Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.16 | ||
Character | \(\chi\) | \(=\) | 105.101 |
Dual form | 105.4.s.a.26.16 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.69077 | − | 2.70822i | 1.65844 | − | 0.957499i | 0.685000 | − | 0.728543i | \(-0.259802\pi\) |
0.973437 | − | 0.228955i | \(-0.0735310\pi\) | |||||||
\(3\) | −2.85230 | + | 4.34332i | −0.548925 | + | 0.835871i | ||||
\(4\) | 10.6689 | − | 18.4790i | 1.33361 | − | 2.30988i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | −1.61684 | + | 28.0981i | −0.110012 | + | 1.91183i | ||||
\(7\) | 14.5222 | − | 11.4937i | 0.784125 | − | 0.620602i | ||||
\(8\) | − | 72.2429i | − | 3.19271i | ||||||
\(9\) | −10.7288 | − | 24.7769i | −0.397362 | − | 0.917662i | ||||
\(10\) | −23.4538 | − | 13.5411i | −0.741675 | − | 0.428206i | ||||
\(11\) | 38.4696 | + | 22.2104i | 1.05446 | + | 0.608790i | 0.923893 | − | 0.382650i | \(-0.124989\pi\) |
0.130562 | + | 0.991440i | \(0.458322\pi\) | |||||||
\(12\) | 49.8294 | + | 99.0459i | 1.19871 | + | 2.38267i | ||||
\(13\) | 22.9471i | 0.489568i | 0.969578 | + | 0.244784i | \(0.0787171\pi\) | ||||
−0.969578 | + | 0.244784i | \(0.921283\pi\) | |||||||
\(14\) | 36.9928 | − | 93.2436i | 0.706196 | − | 1.78003i | ||||
\(15\) | 25.9379 | + | 1.49253i | 0.446475 | + | 0.0256913i | ||||
\(16\) | −110.298 | − | 191.042i | −1.72341 | − | 2.98504i | ||||
\(17\) | −32.3140 | + | 55.9695i | −0.461018 | + | 0.798506i | −0.999012 | − | 0.0444424i | \(-0.985849\pi\) |
0.537994 | + | 0.842949i | \(0.319182\pi\) | |||||||
\(18\) | −117.427 | − | 87.1667i | −1.53766 | − | 1.14141i | ||||
\(19\) | −15.6960 | + | 9.06207i | −0.189521 | + | 0.109420i | −0.591758 | − | 0.806115i | \(-0.701566\pi\) |
0.402237 | + | 0.915535i | \(0.368233\pi\) | |||||||
\(20\) | −106.689 | −1.19282 | ||||||||
\(21\) | 8.49916 | + | 95.8580i | 0.0883176 | + | 0.996092i | ||||
\(22\) | 240.602 | 2.33166 | ||||||||
\(23\) | −76.2989 | + | 44.0512i | −0.691714 | + | 0.399361i | −0.804254 | − | 0.594286i | \(-0.797435\pi\) |
0.112540 | + | 0.993647i | \(0.464101\pi\) | |||||||
\(24\) | 313.774 | + | 206.058i | 2.66870 | + | 1.75256i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 62.1458 | + | 107.640i | 0.468761 | + | 0.811918i | ||||
\(27\) | 138.215 | + | 24.0726i | 0.985169 | + | 0.171584i | ||||
\(28\) | −57.4571 | − | 390.981i | −0.387799 | − | 2.63887i | ||||
\(29\) | 308.783i | 1.97722i | 0.150485 | + | 0.988612i | \(0.451916\pi\) | ||||
−0.150485 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(30\) | 125.711 | − | 63.2442i | 0.765050 | − | 0.384892i | ||||
\(31\) | −82.5212 | − | 47.6436i | −0.478105 | − | 0.276034i | 0.241522 | − | 0.970395i | \(-0.422354\pi\) |
−0.719626 | + | 0.694362i | \(0.755687\pi\) | |||||||
\(32\) | −534.254 | − | 308.452i | −2.95137 | − | 1.70397i | ||||
\(33\) | −206.194 | + | 103.735i | −1.08769 | + | 0.547209i | ||||
\(34\) | 350.053i | 1.76570i | ||||||||
\(35\) | −86.0748 | − | 34.1487i | −0.415694 | − | 0.164920i | ||||
\(36\) | −572.316 | − | 66.0838i | −2.64961 | − | 0.305944i | ||||
\(37\) | −83.8935 | − | 145.308i | −0.372757 | − | 0.645634i | 0.617232 | − | 0.786782i | \(-0.288254\pi\) |
−0.989989 | + | 0.141147i | \(0.954921\pi\) | |||||||
\(38\) | −49.0841 | + | 85.0161i | −0.209539 | + | 0.362932i | ||||
\(39\) | −99.6666 | − | 65.4521i | −0.409216 | − | 0.268736i | ||||
\(40\) | −312.821 | + | 180.607i | −1.23653 | + | 0.713912i | ||||
\(41\) | 271.265 | 1.03328 | 0.516639 | − | 0.856203i | \(-0.327183\pi\) | ||||
0.516639 | + | 0.856203i | \(0.327183\pi\) | |||||||
\(42\) | 299.472 | + | 426.630i | 1.10023 | + | 1.56739i | ||||
\(43\) | 225.930 | 0.801257 | 0.400629 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400629 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(44\) | 820.853 | − | 473.920i | 2.81246 | − | 1.62377i | ||||
\(45\) | −80.4651 | + | 108.399i | −0.266556 | + | 0.359093i | ||||
\(46\) | −238.600 | + | 413.268i | −0.764776 | + | 1.32463i | ||||
\(47\) | −31.1914 | − | 54.0251i | −0.0968029 | − | 0.167667i | 0.813557 | − | 0.581486i | \(-0.197528\pi\) |
−0.910360 | + | 0.413818i | \(0.864195\pi\) | |||||||
\(48\) | 1144.36 | + | 65.8494i | 3.44113 | + | 0.198011i | ||||
\(49\) | 78.7889 | − | 333.828i | 0.229705 | − | 0.973260i | ||||
\(50\) | 135.411i | 0.383000i | ||||||||
\(51\) | −150.924 | − | 299.992i | −0.414384 | − | 0.823672i | ||||
\(52\) | 424.040 | + | 244.820i | 1.13084 | + | 0.652892i | ||||
\(53\) | 19.9236 | + | 11.5029i | 0.0516361 | + | 0.0298121i | 0.525596 | − | 0.850734i | \(-0.323842\pi\) |
−0.473960 | + | 0.880547i | \(0.657176\pi\) | |||||||
\(54\) | 713.530 | − | 261.398i | 1.79813 | − | 0.658737i | ||||
\(55\) | − | 222.104i | − | 0.544518i | ||||||
\(56\) | −830.339 | − | 1049.13i | −1.98141 | − | 2.50349i | ||||
\(57\) | 5.41017 | − | 94.0203i | 0.0125718 | − | 0.218479i | ||||
\(58\) | 836.250 | + | 1448.43i | 1.89319 | + | 3.27910i | ||||
\(59\) | −41.0850 | + | 71.1613i | −0.0906578 | + | 0.157024i | −0.907788 | − | 0.419429i | \(-0.862230\pi\) |
0.817130 | + | 0.576453i | \(0.195564\pi\) | |||||||
\(60\) | 304.308 | − | 463.382i | 0.654766 | − | 0.997040i | ||||
\(61\) | 424.943 | − | 245.341i | 0.891941 | − | 0.514962i | 0.0173639 | − | 0.999849i | \(-0.494473\pi\) |
0.874577 | + | 0.484887i | \(0.161139\pi\) | |||||||
\(62\) | −516.117 | −1.05721 | ||||||||
\(63\) | −440.584 | − | 236.501i | −0.881085 | − | 0.472958i | ||||
\(64\) | −1576.64 | −3.07938 | ||||||||
\(65\) | 99.3640 | − | 57.3678i | 0.189609 | − | 0.109471i | ||||
\(66\) | −686.270 | + | 1045.01i | −1.27991 | + | 1.94897i | ||||
\(67\) | −278.306 | + | 482.040i | −0.507470 | + | 0.878963i | 0.492493 | + | 0.870316i | \(0.336086\pi\) |
−0.999963 | + | 0.00864671i | \(0.997248\pi\) | |||||||
\(68\) | 689.508 | + | 1194.26i | 1.22963 | + | 2.12979i | ||||
\(69\) | 26.2991 | − | 457.037i | 0.0458846 | − | 0.797404i | ||||
\(70\) | −496.239 | + | 72.9254i | −0.847312 | + | 0.124518i | ||||
\(71\) | − | 669.023i | − | 1.11829i | −0.829071 | − | 0.559144i | \(-0.811130\pi\) | ||
0.829071 | − | 0.559144i | \(-0.188870\pi\) | |||||||
\(72\) | −1789.95 | + | 775.078i | −2.92983 | + | 1.26866i | ||||
\(73\) | −184.713 | − | 106.644i | −0.296151 | − | 0.170983i | 0.344561 | − | 0.938764i | \(-0.388028\pi\) |
−0.640713 | + | 0.767781i | \(0.721361\pi\) | |||||||
\(74\) | −787.050 | − | 454.404i | −1.23639 | − | 0.713829i | ||||
\(75\) | −58.3818 | − | 116.046i | −0.0898847 | − | 0.178664i | ||||
\(76\) | 386.728i | 0.583694i | ||||||||
\(77\) | 813.943 | − | 119.614i | 1.20464 | − | 0.177030i | ||||
\(78\) | −644.771 | − | 37.1018i | −0.935974 | − | 0.0538583i | ||||
\(79\) | 288.663 | + | 499.979i | 0.411103 | + | 0.712050i | 0.995011 | − | 0.0997694i | \(-0.0318105\pi\) |
−0.583908 | + | 0.811820i | \(0.698477\pi\) | |||||||
\(80\) | −551.492 | + | 955.212i | −0.770733 | + | 1.33495i | ||||
\(81\) | −498.787 | + | 531.651i | −0.684207 | + | 0.729288i | ||||
\(82\) | 1272.44 | − | 734.643i | 1.71363 | − | 0.989363i | ||||
\(83\) | −1281.15 | −1.69426 | −0.847132 | − | 0.531382i | \(-0.821673\pi\) | ||||
−0.847132 | + | 0.531382i | \(0.821673\pi\) | |||||||
\(84\) | 1862.04 | + | 865.640i | 2.41863 | + | 1.12439i | ||||
\(85\) | 323.140 | 0.412347 | ||||||||
\(86\) | 1059.79 | − | 611.868i | 1.32883 | − | 0.767203i | ||||
\(87\) | −1341.14 | − | 880.741i | −1.65271 | − | 1.08535i | ||||
\(88\) | 1604.54 | − | 2779.15i | 1.94369 | − | 3.36657i | ||||
\(89\) | −511.382 | − | 885.739i | −0.609060 | − | 1.05492i | −0.991396 | − | 0.130900i | \(-0.958213\pi\) |
0.382335 | − | 0.924024i | \(-0.375120\pi\) | |||||||
\(90\) | −83.8746 | + | 726.392i | −0.0982351 | + | 0.850760i | ||||
\(91\) | 263.748 | + | 333.243i | 0.303827 | + | 0.383883i | ||||
\(92\) | 1879.90i | 2.13037i | ||||||||
\(93\) | 442.306 | − | 222.522i | 0.493173 | − | 0.248112i | ||||
\(94\) | −292.623 | − | 168.946i | −0.321083 | − | 0.185377i | ||||
\(95\) | 78.4798 | + | 45.3103i | 0.0847564 | + | 0.0489341i | ||||
\(96\) | 2863.56 | − | 1440.64i | 3.04438 | − | 1.53161i | ||||
\(97\) | 472.961i | 0.495072i | 0.968879 | + | 0.247536i | \(0.0796208\pi\) | ||||
−0.968879 | + | 0.247536i | \(0.920379\pi\) | |||||||
\(98\) | −534.499 | − | 1779.29i | −0.550944 | − | 1.83403i | ||||
\(99\) | 137.573 | − | 1191.45i | 0.139663 | − | 1.20954i | ||||
\(100\) | 266.722 | + | 461.975i | 0.266722 | + | 0.461975i | ||||
\(101\) | −330.855 | + | 573.058i | −0.325954 | + | 0.564568i | −0.981705 | − | 0.190409i | \(-0.939019\pi\) |
0.655751 | + | 0.754977i | \(0.272352\pi\) | |||||||
\(102\) | −1520.39 | − | 998.457i | −1.47589 | − | 0.969235i | ||||
\(103\) | −1149.63 | + | 663.739i | −1.09977 | + | 0.634953i | −0.936161 | − | 0.351572i | \(-0.885647\pi\) |
−0.163610 | + | 0.986525i | \(0.552314\pi\) | |||||||
\(104\) | 1657.77 | 1.56305 | ||||||||
\(105\) | 393.830 | − | 276.448i | 0.366036 | − | 0.256938i | ||||
\(106\) | 124.609 | 0.114180 | ||||||||
\(107\) | −11.2649 | + | 6.50382i | −0.0101778 | + | 0.00587615i | −0.505080 | − | 0.863072i | \(-0.668537\pi\) |
0.494902 | + | 0.868949i | \(0.335204\pi\) | |||||||
\(108\) | 1919.44 | − | 2297.26i | 1.71017 | − | 2.04679i | ||||
\(109\) | 656.500 | − | 1137.09i | 0.576893 | − | 0.999208i | −0.418940 | − | 0.908014i | \(-0.637598\pi\) |
0.995833 | − | 0.0911940i | \(-0.0290683\pi\) | |||||||
\(110\) | −601.506 | − | 1041.84i | −0.521376 | − | 0.903049i | ||||
\(111\) | 870.407 | + | 50.0855i | 0.744283 | + | 0.0428279i | ||||
\(112\) | −3797.56 | − | 1506.62i | −3.20389 | − | 1.27109i | ||||
\(113\) | 785.985i | 0.654329i | 0.944967 | + | 0.327165i | \(0.106093\pi\) | ||||
−0.944967 | + | 0.327165i | \(0.893907\pi\) | |||||||
\(114\) | −229.249 | − | 455.679i | −0.188344 | − | 0.374371i | ||||
\(115\) | 381.495 | + | 220.256i | 0.309344 | + | 0.178600i | ||||
\(116\) | 5706.00 | + | 3294.36i | 4.56714 | + | 2.63684i | ||||
\(117\) | 568.558 | − | 246.195i | 0.449258 | − | 0.194536i | ||||
\(118\) | 445.068i | 0.347219i | ||||||||
\(119\) | 174.027 | + | 1184.21i | 0.134059 | + | 0.912238i | ||||
\(120\) | 107.825 | − | 1873.82i | 0.0820250 | − | 1.42547i | ||||
\(121\) | 321.105 | + | 556.169i | 0.241251 | + | 0.417858i | ||||
\(122\) | 1328.87 | − | 2301.67i | 0.986151 | − | 1.70806i | ||||
\(123\) | −773.728 | + | 1178.19i | −0.567193 | + | 0.863688i | ||||
\(124\) | −1760.81 | + | 1016.61i | −1.27521 | + | 0.736242i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −2707.17 | + | 83.8237i | −1.91408 | + | 0.0592667i | ||||
\(127\) | −443.373 | −0.309787 | −0.154894 | − | 0.987931i | \(-0.549503\pi\) | ||||
−0.154894 | + | 0.987931i | \(0.549503\pi\) | |||||||
\(128\) | −3121.63 | + | 1802.27i | −2.15559 | + | 1.24453i | ||||
\(129\) | −644.421 | + | 981.287i | −0.439830 | + | 0.669748i | ||||
\(130\) | 310.729 | − | 538.198i | 0.209636 | − | 0.363101i | ||||
\(131\) | −1234.95 | − | 2138.99i | −0.823648 | − | 1.42660i | −0.902948 | − | 0.429750i | \(-0.858602\pi\) |
0.0792995 | − | 0.996851i | \(-0.474732\pi\) | |||||||
\(132\) | −282.936 | + | 4916.98i | −0.186564 | + | 3.24219i | ||||
\(133\) | −123.783 | + | 312.006i | −0.0807020 | + | 0.203416i | ||||
\(134\) | 3014.85i | 1.94361i | ||||||||
\(135\) | −241.301 | − | 658.672i | −0.153836 | − | 0.419922i | ||||
\(136\) | 4043.40 | + | 2334.46i | 2.54940 | + | 1.47190i | ||||
\(137\) | −1584.16 | − | 914.618i | −0.987915 | − | 0.570373i | −0.0832645 | − | 0.996527i | \(-0.526535\pi\) |
−0.904650 | + | 0.426155i | \(0.859868\pi\) | |||||||
\(138\) | −1114.39 | − | 2215.08i | −0.687416 | − | 1.36638i | ||||
\(139\) | − | 2449.22i | − | 1.49453i | −0.664525 | − | 0.747266i | \(-0.731366\pi\) | ||
0.664525 | − | 0.747266i | \(-0.268634\pi\) | |||||||
\(140\) | −1549.35 | + | 1226.25i | −0.935317 | + | 0.740264i | ||||
\(141\) | 323.615 | + | 18.6216i | 0.193286 | + | 0.0111222i | ||||
\(142\) | −1811.86 | − | 3138.23i | −1.07076 | − | 1.85461i | ||||
\(143\) | −509.665 | + | 882.766i | −0.298044 | + | 0.516228i | ||||
\(144\) | −3550.06 | + | 4782.50i | −2.05444 | + | 2.76765i | ||||
\(145\) | 1337.07 | − | 771.957i | 0.765776 | − | 0.442121i | ||||
\(146\) | −1155.26 | −0.654864 | ||||||||
\(147\) | 1225.19 | + | 1294.38i | 0.687429 | + | 0.726251i | ||||
\(148\) | −3580.19 | −1.98845 | ||||||||
\(149\) | 733.815 | − | 423.668i | 0.403466 | − | 0.232941i | −0.284512 | − | 0.958672i | \(-0.591832\pi\) |
0.687979 | + | 0.725731i | \(0.258498\pi\) | |||||||
\(150\) | −588.132 | − | 386.232i | −0.320138 | − | 0.210238i | ||||
\(151\) | 209.435 | − | 362.753i | 0.112872 | − | 0.195499i | −0.804055 | − | 0.594554i | \(-0.797328\pi\) |
0.916927 | + | 0.399055i | \(0.130662\pi\) | |||||||
\(152\) | 654.670 | + | 1133.92i | 0.349347 | + | 0.605087i | ||||
\(153\) | 1733.44 | + | 200.156i | 0.915950 | + | 0.105762i | ||||
\(154\) | 3494.08 | − | 2765.41i | 1.82832 | − | 1.44704i | ||||
\(155\) | 476.436i | 0.246892i | ||||||||
\(156\) | −2272.82 | + | 1143.44i | −1.16648 | + | 0.586850i | ||||
\(157\) | 2635.77 | + | 1521.76i | 1.33985 | + | 0.773565i | 0.986786 | − | 0.162032i | \(-0.0518047\pi\) |
0.353069 | + | 0.935597i | \(0.385138\pi\) | |||||||
\(158\) | 2708.10 | + | 1563.52i | 1.36357 | + | 0.787260i | ||||
\(159\) | −106.789 | + | 53.7247i | −0.0532635 | + | 0.0267965i | ||||
\(160\) | 3084.52i | 1.52408i | ||||||||
\(161\) | −601.716 | + | 1516.68i | −0.294546 | + | 0.742429i | ||||
\(162\) | −899.867 | + | 3844.67i | −0.436421 | + | 1.86461i | ||||
\(163\) | 453.547 | + | 785.567i | 0.217942 | + | 0.377487i | 0.954179 | − | 0.299237i | \(-0.0967322\pi\) |
−0.736237 | + | 0.676724i | \(0.763399\pi\) | |||||||
\(164\) | 2894.08 | − | 5012.70i | 1.37799 | − | 2.38675i | ||||
\(165\) | 964.668 | + | 633.507i | 0.455147 | + | 0.298900i | ||||
\(166\) | −6009.55 | + | 3469.62i | −2.80983 | + | 1.62226i | ||||
\(167\) | −1763.11 | −0.816967 | −0.408483 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408483 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(168\) | 6925.06 | − | 614.004i | 3.18024 | − | 0.281973i | ||||
\(169\) | 1670.43 | 0.760323 | ||||||||
\(170\) | 1515.78 | − | 875.133i | 0.683851 | − | 0.394822i | ||||
\(171\) | 392.928 | + | 291.672i | 0.175719 | + | 0.130437i | ||||
\(172\) | 2410.42 | − | 4174.97i | 1.06856 | − | 1.85081i | ||||
\(173\) | 861.685 | + | 1492.48i | 0.378686 | + | 0.655904i | 0.990871 | − | 0.134811i | \(-0.0430426\pi\) |
−0.612185 | + | 0.790714i | \(0.709709\pi\) | |||||||
\(174\) | −8676.21 | − | 499.251i | −3.78013 | − | 0.217518i | ||||
\(175\) | 67.3187 | + | 458.086i | 0.0290790 | + | 0.197875i | ||||
\(176\) | − | 9799.08i | − | 4.19678i | ||||||
\(177\) | −191.889 | − | 381.418i | −0.0814874 | − | 0.161973i | ||||
\(178\) | −4797.55 | − | 2769.86i | −2.02018 | − | 1.16635i | ||||
\(179\) | 173.172 | + | 99.9810i | 0.0723100 | + | 0.0417482i | 0.535719 | − | 0.844396i | \(-0.320041\pi\) |
−0.463409 | + | 0.886144i | \(0.653374\pi\) | |||||||
\(180\) | 1144.64 | + | 2643.41i | 0.473979 | + | 1.09460i | ||||
\(181\) | − | 266.755i | − | 0.109546i | −0.998499 | − | 0.0547729i | \(-0.982557\pi\) | ||
0.998499 | − | 0.0547729i | \(-0.0174435\pi\) | |||||||
\(182\) | 2139.67 | + | 848.879i | 0.871446 | + | 0.345731i | ||||
\(183\) | −146.472 | + | 2545.45i | −0.0591666 | + | 1.02822i | ||||
\(184\) | 3182.38 | + | 5512.05i | 1.27505 | + | 2.20844i | ||||
\(185\) | −419.468 | + | 726.539i | −0.166702 | + | 0.288736i | ||||
\(186\) | 1472.12 | − | 2241.66i | 0.580328 | − | 0.883690i | ||||
\(187\) | −2486.21 | + | 1435.42i | −0.972245 | + | 0.561326i | ||||
\(188\) | −1331.11 | −0.516388 | ||||||||
\(189\) | 2283.88 | − | 1239.02i | 0.878982 | − | 0.476855i | ||||
\(190\) | 490.841 | 0.187418 | ||||||||
\(191\) | 1178.07 | − | 680.162i | 0.446296 | − | 0.257669i | −0.259969 | − | 0.965617i | \(-0.583712\pi\) |
0.706265 | + | 0.707948i | \(0.250379\pi\) | |||||||
\(192\) | 4497.06 | − | 6847.86i | 1.69035 | − | 2.57397i | ||||
\(193\) | −1749.00 | + | 3029.35i | −0.652308 | + | 1.12983i | 0.330253 | + | 0.943892i | \(0.392866\pi\) |
−0.982561 | + | 0.185939i | \(0.940467\pi\) | |||||||
\(194\) | 1280.88 | + | 2218.55i | 0.474031 | + | 0.821045i | ||||
\(195\) | −34.2493 | + | 595.199i | −0.0125777 | + | 0.218580i | ||||
\(196\) | −5328.23 | − | 5017.51i | −1.94177 | − | 1.82854i | ||||
\(197\) | − | 3118.87i | − | 1.12797i | −0.825784 | − | 0.563986i | \(-0.809267\pi\) | ||
0.825784 | − | 0.563986i | \(-0.190733\pi\) | |||||||
\(198\) | −2581.37 | − | 5961.37i | −0.926514 | − | 2.13968i | ||||
\(199\) | 3212.10 | + | 1854.51i | 1.14422 | + | 0.660615i | 0.947472 | − | 0.319839i | \(-0.103629\pi\) |
0.196747 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(200\) | 1564.10 | + | 903.036i | 0.552994 | + | 0.319271i | ||||
\(201\) | −1299.84 | − | 2583.69i | −0.456137 | − | 0.906664i | ||||
\(202\) | 3584.11i | 1.24840i | ||||||||
\(203\) | 3549.06 | + | 4484.21i | 1.22707 | + | 1.55039i | ||||
\(204\) | −7153.74 | − | 411.644i | −2.45521 | − | 0.141279i | ||||
\(205\) | −678.162 | − | 1174.61i | −0.231048 | − | 0.400187i | ||||
\(206\) | −3595.10 | + | 6226.89i | −1.21593 | + | 2.10606i | ||||
\(207\) | 1910.04 | + | 1417.83i | 0.641340 | + | 0.476069i | ||||
\(208\) | 4383.87 | − | 2531.03i | 1.46138 | − | 0.843728i | ||||
\(209\) | −805.089 | −0.266455 | ||||||||
\(210\) | 1098.68 | − | 2363.33i | 0.361030 | − | 0.776595i | ||||
\(211\) | −3228.76 | −1.05344 | −0.526722 | − | 0.850038i | \(-0.676579\pi\) | ||||
−0.526722 | + | 0.850038i | \(0.676579\pi\) | |||||||
\(212\) | 425.124 | − | 245.445i | 0.137725 | − | 0.0795154i | ||||
\(213\) | 2905.78 | + | 1908.25i | 0.934744 | + | 0.613856i | ||||
\(214\) | −35.2275 | + | 61.0158i | −0.0112528 | + | 0.0194904i | ||||
\(215\) | −564.826 | − | 978.307i | −0.179167 | − | 0.310326i | ||||
\(216\) | 1739.07 | − | 9985.08i | 0.547819 | − | 3.14536i | ||||
\(217\) | −1745.99 | + | 256.585i | −0.546201 | + | 0.0802678i | ||||
\(218\) | − | 7111.78i | − | 2.20950i | ||||||
\(219\) | 990.046 | − | 498.086i | 0.305485 | − | 0.153687i | ||||
\(220\) | −4104.26 | − | 2369.60i | −1.25777 | − | 0.726174i | ||||
\(221\) | −1284.34 | − | 741.514i | −0.390923 | − | 0.225700i | ||||
\(222\) | 4218.52 | − | 2122.31i | 1.27535 | − | 0.641623i | ||||
\(223\) | − | 573.232i | − | 0.172137i | −0.996289 | − | 0.0860683i | \(-0.972570\pi\) | ||
0.996289 | − | 0.0860683i | \(-0.0274303\pi\) | |||||||
\(224\) | −11303.8 | + | 1661.17i | −3.37173 | + | 0.495497i | ||||
\(225\) | 670.545 | + | 77.4261i | 0.198680 | + | 0.0229411i | ||||
\(226\) | 2128.62 | + | 3686.87i | 0.626520 | + | 1.08516i | ||||
\(227\) | −599.567 | + | 1038.48i | −0.175307 | + | 0.303640i | −0.940267 | − | 0.340437i | \(-0.889425\pi\) |
0.764961 | + | 0.644077i | \(0.222758\pi\) | |||||||
\(228\) | −1679.68 | − | 1103.06i | −0.487893 | − | 0.320404i | ||||
\(229\) | 3537.94 | − | 2042.63i | 1.02093 | − | 0.589436i | 0.106559 | − | 0.994306i | \(-0.466017\pi\) |
0.914374 | + | 0.404871i | \(0.132683\pi\) | |||||||
\(230\) | 2386.00 | 0.684036 | ||||||||
\(231\) | −1802.09 | + | 3876.39i | −0.513284 | + | 1.10410i | ||||
\(232\) | 22307.3 | 6.31271 | ||||||||
\(233\) | −471.919 | + | 272.462i | −0.132688 | + | 0.0766077i | −0.564875 | − | 0.825177i | \(-0.691076\pi\) |
0.432186 | + | 0.901784i | \(0.357742\pi\) | |||||||
\(234\) | 2000.23 | − | 2694.62i | 0.558798 | − | 0.752790i | ||||
\(235\) | −155.957 | + | 270.126i | −0.0432916 | + | 0.0749832i | ||||
\(236\) | 876.660 | + | 1518.42i | 0.241804 | + | 0.418817i | ||||
\(237\) | −2994.92 | − | 172.335i | −0.820847 | − | 0.0472336i | ||||
\(238\) | 4023.41 | + | 5083.55i | 1.09580 | + | 1.38453i | ||||
\(239\) | 2085.41i | 0.564411i | 0.959354 | + | 0.282205i | \(0.0910659\pi\) | ||||
−0.959354 | + | 0.282205i | \(0.908934\pi\) | |||||||
\(240\) | −2575.77 | − | 5119.85i | −0.692771 | − | 1.37702i | ||||
\(241\) | 733.059 | + | 423.232i | 0.195936 | + | 0.113124i | 0.594758 | − | 0.803905i | \(-0.297248\pi\) |
−0.398823 | + | 0.917028i | \(0.630581\pi\) | |||||||
\(242\) | 3012.45 | + | 1739.24i | 0.800198 | + | 0.461994i | ||||
\(243\) | −886.439 | − | 3682.82i | −0.234013 | − | 0.972234i | ||||
\(244\) | − | 10470.0i | − | 2.74703i | ||||||
\(245\) | −1642.49 | + | 493.405i | −0.428306 | + | 0.128663i | ||||
\(246\) | −438.591 | + | 7622.03i | −0.113673 | + | 1.97546i | ||||
\(247\) | −207.948 | − | 360.177i | −0.0535686 | − | 0.0927835i | ||||
\(248\) | −3441.91 | + | 5961.57i | −0.881297 | + | 1.52645i | ||||
\(249\) | 3654.21 | − | 5564.42i | 0.930025 | − | 1.41619i | ||||
\(250\) | 586.346 | − | 338.527i | 0.148335 | − | 0.0856413i | ||||
\(251\) | 2920.18 | 0.734343 | 0.367172 | − | 0.930153i | \(-0.380326\pi\) | ||||
0.367172 | + | 0.930153i | \(0.380326\pi\) | |||||||
\(252\) | −9070.84 | + | 5618.35i | −2.26750 | + | 1.40446i | ||||
\(253\) | −3913.58 | −0.972509 | ||||||||
\(254\) | −2079.76 | + | 1200.75i | −0.513763 | + | 0.296621i | ||||
\(255\) | −921.693 | + | 1403.50i | −0.226348 | + | 0.344669i | ||||
\(256\) | −3455.32 | + | 5984.79i | −0.843585 | + | 1.46113i | ||||
\(257\) | −1596.86 | − | 2765.85i | −0.387586 | − | 0.671318i | 0.604538 | − | 0.796576i | \(-0.293358\pi\) |
−0.992124 | + | 0.125258i | \(0.960024\pi\) | |||||||
\(258\) | −365.293 | + | 6348.22i | −0.0881478 | + | 1.53187i | ||||
\(259\) | −2888.45 | − | 1145.94i | −0.692970 | − | 0.274924i | ||||
\(260\) | − | 2448.20i | − | 0.583965i | ||||||
\(261\) | 7650.67 | − | 3312.86i | 1.81442 | − | 0.785674i | ||||
\(262\) | −11585.7 | − | 6689.01i | −2.73194 | − | 1.57728i | ||||
\(263\) | −3540.11 | − | 2043.89i | −0.830010 | − | 0.479207i | 0.0238458 | − | 0.999716i | \(-0.492409\pi\) |
−0.853856 | + | 0.520509i | \(0.825742\pi\) | |||||||
\(264\) | 7494.09 | + | 14896.0i | 1.74708 | + | 3.47267i | ||||
\(265\) | − | 115.029i | − | 0.0266648i | ||||||
\(266\) | 264.342 | + | 1798.78i | 0.0609318 | + | 0.414625i | ||||
\(267\) | 5305.66 | + | 305.301i | 1.21611 | + | 0.0699780i | ||||
\(268\) | 5938.41 | + | 10285.6i | 1.35353 | + | 2.34438i | ||||
\(269\) | −2040.61 | + | 3534.43i | −0.462520 | + | 0.801109i | −0.999086 | − | 0.0427501i | \(-0.986388\pi\) |
0.536566 | + | 0.843859i | \(0.319721\pi\) | |||||||
\(270\) | −2915.71 | − | 2436.18i | −0.657202 | − | 0.549116i | ||||
\(271\) | −3822.65 | + | 2207.01i | −0.856861 | + | 0.494709i | −0.862960 | − | 0.505272i | \(-0.831392\pi\) |
0.00609886 | + | 0.999981i | \(0.498059\pi\) | |||||||
\(272\) | 14256.7 | 3.17809 | ||||||||
\(273\) | −2199.67 | + | 195.031i | −0.487655 | + | 0.0432375i | ||||
\(274\) | −9907.93 | −2.18453 | ||||||||
\(275\) | −961.739 | + | 555.260i | −0.210891 | + | 0.121758i | ||||
\(276\) | −8165.02 | − | 5362.05i | −1.78071 | − | 1.16941i | ||||
\(277\) | 2349.99 | − | 4070.31i | 0.509738 | − | 0.882892i | −0.490199 | − | 0.871611i | \(-0.663076\pi\) |
0.999936 | − | 0.0112809i | \(-0.00359091\pi\) | |||||||
\(278\) | −6633.01 | − | 11488.7i | −1.43101 | − | 2.47859i | ||||
\(279\) | −295.109 | + | 2555.77i | −0.0633251 | + | 0.548424i | ||||
\(280\) | −2467.00 | + | 6218.29i | −0.526541 | + | 1.32719i | ||||
\(281\) | 5240.30i | 1.11249i | 0.831018 | + | 0.556246i | \(0.187759\pi\) | ||||
−0.831018 | + | 0.556246i | \(0.812241\pi\) | |||||||
\(282\) | 1568.44 | − | 789.070i | 0.331202 | − | 0.166626i | ||||
\(283\) | −3198.19 | − | 1846.48i | −0.671777 | − | 0.387851i | 0.124972 | − | 0.992160i | \(-0.460116\pi\) |
−0.796750 | + | 0.604309i | \(0.793449\pi\) | |||||||
\(284\) | −12362.9 | − | 7137.71i | −2.58310 | − | 1.49136i | ||||
\(285\) | −420.645 | + | 211.624i | −0.0874276 | + | 0.0439843i | ||||
\(286\) | 5521.13i | 1.14151i | ||||||||
\(287\) | 3939.36 | − | 3117.84i | 0.810220 | − | 0.641255i | ||||
\(288\) | −1910.58 | + | 16546.5i | −0.390909 | + | 3.38545i | ||||
\(289\) | 368.108 | + | 637.582i | 0.0749253 | + | 0.129774i | ||||
\(290\) | 4181.25 | − | 7242.14i | 0.846660 | − | 1.46646i | ||||
\(291\) | −2054.22 | − | 1349.03i | −0.413816 | − | 0.271757i | ||||
\(292\) | −3941.36 | + | 2275.54i | −0.789899 | + | 0.456048i | ||||
\(293\) | −3440.35 | −0.685964 | −0.342982 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342982 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(294\) | 9252.56 | + | 2753.57i | 1.83544 | + | 0.546229i | ||||
\(295\) | 410.850 | 0.0810868 | ||||||||
\(296\) | −10497.5 | + | 6060.71i | −2.06133 | + | 1.19011i | ||||
\(297\) | 4782.42 | + | 3995.88i | 0.934358 | + | 0.780689i | ||||
\(298\) | 2294.77 | − | 3974.66i | 0.446082 | − | 0.772637i | ||||
\(299\) | −1010.85 | − | 1750.84i | −0.195515 | − | 0.338641i | ||||
\(300\) | −2767.27 | − | 159.236i | −0.532562 | − | 0.0306450i | ||||
\(301\) | 3281.01 | − | 2596.78i | 0.628286 | − | 0.497262i | ||||
\(302\) | − | 2268.79i | − | 0.432298i | ||||||
\(303\) | −1545.27 | − | 3071.54i | −0.292982 | − | 0.582361i | ||||
\(304\) | 3462.48 | + | 1999.06i | 0.653246 | + | 0.377152i | ||||
\(305\) | −2124.72 | − | 1226.70i | −0.398888 | − | 0.230298i | ||||
\(306\) | 8673.23 | − | 3755.64i | 1.62031 | − | 0.701621i | ||||
\(307\) | − | 962.266i | − | 0.178891i | −0.995992 | − | 0.0894453i | \(-0.971491\pi\) | ||
0.995992 | − | 0.0894453i | \(-0.0285094\pi\) | |||||||
\(308\) | 6473.49 | − | 16317.0i | 1.19760 | − | 3.01866i | ||||
\(309\) | 396.260 | − | 6886.39i | 0.0729529 | − | 1.26781i | ||||
\(310\) | 1290.29 | + | 2234.85i | 0.236399 | + | 0.409455i | ||||
\(311\) | 4433.22 | − | 7678.57i | 0.808312 | − | 1.40004i | −0.105721 | − | 0.994396i | \(-0.533715\pi\) |
0.914032 | − | 0.405641i | \(-0.132952\pi\) | |||||||
\(312\) | −4728.45 | + | 7200.20i | −0.857999 | + | 1.30651i | ||||
\(313\) | 6119.35 | − | 3533.01i | 1.10507 | − | 0.638011i | 0.167521 | − | 0.985869i | \(-0.446424\pi\) |
0.937548 | + | 0.347857i | \(0.113091\pi\) | |||||||
\(314\) | 16485.0 | 2.96275 | ||||||||
\(315\) | 77.3791 | + | 2499.04i | 0.0138407 | + | 0.446999i | ||||
\(316\) | 12318.8 | 2.19300 | ||||||||
\(317\) | 5750.08 | − | 3319.81i | 1.01879 | − | 0.588200i | 0.105038 | − | 0.994468i | \(-0.466504\pi\) |
0.913754 | + | 0.406269i | \(0.133170\pi\) | |||||||
\(318\) | −355.423 | + | 541.217i | −0.0626764 | + | 0.0954400i | ||||
\(319\) | −6858.19 | + | 11878.7i | −1.20371 | + | 2.08489i | ||||
\(320\) | 3941.61 | + | 6827.07i | 0.688571 | + | 1.19264i | ||||
\(321\) | 3.88286 | − | 67.4780i | 0.000675140 | − | 0.0117329i | ||||
\(322\) | 1284.98 | + | 8743.96i | 0.222389 | + | 1.51330i | ||||
\(323\) | − | 1171.33i | − | 0.201778i | ||||||
\(324\) | 4502.90 | + | 14889.2i | 0.772102 | + | 2.55302i | ||||
\(325\) | −496.820 | − | 286.839i | −0.0847957 | − | 0.0489568i | ||||
\(326\) | 4254.97 | + | 2456.61i | 0.722887 | + | 0.417359i | ||||
\(327\) | 3066.21 | + | 6094.71i | 0.518538 | + | 1.03070i | ||||
\(328\) | − | 19596.9i | − | 3.29896i | ||||||
\(329\) | −1073.92 | − | 426.058i | −0.179960 | − | 0.0713962i | ||||
\(330\) | 6240.71 | + | 359.106i | 1.04103 | + | 0.0599035i | ||||
\(331\) | −5714.37 | − | 9897.58i | −0.948913 | − | 1.64357i | −0.747720 | − | 0.664014i | \(-0.768851\pi\) |
−0.201194 | − | 0.979552i | \(-0.564482\pi\) | |||||||
\(332\) | −13668.4 | + | 23674.3i | −2.25948 | + | 3.91354i | ||||
\(333\) | −2700.20 | + | 3637.59i | −0.444354 | + | 0.598616i | ||||
\(334\) | −8270.33 | + | 4774.88i | −1.35489 | + | 0.782244i | ||||
\(335\) | 2783.06 | 0.453895 | ||||||||
\(336\) | 17375.5 | − | 12196.7i | 2.82116 | − | 1.98031i | ||||
\(337\) | −3287.98 | −0.531477 | −0.265738 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265738 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(338\) | 7835.59 | − | 4523.88i | 1.26095 | − | 0.728008i | ||||
\(339\) | −3413.78 | − | 2241.86i | −0.546935 | − | 0.359178i | ||||
\(340\) | 3447.54 | − | 5971.31i | 0.549909 | − | 0.952470i | ||||
\(341\) | −2116.37 | − | 3665.66i | −0.336093 | − | 0.582131i | ||||
\(342\) | 2633.05 | + | 304.031i | 0.416312 | + | 0.0480705i | ||||
\(343\) | −2692.74 | − | 5753.50i | −0.423890 | − | 0.905714i | ||||
\(344\) | − | 16321.9i | − | 2.55819i | ||||||
\(345\) | −2044.78 | + | 1028.72i | −0.319093 | + | 0.160534i | ||||
\(346\) | 8083.93 | + | 4667.26i | 1.25605 | + | 0.725183i | ||||
\(347\) | −4738.46 | − | 2735.75i | −0.733066 | − | 0.423236i | 0.0864768 | − | 0.996254i | \(-0.472439\pi\) |
−0.819543 | + | 0.573018i | \(0.805772\pi\) | |||||||
\(348\) | −30583.7 | + | 15386.5i | −4.71108 | + | 2.37012i | ||||
\(349\) | − | 5647.28i | − | 0.866165i | −0.901354 | − | 0.433083i | \(-0.857426\pi\) | ||
0.901354 | − | 0.433083i | \(-0.142574\pi\) | |||||||
\(350\) | 1556.37 | + | 1966.46i | 0.237690 | + | 0.300320i | ||||
\(351\) | −552.397 | + | 3171.65i | −0.0840022 | + | 0.482308i | ||||
\(352\) | −13701.7 | − | 23732.0i | −2.07472 | − | 3.59352i | ||||
\(353\) | −5123.73 | + | 8874.56i | −0.772546 | + | 1.33809i | 0.163618 | + | 0.986524i | \(0.447684\pi\) |
−0.936164 | + | 0.351565i | \(0.885650\pi\) | |||||||
\(354\) | −1933.07 | − | 1269.47i | −0.290230 | − | 0.190597i | ||||
\(355\) | −2896.95 | + | 1672.56i | −0.433111 | + | 0.250057i | ||||
\(356\) | −21823.5 | −3.24899 | ||||||||
\(357\) | −5639.77 | − | 2621.86i | −0.836102 | − | 0.388694i | ||||
\(358\) | 1083.08 | 0.159895 | ||||||||
\(359\) | 757.417 | − | 437.295i | 0.111351 | − | 0.0642884i | −0.443290 | − | 0.896378i | \(-0.646189\pi\) |
0.554641 | + | 0.832090i | \(0.312856\pi\) | |||||||
\(360\) | 7831.06 | + | 5813.03i | 1.14648 | + | 0.851037i | ||||
\(361\) | −3265.26 | + | 5655.59i | −0.476054 | + | 0.824551i | ||||
\(362\) | −722.431 | − | 1251.29i | −0.104890 | − | 0.181675i | ||||
\(363\) | −3331.51 | − | 191.703i | −0.481704 | − | 0.0277185i | ||||
\(364\) | 8971.89 | − | 1318.48i | 1.29191 | − | 0.189854i | ||||
\(365\) | 1066.44i | 0.152932i | ||||||||
\(366\) | 6206.56 | + | 12336.8i | 0.886399 | + | 1.76190i | ||||
\(367\) | 2917.76 | + | 1684.57i | 0.415002 | + | 0.239602i | 0.692937 | − | 0.720998i | \(-0.256316\pi\) |
−0.277934 | + | 0.960600i | \(0.589650\pi\) | |||||||
\(368\) | 16831.3 | + | 9717.55i | 2.38422 | + | 1.37653i | ||||
\(369\) | −2910.34 | − | 6721.09i | −0.410586 | − | 0.948200i | ||||
\(370\) | 4544.04i | 0.638468i | ||||||||
\(371\) | 421.545 | − | 61.9488i | 0.0589907 | − | 0.00866905i | ||||
\(372\) | 606.927 | − | 10547.4i | 0.0845905 | − | 1.47005i | ||||
\(373\) | 5197.92 | + | 9003.06i | 0.721549 | + | 1.24976i | 0.960379 | + | 0.278699i | \(0.0899030\pi\) |
−0.238829 | + | 0.971062i | \(0.576764\pi\) | |||||||
\(374\) | −7774.83 | + | 13466.4i | −1.07494 | + | 1.86185i | ||||
\(375\) | −356.537 | + | 542.914i | −0.0490974 | + | 0.0747626i | ||||
\(376\) | −3902.93 | + | 2253.36i | −0.535314 | + | 0.309064i | ||||
\(377\) | −7085.68 | −0.967987 | ||||||||
\(378\) | 7357.59 | − | 11997.2i | 1.00115 | − | 1.63246i | ||||
\(379\) | −10819.1 | −1.46634 | −0.733169 | − | 0.680047i | \(-0.761959\pi\) | ||||
−0.733169 | + | 0.680047i | \(0.761959\pi\) | |||||||
\(380\) | 1674.58 | − | 966.820i | 0.226064 | − | 0.130518i | ||||
\(381\) | 1264.63 | − | 1925.71i | 0.170050 | − | 0.258942i | ||||
\(382\) | 3684.05 | − | 6380.96i | 0.493435 | − | 0.854655i | ||||
\(383\) | 5329.00 | + | 9230.09i | 0.710964 | + | 1.23142i | 0.964496 | + | 0.264098i | \(0.0850742\pi\) |
−0.253532 | + | 0.967327i | \(0.581592\pi\) | |||||||
\(384\) | 1075.98 | − | 18698.9i | 0.142991 | − | 2.48495i | ||||
\(385\) | −2552.80 | − | 3225.44i | −0.337929 | − | 0.426971i | ||||
\(386\) | 18946.6i | 2.49834i | ||||||||
\(387\) | −2423.96 | − | 5597.85i | −0.318389 | − | 0.735283i | ||||
\(388\) | 8739.86 | + | 5045.96i | 1.14355 | + | 0.660232i | ||||
\(389\) | 13027.0 | + | 7521.13i | 1.69793 | + | 0.980299i | 0.947723 | + | 0.319094i | \(0.103379\pi\) |
0.750205 | + | 0.661205i | \(0.229955\pi\) | |||||||
\(390\) | 1451.27 | + | 2884.70i | 0.188431 | + | 0.374544i | ||||
\(391\) | − | 5693.89i | − | 0.736451i | ||||||
\(392\) | −24116.7 | − | 5691.94i | −3.10734 | − | 0.733383i | ||||
\(393\) | 12812.8 | + | 737.279i | 1.64458 | + | 0.0946331i | ||||
\(394\) | −8446.58 | − | 14629.9i | −1.08003 | − | 1.87067i | ||||
\(395\) | 1443.31 | − | 2499.89i | 0.183851 | − | 0.318439i | ||||
\(396\) | −20549.0 | − | 15253.6i | −2.60764 | − | 1.93566i | ||||
\(397\) | −241.393 | + | 139.368i | −0.0305168 | + | 0.0176189i | −0.515181 | − | 0.857082i | \(-0.672275\pi\) |
0.484664 | + | 0.874700i | \(0.338942\pi\) | |||||||
\(398\) | 20089.6 | 2.53015 | ||||||||
\(399\) | −1002.07 | − | 1427.56i | −0.125731 | − | 0.179117i | ||||
\(400\) | 5514.92 | 0.689365 | ||||||||
\(401\) | 1862.25 | − | 1075.17i | 0.231911 | − | 0.133894i | −0.379542 | − | 0.925174i | \(-0.623919\pi\) |
0.611453 | + | 0.791281i | \(0.290585\pi\) | |||||||
\(402\) | −13094.4 | − | 8599.25i | −1.62460 | − | 1.06689i | ||||
\(403\) | 1093.28 | − | 1893.62i | 0.135137 | − | 0.234065i | ||||
\(404\) | 7059.70 | + | 12227.8i | 0.869389 | + | 1.50583i | ||||
\(405\) | 3549.08 | + | 830.682i | 0.435445 | + | 0.101918i | ||||
\(406\) | 28792.0 | + | 11422.7i | 3.51952 | + | 1.39631i | ||||
\(407\) | − | 7453.24i | − | 0.907723i | ||||||
\(408\) | −21672.3 | + | 10903.2i | −2.62975 | + | 1.32301i | ||||
\(409\) | 2743.48 | + | 1583.95i | 0.331678 | + | 0.191494i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
−0.324908 | + | 0.945746i | \(0.605333\pi\) | |||||||
\(410\) | −6362.20 | − | 3673.22i | −0.766357 | − | 0.442457i | ||||
\(411\) | 8490.99 | − | 4271.76i | 1.01905 | − | 0.512678i | ||||
\(412\) | 28325.4i | 3.38711i | ||||||||
\(413\) | 221.263 | + | 1505.64i | 0.0263623 | + | 0.179389i | ||||
\(414\) | 12799.4 | + | 1477.91i | 1.51946 | + | 0.175448i | ||||
\(415\) | 3202.86 | + | 5547.52i | 0.378849 | + | 0.656186i | ||||
\(416\) | 7078.09 | − | 12259.6i | 0.834211 | − | 1.44490i | ||||
\(417\) | 10637.7 | + | 6985.90i | 1.24924 | + | 0.820386i | ||||
\(418\) | −3776.49 | + | 2180.35i | −0.441899 | + | 0.255131i | ||||
\(419\) | −5925.57 | −0.690890 | −0.345445 | − | 0.938439i | \(-0.612272\pi\) | ||||
−0.345445 | + | 0.938439i | \(0.612272\pi\) | |||||||
\(420\) | −906.764 | − | 10227.0i | −0.105347 | − | 1.18815i | ||||
\(421\) | −568.868 | −0.0658550 | −0.0329275 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329275 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(422\) | −15145.3 | + | 8744.17i | −1.74707 | + | 1.00867i | ||||
\(423\) | −1003.93 | + | 1352.45i | −0.115396 | + | 0.155457i | ||||
\(424\) | 831.001 | − | 1439.34i | 0.0951816 | − | 0.164859i | ||||
\(425\) | −807.851 | − | 1399.24i | −0.0922035 | − | 0.159701i | ||||
\(426\) | 18798.3 | + | 1081.70i | 2.13798 | + | 0.123025i | ||||
\(427\) | 3351.23 | − | 8447.07i | 0.379807 | − | 0.957336i | ||||
\(428\) | 277.553i | 0.0313459i | ||||||||
\(429\) | −2380.41 | − | 4731.55i | −0.267896 | − | 0.532497i | ||||
\(430\) | −5298.93 | − | 3059.34i | −0.594273 | − | 0.343104i | ||||
\(431\) | −9170.19 | − | 5294.41i | −1.02485 | − | 0.591700i | −0.109348 | − | 0.994003i | \(-0.534876\pi\) |
−0.915506 | + | 0.402303i | \(0.868210\pi\) | |||||||
\(432\) | −10646.0 | − | 29060.2i | −1.18567 | − | 3.23648i | ||||
\(433\) | − | 10574.5i | − | 1.17362i | −0.809723 | − | 0.586812i | \(-0.800383\pi\) | ||
0.809723 | − | 0.586812i | \(-0.199617\pi\) | |||||||
\(434\) | −7495.16 | + | 5932.10i | −0.828984 | + | 0.656106i | ||||
\(435\) | −460.868 | + | 8009.16i | −0.0507975 | + | 0.882781i | ||||
\(436\) | −14008.2 | − | 24263.0i | −1.53870 | − | 2.66510i | ||||
\(437\) | 798.390 | − | 1382.85i | 0.0873963 | − | 0.151375i | ||||
\(438\) | 3295.15 | − | 5017.66i | 0.359471 | − | 0.547382i | ||||
\(439\) | −939.951 | + | 542.681i | −0.102190 | + | 0.0589994i | −0.550224 | − | 0.835017i | \(-0.685458\pi\) |
0.448034 | + | 0.894017i | \(0.352124\pi\) | |||||||
\(440\) | −16045.4 | −1.73849 | ||||||||
\(441\) | −9116.53 | + | 1629.43i | −0.984400 | + | 0.175945i | ||||
\(442\) | −8032.72 | −0.864429 | ||||||||
\(443\) | −257.587 | + | 148.718i | −0.0276260 | + | 0.0159499i | −0.513749 | − | 0.857940i | \(-0.671744\pi\) |
0.486123 | + | 0.873890i | \(0.338411\pi\) | |||||||
\(444\) | 10211.8 | − | 15549.9i | 1.09151 | − | 1.66209i | ||||
\(445\) | −2556.91 | + | 4428.70i | −0.272380 | + | 0.471776i | ||||
\(446\) | −1552.44 | − | 2688.90i | −0.164821 | − | 0.285478i | ||||
\(447\) | −252.935 | + | 4395.62i | −0.0267638 | + | 0.465113i | ||||
\(448\) | −22896.3 | + | 18121.5i | −2.41462 | + | 1.91107i | ||||
\(449\) | 8313.87i | 0.873843i | 0.899500 | + | 0.436922i | \(0.143931\pi\) | ||||
−0.899500 | + | 0.436922i | \(0.856069\pi\) | |||||||
\(450\) | 3355.06 | − | 1452.79i | 0.351464 | − | 0.152189i | ||||
\(451\) | 10435.4 | + | 6024.90i | 1.08955 | + | 0.629050i | ||||
\(452\) | 14524.2 | + | 8385.56i | 1.51142 | + | 0.872619i | ||||
\(453\) | 978.177 | + | 1944.32i | 0.101454 | + | 0.201661i | ||||
\(454\) | 6495.03i | 0.671425i | ||||||||
\(455\) | 783.615 | − | 1975.17i | 0.0807394 | − | 0.203511i | ||||
\(456\) | −6792.29 | − | 390.846i | −0.697540 | − | 0.0401382i | ||||
\(457\) | −2604.24 | − | 4510.68i | −0.266568 | − | 0.461709i | 0.701406 | − | 0.712762i | \(-0.252556\pi\) |
−0.967973 | + | 0.251054i | \(0.919223\pi\) | |||||||
\(458\) | 11063.8 | − | 19163.0i | 1.12877 | − | 1.95508i | ||||
\(459\) | −5813.63 | + | 6957.97i | −0.591192 | + | 0.707561i | ||||
\(460\) | 8140.23 | − | 4699.76i | 0.825087 | − | 0.476364i | ||||
\(461\) | 7763.38 | 0.784332 | 0.392166 | − | 0.919895i | \(-0.371726\pi\) | ||||
0.392166 | + | 0.919895i | \(0.371726\pi\) | |||||||
\(462\) | 2044.92 | + | 23063.7i | 0.205927 | + | 2.32255i | ||||
\(463\) | 9492.44 | 0.952810 | 0.476405 | − | 0.879226i | \(-0.341940\pi\) | ||||
0.476405 | + | 0.879226i | \(0.341940\pi\) | |||||||
\(464\) | 58990.6 | − | 34058.2i | 5.90209 | − | 3.40757i | ||||
\(465\) | −2069.31 | − | 1358.94i | −0.206370 | − | 0.135525i | ||||
\(466\) | −1475.77 | + | 2556.11i | −0.146704 | + | 0.254098i | ||||
\(467\) | 1807.27 | + | 3130.28i | 0.179080 | + | 0.310176i | 0.941566 | − | 0.336829i | \(-0.109354\pi\) |
−0.762486 | + | 0.647005i | \(0.776021\pi\) | |||||||
\(468\) | 1516.43 | − | 13133.0i | 0.149780 | − | 1.29717i | ||||
\(469\) | 1498.82 | + | 10199.0i | 0.147567 | + | 1.00415i | ||||
\(470\) | 1689.46i | 0.165806i | ||||||||
\(471\) | −14127.5 | + | 7107.45i | −1.38208 | + | 0.695317i | ||||
\(472\) | 5140.89 | + | 2968.10i | 0.501332 | + | 0.289444i | ||||
\(473\) | 8691.44 | + | 5018.01i | 0.844890 | + | 0.487798i | ||||
\(474\) | −14515.2 | + | 7302.50i | −1.40655 | + | 0.707626i | ||||
\(475\) | − | 453.103i | − | 0.0437680i | ||||||
\(476\) | 23739.7 | + | 9418.32i | 2.28594 | + | 0.906907i | ||||
\(477\) | 71.2498 | − | 617.056i | 0.00683922 | − | 0.0592307i | ||||
\(478\) | 5647.75 | + | 9782.18i | 0.540422 | + | 0.936039i | ||||
\(479\) | 44.6749 | − | 77.3792i | 0.00426148 | − | 0.00738110i | −0.863887 | − | 0.503686i | \(-0.831977\pi\) |
0.868148 | + | 0.496305i | \(0.165310\pi\) | |||||||
\(480\) | −13397.0 | − | 8797.97i | −1.27393 | − | 0.836605i | ||||
\(481\) | 3334.40 | − | 1925.12i | 0.316082 | − | 0.182490i | ||||
\(482\) | 4584.81 | 0.433263 | ||||||||
\(483\) | −4871.14 | − | 6939.47i | −0.458891 | − | 0.653740i | ||||
\(484\) | 13703.3 | 1.28693 | ||||||||
\(485\) | 2047.98 | − | 1182.40i | 0.191740 | − | 0.110701i | ||||
\(486\) | −14131.9 | − | 14874.6i | −1.31901 | − | 1.38832i | ||||
\(487\) | −4558.91 | + | 7896.27i | −0.424197 | + | 0.734731i | −0.996345 | − | 0.0854193i | \(-0.972777\pi\) |
0.572148 | + | 0.820151i | \(0.306110\pi\) | |||||||
\(488\) | −17724.1 | − | 30699.1i | −1.64413 | − | 2.84771i | ||||
\(489\) | −4705.62 | − | 270.773i | −0.435164 | − | 0.0250405i | ||||
\(490\) | −6368.30 | + | 6762.67i | −0.587123 | + | 0.623482i | ||||
\(491\) | 8849.23i | 0.813361i | 0.913570 | + | 0.406680i | \(0.133314\pi\) | ||||
−0.913570 | + | 0.406680i | \(0.866686\pi\) | |||||||
\(492\) | 13516.9 | + | 26867.7i | 1.23860 | + | 2.46197i | ||||
\(493\) | −17282.4 | − | 9978.01i | −1.57883 | − | 0.911536i | ||||
\(494\) | −1950.88 | − | 1126.34i | −0.177680 | − | 0.102584i | ||||
\(495\) | −5503.04 | + | 2382.91i | −0.499684 | + | 0.216371i | ||||
\(496\) | 21020.1i | 1.90288i | ||||||||
\(497\) | −7689.56 | − | 9715.68i | −0.694012 | − | 0.876877i | ||||
\(498\) | 2071.40 | − | 35997.8i | 0.186389 | − | 3.23915i | ||||
\(499\) | 8611.60 | + | 14915.7i | 0.772562 | + | 1.33812i | 0.936155 | + | 0.351588i | \(0.114358\pi\) |
−0.163593 | + | 0.986528i | \(0.552308\pi\) | |||||||
\(500\) | 1333.61 | − | 2309.88i | 0.119282 | − | 0.206602i | ||||
\(501\) | 5028.91 | − | 7657.74i | 0.448454 | − | 0.682879i | ||||
\(502\) | 13697.9 | − | 7908.48i | 1.21786 | − | 0.703133i | ||||
\(503\) | −3093.21 | −0.274193 | −0.137097 | − | 0.990558i | \(-0.543777\pi\) | ||||
−0.137097 | + | 0.990558i | \(0.543777\pi\) | |||||||
\(504\) | −17085.5 | + | 31829.0i | −1.51002 | + | 2.81305i | ||||
\(505\) | 3308.55 | 0.291542 | ||||||||
\(506\) | −18357.7 | + | 10598.8i | −1.61284 | + | 0.931176i | ||||
\(507\) | −4764.56 | + | 7255.20i | −0.417360 | + | 0.635532i | ||||
\(508\) | −4730.29 | + | 8193.09i | −0.413135 | + | 0.715570i | ||||
\(509\) | 9975.53 | + | 17278.1i | 0.868679 | + | 1.50460i | 0.863347 | + | 0.504610i | \(0.168364\pi\) |
0.00533139 | + | 0.999986i | \(0.498303\pi\) | |||||||
\(510\) | −522.465 | + | 9079.63i | −0.0453630 | + | 0.788339i | ||||
\(511\) | −3908.18 | + | 574.332i | −0.338332 | + | 0.0497200i | ||||
\(512\) | 8594.64i | 0.741861i | ||||||||
\(513\) | −2387.57 | + | 874.675i | −0.205485 | + | 0.0752785i | ||||
\(514\) | −14981.0 | − | 8649.30i | −1.28557 | − | 0.742226i | ||||
\(515\) | 5748.15 | + | 3318.69i | 0.491832 | + | 0.283960i | ||||
\(516\) | 11258.0 | + | 22377.5i | 0.960474 | + | 1.90914i | ||||
\(517\) | − | 2771.10i | − | 0.235730i | ||||||
\(518\) | −16652.5 | + | 2447.19i | −1.41249 | + | 0.207574i | ||||
\(519\) | −8940.11 | − | 514.436i | −0.756122 | − | 0.0435092i | ||||
\(520\) | −4144.42 | − | 7178.34i | −0.349509 | − | 0.605367i | ||||
\(521\) | 6479.49 | − | 11222.8i | 0.544859 | − | 0.943723i | −0.453757 | − | 0.891125i | \(-0.649917\pi\) |
0.998616 | − | 0.0525977i | \(-0.0167501\pi\) | |||||||
\(522\) | 26915.6 | − | 36259.5i | 2.25682 | − | 3.04030i | ||||
\(523\) | 17989.0 | − | 10385.9i | 1.50402 | − | 0.868347i | 0.504033 | − | 0.863685i | \(-0.331849\pi\) |
0.999989 | − | 0.00466274i | \(-0.00148420\pi\) | |||||||
\(524\) | −52702.0 | −4.39370 | ||||||||
\(525\) | −2181.63 | − | 1014.21i | −0.181360 | − | 0.0843122i | ||||
\(526\) | −22141.1 | −1.83536 | ||||||||
\(527\) | 5333.18 | − | 3079.11i | 0.440829 | − | 0.254513i | ||||
\(528\) | 42560.5 | + | 27949.9i | 3.50797 | + | 2.30372i | ||||
\(529\) | −2202.48 | + | 3814.81i | −0.181021 | + | 0.313538i | ||||
\(530\) | −311.523 | − | 539.573i | −0.0255315 | − | 0.0442218i | ||||
\(531\) | 2203.95 | + | 254.484i | 0.180119 | + | 0.0207979i | ||||
\(532\) | 4444.94 | + | 5616.14i | 0.362242 | + | 0.457689i | ||||
\(533\) | 6224.74i | 0.505860i | ||||||||
\(534\) | 25714.4 | − | 12936.8i | 2.08384 | − | 1.04837i | ||||
\(535\) | 56.3247 | + | 32.5191i | 0.00455164 | + | 0.00262789i | ||||
\(536\) | 34823.9 | + | 20105.6i | 2.80628 | + | 1.62021i | ||||
\(537\) | −928.188 | + | 466.965i | −0.0745889 | + | 0.0375252i | ||||
\(538\) | 22105.6i | 1.77145i | ||||||||
\(539\) | 10445.4 | − | 11092.3i | 0.834725 | − | 0.886417i | ||||
\(540\) | −14746.0 | − | 2568.27i | −1.17512 | − | 0.204668i | ||||
\(541\) | 5548.29 | + | 9609.91i | 0.440923 | + | 0.763701i | 0.997758 | − | 0.0669217i | \(-0.0213178\pi\) |
−0.556835 | + | 0.830623i | \(0.687984\pi\) | |||||||
\(542\) | −11954.1 | + | 20705.1i | −0.947366 | + | 1.64089i | ||||
\(543\) | 1158.60 | + | 760.867i | 0.0915662 | + | 0.0601324i | ||||
\(544\) | 34527.8 | − | 19934.6i | 2.72126 | − | 1.57112i | ||||
\(545\) | −6565.00 | −0.515989 | ||||||||
\(546\) | −9789.94 | + | 6872.02i | −0.767346 | + | 0.538636i | ||||
\(547\) | 3805.15 | 0.297434 | 0.148717 | − | 0.988880i | \(-0.452486\pi\) | ||||
0.148717 | + | 0.988880i | \(0.452486\pi\) | |||||||
\(548\) | −33802.5 | + | 19515.9i | −2.63498 | + | 1.52131i | ||||
\(549\) | −10637.9 | − | 7896.55i | −0.826985 | − | 0.613874i | ||||
\(550\) | −3007.53 | + | 5209.19i | −0.233166 | + | 0.403856i | ||||
\(551\) | −2798.21 | − | 4846.64i | −0.216348 | − | 0.374726i | ||||
\(552\) | −33017.7 | − | 1899.92i | −2.54588 | − | 0.146496i | ||||
\(553\) | 9938.63 | + | 3942.98i | 0.764256 | + | 0.303206i | ||||
\(554\) | − | 25457.1i | − | 1.95229i | ||||||
\(555\) | −1959.14 | − | 3894.19i | −0.149840 | − | 0.297836i | ||||
\(556\) | −45259.1 | − | 26130.4i | −3.45218 | − | 1.99312i | ||||
\(557\) | 2655.83 | + | 1533.34i | 0.202031 | + | 0.116643i | 0.597602 | − | 0.801793i | \(-0.296120\pi\) |
−0.395572 | + | 0.918435i | \(0.629453\pi\) | |||||||
\(558\) | 5537.30 | + | 12787.8i | 0.420094 | + | 0.970160i | ||||
\(559\) | 5184.45i | 0.392270i | ||||||||
\(560\) | 2970.06 | + | 20210.5i | 0.224121 | + | 1.52509i | ||||
\(561\) | 856.960 | − | 14892.6i | 0.0644936 | − | 1.12080i | ||||
\(562\) | 14191.9 | + | 24581.0i | 1.06521 | + | 1.84500i | ||||
\(563\) | 7931.28 | − | 13737.4i | 0.593718 | − | 1.02835i | −0.400008 | − | 0.916512i | \(-0.630993\pi\) |
0.993726 | − | 0.111839i | \(-0.0356741\pi\) | |||||||
\(564\) | 3796.72 | − | 5781.42i | 0.283459 | − | 0.431634i | ||||
\(565\) | 3403.41 | − | 1964.96i | 0.253421 | − | 0.146312i | ||||
\(566\) | −20002.6 | −1.48547 | ||||||||
\(567\) | −1132.84 | + | 13453.7i | −0.0839059 | + | 0.996474i | ||||
\(568\) | −48332.1 | −3.57037 | ||||||||
\(569\) | −9173.42 | + | 5296.28i | −0.675870 | + | 0.390213i | −0.798297 | − | 0.602264i | \(-0.794265\pi\) |
0.122427 | + | 0.992477i | \(0.460932\pi\) | |||||||
\(570\) | −1400.02 | + | 2131.88i | −0.102878 | + | 0.156657i | ||||
\(571\) | 5552.17 | − | 9616.64i | 0.406920 | − | 0.704805i | −0.587623 | − | 0.809135i | \(-0.699936\pi\) |
0.994543 | + | 0.104329i | \(0.0332696\pi\) | |||||||
\(572\) | 10875.1 | + | 18836.2i | 0.794948 | + | 1.37689i | ||||
\(573\) | −406.065 | + | 7056.77i | −0.0296049 | + | 0.514487i | ||||
\(574\) | 10034.8 | − | 25293.7i | 0.729697 | − | 1.83927i | ||||
\(575\) | − | 2202.56i | − | 0.159745i | ||||||
\(576\) | 16915.5 | + | 39064.3i | 1.22363 | + | 2.82583i | ||||
\(577\) | 16951.9 | + | 9787.19i | 1.22308 | + | 0.706146i | 0.965573 | − | 0.260130i | \(-0.0837656\pi\) |
0.257507 | + | 0.966276i | \(0.417099\pi\) | |||||||
\(578\) | 3453.42 | + | 1993.83i | 0.248518 | + | 0.143482i | ||||
\(579\) | −8168.76 | − | 16237.1i | −0.586325 | − | 1.16544i | ||||
\(580\) | − | 32943.6i | − | 2.35846i | ||||||
\(581\) | −18605.1 | + | 14725.1i | −1.32852 | + | 1.05146i | ||||
\(582\) | −13289.3 | − | 764.702i | −0.946496 | − | 0.0544638i | ||||
\(583\) | 510.968 | + | 885.022i | 0.0362986 | + | 0.0628711i | ||||
\(584\) | −7704.28 | + | 13344.2i | −0.545899 | + | 0.945526i | ||||
\(585\) | −2487.45 | − | 1846.44i | −0.175801 | − | 0.130497i | ||||
\(586\) | −16137.9 | + | 9317.22i | −1.13763 | + | 0.656810i | ||||
\(587\) | 4516.62 | 0.317582 | 0.158791 | − | 0.987312i | \(-0.449240\pi\) | ||||
0.158791 | + | 0.987312i | \(0.449240\pi\) | |||||||
\(588\) | 36990.3 | − | 8830.74i | 2.59431 | − | 0.619343i | ||||
\(589\) | 1727.00 | 0.120815 | ||||||||
\(590\) | 1927.20 | − | 1112.67i | 0.134477 | − | 0.0776405i | ||||
\(591\) | 13546.2 | + | 8895.96i | 0.942839 | + | 0.619172i | ||||
\(592\) | −18506.6 | + | 32054.4i | −1.28483 | + | 2.22539i | ||||
\(593\) | 4634.46 | + | 8027.12i | 0.320935 | + | 0.555875i | 0.980681 | − | 0.195613i | \(-0.0626696\pi\) |
−0.659746 | + | 0.751488i | \(0.729336\pi\) | |||||||
\(594\) | 33255.0 | + | 5791.92i | 2.29708 | + | 0.400076i | ||||
\(595\) | 4692.71 | − | 3714.08i | 0.323332 | − | 0.255903i | ||||
\(596\) | − | 18080.2i | − | 1.24261i | ||||||
\(597\) | −17216.6 | + | 8661.55i | −1.18028 | + | 0.593792i | ||||
\(598\) | −9483.31 | − | 5475.19i | −0.648497 | − | 0.374410i | ||||
\(599\) | −11438.3 | − | 6603.93i | −0.780230 | − | 0.450466i | 0.0562818 | − | 0.998415i | \(-0.482075\pi\) |
−0.836512 | + | 0.547949i | \(0.815409\pi\) | |||||||
\(600\) | −8383.46 | + | 4217.67i | −0.570422 | + | 0.286976i | ||||
\(601\) | − | 20312.8i | − | 1.37866i | −0.724446 | − | 0.689332i | \(-0.757904\pi\) | ||
0.724446 | − | 0.689332i | \(-0.242096\pi\) | |||||||
\(602\) | 8357.80 | − | 21066.6i | 0.565845 | − | 1.42626i | ||||
\(603\) | 14929.3 | + | 1723.85i | 1.00824 | + | 0.116419i | ||||
\(604\) | −4468.88 | − | 7740.32i | −0.301053 | − | 0.521439i | ||||
\(605\) | 1605.52 | − | 2780.85i | 0.107891 | − | 0.186872i | ||||
\(606\) | −15566.9 | − | 10223.0i | −1.04350 | − | 0.685279i | ||||
\(607\) | −5906.71 | + | 3410.24i | −0.394969 | + | 0.228035i | −0.684311 | − | 0.729191i | \(-0.739897\pi\) |
0.289342 | + | 0.957226i | \(0.406563\pi\) | |||||||
\(608\) | 11180.9 | 0.745795 | ||||||||
\(609\) | −29599.3 | + | 2624.40i | −1.96950 | + | 0.174624i | ||||
\(610\) | −13288.7 | −0.882041 | ||||||||
\(611\) | 1239.72 | − | 715.753i | 0.0820847 | − | 0.0473916i | ||||
\(612\) | 22192.5 | − | 29896.8i | 1.46582 | − | 1.97468i | ||||
\(613\) | −8226.29 | + | 14248.4i | −0.542018 | + | 0.938802i | 0.456770 | + | 0.889585i | \(0.349006\pi\) |
−0.998788 | + | 0.0492177i | \(0.984327\pi\) | |||||||
\(614\) | −2606.02 | − | 4513.77i | −0.171288 | − | 0.296679i | ||||
\(615\) | 7036.02 | + | 404.871i | 0.461333 | + | 0.0265463i | ||||
\(616\) | −8641.27 | − | 58801.6i | −0.565205 | − | 3.84608i | ||||
\(617\) | − | 12385.4i | − | 0.808130i | −0.914730 | − | 0.404065i | \(-0.867597\pi\) | ||
0.914730 | − | 0.404065i | \(-0.132403\pi\) | |||||||
\(618\) | −16791.1 | − | 33375.6i | −1.09294 | − | 2.17243i | ||||
\(619\) | 16122.6 | + | 9308.36i | 1.04688 | + | 0.604418i | 0.921775 | − | 0.387725i | \(-0.126739\pi\) |
0.125108 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(620\) | 8804.07 | + | 5083.03i | 0.570290 | + | 0.329257i | ||||
\(621\) | −11606.1 | + | 4251.84i | −0.749980 | + | 0.274751i | ||||
\(622\) | − | 48024.5i | − | 3.09583i | ||||||
\(623\) | −17606.8 | − | 6985.21i | −1.13227 | − | 0.449208i | ||||
\(624\) | −1511.06 | + | 26259.8i | −0.0969401 | + | 1.68467i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 19136.3 | − | 33145.1i | 1.22179 | − | 2.11620i | ||||
\(627\) | 2296.36 | − | 3496.76i | 0.146264 | − | 0.222722i | ||||
\(628\) | 56241.3 | − | 32470.9i | 3.57368 | − | 2.06327i | ||||
\(629\) | 10843.7 | 0.687390 | ||||||||
\(630\) | 7130.90 | + | 11512.8i | 0.450955 | + | 0.728068i | ||||
\(631\) | 2351.97 | 0.148385 | 0.0741923 | − | 0.997244i | \(-0.476362\pi\) | ||||
0.0741923 | + | 0.997244i | \(0.476362\pi\) | |||||||
\(632\) | 36119.9 | − | 20853.8i | 2.27337 | − | 1.31253i | ||||
\(633\) | 9209.38 | − | 14023.5i | 0.578262 | − | 0.880544i | ||||
\(634\) | 17981.5 | − | 31144.9i | 1.12640 | − | 1.95098i | ||||
\(635\) | 1108.43 | + | 1919.86i | 0.0692706 | + | 0.119980i | ||||
\(636\) | −146.534 | + | 2546.53i | −0.00913592 | + | 0.158768i | ||||
\(637\) | 7660.40 | + | 1807.98i | 0.476477 | + | 0.112456i | ||||
\(638\) | 74293.8i | 4.61022i | ||||||||
\(639\) | −16576.3 | + | 7177.79i | −1.02621 | + | 0.444365i | ||||
\(640\) | 15608.2 | + | 9011.37i | 0.964010 | + | 0.556572i | ||||
\(641\) | 3691.03 | + | 2131.02i | 0.227437 | + | 0.131311i | 0.609389 | − | 0.792871i | \(-0.291415\pi\) |
−0.381952 | + | 0.924182i | \(0.624748\pi\) | |||||||
\(642\) | −164.531 | − | 327.039i | −0.0101145 | − | 0.0201047i | ||||
\(643\) | − | 6939.64i | − | 0.425618i | −0.977094 | − | 0.212809i | \(-0.931739\pi\) | ||
0.977094 | − | 0.212809i | \(-0.0682612\pi\) | |||||||
\(644\) | 21607.1 | + | 27300.4i | 1.32211 | + | 1.67047i | ||||
\(645\) | 5860.15 | + | 337.208i | 0.357741 | + | 0.0205854i | ||||
\(646\) | −3172.21 | − | 5494.42i | −0.193203 | − | 0.334637i | ||||
\(647\) | 16226.1 | − | 28104.5i | 0.985958 | − | 1.70773i | 0.348358 | − | 0.937362i | \(-0.386740\pi\) |
0.637600 | − | 0.770367i | \(-0.279927\pi\) | |||||||
\(648\) | 38408.0 | + | 36033.8i | 2.32841 | + | 2.18448i | ||||
\(649\) | −3161.04 | + | 1825.03i | −0.191189 | + | 0.110383i | ||||
\(650\) | −3107.29 | −0.187504 | ||||||||
\(651\) | 3865.66 | − | 8315.25i | 0.232730 | − | 0.500615i | ||||
\(652\) | 19355.3 | 1.16260 | ||||||||
\(653\) | 15239.5 | − | 8798.55i | 0.913276 | − | 0.527280i | 0.0317925 | − | 0.999494i | \(-0.489878\pi\) |
0.881484 | + | 0.472214i | \(0.156545\pi\) | |||||||
\(654\) | 30888.7 | + | 20284.9i | 1.84686 | + | 1.21285i | ||||
\(655\) | −6174.74 | + | 10695.0i | −0.368347 | + | 0.637995i | ||||
\(656\) | −29920.0 | − | 51823.0i | −1.78076 | − | 3.08437i | ||||
\(657\) | −660.563 | + | 5720.77i | −0.0392253 | + | 0.339709i | ||||
\(658\) | −6191.35 | + | 909.859i | −0.366815 | + | 0.0539058i | ||||
\(659\) | − | 11521.1i | − | 0.681027i | −0.940240 | − | 0.340514i | \(-0.889399\pi\) | ||
0.940240 | − | 0.340514i | \(-0.110601\pi\) | |||||||
\(660\) | 21998.5 | − | 11067.3i | 1.29741 | − | 0.652719i | ||||
\(661\) | 23492.6 | + | 13563.5i | 1.38239 | + | 0.798120i | 0.992442 | − | 0.122718i | \(-0.0391612\pi\) |
0.389944 | + | 0.920839i | \(0.372495\pi\) | |||||||
\(662\) | −53609.6 | − | 30951.5i | −3.14742 | − | 1.81717i | ||||
\(663\) | 6883.95 | − | 3463.27i | 0.403244 | − | 0.202869i | ||||
\(664\) | 92553.6i | 5.40930i | ||||||||
\(665\) | 1660.48 | − | 244.019i | 0.0968283 | − | 0.0142295i | ||||
\(666\) | −2814.61 | + | 24375.8i | −0.163760 | + | 1.41823i | ||||
\(667\) | −13602.2 | − | 23559.8i | −0.789627 | − | 1.36767i | ||||
\(668\) | −18810.4 | + | 32580.5i | −1.08951 | + | 1.88709i | ||||
\(669\) | 2489.73 | + | 1635.03i | 0.143884 | + | 0.0944901i | ||||
\(670\) | 13054.7 | − | 7537.12i | 0.752755 | − | 0.434604i | ||||
\(671\) | 21796.5 | 1.25402 | ||||||||
\(672\) | 25026.9 | − | 53834.2i | 1.43666 | − | 3.09032i | ||||
\(673\) | −13645.5 | −0.781566 | −0.390783 | − | 0.920483i | \(-0.627796\pi\) | ||||
−0.390783 | + | 0.920483i | \(0.627796\pi\) | |||||||
\(674\) | −15423.1 | + | 8904.56i | −0.881420 | + | 0.508888i | ||||
\(675\) | −2248.88 | + | 2691.54i | −0.128236 | + | 0.153478i | ||||
\(676\) | 17821.6 | − | 30867.9i | 1.01397 | − | 1.75625i | ||||
\(677\) | −3038.14 | − | 5262.22i | −0.172475 | − | 0.298735i | 0.766810 | − | 0.641874i | \(-0.221843\pi\) |
−0.939284 | + | 0.343140i | \(0.888510\pi\) | |||||||
\(678\) | −22084.7 | − | 1270.81i | −1.25097 | − | 0.0719840i | ||||
\(679\) | 5436.09 | + | 6868.44i | 0.307243 | + | 0.388198i | ||||
\(680\) | − | 23344.6i | − | 1.31651i | ||||||
\(681\) | −2800.30 | − | 5566.17i | −0.157574 | − | 0.313210i | ||||
\(682\) | −19854.8 | − | 11463.2i | −1.11478 | − | 0.643618i | ||||
\(683\) | −6220.19 | − | 3591.23i | −0.348476 | − | 0.201193i | 0.315538 | − | 0.948913i | \(-0.397815\pi\) |
−0.664014 | + | 0.747720i | \(0.731148\pi\) | |||||||
\(684\) | 9581.91 | − | 4149.12i | 0.535634 | − | 0.231938i | ||||
\(685\) | 9146.18i | 0.510157i | ||||||||
\(686\) | −28212.7 | − | 19695.8i | −1.57021 | − | 1.09619i | ||||
\(687\) | −1219.48 | + | 21192.6i | −0.0677233 | + | 1.17692i | ||||
\(688\) | −24919.8 | − | 43162.3i | −1.38090 | − | 2.39178i | ||||
\(689\) | −263.958 | + | 457.189i | −0.0145951 | + | 0.0252794i | ||||
\(690\) | −6805.59 | + | 10363.2i | −0.375485 | + | 0.571766i | ||||
\(691\) | −13426.5 | + | 7751.80i | −0.739173 | + | 0.426762i | −0.821769 | − | 0.569821i | \(-0.807012\pi\) |
0.0825954 | + | 0.996583i | \(0.473679\pi\) | |||||||
\(692\) | 36772.8 | 2.02008 | ||||||||
\(693\) | −11696.3 | − | 18883.6i | −0.641132 | − | 1.03511i | ||||
\(694\) | −29636.0 | −1.62099 | ||||||||
\(695\) | −10605.4 | + | 6123.04i | −0.578830 | + | 0.334187i | ||||
\(696\) | −63627.2 | + | 96887.8i | −3.46521 | + | 5.27662i | ||||
\(697\) | −8765.65 | + | 15182.6i | −0.476360 | + | 0.825079i | ||||
\(698\) | −15294.0 | − | 26490.1i | −0.829352 | − | 1.43648i | ||||
\(699\) | 162.663 | − | 2826.84i | 0.00880185 | − | 0.152962i | ||||
\(700\) | 9183.20 | + | 3643.28i | 0.495846 | + | 0.196718i | ||||
\(701\) | − | 20937.6i | − | 1.12811i | −0.825739 | − | 0.564053i | \(-0.809241\pi\) | ||
0.825739 | − | 0.564053i | \(-0.190759\pi\) | |||||||
\(702\) | 5998.34 | + | 16373.5i | 0.322497 | + | 0.880309i | ||||
\(703\) | 2633.58 | + | 1520.50i | 0.141291 | + | 0.0815742i | ||||
\(704\) | −60652.8 | − | 35017.9i | −3.24707 | − | 1.87470i | ||||
\(705\) | −728.404 | − | 1447.85i | −0.0389125 | − | 0.0773463i | ||||
\(706\) | 55504.7i | 2.95885i | ||||||||
\(707\) | 1781.82 | + | 12124.8i | 0.0947839 | + | 0.644980i | ||||
\(708\) | −9095.47 | − | 523.377i | −0.482809 | − | 0.0277821i | ||||
\(709\) | −2420.87 | − | 4193.07i | −0.128234 | − | 0.222107i | 0.794759 | − | 0.606926i | \(-0.207597\pi\) |
−0.922992 | + | 0.384818i | \(0.874264\pi\) | |||||||
\(710\) | −9059.29 | + | 15691.1i | −0.478858 | + | 0.829406i | ||||
\(711\) | 9290.91 | − | 12516.3i | 0.490065 | − | 0.660195i | ||||
\(712\) | −63988.3 | + | 36943.7i | −3.36807 | + | 1.94456i | ||||
\(713\) | 8395.04 | 0.440949 | ||||||||
\(714\) | −33555.4 | + | 2975.16i | −1.75880 | + | 0.155942i | ||||
\(715\) | 5096.65 | 0.266579 | ||||||||
\(716\) | 3695.10 | − | 2133.37i | 0.192866 | − | 0.111351i | ||||
\(717\) | −9057.60 | − | 5948.22i | −0.471775 | − | 0.309819i | ||||
\(718\) | 2368.58 | − | 4102.50i | 0.123112 | − | 0.213236i | ||||
\(719\) | 13205.6 | + | 22872.8i | 0.684961 | + | 1.18639i | 0.973449 | + | 0.228903i | \(0.0735140\pi\) |
−0.288488 | + | 0.957483i | \(0.593153\pi\) | |||||||
\(720\) | 29584.0 | + | 3415.99i | 1.53129 | + | 0.176814i | ||||
\(721\) | −9066.33 | + | 22852.5i | −0.468305 | + | 1.18040i | ||||
\(722\) | 35372.1i | 1.82329i | ||||||||
\(723\) | −3929.13 | + | 1976.72i | −0.202111 | + | 0.101681i | ||||
\(724\) | −4929.38 | − | 2845.98i | −0.253037 | − | 0.146091i | ||||
\(725\) | −6685.34 | − | 3859.78i | −0.342465 | − | 0.197722i | ||||
\(726\) | −16146.5 | + | 8123.20i | −0.825417 | + | 0.415262i | ||||
\(727\) | − | 16397.6i | − | 0.836524i | −0.908326 | − | 0.418262i | \(-0.862639\pi\) | ||
0.908326 | − | 0.418262i | \(-0.137361\pi\) | |||||||
\(728\) | 24074.4 | − | 19053.9i | 1.22563 | − | 0.970034i | ||||
\(729\) | 18524.0 | + | 6654.41i | 0.941118 | + | 0.338079i | ||||
\(730\) | 2888.15 | + | 5002.43i | 0.146432 | + | 0.253628i | ||||
\(731\) | −7300.72 | + | 12645.2i | −0.369394 | + | 0.639809i | ||||
\(732\) | 45474.7 | + | 29863.7i | 2.29616 | + | 1.50791i | ||||
\(733\) | −16789.2 | + | 9693.24i | −0.846006 | + | 0.488442i | −0.859301 | − | 0.511470i | \(-0.829101\pi\) |
0.0132952 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(734\) | 18248.7 | 0.917673 | ||||||||
\(735\) | 2541.86 | − | 8541.19i | 0.127562 | − | 0.428635i | ||||
\(736\) | 54350.7 | 2.72200 | ||||||||
\(737\) | −21412.6 | + | 12362.6i | −1.07021 | + | 0.617885i | ||||
\(738\) | −31853.9 | − | 23645.2i | −1.58883 | − | 1.17939i | ||||
\(739\) | 15662.9 | − | 27129.0i | 0.779661 | − | 1.35041i | −0.152476 | − | 0.988307i | \(-0.548725\pi\) |
0.932137 | − | 0.362105i | \(-0.117942\pi\) | |||||||
\(740\) | 8950.49 | + | 15502.7i | 0.444630 | + | 0.770122i | ||||
\(741\) | 2157.50 | + | 124.148i | 0.106960 | + | 0.00615477i | ||||
\(742\) | 1809.60 | − | 1432.22i | 0.0895317 | − | 0.0708606i | ||||
\(743\) | − | 21594.1i | − | 1.06623i | −0.846042 | − | 0.533116i | \(-0.821021\pi\) | ||
0.846042 | − | 0.533116i | \(-0.178979\pi\) | |||||||
\(744\) | −16075.6 | − | 31953.5i | −0.792151 | − | 1.57456i | ||||
\(745\) | −3669.08 | − | 2118.34i | −0.180436 | − | 0.104175i | ||||
\(746\) | 48764.4 | + | 28154.2i | 2.39329 | + | 1.38177i | ||||
\(747\) | 13745.1 | + | 31742.8i | 0.673237 | + | 1.55476i | ||||
\(748\) | 61257.0i | 2.99435i | ||||||||
\(749\) | −88.8387 | + | 223.926i | −0.00433391 | + | 0.0109240i | ||||
\(750\) | −202.105 | + | 3512.27i | −0.00983976 | + | 0.171000i | ||||
\(751\) | 4800.78 | + | 8315.20i | 0.233266 | + | 0.404029i | 0.958767 | − | 0.284192i | \(-0.0917253\pi\) |
−0.725501 | + | 0.688221i | \(0.758392\pi\) | |||||||
\(752\) | −6880.72 | + | 11917.8i | −0.333662 | + | 0.577920i | ||||
\(753\) | −8329.23 | + | 12683.3i | −0.403100 | + | 0.613816i | ||||
\(754\) | −33237.3 | + | 19189.5i | −1.60534 | + | 0.926846i | ||||
\(755\) | −2094.35 | −0.100955 | ||||||||
\(756\) | 1470.46 | − | 55422.7i | 0.0707409 | − | 2.66628i | ||||
\(757\) | −37494.0 | −1.80019 | −0.900093 | − | 0.435697i | \(-0.856502\pi\) | ||||
−0.900093 | + | 0.435697i | \(0.856502\pi\) | |||||||
\(758\) | −50750.1 | + | 29300.6i | −2.43183 | + | 1.40402i | ||||
\(759\) | 11162.7 | − | 16997.9i | 0.533835 | − | 0.812892i | ||||
\(760\) | 3273.35 | − | 5669.61i | 0.156233 | − | 0.270603i | ||||
\(761\) | 20075.9 | + | 34772.5i | 0.956309 | + | 1.65638i | 0.731343 | + | 0.682010i | \(0.238894\pi\) |
0.224966 | + | 0.974367i | \(0.427773\pi\) | |||||||
\(762\) | 716.862 | − | 12457.9i | 0.0340803 | − | 0.592262i | ||||
\(763\) | −3535.58 | − | 24058.7i | −0.167754 | − | 1.14153i | ||||
\(764\) | − | 29026.2i | − | 1.37452i | ||||||
\(765\) | −3466.90 | − | 8006.40i | −0.163851 | − | 0.378395i | ||||
\(766\) | 49994.2 | + | 28864.1i | 2.35818 | + | 1.36149i | ||||
\(767\) | −1632.95 | − | 942.782i | −0.0768739 | − | 0.0443832i | ||||
\(768\) | −16138.2 | − | 32078.0i | −0.758253 | − | 1.50718i | ||||
\(769\) | − | 10187.4i | − | 0.477722i | −0.971054 | − | 0.238861i | \(-0.923226\pi\) | ||
0.971054 | − | 0.238861i | \(-0.0767740\pi\) | |||||||
\(770\) | −20709.8 | − | 8216.26i | −0.969258 | − | 0.384537i | ||||
\(771\) | 16567.7 | + | 953.346i | 0.773892 | + | 0.0445317i | ||||
\(772\) | 37319.6 | + | 64639.5i | 1.73985 | + | 3.01350i | ||||
\(773\) | −15595.5 | + | 27012.3i | −0.725657 | + | 1.25687i | 0.233047 | + | 0.972466i | \(0.425131\pi\) |
−0.958703 | + | 0.284409i | \(0.908203\pi\) | |||||||
\(774\) | −26530.4 | − | 19693.6i | −1.23206 | − | 0.914563i | ||||
\(775\) | 2063.03 | − | 1191.09i | 0.0956209 | − | 0.0552068i | ||||
\(776\) | 34168.1 | 1.58062 | ||||||||
\(777\) | 13215.9 | − | 9276.87i | 0.610190 | − | 0.428321i | ||||
\(778\) | 81475.4 | 3.75454 | ||||||||
\(779\) | −4257.76 | + | 2458.22i | −0.195828 | + | 0.113061i | ||||
\(780\) | 10633.3 | + | 6982.99i | 0.488119 | + | 0.320553i | ||||
\(781\) | 14859.3 | − | 25737.0i | 0.680802 | − | 1.17918i | ||||
\(782\) | −15420.3 | − | 26708.7i | −0.705150 | − | 1.22136i | ||||
\(783\) | −7433.20 | + | 42678.5i | −0.339260 | + | 1.94790i | ||||
\(784\) | −72465.6 | + | 21768.7i | −3.30109 | + | 0.991649i | ||||
\(785\) | − | 15217.6i | − | 0.691898i | ||||||
\(786\) | 62098.4 | − | 31241.3i | 2.81804 | − | 1.41774i | ||||
\(787\) | 30648.1 | + | 17694.7i | 1.38817 | + | 0.801459i | 0.993109 | − | 0.117197i | \(-0.0373910\pi\) |
0.395059 | + | 0.918656i | \(0.370724\pi\) | |||||||
\(788\) | −57633.7 | − | 33274.8i | −2.60548 | − | 1.50427i | ||||
\(789\) | 18974.7 | − | 9546.06i | 0.856169 | − | 0.430733i | ||||
\(790\) | − | 15635.2i | − | 0.704147i | ||||||
\(791\) | 9033.89 | + | 11414.2i | 0.406078 | + | 0.513076i | ||||
\(792\) | −86073.5 | − | 9938.68i | −3.86173 | − | 0.445904i | ||||
\(793\) | 5629.87 | + | 9751.22i | 0.252109 | + | 0.436666i | ||||
\(794\) | −754.880 | + | 1307.49i | −0.0337402 | + | 0.0584397i | ||||
\(795\) | 499.607 | + | 328.097i | 0.0222883 | + | 0.0146370i | ||||
\(796\) | 68538.9 | − | 39570.9i | 3.05188 | − | 1.76200i | ||||
\(797\) | −1039.98 | −0.0462209 | −0.0231104 | − | 0.999733i | \(-0.507357\pi\) | ||||
−0.0231104 | + | 0.999733i | \(0.507357\pi\) | |||||||
\(798\) | −8566.65 | − | 3982.54i | −0.380020 | − | 0.176667i | ||||
\(799\) | 4031.68 | 0.178511 | ||||||||
\(800\) | 13356.4 | − | 7711.30i | 0.590273 | − | 0.340794i | ||||
\(801\) | −16459.3 | + | 22173.3i | −0.726046 | + | 0.978098i | ||||
\(802\) | 5823.58 | − | 10086.7i | 0.256406 | − | 0.444109i | ||||
\(803\) | −4737.22 | − | 8205.11i | −0.208185 | − | 0.360588i | ||||
\(804\) | −61611.9 | − | 3545.30i | −2.70259 | − | 0.155514i | ||||
\(805\) | 8071.70 | − | 1186.19i | 0.353404 | − | 0.0519350i | ||||
\(806\) | − | 11843.4i | − | 0.517576i | ||||||
\(807\) | −9530.74 | − | 18944.3i | −0.415735 | − | 0.826356i | ||||
\(808\) | 41399.4 | + | 23901.9i | 1.80251 | + | 1.04068i | ||||
\(809\) | 8457.97 | + | 4883.21i | 0.367573 | + | 0.212218i | 0.672397 | − | 0.740190i | \(-0.265265\pi\) |
−0.304825 | + | 0.952408i | \(0.598598\pi\) | |||||||
\(810\) | 18897.6 | − | 5715.15i | 0.819745 | − | 0.247913i | ||||
\(811\) | − | 19662.3i | − | 0.851341i | −0.904878 | − | 0.425671i | \(-0.860038\pi\) | ||
0.904878 | − | 0.425671i | \(-0.139962\pi\) | |||||||
\(812\) | 120728. | − | 17741.8i | 5.21764 | − | 0.766766i | ||||
\(813\) | 1317.61 | − | 22898.0i | 0.0568396 | − | 0.987784i | ||||
\(814\) | −20185.0 | − | 34961.4i | −0.869144 | − | 1.50540i | ||||
\(815\) | 2267.74 | − | 3927.84i | 0.0974667 | − | 0.168817i | ||||
\(816\) | −40664.5 | + | 61921.5i | −1.74454 | + | 2.65648i | ||||
\(817\) | −3546.20 | + | 2047.40i | −0.151855 | + | 0.0876736i | ||||
\(818\) | 17158.7 | 0.733422 | ||||||||
\(819\) | 5427.03 | − | 10110.1i | 0.231545 | − | 0.431351i | ||||
\(820\) | −28940.8 | −1.23251 | ||||||||
\(821\) | −10679.9 | + | 6166.06i | −0.453998 | + | 0.262116i | −0.709517 | − | 0.704688i | \(-0.751087\pi\) |
0.255519 | + | 0.966804i | \(0.417754\pi\) | |||||||
\(822\) | 28260.4 | − | 43033.3i | 1.19914 | − | 1.82598i | ||||
\(823\) | −17347.5 | + | 30046.7i | −0.734744 | + | 1.27261i | 0.220091 | + | 0.975479i | \(0.429364\pi\) |
−0.954836 | + | 0.297135i | \(0.903969\pi\) | |||||||
\(824\) | 47950.4 | + | 83052.5i | 2.02722 | + | 3.51125i | ||||
\(825\) | 331.497 | − | 5760.90i | 0.0139894 | − | 0.243114i | ||||
\(826\) | 5115.49 | + | 6463.37i | 0.215485 | + | 0.272263i | ||||
\(827\) | 28297.8i | 1.18986i | 0.803779 | + | 0.594928i | \(0.202819\pi\) | ||||
−0.803779 | + | 0.594928i | \(0.797181\pi\) | |||||||
\(828\) | 46578.2 | − | 20169.1i | 1.95496 | − | 0.846526i | ||||
\(829\) | −22663.5 | − | 13084.8i | −0.949500 | − | 0.548194i | −0.0565744 | − | 0.998398i | \(-0.518018\pi\) |
−0.892926 | + | 0.450204i | \(0.851351\pi\) | |||||||
\(830\) | 30047.8 | + | 17348.1i | 1.25659 | + | 0.725495i | ||||
\(831\) | 10975.7 | + | 21816.5i | 0.458176 | + | 0.910717i | ||||
\(832\) | − | 36179.4i | − | 1.50757i | ||||||
\(833\) | 16138.2 | + | 15197.1i | 0.671256 | + | 0.632111i | ||||
\(834\) | 68818.4 | + | 3959.99i | 2.85730 | + | 0.164416i | ||||
\(835\) | 4407.77 | + | 7634.48i | 0.182679 | + | 0.316410i | ||||
\(836\) | −8589.38 | + | 14877.3i | −0.355347 | + | 0.615479i | ||||
\(837\) | −10258.8 | − | 8571.59i | −0.423651 | − | 0.353975i | ||||
\(838\) | −27795.5 | + | 16047.7i | −1.14580 | + | 0.661527i | ||||
\(839\) | −4964.87 | −0.204298 | −0.102149 | − | 0.994769i | \(-0.532572\pi\) | ||||
−0.102149 | + | 0.994769i | \(0.532572\pi\) | |||||||
\(840\) | −19971.4 | − | 28451.4i | −0.820330 | − | 1.16865i | ||||
\(841\) | −70957.8 | −2.90942 | ||||||||
\(842\) | −2668.43 | + | 1540.62i | −0.109216 | + | 0.0630560i | ||||
\(843\) | −22760.3 | − | 14946.9i | −0.929900 | − | 0.610675i | ||||
\(844\) | −34447.1 | + | 59664.2i | −1.40488 | + | 2.43333i | ||||
\(845\) | −4176.07 | − | 7233.17i | −0.170013 | − | 0.294472i | ||||
\(846\) | −1046.47 | + | 9062.87i | −0.0425275 | + | 0.368307i | ||||
\(847\) | 11055.6 | + | 4386.12i | 0.448495 | + | 0.177933i | ||||
\(848\) | − | 5075.00i | − | 0.205514i | ||||||
\(849\) | 17142.0 | − | 8624.06i | 0.692949 | − | 0.348618i | ||||
\(850\) | −7578.88 | − | 4375.67i | −0.305827 | − | 0.176570i | ||||
\(851\) | 12802.0 | + | 7391.22i | 0.515683 | + | 0.297729i | ||||
\(852\) | 66264.0 | − | 33337.0i | 2.66451 | − | 1.34050i | ||||
\(853\) | − | 37172.7i | − | 1.49211i | −0.665885 | − | 0.746054i | \(-0.731946\pi\) | ||
0.665885 | − | 0.746054i | \(-0.268054\pi\) | |||||||
\(854\) | −7156.64 | − | 48699.1i | −0.286763 | − | 1.95134i | ||||
\(855\) | 280.656 | − | 2430.61i | 0.0112260 | − | 0.0972223i | ||||
\(856\) | 469.854 | + | 813.811i | 0.0187609 | + | 0.0324947i | ||||
\(857\) | −3226.39 | + | 5588.27i | −0.128601 | + | 0.222744i | −0.923135 | − | 0.384476i | \(-0.874382\pi\) |
0.794534 | + | 0.607220i | \(0.207715\pi\) | |||||||
\(858\) | −23980.0 | − | 15747.9i | −0.954154 | − | 0.626603i | ||||
\(859\) | 10830.0 | − | 6252.69i | 0.430168 | − | 0.248358i | −0.269250 | − | 0.963070i | \(-0.586776\pi\) |
0.699418 | + | 0.714713i | \(0.253443\pi\) | |||||||
\(860\) | −24104.2 | −0.955752 | ||||||||
\(861\) | 2305.52 | + | 26002.9i | 0.0912567 | + | 1.02924i | ||||
\(862\) | −57353.6 | −2.26621 | ||||||||
\(863\) | −8338.96 | + | 4814.50i | −0.328924 | + | 0.189904i | −0.655363 | − | 0.755314i | \(-0.727484\pi\) |
0.326439 | + | 0.945218i | \(0.394151\pi\) | |||||||
\(864\) | −66417.0 | − | 55493.7i | −2.61522 | − | 2.18511i | ||||
\(865\) | 4308.43 | − | 7462.41i | 0.169354 | − | 0.293329i | ||||
\(866\) | −28638.1 | − | 49602.6i | −1.12374 | − | 1.94638i | ||||
\(867\) | −3819.17 | − | 219.765i | −0.149603 | − | 0.00860855i | ||||
\(868\) | −13886.3 | + | 35001.7i | −0.543010 | + | 1.36870i | ||||
\(869\) | 25645.3i | 1.00110i | ||||||||
\(870\) | 19528.7 | + | 38817.2i | 0.761018 | + | 1.51268i | ||||
\(871\) | −11061.4 | − | 6386.32i | −0.430313 | − | 0.248441i | ||||
\(872\) | −82146.8 | − | 47427.5i | −3.19018 | − | 1.84185i | ||||
\(873\) | 11718.5 | − | 5074.30i | 0.454309 | − | 0.196723i | ||||
\(874\) | − | 8648.85i | − | 0.334727i | ||||||
\(875\) | 1815.28 | − | 1436.71i | 0.0701343 | − | 0.0555084i | ||||
\(876\) | 1358.53 | − | 23609.1i | 0.0523977 | − | 0.910590i | ||||
\(877\) | 5716.73 | + | 9901.67i | 0.220114 | + | 0.381249i | 0.954843 | − | 0.297112i | \(-0.0960236\pi\) |
−0.734728 | + | 0.678362i | \(0.762690\pi\) | |||||||
\(878\) | −2939.39 | + | 5091.18i | −0.112984 | + | 0.195694i | ||||
\(879\) | 9812.91 | − | 14942.5i | 0.376543 | − | 0.573378i | ||||
\(880\) | −42431.3 | + | 24497.7i | −1.62541 | + | 0.938429i | ||||
\(881\) | −20616.7 | −0.788414 | −0.394207 | − | 0.919022i | \(-0.628981\pi\) | ||||
−0.394207 | + | 0.919022i | \(0.628981\pi\) | |||||||
\(882\) | −38350.7 | + | 32332.8i | −1.46410 | + | 1.23436i | ||||
\(883\) | 9685.44 | 0.369129 | 0.184565 | − | 0.982820i | \(-0.440913\pi\) | ||||
0.184565 | + | 0.982820i | \(0.440913\pi\) | |||||||
\(884\) | −27404.9 | + | 15822.2i | −1.04268 | + | 0.601990i | ||||
\(885\) | −1171.87 | + | 1784.45i | −0.0445106 | + | 0.0677781i | ||||
\(886\) | −805.520 | + | 1395.20i | −0.0305440 | + | 0.0529037i | ||||
\(887\) | 16109.0 | + | 27901.6i | 0.609793 | + | 1.05619i | 0.991274 | + | 0.131816i | \(0.0420809\pi\) |
−0.381481 | + | 0.924377i | \(0.624586\pi\) | |||||||
\(888\) | 3618.32 | − | 62880.7i | 0.136737 | − | 2.37628i | ||||
\(889\) | −6438.75 | + | 5096.00i | −0.242912 | + | 0.192255i | ||||
\(890\) | 27698.6i | 1.04321i | ||||||||
\(891\) | −30996.3 | + | 9374.12i | −1.16545 | + | 0.352463i | ||||
\(892\) | −10592.8 | − | 6115.73i | −0.397614 | − | 0.229563i | ||||
\(893\) | 979.159 | + | 565.317i | 0.0366924 | + | 0.0211844i | ||||
\(894\) | 10717.8 | + | 21303.8i | 0.400959 | + | 0.796987i | ||||
\(895\) | − | 999.810i | − | 0.0373407i | ||||||
\(896\) | −24618.1 | + | 62052.2i | −0.917895 | + | 2.31363i | ||||
\(897\) | 10487.7 | + | 603.489i | 0.390384 | + | 0.0224637i | ||||
\(898\) | 22515.7 | + | 38998.4i | 0.836704 | + | 1.44921i | ||||
\(899\) | 14711.5 | − | 25481.1i | 0.545781 | − | 0.945320i | ||||
\(900\) | 8584.71 | − | 11565.0i | 0.317952 | − | 0.428332i | ||||
\(901\) | −1287.62 | + | 743.409i | −0.0476103 | + | 0.0274878i | ||||
\(902\) | 65266.9 | 2.40926 | ||||||||
\(903\) | 1920.22 | + | 21657.2i | 0.0707651 | + | 0.798126i | ||||
\(904\) | 56781.8 | 2.08909 | ||||||||
\(905\) | −1155.09 | + | 666.889i | −0.0424269 | + | 0.0244952i | ||||
\(906\) | 9854.05 | + | 6471.25i | 0.361345 | + | 0.237299i | ||||
\(907\) | 12636.0 | − | 21886.1i | 0.462591 | − | 0.801231i | −0.536498 | − | 0.843902i | \(-0.680253\pi\) |
0.999089 | + | 0.0426701i | \(0.0135864\pi\) | |||||||
\(908\) | 12793.4 | + | 22158.8i | 0.467581 | + | 0.809875i | ||||
\(909\) | 17748.3 | + | 2049.35i | 0.647605 | + | 0.0747772i | ||||
\(910\) | −1673.43 | − | 11387.3i | −0.0609601 | − | 0.414817i | ||||
\(911\) | − | 26490.3i | − | 0.963405i | −0.876335 | − | 0.481703i | \(-0.840019\pi\) | ||
0.876335 | − | 0.481703i | \(-0.159981\pi\) | |||||||
\(912\) | −18558.6 | + | 9336.71i | −0.673833 | + | 0.339001i | ||||
\(913\) | −49285.1 | − | 28454.8i | −1.78653 | − | 1.03145i | ||||
\(914\) | −24431.8 | − | 14105.7i | −0.884171 | − | 0.510476i | ||||
\(915\) | 11388.3 | − | 5729.38i | 0.411459 | − | 0.207003i | ||||
\(916\) | − | 87170.2i | − | 3.14430i | ||||||
\(917\) | −42519.2 | − | 16868.8i | −1.53120 | − | 0.607476i | ||||
\(918\) | −8426.69 | + | 48382.8i | −0.302965 | + | 1.73951i | ||||
\(919\) | 11986.2 | + | 20760.6i | 0.430236 | + | 0.745190i | 0.996893 | − | 0.0787630i | \(-0.0250970\pi\) |
−0.566657 | + | 0.823953i | \(0.691764\pi\) | |||||||
\(920\) | 15911.9 | − | 27560.3i | 0.570218 | − | 0.987647i | ||||
\(921\) | 4179.43 | + | 2744.67i | 0.149530 | + | 0.0981976i | ||||
\(922\) | 36416.2 | − | 21024.9i | 1.30076 | − | 0.750996i | ||||
\(923\) | 15352.1 | 0.547478 | ||||||||
\(924\) | 52405.6 | + | 74657.4i | 1.86582 | + | 2.65806i | ||||
\(925\) | 4194.68 | 0.149103 | ||||||||
\(926\) | 44526.8 | − | 25707.6i | 1.58017 | − | 0.912314i | ||||
\(927\) | 28779.5 | + | 21363.1i | 1.01968 | + | 0.756911i | ||||
\(928\) | 95244.6 | − | 164969.i | 3.36914 | − | 5.83551i | ||||
\(929\) | −8343.21 | − | 14450.9i | −0.294652 | − | 0.510353i | 0.680252 | − | 0.732979i | \(-0.261870\pi\) |
−0.974904 | + | 0.222626i | \(0.928537\pi\) | |||||||
\(930\) | −13387.0 | − | 770.320i | −0.472017 | − | 0.0271611i | ||||
\(931\) | 1788.51 | + | 5953.75i | 0.0629602 | + | 0.209588i | ||||
\(932\) | 11627.5i | 0.408659i | ||||||||
\(933\) | 20705.6 | + | 41156.4i | 0.726548 | + | 1.44416i | ||||
\(934\) | 16955.0 | + | 9788.95i | 0.593986 | + | 0.342938i | ||||
\(935\) | 12431.1 | + | 7177.08i | 0.434801 | + | 0.251033i | ||||
\(936\) | −17785.8 | − | 41074.3i | −0.621097 | − | 1.43435i | ||||
\(937\) | 8294.49i | 0.289188i | 0.989491 | + | 0.144594i | \(0.0461876\pi\) | ||||
−0.989491 | + | 0.144594i | \(0.953812\pi\) | |||||||
\(938\) | 34651.8 | + | 43782.2i | 1.20621 | + | 1.52403i | ||||
\(939\) | −2109.25 | + | 36655.5i | −0.0733043 | + | 1.27392i | ||||
\(940\) | 3327.77 | + | 5763.86i | 0.115468 | + | 0.199996i | ||||
\(941\) | −12592.5 | + | 21810.9i | −0.436243 | + | 0.755594i | −0.997396 | − | 0.0721173i | \(-0.977024\pi\) |
0.561154 | + | 0.827712i | \(0.310358\pi\) | |||||||
\(942\) | −47020.2 | + | 71599.7i | −1.62633 | + | 2.47648i | ||||
\(943\) | −20697.2 | + | 11949.5i | −0.714733 | + | 0.412651i | ||||
\(944\) | 18126.4 | 0.624963 | ||||||||
\(945\) | −11074.8 | − | 6791.92i | −0.381232 | − | 0.233800i | ||||
\(946\) | 54359.4 | 1.86826 | ||||||||
\(947\) | 29961.5 | − | 17298.3i | 1.02811 | − | 0.593578i | 0.111665 | − | 0.993746i | \(-0.464381\pi\) |
0.916442 | + | 0.400168i | \(0.131048\pi\) | |||||||
\(948\) | −35136.9 | + | 53504.5i | −1.20379 | + | 1.83306i | ||||
\(949\) | 2447.18 | − | 4238.63i | 0.0837078 | − | 0.144986i | ||||
\(950\) | −1227.10 | − | 2125.40i | −0.0419078 | − | 0.0725865i | ||||
\(951\) | −1981.97 | + | 34443.5i | −0.0675812 | + | 1.17446i | ||||
\(952\) | 85550.7 | − | 12572.2i | 2.91251 | − | 0.428012i | ||||
\(953\) | − | 30037.8i | − | 1.02101i | −0.859876 | − | 0.510504i | \(-0.829459\pi\) | ||
0.859876 | − | 0.510504i | \(-0.170541\pi\) | |||||||
\(954\) | −1336.90 | − | 3087.42i | −0.0453709 | − | 0.104779i | ||||
\(955\) | −5890.37 | − | 3400.81i | −0.199590 | − | 0.115233i | ||||
\(956\) | 38536.4 | + | 22249.0i | 1.30372 | + | 0.752702i | ||||
\(957\) | −32031.5 | − | 63669.0i | −1.08195 | − | 2.15060i | ||||
\(958\) | − | 483.957i | − | 0.0163214i | ||||||
\(959\) | −33517.9 | + | 4925.67i | −1.12862 | + | 0.165858i | ||||
\(960\) | −40894.7 | − | 2353.19i | −1.37487 | − | 0.0791133i | ||||
\(961\) | −10355.7 | − | 17936.5i | −0.347611 | − | 0.602079i | ||||
\(962\) | 10427.3 | − | 18060.5i | 0.349468 | − | 0.605296i | ||||
\(963\) | 282.003 | + | 209.332i | 0.00943658 | + | 0.00700481i | ||||
\(964\) | 15641.8 | − | 9030.81i | 0.522603 | − | 0.301725i | ||||
\(965\) | 17490.0 | 0.583442 | ||||||||
\(966\) | −41642.9 | − | 19359.3i | −1.38700 | − | 0.644799i | ||||
\(967\) | −12240.3 | −0.407055 | −0.203528 | − | 0.979069i | \(-0.565241\pi\) | ||||
−0.203528 | + | 0.979069i | \(0.565241\pi\) | |||||||
\(968\) | 40179.3 | − | 23197.5i | 1.33410 | − | 0.770244i | ||||
\(969\) | 5087.45 | + | 3340.98i | 0.168661 | + | 0.110761i | ||||
\(970\) | 6404.41 | − | 11092.8i | 0.211993 | − | 0.367183i | ||||
\(971\) | −23693.7 | − | 41038.7i | −0.783076 | − | 1.35633i | −0.930142 | − | 0.367201i | \(-0.880316\pi\) |
0.147065 | − | 0.989127i | \(-0.453017\pi\) | |||||||
\(972\) | −77512.1 | − | 22910.9i | −2.55782 | − | 0.756038i | ||||
\(973\) | −28150.6 | − | 35568.0i | −0.927510 | − | 1.17190i | ||||
\(974\) | 49386.1i | 1.62467i | ||||||||
\(975\) | 2662.91 | − | 1339.69i | 0.0874681 | − | 0.0440047i | ||||
\(976\) | −93741.0 | − | 54121.4i | −3.07436 | − | 1.77498i | ||||
\(977\) | −23011.9 | − | 13285.9i | −0.753549 | − | 0.435061i | 0.0734261 | − | 0.997301i | \(-0.476607\pi\) |
−0.826975 | + | 0.562239i | \(0.809940\pi\) | |||||||
\(978\) | −22806.3 | + | 11473.7i | −0.745669 | + | 0.375141i | ||||
\(979\) | − | 45432.0i | − | 1.48316i | ||||||
\(980\) | −8405.88 | + | 35615.7i | −0.273996 | + | 1.16092i | ||||
\(981\) | −35217.0 | − | 4066.42i | −1.14617 | − | 0.132345i | ||||
\(982\) | 23965.6 | + | 41509.7i | 0.778792 | + | 1.34891i | ||||
\(983\) | 21278.4 | − | 36855.2i | 0.690412 | − | 1.19583i | −0.281291 | − | 0.959623i | \(-0.590763\pi\) |
0.971703 | − | 0.236206i | \(-0.0759041\pi\) | |||||||
\(984\) | 85115.7 | + | 55896.3i | 2.75751 | + | 1.81088i | ||||
\(985\) | −13505.1 | + | 7797.18i | −0.436862 | + | 0.252222i | ||||
\(986\) | −108090. | −3.49118 | ||||||||
\(987\) | 4913.64 | − | 3449.12i | 0.158463 | − | 0.111233i | ||||
\(988\) | −8874.30 | −0.285758 | ||||||||
\(989\) | −17238.2 | + | 9952.51i | −0.554241 | + | 0.319991i | ||||
\(990\) | −19360.1 | + | 26081.1i | −0.621519 | + | 0.837284i | ||||
\(991\) | −18686.0 | + | 32365.1i | −0.598971 | + | 1.03745i | 0.394002 | + | 0.919110i | \(0.371090\pi\) |
−0.992973 | + | 0.118339i | \(0.962243\pi\) | |||||||
\(992\) | 29391.5 | + | 50907.6i | 0.940708 | + | 1.62935i | ||||
\(993\) | 59287.4 | + | 3411.55i | 1.89469 | + | 0.109025i | ||||
\(994\) | −62382.1 | − | 24749.0i | −1.99058 | − | 0.789730i | ||||
\(995\) | − | 18545.1i | − | 0.590872i | ||||||
\(996\) | −63838.7 | − | 126892.i | −2.03093 | − | 4.03688i | ||||
\(997\) | −32689.2 | − | 18873.1i | −1.03839 | − | 0.599516i | −0.119015 | − | 0.992892i | \(-0.537974\pi\) |
−0.919378 | + | 0.393376i | \(0.871307\pi\) | |||||||
\(998\) | 80790.0 | + | 46644.1i | 2.56249 | + | 1.47945i | ||||
\(999\) | −8097.45 | − | 22103.3i | −0.256448 | − | 0.700018i |
(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 | 105.4.s.a.101.16 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.b.101.1 | yes | 32 | ||
7.5 | odd | 6 | 105.4.s.b.26.1 | yes | 32 | ||
21.5 | even | 6 | inner | 105.4.s.a.26.16 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.16 | ✓ | 32 | 21.5 | even | 6 | inner | |
105.4.s.a.101.16 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.26.1 | yes | 32 | 7.5 | odd | 6 | ||
105.4.s.b.101.1 | yes | 32 | 3.2 | odd | 2 |