Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,6,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (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: | \(11.8684026662\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.12 | ||
Character | \(\chi\) | \(=\) | 74.27 |
Dual form | 74.6.e.a.11.12 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.46410 | + | 2.00000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.156146 | − | 0.270453i | −0.0100168 | − | 0.0173496i | 0.860974 | − | 0.508650i | \(-0.169855\pi\) |
−0.870990 | + | 0.491300i | \(0.836522\pi\) | |||||||
\(4\) | 8.00000 | + | 13.8564i | 0.250000 | + | 0.433013i | ||||
\(5\) | −53.2403 | + | 30.7383i | −0.952391 | + | 0.549863i | −0.893823 | − | 0.448420i | \(-0.851987\pi\) |
−0.0585682 | + | 0.998283i | \(0.518653\pi\) | |||||||
\(6\) | − | 1.24917i | − | 0.0141659i | ||||||
\(7\) | 45.8234 | + | 79.3684i | 0.353461 | + | 0.612213i | 0.986853 | − | 0.161618i | \(-0.0516713\pi\) |
−0.633392 | + | 0.773831i | \(0.718338\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 121.451 | − | 210.360i | 0.499799 | − | 0.865678i | ||||
\(10\) | −245.906 | −0.777624 | ||||||||
\(11\) | −663.143 | −1.65244 | −0.826220 | − | 0.563348i | \(-0.809513\pi\) | ||||
−0.826220 | + | 0.563348i | \(0.809513\pi\) | |||||||
\(12\) | 2.49834 | − | 4.32725i | 0.00500840 | − | 0.00867480i | ||||
\(13\) | −822.701 | + | 474.987i | −1.35016 | + | 0.779512i | −0.988271 | − | 0.152711i | \(-0.951200\pi\) |
−0.361884 | + | 0.932223i | \(0.617866\pi\) | |||||||
\(14\) | 366.587i | 0.499870i | ||||||||
\(15\) | 16.6265 | + | 9.59934i | 0.0190798 | + | 0.0110157i | ||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | 314.768 | + | 181.731i | 0.264161 | + | 0.152513i | 0.626231 | − | 0.779637i | \(-0.284597\pi\) |
−0.362070 | + | 0.932151i | \(0.617930\pi\) | |||||||
\(18\) | 841.439 | − | 485.805i | 0.612127 | − | 0.353411i | ||||
\(19\) | −358.783 | + | 207.144i | −0.228007 | + | 0.131640i | −0.609652 | − | 0.792669i | \(-0.708691\pi\) |
0.381645 | + | 0.924309i | \(0.375358\pi\) | |||||||
\(20\) | −851.844 | − | 491.813i | −0.476196 | − | 0.274932i | ||||
\(21\) | 14.3103 | − | 24.7862i | 0.00708110 | − | 0.0122648i | ||||
\(22\) | −2297.20 | − | 1326.29i | −1.01191 | − | 0.584226i | ||||
\(23\) | 2549.08i | 1.00476i | 0.864646 | + | 0.502382i | \(0.167543\pi\) | ||||
−0.864646 | + | 0.502382i | \(0.832457\pi\) | |||||||
\(24\) | 17.3090 | − | 9.99336i | 0.00613401 | − | 0.00354147i | ||||
\(25\) | 327.185 | − | 566.701i | 0.104699 | − | 0.181344i | ||||
\(26\) | −3799.89 | −1.10240 | ||||||||
\(27\) | −151.744 | −0.0400591 | ||||||||
\(28\) | −733.174 | + | 1269.89i | −0.176731 | + | 0.306107i | ||||
\(29\) | 3496.43i | 0.772023i | 0.922494 | + | 0.386011i | \(0.126147\pi\) | ||||
−0.922494 | + | 0.386011i | \(0.873853\pi\) | |||||||
\(30\) | 38.3974 | + | 66.5062i | 0.00778930 | + | 0.0134915i | ||||
\(31\) | − | 6800.69i | − | 1.27101i | −0.772097 | − | 0.635504i | \(-0.780792\pi\) | ||
0.772097 | − | 0.635504i | \(-0.219208\pi\) | |||||||
\(32\) | −886.810 | + | 512.000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 103.547 | + | 179.349i | 0.0165521 | + | 0.0286692i | ||||
\(34\) | 726.926 | + | 1259.07i | 0.107843 | + | 0.186790i | ||||
\(35\) | −4879.30 | − | 2817.06i | −0.673267 | − | 0.388711i | ||||
\(36\) | 3886.44 | 0.499799 | ||||||||
\(37\) | 7105.90 | − | 4341.68i | 0.853325 | − | 0.521379i | ||||
\(38\) | −1657.15 | −0.186167 | ||||||||
\(39\) | 256.923 | + | 148.335i | 0.0270484 | + | 0.0156164i | ||||
\(40\) | −1967.25 | − | 3407.38i | −0.194406 | − | 0.336721i | ||||
\(41\) | 2400.93 | + | 4158.53i | 0.223059 | + | 0.386349i | 0.955735 | − | 0.294228i | \(-0.0950625\pi\) |
−0.732677 | + | 0.680577i | \(0.761729\pi\) | |||||||
\(42\) | 99.1447 | − | 57.2412i | 0.00867254 | − | 0.00500709i | ||||
\(43\) | 5359.33i | 0.442017i | 0.975272 | + | 0.221009i | \(0.0709349\pi\) | ||||
−0.975272 | + | 0.221009i | \(0.929065\pi\) | |||||||
\(44\) | −5305.15 | − | 9188.78i | −0.413110 | − | 0.715527i | ||||
\(45\) | 14932.8i | 1.09929i | ||||||||
\(46\) | −5098.16 | + | 8830.27i | −0.355238 | + | 0.615290i | ||||
\(47\) | 29600.2 | 1.95457 | 0.977284 | − | 0.211935i | \(-0.0679765\pi\) | ||||
0.977284 | + | 0.211935i | \(0.0679765\pi\) | |||||||
\(48\) | 79.9469 | 0.00500840 | ||||||||
\(49\) | 4203.94 | − | 7281.43i | 0.250130 | − | 0.433238i | ||||
\(50\) | 2266.80 | − | 1308.74i | 0.128230 | − | 0.0740334i | ||||
\(51\) | − | 113.507i | − | 0.00611078i | ||||||
\(52\) | −13163.2 | − | 7599.79i | −0.675078 | − | 0.389756i | ||||
\(53\) | −16098.5 | + | 27883.4i | −0.787219 | + | 1.36350i | 0.140446 | + | 0.990088i | \(0.455146\pi\) |
−0.927665 | + | 0.373414i | \(0.878187\pi\) | |||||||
\(54\) | −525.656 | − | 303.488i | −0.0245311 | − | 0.0141630i | ||||
\(55\) | 35305.9 | − | 20383.9i | 1.57377 | − | 0.908616i | ||||
\(56\) | −5079.58 | + | 2932.70i | −0.216450 | + | 0.124967i | ||||
\(57\) | 112.045 | + | 64.6894i | 0.00456780 | + | 0.00263722i | ||||
\(58\) | −6992.87 | + | 12112.0i | −0.272951 | + | 0.472766i | ||||
\(59\) | −18668.7 | − | 10778.4i | −0.698205 | − | 0.403109i | 0.108473 | − | 0.994099i | \(-0.465404\pi\) |
−0.806679 | + | 0.590990i | \(0.798737\pi\) | |||||||
\(60\) | 307.179i | 0.0110157i | ||||||||
\(61\) | 5691.64 | − | 3286.07i | 0.195845 | − | 0.113071i | −0.398871 | − | 0.917007i | \(-0.630598\pi\) |
0.594716 | + | 0.803936i | \(0.297264\pi\) | |||||||
\(62\) | 13601.4 | − | 23558.3i | 0.449369 | − | 0.778331i | ||||
\(63\) | 22261.2 | 0.706639 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 29200.6 | − | 50576.8i | 0.857250 | − | 1.48480i | ||||
\(66\) | 828.379i | 0.0234083i | ||||||||
\(67\) | 10718.3 | + | 18564.6i | 0.291702 | + | 0.505242i | 0.974212 | − | 0.225634i | \(-0.0724452\pi\) |
−0.682511 | + | 0.730876i | \(0.739112\pi\) | |||||||
\(68\) | 5815.41i | 0.152513i | ||||||||
\(69\) | 689.407 | − | 398.029i | 0.0174322 | − | 0.0100645i | ||||
\(70\) | −11268.3 | − | 19517.2i | −0.274860 | − | 0.476072i | ||||
\(71\) | 25692.8 | + | 44501.2i | 0.604875 | + | 1.04767i | 0.992071 | + | 0.125677i | \(0.0401103\pi\) |
−0.387196 | + | 0.921997i | \(0.626556\pi\) | |||||||
\(72\) | 13463.0 | + | 7772.88i | 0.306063 | + | 0.176706i | ||||
\(73\) | 56304.3 | 1.23661 | 0.618307 | − | 0.785936i | \(-0.287819\pi\) | ||||
0.618307 | + | 0.785936i | \(0.287819\pi\) | |||||||
\(74\) | 33298.9 | − | 828.232i | 0.706888 | − | 0.0175822i | ||||
\(75\) | −204.355 | −0.00419500 | ||||||||
\(76\) | −5740.53 | − | 3314.30i | −0.114004 | − | 0.0658200i | ||||
\(77\) | −30387.5 | − | 52632.6i | −0.584074 | − | 1.01165i | ||||
\(78\) | 593.339 | + | 1027.69i | 0.0110425 | + | 0.0191261i | ||||
\(79\) | −47259.6 | + | 27285.4i | −0.851966 | + | 0.491883i | −0.861314 | − | 0.508073i | \(-0.830358\pi\) |
0.00934741 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(80\) | − | 15738.0i | − | 0.274932i | ||||||
\(81\) | −29489.0 | − | 51076.4i | −0.499398 | − | 0.864983i | ||||
\(82\) | 19207.4i | 0.315453i | ||||||||
\(83\) | −48664.4 | + | 84289.3i | −0.775383 | + | 1.34300i | 0.159196 | + | 0.987247i | \(0.449110\pi\) |
−0.934579 | + | 0.355756i | \(0.884223\pi\) | |||||||
\(84\) | 457.930 | 0.00708110 | ||||||||
\(85\) | −22344.5 | −0.335446 | ||||||||
\(86\) | −10718.7 | + | 18565.3i | −0.156277 | + | 0.270679i | ||||
\(87\) | 945.622 | − | 545.955i | 0.0133943 | − | 0.00773319i | ||||
\(88\) | − | 42441.2i | − | 0.584226i | ||||||
\(89\) | −96883.9 | − | 55936.0i | −1.29651 | − | 0.748542i | −0.316713 | − | 0.948522i | \(-0.602579\pi\) |
−0.979800 | + | 0.199980i | \(0.935912\pi\) | |||||||
\(90\) | −29865.6 | + | 51728.8i | −0.388656 | + | 0.673172i | ||||
\(91\) | −75397.9 | − | 43531.0i | −0.954455 | − | 0.551055i | ||||
\(92\) | −35321.1 | + | 20392.6i | −0.435075 | + | 0.251191i | ||||
\(93\) | −1839.27 | + | 1061.90i | −0.0220515 | + | 0.0127314i | ||||
\(94\) | 102538. | + | 59200.5i | 1.19692 | + | 0.691044i | ||||
\(95\) | 12734.5 | − | 22056.8i | 0.144768 | − | 0.250745i | ||||
\(96\) | 276.944 | + | 159.894i | 0.00306700 | + | 0.00177074i | ||||
\(97\) | 36468.9i | 0.393544i | 0.980449 | + | 0.196772i | \(0.0630459\pi\) | ||||
−0.980449 | + | 0.196772i | \(0.936954\pi\) | |||||||
\(98\) | 29125.7 | − | 16815.7i | 0.306346 | − | 0.176869i | ||||
\(99\) | −80539.6 | + | 139499.i | −0.825888 | + | 1.43048i | ||||
\(100\) | 10469.9 | 0.104699 | ||||||||
\(101\) | 29133.0 | 0.284172 | 0.142086 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142086 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(102\) | 227.014 | − | 393.199i | 0.00216049 | − | 0.00374207i | ||||
\(103\) | 88379.2i | 0.820837i | 0.911897 | + | 0.410419i | \(0.134617\pi\) | ||||
−0.911897 | + | 0.410419i | \(0.865383\pi\) | |||||||
\(104\) | −30399.1 | − | 52652.9i | −0.275599 | − | 0.477352i | ||||
\(105\) | 1759.50i | 0.0155745i | ||||||||
\(106\) | −111534. | + | 64394.0i | −0.964142 | + | 0.556648i | ||||
\(107\) | −25773.6 | − | 44641.2i | −0.217629 | − | 0.376944i | 0.736454 | − | 0.676488i | \(-0.236499\pi\) |
−0.954083 | + | 0.299544i | \(0.903165\pi\) | |||||||
\(108\) | −1213.95 | − | 2102.62i | −0.0100148 | − | 0.0173461i | ||||
\(109\) | −84456.3 | − | 48760.9i | −0.680873 | − | 0.393102i | 0.119311 | − | 0.992857i | \(-0.461931\pi\) |
−0.800184 | + | 0.599755i | \(0.795265\pi\) | |||||||
\(110\) | 163071. | 1.28498 | ||||||||
\(111\) | −2283.78 | − | 1243.88i | −0.0175933 | − | 0.00958230i | ||||
\(112\) | −23461.6 | −0.176731 | ||||||||
\(113\) | −120401. | − | 69513.5i | −0.887021 | − | 0.512122i | −0.0140541 | − | 0.999901i | \(-0.504474\pi\) |
−0.872967 | + | 0.487779i | \(0.837807\pi\) | |||||||
\(114\) | 258.758 | + | 448.182i | 0.00186480 | + | 0.00322992i | ||||
\(115\) | −78354.4 | − | 135714.i | −0.552483 | − | 0.956928i | ||||
\(116\) | −48448.0 | + | 27971.5i | −0.334296 | + | 0.193006i | ||||
\(117\) | 230751.i | 1.55840i | ||||||||
\(118\) | −43113.4 | − | 74674.6i | −0.285041 | − | 0.493706i | ||||
\(119\) | 33310.2i | 0.215630i | ||||||||
\(120\) | −614.358 | + | 1064.10i | −0.00389465 | + | 0.00674573i | ||||
\(121\) | 278708. | 1.73056 | ||||||||
\(122\) | 26288.6 | 0.159907 | ||||||||
\(123\) | 749.792 | − | 1298.68i | 0.00446867 | − | 0.00773996i | ||||
\(124\) | 94233.1 | − | 54405.5i | 0.550363 | − | 0.317752i | ||||
\(125\) | − | 151886.i | − | 0.869446i | ||||||
\(126\) | 77115.1 | + | 44522.4i | 0.432726 | + | 0.249835i | ||||
\(127\) | −22216.9 | + | 38480.8i | −0.122229 | + | 0.211707i | −0.920646 | − | 0.390397i | \(-0.872338\pi\) |
0.798417 | + | 0.602104i | \(0.205671\pi\) | |||||||
\(128\) | −14189.0 | − | 8192.00i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 1449.45 | − | 836.840i | 0.00766882 | − | 0.00442760i | ||||
\(130\) | 202307. | − | 116802.i | 1.04991 | − | 0.606168i | ||||
\(131\) | 46055.8 | + | 26590.3i | 0.234480 | + | 0.135377i | 0.612637 | − | 0.790364i | \(-0.290109\pi\) |
−0.378157 | + | 0.925741i | \(0.623442\pi\) | |||||||
\(132\) | −1656.76 | + | 2869.59i | −0.00827607 | + | 0.0143346i | ||||
\(133\) | −32881.3 | − | 18984.0i | −0.161183 | − | 0.0930592i | ||||
\(134\) | 85746.4i | 0.412528i | ||||||||
\(135\) | 8078.88 | − | 4664.34i | 0.0381519 | − | 0.0220270i | ||||
\(136\) | −11630.8 | + | 20145.2i | −0.0539216 | + | 0.0933950i | ||||
\(137\) | −432891. | −1.97050 | −0.985252 | − | 0.171110i | \(-0.945265\pi\) | ||||
−0.985252 | + | 0.171110i | \(0.945265\pi\) | |||||||
\(138\) | 3184.24 | 0.0142334 | ||||||||
\(139\) | 45741.9 | − | 79227.2i | 0.200806 | − | 0.347806i | −0.747982 | − | 0.663719i | \(-0.768977\pi\) |
0.948788 | + | 0.315912i | \(0.102311\pi\) | |||||||
\(140\) | − | 90146.0i | − | 0.388711i | ||||||
\(141\) | −4621.97 | − | 8005.49i | −0.0195785 | − | 0.0339109i | ||||
\(142\) | 205542.i | 0.855423i | ||||||||
\(143\) | 545569. | − | 314984.i | 2.23105 | − | 1.28810i | ||||
\(144\) | 31091.5 | + | 53852.1i | 0.124950 | + | 0.216419i | ||||
\(145\) | −107474. | − | 186151.i | −0.424507 | − | 0.735268i | ||||
\(146\) | 195044. | + | 112609.i | 0.757269 | + | 0.437209i | ||||
\(147\) | −2625.72 | −0.0100220 | ||||||||
\(148\) | 117007. | + | 63728.7i | 0.439095 | + | 0.239156i | ||||
\(149\) | 315171. | 1.16300 | 0.581501 | − | 0.813546i | \(-0.302466\pi\) | ||||
0.581501 | + | 0.813546i | \(0.302466\pi\) | |||||||
\(150\) | −707.906 | − | 408.709i | −0.00256890 | − | 0.00148316i | ||||
\(151\) | 90511.3 | + | 156770.i | 0.323043 | + | 0.559527i | 0.981114 | − | 0.193428i | \(-0.0619607\pi\) |
−0.658071 | + | 0.752956i | \(0.728627\pi\) | |||||||
\(152\) | −13257.2 | − | 22962.1i | −0.0465417 | − | 0.0806127i | ||||
\(153\) | 76458.0 | − | 44143.0i | 0.264055 | − | 0.152452i | ||||
\(154\) | − | 243100.i | − | 0.826005i | ||||||
\(155\) | 209041. | + | 362070.i | 0.698881 | + | 1.21050i | ||||
\(156\) | 4746.71i | 0.0156164i | ||||||||
\(157\) | 297208. | − | 514779.i | 0.962300 | − | 1.66675i | 0.245601 | − | 0.969371i | \(-0.421015\pi\) |
0.716699 | − | 0.697382i | \(-0.245652\pi\) | |||||||
\(158\) | −218283. | −0.695628 | ||||||||
\(159\) | 10054.9 | 0.0315416 | ||||||||
\(160\) | 31476.0 | − | 54518.0i | 0.0972030 | − | 0.168361i | ||||
\(161\) | −202316. | + | 116807.i | −0.615129 | + | 0.355145i | ||||
\(162\) | − | 235912.i | − | 0.706256i | ||||||
\(163\) | 368399. | + | 212695.i | 1.08605 | + | 0.627031i | 0.932522 | − | 0.361113i | \(-0.117603\pi\) |
0.153528 | + | 0.988144i | \(0.450936\pi\) | |||||||
\(164\) | −38414.8 | + | 66536.4i | −0.111529 | + | 0.193175i | ||||
\(165\) | −11025.8 | − | 6365.74i | −0.0315282 | − | 0.0182028i | ||||
\(166\) | −337157. | + | 194658.i | −0.949647 | + | 0.548279i | ||||
\(167\) | −533630. | + | 308091.i | −1.48064 | + | 0.854847i | −0.999759 | − | 0.0219400i | \(-0.993016\pi\) |
−0.480879 | + | 0.876787i | \(0.659682\pi\) | |||||||
\(168\) | 1586.31 | + | 915.859i | 0.00433627 | + | 0.00250355i | ||||
\(169\) | 265578. | − | 459995.i | 0.715279 | − | 1.23890i | ||||
\(170\) | −77403.5 | − | 44688.9i | −0.205418 | − | 0.118598i | ||||
\(171\) | 100631.i | 0.263174i | ||||||||
\(172\) | −74261.1 | + | 42874.6i | −0.191399 | + | 0.110504i | ||||
\(173\) | −168690. | + | 292180.i | −0.428523 | + | 0.742224i | −0.996742 | − | 0.0806532i | \(-0.974299\pi\) |
0.568219 | + | 0.822877i | \(0.307633\pi\) | |||||||
\(174\) | 4367.64 | 0.0109364 | ||||||||
\(175\) | 59970.8 | 0.148028 | ||||||||
\(176\) | 84882.3 | − | 147021.i | 0.206555 | − | 0.357764i | ||||
\(177\) | 6732.00i | 0.0161514i | ||||||||
\(178\) | −223744. | − | 387536.i | −0.529299 | − | 0.916773i | ||||
\(179\) | 498800.i | 1.16357i | 0.813341 | + | 0.581787i | \(0.197646\pi\) | ||||
−0.813341 | + | 0.581787i | \(0.802354\pi\) | |||||||
\(180\) | −206915. | + | 119462.i | −0.476004 | + | 0.274821i | ||||
\(181\) | −176909. | − | 306415.i | −0.401378 | − | 0.695207i | 0.592515 | − | 0.805560i | \(-0.298135\pi\) |
−0.993892 | + | 0.110353i | \(0.964802\pi\) | |||||||
\(182\) | −174124. | − | 301591.i | −0.389655 | − | 0.674902i | ||||
\(183\) | −1777.46 | − | 1026.22i | −0.00392348 | − | 0.00226522i | ||||
\(184\) | −163141. | −0.355238 | ||||||||
\(185\) | −244864. | + | 449575.i | −0.526012 | + | 0.965769i | ||||
\(186\) | −8495.22 | −0.0180050 | ||||||||
\(187\) | −208736. | − | 120514.i | −0.436510 | − | 0.252019i | ||||
\(188\) | 236802. | + | 410153.i | 0.488642 | + | 0.846353i | ||||
\(189\) | −6953.41 | − | 12043.7i | −0.0141594 | − | 0.0245247i | ||||
\(190\) | 88227.1 | − | 50937.9i | 0.177304 | − | 0.102366i | ||||
\(191\) | 342207.i | 0.678743i | 0.940653 | + | 0.339371i | \(0.110214\pi\) | ||||
−0.940653 | + | 0.339371i | \(0.889786\pi\) | |||||||
\(192\) | 639.575 | + | 1107.78i | 0.00125210 | + | 0.00216870i | ||||
\(193\) | 426157.i | 0.823525i | 0.911291 | + | 0.411762i | \(0.135087\pi\) | ||||
−0.911291 | + | 0.411762i | \(0.864913\pi\) | |||||||
\(194\) | −72937.8 | + | 126332.i | −0.139139 | + | 0.240995i | ||||
\(195\) | −18238.2 | −0.0343476 | ||||||||
\(196\) | 134526. | 0.250130 | ||||||||
\(197\) | 197132. | − | 341443.i | 0.361903 | − | 0.626835i | −0.626371 | − | 0.779525i | \(-0.715460\pi\) |
0.988274 | + | 0.152690i | \(0.0487937\pi\) | |||||||
\(198\) | −557995. | + | 322158.i | −1.01150 | + | 0.583991i | ||||
\(199\) | − | 527707.i | − | 0.944627i | −0.881431 | − | 0.472313i | \(-0.843419\pi\) | ||
0.881431 | − | 0.472313i | \(-0.156581\pi\) | |||||||
\(200\) | 36268.8 | + | 20939.8i | 0.0641148 | + | 0.0370167i | ||||
\(201\) | 3347.25 | − | 5797.60i | 0.00584383 | − | 0.0101218i | ||||
\(202\) | 100920. | + | 58266.0i | 0.174019 | + | 0.100470i | ||||
\(203\) | −277506. | + | 160218.i | −0.472642 | + | 0.272880i | ||||
\(204\) | 1572.80 | − | 908.054i | 0.00264604 | − | 0.00152769i | ||||
\(205\) | −255652. | − | 147601.i | −0.424878 | − | 0.245304i | ||||
\(206\) | −176758. | + | 306155.i | −0.290210 | + | 0.502658i | ||||
\(207\) | 536224. | + | 309589.i | 0.869802 | + | 0.502180i | ||||
\(208\) | − | 243193.i | − | 0.389756i | ||||||
\(209\) | 237925. | − | 137366.i | 0.376768 | − | 0.217527i | ||||
\(210\) | −3518.99 | + | 6095.08i | −0.00550643 | + | 0.00953742i | ||||
\(211\) | 36670.3 | 0.0567033 | 0.0283516 | − | 0.999598i | \(-0.490974\pi\) | ||||
0.0283516 | + | 0.999598i | \(0.490974\pi\) | |||||||
\(212\) | −515152. | −0.787219 | ||||||||
\(213\) | 8023.67 | − | 13897.4i | 0.0121178 | − | 0.0209887i | ||||
\(214\) | − | 206189.i | − | 0.307773i | ||||||
\(215\) | −164737. | − | 285332.i | −0.243049 | − | 0.420973i | ||||
\(216\) | − | 9711.60i | − | 0.0141630i | ||||||
\(217\) | 539760. | − | 311630.i | 0.778128 | − | 0.449252i | ||||
\(218\) | −195043. | − | 337825.i | −0.277965 | − | 0.481450i | ||||
\(219\) | −8791.71 | − | 15227.7i | −0.0123869 | − | 0.0214548i | ||||
\(220\) | 564895. | + | 326142.i | 0.786884 | + | 0.454308i | ||||
\(221\) | −345280. | −0.475544 | ||||||||
\(222\) | −5423.50 | − | 8876.48i | −0.00738579 | − | 0.0120881i | ||||
\(223\) | 214588. | 0.288964 | 0.144482 | − | 0.989507i | \(-0.453848\pi\) | ||||
0.144482 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(224\) | −81273.2 | − | 46923.1i | −0.108225 | − | 0.0624837i | ||||
\(225\) | −79474.0 | − | 137653.i | −0.104657 | − | 0.181271i | ||||
\(226\) | −278054. | − | 481604.i | −0.362125 | − | 0.627219i | ||||
\(227\) | 132989. | − | 76781.5i | 0.171298 | − | 0.0988990i | −0.411900 | − | 0.911229i | \(-0.635135\pi\) |
0.583198 | + | 0.812330i | \(0.301801\pi\) | |||||||
\(228\) | 2070.06i | 0.00263722i | ||||||||
\(229\) | −360127. | − | 623757.i | −0.453802 | − | 0.786008i | 0.544816 | − | 0.838555i | \(-0.316599\pi\) |
−0.998618 | + | 0.0525472i | \(0.983266\pi\) | |||||||
\(230\) | − | 626835.i | − | 0.781328i | ||||||
\(231\) | −9489.78 | + | 16436.8i | −0.0117011 | + | 0.0202669i | ||||
\(232\) | −223772. | −0.272951 | ||||||||
\(233\) | −327671. | −0.395411 | −0.197705 | − | 0.980262i | \(-0.563349\pi\) | ||||
−0.197705 | + | 0.980262i | \(0.563349\pi\) | |||||||
\(234\) | −461502. | + | 799344.i | −0.550977 | + | 0.954321i | ||||
\(235\) | −1.57593e6 | + | 909861.i | −1.86151 | + | 1.07474i | ||||
\(236\) | − | 344907.i | − | 0.403109i | ||||||
\(237\) | 14758.8 | + | 8521.02i | 0.0170679 | + | 0.00985418i | ||||
\(238\) | −66620.4 | + | 115390.i | −0.0762368 | + | 0.132046i | ||||
\(239\) | 948945. | + | 547873.i | 1.07460 | + | 0.620420i | 0.929434 | − | 0.368988i | \(-0.120296\pi\) |
0.145164 | + | 0.989408i | \(0.453629\pi\) | |||||||
\(240\) | −4256.40 | + | 2457.43i | −0.00476995 | + | 0.00275393i | ||||
\(241\) | 3782.03 | − | 2183.56i | 0.00419452 | − | 0.00242171i | −0.497901 | − | 0.867234i | \(-0.665896\pi\) |
0.502096 | + | 0.864812i | \(0.332562\pi\) | |||||||
\(242\) | 965473. | + | 557416.i | 1.05975 | + | 0.611845i | ||||
\(243\) | −27646.1 | + | 47884.4i | −0.0300343 | + | 0.0520209i | ||||
\(244\) | 91066.3 | + | 52577.1i | 0.0979226 | + | 0.0565356i | ||||
\(245\) | 516887.i | 0.550149i | ||||||||
\(246\) | 5194.71 | − | 2999.17i | 0.00547298 | − | 0.00315982i | ||||
\(247\) | 196781. | − | 340835.i | 0.205230 | − | 0.355469i | ||||
\(248\) | 435244. | 0.449369 | ||||||||
\(249\) | 30395.1 | 0.0310674 | ||||||||
\(250\) | 303772. | − | 526148.i | 0.307395 | − | 0.532425i | ||||
\(251\) | 575003.i | 0.576084i | 0.957618 | + | 0.288042i | \(0.0930043\pi\) | ||||
−0.957618 | + | 0.288042i | \(0.906996\pi\) | |||||||
\(252\) | 178090. | + | 308461.i | 0.176660 | + | 0.305984i | ||||
\(253\) | − | 1.69041e6i | − | 1.66031i | ||||||
\(254\) | −153923. | + | 88867.7i | −0.149699 | + | 0.0864290i | ||||
\(255\) | 3489.00 | + | 6043.13i | 0.00336009 | + | 0.00581985i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 272739. | + | 157466.i | 0.257581 | + | 0.148714i | 0.623231 | − | 0.782038i | \(-0.285820\pi\) |
−0.365650 | + | 0.930753i | \(0.619153\pi\) | |||||||
\(258\) | 6694.72 | 0.00626157 | ||||||||
\(259\) | 670208. | + | 365033.i | 0.620813 | + | 0.338129i | ||||
\(260\) | 934418. | 0.857250 | ||||||||
\(261\) | 735509. | + | 424646.i | 0.668323 | + | 0.385857i | ||||
\(262\) | 106361. | + | 184223.i | 0.0957261 | + | 0.165803i | ||||
\(263\) | 844932. | + | 1.46346e6i | 0.753238 | + | 1.30465i | 0.946246 | + | 0.323449i | \(0.104842\pi\) |
−0.193008 | + | 0.981197i | \(0.561824\pi\) | |||||||
\(264\) | −11478.4 | + | 6627.03i | −0.0101361 | + | 0.00585207i | ||||
\(265\) | − | 1.97936e6i | − | 1.73145i | ||||||
\(266\) | −75936.2 | − | 131525.i | −0.0658028 | − | 0.113974i | ||||
\(267\) | 34936.8i | 0.0299919i | ||||||||
\(268\) | −171493. | + | 297034.i | −0.145851 | + | 0.252621i | ||||
\(269\) | 198935. | 0.167622 | 0.0838110 | − | 0.996482i | \(-0.473291\pi\) | ||||
0.0838110 | + | 0.996482i | \(0.473291\pi\) | |||||||
\(270\) | 37314.7 | 0.0311509 | ||||||||
\(271\) | −89997.7 | + | 155881.i | −0.0744403 | + | 0.128934i | −0.900843 | − | 0.434146i | \(-0.857050\pi\) |
0.826402 | + | 0.563080i | \(0.190384\pi\) | |||||||
\(272\) | −80580.6 | + | 46523.3i | −0.0660402 | + | 0.0381283i | ||||
\(273\) | 27188.8i | 0.0220792i | ||||||||
\(274\) | −1.49958e6 | − | 865782.i | −1.20668 | − | 0.696678i | ||||
\(275\) | −216970. | + | 375804.i | −0.173009 | + | 0.299660i | ||||
\(276\) | 11030.5 | + | 6368.47i | 0.00871612 | + | 0.00503225i | ||||
\(277\) | −1.04083e6 | + | 600922.i | −0.815041 | + | 0.470564i | −0.848703 | − | 0.528869i | \(-0.822616\pi\) |
0.0336624 | + | 0.999433i | \(0.489283\pi\) | |||||||
\(278\) | 316909. | − | 182967.i | 0.245936 | − | 0.141991i | ||||
\(279\) | −1.43059e6 | − | 825952.i | −1.10028 | − | 0.635249i | ||||
\(280\) | 180292. | − | 312275.i | 0.137430 | − | 0.238036i | ||||
\(281\) | 877906. | + | 506859.i | 0.663258 | + | 0.382932i | 0.793517 | − | 0.608548i | \(-0.208248\pi\) |
−0.130259 | + | 0.991480i | \(0.541581\pi\) | |||||||
\(282\) | − | 36975.8i | − | 0.0276882i | ||||||
\(283\) | 774248. | − | 447012.i | 0.574664 | − | 0.331782i | −0.184346 | − | 0.982861i | \(-0.559017\pi\) |
0.759010 | + | 0.651079i | \(0.225683\pi\) | |||||||
\(284\) | −411085. | + | 712020.i | −0.302438 | + | 0.523837i | ||||
\(285\) | −7953.77 | −0.00580044 | ||||||||
\(286\) | 2.51987e6 | 1.82164 | ||||||||
\(287\) | −220037. | + | 381115.i | −0.157685 | + | 0.273119i | ||||
\(288\) | 248732.i | 0.176706i | ||||||||
\(289\) | −643876. | − | 1.11523e6i | −0.453479 | − | 0.785449i | ||||
\(290\) | − | 859795.i | − | 0.600344i | ||||||
\(291\) | 9863.13 | − | 5694.48i | 0.00682782 | − | 0.00394205i | ||||
\(292\) | 450434. | + | 780175.i | 0.309154 | + | 0.535470i | ||||
\(293\) | 113588. | + | 196741.i | 0.0772973 | + | 0.133883i | 0.902083 | − | 0.431563i | \(-0.142038\pi\) |
−0.824786 | + | 0.565445i | \(0.808704\pi\) | |||||||
\(294\) | −9095.75 | − | 5251.43i | −0.00613720 | − | 0.00354331i | ||||
\(295\) | 1.32523e6 | 0.886619 | ||||||||
\(296\) | 277868. | + | 454777.i | 0.184335 | + | 0.301696i | ||||
\(297\) | 100628. | 0.0661953 | ||||||||
\(298\) | 1.09178e6 | + | 630341.i | 0.712190 | + | 0.411183i | ||||
\(299\) | −1.21078e6 | − | 2.09713e6i | −0.783226 | − | 1.35659i | ||||
\(300\) | −1634.84 | − | 2831.62i | −0.00104875 | − | 0.00181649i | ||||
\(301\) | −425362. | + | 245583.i | −0.270609 | + | 0.156236i | ||||
\(302\) | 724091.i | 0.456852i | ||||||||
\(303\) | −4549.01 | − | 7879.12i | −0.00284649 | − | 0.00493027i | ||||
\(304\) | − | 106058.i | − | 0.0658200i | ||||||
\(305\) | −202016. | + | 349903.i | −0.124347 | + | 0.215376i | ||||
\(306\) | 353144. | 0.215600 | ||||||||
\(307\) | 2.25873e6 | 1.36778 | 0.683892 | − | 0.729583i | \(-0.260286\pi\) | ||||
0.683892 | + | 0.729583i | \(0.260286\pi\) | |||||||
\(308\) | 486199. | − | 842122.i | 0.292037 | − | 0.505823i | ||||
\(309\) | 23902.5 | − | 13800.1i | 0.0142412 | − | 0.00822216i | ||||
\(310\) | 1.67233e6i | 0.988367i | ||||||||
\(311\) | −2.89693e6 | − | 1.67254e6i | −1.69839 | − | 0.980564i | −0.947293 | − | 0.320369i | \(-0.896193\pi\) |
−0.751094 | − | 0.660195i | \(-0.770474\pi\) | |||||||
\(312\) | −9493.43 | + | 16443.1i | −0.00552124 | + | 0.00956307i | ||||
\(313\) | −1.45213e6 | − | 838389.i | −0.837809 | − | 0.483709i | 0.0187096 | − | 0.999825i | \(-0.494044\pi\) |
−0.856519 | + | 0.516115i | \(0.827378\pi\) | |||||||
\(314\) | 2.05911e6 | − | 1.18883e6i | 1.17857 | − | 0.680449i | ||||
\(315\) | −1.18519e6 | + | 684272.i | −0.672997 | + | 0.388555i | ||||
\(316\) | −756154. | − | 436566.i | −0.425983 | − | 0.245942i | ||||
\(317\) | −389504. | + | 674640.i | −0.217703 | + | 0.377072i | −0.954105 | − | 0.299472i | \(-0.903190\pi\) |
0.736403 | + | 0.676544i | \(0.236523\pi\) | |||||||
\(318\) | 34831.1 | + | 20109.8i | 0.0193152 | + | 0.0111516i | ||||
\(319\) | − | 2.31864e6i | − | 1.27572i | ||||||
\(320\) | 218072. | − | 125904.i | 0.119049 | − | 0.0687329i | ||||
\(321\) | −8048.91 | + | 13941.1i | −0.00435988 | + | 0.00755153i | ||||
\(322\) | −934460. | −0.502251 | ||||||||
\(323\) | −150578. | −0.0803074 | ||||||||
\(324\) | 471823. | − | 817222.i | 0.249699 | − | 0.432491i | ||||
\(325\) | 621633.i | 0.326457i | ||||||||
\(326\) | 850782. | + | 1.47360e6i | 0.443378 | + | 0.767953i | ||||
\(327\) | 30455.3i | 0.0157505i | ||||||||
\(328\) | −266146. | + | 153659.i | −0.136595 | + | 0.0788632i | ||||
\(329\) | 1.35638e6 | + | 2.34932e6i | 0.690864 | + | 1.19661i | ||||
\(330\) | −25463.0 | − | 44103.1i | −0.0128713 | − | 0.0222938i | ||||
\(331\) | 1.73437e6 | + | 1.00134e6i | 0.870104 | + | 0.502355i | 0.867383 | − | 0.497641i | \(-0.165800\pi\) |
0.00272149 | + | 0.999996i | \(0.499134\pi\) | |||||||
\(332\) | −1.55726e6 | −0.775383 | ||||||||
\(333\) | −50294.9 | − | 2.02210e6i | −0.0248550 | − | 0.999290i | ||||
\(334\) | −2.46473e6 | −1.20894 | ||||||||
\(335\) | −1.14129e6 | − | 658924.i | −0.555628 | − | 0.320792i | ||||
\(336\) | 3663.44 | + | 6345.26i | 0.00177027 | + | 0.00306620i | ||||
\(337\) | 809317. | + | 1.40178e6i | 0.388190 | + | 0.672364i | 0.992206 | − | 0.124608i | \(-0.0397672\pi\) |
−0.604016 | + | 0.796972i | \(0.706434\pi\) | |||||||
\(338\) | 1.83998e6 | − | 1.06231e6i | 0.876035 | − | 0.505779i | ||||
\(339\) | 43417.1i | 0.0205193i | ||||||||
\(340\) | −178756. | − | 309614.i | −0.0838615 | − | 0.145252i | ||||
\(341\) | 4.50983e6i | 2.10027i | ||||||||
\(342\) | −201263. | + | 348597.i | −0.0930461 | + | 0.161161i | ||||
\(343\) | 2.31086e6 | 1.06057 | ||||||||
\(344\) | −342997. | −0.156277 | ||||||||
\(345\) | −24469.5 | + | 42382.4i | −0.0110682 | + | 0.0191707i | ||||
\(346\) | −1.16872e6 | + | 674761.i | −0.524832 | + | 0.303012i | ||||
\(347\) | − | 1.94133e6i | − | 0.865519i | −0.901509 | − | 0.432760i | \(-0.857540\pi\) | ||
0.901509 | − | 0.432760i | \(-0.142460\pi\) | |||||||
\(348\) | 15130.0 | + | 8735.28i | 0.00669714 | + | 0.00386660i | ||||
\(349\) | −614727. | + | 1.06474e6i | −0.270158 | + | 0.467928i | −0.968902 | − | 0.247444i | \(-0.920409\pi\) |
0.698744 | + | 0.715372i | \(0.253743\pi\) | |||||||
\(350\) | 207745. | + | 119942.i | 0.0906485 | + | 0.0523359i | ||||
\(351\) | 124840. | − | 72076.3i | 0.0540860 | − | 0.0312266i | ||||
\(352\) | 588082. | − | 339529.i | 0.252977 | − | 0.146056i | ||||
\(353\) | −1.12988e6 | − | 652336.i | −0.482608 | − | 0.278634i | 0.238894 | − | 0.971046i | \(-0.423215\pi\) |
−0.721503 | + | 0.692411i | \(0.756548\pi\) | |||||||
\(354\) | −13464.0 | + | 23320.3i | −0.00571039 | + | 0.00989069i | ||||
\(355\) | −2.73578e6 | − | 1.57951e6i | −1.15216 | − | 0.665197i | ||||
\(356\) | − | 1.78995e6i | − | 0.748542i | ||||||
\(357\) | 9008.85 | − | 5201.26i | 0.00374110 | − | 0.00215992i | ||||
\(358\) | −997601. | + | 1.72789e6i | −0.411386 | + | 0.712541i | ||||
\(359\) | −3.31055e6 | −1.35570 | −0.677852 | − | 0.735199i | \(-0.737089\pi\) | ||||
−0.677852 | + | 0.735199i | \(0.737089\pi\) | |||||||
\(360\) | −955700. | −0.388656 | ||||||||
\(361\) | −1.15223e6 | + | 1.99573e6i | −0.465342 | + | 0.805996i | ||||
\(362\) | − | 1.41527e6i | − | 0.567634i | ||||||
\(363\) | −43519.2 | − | 75377.5i | −0.0173346 | − | 0.0300245i | ||||
\(364\) | − | 1.39299e6i | − | 0.551055i | ||||||
\(365\) | −2.99766e6 | + | 1.73070e6i | −1.17774 | + | 0.679969i | ||||
\(366\) | −4104.86 | − | 7109.83i | −0.00160175 | − | 0.00277432i | ||||
\(367\) | 2.14958e6 | + | 3.72318e6i | 0.833084 | + | 1.44294i | 0.895581 | + | 0.444898i | \(0.146760\pi\) |
−0.0624974 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(368\) | −565137. | − | 326282.i | −0.217538 | − | 0.125595i | ||||
\(369\) | 1.16638e6 | 0.445938 | ||||||||
\(370\) | −1.74738e6 | + | 1.06765e6i | −0.663566 | + | 0.405437i | ||||
\(371\) | −2.95075e6 | −1.11301 | ||||||||
\(372\) | −29428.3 | − | 16990.4i | −0.0110257 | − | 0.00636571i | ||||
\(373\) | −2.34546e6 | − | 4.06246e6i | −0.872884 | − | 1.51188i | −0.859000 | − | 0.511975i | \(-0.828914\pi\) |
−0.0138836 | − | 0.999904i | \(-0.504419\pi\) | |||||||
\(374\) | −482056. | − | 834946.i | −0.178204 | − | 0.308659i | ||||
\(375\) | −41078.1 | + | 23716.4i | −0.0150845 | + | 0.00870906i | ||||
\(376\) | 1.89442e6i | 0.691044i | ||||||||
\(377\) | −1.66076e6 | − | 2.87652e6i | −0.601801 | − | 1.04235i | ||||
\(378\) | − | 55627.3i | − | 0.0200243i | ||||||
\(379\) | 347179. | − | 601332.i | 0.124153 | − | 0.215039i | −0.797249 | − | 0.603651i | \(-0.793712\pi\) |
0.921401 | + | 0.388612i | \(0.127045\pi\) | |||||||
\(380\) | 407503. | 0.144768 | ||||||||
\(381\) | 13876.4 | 0.00489737 | ||||||||
\(382\) | −684413. | + | 1.18544e6i | −0.239972 | + | 0.415643i | ||||
\(383\) | 1.48984e6 | − | 860158.i | 0.518970 | − | 0.299627i | −0.217543 | − | 0.976051i | \(-0.569804\pi\) |
0.736513 | + | 0.676423i | \(0.236471\pi\) | |||||||
\(384\) | 5116.60i | 0.00177074i | ||||||||
\(385\) | 3.23567e6 | + | 1.86812e6i | 1.11253 | + | 0.642321i | ||||
\(386\) | −852314. | + | 1.47625e6i | −0.291160 | + | 0.504304i | ||||
\(387\) | 1.12739e6 | + | 650897.i | 0.382645 | + | 0.220920i | ||||
\(388\) | −505328. | + | 291751.i | −0.170409 | + | 0.0983860i | ||||
\(389\) | 3.78997e6 | − | 2.18814e6i | 1.26988 | − | 0.733165i | 0.294914 | − | 0.955524i | \(-0.404709\pi\) |
0.974965 | + | 0.222359i | \(0.0713757\pi\) | |||||||
\(390\) | −63179.1 | − | 36476.5i | −0.0210335 | − | 0.0121437i | ||||
\(391\) | −463248. | + | 802369.i | −0.153240 | + | 0.265419i | ||||
\(392\) | 466012. | + | 269052.i | 0.153173 | + | 0.0884344i | ||||
\(393\) | − | 16607.9i | − | 0.00542418i | ||||||
\(394\) | 1.36577e6 | − | 788530.i | 0.443239 | − | 0.255904i | ||||
\(395\) | 1.67741e6 | − | 2.90536e6i | 0.540937 | − | 0.936930i | ||||
\(396\) | −2.57727e6 | −0.825888 | ||||||||
\(397\) | 3.18838e6 | 1.01530 | 0.507650 | − | 0.861563i | \(-0.330514\pi\) | ||||
0.507650 | + | 0.861563i | \(0.330514\pi\) | |||||||
\(398\) | 1.05541e6 | − | 1.82803e6i | 0.333976 | − | 0.578463i | ||||
\(399\) | 11857.2i | 0.00372862i | ||||||||
\(400\) | 83759.3 | + | 145075.i | 0.0261748 | + | 0.0453360i | ||||
\(401\) | 5.78136e6i | 1.79543i | 0.440574 | + | 0.897716i | \(0.354775\pi\) | ||||
−0.440574 | + | 0.897716i | \(0.645225\pi\) | |||||||
\(402\) | 23190.4 | − | 13389.0i | 0.00715720 | − | 0.00413221i | ||||
\(403\) | 3.23024e6 | + | 5.59493e6i | 0.990767 | + | 1.71606i | ||||
\(404\) | 233064. | + | 403679.i | 0.0710431 | + | 0.123050i | ||||
\(405\) | 3.14000e6 | + | 1.81288e6i | 0.951244 | + | 0.549201i | ||||
\(406\) | −1.28175e6 | −0.385911 | ||||||||
\(407\) | −4.71223e6 | + | 2.87916e6i | −1.41007 | + | 0.861548i | ||||
\(408\) | 7264.43 | 0.00216049 | ||||||||
\(409\) | −815854. | − | 471034.i | −0.241159 | − | 0.139233i | 0.374550 | − | 0.927207i | \(-0.377797\pi\) |
−0.615709 | + | 0.787973i | \(0.711131\pi\) | |||||||
\(410\) | −590403. | − | 1.02261e6i | −0.173456 | − | 0.300434i | ||||
\(411\) | 67594.4 | + | 117077.i | 0.0197381 | + | 0.0341874i | ||||
\(412\) | −1.22462e6 | + | 707034.i | −0.355433 | + | 0.205209i | ||||
\(413\) | − | 1.97560e6i | − | 0.569934i | ||||||
\(414\) | 1.23836e6 | + | 2.14490e6i | 0.355095 | + | 0.615043i | ||||
\(415\) | − | 5.98344e6i | − | 1.70542i | ||||||
\(416\) | 486386. | − | 842446.i | 0.137800 | − | 0.238676i | ||||
\(417\) | −28569.7 | −0.00804573 | ||||||||
\(418\) | 1.09893e6 | 0.307630 | ||||||||
\(419\) | −568648. | + | 984926.i | −0.158237 | + | 0.274075i | −0.934233 | − | 0.356663i | \(-0.883914\pi\) |
0.775996 | + | 0.630738i | \(0.217248\pi\) | |||||||
\(420\) | −24380.3 | + | 14076.0i | −0.00674397 | + | 0.00389363i | ||||
\(421\) | 1.34421e6i | 0.369626i | 0.982774 | + | 0.184813i | \(0.0591680\pi\) | ||||
−0.982774 | + | 0.184813i | \(0.940832\pi\) | |||||||
\(422\) | 127030. | + | 73340.6i | 0.0347235 | + | 0.0200476i | ||||
\(423\) | 3.59499e6 | − | 6.22670e6i | 0.976892 | − | 1.69203i | ||||
\(424\) | −1.78454e6 | − | 1.03030e6i | −0.482071 | − | 0.278324i | ||||
\(425\) | 205975. | − | 118920.i | 0.0553148 | − | 0.0319360i | ||||
\(426\) | 55589.6 | − | 32094.7i | 0.0148412 | − | 0.00856859i | ||||
\(427\) | 521620. | + | 301158.i | 0.138447 | + | 0.0799327i | ||||
\(428\) | 412378. | − | 714260.i | 0.108814 | − | 0.188472i | ||||
\(429\) | −170377. | − | 98367.3i | −0.0446959 | − | 0.0258052i | ||||
\(430\) | − | 1.31789e6i | − | 0.343723i | ||||||
\(431\) | 4.04990e6 | − | 2.33821e6i | 1.05015 | − | 0.606304i | 0.127458 | − | 0.991844i | \(-0.459318\pi\) |
0.922691 | + | 0.385540i | \(0.125985\pi\) | |||||||
\(432\) | 19423.2 | − | 33642.0i | 0.00500739 | − | 0.00867305i | ||||
\(433\) | 995189. | 0.255086 | 0.127543 | − | 0.991833i | \(-0.459291\pi\) | ||||
0.127543 | + | 0.991833i | \(0.459291\pi\) | |||||||
\(434\) | 2.49304e6 | 0.635339 | ||||||||
\(435\) | −33563.4 | + | 58133.6i | −0.00850440 | + | 0.0147300i | ||||
\(436\) | − | 1.56035e6i | − | 0.393102i | ||||||
\(437\) | −528026. | − | 914567.i | −0.132267 | − | 0.229093i | ||||
\(438\) | − | 70333.7i | − | 0.0175177i | ||||||
\(439\) | −2.90716e6 | + | 1.67845e6i | −0.719960 | + | 0.415669i | −0.814738 | − | 0.579829i | \(-0.803119\pi\) |
0.0947780 | + | 0.995498i | \(0.469786\pi\) | |||||||
\(440\) | 1.30457e6 | + | 2.25958e6i | 0.321244 | + | 0.556411i | ||||
\(441\) | −1.02115e6 | − | 1.76868e6i | −0.250030 | − | 0.433064i | ||||
\(442\) | −1.19609e6 | − | 690560.i | −0.291210 | − | 0.168130i | ||||
\(443\) | −1.19977e6 | −0.290462 | −0.145231 | − | 0.989398i | \(-0.546393\pi\) | ||||
−0.145231 | + | 0.989398i | \(0.546393\pi\) | |||||||
\(444\) | −1034.60 | − | 41596.0i | −0.000249067 | − | 0.0100137i | ||||
\(445\) | 6.87750e6 | 1.64638 | ||||||||
\(446\) | 743355. | + | 429176.i | 0.176953 | + | 0.102164i | ||||
\(447\) | −49212.8 | − | 85239.0i | −0.0116495 | − | 0.0201776i | ||||
\(448\) | −187693. | − | 325093.i | −0.0441827 | − | 0.0765266i | ||||
\(449\) | 4.08529e6 | − | 2.35865e6i | 0.956329 | − | 0.552137i | 0.0612879 | − | 0.998120i | \(-0.480479\pi\) |
0.895041 | + | 0.445983i | \(0.147146\pi\) | |||||||
\(450\) | − | 635792.i | − | 0.148007i | ||||||
\(451\) | −1.59216e6 | − | 2.75770e6i | −0.368591 | − | 0.638419i | ||||
\(452\) | − | 2.22443e6i | − | 0.512122i | ||||||
\(453\) | 28266.0 | − | 48958.2i | 0.00647171 | − | 0.0112093i | ||||
\(454\) | 614252. | 0.139864 | ||||||||
\(455\) | 5.35227e6 | 1.21202 | ||||||||
\(456\) | −4140.12 | + | 7170.90i | −0.000932398 | + | 0.00161496i | ||||
\(457\) | −1.31832e6 | + | 761130.i | −0.295276 | + | 0.170478i | −0.640319 | − | 0.768109i | \(-0.721198\pi\) |
0.345043 | + | 0.938587i | \(0.387864\pi\) | |||||||
\(458\) | − | 2.88101e6i | − | 0.641773i | ||||||
\(459\) | −47764.1 | − | 27576.6i | −0.0105821 | − | 0.00610955i | ||||
\(460\) | 1.25367e6 | − | 2.17142e6i | 0.276241 | − | 0.478464i | ||||
\(461\) | 7.19579e6 | + | 4.15449e6i | 1.57698 | + | 0.910470i | 0.995278 | + | 0.0970689i | \(0.0309467\pi\) |
0.581703 | + | 0.813401i | \(0.302387\pi\) | |||||||
\(462\) | −65747.1 | + | 37959.1i | −0.0143308 | + | 0.00827392i | ||||
\(463\) | 1.00620e6 | − | 580927.i | 0.218137 | − | 0.125942i | −0.386950 | − | 0.922101i | \(-0.626471\pi\) |
0.605087 | + | 0.796159i | \(0.293138\pi\) | |||||||
\(464\) | −775168. | − | 447543.i | −0.167148 | − | 0.0965029i | ||||
\(465\) | 65282.1 | − | 113072.i | 0.0140011 | − | 0.0242506i | ||||
\(466\) | −1.13509e6 | − | 655342.i | −0.242139 | − | 0.139799i | ||||
\(467\) | − | 683753.i | − | 0.145080i | −0.997366 | − | 0.0725399i | \(-0.976890\pi\) | ||
0.997366 | − | 0.0725399i | \(-0.0231105\pi\) | |||||||
\(468\) | −3.19738e6 | + | 1.84601e6i | −0.674807 | + | 0.389600i | ||||
\(469\) | −982297. | + | 1.70139e6i | −0.206211 | + | 0.357167i | ||||
\(470\) | −7.27889e6 | −1.51992 | ||||||||
\(471\) | −185631. | −0.0385566 | ||||||||
\(472\) | 689815. | − | 1.19479e6i | 0.142521 | − | 0.246853i | ||||
\(473\) | − | 3.55400e6i | − | 0.730407i | ||||||
\(474\) | 34084.1 | + | 59035.3i | 0.00696796 | + | 0.0120689i | ||||
\(475\) | 271097.i | 0.0551303i | ||||||||
\(476\) | −461560. | + | 266482.i | −0.0933707 | + | 0.0539076i | ||||
\(477\) | 3.91036e6 | + | 6.77295e6i | 0.786903 | + | 1.36296i | ||||
\(478\) | 2.19149e6 | + | 3.79578e6i | 0.438703 | + | 0.759856i | ||||
\(479\) | −1.52516e6 | − | 880550.i | −0.303722 | − | 0.175354i | 0.340392 | − | 0.940284i | \(-0.389440\pi\) |
−0.644114 | + | 0.764930i | \(0.722774\pi\) | |||||||
\(480\) | −19659.4 | −0.00389465 | ||||||||
\(481\) | −3.78379e6 | + | 6.94711e6i | −0.745700 | + | 1.36912i | ||||
\(482\) | 17468.4 | 0.00342481 | ||||||||
\(483\) | 63181.9 | + | 36478.1i | 0.0123232 | + | 0.00711483i | ||||
\(484\) | 2.22966e6 | + | 3.86189e6i | 0.432639 | + | 0.749353i | ||||
\(485\) | −1.12099e6 | − | 1.94161e6i | −0.216395 | − | 0.374808i | ||||
\(486\) | −191537. | + | 110584.i | −0.0367843 | + | 0.0212375i | ||||
\(487\) | − | 684640.i | − | 0.130810i | −0.997859 | − | 0.0654048i | \(-0.979166\pi\) | ||
0.997859 | − | 0.0654048i | \(-0.0208339\pi\) | |||||||
\(488\) | 210309. | + | 364265.i | 0.0399767 | + | 0.0692417i | ||||
\(489\) | − | 132846.i | − | 0.0251234i | ||||||
\(490\) | −1.03377e6 | + | 1.79055e6i | −0.194507 | + | 0.336896i | ||||
\(491\) | 1.59699e6 | 0.298950 | 0.149475 | − | 0.988765i | \(-0.452242\pi\) | ||||
0.149475 | + | 0.988765i | \(0.452242\pi\) | |||||||
\(492\) | 23993.3 | 0.00446867 | ||||||||
\(493\) | −635412. | + | 1.10057e6i | −0.117744 | + | 0.203938i | ||||
\(494\) | 1.36334e6 | − | 787124.i | 0.251354 | − | 0.145119i | ||||
\(495\) | − | 9.90259e6i | − | 1.81650i | ||||||
\(496\) | 1.50773e6 | + | 870488.i | 0.275181 | + | 0.158876i | ||||
\(497\) | −2.35466e6 | + | 4.07839e6i | −0.427600 | + | 0.740625i | ||||
\(498\) | 105292. | + | 60790.2i | 0.0190248 | + | 0.0109840i | ||||
\(499\) | −6.65215e6 | + | 3.84062e6i | −1.19594 | + | 0.690479i | −0.959648 | − | 0.281203i | \(-0.909267\pi\) |
−0.236296 | + | 0.971681i | \(0.575933\pi\) | |||||||
\(500\) | 2.10459e6 | − | 1.21509e6i | 0.376481 | − | 0.217361i | ||||
\(501\) | 166649. | + | 96214.7i | 0.0296625 | + | 0.0171256i | ||||
\(502\) | −1.15001e6 | + | 1.99187e6i | −0.203677 | + | 0.352778i | ||||
\(503\) | −2.32928e6 | − | 1.34481e6i | −0.410489 | − | 0.236996i | 0.280511 | − | 0.959851i | \(-0.409496\pi\) |
−0.691000 | + | 0.722855i | \(0.742830\pi\) | |||||||
\(504\) | 1.42472e6i | 0.249835i | ||||||||
\(505\) | −1.55105e6 | + | 895498.i | −0.270643 | + | 0.156256i | ||||
\(506\) | 3.38081e6 | − | 5.85574e6i | 0.587009 | − | 1.01673i | ||||
\(507\) | −165876. | −0.0286592 | ||||||||
\(508\) | −710941. | −0.122229 | ||||||||
\(509\) | −180380. | + | 312427.i | −0.0308598 | + | 0.0534508i | −0.881043 | − | 0.473036i | \(-0.843158\pi\) |
0.850183 | + | 0.526487i | \(0.176491\pi\) | |||||||
\(510\) | 27912.0i | 0.00475189i | ||||||||
\(511\) | 2.58005e6 | + | 4.46878e6i | 0.437095 | + | 0.757071i | ||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | 54443.1 | − | 31432.8i | 0.00913376 | − | 0.00527338i | ||||
\(514\) | 629863. | + | 1.09095e6i | 0.105157 | + | 0.182137i | ||||
\(515\) | −2.71663e6 | − | 4.70533e6i | −0.451348 | − | 0.781758i | ||||
\(516\) | 23191.2 | + | 13389.4i | 0.00383441 | + | 0.00221380i | ||||
\(517\) | −1.96292e7 | −3.22981 | ||||||||
\(518\) | 1.59160e6 | + | 2.60493e6i | 0.260622 | + | 0.426552i | ||||
\(519\) | 105361. | 0.0171697 | ||||||||
\(520\) | 3.23692e6 | + | 1.86884e6i | 0.524957 | + | 0.303084i | ||||
\(521\) | −5.20222e6 | − | 9.01051e6i | −0.839643 | − | 1.45430i | −0.890193 | − | 0.455583i | \(-0.849431\pi\) |
0.0505504 | − | 0.998722i | \(-0.483902\pi\) | |||||||
\(522\) | 1.69858e6 | + | 2.94203e6i | 0.272842 | + | 0.472576i | ||||
\(523\) | −1.05710e7 | + | 6.10317e6i | −1.68990 | + | 0.975667i | −0.735322 | + | 0.677717i | \(0.762969\pi\) |
−0.954582 | + | 0.297949i | \(0.903697\pi\) | |||||||
\(524\) | 850891.i | 0.135377i | ||||||||
\(525\) | −9364.22 | − | 16219.3i | −0.00148277 | − | 0.00256823i | ||||
\(526\) | 6.75945e6i | 1.06524i | ||||||||
\(527\) | 1.23590e6 | − | 2.14064e6i | 0.193846 | − | 0.335751i | ||||
\(528\) | −53016.3 | −0.00827607 | ||||||||
\(529\) | −61466.3 | −0.00954987 | ||||||||
\(530\) | 3.95872e6 | − | 6.85670e6i | 0.612160 | − | 1.06029i | ||||
\(531\) | −4.53466e6 | + | 2.61809e6i | −0.697925 | + | 0.402947i | ||||
\(532\) | − | 607489.i | − | 0.0930592i | ||||||
\(533\) | −3.95049e6 | − | 2.28082e6i | −0.602328 | − | 0.347754i | ||||
\(534\) | −69873.6 | + | 121025.i | −0.0106038 | + | 0.0183662i | ||||
\(535\) | 2.74439e6 | + | 1.58447e6i | 0.414535 | + | 0.239332i | ||||
\(536\) | −1.18814e6 | + | 685971.i | −0.178630 | + | 0.103132i | ||||
\(537\) | 134902. | − | 77885.8i | 0.0201875 | − | 0.0116553i | ||||
\(538\) | 689132. | + | 397870.i | 0.102647 | + | 0.0592633i | ||||
\(539\) | −2.78781e6 | + | 4.82863e6i | −0.413325 | + | 0.715900i | ||||
\(540\) | 129262. | + | 74629.5i | 0.0190760 | + | 0.0110135i | ||||
\(541\) | 5.12434e6i | 0.752740i | 0.926469 | + | 0.376370i | \(0.122828\pi\) | ||||
−0.926469 | + | 0.376370i | \(0.877172\pi\) | |||||||
\(542\) | −623523. | + | 359991.i | −0.0911704 | + | 0.0526373i | ||||
\(543\) | −55247.4 | + | 95691.3i | −0.00804104 | + | 0.0139275i | ||||
\(544\) | −372186. | −0.0539216 | ||||||||
\(545\) | 5.99530e6 | 0.864609 | ||||||||
\(546\) | −54377.6 | + | 94184.8i | −0.00780618 | + | 0.0135207i | ||||
\(547\) | 2.94719e6i | 0.421153i | 0.977577 | + | 0.210577i | \(0.0675341\pi\) | ||||
−0.977577 | + | 0.210577i | \(0.932466\pi\) | |||||||
\(548\) | −3.46313e6 | − | 5.99832e6i | −0.492626 | − | 0.853253i | ||||
\(549\) | − | 1.59639e6i | − | 0.226052i | ||||||
\(550\) | −1.50321e6 | + | 867881.i | −0.211892 | + | 0.122336i | ||||
\(551\) | −724264. | − | 1.25446e6i | −0.101629 | − | 0.176027i | ||||
\(552\) | 25473.9 | + | 44122.1i | 0.00355834 | + | 0.00616323i | ||||
\(553\) | −4.33119e6 | − | 2.50061e6i | −0.602274 | − | 0.347723i | ||||
\(554\) | −4.80738e6 | −0.665478 | ||||||||
\(555\) | 159824. | − | 3975.24i | 0.0220246 | − | 0.000547811i | ||||
\(556\) | 1.46374e6 | 0.200806 | ||||||||
\(557\) | −1.92528e6 | − | 1.11156e6i | −0.262939 | − | 0.151808i | 0.362735 | − | 0.931892i | \(-0.381843\pi\) |
−0.625675 | + | 0.780084i | \(0.715176\pi\) | |||||||
\(558\) | −3.30381e6 | − | 5.72236e6i | −0.449189 | − | 0.778018i | ||||
\(559\) | −2.54561e6 | − | 4.40913e6i | −0.344558 | − | 0.596792i | ||||
\(560\) | 1.24910e6 | − | 721168.i | 0.168317 | − | 0.0971777i | ||||
\(561\) | 75271.3i | 0.0100977i | ||||||||
\(562\) | 2.02744e6 | + | 3.51162e6i | 0.270774 | + | 0.468994i | ||||
\(563\) | − | 1.27133e6i | − | 0.169039i | −0.996422 | − | 0.0845193i | \(-0.973065\pi\) | ||
0.996422 | − | 0.0845193i | \(-0.0269355\pi\) | |||||||
\(564\) | 73951.5 | − | 128088.i | 0.00978925 | − | 0.0169555i | ||||
\(565\) | 8.54691e6 | 1.12639 | ||||||||
\(566\) | 3.57610e6 | 0.469211 | ||||||||
\(567\) | 2.70257e6 | − | 4.68098e6i | 0.353036 | − | 0.611476i | ||||
\(568\) | −2.84808e6 | + | 1.64434e6i | −0.370409 | + | 0.213856i | ||||
\(569\) | 1.02957e7i | 1.33313i | 0.745445 | + | 0.666567i | \(0.232237\pi\) | ||||
−0.745445 | + | 0.666567i | \(0.767763\pi\) | |||||||
\(570\) | −27552.7 | − | 15907.5i | −0.00355203 | − | 0.00205076i | ||||
\(571\) | 2.87183e6 | − | 4.97416e6i | 0.368611 | − | 0.638453i | −0.620738 | − | 0.784018i | \(-0.713167\pi\) |
0.989349 | + | 0.145565i | \(0.0465001\pi\) | |||||||
\(572\) | 8.72910e6 | + | 5.03975e6i | 1.11553 | + | 0.644049i | ||||
\(573\) | 92550.9 | − | 53434.3i | 0.0117759 | − | 0.00679882i | ||||
\(574\) | −1.52446e6 | + | 880148.i | −0.193124 | + | 0.111500i | ||||
\(575\) | 1.44457e6 | + | 834020.i | 0.182208 | + | 0.105198i | ||||
\(576\) | −497464. | + | 861633.i | −0.0624749 | + | 0.108210i | ||||
\(577\) | 1.13566e7 | + | 6.55674e6i | 1.42007 | + | 0.819877i | 0.996304 | − | 0.0858952i | \(-0.0273750\pi\) |
0.423765 | + | 0.905772i | \(0.360708\pi\) | |||||||
\(578\) | − | 5.15101e6i | − | 0.641317i | ||||||
\(579\) | 115256. | − | 66542.9i | 0.0142878 | − | 0.00824907i | ||||
\(580\) | 1.71959e6 | − | 2.97842e6i | 0.212253 | − | 0.367634i | ||||
\(581\) | −8.91987e6 | −1.09627 | ||||||||
\(582\) | 45555.9 | 0.00557490 | ||||||||
\(583\) | 1.06756e7 | − | 1.84907e7i | 1.30083 | − | 2.25311i | ||||
\(584\) | 3.60347e6i | 0.437209i | ||||||||
\(585\) | −7.09289e6 | − | 1.22852e7i | −0.856906 | − | 1.48421i | ||||
\(586\) | 908705.i | 0.109315i | ||||||||
\(587\) | −735895. | + | 424869.i | −0.0881497 | + | 0.0508933i | −0.543427 | − | 0.839456i | \(-0.682873\pi\) |
0.455277 | + | 0.890350i | \(0.349540\pi\) | |||||||
\(588\) | −21005.7 | − | 36383.0i | −0.00250550 | − | 0.00433966i | ||||
\(589\) | 1.40872e6 | + | 2.43997e6i | 0.167315 | + | 0.289799i | ||||
\(590\) | 4.59074e6 | + | 2.65047e6i | 0.542941 | + | 0.313467i | ||||
\(591\) | −123126. | −0.0145004 | ||||||||
\(592\) | 53006.8 | + | 2.13113e6i | 0.00621624 | + | 0.249923i | ||||
\(593\) | 8.97746e6 | 1.04838 | 0.524188 | − | 0.851603i | \(-0.324369\pi\) | ||||
0.524188 | + | 0.851603i | \(0.324369\pi\) | |||||||
\(594\) | 348585. | + | 201256.i | 0.0405362 | + | 0.0234036i | ||||
\(595\) | −1.02390e6 | − | 1.77344e6i | −0.118567 | − | 0.205364i | ||||
\(596\) | 2.52137e6 | + | 4.36713e6i | 0.290750 | + | 0.503594i | ||||
\(597\) | −142720. | + | 82399.5i | −0.0163889 | + | 0.00946213i | ||||
\(598\) | − | 9.68623e6i | − | 1.10765i | ||||||
\(599\) | 6.14854e6 | + | 1.06496e7i | 0.700172 | + | 1.21273i | 0.968406 | + | 0.249380i | \(0.0802268\pi\) |
−0.268234 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(600\) | − | 13078.7i | − | 0.00148316i | ||||||
\(601\) | −4.42499e6 | + | 7.66431e6i | −0.499719 | + | 0.865539i | −1.00000 | 0.000323947i | \(-0.999897\pi\) | |
0.500281 | + | 0.865863i | \(0.333230\pi\) | |||||||
\(602\) | −1.96466e6 | −0.220951 | ||||||||
\(603\) | 5.20700e6 | 0.583169 | ||||||||
\(604\) | −1.44818e6 | + | 2.50832e6i | −0.161522 | + | 0.279764i | ||||
\(605\) | −1.48385e7 | + | 8.56701e6i | −1.64817 | + | 0.951570i | ||||
\(606\) | − | 36392.1i | − | 0.00402555i | ||||||
\(607\) | −7.14910e6 | − | 4.12754e6i | −0.787553 | − | 0.454694i | 0.0515473 | − | 0.998671i | \(-0.483585\pi\) |
−0.839100 | + | 0.543977i | \(0.816918\pi\) | |||||||
\(608\) | 212115. | − | 367394.i | 0.0232709 | − | 0.0403063i | ||||
\(609\) | 86663.2 | + | 50035.0i | 0.00946872 | + | 0.00546677i | ||||
\(610\) | −1.39961e6 | + | 808066.i | −0.152294 | + | 0.0879270i | ||||
\(611\) | −2.43522e7 | + | 1.40597e7i | −2.63897 | + | 1.52361i | ||||
\(612\) | 1.22333e6 | + | 706288.i | 0.132027 | + | 0.0762261i | ||||
\(613\) | 8.69044e6 | − | 1.50523e7i | 0.934094 | − | 1.61790i | 0.157852 | − | 0.987463i | \(-0.449543\pi\) |
0.776242 | − | 0.630435i | \(-0.217124\pi\) | |||||||
\(614\) | 7.82446e6 | + | 4.51745e6i | 0.837594 | + | 0.483585i | ||||
\(615\) | 92189.3i | 0.00982862i | ||||||||
\(616\) | 3.36849e6 | − | 1.94480e6i | 0.357671 | − | 0.206501i | ||||
\(617\) | 6.00445e6 | − | 1.04000e7i | 0.634980 | − | 1.09982i | −0.351539 | − | 0.936173i | \(-0.614341\pi\) |
0.986519 | − | 0.163645i | \(-0.0523252\pi\) | |||||||
\(618\) | 110401. | 0.0116279 | ||||||||
\(619\) | 1.40838e6 | 0.147738 | 0.0738691 | − | 0.997268i | \(-0.476465\pi\) | ||||
0.0738691 | + | 0.997268i | \(0.476465\pi\) | |||||||
\(620\) | −3.34466e6 | + | 5.79313e6i | −0.349440 | + | 0.605249i | ||||
\(621\) | − | 386807.i | − | 0.0402499i | ||||||
\(622\) | −6.69017e6 | − | 1.15877e7i | −0.693364 | − | 1.20094i | ||||
\(623\) | − | 1.02527e7i | − | 1.05832i | ||||||
\(624\) | −65772.4 | + | 37973.7i | −0.00676211 | + | 0.00390411i | ||||
\(625\) | 5.69117e6 | + | 9.85739e6i | 0.582775 | + | 1.00940i | ||||
\(626\) | −3.35355e6 | − | 5.80853e6i | −0.342034 | − | 0.592421i | ||||
\(627\) | −74302.1 | − | 42898.4i | −0.00754801 | − | 0.00435785i | ||||
\(628\) | 9.51064e6 | 0.962300 | ||||||||
\(629\) | 3.02573e6 | − | 75257.9i | 0.304932 | − | 0.00758447i | ||||
\(630\) | −5.47417e6 | −0.549499 | ||||||||
\(631\) | 1.06055e7 | + | 6.12310e6i | 1.06037 | + | 0.612207i | 0.925536 | − | 0.378661i | \(-0.123615\pi\) |
0.134838 | + | 0.990868i | \(0.456949\pi\) | |||||||
\(632\) | −1.74626e6 | − | 3.02462e6i | −0.173907 | − | 0.301216i | ||||
\(633\) | −5725.93 | − | 9917.60i | −0.000567985 | − | 0.000983779i | ||||
\(634\) | −2.69856e6 | + | 1.55802e6i | −0.266630 | + | 0.153939i | ||||
\(635\) | − | 2.73164e6i | − | 0.268837i | ||||||
\(636\) | 80439.0 | + | 139324.i | 0.00788541 | + | 0.0136579i | ||||
\(637\) | 7.98726e6i | 0.779918i | ||||||||
\(638\) | 4.63727e6 | − | 8.03199e6i | 0.451036 | − | 0.781217i | ||||
\(639\) | 1.24817e7 | 1.20926 | ||||||||
\(640\) | 1.00723e6 | 0.0972030 | ||||||||
\(641\) | −8.61348e6 | + | 1.49190e7i | −0.828006 | + | 1.43415i | 0.0715943 | + | 0.997434i | \(0.477191\pi\) |
−0.899600 | + | 0.436714i | \(0.856142\pi\) | |||||||
\(642\) | −55764.5 | + | 32195.6i | −0.00533974 | + | 0.00308290i | ||||
\(643\) | − | 1.00571e7i | − | 0.959279i | −0.877466 | − | 0.479640i | \(-0.840767\pi\) | ||
0.877466 | − | 0.479640i | \(-0.159233\pi\) | |||||||
\(644\) | −3.23706e6 | − | 1.86892e6i | −0.307565 | − | 0.177573i | ||||
\(645\) | −51446.0 | + | 89107.2i | −0.00486914 | + | 0.00843361i | ||||
\(646\) | −521618. | − | 301156.i | −0.0491780 | − | 0.0283929i | ||||
\(647\) | 9.80893e6 | − | 5.66319e6i | 0.921215 | − | 0.531864i | 0.0371925 | − | 0.999308i | \(-0.488159\pi\) |
0.884022 | + | 0.467444i | \(0.154825\pi\) | |||||||
\(648\) | 3.26889e6 | − | 1.88729e6i | 0.305818 | − | 0.176564i | ||||
\(649\) | 1.23800e7 | + | 7.14760e6i | 1.15374 | + | 0.666113i | ||||
\(650\) | −1.24327e6 | + | 2.15340e6i | −0.115420 | + | 0.199913i | ||||
\(651\) | −168563. | − | 97319.9i | −0.0155887 | − | 0.00900013i | ||||
\(652\) | 6.80625e6i | 0.627031i | ||||||||
\(653\) | 5.03854e6 | − | 2.90901e6i | 0.462405 | − | 0.266969i | −0.250650 | − | 0.968078i | \(-0.580644\pi\) |
0.713055 | + | 0.701108i | \(0.247311\pi\) | |||||||
\(654\) | −60910.6 | + | 105500.i | −0.00556864 | + | 0.00964516i | ||||
\(655\) | −3.26937e6 | −0.297756 | ||||||||
\(656\) | −1.22927e6 | −0.111529 | ||||||||
\(657\) | 6.83823e6 | − | 1.18442e7i | 0.618059 | − | 1.07051i | ||||
\(658\) | 1.08511e7i | 0.977029i | ||||||||
\(659\) | 7.95281e6 | + | 1.37747e7i | 0.713357 | + | 1.23557i | 0.963590 | + | 0.267385i | \(0.0861594\pi\) |
−0.250233 | + | 0.968186i | \(0.580507\pi\) | |||||||
\(660\) | − | 203704.i | − | 0.0182028i | ||||||
\(661\) | 866617. | − | 500342.i | 0.0771478 | − | 0.0445413i | −0.460930 | − | 0.887437i | \(-0.652484\pi\) |
0.538078 | + | 0.842895i | \(0.319151\pi\) | |||||||
\(662\) | 4.00535e6 | + | 6.93747e6i | 0.355219 | + | 0.615257i | ||||
\(663\) | 53914.2 | + | 93382.2i | 0.00476343 | + | 0.00825050i | ||||
\(664\) | −5.39451e6 | − | 3.11452e6i | −0.474823 | − | 0.274139i | ||||
\(665\) | 2.33415e6 | 0.204679 | ||||||||
\(666\) | 3.86997e6 | − | 7.10534e6i | 0.338082 | − | 0.620725i | ||||
\(667\) | −8.91269e6 | −0.775700 | ||||||||
\(668\) | −8.53808e6 | − | 4.92946e6i | −0.740319 | − | 0.427423i | ||||
\(669\) | −33507.1 | − | 58036.1i | −0.00289449 | − | 0.00501340i | ||||
\(670\) | −2.63570e6 | − | 4.56516e6i | −0.226834 | − | 0.392888i | ||||
\(671\) | −3.77437e6 | + | 2.17914e6i | −0.323622 | + | 0.186844i | ||||
\(672\) | 29307.5i | 0.00250355i | ||||||||
\(673\) | −9.84356e6 | − | 1.70496e7i | −0.837751 | − | 1.45103i | −0.891771 | − | 0.452487i | \(-0.850537\pi\) |
0.0540205 | − | 0.998540i | \(-0.482796\pi\) | |||||||
\(674\) | 6.47454e6i | 0.548983i | ||||||||
\(675\) | −49648.2 | + | 85993.3i | −0.00419415 | + | 0.00726449i | ||||
\(676\) | 8.49850e6 | 0.715279 | ||||||||
\(677\) | −6.17552e6 | −0.517848 | −0.258924 | − | 0.965898i | \(-0.583368\pi\) | ||||
−0.258924 | + | 0.965898i | \(0.583368\pi\) | |||||||
\(678\) | −86834.3 | + | 150401.i | −0.00725466 | + | 0.0125654i | ||||
\(679\) | −2.89448e6 | + | 1.67113e6i | −0.240933 | + | 0.139103i | ||||
\(680\) | − | 1.43005e6i | − | 0.118598i | ||||||
\(681\) | −41531.6 | − | 23978.3i | −0.00343171 | − | 0.00198130i | ||||
\(682\) | −9.01966e6 | + | 1.56225e7i | −0.742556 | + | 1.28614i | ||||
\(683\) | 1.48354e7 | + | 8.56521e6i | 1.21688 | + | 0.702565i | 0.964249 | − | 0.264998i | \(-0.0853715\pi\) |
0.252629 | + | 0.967563i | \(0.418705\pi\) | |||||||
\(684\) | −1.39439e6 | + | 805051.i | −0.113958 | + | 0.0657935i | ||||
\(685\) | 2.30472e7 | − | 1.33063e7i | 1.87669 | − | 1.08351i | ||||
\(686\) | 8.00506e6 | + | 4.62172e6i | 0.649463 | + | 0.374967i | ||||
\(687\) | −112465. | + | 194795.i | −0.00909128 | + | 0.0157466i | ||||
\(688\) | −1.18818e6 | − | 685994.i | −0.0956996 | − | 0.0552522i | ||||
\(689\) | − | 3.05863e7i | − | 2.45459i | ||||||
\(690\) | −169530. | + | 97878.0i | −0.0135557 | + | 0.00782640i | ||||
\(691\) | −6.93005e6 | + | 1.20032e7i | −0.552130 | + | 0.956317i | 0.445991 | + | 0.895037i | \(0.352851\pi\) |
−0.998121 | + | 0.0612793i | \(0.980482\pi\) | |||||||
\(692\) | −5.39809e6 | −0.428523 | ||||||||
\(693\) | −1.47624e7 | −1.16768 | ||||||||
\(694\) | 3.88267e6 | − | 6.72498e6i | 0.306007 | − | 0.530020i | ||||
\(695\) | 5.62410e6i | 0.441663i | ||||||||
\(696\) | 34941.1 | + | 60519.8i | 0.00273410 | + | 0.00473559i | ||||
\(697\) | 1.74530e6i | 0.136078i | ||||||||
\(698\) | −4.25895e6 | + | 2.45891e6i | −0.330875 | + | 0.191031i | ||||
\(699\) | 51164.6 | + | 88619.7i | 0.00396074 | + | 0.00686021i | ||||
\(700\) | 479767. | + | 830980.i | 0.0370071 | + | 0.0640982i | ||||
\(701\) | 1.16794e7 | + | 6.74309e6i | 0.897686 | + | 0.518279i | 0.876449 | − | 0.481495i | \(-0.159906\pi\) |
0.0212371 | + | 0.999774i | \(0.493240\pi\) | |||||||
\(702\) | 576610. | 0.0441611 | ||||||||
\(703\) | −1.65013e6 | + | 3.02966e6i | −0.125930 | + | 0.231210i | ||||
\(704\) | 2.71623e6 | 0.206555 | ||||||||
\(705\) | 492150. | + | 284143.i | 0.0372928 | + | 0.0215310i | ||||
\(706\) | −2.60934e6 | − | 4.51951e6i | −0.197024 | − | 0.341256i | ||||
\(707\) | 1.33497e6 | + | 2.31224e6i | 0.100444 | + | 0.173974i | ||||
\(708\) | −93281.4 | + | 53856.0i | −0.00699378 | + | 0.00403786i | ||||
\(709\) | − | 1.72340e7i | − | 1.28757i | −0.765208 | − | 0.643783i | \(-0.777364\pi\) | ||
0.765208 | − | 0.643783i | \(-0.222636\pi\) | |||||||
\(710\) | −6.31802e6 | − | 1.09431e7i | −0.470365 | − | 0.814697i | ||||
\(711\) | 1.32554e7i | 0.983371i | ||||||||
\(712\) | 3.57990e6 | − | 6.20057e6i | 0.264650 | − | 0.458386i | ||||
\(713\) | 1.73355e7 | 1.27706 | ||||||||
\(714\) | 41610.1 | 0.00305459 | ||||||||
\(715\) | −1.93642e7 | + | 3.35397e7i | −1.41655 | + | 2.45354i | ||||
\(716\) | −6.91158e6 | + | 3.99040e6i | −0.503842 | + | 0.290894i | ||||
\(717\) | − | 342194.i | − | 0.0248585i | ||||||
\(718\) | −1.14681e7 | − | 6.62111e6i | −0.830195 | − | 0.479314i | ||||
\(719\) | −901083. | + | 1.56072e6i | −0.0650044 | + | 0.112591i | −0.896696 | − | 0.442647i | \(-0.854039\pi\) |
0.831692 | + | 0.555238i | \(0.187373\pi\) | |||||||
\(720\) | −3.31064e6 | − | 1.91140e6i | −0.238002 | − | 0.137411i | ||||
\(721\) | −7.01452e6 | + | 4.04983e6i | −0.502527 | + | 0.290134i | ||||
\(722\) | −7.98290e6 | + | 4.60893e6i | −0.569925 | + | 0.329046i | ||||
\(723\) | −1181.10 | − | 681.908i | −8.40312e−5 | − | 4.85155e-5i | ||||
\(724\) | 2.83054e6 | − | 4.90265e6i | 0.200689 | − | 0.347604i | ||||
\(725\) | 1.98143e6 | + | 1.14398e6i | 0.140002 | + | 0.0808301i | ||||
\(726\) | − | 348154.i | − | 0.0245149i | ||||||
\(727\) | 2.11187e7 | − | 1.21929e7i | 1.48194 | − | 0.855601i | 0.482154 | − | 0.876086i | \(-0.339854\pi\) |
0.999790 | + | 0.0204852i | \(0.00652109\pi\) | |||||||
\(728\) | 2.78598e6 | − | 4.82546e6i | 0.194827 | − | 0.337451i | ||||
\(729\) | −1.43144e7 | −0.997593 | ||||||||
\(730\) | −1.38456e7 | −0.961621 | ||||||||
\(731\) | −973959. | + | 1.68695e6i | −0.0674136 | + | 0.116764i | ||||
\(732\) | − | 32838.9i | − | 0.00226522i | ||||||
\(733\) | 979073. | + | 1.69580e6i | 0.0673062 | + | 0.116578i | 0.897715 | − | 0.440577i | \(-0.145226\pi\) |
−0.830408 | + | 0.557155i | \(0.811893\pi\) | |||||||
\(734\) | 1.71966e7i | 1.17816i | ||||||||
\(735\) | 139794. | − | 80710.1i | 0.00954487 | − | 0.00551073i | ||||
\(736\) | −1.30513e6 | − | 2.26055e6i | −0.0888094 | − | 0.153822i | ||||
\(737\) | −7.10777e6 | − | 1.23110e7i | −0.482020 | − | 0.834882i | ||||
\(738\) | 4.04047e6 | + | 2.33276e6i | 0.273080 | + | 0.157663i | ||||
\(739\) | −4.97233e6 | −0.334926 | −0.167463 | − | 0.985878i | \(-0.553557\pi\) | ||||
−0.167463 | + | 0.985878i | \(0.553557\pi\) | |||||||
\(740\) | −8.18841e6 | + | 203667.i | −0.549693 | + | 0.0136723i | ||||
\(741\) | −122906. | −0.00822298 | ||||||||
\(742\) | −1.02217e7 | − | 5.90150e6i | −0.681574 | − | 0.393507i | ||||
\(743\) | 6.97650e6 | + | 1.20837e7i | 0.463624 | + | 0.803020i | 0.999138 | − | 0.0415063i | \(-0.0132157\pi\) |
−0.535515 | + | 0.844526i | \(0.679882\pi\) | |||||||
\(744\) | −67961.7 | − | 117713.i | −0.00450124 | − | 0.00779637i | ||||
\(745\) | −1.67798e7 | + | 9.68781e6i | −1.10763 | + | 0.639492i | ||||
\(746\) | − | 1.87637e7i | − | 1.23444i | ||||||
\(747\) | 1.18207e7 | + | 2.04741e7i | 0.775072 | + | 1.34246i | ||||
\(748\) | − | 3.85645e6i | − | 0.252019i | ||||||
\(749\) | 2.36207e6 | − | 4.09122e6i | 0.153847 | − | 0.266470i | ||||
\(750\) | −189731. | −0.0123165 | ||||||||
\(751\) | 1.51158e7 | 0.977985 | 0.488993 | − | 0.872288i | \(-0.337364\pi\) | ||||
0.488993 | + | 0.872288i | \(0.337364\pi\) | |||||||
\(752\) | −3.78883e6 | + | 6.56245e6i | −0.244321 | + | 0.423176i | ||||
\(753\) | 155512. | − | 89784.6i | 0.00999483 | − | 0.00577051i | ||||
\(754\) | − | 1.32861e7i | − | 0.851076i | ||||||
\(755\) | −9.63770e6 | − | 5.56433e6i | −0.615327 | − | 0.355259i | ||||
\(756\) | 111255. | − | 192699.i | 0.00707968 | − | 0.0122624i | ||||
\(757\) | −1.88570e7 | − | 1.08871e7i | −1.19601 | − | 0.690515i | −0.236344 | − | 0.971669i | \(-0.575949\pi\) |
−0.959662 | + | 0.281155i | \(0.909283\pi\) | |||||||
\(758\) | 2.40533e6 | − | 1.38872e6i | 0.152055 | − | 0.0877892i | ||||
\(759\) | −457176. | + | 263951.i | −0.0288057 | + | 0.0166310i | ||||
\(760\) | 1.41163e6 | + | 815007.i | 0.0886519 | + | 0.0511832i | ||||
\(761\) | 1.12965e7 | − | 1.95660e7i | 0.707100 | − | 1.22473i | −0.258829 | − | 0.965923i | \(-0.583337\pi\) |
0.965928 | − | 0.258809i | \(-0.0833301\pi\) | |||||||
\(762\) | 48069.1 | + | 27752.7i | 0.00299902 | + | 0.00173148i | ||||
\(763\) | − | 8.93755e6i | − | 0.555785i | ||||||
\(764\) | −4.74175e6 | + | 2.73765e6i | −0.293904 | + | 0.169686i | ||||
\(765\) | −2.71376e6 | + | 4.70037e6i | −0.167656 | + | 0.290388i | ||||
\(766\) | 6.88126e6 | 0.423737 | ||||||||
\(767\) | 2.04783e7 | 1.25691 | ||||||||
\(768\) | −10233.2 | + | 17724.4i | −0.000626049 | + | 0.00108435i | ||||
\(769\) | 1.16795e7i | 0.712211i | 0.934446 | + | 0.356105i | \(0.115896\pi\) | ||||
−0.934446 | + | 0.356105i | \(0.884104\pi\) | |||||||
\(770\) | 7.47247e6 | + | 1.29427e7i | 0.454190 | + | 0.786680i | ||||
\(771\) | − | 98350.8i | − | 0.00595857i | ||||||
\(772\) | −5.90501e6 | + | 3.40926e6i | −0.356597 | + | 0.205881i | ||||
\(773\) | −5.49427e6 | − | 9.51635e6i | −0.330720 | − | 0.572825i | 0.651933 | − | 0.758277i | \(-0.273958\pi\) |
−0.982653 | + | 0.185452i | \(0.940625\pi\) | |||||||
\(774\) | 2.60359e6 | + | 4.50955e6i | 0.156214 | + | 0.270571i | ||||
\(775\) | −3.85395e6 | − | 2.22508e6i | −0.230490 | − | 0.133073i | ||||
\(776\) | −2.33401e6 | −0.139139 | ||||||||
\(777\) | −5926.12 | − | 238259.i | −0.000352142 | − | 0.0141578i | ||||
\(778\) | 1.75051e7 | 1.03685 | ||||||||
\(779\) | −1.72282e6 | − | 994673.i | −0.101718 | − | 0.0587269i | ||||
\(780\) | −145906. | − | 252716.i | −0.00858690 | − | 0.0148729i | ||||
\(781\) | −1.70380e7 | − | 2.95107e7i | −0.999520 | − | 1.73122i | ||||
\(782\) | −3.20948e6 | + | 1.85299e6i | −0.187680 | + | 0.108357i | ||||
\(783\) | − | 530562.i | − | 0.0309266i | ||||||
\(784\) | 1.07621e6 | + | 1.86405e6i | 0.0625325 | + | 0.108310i | ||||
\(785\) | 3.65426e7i | 2.11653i | ||||||||
\(786\) | 33215.9 | − | 57531.6i | 0.00191774 | − | 0.00332162i | ||||
\(787\) | 3.83836e6 | 0.220906 | 0.110453 | − | 0.993881i | \(-0.464770\pi\) | ||||
0.110453 | + | 0.993881i | \(0.464770\pi\) | |||||||
\(788\) | 6.30824e6 | 0.361903 | ||||||||
\(789\) | 263866. | − | 457029.i | 0.0150901 | − | 0.0261367i | ||||
\(790\) | 1.16214e7 | − | 6.70964e6i | 0.662510 | − | 0.382500i | ||||
\(791\) | − | 1.27414e7i | − | 0.724061i | ||||||
\(792\) | −8.92791e6 | − | 5.15453e6i | −0.505751 | − | 0.291996i | ||||
\(793\) | −3.12168e6 | + | 5.40691e6i | −0.176281 | + | 0.305328i | ||||
\(794\) | 1.10449e7 | + | 6.37677e6i | 0.621742 | + | 0.358963i | ||||
\(795\) | −535325. | + | 309070.i | −0.0300400 | + | 0.0173436i | ||||
\(796\) | 7.31212e6 | − | 4.22166e6i | 0.409035 | − | 0.236157i | ||||
\(797\) | 9.10462e6 | + | 5.25655e6i | 0.507710 | + | 0.293127i | 0.731892 | − | 0.681421i | \(-0.238638\pi\) |
−0.224182 | + | 0.974547i | \(0.571971\pi\) | |||||||
\(798\) | −23714.3 | + | 41074.4i | −0.00131827 | + | 0.00228330i | ||||
\(799\) | 9.31721e6 | + | 5.37930e6i | 0.516320 | + | 0.298098i | ||||
\(800\) | 670074.i | 0.0370167i | ||||||||
\(801\) | −2.35333e7 | + | 1.35870e7i | −1.29599 | + | 0.748241i | ||||
\(802\) | −1.15627e7 | + | 2.00272e7i | −0.634781 | + | 1.09947i | ||||
\(803\) | −3.73378e7 | −2.04343 | ||||||||
\(804\) | 107112. | 0.00584383 | ||||||||
\(805\) | 7.18092e6 | − | 1.24377e7i | 0.390562 | − | 0.676474i | ||||
\(806\) | 2.58419e7i | 1.40116i | ||||||||
\(807\) | −31063.0 | − | 53802.7i | −0.00167903 | − | 0.00290817i | ||||
\(808\) | 1.86451e6i | 0.100470i | ||||||||
\(809\) | −1.92339e7 | + | 1.11047e7i | −1.03323 | + | 0.596533i | −0.917907 | − | 0.396796i | \(-0.870122\pi\) |
−0.115318 | + | 0.993329i | \(0.536789\pi\) | |||||||
\(810\) | 7.25152e6 | + | 1.25600e7i | 0.388344 | + | 0.672631i | ||||
\(811\) | −972286. | − | 1.68405e6i | −0.0519089 | − | 0.0899088i | 0.838903 | − | 0.544280i | \(-0.183197\pi\) |
−0.890812 | + | 0.454371i | \(0.849864\pi\) | |||||||
\(812\) | −4.44010e6 | − | 2.56349e6i | −0.236321 | − | 0.136440i | ||||
\(813\) | 56211.3 | 0.00298261 | ||||||||
\(814\) | −2.20819e7 | + | 549236.i | −1.16809 | + | 0.0290535i | ||||
\(815\) | −2.61516e7 | −1.37913 | ||||||||
\(816\) | 25164.7 | + | 14528.9i | 0.00132302 | + | 0.000763847i | ||||
\(817\) | −1.11015e6 | − | 1.92284e6i | −0.0581871 | − | 0.100783i | ||||
\(818\) | −1.88413e6 | − | 3.26342e6i | −0.0984529 | − | 0.170525i | ||||
\(819\) | −1.83143e7 | + | 1.05738e7i | −0.954072 | + | 0.550834i | ||||
\(820\) | − | 4.72322e6i | − | 0.245304i | ||||||
\(821\) | −3.55996e6 | − | 6.16603e6i | −0.184326 | − | 0.319263i | 0.759023 | − | 0.651064i | \(-0.225677\pi\) |
−0.943349 | + | 0.331801i | \(0.892344\pi\) | |||||||
\(822\) | 540755.i | 0.0279139i | ||||||||
\(823\) | 1.21003e7 | − | 2.09583e7i | 0.622726 | − | 1.07859i | −0.366250 | − | 0.930516i | \(-0.619359\pi\) |
0.988976 | − | 0.148076i | \(-0.0473080\pi\) | |||||||
\(824\) | −5.65627e6 | −0.290210 | ||||||||
\(825\) | 135516. | 0.00693198 | ||||||||
\(826\) | 3.95121e6 | − | 6.84369e6i | 0.201502 | − | 0.349012i | ||||
\(827\) | −1.73790e7 | + | 1.00338e7i | −0.883612 | + | 0.510154i | −0.871848 | − | 0.489777i | \(-0.837078\pi\) |
−0.0117647 | + | 0.999931i | \(0.503745\pi\) | |||||||
\(828\) | 9.90685e6i | 0.502180i | ||||||||
\(829\) | 1.79827e7 | + | 1.03823e7i | 0.908799 | + | 0.524695i | 0.880045 | − | 0.474891i | \(-0.157513\pi\) |
0.0287544 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(830\) | 1.19669e7 | − | 2.07273e7i | 0.602957 | − | 1.04435i | ||||
\(831\) | 325043. | + | 187664.i | 0.0163282 | + | 0.00942708i | ||||
\(832\) | 3.36978e6 | − | 1.94555e6i | 0.168769 | − | 0.0974391i | ||||
\(833\) | 2.64653e6 | − | 1.52798e6i | 0.132149 | − | 0.0762964i | ||||
\(834\) | −98968.3 | − | 57139.4i | −0.00492698 | − | 0.00284459i | ||||
\(835\) | 1.89404e7 | − | 3.28057e7i | 0.940098 | − | 1.62830i | ||||
\(836\) | 3.80680e6 | + | 2.19785e6i | 0.188384 | + | 0.108764i | ||||
\(837\) | 1.03196e6i | 0.0509155i | ||||||||
\(838\) | −3.93971e6 | + | 2.27459e6i | −0.193800 | + | 0.111890i | ||||
\(839\) | 1.13624e7 | − | 1.96803e7i | 0.557271 | − | 0.965223i | −0.440451 | − | 0.897776i | \(-0.645182\pi\) |
0.997723 | − | 0.0674461i | \(-0.0214851\pi\) | |||||||
\(840\) | −112608. | −0.00550643 | ||||||||
\(841\) | 8.28611e6 | 0.403981 | ||||||||
\(842\) | −2.68842e6 | + | 4.65649e6i | −0.130683 | + | 0.226349i | ||||
\(843\) | − | 316577.i | − | 0.0153430i | ||||||
\(844\) | 293362. | + | 508118.i | 0.0141758 | + | 0.0245532i | ||||
\(845\) | 3.26537e7i | 1.57322i | ||||||||
\(846\) | 2.49068e7 | − | 1.43799e7i | 1.19644 | − | 0.690767i | ||||
\(847\) | 1.27713e7 | + | 2.21206e7i | 0.611685 | + | 1.05947i | ||||
\(848\) | −4.12121e6 | − | 7.13815e6i | −0.196805 | − | 0.340876i | ||||
\(849\) | −241792. | − | 139599.i | −0.0115126 | − | 0.00664679i | ||||
\(850\) | 951356. | 0.0451644 | ||||||||
\(851\) | 1.10673e7 | + | 1.81135e7i | 0.523863 | + | 0.857390i | ||||
\(852\) | 256758. | 0.0121178 | ||||||||
\(853\) | 1.74029e7 | + | 1.00476e7i | 0.818933 | + | 0.472811i | 0.850048 | − | 0.526704i | \(-0.176573\pi\) |
−0.0311152 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(854\) | 1.20463e6 | + | 2.08648e6i | 0.0565209 | + | 0.0978971i | ||||
\(855\) | −3.09324e6 | − | 5.35764e6i | −0.144710 | − | 0.250645i | ||||
\(856\) | 2.85704e6 | − | 1.64951e6i | 0.133270 | − | 0.0769433i | ||||
\(857\) | − | 2.00912e7i | − | 0.934447i | −0.884139 | − | 0.467223i | \(-0.845254\pi\) | ||
0.884139 | − | 0.467223i | \(-0.154746\pi\) | |||||||
\(858\) | −393469. | − | 681508.i | −0.0182470 | − | 0.0316048i | ||||
\(859\) | 6.88478e6i | 0.318352i | 0.987250 | + | 0.159176i | \(0.0508837\pi\) | ||||
−0.987250 | + | 0.159176i | \(0.949116\pi\) | |||||||
\(860\) | 2.63579e6 | − | 4.56532e6i | 0.121525 | − | 0.210487i | ||||
\(861\) | 137432. | 0.00631800 | ||||||||
\(862\) | 1.87057e7 | 0.857443 | ||||||||
\(863\) | 1.79864e6 | − | 3.11534e6i | 0.0822088 | − | 0.142390i | −0.821990 | − | 0.569502i | \(-0.807136\pi\) |
0.904198 | + | 0.427113i | \(0.140469\pi\) | |||||||
\(864\) | 134568. | − | 77692.8i | 0.00613278 | − | 0.00354076i | ||||
\(865\) | − | 2.07410e7i | − | 0.942517i | ||||||
\(866\) | 3.44744e6 | + | 1.99038e6i | 0.156207 | + | 0.0901864i | ||||
\(867\) | −201078. | + | 348277.i | −0.00908482 | + | 0.0157354i | ||||
\(868\) | 8.63615e6 | + | 4.98609e6i | 0.389064 | + | 0.224626i | ||||
\(869\) | 3.13399e7 | − | 1.80941e7i | 1.40782 | − | 0.812807i | ||||
\(870\) | −232534. | + | 134254.i | −0.0104157 | + | 0.00601352i | ||||
\(871\) | −1.76359e7 | − | 1.01821e7i | −0.787685 | − | 0.454770i | ||||
\(872\) | 3.12070e6 | − | 5.40520e6i | 0.138983 | − | 0.240725i | ||||
\(873\) | 7.67158e6 | + | 4.42919e6i | 0.340682 | + | 0.196693i | ||||
\(874\) | − | 4.22421e6i | − | 0.187054i | ||||||
\(875\) | 1.20549e7 | − | 6.95992e6i | 0.532286 | − | 0.307315i | ||||
\(876\) | 140667. | − | 243643.i | 0.00619345 | − | 0.0107274i | ||||
\(877\) | −2.25697e7 | −0.990892 | −0.495446 | − | 0.868639i | \(-0.664995\pi\) | ||||
−0.495446 | + | 0.868639i | \(0.664995\pi\) | |||||||
\(878\) | −1.34276e7 | −0.587845 | ||||||||
\(879\) | 35472.8 | − | 61440.6i | 0.00154854 | − | 0.00268215i | ||||
\(880\) | 1.04366e7i | 0.454308i | ||||||||
\(881\) | −1.12402e6 | − | 1.94687e6i | −0.0487906 | − | 0.0845078i | 0.840599 | − | 0.541658i | \(-0.182203\pi\) |
−0.889389 | + | 0.457151i | \(0.848870\pi\) | |||||||
\(882\) | − | 8.16917e6i | − | 0.353595i | ||||||
\(883\) | −1.77794e7 | + | 1.02650e7i | −0.767391 | + | 0.443053i | −0.831943 | − | 0.554861i | \(-0.812771\pi\) |
0.0645523 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(884\) | −2.76224e6 | − | 4.78434e6i | −0.118886 | − | 0.205917i | ||||
\(885\) | −206930. | − | 358414.i | −0.00888108 | − | 0.0153825i | ||||
\(886\) | −4.15614e6 | − | 2.39955e6i | −0.177871 | − | 0.102694i | ||||
\(887\) | 5.20065e6 | 0.221946 | 0.110973 | − | 0.993823i | \(-0.464603\pi\) | ||||
0.110973 | + | 0.993823i | \(0.464603\pi\) | |||||||
\(888\) | 79608.1 | − | 146162.i | 0.00338785 | − | 0.00622017i | ||||
\(889\) | −4.07222e6 | −0.172813 | ||||||||
\(890\) | 2.38244e7 | + | 1.37550e7i | 1.00820 | + | 0.582084i | ||||
\(891\) | 1.95554e7 | + | 3.38710e7i | 0.825225 | + | 1.42933i | ||||
\(892\) | 1.71670e6 | + | 2.97342e6i | 0.0722410 | + | 0.125125i | ||||
\(893\) | −1.06201e7 | + | 6.13150e6i | −0.445655 | + | 0.257299i | ||||
\(894\) | − | 393702.i | − | 0.0164749i | ||||||
\(895\) | −1.53323e7 | − | 2.65563e7i | −0.639807 | − | 1.10818i | ||||
\(896\) | − | 1.50154e6i | − | 0.0624837i | ||||||
\(897\) | −378117. | + | 654919.i | −0.0156908 | + | 0.0271773i | ||||
\(898\) | 1.88692e7 | 0.780840 | ||||||||
\(899\) | 2.37781e7 | 0.981248 | ||||||||
\(900\) | 1.27158e6 | − | 2.20245e6i | 0.0523285 | − | 0.0906357i | ||||
\(901\) | −1.01346e7 | + | 5.85120e6i | −0.415905 | + | 0.240123i | ||||
\(902\) | − | 1.27373e7i | − | 0.521267i | ||||||
\(903\) | 132837. | + | 76693.6i | 0.00542126 | + | 0.00312997i | ||||
\(904\) | 4.44887e6 | − | 7.70566e6i | 0.181062 | − | 0.313609i | ||||
\(905\) | 1.88374e7 | + | 1.08758e7i | 0.764538 | + | 0.441406i | ||||
\(906\) | 195833. | − | 113064.i | 0.00792620 | − | 0.00457619i | ||||
\(907\) | 1.68636e7 | − | 9.73621e6i | 0.680663 | − | 0.392981i | −0.119442 | − | 0.992841i | \(-0.538110\pi\) |
0.800105 | + | 0.599860i | \(0.204777\pi\) | |||||||
\(908\) | 2.12783e6 | + | 1.22850e6i | 0.0856490 | + | 0.0494495i | ||||
\(909\) | 3.53824e6 | − | 6.12841e6i | 0.142029 | − | 0.246002i | ||||
\(910\) | 1.85408e7 | + | 1.07045e7i | 0.742207 | + | 0.428514i | ||||
\(911\) | − | 4.46839e6i | − | 0.178384i | −0.996014 | − | 0.0891918i | \(-0.971572\pi\) | ||
0.996014 | − | 0.0891918i | \(-0.0284284\pi\) | |||||||
\(912\) | −28683.6 | + | 16560.5i | −0.00114195 | + | 0.000659305i | ||||
\(913\) | 3.22715e7 | − | 5.58959e7i | 1.28127 | − | 2.21923i | ||||
\(914\) | −6.08904e6 | −0.241092 | ||||||||
\(915\) | 126176. | 0.00498225 | ||||||||
\(916\) | 5.76202e6 | − | 9.98012e6i | 0.226901 | − | 0.393004i | ||||
\(917\) | 4.87383e6i | 0.191402i | ||||||||
\(918\) | −110306. | − | 191056.i | −0.00432010 | − | 0.00748264i | ||||
\(919\) | 4.25835e7i | 1.66323i | 0.555352 | + | 0.831615i | \(0.312583\pi\) | ||||
−0.555352 | + | 0.831615i | \(0.687417\pi\) | |||||||
\(920\) | 8.68568e6 | − | 5.01468e6i | 0.338325 | − | 0.195332i | ||||
\(921\) | −352692. | − | 610880.i | −0.0137008 | − | 0.0237305i | ||||
\(922\) | 1.66180e7 | + | 2.87832e7i | 0.643800 | + | 1.11509i | ||||
\(923\) | −4.22750e7 | − | 2.44075e7i | −1.63335 | − | 0.943015i | ||||
\(924\) | −303673. | −0.0117011 | ||||||||
\(925\) | −135492. | − | 5.44745e6i | −0.00520668 | − | 0.209333i | ||||
\(926\) | 4.64742e6 | 0.178108 | ||||||||
\(927\) | 1.85914e7 | + | 1.07338e7i | 0.710581 | + | 0.410254i | ||||
\(928\) | −1.79017e6 | − | 3.10067e6i | −0.0682378 | − | 0.118191i | ||||
\(929\) | −1.33842e7 | − | 2.31820e7i | −0.508806 | − | 0.881277i | −0.999948 | − | 0.0101979i | \(-0.996754\pi\) |
0.491142 | − | 0.871079i | \(-0.336579\pi\) | |||||||
\(930\) | 452288. | − | 261128.i | 0.0171478 | − | 0.00990026i | ||||
\(931\) | 3.48328e6i | 0.131708i | ||||||||
\(932\) | −2.62137e6 | − | 4.54034e6i | −0.0988526 | − | 0.171218i | ||||
\(933\) | 1.04464e6i | 0.0392884i | ||||||||
\(934\) | 1.36751e6 | − | 2.36859e6i | 0.0512935 | − | 0.0888429i | ||||
\(935\) | 1.48176e7 | 0.554304 | ||||||||
\(936\) | −1.47681e7 | −0.550977 | ||||||||
\(937\) | 1.51031e7 | − | 2.61593e7i | 0.561975 | − | 0.973369i | −0.435349 | − | 0.900262i | \(-0.643375\pi\) |
0.997324 | − | 0.0731077i | \(-0.0232917\pi\) | |||||||
\(938\) | −6.80556e6 | + | 3.92919e6i | −0.252555 | + | 0.145813i | ||||
\(939\) | 523645.i | 0.0193809i | ||||||||
\(940\) | −2.52148e7 | − | 1.45578e7i | −0.930756 | − | 0.537372i | ||||
\(941\) | 1.58961e7 | − | 2.75329e7i | 0.585217 | − | 1.01363i | −0.409631 | − | 0.912251i | \(-0.634343\pi\) |
0.994848 | − | 0.101375i | \(-0.0323242\pi\) | |||||||
\(942\) | −643046. | − | 371263.i | −0.0236110 | − | 0.0136318i | ||||
\(943\) | −1.06004e7 | + | 6.12015e6i | −0.388190 | + | 0.224121i | ||||
\(944\) | 4.77918e6 | − | 2.75926e6i | 0.174551 | − | 0.100777i | ||||
\(945\) | 740403. | + | 427472.i | 0.0269705 | + | 0.0155714i | ||||
\(946\) | 7.10801e6 | − | 1.23114e7i | 0.258238 | − | 0.447281i | ||||
\(947\) | 3.36731e6 | + | 1.94411e6i | 0.122013 | + | 0.0704445i | 0.559765 | − | 0.828652i | \(-0.310892\pi\) |
−0.437751 | + | 0.899096i | \(0.644225\pi\) | |||||||
\(948\) | 272672.i | 0.00985418i | ||||||||
\(949\) | −4.63216e7 | + | 2.67438e7i | −1.66962 | + | 0.963956i | ||||
\(950\) | −542194. | + | 939107.i | −0.0194915 | + | 0.0337603i | ||||
\(951\) | 243278. | 0.00872272 | ||||||||
\(952\) | −2.13185e6 | −0.0762368 | ||||||||
\(953\) | −1.36555e7 | + | 2.36520e7i | −0.487052 | + | 0.843598i | −0.999889 | − | 0.0148876i | \(-0.995261\pi\) |
0.512838 | + | 0.858486i | \(0.328594\pi\) | |||||||
\(954\) | 3.12829e7i | 1.11285i | ||||||||
\(955\) | −1.05188e7 | − | 1.82192e7i | −0.373216 | − | 0.646428i | ||||
\(956\) | 1.75319e7i | 0.620420i | ||||||||
\(957\) | −627083. | + | 362046.i | −0.0221332 | + | 0.0127786i | ||||
\(958\) | −3.52220e6 | − | 6.10063e6i | −0.123994 | − | 0.214764i | ||||
\(959\) | −1.98365e7 | − | 3.43579e7i | −0.696497 | − | 1.20637i | ||||
\(960\) | −68102.3 | − | 39318.9i | −0.00238498 | − | 0.00137697i | ||||
\(961\) | −1.76202e7 | −0.615463 | ||||||||
\(962\) | −2.70016e7 | + | 1.64979e7i | −0.940703 | + | 0.574767i | ||||
\(963\) | −1.25210e7 | −0.435083 | ||||||||
\(964\) | 60512.5 | + | 34936.9i | 0.00209726 | + | 0.00121085i | ||||
\(965\) | −1.30993e7 | − | 2.26887e7i | −0.452826 | − | 0.784317i | ||||
\(966\) | 145912. | + | 252728.i | 0.00503094 | + | 0.00871385i | ||||
\(967\) | −3.78068e7 | + | 2.18278e7i | −1.30018 | + | 0.750660i | −0.980435 | − | 0.196843i | \(-0.936931\pi\) |
−0.319747 | + | 0.947503i | \(0.603598\pi\) | |||||||
\(968\) | 1.78373e7i | 0.611845i | ||||||||
\(969\) | 23512.2 | + | 40724.3i | 0.000804422 | + | 0.00139330i | ||||
\(970\) | − | 8.96793e6i | − | 0.306029i | ||||||
\(971\) | −2.71134e7 | + | 4.69618e7i | −0.922861 | + | 1.59844i | −0.127895 | + | 0.991788i | \(0.540822\pi\) |
−0.794966 | + | 0.606654i | \(0.792511\pi\) | |||||||
\(972\) | −884674. | −0.0300343 | ||||||||
\(973\) | 8.38418e6 | 0.283909 | ||||||||
\(974\) | 1.36928e6 | − | 2.37166e6i | 0.0462482 | − | 0.0801042i | ||||
\(975\) | 168123. | − | 97065.8i | 0.00566390 | − | 0.00327005i | ||||
\(976\) | 1.68247e6i | 0.0565356i | ||||||||
\(977\) | −1.38931e7 | − | 8.02119e6i | −0.465654 | − | 0.268845i | 0.248765 | − | 0.968564i | \(-0.419975\pi\) |
−0.714419 | + | 0.699719i | \(0.753309\pi\) | |||||||
\(978\) | 265693. | − | 460194.i | 0.00888245 | − | 0.0153849i | ||||
\(979\) | 6.42479e7 | + | 3.70936e7i | 2.14241 | + | 1.23692i | ||||
\(980\) | −7.16220e6 | + | 4.13510e6i | −0.238222 | + | 0.137537i | ||||
\(981\) | −2.05146e7 | + | 1.18441e7i | −0.680599 | + | 0.392944i | ||||
\(982\) | 5.53214e6 | + | 3.19398e6i | 0.183069 | + | 0.105695i | ||||
\(983\) | 2.24868e7 | − | 3.89482e7i | 0.742238 | − | 1.28559i | −0.209236 | − | 0.977865i | \(-0.567098\pi\) |
0.951474 | − | 0.307728i | \(-0.0995688\pi\) | |||||||
\(984\) | 83115.4 | + | 47986.7i | 0.00273649 | + | 0.00157991i | ||||
\(985\) | 2.42381e7i | 0.795989i | ||||||||
\(986\) | −4.40226e6 | + | 2.54165e6i | −0.144206 | + | 0.0832574i | ||||
\(987\) | 423588. | − | 733677.i | 0.0138405 | − | 0.0239724i | ||||
\(988\) | 6.29699e6 | 0.205230 | ||||||||
\(989\) | −1.36614e7 | −0.444123 | ||||||||
\(990\) | 1.98052e7 | − | 3.43036e7i | 0.642231 | − | 1.11238i | ||||
\(991\) | 1.63032e7i | 0.527337i | 0.964613 | + | 0.263669i | \(0.0849325\pi\) | ||||
−0.964613 | + | 0.263669i | \(0.915067\pi\) | |||||||
\(992\) | 3.48195e6 | + | 6.03092e6i | 0.112342 | + | 0.194583i | ||||
\(993\) | − | 625421.i | − | 0.0201279i | ||||||
\(994\) | −1.63136e7 | + | 9.41865e6i | −0.523701 | + | 0.302359i | ||||
\(995\) | 1.62208e7 | + | 2.80953e7i | 0.519415 | + | 0.899654i | ||||
\(996\) | 243161. | + | 421167.i | 0.00776685 | + | 0.0134526i | ||||
\(997\) | 4.18673e7 | + | 2.41721e7i | 1.33394 | + | 0.770151i | 0.985901 | − | 0.167328i | \(-0.0535140\pi\) |
0.348040 | + | 0.937480i | \(0.386847\pi\) | |||||||
\(998\) | −3.07250e7 | −0.976484 | ||||||||
\(999\) | −1.07828e6 | + | 658823.i | −0.0341835 | + | 0.0208860i |
(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 | 74.6.e.a.27.12 | yes | 28 | |
37.11 | even | 6 | inner | 74.6.e.a.11.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.6.e.a.11.12 | ✓ | 28 | 37.11 | even | 6 | inner | |
74.6.e.a.27.12 | yes | 28 | 1.1 | even | 1 | trivial |