Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.4.e.j.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20711 | + | 2.09077i | −0.426777 | + | 0.739199i | −0.996585 | − | 0.0825791i | \(-0.973684\pi\) |
0.569808 | + | 0.821778i | \(0.307018\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.08579 | + | 1.88064i | 0.135723 | + | 0.235080i | ||||
\(5\) | 9.94975 | − | 17.2335i | 0.889932 | − | 1.54141i | 0.0499787 | − | 0.998750i | \(-0.484085\pi\) |
0.839954 | − | 0.542658i | \(-0.182582\pi\) | |||||||
\(6\) | 7.24264 | 0.492799 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −24.5563 | −1.08525 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 24.0208 | + | 41.6053i | 0.759605 | + | 1.31567i | ||||
\(11\) | −11.9706 | − | 20.7336i | −0.328115 | − | 0.568311i | 0.654023 | − | 0.756475i | \(-0.273080\pi\) |
−0.982138 | + | 0.188163i | \(0.939747\pi\) | |||||||
\(12\) | 3.25736 | − | 5.64191i | 0.0783599 | − | 0.135723i | ||||
\(13\) | −87.3553 | −1.86369 | −0.931847 | − | 0.362852i | \(-0.881803\pi\) | ||||
−0.931847 | + | 0.362852i | \(0.881803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −59.6985 | −1.02761 | ||||||||
\(16\) | 20.9558 | − | 36.2966i | 0.327435 | − | 0.567134i | ||||
\(17\) | −2.81981 | − | 4.88405i | −0.0402296 | − | 0.0696797i | 0.845210 | − | 0.534435i | \(-0.179476\pi\) |
−0.885439 | + | 0.464755i | \(0.846142\pi\) | |||||||
\(18\) | −10.8640 | − | 18.8169i | −0.142259 | − | 0.246400i | ||||
\(19\) | 32.4437 | − | 56.1941i | 0.391741 | − | 0.678516i | −0.600938 | − | 0.799296i | \(-0.705206\pi\) |
0.992679 | + | 0.120780i | \(0.0385395\pi\) | |||||||
\(20\) | 43.2132 | 0.483138 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 57.7990 | 0.560127 | ||||||||
\(23\) | 12.7990 | − | 22.1685i | 0.116034 | − | 0.200976i | −0.802159 | − | 0.597111i | \(-0.796315\pi\) |
0.918192 | + | 0.396135i | \(0.129649\pi\) | |||||||
\(24\) | 36.8345 | + | 63.7993i | 0.313284 | + | 0.542624i | ||||
\(25\) | −135.495 | − | 234.684i | −1.08396 | − | 1.87747i | ||||
\(26\) | 105.447 | − | 182.640i | 0.795381 | − | 1.37764i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 60.3188 | 0.386238 | 0.193119 | − | 0.981175i | \(-0.438140\pi\) | ||||
0.193119 | + | 0.981175i | \(0.438140\pi\) | |||||||
\(30\) | 72.0624 | − | 124.816i | 0.438558 | − | 0.759605i | ||||
\(31\) | −61.3553 | − | 106.271i | −0.355476 | − | 0.615702i | 0.631724 | − | 0.775194i | \(-0.282348\pi\) |
−0.987199 | + | 0.159492i | \(0.949014\pi\) | |||||||
\(32\) | −47.6335 | − | 82.5037i | −0.263140 | − | 0.455773i | ||||
\(33\) | −35.9117 | + | 62.2009i | −0.189437 | + | 0.328115i | ||||
\(34\) | 13.6152 | 0.0686762 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19.5442 | −0.0904822 | ||||||||
\(37\) | 28.0589 | − | 48.5994i | 0.124672 | − | 0.215938i | −0.796933 | − | 0.604068i | \(-0.793546\pi\) |
0.921605 | + | 0.388130i | \(0.126879\pi\) | |||||||
\(38\) | 78.3259 | + | 135.664i | 0.334372 | + | 0.579149i | ||||
\(39\) | 131.033 | + | 226.956i | 0.538002 | + | 0.931847i | ||||
\(40\) | −244.329 | + | 423.191i | −0.965797 | + | 1.67281i | ||||
\(41\) | 299.713 | 1.14164 | 0.570820 | − | 0.821075i | \(-0.306625\pi\) | ||||
0.570820 | + | 0.821075i | \(0.306625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −501.421 | −1.77828 | −0.889140 | − | 0.457635i | \(-0.848697\pi\) | ||||
−0.889140 | + | 0.457635i | \(0.848697\pi\) | |||||||
\(44\) | 25.9949 | − | 45.0246i | 0.0890656 | − | 0.154266i | ||||
\(45\) | 89.5477 | + | 155.101i | 0.296644 | + | 0.513803i | ||||
\(46\) | 30.8995 | + | 53.5195i | 0.0990409 | + | 0.171544i | ||||
\(47\) | 152.777 | − | 264.617i | 0.474144 | − | 0.821242i | −0.525418 | − | 0.850844i | \(-0.676091\pi\) |
0.999562 | + | 0.0296028i | \(0.00942425\pi\) | |||||||
\(48\) | −125.735 | −0.378089 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 654.227 | 1.85043 | ||||||||
\(51\) | −8.45942 | + | 14.6521i | −0.0232266 | + | 0.0402296i | ||||
\(52\) | −94.8492 | − | 164.284i | −0.252947 | − | 0.438116i | ||||
\(53\) | 187.558 | + | 324.861i | 0.486097 | + | 0.841944i | 0.999872 | − | 0.0159802i | \(-0.00508689\pi\) |
−0.513775 | + | 0.857925i | \(0.671754\pi\) | |||||||
\(54\) | −32.5919 | + | 56.4508i | −0.0821332 | + | 0.142259i | ||||
\(55\) | −476.416 | −1.16800 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −194.662 | −0.452344 | ||||||||
\(58\) | −72.8112 | + | 126.113i | −0.164838 | + | 0.285507i | ||||
\(59\) | −313.806 | − | 543.528i | −0.692442 | − | 1.19934i | −0.971035 | − | 0.238936i | \(-0.923202\pi\) |
0.278593 | − | 0.960409i | \(-0.410132\pi\) | |||||||
\(60\) | −64.8198 | − | 112.271i | −0.139470 | − | 0.241569i | ||||
\(61\) | 1.87868 | − | 3.25397i | 0.00394328 | − | 0.00682997i | −0.864047 | − | 0.503411i | \(-0.832078\pi\) |
0.867990 | + | 0.496581i | \(0.165411\pi\) | |||||||
\(62\) | 296.250 | 0.606835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 565.288 | 1.10408 | ||||||||
\(65\) | −869.164 | + | 1505.44i | −1.65856 | + | 2.87271i | ||||
\(66\) | −86.6985 | − | 150.166i | −0.161695 | − | 0.280063i | ||||
\(67\) | 406.524 | + | 704.120i | 0.741266 | + | 1.28391i | 0.951919 | + | 0.306349i | \(0.0991075\pi\) |
−0.210653 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(68\) | 6.12341 | − | 10.6061i | 0.0109202 | − | 0.0189143i | ||||
\(69\) | −76.7939 | −0.133984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 165.902 | 0.277310 | 0.138655 | − | 0.990341i | \(-0.455722\pi\) | ||||
0.138655 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(72\) | 110.504 | − | 191.398i | 0.180875 | − | 0.313284i | ||||
\(73\) | 309.550 | + | 536.156i | 0.496302 | + | 0.859621i | 0.999991 | − | 0.00426452i | \(-0.00135744\pi\) |
−0.503689 | + | 0.863885i | \(0.668024\pi\) | |||||||
\(74\) | 67.7401 | + | 117.329i | 0.106414 | + | 0.184314i | ||||
\(75\) | −406.485 | + | 704.052i | −0.625824 | + | 1.08396i | ||||
\(76\) | 140.908 | 0.212674 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −632.683 | −0.918427 | ||||||||
\(79\) | 69.1228 | − | 119.724i | 0.0984421 | − | 0.170507i | −0.812598 | − | 0.582825i | \(-0.801947\pi\) |
0.911040 | + | 0.412318i | \(0.135281\pi\) | |||||||
\(80\) | −417.011 | − | 722.284i | −0.582790 | − | 1.00942i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −361.785 | + | 626.631i | −0.487226 | + | 0.843900i | ||||
\(83\) | −621.137 | −0.821430 | −0.410715 | − | 0.911764i | \(-0.634721\pi\) | ||||
−0.410715 | + | 0.911764i | \(0.634721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.225 | −0.143207 | ||||||||
\(86\) | 605.269 | − | 1048.36i | 0.758928 | − | 1.31450i | ||||
\(87\) | −90.4781 | − | 156.713i | −0.111497 | − | 0.193119i | ||||
\(88\) | 293.953 | + | 509.142i | 0.356086 | + | 0.616758i | ||||
\(89\) | 142.709 | − | 247.180i | 0.169968 | − | 0.294393i | −0.768440 | − | 0.639921i | \(-0.778967\pi\) |
0.938408 | + | 0.345528i | \(0.112300\pi\) | |||||||
\(90\) | −432.375 | −0.506403 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 55.5879 | 0.0629939 | ||||||||
\(93\) | −184.066 | + | 318.812i | −0.205234 | + | 0.355476i | ||||
\(94\) | 368.836 | + | 638.842i | 0.404707 | + | 0.700974i | ||||
\(95\) | −645.612 | − | 1118.23i | −0.697247 | − | 1.20767i | ||||
\(96\) | −142.901 | + | 247.511i | −0.151924 | + | 0.263140i | ||||
\(97\) | 603.114 | 0.631309 | 0.315654 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315654 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 215.470 | 0.218743 | ||||||||
\(100\) | 294.237 | − | 509.634i | 0.294237 | − | 0.509634i | ||||
\(101\) | 228.605 | + | 395.955i | 0.225218 | + | 0.390089i | 0.956385 | − | 0.292110i | \(-0.0943573\pi\) |
−0.731167 | + | 0.682199i | \(0.761024\pi\) | |||||||
\(102\) | −20.4228 | − | 35.3734i | −0.0198251 | − | 0.0343381i | ||||
\(103\) | 393.022 | − | 680.735i | 0.375977 | − | 0.651211i | −0.614496 | − | 0.788920i | \(-0.710640\pi\) |
0.990473 | + | 0.137709i | \(0.0439738\pi\) | |||||||
\(104\) | 2145.13 | 2.02257 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −905.612 | −0.829819 | ||||||||
\(107\) | 98.2304 | − | 170.140i | 0.0887504 | − | 0.153720i | −0.818233 | − | 0.574887i | \(-0.805046\pi\) |
0.906983 | + | 0.421167i | \(0.138379\pi\) | |||||||
\(108\) | 29.3162 | + | 50.7772i | 0.0261200 | + | 0.0452411i | ||||
\(109\) | 153.172 | + | 265.301i | 0.134598 | + | 0.233130i | 0.925444 | − | 0.378885i | \(-0.123692\pi\) |
−0.790846 | + | 0.612015i | \(0.790359\pi\) | |||||||
\(110\) | 575.085 | − | 996.077i | 0.498475 | − | 0.863384i | ||||
\(111\) | −168.353 | −0.143958 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1997.63 | 1.66302 | 0.831508 | − | 0.555512i | \(-0.187478\pi\) | ||||
0.831508 | + | 0.555512i | \(0.187478\pi\) | |||||||
\(114\) | 234.978 | − | 406.993i | 0.193050 | − | 0.334372i | ||||
\(115\) | −254.693 | − | 441.142i | −0.206524 | − | 0.357710i | ||||
\(116\) | 65.4933 | + | 113.438i | 0.0524215 | + | 0.0907968i | ||||
\(117\) | 393.099 | − | 680.867i | 0.310616 | − | 0.538002i | ||||
\(118\) | 1515.19 | 1.18207 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1465.98 | 1.11521 | ||||||||
\(121\) | 378.911 | − | 656.294i | 0.284682 | − | 0.493083i | ||||
\(122\) | 4.53553 | + | 7.85578i | 0.00336580 | + | 0.00582974i | ||||
\(123\) | −449.569 | − | 778.677i | −0.329563 | − | 0.570820i | ||||
\(124\) | 133.238 | − | 230.774i | 0.0964927 | − | 0.167130i | ||||
\(125\) | −2905.13 | −2.07874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2311.40 | −1.61499 | −0.807494 | − | 0.589875i | \(-0.799177\pi\) | ||||
−0.807494 | + | 0.589875i | \(0.799177\pi\) | |||||||
\(128\) | −301.295 | + | 521.859i | −0.208055 | + | 0.360361i | ||||
\(129\) | 752.132 | + | 1302.73i | 0.513345 | + | 0.889140i | ||||
\(130\) | −2098.35 | − | 3634.44i | −1.41567 | − | 2.45201i | ||||
\(131\) | −77.5088 | + | 134.249i | −0.0516945 | + | 0.0895374i | −0.890715 | − | 0.454563i | \(-0.849796\pi\) |
0.839020 | + | 0.544100i | \(0.183129\pi\) | |||||||
\(132\) | −155.970 | −0.102844 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1962.87 | −1.26542 | ||||||||
\(135\) | 268.643 | − | 465.304i | 0.171268 | − | 0.296644i | ||||
\(136\) | 69.2441 | + | 119.934i | 0.0436591 | + | 0.0756197i | ||||
\(137\) | −258.468 | − | 447.680i | −0.161186 | − | 0.279181i | 0.774109 | − | 0.633053i | \(-0.218198\pi\) |
−0.935294 | + | 0.353871i | \(0.884865\pi\) | |||||||
\(138\) | 92.6985 | − | 160.558i | 0.0571813 | − | 0.0990409i | ||||
\(139\) | −958.067 | −0.584620 | −0.292310 | − | 0.956324i | \(-0.594424\pi\) | ||||
−0.292310 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −916.660 | −0.547494 | ||||||||
\(142\) | −200.262 | + | 346.864i | −0.118349 | + | 0.204987i | ||||
\(143\) | 1045.69 | + | 1811.19i | 0.611505 | + | 1.05916i | ||||
\(144\) | 188.603 | + | 326.669i | 0.109145 | + | 0.189045i | ||||
\(145\) | 600.156 | − | 1039.50i | 0.343726 | − | 0.595351i | ||||
\(146\) | −1494.64 | −0.847241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 121.864 | 0.0676834 | ||||||||
\(149\) | 885.313 | − | 1533.41i | 0.486763 | − | 0.843098i | −0.513121 | − | 0.858316i | \(-0.671511\pi\) |
0.999884 | + | 0.0152182i | \(0.00484428\pi\) | |||||||
\(150\) | −981.341 | − | 1699.73i | −0.534175 | − | 0.925217i | ||||
\(151\) | 1270.12 | + | 2199.91i | 0.684508 | + | 1.18560i | 0.973591 | + | 0.228299i | \(0.0733163\pi\) |
−0.289083 | + | 0.957304i | \(0.593350\pi\) | |||||||
\(152\) | −796.698 | + | 1379.92i | −0.425136 | + | 0.736358i | ||||
\(153\) | 50.7565 | 0.0268197 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2441.88 | −1.26540 | ||||||||
\(156\) | −284.548 | + | 492.851i | −0.146039 | + | 0.252947i | ||||
\(157\) | −541.672 | − | 938.203i | −0.275351 | − | 0.476922i | 0.694873 | − | 0.719133i | \(-0.255461\pi\) |
−0.970224 | + | 0.242211i | \(0.922127\pi\) | |||||||
\(158\) | 166.877 | + | 289.040i | 0.0840256 | + | 0.145537i | ||||
\(159\) | 562.675 | − | 974.582i | 0.280648 | − | 0.486097i | ||||
\(160\) | −1895.77 | −0.936709 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 195.551 | 0.0948393 | ||||||||
\(163\) | −1484.36 | + | 2570.99i | −0.713277 | + | 1.23543i | 0.250343 | + | 0.968157i | \(0.419457\pi\) |
−0.963620 | + | 0.267275i | \(0.913877\pi\) | |||||||
\(164\) | 325.424 | + | 563.651i | 0.154947 | + | 0.268377i | ||||
\(165\) | 714.624 | + | 1237.77i | 0.337172 | + | 0.584000i | ||||
\(166\) | 749.779 | − | 1298.65i | 0.350567 | − | 0.607200i | ||||
\(167\) | 2091.53 | 0.969149 | 0.484574 | − | 0.874750i | \(-0.338975\pi\) | ||||
0.484574 | + | 0.874750i | \(0.338975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5433.96 | 2.47335 | ||||||||
\(170\) | 135.468 | − | 234.638i | 0.0611172 | − | 0.105858i | ||||
\(171\) | 291.993 | + | 505.746i | 0.130580 | + | 0.226172i | ||||
\(172\) | −544.437 | − | 942.992i | −0.241354 | − | 0.418037i | ||||
\(173\) | −235.074 | + | 407.160i | −0.103308 | + | 0.178935i | −0.913046 | − | 0.407857i | \(-0.866276\pi\) |
0.809738 | + | 0.586792i | \(0.199609\pi\) | |||||||
\(174\) | 436.867 | 0.190338 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1003.41 | −0.429745 | ||||||||
\(177\) | −941.418 | + | 1630.58i | −0.399782 | + | 0.692442i | ||||
\(178\) | 344.530 | + | 596.744i | 0.145077 | + | 0.251280i | ||||
\(179\) | −528.230 | − | 914.922i | −0.220569 | − | 0.382036i | 0.734412 | − | 0.678704i | \(-0.237458\pi\) |
−0.954981 | + | 0.296668i | \(0.904125\pi\) | |||||||
\(180\) | −194.459 | + | 336.814i | −0.0805231 | + | 0.139470i | ||||
\(181\) | 406.470 | 0.166921 | 0.0834605 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834605 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.2721 | −0.00455331 | ||||||||
\(184\) | −314.296 | + | 544.377i | −0.125925 | + | 0.218109i | ||||
\(185\) | −558.357 | − | 967.103i | −0.221899 | − | 0.384340i | ||||
\(186\) | −444.375 | − | 769.680i | −0.175178 | − | 0.303417i | ||||
\(187\) | −67.5093 | + | 116.930i | −0.0263998 | + | 0.0457259i | ||||
\(188\) | 663.531 | 0.257410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3117.29 | 1.19027 | ||||||||
\(191\) | −89.7048 | + | 155.373i | −0.0339833 | + | 0.0588608i | −0.882517 | − | 0.470281i | \(-0.844153\pi\) |
0.848534 | + | 0.529142i | \(0.177486\pi\) | |||||||
\(192\) | −847.933 | − | 1468.66i | −0.318720 | − | 0.552040i | ||||
\(193\) | 1194.18 | + | 2068.39i | 0.445385 | + | 0.771429i | 0.998079 | − | 0.0619551i | \(-0.0197336\pi\) |
−0.552694 | + | 0.833384i | \(0.686400\pi\) | |||||||
\(194\) | −728.023 | + | 1260.97i | −0.269428 | + | 0.466663i | ||||
\(195\) | 5214.98 | 1.91514 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2665.35 | −0.963952 | −0.481976 | − | 0.876184i | \(-0.660081\pi\) | ||||
−0.481976 | + | 0.876184i | \(0.660081\pi\) | |||||||
\(198\) | −260.095 | + | 450.499i | −0.0933544 | + | 0.161695i | ||||
\(199\) | −671.153 | − | 1162.47i | −0.239079 | − | 0.414098i | 0.721371 | − | 0.692549i | \(-0.243512\pi\) |
−0.960450 | + | 0.278451i | \(0.910179\pi\) | |||||||
\(200\) | 3327.26 | + | 5762.99i | 1.17636 | + | 2.03752i | ||||
\(201\) | 1219.57 | − | 2112.36i | 0.427970 | − | 0.741266i | ||||
\(202\) | −1103.80 | −0.384471 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −36.7405 | −0.0126095 | ||||||||
\(205\) | 2982.07 | − | 5165.09i | 1.01598 | − | 1.75973i | ||||
\(206\) | 948.840 | + | 1643.44i | 0.320916 | + | 0.555844i | ||||
\(207\) | 115.191 | + | 199.517i | 0.0386779 | + | 0.0669921i | ||||
\(208\) | −1830.60 | + | 3170.70i | −0.610239 | + | 1.05696i | ||||
\(209\) | −1553.48 | −0.514144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 628.442 | 0.205042 | 0.102521 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102521 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(212\) | −407.297 | + | 705.459i | −0.131949 | + | 0.228543i | ||||
\(213\) | −248.854 | − | 431.027i | −0.0800525 | − | 0.138655i | ||||
\(214\) | 237.149 | + | 410.755i | 0.0757532 | + | 0.131208i | ||||
\(215\) | −4989.02 | + | 8641.23i | −1.58255 | + | 2.74106i | ||||
\(216\) | −663.021 | −0.208856 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −739.578 | −0.229773 | ||||||||
\(219\) | 928.649 | − | 1608.47i | 0.286540 | − | 0.496302i | ||||
\(220\) | −517.286 | − | 895.966i | −0.158525 | − | 0.274573i | ||||
\(221\) | 246.325 | + | 426.647i | 0.0749756 | + | 0.129862i | ||||
\(222\) | 203.220 | − | 351.988i | 0.0614381 | − | 0.106414i | ||||
\(223\) | 969.970 | 0.291273 | 0.145637 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145637 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2438.91 | 0.722640 | ||||||||
\(226\) | −2411.35 | + | 4176.58i | −0.709737 | + | 1.22930i | ||||
\(227\) | −2374.32 | − | 4112.44i | −0.694225 | − | 1.20243i | −0.970441 | − | 0.241338i | \(-0.922414\pi\) |
0.276216 | − | 0.961096i | \(-0.410920\pi\) | |||||||
\(228\) | −211.361 | − | 366.088i | −0.0613936 | − | 0.106337i | ||||
\(229\) | −2401.00 | + | 4158.65i | −0.692848 | + | 1.20005i | 0.278052 | + | 0.960566i | \(0.410311\pi\) |
−0.970901 | + | 0.239482i | \(0.923022\pi\) | |||||||
\(230\) | 1229.77 | 0.352559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1481.21 | −0.419164 | ||||||||
\(233\) | 1577.64 | − | 2732.56i | 0.443583 | − | 0.768309i | −0.554369 | − | 0.832271i | \(-0.687040\pi\) |
0.997952 | + | 0.0639623i | \(0.0203737\pi\) | |||||||
\(234\) | 949.025 | + | 1643.76i | 0.265127 | + | 0.459213i | ||||
\(235\) | −3040.18 | − | 5265.74i | −0.843912 | − | 1.46170i | ||||
\(236\) | 681.453 | − | 1180.31i | 0.187961 | − | 0.325558i | ||||
\(237\) | −414.737 | −0.113671 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4241.93 | 1.14806 | 0.574032 | − | 0.818833i | \(-0.305378\pi\) | ||||
0.574032 | + | 0.818833i | \(0.305378\pi\) | |||||||
\(240\) | −1251.03 | + | 2166.85i | −0.336474 | + | 0.582790i | ||||
\(241\) | −2171.49 | − | 3761.14i | −0.580407 | − | 1.00530i | −0.995431 | − | 0.0954844i | \(-0.969560\pi\) |
0.415024 | − | 0.909811i | \(-0.363773\pi\) | |||||||
\(242\) | 914.773 | + | 1584.43i | 0.242991 | + | 0.420873i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 8.15938 | 0.00214078 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2170.71 | 0.562600 | ||||||||
\(247\) | −2834.13 | + | 4908.85i | −0.730086 | + | 1.26455i | ||||
\(248\) | 1506.66 | + | 2609.62i | 0.385779 | + | 0.668189i | ||||
\(249\) | 931.706 | + | 1613.76i | 0.237126 | + | 0.410715i | ||||
\(250\) | 3506.80 | − | 6073.95i | 0.887157 | − | 1.53660i | ||||
\(251\) | −3003.01 | −0.755172 | −0.377586 | − | 0.925974i | \(-0.623246\pi\) | ||||
−0.377586 | + | 0.925974i | \(0.623246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −612.844 | −0.152289 | ||||||||
\(254\) | 2790.11 | − | 4832.61i | 0.689239 | − | 1.19380i | ||||
\(255\) | 168.338 | + | 291.570i | 0.0413402 | + | 0.0716033i | ||||
\(256\) | 1533.76 | + | 2656.55i | 0.374454 | + | 0.648573i | ||||
\(257\) | 2234.42 | − | 3870.13i | 0.542332 | − | 0.939347i | −0.456437 | − | 0.889756i | \(-0.650875\pi\) |
0.998770 | − | 0.0495916i | \(-0.0157920\pi\) | |||||||
\(258\) | −3631.61 | −0.876335 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3774.90 | −0.900422 | ||||||||
\(261\) | −271.434 | + | 470.138i | −0.0643731 | + | 0.111497i | ||||
\(262\) | −187.123 | − | 324.106i | −0.0441240 | − | 0.0764250i | ||||
\(263\) | −3080.07 | − | 5334.83i | −0.722148 | − | 1.25080i | −0.960137 | − | 0.279530i | \(-0.909821\pi\) |
0.237989 | − | 0.971268i | \(-0.423512\pi\) | |||||||
\(264\) | 881.860 | − | 1527.43i | 0.205586 | − | 0.356086i | ||||
\(265\) | 7464.64 | 1.73037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −856.255 | −0.196262 | ||||||||
\(268\) | −882.796 | + | 1529.05i | −0.201214 | + | 0.348513i | ||||
\(269\) | 2494.45 | + | 4320.52i | 0.565388 | + | 0.979281i | 0.997013 | + | 0.0772281i | \(0.0246070\pi\) |
−0.431625 | + | 0.902053i | \(0.642060\pi\) | |||||||
\(270\) | 648.562 | + | 1123.34i | 0.146186 | + | 0.253202i | ||||
\(271\) | 2216.86 | − | 3839.72i | 0.496918 | − | 0.860688i | −0.503075 | − | 0.864243i | \(-0.667798\pi\) |
0.999994 | + | 0.00355459i | \(0.00113146\pi\) | |||||||
\(272\) | −236.366 | −0.0526903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1247.99 | 0.275161 | ||||||||
\(275\) | −3243.90 | + | 5618.60i | −0.711326 | + | 1.23205i | ||||
\(276\) | −83.3818 | − | 144.422i | −0.0181848 | − | 0.0314969i | ||||
\(277\) | −556.184 | − | 963.339i | −0.120642 | − | 0.208958i | 0.799379 | − | 0.600827i | \(-0.205162\pi\) |
−0.920021 | + | 0.391869i | \(0.871829\pi\) | |||||||
\(278\) | 1156.49 | − | 2003.10i | 0.249502 | − | 0.432151i | ||||
\(279\) | 1104.40 | 0.236984 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2813.22 | 0.597233 | 0.298616 | − | 0.954373i | \(-0.403475\pi\) | ||||
0.298616 | + | 0.954373i | \(0.403475\pi\) | |||||||
\(282\) | 1106.51 | − | 1916.53i | 0.233658 | − | 0.404707i | ||||
\(283\) | 1573.77 | + | 2725.85i | 0.330569 | + | 0.572562i | 0.982623 | − | 0.185610i | \(-0.0594262\pi\) |
−0.652055 | + | 0.758172i | \(0.726093\pi\) | |||||||
\(284\) | 180.135 | + | 312.002i | 0.0376374 | + | 0.0651899i | ||||
\(285\) | −1936.84 | + | 3354.70i | −0.402555 | + | 0.697247i | ||||
\(286\) | −5049.05 | −1.04390 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 857.403 | 0.175427 | ||||||||
\(289\) | 2440.60 | − | 4227.24i | 0.496763 | − | 0.860419i | ||||
\(290\) | 1448.91 | + | 2509.58i | 0.293389 | + | 0.508164i | ||||
\(291\) | −904.671 | − | 1566.94i | −0.182243 | − | 0.315654i | ||||
\(292\) | −672.210 | + | 1164.30i | −0.134720 | + | 0.233341i | ||||
\(293\) | −9143.04 | −1.82301 | −0.911505 | − | 0.411289i | \(-0.865079\pi\) | ||||
−0.911505 | + | 0.411289i | \(0.865079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12489.2 | −2.46491 | ||||||||
\(296\) | −689.024 | + | 1193.42i | −0.135300 | + | 0.234346i | ||||
\(297\) | −323.205 | − | 559.808i | −0.0631457 | − | 0.109372i | ||||
\(298\) | 2137.33 | + | 3701.97i | 0.415478 | + | 0.719629i | ||||
\(299\) | −1118.06 | + | 1936.54i | −0.216251 | + | 0.374558i | ||||
\(300\) | −1765.42 | −0.339756 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6132.67 | −1.16853 | ||||||||
\(303\) | 685.814 | − | 1187.86i | 0.130030 | − | 0.225218i | ||||
\(304\) | −1359.77 | − | 2355.19i | −0.256540 | − | 0.444340i | ||||
\(305\) | −37.3848 | − | 64.7523i | −0.00701851 | − | 0.0121564i | ||||
\(306\) | −61.2685 | + | 106.120i | −0.0114460 | + | 0.0198251i | ||||
\(307\) | 4648.90 | 0.864257 | 0.432129 | − | 0.901812i | \(-0.357763\pi\) | ||||
0.432129 | + | 0.901812i | \(0.357763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2358.13 | −0.434141 | ||||||||
\(310\) | 2947.61 | − | 5105.41i | 0.540042 | − | 0.935380i | ||||
\(311\) | −3208.59 | − | 5557.44i | −0.585024 | − | 1.01329i | −0.994872 | − | 0.101138i | \(-0.967752\pi\) |
0.409849 | − | 0.912154i | \(-0.365582\pi\) | |||||||
\(312\) | −3217.69 | − | 5573.21i | −0.583865 | − | 1.01128i | ||||
\(313\) | 2934.11 | − | 5082.02i | 0.529858 | − | 0.917741i | −0.469535 | − | 0.882914i | \(-0.655578\pi\) |
0.999393 | − | 0.0348275i | \(-0.0110882\pi\) | |||||||
\(314\) | 2615.42 | 0.470054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 300.210 | 0.0534435 | ||||||||
\(317\) | 1987.26 | − | 3442.04i | 0.352100 | − | 0.609855i | −0.634517 | − | 0.772909i | \(-0.718801\pi\) |
0.986617 | + | 0.163054i | \(0.0521344\pi\) | |||||||
\(318\) | 1358.42 | + | 2352.85i | 0.239548 | + | 0.414910i | ||||
\(319\) | −722.049 | − | 1250.63i | −0.126730 | − | 0.219504i | ||||
\(320\) | 5624.48 | − | 9741.88i | 0.982556 | − | 1.70184i | ||||
\(321\) | −589.383 | −0.102480 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −365.939 | −0.0630384 | ||||||||
\(324\) | 87.9487 | − | 152.332i | 0.0150804 | − | 0.0261200i | ||||
\(325\) | 11836.2 | + | 20500.9i | 2.02017 | + | 3.49903i | ||||
\(326\) | −3583.57 | − | 6206.92i | −0.608820 | − | 1.05451i | ||||
\(327\) | 459.515 | − | 795.903i | 0.0777102 | − | 0.134598i | ||||
\(328\) | −7359.85 | −1.23896 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3450.51 | −0.575589 | ||||||||
\(331\) | 4456.41 | − | 7718.73i | 0.740020 | − | 1.28175i | −0.212466 | − | 0.977168i | \(-0.568149\pi\) |
0.952486 | − | 0.304583i | \(-0.0985172\pi\) | |||||||
\(332\) | −674.422 | − | 1168.13i | −0.111487 | − | 0.193101i | ||||
\(333\) | 252.530 | + | 437.395i | 0.0415572 | + | 0.0719792i | ||||
\(334\) | −2524.71 | + | 4372.92i | −0.413610 | + | 0.716394i | ||||
\(335\) | 16179.2 | 2.63871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3977.06 | 0.642862 | 0.321431 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321431 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(338\) | −6559.36 | + | 11361.2i | −1.05557 | + | 1.82830i | ||||
\(339\) | −2996.44 | − | 5189.99i | −0.480072 | − | 0.831508i | ||||
\(340\) | −121.853 | − | 211.055i | −0.0194365 | − | 0.0336649i | ||||
\(341\) | −1468.92 | + | 2544.24i | −0.233273 | + | 0.404042i | ||||
\(342\) | −1409.87 | −0.222915 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12313.1 | 1.92987 | ||||||||
\(345\) | −764.080 | + | 1323.43i | −0.119237 | + | 0.206524i | ||||
\(346\) | −567.518 | − | 982.971i | −0.0881791 | − | 0.152731i | ||||
\(347\) | −3413.21 | − | 5911.86i | −0.528043 | − | 0.914597i | −0.999466 | − | 0.0326898i | \(-0.989593\pi\) |
0.471423 | − | 0.881907i | \(-0.343741\pi\) | |||||||
\(348\) | 196.480 | − | 340.313i | 0.0302656 | − | 0.0524215i | ||||
\(349\) | 807.342 | 0.123828 | 0.0619141 | − | 0.998081i | \(-0.480280\pi\) | ||||
0.0619141 | + | 0.998081i | \(0.480280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2358.59 | −0.358668 | ||||||||
\(352\) | −1140.40 | + | 1975.23i | −0.172680 | + | 0.299091i | ||||
\(353\) | −3959.60 | − | 6858.23i | −0.597020 | − | 1.03407i | −0.993258 | − | 0.115922i | \(-0.963018\pi\) |
0.396238 | − | 0.918148i | \(-0.370316\pi\) | |||||||
\(354\) | −2272.79 | − | 3936.58i | −0.341235 | − | 0.591036i | ||||
\(355\) | 1650.69 | − | 2859.07i | 0.246787 | − | 0.427448i | ||||
\(356\) | 619.807 | 0.0922744 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2550.52 | 0.376534 | ||||||||
\(359\) | 4409.61 | − | 7637.66i | 0.648273 | − | 1.12284i | −0.335262 | − | 0.942125i | \(-0.608825\pi\) |
0.983535 | − | 0.180717i | \(-0.0578419\pi\) | |||||||
\(360\) | −2198.97 | − | 3808.72i | −0.321932 | − | 0.557603i | ||||
\(361\) | 1324.32 | + | 2293.79i | 0.193078 | + | 0.334420i | ||||
\(362\) | −490.653 | + | 849.836i | −0.0712380 | + | 0.123388i | ||||
\(363\) | −2273.47 | −0.328722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12319.8 | 1.76670 | ||||||||
\(366\) | 13.6066 | − | 23.5673i | 0.00194325 | − | 0.00336580i | ||||
\(367\) | −5580.89 | − | 9666.39i | −0.793788 | − | 1.37488i | −0.923606 | − | 0.383344i | \(-0.874772\pi\) |
0.129817 | − | 0.991538i | \(-0.458561\pi\) | |||||||
\(368\) | −536.427 | − | 929.119i | −0.0759870 | − | 0.131613i | ||||
\(369\) | −1348.71 | + | 2336.03i | −0.190273 | + | 0.329563i | ||||
\(370\) | 2695.99 | 0.378805 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −799.426 | −0.111420 | ||||||||
\(373\) | −1363.93 | + | 2362.39i | −0.189334 | + | 0.327936i | −0.945028 | − | 0.326988i | \(-0.893966\pi\) |
0.755694 | + | 0.654924i | \(0.227300\pi\) | |||||||
\(374\) | −162.982 | − | 282.293i | −0.0225337 | − | 0.0390295i | ||||
\(375\) | 4357.69 | + | 7547.74i | 0.600080 | + | 1.03937i | ||||
\(376\) | −3751.64 | + | 6498.03i | −0.514564 | + | 0.891250i | ||||
\(377\) | −5269.17 | −0.719830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4086.49 | 0.553849 | 0.276924 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276924 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(380\) | 1401.99 | − | 2428.32i | 0.189265 | − | 0.327817i | ||||
\(381\) | 3467.10 | + | 6005.19i | 0.466207 | + | 0.807494i | ||||
\(382\) | −216.566 | − | 375.104i | −0.0290066 | − | 0.0502408i | ||||
\(383\) | 6516.47 | − | 11286.9i | 0.869389 | − | 1.50583i | 0.00676631 | − | 0.999977i | \(-0.497846\pi\) |
0.862622 | − | 0.505848i | \(-0.168820\pi\) | |||||||
\(384\) | 1807.77 | 0.240241 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5766.03 | −0.760319 | ||||||||
\(387\) | 2256.40 | − | 3908.19i | 0.296380 | − | 0.513345i | ||||
\(388\) | 654.853 | + | 1134.24i | 0.0856833 | + | 0.148408i | ||||
\(389\) | 97.4957 | + | 168.868i | 0.0127075 | + | 0.0220101i | 0.872309 | − | 0.488955i | \(-0.162622\pi\) |
−0.859602 | + | 0.510965i | \(0.829288\pi\) | |||||||
\(390\) | −6295.04 | + | 10903.3i | −0.817338 | + | 1.41567i | ||||
\(391\) | −144.363 | −0.0186719 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 465.053 | 0.0596916 | ||||||||
\(394\) | 3217.37 | − | 5572.64i | 0.411392 | − | 0.712553i | ||||
\(395\) | −1375.51 | − | 2382.45i | −0.175214 | − | 0.303479i | ||||
\(396\) | 233.955 | + | 405.221i | 0.0296885 | + | 0.0514220i | ||||
\(397\) | −7091.48 | + | 12282.8i | −0.896501 | + | 1.55279i | −0.0645653 | + | 0.997913i | \(0.520566\pi\) |
−0.831936 | + | 0.554872i | \(0.812767\pi\) | |||||||
\(398\) | 3240.61 | 0.408134 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11357.6 | −1.41971 | ||||||||
\(401\) | −5002.52 | + | 8664.63i | −0.622978 | + | 1.07903i | 0.365950 | + | 0.930634i | \(0.380744\pi\) |
−0.988928 | + | 0.148395i | \(0.952589\pi\) | |||||||
\(402\) | 2944.31 | + | 5099.69i | 0.365295 | + | 0.632710i | ||||
\(403\) | 5359.72 | + | 9283.30i | 0.662498 | + | 1.14748i | ||||
\(404\) | −496.431 | + | 859.844i | −0.0611346 | + | 0.105888i | ||||
\(405\) | −1611.86 | −0.197763 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1343.52 | −0.163626 | ||||||||
\(408\) | 207.732 | − | 359.803i | 0.0252066 | − | 0.0436591i | ||||
\(409\) | 2317.47 | + | 4013.97i | 0.280174 | + | 0.485276i | 0.971428 | − | 0.237336i | \(-0.0762744\pi\) |
−0.691253 | + | 0.722613i | \(0.742941\pi\) | |||||||
\(410\) | 7199.35 | + | 12469.6i | 0.867196 | + | 1.50203i | ||||
\(411\) | −775.404 | + | 1343.04i | −0.0930605 | + | 0.161186i | ||||
\(412\) | 1706.95 | 0.204115 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −556.191 | −0.0660273 | ||||||||
\(415\) | −6180.16 | + | 10704.3i | −0.731017 | + | 1.26616i | ||||
\(416\) | 4161.04 | + | 7207.14i | 0.490413 | + | 0.849420i | ||||
\(417\) | 1437.10 | + | 2489.13i | 0.168765 | + | 0.292310i | ||||
\(418\) | 1875.21 | − | 3247.96i | 0.219425 | − | 0.380055i | ||||
\(419\) | −4998.31 | −0.582777 | −0.291388 | − | 0.956605i | \(-0.594117\pi\) | ||||
−0.291388 | + | 0.956605i | \(0.594117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −704.160 | −0.0815170 | −0.0407585 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407585 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(422\) | −758.597 | + | 1313.93i | −0.0875069 | + | 0.151566i | ||||
\(423\) | 1374.99 | + | 2381.55i | 0.158048 | + | 0.273747i | ||||
\(424\) | −4605.75 | − | 7977.39i | −0.527535 | − | 0.913718i | ||||
\(425\) | −764.139 | + | 1323.53i | −0.0872145 | + | 0.151060i | ||||
\(426\) | 1201.57 | 0.136658 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 426.629 | 0.0481820 | ||||||||
\(429\) | 3137.08 | − | 5433.58i | 0.353053 | − | 0.611505i | ||||
\(430\) | −12044.5 | − | 20861.8i | −1.35079 | − | 2.33964i | ||||
\(431\) | 5166.39 | + | 8948.45i | 0.577393 | + | 1.00007i | 0.995777 | + | 0.0918037i | \(0.0292632\pi\) |
−0.418384 | + | 0.908270i | \(0.637403\pi\) | |||||||
\(432\) | 565.808 | − | 980.008i | 0.0630149 | − | 0.109145i | ||||
\(433\) | −11106.8 | −1.23270 | −0.616348 | − | 0.787474i | \(-0.711389\pi\) | ||||
−0.616348 | + | 0.787474i | \(0.711389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3600.94 | −0.396901 | ||||||||
\(436\) | −332.623 | + | 576.120i | −0.0365362 | + | 0.0632825i | ||||
\(437\) | −830.492 | − | 1438.45i | −0.0909103 | − | 0.157461i | ||||
\(438\) | 2241.96 | + | 3883.19i | 0.244577 | + | 0.423620i | ||||
\(439\) | −3649.64 | + | 6321.36i | −0.396783 | + | 0.687249i | −0.993327 | − | 0.115332i | \(-0.963207\pi\) |
0.596544 | + | 0.802581i | \(0.296540\pi\) | |||||||
\(440\) | 11699.0 | 1.26757 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1189.36 | −0.127991 | ||||||||
\(443\) | −8044.83 | + | 13934.1i | −0.862802 | + | 1.49442i | 0.00641088 | + | 0.999979i | \(0.497959\pi\) |
−0.869213 | + | 0.494438i | \(0.835374\pi\) | |||||||
\(444\) | −182.796 | − | 316.611i | −0.0195385 | − | 0.0338417i | ||||
\(445\) | −2839.84 | − | 4918.75i | −0.302520 | − | 0.523980i | ||||
\(446\) | −1170.86 | + | 2027.98i | −0.124309 | + | 0.215309i | ||||
\(447\) | −5311.88 | −0.562065 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13561.7 | 1.42543 | 0.712715 | − | 0.701454i | \(-0.247466\pi\) | ||||
0.712715 | + | 0.701454i | \(0.247466\pi\) | |||||||
\(450\) | −2944.02 | + | 5099.20i | −0.308406 | + | 0.534175i | ||||
\(451\) | −3587.73 | − | 6214.13i | −0.374589 | − | 0.648807i | ||||
\(452\) | 2169.00 | + | 3756.81i | 0.225710 | + | 0.390941i | ||||
\(453\) | 3810.35 | − | 6599.73i | 0.395201 | − | 0.684508i | ||||
\(454\) | 11464.2 | 1.18512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4780.19 | 0.490905 | ||||||||
\(457\) | −5424.28 | + | 9395.14i | −0.555224 | + | 0.961676i | 0.442662 | + | 0.896688i | \(0.354034\pi\) |
−0.997886 | + | 0.0649876i | \(0.979299\pi\) | |||||||
\(458\) | −5796.52 | − | 10039.9i | −0.591383 | − | 1.02431i | ||||
\(459\) | −76.1347 | − | 131.869i | −0.00774219 | − | 0.0134099i | ||||
\(460\) | 553.085 | − | 957.972i | 0.0560603 | − | 0.0970993i | ||||
\(461\) | 1758.69 | 0.177679 | 0.0888397 | − | 0.996046i | \(-0.471684\pi\) | ||||
0.0888397 | + | 0.996046i | \(0.471684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5411.95 | −0.543228 | −0.271614 | − | 0.962406i | \(-0.587557\pi\) | ||||
−0.271614 | + | 0.962406i | \(0.587557\pi\) | |||||||
\(464\) | 1264.03 | − | 2189.37i | 0.126468 | − | 0.219049i | ||||
\(465\) | 3662.82 | + | 6344.19i | 0.365289 | + | 0.632699i | ||||
\(466\) | 3808.77 | + | 6596.98i | 0.378622 | + | 0.655792i | ||||
\(467\) | 4055.67 | − | 7024.63i | 0.401872 | − | 0.696062i | −0.592080 | − | 0.805879i | \(-0.701693\pi\) |
0.993952 | + | 0.109817i | \(0.0350264\pi\) | |||||||
\(468\) | 1707.29 | 0.168631 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 14679.3 | 1.44065 | ||||||||
\(471\) | −1625.02 | + | 2814.61i | −0.158974 | + | 0.275351i | ||||
\(472\) | 7705.93 | + | 13347.1i | 0.751471 | + | 1.30159i | ||||
\(473\) | 6002.30 | + | 10396.3i | 0.583480 | + | 1.01062i | ||||
\(474\) | 500.632 | − | 867.119i | 0.0485122 | − | 0.0840256i | ||||
\(475\) | −17583.8 | −1.69853 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3376.05 | −0.324065 | ||||||||
\(478\) | −5120.46 | + | 8868.90i | −0.489967 | + | 0.848648i | ||||
\(479\) | 1047.88 | + | 1814.98i | 0.0999559 | + | 0.173129i | 0.911666 | − | 0.410932i | \(-0.134797\pi\) |
−0.811710 | + | 0.584060i | \(0.801463\pi\) | |||||||
\(480\) | 2843.65 | + | 4925.34i | 0.270405 | + | 0.468355i | ||||
\(481\) | −2451.09 | + | 4245.42i | −0.232350 | + | 0.402441i | ||||
\(482\) | 10484.9 | 0.990817 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1645.67 | 0.154552 | ||||||||
\(485\) | 6000.83 | − | 10393.7i | 0.561822 | − | 0.973104i | ||||
\(486\) | −293.327 | − | 508.057i | −0.0273777 | − | 0.0474196i | ||||
\(487\) | −4805.04 | − | 8322.57i | −0.447099 | − | 0.774398i | 0.551097 | − | 0.834441i | \(-0.314209\pi\) |
−0.998196 | + | 0.0600435i | \(0.980876\pi\) | |||||||
\(488\) | −46.1335 | + | 79.9056i | −0.00427944 | + | 0.00741221i | ||||
\(489\) | 8906.17 | 0.823622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11717.3 | −1.07698 | −0.538488 | − | 0.842633i | \(-0.681004\pi\) | ||||
−0.538488 | + | 0.842633i | \(0.681004\pi\) | |||||||
\(492\) | 976.272 | − | 1690.95i | 0.0894588 | − | 0.154947i | ||||
\(493\) | −170.087 | − | 294.600i | −0.0155382 | − | 0.0269130i | ||||
\(494\) | −6842.19 | − | 11851.0i | −0.623167 | − | 1.07936i | ||||
\(495\) | 2143.87 | − | 3713.30i | 0.194667 | − | 0.337172i | ||||
\(496\) | −5143.01 | −0.465581 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4498.67 | −0.404800 | ||||||||
\(499\) | 4597.59 | − | 7963.26i | 0.412458 | − | 0.714398i | −0.582700 | − | 0.812687i | \(-0.698004\pi\) |
0.995158 | + | 0.0982893i | \(0.0313370\pi\) | |||||||
\(500\) | −3154.35 | − | 5463.49i | −0.282133 | − | 0.488669i | ||||
\(501\) | −3137.30 | − | 5433.97i | −0.279769 | − | 0.484574i | ||||
\(502\) | 3624.95 | − | 6278.60i | 0.322290 | − | 0.558222i | ||||
\(503\) | −16118.8 | −1.42883 | −0.714414 | − | 0.699724i | \(-0.753307\pi\) | ||||
−0.714414 | + | 0.699724i | \(0.753307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9098.23 | 0.801715 | ||||||||
\(506\) | 739.769 | − | 1281.32i | 0.0649935 | − | 0.112572i | ||||
\(507\) | −8150.93 | − | 14117.8i | −0.713995 | − | 1.23668i | ||||
\(508\) | −2509.69 | − | 4346.90i | −0.219192 | − | 0.379651i | ||||
\(509\) | 2459.39 | − | 4259.79i | 0.214166 | − | 0.370947i | −0.738848 | − | 0.673872i | \(-0.764630\pi\) |
0.953014 | + | 0.302925i | \(0.0979632\pi\) | |||||||
\(510\) | −812.808 | −0.0705721 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12226.4 | −1.05534 | ||||||||
\(513\) | 875.979 | − | 1517.24i | 0.0753906 | − | 0.130580i | ||||
\(514\) | 5394.37 | + | 9343.33i | 0.462910 | + | 0.801783i | ||||
\(515\) | −7820.95 | − | 13546.3i | −0.669188 | − | 1.15907i | ||||
\(516\) | −1633.31 | + | 2828.98i | −0.139346 | + | 0.241354i | ||||
\(517\) | −7315.29 | −0.622294 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1410.44 | 0.119290 | ||||||||
\(520\) | 21343.5 | − | 36968.0i | 1.79995 | − | 3.11760i | ||||
\(521\) | 6981.69 | + | 12092.6i | 0.587089 | + | 1.01687i | 0.994611 | + | 0.103673i | \(0.0330596\pi\) |
−0.407522 | + | 0.913195i | \(0.633607\pi\) | |||||||
\(522\) | −655.301 | − | 1135.01i | −0.0549458 | − | 0.0951690i | ||||
\(523\) | −6877.63 | + | 11912.4i | −0.575024 | + | 0.995972i | 0.421015 | + | 0.907054i | \(0.361674\pi\) |
−0.996039 | + | 0.0889177i | \(0.971659\pi\) | |||||||
\(524\) | −336.632 | −0.0280646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14871.9 | 1.23278 | ||||||||
\(527\) | −346.020 | + | 599.325i | −0.0286013 | + | 0.0495389i | ||||
\(528\) | 1505.12 | + | 2606.94i | 0.124057 | + | 0.214872i | ||||
\(529\) | 5755.87 | + | 9969.46i | 0.473072 | + | 0.819385i | ||||
\(530\) | −9010.61 | + | 15606.8i | −0.738483 | + | 1.27909i | ||||
\(531\) | 5648.51 | 0.461628 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26181.5 | −2.12767 | ||||||||
\(534\) | 1033.59 | − | 1790.23i | 0.0837601 | − | 0.145077i | ||||
\(535\) | −1954.74 | − | 3385.70i | −0.157964 | − | 0.273601i | ||||
\(536\) | −9982.74 | − | 17290.6i | −0.804457 | − | 1.39336i | ||||
\(537\) | −1584.69 | + | 2744.77i | −0.127345 | + | 0.220569i | ||||
\(538\) | −12044.3 | −0.965178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1166.76 | 0.0929800 | ||||||||
\(541\) | −7231.34 | + | 12525.1i | −0.574676 | + | 0.995368i | 0.421401 | + | 0.906875i | \(0.361539\pi\) |
−0.996077 | + | 0.0884937i | \(0.971795\pi\) | |||||||
\(542\) | 5351.98 | + | 9269.91i | 0.424146 | + | 0.734643i | ||||
\(543\) | −609.706 | − | 1056.04i | −0.0481860 | − | 0.0834605i | ||||
\(544\) | −268.634 | + | 465.289i | −0.0211721 | + | 0.0366711i | ||||
\(545\) | 6096.07 | 0.479132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13682.5 | 1.06951 | 0.534755 | − | 0.845007i | \(-0.320404\pi\) | ||||
0.534755 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(548\) | 561.282 | − | 972.169i | 0.0437533 | − | 0.0757829i | ||||
\(549\) | 16.9081 | + | 29.2857i | 0.00131443 | + | 0.00227666i | ||||
\(550\) | −7831.47 | − | 13564.5i | −0.607155 | − | 1.05162i | ||||
\(551\) | 1956.96 | − | 3389.56i | 0.151306 | − | 0.262069i | ||||
\(552\) | 1885.78 | 0.145406 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2685.49 | 0.205949 | ||||||||
\(555\) | −1675.07 | + | 2901.31i | −0.128113 | + | 0.221899i | ||||
\(556\) | −1040.26 | − | 1801.78i | −0.0793466 | − | 0.137432i | ||||
\(557\) | 3831.56 | + | 6636.46i | 0.291470 | + | 0.504840i | 0.974157 | − | 0.225870i | \(-0.0725225\pi\) |
−0.682688 | + | 0.730710i | \(0.739189\pi\) | |||||||
\(558\) | −1333.12 | + | 2309.04i | −0.101139 | + | 0.175178i | ||||
\(559\) | 43801.8 | 3.31417 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 405.056 | 0.0304839 | ||||||||
\(562\) | −3395.85 | + | 5881.79i | −0.254885 | + | 0.441474i | ||||
\(563\) | 8735.24 | + | 15129.9i | 0.653902 | + | 1.13259i | 0.982168 | + | 0.188006i | \(0.0602023\pi\) |
−0.328266 | + | 0.944585i | \(0.606464\pi\) | |||||||
\(564\) | −995.297 | − | 1723.91i | −0.0743078 | − | 0.128705i | ||||
\(565\) | 19875.9 | − | 34426.0i | 1.47997 | − | 2.56339i | ||||
\(566\) | −7598.83 | −0.564316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4073.96 | −0.300950 | ||||||||
\(569\) | 6936.96 | − | 12015.2i | 0.511094 | − | 0.885240i | −0.488824 | − | 0.872383i | \(-0.662574\pi\) |
0.999917 | − | 0.0128577i | \(-0.00409284\pi\) | |||||||
\(570\) | −4675.94 | − | 8098.96i | −0.343603 | − | 0.595137i | ||||
\(571\) | 1888.76 | + | 3271.43i | 0.138428 | + | 0.239764i | 0.926902 | − | 0.375305i | \(-0.122462\pi\) |
−0.788474 | + | 0.615068i | \(0.789129\pi\) | |||||||
\(572\) | −2270.80 | + | 3933.14i | −0.165991 | + | 0.287505i | ||||
\(573\) | 538.229 | 0.0392405 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6936.79 | −0.503103 | ||||||||
\(576\) | −2543.80 | + | 4405.99i | −0.184013 | + | 0.318720i | ||||
\(577\) | 6940.23 | + | 12020.8i | 0.500738 | + | 0.867303i | 1.00000 | 0.000852075i | \(0.000271224\pi\) | |
−0.499262 | + | 0.866451i | \(0.666395\pi\) | |||||||
\(578\) | 5892.12 | + | 10205.5i | 0.424014 | + | 0.734414i | ||||
\(579\) | 3582.55 | − | 6205.16i | 0.257143 | − | 0.445385i | ||||
\(580\) | 2606.57 | 0.186607 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4368.14 | 0.311108 | ||||||||
\(583\) | 4490.36 | − | 7777.53i | 0.318991 | − | 0.552509i | ||||
\(584\) | −7601.41 | − | 13166.0i | −0.538611 | − | 0.932901i | ||||
\(585\) | −7822.47 | − | 13548.9i | −0.552854 | − | 0.957571i | ||||
\(586\) | 11036.6 | − | 19116.0i | 0.778018 | − | 1.34757i | ||||
\(587\) | 2395.61 | 0.168445 | 0.0842227 | − | 0.996447i | \(-0.473159\pi\) | ||||
0.0842227 | + | 0.996447i | \(0.473159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7962.36 | −0.557018 | ||||||||
\(590\) | 15075.8 | − | 26112.0i | 1.05196 | − | 1.82206i | ||||
\(591\) | 3998.03 | + | 6924.79i | 0.278269 | + | 0.481976i | ||||
\(592\) | −1175.99 | − | 2036.88i | −0.0816437 | − | 0.141411i | ||||
\(593\) | 3301.75 | − | 5718.80i | 0.228645 | − | 0.396025i | −0.728762 | − | 0.684767i | \(-0.759904\pi\) |
0.957407 | + | 0.288742i | \(0.0932371\pi\) | |||||||
\(594\) | 1560.57 | 0.107796 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3845.04 | 0.264260 | ||||||||
\(597\) | −2013.46 | + | 3487.41i | −0.138033 | + | 0.239079i | ||||
\(598\) | −2699.24 | − | 4675.21i | −0.184582 | − | 0.319705i | ||||
\(599\) | −8626.05 | − | 14940.8i | −0.588399 | − | 1.01914i | −0.994442 | − | 0.105283i | \(-0.966425\pi\) |
0.406044 | − | 0.913854i | \(-0.366908\pi\) | |||||||
\(600\) | 9981.78 | − | 17289.0i | 0.679174 | − | 1.17636i | ||||
\(601\) | −12833.1 | −0.871005 | −0.435503 | − | 0.900187i | \(-0.643429\pi\) | ||||
−0.435503 | + | 0.900187i | \(0.643429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7317.43 | −0.494177 | ||||||||
\(604\) | −2758.15 | + | 4777.26i | −0.185807 | + | 0.321828i | ||||
\(605\) | −7540.14 | − | 13059.9i | −0.506695 | − | 0.877621i | ||||
\(606\) | 1655.70 | + | 2867.76i | 0.110987 | + | 0.192235i | ||||
\(607\) | 4310.08 | − | 7465.28i | 0.288206 | − | 0.499187i | −0.685176 | − | 0.728378i | \(-0.740275\pi\) |
0.973381 | + | 0.229191i | \(0.0736080\pi\) | |||||||
\(608\) | −6181.62 | −0.412332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 180.510 | 0.0119813 | ||||||||
\(611\) | −13345.9 | + | 23115.7i | −0.883659 | + | 1.53054i | ||||
\(612\) | 55.1107 | + | 95.4546i | 0.00364006 | + | 0.00630477i | ||||
\(613\) | −2568.37 | − | 4448.54i | −0.169226 | − | 0.293107i | 0.768922 | − | 0.639342i | \(-0.220793\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(614\) | −5611.72 | + | 9719.79i | −0.368845 | + | 0.638858i | ||||
\(615\) | −17892.4 | −1.17316 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1759.82 | −0.114826 | −0.0574131 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574131 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(618\) | 2846.52 | − | 4930.32i | 0.185281 | − | 0.320916i | ||||
\(619\) | −1780.12 | − | 3083.26i | −0.115588 | − | 0.200205i | 0.802427 | − | 0.596751i | \(-0.203542\pi\) |
−0.918015 | + | 0.396546i | \(0.870209\pi\) | |||||||
\(620\) | −2651.36 | − | 4592.29i | −0.171744 | − | 0.297469i | ||||
\(621\) | 345.573 | − | 598.550i | 0.0223307 | − | 0.0386779i | ||||
\(622\) | 15492.4 | 0.998698 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 10983.6 | 0.704643 | ||||||||
\(625\) | −11968.4 | + | 20729.9i | −0.765977 | + | 1.32671i | ||||
\(626\) | 7083.56 | + | 12269.1i | 0.452262 | + | 0.783341i | ||||
\(627\) | 2330.21 | + | 4036.05i | 0.148421 | + | 0.257072i | ||||
\(628\) | 1176.28 | − | 2037.38i | 0.0747431 | − | 0.129459i | ||||
\(629\) | −316.482 | −0.0200620 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27321.4 | −1.72369 | −0.861845 | − | 0.507172i | \(-0.830691\pi\) | ||||
−0.861845 | + | 0.507172i | \(0.830691\pi\) | |||||||
\(632\) | −1697.40 | + | 2939.99i | −0.106834 | + | 0.185042i | ||||
\(633\) | −942.664 | − | 1632.74i | −0.0591904 | − | 0.102521i | ||||
\(634\) | 4797.67 | + | 8309.81i | 0.300536 | + | 0.520544i | ||||
\(635\) | −22997.8 | + | 39833.4i | −1.43723 | + | 2.48936i | ||||
\(636\) | 2443.78 | 0.152362 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3486.36 | 0.216342 | ||||||||
\(639\) | −746.561 | + | 1293.08i | −0.0462183 | + | 0.0800525i | ||||
\(640\) | 5995.63 | + | 10384.7i | 0.370309 | + | 0.641395i | ||||
\(641\) | 10963.5 | + | 18989.4i | 0.675558 | + | 1.17010i | 0.976306 | + | 0.216397i | \(0.0694305\pi\) |
−0.300748 | + | 0.953704i | \(0.597236\pi\) | |||||||
\(642\) | 711.448 | − | 1232.26i | 0.0437361 | − | 0.0757532i | ||||
\(643\) | 5826.04 | 0.357320 | 0.178660 | − | 0.983911i | \(-0.442824\pi\) | ||||
0.178660 | + | 0.983911i | \(0.442824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29934.1 | 1.82737 | ||||||||
\(646\) | 441.728 | − | 765.095i | 0.0269033 | − | 0.0465979i | ||||
\(647\) | 12105.4 | + | 20967.1i | 0.735565 | + | 1.27404i | 0.954475 | + | 0.298291i | \(0.0964166\pi\) |
−0.218910 | + | 0.975745i | \(0.570250\pi\) | |||||||
\(648\) | 994.532 | + | 1722.58i | 0.0602915 | + | 0.104428i | ||||
\(649\) | −7512.87 | + | 13012.7i | −0.454401 | + | 0.787045i | ||||
\(650\) | −57150.3 | −3.44864 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6446.80 | −0.387233 | ||||||||
\(653\) | 12811.7 | − | 22190.4i | 0.767778 | − | 1.32983i | −0.170988 | − | 0.985273i | \(-0.554696\pi\) |
0.938765 | − | 0.344557i | \(-0.111971\pi\) | |||||||
\(654\) | 1109.37 | + | 1921.48i | 0.0663298 | + | 0.114887i | ||||
\(655\) | 1542.39 | + | 2671.49i | 0.0920092 | + | 0.159365i | ||||
\(656\) | 6280.73 | − | 10878.6i | 0.373813 | − | 0.647463i | ||||
\(657\) | −5571.90 | −0.330868 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23273.7 | −1.37574 | −0.687871 | − | 0.725833i | \(-0.741455\pi\) | ||||
−0.687871 | + | 0.725833i | \(0.741455\pi\) | |||||||
\(660\) | −1551.86 | + | 2687.90i | −0.0915243 | + | 0.158525i | ||||
\(661\) | −10018.2 | − | 17352.1i | −0.589508 | − | 1.02106i | −0.994297 | − | 0.106647i | \(-0.965988\pi\) |
0.404789 | − | 0.914410i | \(-0.367345\pi\) | |||||||
\(662\) | 10758.7 | + | 18634.7i | 0.631646 | + | 1.09404i | ||||
\(663\) | 738.975 | − | 1279.94i | 0.0432872 | − | 0.0749756i | ||||
\(664\) | 15252.9 | 0.891454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1219.32 | −0.0709426 | ||||||||
\(667\) | 772.019 | − | 1337.18i | 0.0448166 | − | 0.0776247i | ||||
\(668\) | 2270.96 | + | 3933.42i | 0.131536 | + | 0.227827i | ||||
\(669\) | −1454.95 | − | 2520.06i | −0.0840834 | − | 0.145637i | ||||
\(670\) | −19530.1 | + | 33827.1i | −1.12614 | + | 1.95053i | ||||
\(671\) | −89.9554 | −0.00517540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18127.8 | −1.03830 | −0.519149 | − | 0.854684i | \(-0.673751\pi\) | ||||
−0.519149 | + | 0.854684i | \(0.673751\pi\) | |||||||
\(674\) | −4800.74 | + | 8315.12i | −0.274358 | + | 0.475203i | ||||
\(675\) | −3658.36 | − | 6336.47i | −0.208608 | − | 0.361320i | ||||
\(676\) | 5900.11 | + | 10219.3i | 0.335692 | + | 0.581435i | ||||
\(677\) | 6907.73 | − | 11964.5i | 0.392150 | − | 0.679224i | −0.600583 | − | 0.799563i | \(-0.705065\pi\) |
0.992733 | + | 0.120339i | \(0.0383980\pi\) | |||||||
\(678\) | 14468.1 | 0.819533 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2755.85 | 0.155415 | ||||||||
\(681\) | −7122.96 | + | 12337.3i | −0.400811 | + | 0.694225i | ||||
\(682\) | −3546.28 | − | 6142.33i | −0.199111 | − | 0.344871i | ||||
\(683\) | 2302.11 | + | 3987.38i | 0.128972 | + | 0.223386i | 0.923279 | − | 0.384131i | \(-0.125499\pi\) |
−0.794306 | + | 0.607517i | \(0.792166\pi\) | |||||||
\(684\) | −634.084 | + | 1098.27i | −0.0354456 | + | 0.0613936i | ||||
\(685\) | −10286.8 | −0.573777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14406.0 | 0.800032 | ||||||||
\(688\) | −10507.7 | + | 18199.9i | −0.582271 | + | 1.00852i | ||||
\(689\) | −16384.2 | − | 28378.3i | −0.905935 | − | 1.56913i | ||||
\(690\) | −1844.65 | − | 3195.03i | −0.101775 | − | 0.176279i | ||||
\(691\) | 8956.83 | − | 15513.7i | 0.493103 | − | 0.854079i | −0.506866 | − | 0.862025i | \(-0.669196\pi\) |
0.999968 | + | 0.00794632i | \(0.00252942\pi\) | |||||||
\(692\) | −1020.96 | −0.0560854 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16480.5 | 0.901426 | ||||||||
\(695\) | −9532.53 | + | 16510.8i | −0.520272 | + | 0.901138i | ||||
\(696\) | 2221.81 | + | 3848.29i | 0.121002 | + | 0.209582i | ||||
\(697\) | −845.132 | − | 1463.81i | −0.0459278 | − | 0.0795492i | ||||
\(698\) | −974.548 | + | 1687.97i | −0.0528470 | + | 0.0915336i | ||||
\(699\) | −9465.86 | −0.512206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11303.7 | 0.609035 | 0.304518 | − | 0.952507i | \(-0.401505\pi\) | ||||
0.304518 | + | 0.952507i | \(0.401505\pi\) | |||||||
\(702\) | 2847.07 | − | 4931.28i | 0.153071 | − | 0.265127i | ||||
\(703\) | −1820.66 | − | 3153.48i | −0.0976780 | − | 0.169183i | ||||
\(704\) | −6766.82 | − | 11720.5i | −0.362264 | − | 0.627460i | ||||
\(705\) | −9120.54 | + | 15797.2i | −0.487233 | + | 0.843912i | ||||
\(706\) | 19118.6 | 1.01918 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4088.72 | −0.217039 | ||||||||
\(709\) | 8023.15 | − | 13896.5i | 0.424987 | − | 0.736099i | −0.571432 | − | 0.820649i | \(-0.693612\pi\) |
0.996419 | + | 0.0845505i | \(0.0269454\pi\) | |||||||
\(710\) | 3985.11 | + | 6902.42i | 0.210646 | + | 0.364849i | ||||
\(711\) | 622.105 | + | 1077.52i | 0.0328140 | + | 0.0568355i | ||||
\(712\) | −3504.42 | + | 6069.83i | −0.184457 | + | 0.319489i | ||||
\(713\) | −3141.15 | −0.164989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41617.5 | 2.17679 | ||||||||
\(716\) | 1147.09 | − | 1986.82i | 0.0598726 | − | 0.103702i | ||||
\(717\) | −6362.89 | − | 11020.9i | −0.331418 | − | 0.574032i | ||||
\(718\) | 10645.7 | + | 18438.9i | 0.553336 | + | 0.958406i | ||||
\(719\) | −12595.2 | + | 21815.6i | −0.653300 | + | 1.13155i | 0.329017 | + | 0.944324i | \(0.393283\pi\) |
−0.982317 | + | 0.187225i | \(0.940051\pi\) | |||||||
\(720\) | 7506.19 | 0.388527 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6394.38 | −0.329604 | ||||||||
\(723\) | −6514.48 | + | 11283.4i | −0.335098 | + | 0.580407i | ||||
\(724\) | 441.340 | + | 764.424i | 0.0226551 | + | 0.0392397i | ||||
\(725\) | −8172.89 | − | 14155.9i | −0.418667 | − | 0.725152i | ||||
\(726\) | 2744.32 | − | 4753.30i | 0.140291 | − | 0.242991i | ||||
\(727\) | −11277.2 | −0.575307 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −14871.3 | + | 25757.8i | −0.753987 | + | 1.30594i | ||||
\(731\) | 1413.91 | + | 2448.96i | 0.0715395 | + | 0.123910i | ||||
\(732\) | −12.2391 | − | 21.1987i | −0.000617990 | − | 0.00107039i | ||||
\(733\) | 11860.0 | − | 20542.2i | 0.597626 | − | 1.03512i | −0.395544 | − | 0.918447i | \(-0.629444\pi\) |
0.993171 | − | 0.116672i | \(-0.0372226\pi\) | |||||||
\(734\) | 26946.9 | 1.35508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2438.64 | −0.122133 | ||||||||
\(737\) | 9732.64 | − | 16857.4i | 0.486440 | − | 0.842539i | ||||
\(738\) | −3256.07 | − | 5639.67i | −0.162409 | − | 0.281300i | ||||
\(739\) | −4062.36 | − | 7036.21i | −0.202214 | − | 0.350245i | 0.747027 | − | 0.664793i | \(-0.231480\pi\) |
−0.949242 | + | 0.314548i | \(0.898147\pi\) | |||||||
\(740\) | 1212.51 | − | 2100.14i | 0.0602336 | − | 0.104328i | ||||
\(741\) | 17004.8 | 0.843030 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20955.3 | 1.03469 | 0.517346 | − | 0.855777i | \(-0.326920\pi\) | ||||
0.517346 | + | 0.855777i | \(0.326920\pi\) | |||||||
\(744\) | 4519.99 | − | 7828.85i | 0.222730 | − | 0.385779i | ||||
\(745\) | −17617.3 | − | 30514.0i | −0.866372 | − | 1.50060i | ||||
\(746\) | −3292.81 | − | 5703.32i | −0.161607 | − | 0.279911i | ||||
\(747\) | 2795.12 | − | 4841.28i | 0.136905 | − | 0.237126i | ||||
\(748\) | −293.203 | −0.0143323 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21040.8 | −1.02440 | ||||||||
\(751\) | 19104.0 | − | 33089.2i | 0.928251 | − | 1.60778i | 0.142004 | − | 0.989866i | \(-0.454645\pi\) |
0.786247 | − | 0.617912i | \(-0.212021\pi\) | |||||||
\(752\) | −6403.13 | − | 11090.5i | −0.310503 | − | 0.537807i | ||||
\(753\) | 4504.51 | + | 7802.04i | 0.217999 | + | 0.377586i | ||||
\(754\) | 6360.45 | − | 11016.6i | 0.307207 | − | 0.532097i | ||||
\(755\) | 50549.4 | 2.43666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30958.1 | 1.48638 | 0.743191 | − | 0.669079i | \(-0.233311\pi\) | ||||
0.743191 | + | 0.669079i | \(0.233311\pi\) | |||||||
\(758\) | −4932.82 | + | 8543.90i | −0.236370 | + | 0.409404i | ||||
\(759\) | 919.267 | + | 1592.22i | 0.0439621 | + | 0.0761447i | ||||
\(760\) | 15853.9 | + | 27459.7i | 0.756685 | + | 1.31062i | ||||
\(761\) | −20024.7 | + | 34683.8i | −0.953871 | + | 1.65215i | −0.216939 | + | 0.976185i | \(0.569607\pi\) |
−0.736932 | + | 0.675967i | \(0.763726\pi\) | |||||||
\(762\) | −16740.6 | −0.795865 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −389.601 | −0.0184493 | ||||||||
\(765\) | 505.014 | − | 874.710i | 0.0238678 | − | 0.0413402i | ||||
\(766\) | 15732.1 | + | 27248.9i | 0.742070 | + | 1.28530i | ||||
\(767\) | 27412.6 | + | 47480.1i | 1.29050 | + | 2.23521i | ||||
\(768\) | 4601.29 | − | 7969.66i | 0.216191 | − | 0.374454i | ||||
\(769\) | 8002.01 | 0.375240 | 0.187620 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187620 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13406.5 | −0.626231 | ||||||||
\(772\) | −2593.26 | + | 4491.65i | −0.120898 | + | 0.209402i | ||||
\(773\) | −6966.68 | − | 12066.6i | −0.324158 | − | 0.561458i | 0.657184 | − | 0.753730i | \(-0.271748\pi\) |
−0.981342 | + | 0.192273i | \(0.938414\pi\) | |||||||
\(774\) | 5447.42 | + | 9435.21i | 0.252976 | + | 0.438168i | ||||
\(775\) | −16626.7 | + | 28798.2i | −0.770642 | + | 1.33479i | ||||
\(776\) | −14810.3 | −0.685126 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −470.751 | −0.0216931 | ||||||||
\(779\) | 9723.78 | − | 16842.1i | 0.447228 | − | 0.774621i | ||||
\(780\) | 5662.36 | + | 9807.49i | 0.259929 | + | 0.450211i | ||||
\(781\) | −1985.95 | − | 3439.76i | −0.0909894 | − | 0.157598i | ||||
\(782\) | 174.261 | − | 301.829i | 0.00796875 | − | 0.0138023i | ||||
\(783\) | 1628.61 | 0.0743316 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21558.0 | −0.980175 | ||||||||
\(786\) | −561.368 | + | 972.319i | −0.0254750 | + | 0.0441240i | ||||
\(787\) | 18790.9 | + | 32546.7i | 0.851108 | + | 1.47416i | 0.880209 | + | 0.474586i | \(0.157402\pi\) |
−0.0291013 | + | 0.999576i | \(0.509265\pi\) | |||||||
\(788\) | −2894.01 | − | 5012.56i | −0.130831 | − | 0.226606i | ||||
\(789\) | −9240.20 | + | 16004.5i | −0.416933 | + | 0.722148i | ||||
\(790\) | 6641.54 | 0.299108 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5291.16 | −0.237390 | ||||||||
\(793\) | −164.113 | + | 284.252i | −0.00734907 | + | 0.0127290i | ||||
\(794\) | −17120.3 | − | 29653.3i | −0.765212 | − | 1.32539i | ||||
\(795\) | −11197.0 | − | 19393.7i | −0.499516 | − | 0.865187i | ||||
\(796\) | 1457.46 | − | 2524.39i | 0.0648973 | − | 0.112405i | ||||
\(797\) | 9458.78 | 0.420385 | 0.210193 | − | 0.977660i | \(-0.432591\pi\) | ||||
0.210193 | + | 0.977660i | \(0.432591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1723.20 | −0.0762985 | ||||||||
\(800\) | −12908.2 | + | 22357.7i | −0.570467 | + | 0.988078i | ||||
\(801\) | 1284.38 | + | 2224.62i | 0.0566560 | + | 0.0981310i | ||||
\(802\) | −12077.2 | − | 20918.3i | −0.531745 | − | 0.921009i | ||||
\(803\) | 7410.97 | − | 12836.2i | 0.325688 | − | 0.564108i | ||||
\(804\) | 5296.78 | 0.232342 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25879.0 | −1.13095 | ||||||||
\(807\) | 7483.36 | − | 12961.6i | 0.326427 | − | 0.565388i | ||||
\(808\) | −5613.69 | − | 9723.20i | −0.244417 | − | 0.423343i | ||||
\(809\) | 954.968 | + | 1654.05i | 0.0415017 | + | 0.0718831i | 0.886030 | − | 0.463628i | \(-0.153452\pi\) |
−0.844528 | + | 0.535511i | \(0.820119\pi\) | |||||||
\(810\) | 1945.69 | − | 3370.03i | 0.0844005 | − | 0.146186i | ||||
\(811\) | −43110.6 | −1.86661 | −0.933303 | − | 0.359091i | \(-0.883087\pi\) | ||||
−0.933303 | + | 0.359091i | \(0.883087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13301.2 | −0.573792 | ||||||||
\(814\) | 1621.77 | − | 2809.00i | 0.0698319 | − | 0.120952i | ||||
\(815\) | 29538.0 | + | 51161.4i | 1.26954 | + | 2.19890i | ||||
\(816\) | 354.548 | + | 614.096i | 0.0152104 | + | 0.0263452i | ||||
\(817\) | −16267.9 | + | 28176.9i | −0.696626 | + | 1.20659i | ||||
\(818\) | −11189.7 | −0.478287 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12951.5 | 0.551570 | ||||||||
\(821\) | −2013.28 | + | 3487.10i | −0.0855834 | + | 0.148235i | −0.905640 | − | 0.424048i | \(-0.860609\pi\) |
0.820056 | + | 0.572283i | \(0.193942\pi\) | |||||||
\(822\) | −1871.99 | − | 3242.38i | −0.0794321 | − | 0.137580i | ||||
\(823\) | −19834.0 | − | 34353.5i | −0.840062 | − | 1.45503i | −0.889842 | − | 0.456269i | \(-0.849185\pi\) |
0.0497799 | − | 0.998760i | \(-0.484148\pi\) | |||||||
\(824\) | −9651.19 | + | 16716.4i | −0.408028 | + | 0.706726i | ||||
\(825\) | 19463.4 | 0.821368 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30137.7 | 1.26722 | 0.633611 | − | 0.773652i | \(-0.281572\pi\) | ||||
0.633611 | + | 0.773652i | \(0.281572\pi\) | |||||||
\(828\) | −250.145 | + | 433.265i | −0.0104990 | + | 0.0181848i | ||||
\(829\) | 11639.0 | + | 20159.3i | 0.487622 | + | 0.844587i | 0.999899 | − | 0.0142341i | \(-0.00453100\pi\) |
−0.512276 | + | 0.858821i | \(0.671198\pi\) | |||||||
\(830\) | −14920.2 | − | 25842.6i | −0.623962 | − | 1.08073i | ||||
\(831\) | −1668.55 | + | 2890.02i | −0.0696528 | + | 0.120642i | ||||
\(832\) | −49381.0 | −2.05766 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6938.94 | −0.288100 | ||||||||
\(835\) | 20810.2 | − | 36044.4i | 0.862477 | − | 1.49385i | ||||
\(836\) | −1686.74 | − | 2921.52i | −0.0697813 | − | 0.120865i | ||||
\(837\) | −1656.59 | − | 2869.31i | −0.0684113 | − | 0.118492i | ||||
\(838\) | 6033.49 | − | 10450.3i | 0.248716 | − | 0.430788i | ||||
\(839\) | 9494.43 | 0.390684 | 0.195342 | − | 0.980735i | \(-0.437418\pi\) | ||||
0.195342 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20750.6 | −0.850820 | ||||||||
\(842\) | 849.996 | − | 1472.24i | 0.0347896 | − | 0.0602573i | ||||
\(843\) | −4219.83 | − | 7308.95i | −0.172406 | − | 0.298616i | ||||
\(844\) | 682.354 | + | 1181.87i | 0.0278289 | + | 0.0482011i | ||||
\(845\) | 54066.5 | − | 93645.9i | 2.20112 | − | 3.81245i | ||||
\(846\) | −6639.04 | −0.269805 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15721.8 | 0.636661 | ||||||||
\(849\) | 4721.31 | − | 8177.55i | 0.190854 | − | 0.330569i | ||||
\(850\) | −1844.79 | − | 3195.28i | −0.0744423 | − | 0.128938i | ||||
\(851\) | −718.251 | − | 1244.05i | −0.0289322 | − | 0.0501121i | ||||
\(852\) | 540.404 | − | 936.007i | 0.0217300 | − | 0.0376374i | ||||
\(853\) | 12692.4 | 0.509471 | 0.254736 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254736 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11621.0 | 0.464831 | ||||||||
\(856\) | −2412.18 | + | 4178.02i | −0.0963162 | + | 0.166825i | ||||
\(857\) | 11103.0 | + | 19231.0i | 0.442557 | + | 0.766531i | 0.997878 | − | 0.0651047i | \(-0.0207381\pi\) |
−0.555322 | + | 0.831636i | \(0.687405\pi\) | |||||||
\(858\) | 7573.58 | + | 13117.8i | 0.301349 | + | 0.521952i | ||||
\(859\) | 9910.24 | − | 17165.0i | 0.393636 | − | 0.681797i | −0.599290 | − | 0.800532i | \(-0.704550\pi\) |
0.992926 | + | 0.118735i | \(0.0378838\pi\) | |||||||
\(860\) | −21668.0 | −0.859155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24945.5 | −0.985671 | ||||||||
\(863\) | −18206.9 | + | 31535.3i | −0.718157 | + | 1.24389i | 0.243572 | + | 0.969883i | \(0.421681\pi\) |
−0.961729 | + | 0.274002i | \(0.911652\pi\) | |||||||
\(864\) | −1286.10 | − | 2227.60i | −0.0506414 | − | 0.0877135i | ||||
\(865\) | 4677.85 | + | 8102.27i | 0.183875 | + | 0.318480i | ||||
\(866\) | 13407.1 | − | 23221.7i | 0.526086 | − | 0.911208i | ||||
\(867\) | −14643.6 | −0.573613 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3309.76 | −0.129201 | ||||||||
\(870\) | 4346.72 | − | 7528.74i | 0.169388 | − | 0.293389i | ||||
\(871\) | −35512.0 | − | 61508.7i | −1.38149 | − | 2.39281i | ||||
\(872\) | −3761.33 | − | 6514.82i | −0.146072 | − | 0.253004i | ||||
\(873\) | −2714.01 | + | 4700.81i | −0.105218 | + | 0.182243i | ||||
\(874\) | 4009.97 | 0.155194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4033.26 | 0.155561 | ||||||||
\(877\) | −9721.31 | + | 16837.8i | −0.374305 | + | 0.648315i | −0.990223 | − | 0.139496i | \(-0.955452\pi\) |
0.615918 | + | 0.787810i | \(0.288785\pi\) | |||||||
\(878\) | −8811.01 | − | 15261.1i | −0.338676 | − | 0.586603i | ||||
\(879\) | 13714.6 | + | 23754.3i | 0.526258 | + | 0.911505i | ||||
\(880\) | −9983.71 | + | 17292.3i | −0.382444 | + | 0.662412i | ||||
\(881\) | 25184.2 | 0.963082 | 0.481541 | − | 0.876423i | \(-0.340077\pi\) | ||||
0.481541 | + | 0.876423i | \(0.340077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4050.03 | −0.154354 | −0.0771769 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771769 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(884\) | −534.913 | + | 926.496i | −0.0203519 | + | 0.0352505i | ||||
\(885\) | 18733.8 | + | 32447.8i | 0.711557 | + | 1.23245i | ||||
\(886\) | −19421.9 | − | 33639.8i | −0.736448 | − | 1.27556i | ||||
\(887\) | 20802.1 | − | 36030.3i | 0.787447 | − | 1.36390i | −0.140080 | − | 0.990140i | \(-0.544736\pi\) |
0.927526 | − | 0.373758i | \(-0.121931\pi\) | |||||||
\(888\) | 4134.14 | 0.156231 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13712.0 | 0.516434 | ||||||||
\(891\) | −969.616 | + | 1679.42i | −0.0364572 | + | 0.0631457i | ||||
\(892\) | 1053.18 | + | 1824.16i | 0.0395326 | + | 0.0684725i | ||||
\(893\) | −9913.27 | − | 17170.3i | −0.371484 | − | 0.643428i | ||||
\(894\) | 6412.00 | − | 11105.9i | 0.239876 | − | 0.415478i | ||||
\(895\) | −21023.0 | −0.785165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6708.36 | 0.249705 | ||||||||
\(898\) | −16370.5 | + | 28354.5i | −0.608340 | + | 1.05368i | ||||
\(899\) | −3700.88 | − | 6410.11i | −0.137298 | − | 0.237808i | ||||
\(900\) | 2648.13 | + | 4586.70i | 0.0980791 | + | 0.169878i | ||||
\(901\) | 1057.76 | − | 1832.09i | 0.0391110 | − | 0.0677422i | ||||
\(902\) | 17323.1 | 0.639463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49054.4 | −1.80478 | ||||||||
\(905\) | 4044.28 | − | 7004.90i | 0.148548 | − | 0.257294i | ||||
\(906\) | 9199.01 | + | 15933.1i | 0.337325 | + | 0.584264i | ||||
\(907\) | 1786.30 | + | 3093.96i | 0.0653949 | + | 0.113267i | 0.896869 | − | 0.442296i | \(-0.145836\pi\) |
−0.831474 | + | 0.555563i | \(0.812503\pi\) | |||||||
\(908\) | 5156.01 | − | 8930.47i | 0.188445 | − | 0.326397i | ||||
\(909\) | −4114.88 | −0.150145 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29457.7 | 1.07133 | 0.535663 | − | 0.844432i | \(-0.320062\pi\) | ||||
0.535663 | + | 0.844432i | \(0.320062\pi\) | |||||||
\(912\) | −4079.30 | + | 7065.56i | −0.148113 | + | 0.256540i | ||||
\(913\) | 7435.36 | + | 12878.4i | 0.269523 | + | 0.466828i | ||||
\(914\) | −13095.4 | − | 22681.9i | −0.473913 | − | 0.820842i | ||||
\(915\) | −112.154 | + | 194.257i | −0.00405214 | + | 0.00701851i | ||||
\(916\) | −10427.9 | −0.376143 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 367.611 | 0.0132167 | ||||||||
\(919\) | 1655.32 | − | 2867.10i | 0.0594168 | − | 0.102913i | −0.834787 | − | 0.550573i | \(-0.814409\pi\) |
0.894204 | + | 0.447660i | \(0.147743\pi\) | |||||||
\(920\) | 6254.34 | + | 10832.8i | 0.224130 | + | 0.388204i | ||||
\(921\) | −6973.36 | − | 12078.2i | −0.249490 | − | 0.432129i | ||||
\(922\) | −2122.92 | + | 3677.01i | −0.0758295 | + | 0.131340i | ||||
\(923\) | −14492.5 | −0.516820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15207.3 | −0.540556 | ||||||||
\(926\) | 6532.80 | − | 11315.1i | 0.231837 | − | 0.401554i | ||||
\(927\) | 3537.20 | + | 6126.61i | 0.125326 | + | 0.217070i | ||||
\(928\) | −2873.19 | − | 4976.52i | −0.101635 | − | 0.176037i | ||||
\(929\) | −15733.8 | + | 27251.7i | −0.555660 | + | 0.962431i | 0.442192 | + | 0.896920i | \(0.354201\pi\) |
−0.997852 | + | 0.0655103i | \(0.979132\pi\) | |||||||
\(930\) | −17685.7 | −0.623587 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6851.94 | 0.240818 | ||||||||
\(933\) | −9625.77 | + | 16672.3i | −0.337764 | + | 0.585024i | ||||
\(934\) | 9791.26 | + | 16959.0i | 0.343019 | + | 0.594126i | ||||
\(935\) | 1343.40 | + | 2326.84i | 0.0469881 | + | 0.0813859i | ||||
\(936\) | −9653.08 | + | 16719.6i | −0.337095 | + | 0.583865i | ||||
\(937\) | 17363.4 | 0.605375 | 0.302688 | − | 0.953090i | \(-0.402116\pi\) | ||||
0.302688 | + | 0.953090i | \(0.402116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17604.6 | −0.611828 | ||||||||
\(940\) | 6601.97 | − | 11434.9i | 0.229077 | − | 0.396773i | ||||
\(941\) | −2773.89 | − | 4804.51i | −0.0960958 | − | 0.166443i | 0.813970 | − | 0.580907i | \(-0.197302\pi\) |
−0.910065 | + | 0.414465i | \(0.863969\pi\) | |||||||
\(942\) | −3923.13 | − | 6795.07i | −0.135693 | − | 0.235027i | ||||
\(943\) | 3836.02 | − | 6644.18i | 0.132469 | − | 0.229443i | ||||
\(944\) | −26304.3 | −0.906919 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28981.6 | −0.996062 | ||||||||
\(947\) | 18980.1 | − | 32874.6i | 0.651290 | − | 1.12807i | −0.331520 | − | 0.943448i | \(-0.607562\pi\) |
0.982810 | − | 0.184619i | \(-0.0591052\pi\) | |||||||
\(948\) | −450.316 | − | 779.969i | −0.0154278 | − | 0.0267218i | ||||
\(949\) | −27040.8 | − | 46836.1i | −0.924955 | − | 1.60207i | ||||
\(950\) | 21225.5 | − | 36763.7i | 0.724892 | − | 1.25555i | ||||
\(951\) | −11923.6 | −0.406570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10019.3 | −0.340563 | −0.170282 | − | 0.985395i | \(-0.554468\pi\) | ||||
−0.170282 | + | 0.985395i | \(0.554468\pi\) | |||||||
\(954\) | 4075.26 | − | 7058.55i | 0.138303 | − | 0.239548i | ||||
\(955\) | 1785.08 | + | 3091.85i | 0.0604857 | + | 0.104764i | ||||
\(956\) | 4605.83 | + | 7977.53i | 0.155819 | + | 0.269887i | ||||
\(957\) | −2166.15 | + | 3751.88i | −0.0731679 | + | 0.126730i | ||||
\(958\) | −5059.61 | −0.170635 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −33746.9 | −1.13456 | ||||||||
\(961\) | 7366.54 | − | 12759.2i | 0.247274 | − | 0.428291i | ||||
\(962\) | −5917.46 | − | 10249.3i | −0.198323 | − | 0.343505i | ||||
\(963\) | 884.074 | + | 1531.26i | 0.0295835 | + | 0.0512401i | ||||
\(964\) | 4715.56 | − | 8167.58i | 0.157550 | − | 0.272884i | ||||
\(965\) | 47527.3 | 1.58545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27834.4 | 0.925641 | 0.462820 | − | 0.886452i | \(-0.346837\pi\) | ||||
0.462820 | + | 0.886452i | \(0.346837\pi\) | |||||||
\(968\) | −9304.68 | + | 16116.2i | −0.308950 | + | 0.535117i | ||||
\(969\) | 548.909 | + | 950.738i | 0.0181976 | + | 0.0315192i | ||||
\(970\) | 14487.3 | + | 25092.7i | 0.479545 | + | 0.830597i | ||||
\(971\) | −9137.67 | + | 15826.9i | −0.302000 | + | 0.523079i | −0.976589 | − | 0.215115i | \(-0.930988\pi\) |
0.674589 | + | 0.738193i | \(0.264321\pi\) | |||||||
\(972\) | −527.692 | −0.0174133 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23200.8 | 0.763245 | ||||||||
\(975\) | 35508.6 | − | 61502.7i | 1.16634 | − | 2.02017i | ||||
\(976\) | −78.7386 | − | 136.379i | −0.00258234 | − | 0.00447274i | ||||
\(977\) | 21514.5 | + | 37264.2i | 0.704513 | + | 1.22025i | 0.966867 | + | 0.255280i | \(0.0821677\pi\) |
−0.262354 | + | 0.964972i | \(0.584499\pi\) | |||||||
\(978\) | −10750.7 | + | 18620.8i | −0.351502 | + | 0.608820i | ||||
\(979\) | −6833.24 | −0.223076 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2757.09 | −0.0897320 | ||||||||
\(982\) | 14144.0 | − | 24498.2i | 0.459628 | − | 0.796099i | ||||
\(983\) | 15279.6 | + | 26465.1i | 0.495772 | + | 0.858702i | 0.999988 | − | 0.00487535i | \(-0.00155188\pi\) |
−0.504216 | + | 0.863577i | \(0.668219\pi\) | |||||||
\(984\) | 11039.8 | + | 19121.5i | 0.357658 | + | 0.619481i | ||||
\(985\) | −26519.6 | + | 45933.3i | −0.857853 | + | 1.48584i | ||||
\(986\) | 821.253 | 0.0265254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12309.0 | −0.396358 | ||||||||
\(989\) | −6417.69 | + | 11115.8i | −0.206340 | + | 0.357392i | ||||
\(990\) | 5175.77 | + | 8964.69i | 0.166158 | + | 0.287795i | ||||
\(991\) | 22473.0 | + | 38924.3i | 0.720360 | + | 1.24770i | 0.960855 | + | 0.277050i | \(0.0893569\pi\) |
−0.240495 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(992\) | −5845.14 | + | 10124.1i | −0.187080 | + | 0.324032i | ||||
\(993\) | −26738.5 | −0.854501 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26711.2 | −0.851058 | ||||||||
\(996\) | −2023.27 | + | 3504.40i | −0.0643671 | + | 0.111487i | ||||
\(997\) | 14503.1 | + | 25120.0i | 0.460698 | + | 0.797953i | 0.998996 | − | 0.0448018i | \(-0.0142656\pi\) |
−0.538297 | + | 0.842755i | \(0.680932\pi\) | |||||||
\(998\) | 11099.6 | + | 19225.0i | 0.352055 | + | 0.609777i | ||||
\(999\) | 757.590 | − | 1312.18i | 0.0239931 | − | 0.0415572i |
(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 | 147.4.e.j.79.1 | 4 | ||
3.2 | odd | 2 | 441.4.e.u.226.2 | 4 | |||
7.2 | even | 3 | 147.4.a.k.1.2 | yes | 2 | ||
7.3 | odd | 6 | 147.4.e.k.67.1 | 4 | |||
7.4 | even | 3 | inner | 147.4.e.j.67.1 | 4 | ||
7.5 | odd | 6 | 147.4.a.j.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 147.4.e.k.79.1 | 4 | |||
21.2 | odd | 6 | 441.4.a.o.1.1 | 2 | |||
21.5 | even | 6 | 441.4.a.n.1.1 | 2 | |||
21.11 | odd | 6 | 441.4.e.u.361.2 | 4 | |||
21.17 | even | 6 | 441.4.e.v.361.2 | 4 | |||
21.20 | even | 2 | 441.4.e.v.226.2 | 4 | |||
28.19 | even | 6 | 2352.4.a.cf.1.2 | 2 | |||
28.23 | odd | 6 | 2352.4.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.2 | ✓ | 2 | 7.5 | odd | 6 | ||
147.4.a.k.1.2 | yes | 2 | 7.2 | even | 3 | ||
147.4.e.j.67.1 | 4 | 7.4 | even | 3 | inner | ||
147.4.e.j.79.1 | 4 | 1.1 | even | 1 | trivial | ||
147.4.e.k.67.1 | 4 | 7.3 | odd | 6 | |||
147.4.e.k.79.1 | 4 | 7.6 | odd | 2 | |||
441.4.a.n.1.1 | 2 | 21.5 | even | 6 | |||
441.4.a.o.1.1 | 2 | 21.2 | odd | 6 | |||
441.4.e.u.226.2 | 4 | 3.2 | odd | 2 | |||
441.4.e.u.361.2 | 4 | 21.11 | odd | 6 | |||
441.4.e.v.226.2 | 4 | 21.20 | even | 2 | |||
441.4.e.v.361.2 | 4 | 21.17 | even | 6 | |||
2352.4.a.bl.1.1 | 2 | 28.23 | odd | 6 | |||
2352.4.a.cf.1.2 | 2 | 28.19 | even | 6 |