −0.681713 | − | 0.731619i | \(-0.738765\pi\) | ||||
−0.681713 | + | 0.731619i | \(0.738765\pi\) | |||||||
\(594\) | −47.1934 | −0.00325988 | ||||||||
\(595\) | −6728.55 | −0.463603 | ||||||||
\(596\) | 12911.5 | 0.887376 | ||||||||
\(597\) | −2165.53 | −0.148457 | ||||||||
\(598\) | 1331.67 | 0.0910634 | ||||||||
\(599\) | −5165.49 | −0.352347 | −0.176174 | − | 0.984359i | \(-0.556372\pi\) | ||||
−0.176174 | + | 0.984359i | \(0.556372\pi\) | |||||||
\(600\) | 512.719 | 0.0348861 | ||||||||
\(601\) | 6219.53 | 0.422130 | 0.211065 | − | 0.977472i | \(-0.432307\pi\) | ||||
0.211065 | + | 0.977472i | \(0.432307\pi\) | |||||||
\(602\) | 79.9417 | 0.00541226 | ||||||||
\(603\) | 612.358 | 0.0413551 | ||||||||
\(604\) | 17676.9 | 1.19083 | ||||||||
\(605\) | 918.895 | 0.0617494 | ||||||||
\(606\) | −850.231 | −0.0569938 | ||||||||
\(607\) | −17723.6 | −1.18514 | −0.592570 | − | 0.805519i | \(-0.701886\pi\) | ||||
−0.592570 | + | 0.805519i | \(0.701886\pi\) | |||||||
\(608\) | 4507.33 | 0.300652 | ||||||||
\(609\) | 6128.21 | 0.407763 | ||||||||
\(610\) | −73.6098 | −0.00488586 | ||||||||
\(611\) | 7310.62 | 0.484053 | ||||||||
\(612\) | −3922.04 | −0.259051 | ||||||||
\(613\) | 20623.5 | 1.35885 | 0.679425 | − | 0.733745i | \(-0.262229\pi\) | ||||
0.679425 | + | 0.733745i | \(0.262229\pi\) | |||||||
\(614\) | 350.515 | 0.0230385 | ||||||||
\(615\) | −5628.83 | −0.369067 | ||||||||
\(616\) | 452.731 | 0.0296121 | ||||||||
\(617\) | 27619.0 | 1.80211 | 0.901054 | − | 0.433707i | \(-0.142795\pi\) | ||||
0.901054 | + | 0.433707i | \(0.142795\pi\) | |||||||
\(618\) | 449.183 | 0.0292375 | ||||||||
\(619\) | 233.579 | 0.0151669 | 0.00758347 | − | 0.999971i | \(-0.497586\pi\) | ||||
0.00758347 | + | 0.999971i | \(0.497586\pi\) | |||||||
\(620\) | −433.428 | −0.0280756 | ||||||||
\(621\) | 4013.69 | 0.259362 | ||||||||
\(622\) | 347.784 | 0.0224194 | ||||||||
\(623\) | −10219.0 | −0.657169 | ||||||||
\(624\) | −10721.7 | −0.687839 | ||||||||
\(625\) | −2675.81 | −0.171252 | ||||||||
\(626\) | −821.852 | −0.0524725 | ||||||||
\(627\) | −4895.95 | −0.311843 | ||||||||
\(628\) | 13580.8 | 0.862953 | ||||||||
\(629\) | 9617.09 | 0.609632 | ||||||||
\(630\) | 176.091 | 0.0111359 | ||||||||
\(631\) | 7633.29 | 0.481579 | 0.240790 | − | 0.970577i | \(-0.422594\pi\) | ||||
0.240790 | + | 0.970577i | \(0.422594\pi\) | |||||||
\(632\) | 3172.96 | 0.199705 | ||||||||
\(633\) | −15127.5 | −0.949863 | ||||||||
\(634\) | −1514.68 | −0.0948829 | ||||||||
\(635\) | 4332.98 | 0.270786 | ||||||||
\(636\) | −394.029 | −0.0245664 | ||||||||
\(637\) | −4516.14 | −0.280904 | ||||||||
\(638\) | 220.212 | 0.0136650 | ||||||||
\(639\) | 2962.11 | 0.183379 | ||||||||
\(640\) | 2451.89 | 0.151437 | ||||||||
\(641\) | −20909.1 | −1.28840 | −0.644198 | − | 0.764859i | \(-0.722809\pi\) | ||||
−0.644198 | + | 0.764859i | \(0.722809\pi\) | |||||||
\(642\) | −688.014 | −0.0422955 | ||||||||
\(643\) | 12912.3 | 0.791929 | 0.395965 | − | 0.918266i | \(-0.370410\pi\) | ||||
0.395965 | + | 0.918266i | \(0.370410\pi\) | |||||||
\(644\) | −19221.4 | −1.17613 | ||||||||
\(645\) | −706.906 | −0.0431541 | ||||||||
\(646\) | 1288.25 | 0.0784606 | ||||||||
\(647\) | 1284.56 | 0.0780545 | 0.0390272 | − | 0.999238i | \(-0.487574\pi\) | ||||
0.0390272 | + | 0.999238i | \(0.487574\pi\) | |||||||
\(648\) | 205.610 | 0.0124647 | ||||||||
\(649\) | −4084.30 | −0.247031 | ||||||||
\(650\) | 603.134 | 0.0363952 | ||||||||
\(651\) | 348.120 | 0.0209584 | ||||||||
\(652\) | 11372.5 | 0.683098 | ||||||||
\(653\) | 26149.3 | 1.56708 | 0.783538 | − | 0.621344i | \(-0.213413\pi\) | ||||
0.783538 | + | 0.621344i | \(0.213413\pi\) | |||||||
\(654\) | −87.9971 | −0.00526140 | ||||||||
\(655\) | 1302.67 | 0.0777094 | ||||||||
\(656\) | 15662.8 | 0.932209 | ||||||||
\(657\) | 7096.74 | 0.421416 | ||||||||
\(658\) | 334.101 | 0.0197943 | ||||||||
\(659\) | −20467.8 | −1.20988 | −0.604941 | − | 0.796270i | \(-0.706803\pi\) | ||||
−0.604941 | + | 0.796270i | \(0.706803\pi\) | |||||||
\(660\) | −1998.53 | −0.117868 | ||||||||
\(661\) | −23684.0 | −1.39364 | −0.696822 | − | 0.717244i | \(-0.745403\pi\) | ||||
−0.696822 | + | 0.717244i | \(0.745403\pi\) | |||||||
\(662\) | 361.952 | 0.0212503 | ||||||||
\(663\) | −9241.95 | −0.541369 | ||||||||
\(664\) | −2294.13 | −0.134081 | ||||||||
\(665\) | 18268.0 | 1.06527 | ||||||||
\(666\) | −251.686 | −0.0146436 | ||||||||
\(667\) | −18728.6 | −1.08722 | ||||||||
\(668\) | 3328.90 | 0.192813 | ||||||||
\(669\) | 2400.77 | 0.138743 | ||||||||
\(670\) | −82.1048 | −0.00473431 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | −1477.77 | −0.0848305 | ||||||||
\(673\) | 10788.4 | 0.617926 | 0.308963 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308963 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(674\) | 22.5762 | 0.00129021 | ||||||||
\(675\) | 1817.87 | 0.103659 | ||||||||
\(676\) | −7824.75 | −0.445195 | ||||||||
\(677\) | −6014.94 | −0.341467 | −0.170733 | − | 0.985317i | \(-0.554614\pi\) | ||||
−0.170733 | + | 0.985317i | \(0.554614\pi\) | |||||||
\(678\) | 779.730 | 0.0441672 | ||||||||
\(679\) | −9908.55 | −0.560022 | ||||||||
\(680\) | 1053.40 | 0.0594058 | ||||||||
\(681\) | 14106.5 | 0.793778 | ||||||||
\(682\) | 12.5094 | 0.000702361 0 | ||||||||
\(683\) | 5200.97 | 0.291376 | 0.145688 | − | 0.989331i | \(-0.453460\pi\) | ||||
0.145688 | + | 0.989331i | \(0.453460\pi\) | |||||||
\(684\) | 10648.4 | 0.595248 | ||||||||
\(685\) | −20191.2 | −1.12623 | ||||||||
\(686\) | −1090.10 | −0.0606707 | ||||||||
\(687\) | −2980.83 | −0.165540 | ||||||||
\(688\) | 1967.04 | 0.109001 | ||||||||
\(689\) | −928.495 | −0.0513394 | ||||||||
\(690\) | −538.155 | −0.0296916 | ||||||||
\(691\) | 28019.3 | 1.54255 | 0.771277 | − | 0.636500i | \(-0.219619\pi\) | ||||
0.771277 | + | 0.636500i | \(0.219619\pi\) | |||||||
\(692\) | −14646.4 | −0.804584 | ||||||||
\(693\) | 1605.18 | 0.0879881 | ||||||||
\(694\) | −1247.87 | −0.0682543 | ||||||||
\(695\) | −12482.7 | −0.681289 | ||||||||
\(696\) | −959.411 | −0.0522505 | ||||||||
\(697\) | 13501.1 | 0.733701 | ||||||||
\(698\) | 1655.74 | 0.0897863 | ||||||||
\(699\) | 11010.3 | 0.595775 | ||||||||
\(700\) | −8705.72 | −0.470065 | ||||||||
\(701\) | 18707.2 | 1.00793 | 0.503966 | − | 0.863723i | \(-0.331874\pi\) | ||||
0.503966 | + | 0.863723i | \(0.331874\pi\) | |||||||
\(702\) | 241.868 | 0.0130039 | ||||||||
\(703\) | −26110.4 | −1.40082 | ||||||||
\(704\) | 5525.63 | 0.295817 | ||||||||
\(705\) | −2954.38 | −0.157827 | ||||||||
\(706\) | −463.332 | −0.0246993 | ||||||||
\(707\) | 28918.7 | 1.53833 | ||||||||
\(708\) | 8883.08 | 0.471535 | ||||||||
\(709\) | −30439.1 | −1.61236 | −0.806180 | − | 0.591671i | \(-0.798469\pi\) | ||||
−0.806180 | + | 0.591671i | \(0.798469\pi\) | |||||||
\(710\) | −397.159 | −0.0209931 | ||||||||
\(711\) | 11249.9 | 0.593395 | ||||||||
\(712\) | 1599.85 | 0.0842093 | ||||||||
\(713\) | −1063.90 | −0.0558811 | ||||||||
\(714\) | −422.364 | −0.0221381 | ||||||||
\(715\) | −4709.37 | −0.246323 | ||||||||
\(716\) | 6179.84 | 0.322558 | ||||||||
\(717\) | 12139.0 | 0.632274 | ||||||||
\(718\) | −370.761 | −0.0192712 | ||||||||
\(719\) | 28516.1 | 1.47910 | 0.739548 | − | 0.673103i | \(-0.235039\pi\) | ||||
0.739548 | + | 0.673103i | \(0.235039\pi\) | |||||||
\(720\) | 4332.87 | 0.224273 | ||||||||
\(721\) | −15278.0 | −0.789155 | ||||||||
\(722\) | −2407.71 | −0.124107 | ||||||||
\(723\) | −17553.0 | −0.902909 | ||||||||
\(724\) | −16561.1 | −0.850122 | ||||||||
\(725\) | −8482.49 | −0.434526 | ||||||||
\(726\) | 57.6809 | 0.00294867 | ||||||||
\(727\) | 10135.0 | 0.517037 | 0.258519 | − | 0.966006i | \(-0.416766\pi\) | ||||
0.258519 | + | 0.966006i | \(0.416766\pi\) | |||||||
\(728\) | −2320.27 | −0.118125 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −951.529 | −0.0482434 | ||||||||
\(731\) | 1695.56 | 0.0857898 | ||||||||
\(732\) | 1459.38 | 0.0736888 | ||||||||
\(733\) | 20347.8 | 1.02532 | 0.512662 | − | 0.858590i | \(-0.328659\pi\) | ||||
0.512662 | + | 0.858590i | \(0.328659\pi\) | |||||||
\(734\) | 232.680 | 0.0117008 | ||||||||
\(735\) | 1825.07 | 0.0915899 | ||||||||
\(736\) | 4516.24 | 0.226183 | ||||||||
\(737\) | −748.438 | −0.0374071 | ||||||||
\(738\) | −353.333 | −0.0176238 | ||||||||
\(739\) | 3316.79 | 0.165101 | 0.0825507 | − | 0.996587i | \(-0.473693\pi\) | ||||
0.0825507 | + | 0.996587i | \(0.473693\pi\) | |||||||
\(740\) | −10658.3 | −0.529470 | ||||||||
\(741\) | 25091.9 | 1.24396 | ||||||||
\(742\) | −42.4329 | −0.00209941 | ||||||||
\(743\) | −7664.13 | −0.378425 | −0.189212 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189212 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(744\) | −54.5004 | −0.00268559 | ||||||||
\(745\) | −12295.3 | −0.604653 | ||||||||
\(746\) | 1394.90 | 0.0684599 | ||||||||
\(747\) | −8133.95 | −0.398401 | ||||||||
\(748\) | 4793.60 | 0.234320 | ||||||||
\(749\) | 23401.3 | 1.14161 | ||||||||
\(750\) | −696.259 | −0.0338984 | ||||||||
\(751\) | 16167.4 | 0.785564 | 0.392782 | − | 0.919632i | \(-0.371513\pi\) | ||||
0.392782 | + | 0.919632i | \(0.371513\pi\) | |||||||
\(752\) | 8220.86 | 0.398649 | ||||||||
\(753\) | 1610.22 | 0.0779281 | ||||||||
\(754\) | −1128.60 | −0.0545108 | ||||||||
\(755\) | −16833.3 | −0.811426 | ||||||||
\(756\) | −3491.16 | −0.167953 | ||||||||
\(757\) | −39481.5 | −1.89561 | −0.947806 | − | 0.318849i | \(-0.896704\pi\) | ||||
−0.947806 | + | 0.318849i | \(0.896704\pi\) | |||||||
\(758\) | 2104.36 | 0.100836 | ||||||||
\(759\) | −4905.62 | −0.234602 | ||||||||
\(760\) | −2859.98 | −0.136503 | ||||||||
\(761\) | −7737.32 | −0.368565 | −0.184282 | − | 0.982873i | \(-0.558996\pi\) | ||||
−0.184282 | + | 0.982873i | \(0.558996\pi\) | |||||||
\(762\) | 271.990 | 0.0129306 | ||||||||
\(763\) | 2993.02 | 0.142011 | ||||||||
\(764\) | 8194.48 | 0.388044 | ||||||||
\(765\) | 3734.87 | 0.176516 | ||||||||
\(766\) | 519.898 | 0.0245231 | ||||||||
\(767\) | 20932.2 | 0.985422 | ||||||||
\(768\) | −11902.0 | −0.559214 | ||||||||
\(769\) | 37946.6 | 1.77944 | 0.889720 | − | 0.456507i | \(-0.150900\pi\) | ||||
0.889720 | + | 0.456507i | \(0.150900\pi\) | |||||||
\(770\) | −215.222 | −0.0100728 | ||||||||
\(771\) | 2139.69 | 0.0999468 | ||||||||
\(772\) | 9089.83 | 0.423770 | ||||||||
\(773\) | −16563.3 | −0.770686 | −0.385343 | − | 0.922773i | \(-0.625917\pi\) | ||||
−0.385343 | + | 0.922773i | \(0.625917\pi\) | |||||||
\(774\) | −44.3739 | −0.00206071 | ||||||||
\(775\) | −481.857 | −0.0223339 | ||||||||
\(776\) | 1551.25 | 0.0717610 | ||||||||
\(777\) | 8560.54 | 0.395248 | ||||||||
\(778\) | 1305.01 | 0.0601374 | ||||||||
\(779\) | −36655.5 | −1.68590 | ||||||||
\(780\) | 10242.6 | 0.470183 | ||||||||
\(781\) | −3620.36 | −0.165873 | ||||||||
\(782\) | 1290.80 | 0.0590266 | ||||||||
\(783\) | −3401.64 | −0.155255 | ||||||||
\(784\) | −5078.43 | −0.231343 | ||||||||
\(785\) | −12932.7 | −0.588011 | ||||||||
\(786\) | 81.7714 | 0.00371080 | ||||||||
\(787\) | −5332.98 | −0.241550 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(788\) | −4110.96 | −0.185846 | ||||||||
\(789\) | −16440.8 | −0.741834 | ||||||||
\(790\) | −1508.38 | −0.0679314 | ||||||||
\(791\) | −26520.8 | −1.19212 | ||||||||
\(792\) | −251.301 | −0.0112747 | ||||||||
\(793\) | 3438.90 | 0.153996 | ||||||||
\(794\) | 281.016 | 0.0125603 | ||||||||
\(795\) | 375.225 | 0.0167394 | ||||||||
\(796\) | −5756.51 | −0.256324 | ||||||||
\(797\) | −24647.3 | −1.09542 | −0.547711 | − | 0.836668i | \(-0.684501\pi\) | ||||
−0.547711 | + | 0.836668i | \(0.684501\pi\) | |||||||
\(798\) | 1146.72 | 0.0508690 | ||||||||
\(799\) | 7086.25 | 0.313759 | ||||||||
\(800\) | 2045.48 | 0.0903983 | ||||||||
\(801\) | 5672.35 | 0.250216 | ||||||||
\(802\) | 2508.37 | 0.110441 | ||||||||
\(803\) | −8673.79 | −0.381185 | ||||||||
\(804\) | 1627.80 | 0.0714031 | ||||||||
\(805\) | 18304.1 | 0.801412 | ||||||||
\(806\) | −64.1112 | −0.00280176 | ||||||||
\(807\) | 18748.0 | 0.817794 | ||||||||
\(808\) | −4527.41 | −0.197121 | ||||||||
\(809\) | −24675.6 | −1.07237 | −0.536186 | − | 0.844100i | \(-0.680135\pi\) | ||||
−0.536186 | + | 0.844100i | \(0.680135\pi\) | |||||||
\(810\) | −97.7441 | −0.00423997 | ||||||||
\(811\) | 34447.2 | 1.49150 | 0.745749 | − | 0.666226i | \(-0.232092\pi\) | ||||
0.745749 | + | 0.666226i | \(0.232092\pi\) | |||||||
\(812\) | 16290.3 | 0.704037 | ||||||||
\(813\) | 23567.9 | 1.01668 | ||||||||
\(814\) | 307.616 | 0.0132456 | ||||||||
\(815\) | −10829.7 | −0.465459 | ||||||||
\(816\) | −10392.6 | −0.445852 | ||||||||
\(817\) | −4603.44 | −0.197128 | ||||||||
\(818\) | 1085.19 | 0.0463849 | ||||||||
\(819\) | −8226.61 | −0.350990 | ||||||||
\(820\) | −14962.8 | −0.637225 | ||||||||
\(821\) | 19898.1 | 0.845858 | 0.422929 | − | 0.906163i | \(-0.361002\pi\) | ||||
0.422929 | + | 0.906163i | \(0.361002\pi\) | |||||||
\(822\) | −1267.44 | −0.0537801 | ||||||||
\(823\) | −18636.7 | −0.789348 | −0.394674 | − | 0.918821i | \(-0.629142\pi\) | ||||
−0.394674 | + | 0.918821i | \(0.629142\pi\) | |||||||
\(824\) | 2391.86 | 0.101122 | ||||||||
\(825\) | −2221.84 | −0.0937631 | ||||||||
\(826\) | 956.619 | 0.0402967 | ||||||||
\(827\) | −11898.2 | −0.500292 | −0.250146 | − | 0.968208i | \(-0.580479\pi\) | ||||
−0.250146 | + | 0.968208i | \(0.580479\pi\) | |||||||
\(828\) | 10669.4 | 0.447811 | ||||||||
\(829\) | 43352.8 | 1.81629 | 0.908145 | − | 0.418656i | \(-0.137499\pi\) | ||||
0.908145 | + | 0.418656i | \(0.137499\pi\) | |||||||
\(830\) | 1090.60 | 0.0456087 | ||||||||
\(831\) | 245.327 | 0.0102410 | ||||||||
\(832\) | −28319.1 | −1.18003 | ||||||||
\(833\) | −4377.53 | −0.182080 | ||||||||
\(834\) | −783.564 | −0.0325331 | ||||||||
\(835\) | −3170.03 | −0.131381 | ||||||||
\(836\) | −13014.7 | −0.538422 | ||||||||
\(837\) | −193.234 | −0.00797984 | ||||||||
\(838\) | 1359.21 | 0.0560300 | ||||||||
\(839\) | −33554.0 | −1.38071 | −0.690354 | − | 0.723472i | \(-0.742545\pi\) | ||||
−0.690354 | + | 0.723472i | \(0.742545\pi\) | |||||||
\(840\) | 937.669 | 0.0385151 | ||||||||
\(841\) | −8516.39 | −0.349190 | ||||||||
\(842\) | 228.425 | 0.00934920 | ||||||||
\(843\) | 17570.8 | 0.717876 | ||||||||
\(844\) | −40212.6 | −1.64002 | ||||||||
\(845\) | 7451.33 | 0.303353 | ||||||||
\(846\) | −185.452 | −0.00753662 | ||||||||
\(847\) | −1961.89 | −0.0795882 | ||||||||
\(848\) | −1044.10 | −0.0422813 | ||||||||
\(849\) | 15432.8 | 0.623853 | ||||||||
\(850\) | 584.624 | 0.0235911 | ||||||||
\(851\) | −26162.1 | −1.05385 | ||||||||
\(852\) | 7874.03 | 0.316620 | ||||||||
\(853\) | −43025.0 | −1.72702 | −0.863510 | − | 0.504331i | \(-0.831739\pi\) | ||||
−0.863510 | + | 0.504331i | \(0.831739\pi\) | |||||||
\(854\) | 157.161 | 0.00629733 | ||||||||
\(855\) | −10140.2 | −0.405599 | ||||||||
\(856\) | −3663.62 | −0.146285 | ||||||||
\(857\) | 12607.0 | 0.502504 | 0.251252 | − | 0.967922i | \(-0.419158\pi\) | ||||
0.251252 | + | 0.967922i | \(0.419158\pi\) | |||||||
\(858\) | −295.617 | −0.0117625 | ||||||||
\(859\) | 41961.8 | 1.66673 | 0.833364 | − | 0.552724i | \(-0.186412\pi\) | ||||
0.833364 | + | 0.552724i | \(0.186412\pi\) | |||||||
\(860\) | −1879.13 | −0.0745092 | ||||||||
\(861\) | 12017.8 | 0.475687 | ||||||||
\(862\) | 926.563 | 0.0366112 | ||||||||
\(863\) | 16562.7 | 0.653302 | 0.326651 | − | 0.945145i | \(-0.394080\pi\) | ||||
0.326651 | + | 0.945145i | \(0.394080\pi\) | |||||||
\(864\) | 820.276 | 0.0322990 | ||||||||
\(865\) | 13947.4 | 0.548239 | ||||||||
\(866\) | 1618.09 | 0.0634932 | ||||||||
\(867\) | 5780.70 | 0.226439 | ||||||||
\(868\) | 925.389 | 0.0361864 | ||||||||
\(869\) | −13749.9 | −0.536746 | ||||||||
\(870\) | 456.091 | 0.0177735 | ||||||||
\(871\) | 3835.77 | 0.149220 | ||||||||
\(872\) | −468.577 | −0.0181973 | ||||||||
\(873\) | 5500.02 | 0.213227 | ||||||||
\(874\) | −3504.52 | −0.135632 | ||||||||
\(875\) | 23681.7 | 0.914957 | ||||||||
\(876\) | 18864.9 | 0.727610 | ||||||||
\(877\) | −34908.5 | −1.34410 | −0.672050 | − | 0.740506i | \(-0.734586\pi\) | ||||
−0.672050 | + | 0.740506i | \(0.734586\pi\) | |||||||
\(878\) | 1589.93 | 0.0611134 | ||||||||
\(879\) | 210.980 | 0.00809576 | ||||||||
\(880\) | −5295.73 | −0.202863 | ||||||||
\(881\) | 4822.30 | 0.184413 | 0.0922063 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922063 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(882\) | 114.563 | 0.00437363 | ||||||||
\(883\) | −45848.4 | −1.74736 | −0.873682 | − | 0.486497i | \(-0.838274\pi\) | ||||
−0.873682 | + | 0.486497i | \(0.838274\pi\) | |||||||
\(884\) | −24567.4 | −0.934719 | ||||||||
\(885\) | −8459.16 | −0.321301 | ||||||||
\(886\) | 2247.01 | 0.0852029 | ||||||||
\(887\) | 37278.2 | 1.41114 | 0.705570 | − | 0.708641i | \(-0.250691\pi\) | ||||
0.705570 | + | 0.708641i | \(0.250691\pi\) | |||||||
\(888\) | −1340.21 | −0.0506469 | ||||||||
\(889\) | −9251.13 | −0.349013 | ||||||||
\(890\) | −760.548 | −0.0286445 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 6381.85 | 0.239552 | ||||||||
\(893\) | −19239.2 | −0.720958 | ||||||||
\(894\) | −771.803 | −0.0288735 | ||||||||
\(895\) | −5884.93 | −0.219789 | ||||||||
\(896\) | −5234.92 | −0.195186 | ||||||||
\(897\) | 25141.5 | 0.935843 | ||||||||
\(898\) | −1008.26 | −0.0374679 | ||||||||
\(899\) | 901.660 | 0.0334506 | ||||||||
\(900\) | 4832.35 | 0.178976 | ||||||||
\(901\) | −899.998 | −0.0332778 | ||||||||
\(902\) | 431.851 | 0.0159413 | ||||||||
\(903\) | 1509.28 | 0.0556209 | ||||||||
\(904\) | 4152.00 | 0.152758 | ||||||||
\(905\) | 15770.8 | 0.579268 | ||||||||
\(906\) | −1056.66 | −0.0387474 | ||||||||
\(907\) | −25419.1 | −0.930572 | −0.465286 | − | 0.885160i | \(-0.654049\pi\) | ||||
−0.465286 | + | 0.885160i | \(0.654049\pi\) | |||||||
\(908\) | 37498.7 | 1.37052 | ||||||||
\(909\) | −16052.1 | −0.585716 | ||||||||
\(910\) | 1103.02 | 0.0401811 | ||||||||
\(911\) | 27426.2 | 0.997442 | 0.498721 | − | 0.866762i | \(-0.333803\pi\) | ||||
0.498721 | + | 0.866762i | \(0.333803\pi\) | |||||||
\(912\) | 28216.1 | 1.02448 | ||||||||
\(913\) | 9941.50 | 0.360367 | ||||||||
\(914\) | 2637.78 | 0.0954593 | ||||||||
\(915\) | −1389.73 | −0.0502111 | ||||||||
\(916\) | −7923.79 | −0.285818 | ||||||||
\(917\) | −2781.27 | −0.100159 | ||||||||
\(918\) | 234.445 | 0.00842902 | ||||||||
\(919\) | −25914.7 | −0.930193 | −0.465097 | − | 0.885260i | \(-0.653980\pi\) | ||||
−0.465097 | + | 0.885260i | \(0.653980\pi\) | |||||||
\(920\) | −2865.63 | −0.102692 | ||||||||
\(921\) | 6617.64 | 0.236763 | ||||||||
\(922\) | −361.987 | −0.0129299 | ||||||||
\(923\) | 18554.5 | 0.661677 | ||||||||
\(924\) | 4266.97 | 0.151919 | ||||||||
\(925\) | −11849.2 | −0.421190 | ||||||||
\(926\) | 26.5779 | 0.000943200 0 | ||||||||
\(927\) | 8480.46 | 0.300469 | ||||||||
\(928\) | −3827.55 | −0.135394 | ||||||||
\(929\) | 13045.8 | 0.460731 | 0.230365 | − | 0.973104i | \(-0.426008\pi\) | ||||
0.230365 | + | 0.973104i | \(0.426008\pi\) | |||||||
\(930\) | 25.9087 | 0.000913527 0 | ||||||||
\(931\) | 11885.0 | 0.418384 | ||||||||
\(932\) | 29268.0 | 1.02865 | ||||||||
\(933\) | 6566.08 | 0.230401 | ||||||||
\(934\) | −2094.11 | −0.0733634 | ||||||||
\(935\) | −4564.84 | −0.159664 | ||||||||
\(936\) | 1287.93 | 0.0449757 | ||||||||
\(937\) | −36485.9 | −1.27209 | −0.636043 | − | 0.771654i | \(-0.719430\pi\) | ||||
−0.636043 | + | 0.771654i | \(0.719430\pi\) | |||||||
\(938\) | 175.298 | 0.00610200 | ||||||||
\(939\) | −15516.4 | −0.539251 | ||||||||
\(940\) | −7853.48 | −0.272502 | ||||||||
\(941\) | 2182.63 | 0.0756130 | 0.0378065 | − | 0.999285i | \(-0.487963\pi\) | ||||
0.0378065 | + | 0.999285i | \(0.487963\pi\) | |||||||
\(942\) | −811.813 | −0.0280789 | ||||||||
\(943\) | −36727.9 | −1.26832 | ||||||||
\(944\) | 23538.5 | 0.811559 | ||||||||
\(945\) | 3324.55 | 0.114442 | ||||||||
\(946\) | 54.2347 | 0.00186398 | ||||||||
\(947\) | 51756.9 | 1.77600 | 0.888000 | − | 0.459844i | \(-0.152095\pi\) | ||||
0.888000 | + | 0.459844i | \(0.152095\pi\) | |||||||
\(948\) | 29905.0 | 1.02455 | ||||||||
\(949\) | 44453.5 | 1.52057 | ||||||||
\(950\) | −1587.26 | −0.0542078 | ||||||||
\(951\) | −28596.8 | −0.975096 | ||||||||
\(952\) | −2249.05 | −0.0765675 | ||||||||
\(953\) | −33387.3 | −1.13486 | −0.567430 | − | 0.823422i | \(-0.692062\pi\) | ||||
−0.567430 | + | 0.823422i | \(0.692062\pi\) | |||||||
\(954\) | 23.5536 | 0.000799346 0 | ||||||||
\(955\) | −7803.41 | −0.264411 | ||||||||
\(956\) | 32268.6 | 1.09167 | ||||||||
\(957\) | 4157.56 | 0.140433 | ||||||||
\(958\) | −2081.24 | −0.0701897 | ||||||||
\(959\) | 43109.3 | 1.45159 | ||||||||
\(960\) | 11444.3 | 0.384755 | ||||||||
\(961\) | −29739.8 | −0.998281 | ||||||||
\(962\) | −1576.55 | −0.0528377 | ||||||||
\(963\) | −12989.5 | −0.434664 | ||||||||
\(964\) | −46660.3 | −1.55895 | ||||||||
\(965\) | −8656.04 | −0.288754 | ||||||||
\(966\) | 1148.99 | 0.0382692 | ||||||||
\(967\) | 34807.8 | 1.15754 | 0.578772 | − | 0.815490i | \(-0.303532\pi\) | ||||
0.578772 | + | 0.815490i | \(0.303532\pi\) | |||||||
\(968\) | 307.146 | 0.0101984 | ||||||||
\(969\) | 24321.8 | 0.806326 | ||||||||
\(970\) | −737.441 | −0.0244101 | ||||||||
\(971\) | −15226.5 | −0.503236 | −0.251618 | − | 0.967827i | \(-0.580963\pi\) | ||||
−0.251618 | + | 0.967827i | \(0.580963\pi\) | |||||||
\(972\) | 1937.86 | 0.0639476 | ||||||||
\(973\) | 26651.2 | 0.878107 | ||||||||
\(974\) | 3200.67 | 0.105294 | ||||||||
\(975\) | 11387.0 | 0.374027 | ||||||||
\(976\) | 3867.07 | 0.126826 | ||||||||
\(977\) | 17674.8 | 0.578779 | 0.289389 | − | 0.957211i | \(-0.406548\pi\) | ||||
0.289389 | + | 0.957211i | \(0.406548\pi\) | |||||||
\(978\) | −679.804 | −0.0222267 | ||||||||
\(979\) | −6932.88 | −0.226329 | ||||||||
\(980\) | 4851.48 | 0.158138 | ||||||||
\(981\) | −1661.36 | −0.0540705 | ||||||||
\(982\) | −2730.68 | −0.0887369 | ||||||||
\(983\) | 3847.33 | 0.124833 | 0.0624165 | − | 0.998050i | \(-0.480119\pi\) | ||||
0.0624165 | + | 0.998050i | \(0.480119\pi\) | |||||||
\(984\) | −1881.47 | −0.0609543 | ||||||||
\(985\) | 3914.77 | 0.126635 | ||||||||
\(986\) | −1093.96 | −0.0353335 | ||||||||
\(987\) | 6307.75 | 0.203422 | ||||||||
\(988\) | 66700.6 | 2.14780 | ||||||||
\(989\) | −4612.54 | −0.148302 | ||||||||
\(990\) | 119.465 | 0.00383520 | ||||||||
\(991\) | −13287.6 | −0.425929 | −0.212965 | − | 0.977060i | \(-0.568312\pi\) | ||||
−0.212965 | + | 0.977060i | \(0.568312\pi\) | |||||||
\(992\) | −217.428 | −0.00695901 | ||||||||
\(993\) | 6833.56 | 0.218385 | ||||||||
\(994\) | 847.954 | 0.0270578 | ||||||||
\(995\) | 5481.80 | 0.174658 | ||||||||
\(996\) | −21622.1 | −0.687873 | ||||||||
\(997\) | −17299.1 | −0.549515 | −0.274757 | − | 0.961514i | \(-0.588598\pi\) | ||||
−0.274757 | + | 0.961514i | \(0.588598\pi\) | |||||||
\(998\) | 294.618 | 0.00934466 | ||||||||
\(999\) | −4751.77 | −0.150490 |
(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 | 2013.4.a.b.1.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.b.1.17 | ✓ | 36 | 1.1 | even | 1 | trivial |