Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,5,Mod(2,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.f (of order \(12\), degree \(4\), 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: | \(1.34380952009\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + 100636992 x^{2} + 3779136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(-4.89748i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.2 |
Dual form | 13.5.f.a.7.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.34141 | − | 1.69918i | −1.58535 | − | 0.424794i | −0.644775 | − | 0.764372i | \(-0.723049\pi\) |
−0.940578 | + | 0.339578i | \(0.889716\pi\) | |||||||
\(3\) | 7.28678 | + | 12.6211i | 0.809643 | + | 1.40234i | 0.913112 | + | 0.407710i | \(0.133672\pi\) |
−0.103469 | + | 0.994633i | \(0.532994\pi\) | |||||||
\(4\) | 23.4699 | + | 13.5504i | 1.46687 | + | 0.846897i | ||||
\(5\) | −20.2793 | + | 20.2793i | −0.811174 | + | 0.811174i | −0.984810 | − | 0.173636i | \(-0.944448\pi\) |
0.173636 | + | 0.984810i | \(0.444448\pi\) | |||||||
\(6\) | −24.7631 | − | 92.4170i | −0.687863 | − | 2.56714i | ||||
\(7\) | 21.3318 | − | 5.71584i | 0.435343 | − | 0.116650i | −0.0344902 | − | 0.999405i | \(-0.510981\pi\) |
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(8\) | −51.5321 | − | 51.5321i | −0.805189 | − | 0.805189i | ||||
\(9\) | −65.6944 | + | 113.786i | −0.811042 | + | 1.40477i | ||||
\(10\) | 163.058 | − | 94.1415i | 1.63058 | − | 0.941415i | ||||
\(11\) | 19.8619 | − | 74.1257i | 0.164148 | − | 0.612609i | −0.833999 | − | 0.551765i | \(-0.813954\pi\) |
0.998147 | − | 0.0608433i | \(-0.0193790\pi\) | |||||||
\(12\) | 394.954i | 2.74274i | ||||||||
\(13\) | 162.185 | − | 47.5081i | 0.959675 | − | 0.281113i | ||||
\(14\) | −144.986 | −0.739724 | ||||||||
\(15\) | −403.718 | − | 108.176i | −1.79430 | − | 0.480782i | ||||
\(16\) | 22.4185 | + | 38.8299i | 0.0875721 | + | 0.151679i | ||||
\(17\) | 119.941 | + | 69.2480i | 0.415021 | + | 0.239612i | 0.692945 | − | 0.720991i | \(-0.256313\pi\) |
−0.277924 | + | 0.960603i | \(0.589646\pi\) | |||||||
\(18\) | 609.938 | − | 609.938i | 1.88252 | − | 1.88252i | ||||
\(19\) | 57.8912 | + | 216.053i | 0.160364 | + | 0.598485i | 0.998586 | + | 0.0531568i | \(0.0169283\pi\) |
−0.838223 | + | 0.545328i | \(0.816405\pi\) | |||||||
\(20\) | −750.746 | + | 201.162i | −1.87687 | + | 0.502905i | ||||
\(21\) | 227.580 | + | 227.580i | 0.516055 | + | 0.516055i | ||||
\(22\) | −251.905 | + | 436.312i | −0.520465 | + | 0.901472i | ||||
\(23\) | 491.603 | − | 283.827i | 0.929307 | − | 0.536535i | 0.0427144 | − | 0.999087i | \(-0.486399\pi\) |
0.886592 | + | 0.462552i | \(0.153066\pi\) | |||||||
\(24\) | 274.887 | − | 1025.89i | 0.477235 | − | 1.78107i | ||||
\(25\) | − | 197.503i | − | 0.316005i | ||||||
\(26\) | −1109.21 | + | 25.6875i | −1.64084 | + | 0.0379993i | ||||
\(27\) | −734.346 | −1.00733 | ||||||||
\(28\) | 578.107 | + | 154.903i | 0.737381 | + | 0.197581i | ||||
\(29\) | −406.589 | − | 704.232i | −0.483458 | − | 0.837375i | 0.516361 | − | 0.856371i | \(-0.327286\pi\) |
−0.999820 | + | 0.0189964i | \(0.993953\pi\) | |||||||
\(30\) | 2376.33 | + | 1371.98i | 2.64037 | + | 1.52442i | ||||
\(31\) | −666.232 | + | 666.232i | −0.693270 | + | 0.693270i | −0.962950 | − | 0.269680i | \(-0.913082\pi\) |
0.269680 | + | 0.962950i | \(0.413082\pi\) | |||||||
\(32\) | 225.607 | + | 841.977i | 0.220319 | + | 0.822243i | ||||
\(33\) | 1080.28 | − | 289.459i | 0.991988 | − | 0.265802i | ||||
\(34\) | −642.931 | − | 642.931i | −0.556169 | − | 0.556169i | ||||
\(35\) | −316.681 | + | 548.508i | −0.258515 | + | 0.447762i | ||||
\(36\) | −3083.68 | + | 1780.37i | −2.37939 | + | 1.37374i | ||||
\(37\) | 429.906 | − | 1604.43i | 0.314029 | − | 1.17197i | −0.610861 | − | 0.791738i | \(-0.709177\pi\) |
0.924890 | − | 0.380235i | \(-0.124157\pi\) | |||||||
\(38\) | − | 1468.45i | − | 1.01693i | ||||||
\(39\) | 1781.41 | + | 1700.77i | 1.17121 | + | 1.11819i | ||||
\(40\) | 2090.07 | 1.30630 | ||||||||
\(41\) | 907.358 | + | 243.126i | 0.539773 | + | 0.144632i | 0.518397 | − | 0.855140i | \(-0.326529\pi\) |
0.0213753 | + | 0.999772i | \(0.493195\pi\) | |||||||
\(42\) | −1056.48 | − | 1829.88i | −0.598912 | − | 1.03735i | ||||
\(43\) | −2118.01 | − | 1222.83i | −1.14549 | − | 0.661349i | −0.197706 | − | 0.980261i | \(-0.563349\pi\) |
−0.947784 | + | 0.318912i | \(0.896683\pi\) | |||||||
\(44\) | 1470.59 | − | 1470.59i | 0.759600 | − | 0.759600i | ||||
\(45\) | −975.267 | − | 3639.75i | −0.481613 | − | 1.79741i | ||||
\(46\) | −3599.73 | + | 964.545i | −1.70120 | + | 0.455834i | ||||
\(47\) | 908.134 | + | 908.134i | 0.411106 | + | 0.411106i | 0.882124 | − | 0.471018i | \(-0.156113\pi\) |
−0.471018 | + | 0.882124i | \(0.656113\pi\) | |||||||
\(48\) | −326.717 | + | 565.890i | −0.141804 | + | 0.245612i | ||||
\(49\) | −1656.95 | + | 956.642i | −0.690109 | + | 0.398435i | ||||
\(50\) | −335.593 | + | 1252.45i | −0.134237 | + | 0.500980i | ||||
\(51\) | 2018.38i | 0.776002i | ||||||||
\(52\) | 4450.22 | + | 1082.65i | 1.64579 | + | 0.400390i | ||||
\(53\) | 2101.44 | 0.748110 | 0.374055 | − | 0.927407i | \(-0.377967\pi\) | ||||
0.374055 | + | 0.927407i | \(0.377967\pi\) | |||||||
\(54\) | 4656.79 | + | 1247.78i | 1.59698 | + | 0.427909i | ||||
\(55\) | 1100.43 | + | 1906.01i | 0.363780 | + | 0.630085i | ||||
\(56\) | −1393.82 | − | 804.723i | −0.444458 | − | 0.256608i | ||||
\(57\) | −2304.98 | + | 2304.98i | −0.709444 | + | 0.709444i | ||||
\(58\) | 1381.73 | + | 5156.69i | 0.410741 | + | 1.53290i | ||||
\(59\) | −3417.07 | + | 915.600i | −0.981634 | + | 0.263028i | −0.713733 | − | 0.700418i | \(-0.752997\pi\) |
−0.267901 | + | 0.963446i | \(0.586330\pi\) | |||||||
\(60\) | −8009.41 | − | 8009.41i | −2.22483 | − | 2.22483i | ||||
\(61\) | 2816.09 | − | 4877.60i | 0.756809 | − | 1.31083i | −0.187661 | − | 0.982234i | \(-0.560091\pi\) |
0.944470 | − | 0.328598i | \(-0.106576\pi\) | |||||||
\(62\) | 5356.90 | − | 3092.81i | 1.39357 | − | 0.804580i | ||||
\(63\) | −750.998 | + | 2802.76i | −0.189216 | + | 0.706163i | ||||
\(64\) | − | 6440.06i | − | 1.57228i | ||||||
\(65\) | −2325.57 | + | 4252.44i | −0.550431 | + | 1.00649i | ||||
\(66\) | −7342.31 | −1.68556 | ||||||||
\(67\) | −3279.23 | − | 878.668i | −0.730504 | − | 0.195738i | −0.125650 | − | 0.992075i | \(-0.540102\pi\) |
−0.604854 | + | 0.796337i | \(0.706768\pi\) | |||||||
\(68\) | 1876.67 | + | 3250.49i | 0.405854 | + | 0.702960i | ||||
\(69\) | 7164.41 | + | 4136.38i | 1.50481 | + | 0.868804i | ||||
\(70\) | 2940.22 | − | 2940.22i | 0.600045 | − | 0.600045i | ||||
\(71\) | −1904.53 | − | 7107.80i | −0.377808 | − | 1.41000i | −0.849198 | − | 0.528074i | \(-0.822914\pi\) |
0.471390 | − | 0.881925i | \(-0.343752\pi\) | |||||||
\(72\) | 9249.01 | − | 2478.26i | 1.78414 | − | 0.478060i | ||||
\(73\) | 4192.40 | + | 4192.40i | 0.786714 | + | 0.786714i | 0.980954 | − | 0.194240i | \(-0.0622240\pi\) |
−0.194240 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(74\) | −5452.42 | + | 9443.87i | −0.995694 | + | 1.72459i | ||||
\(75\) | 2492.71 | − | 1439.16i | 0.443148 | − | 0.255851i | ||||
\(76\) | −1568.89 | + | 5855.19i | −0.271623 | + | 1.01371i | ||||
\(77\) | − | 1694.76i | − | 0.285843i | ||||||
\(78\) | −8406.75 | − | 13812.2i | −1.38178 | − | 2.27025i | ||||
\(79\) | −3957.00 | −0.634033 | −0.317016 | − | 0.948420i | \(-0.602681\pi\) | ||||
−0.317016 | + | 0.948420i | \(0.602681\pi\) | |||||||
\(80\) | −1242.08 | − | 332.813i | −0.194074 | − | 0.0520021i | ||||
\(81\) | −29.7681 | − | 51.5598i | −0.00453713 | − | 0.00785853i | ||||
\(82\) | −5340.82 | − | 3083.52i | −0.794292 | − | 0.458584i | ||||
\(83\) | 1386.98 | − | 1386.98i | 0.201333 | − | 0.201333i | −0.599238 | − | 0.800571i | \(-0.704530\pi\) |
0.800571 | + | 0.599238i | \(0.204530\pi\) | |||||||
\(84\) | 2257.49 | + | 8425.08i | 0.319940 | + | 1.19403i | ||||
\(85\) | −3836.63 | + | 1028.02i | −0.531021 | + | 0.142287i | ||||
\(86\) | 11353.4 | + | 11353.4i | 1.53507 | + | 1.53507i | ||||
\(87\) | 5925.45 | − | 10263.2i | 0.782857 | − | 1.35595i | ||||
\(88\) | −4843.38 | + | 2796.32i | −0.625436 | + | 0.361096i | ||||
\(89\) | 2395.70 | − | 8940.86i | 0.302449 | − | 1.12875i | −0.632670 | − | 0.774421i | \(-0.718041\pi\) |
0.935119 | − | 0.354333i | \(-0.115292\pi\) | |||||||
\(90\) | 24738.3i | 3.05411i | ||||||||
\(91\) | 3188.15 | − | 1940.46i | 0.384996 | − | 0.234326i | ||||
\(92\) | 15383.8 | 1.81756 | ||||||||
\(93\) | −13263.3 | − | 3553.88i | −1.53350 | − | 0.410901i | ||||
\(94\) | −4215.77 | − | 7301.93i | −0.477113 | − | 0.826384i | ||||
\(95\) | −5555.41 | − | 3207.42i | −0.615558 | − | 0.355393i | ||||
\(96\) | −8982.71 | + | 8982.71i | −0.974686 | + | 0.974686i | ||||
\(97\) | 751.041 | + | 2802.92i | 0.0798215 | + | 0.297898i | 0.994283 | − | 0.106774i | \(-0.0340522\pi\) |
−0.914462 | + | 0.404672i | \(0.867386\pi\) | |||||||
\(98\) | 12132.9 | − | 3251.01i | 1.26332 | − | 0.338505i | ||||
\(99\) | 7129.65 | + | 7129.65i | 0.727441 | + | 0.727441i | ||||
\(100\) | 2676.24 | − | 4635.38i | 0.267624 | − | 0.463538i | ||||
\(101\) | 2484.93 | − | 1434.67i | 0.243596 | − | 0.140640i | −0.373232 | − | 0.927738i | \(-0.621751\pi\) |
0.616829 | + | 0.787098i | \(0.288417\pi\) | |||||||
\(102\) | 3429.58 | − | 12799.4i | 0.329641 | − | 1.23024i | ||||
\(103\) | 5465.63i | 0.515188i | 0.966253 | + | 0.257594i | \(0.0829298\pi\) | ||||
−0.966253 | + | 0.257594i | \(0.917070\pi\) | |||||||
\(104\) | −10805.9 | − | 5909.54i | −0.999068 | − | 0.546370i | ||||
\(105\) | −9230.36 | −0.837221 | ||||||||
\(106\) | −13326.1 | − | 3570.72i | −1.18602 | − | 0.317793i | ||||
\(107\) | −293.203 | − | 507.843i | −0.0256095 | − | 0.0443570i | 0.852937 | − | 0.522015i | \(-0.174819\pi\) |
−0.878546 | + | 0.477658i | \(0.841486\pi\) | |||||||
\(108\) | −17235.0 | − | 9950.64i | −1.47762 | − | 0.853107i | ||||
\(109\) | 5258.17 | − | 5258.17i | 0.442570 | − | 0.442570i | −0.450305 | − | 0.892875i | \(-0.648685\pi\) |
0.892875 | + | 0.450305i | \(0.148685\pi\) | |||||||
\(110\) | −3739.66 | − | 13956.6i | −0.309063 | − | 1.15344i | ||||
\(111\) | 23382.3 | − | 6265.26i | 1.89776 | − | 0.508503i | ||||
\(112\) | 700.172 | + | 700.172i | 0.0558173 | + | 0.0558173i | ||||
\(113\) | −10187.3 | + | 17645.0i | −0.797818 | + | 1.38186i | 0.123217 | + | 0.992380i | \(0.460679\pi\) |
−0.921034 | + | 0.389481i | \(0.872654\pi\) | |||||||
\(114\) | 18533.4 | − | 10700.3i | 1.42609 | − | 0.823351i | ||||
\(115\) | −4213.56 | + | 15725.2i | −0.318606 | + | 1.18905i | ||||
\(116\) | − | 22037.7i | − | 1.63776i | ||||||
\(117\) | −5248.89 | + | 21575.4i | −0.383439 | + | 1.57611i | ||||
\(118\) | 23224.8 | 1.66797 | ||||||||
\(119\) | 2954.37 | + | 791.621i | 0.208627 | + | 0.0559015i | ||||
\(120\) | 15229.9 | + | 26379.0i | 1.05763 | + | 1.83187i | ||||
\(121\) | 7579.36 | + | 4375.95i | 0.517681 | + | 0.298883i | ||||
\(122\) | −26145.9 | + | 26145.9i | −1.75664 | + | 1.75664i | ||||
\(123\) | 3543.21 | + | 13223.4i | 0.234200 | + | 0.874046i | ||||
\(124\) | −24664.1 | + | 6608.72i | −1.60406 | + | 0.429808i | ||||
\(125\) | −8669.35 | − | 8669.35i | −0.554838 | − | 0.554838i | ||||
\(126\) | 9524.77 | − | 16497.4i | 0.599948 | − | 1.03914i | ||||
\(127\) | −3968.07 | + | 2290.97i | −0.246021 | + | 0.142040i | −0.617941 | − | 0.786225i | \(-0.712033\pi\) |
0.371920 | + | 0.928265i | \(0.378700\pi\) | |||||||
\(128\) | −7333.08 | + | 27367.4i | −0.447576 | + | 1.67038i | ||||
\(129\) | − | 35642.1i | − | 2.14183i | ||||||
\(130\) | 21973.1 | − | 23014.9i | 1.30018 | − | 1.36183i | ||||
\(131\) | −28273.1 | −1.64752 | −0.823759 | − | 0.566940i | \(-0.808127\pi\) | ||||
−0.823759 | + | 0.566940i | \(0.808127\pi\) | |||||||
\(132\) | 29276.2 | + | 7844.54i | 1.68022 | + | 0.450215i | ||||
\(133\) | 2469.85 | + | 4277.90i | 0.139626 | + | 0.241840i | ||||
\(134\) | 19301.9 | + | 11144.0i | 1.07496 | + | 0.620627i | ||||
\(135\) | 14892.0 | − | 14892.0i | 0.817122 | − | 0.817122i | ||||
\(136\) | −2612.32 | − | 9749.30i | −0.141237 | − | 0.527103i | ||||
\(137\) | −7065.68 | + | 1893.24i | −0.376455 | + | 0.100871i | −0.442085 | − | 0.896973i | \(-0.645761\pi\) |
0.0656300 | + | 0.997844i | \(0.479094\pi\) | |||||||
\(138\) | −38404.1 | − | 38404.1i | −2.01660 | − | 2.01660i | ||||
\(139\) | 10399.9 | − | 18013.2i | 0.538269 | − | 0.932310i | −0.460728 | − | 0.887541i | \(-0.652412\pi\) |
0.998997 | − | 0.0447683i | \(-0.0142550\pi\) | |||||||
\(140\) | −14865.0 | + | 8582.29i | −0.758417 | + | 0.437872i | ||||
\(141\) | −4844.25 | + | 18079.0i | −0.243662 | + | 0.909361i | ||||
\(142\) | 48309.6i | 2.39584i | ||||||||
\(143\) | −300.265 | − | 12965.7i | −0.0146836 | − | 0.634049i | ||||
\(144\) | −5891.07 | −0.284099 | ||||||||
\(145\) | 22526.7 | + | 6036.01i | 1.07142 | + | 0.287087i | ||||
\(146\) | −19462.1 | − | 33709.4i | −0.913028 | − | 1.58141i | ||||
\(147\) | −24147.7 | − | 13941.7i | −1.11748 | − | 0.645179i | ||||
\(148\) | 31830.4 | − | 31830.4i | 1.45318 | − | 1.45318i | ||||
\(149\) | 56.0657 | + | 209.240i | 0.00252537 | + | 0.00942480i | 0.967177 | − | 0.254104i | \(-0.0817804\pi\) |
−0.964652 | + | 0.263528i | \(0.915114\pi\) | |||||||
\(150\) | −18252.7 | + | 4890.79i | −0.811230 | + | 0.217368i | ||||
\(151\) | 21275.9 | + | 21275.9i | 0.933114 | + | 0.933114i | 0.997899 | − | 0.0647854i | \(-0.0206363\pi\) |
−0.0647854 | + | 0.997899i | \(0.520636\pi\) | |||||||
\(152\) | 8150.41 | − | 14116.9i | 0.352770 | − | 0.611016i | ||||
\(153\) | −15758.9 | + | 9098.41i | −0.673199 | + | 0.388672i | ||||
\(154\) | −2879.70 | + | 10747.2i | −0.121424 | + | 0.453162i | ||||
\(155\) | − | 27021.5i | − | 1.12472i | ||||||
\(156\) | 18763.5 | + | 64055.6i | 0.771019 | + | 2.63213i | ||||
\(157\) | −15748.9 | −0.638926 | −0.319463 | − | 0.947599i | \(-0.603502\pi\) | ||||
−0.319463 | + | 0.947599i | \(0.603502\pi\) | |||||||
\(158\) | 25093.0 | + | 6723.64i | 1.00517 | + | 0.269333i | ||||
\(159\) | 15312.7 | + | 26522.5i | 0.605702 | + | 1.04911i | ||||
\(160\) | −21649.9 | − | 12499.6i | −0.845699 | − | 0.488265i | ||||
\(161\) | 8864.47 | − | 8864.47i | 0.341980 | − | 0.341980i | ||||
\(162\) | 101.162 | + | 377.543i | 0.00385469 | + | 0.0143859i | ||||
\(163\) | 2761.28 | − | 739.883i | 0.103929 | − | 0.0278476i | −0.206480 | − | 0.978451i | \(-0.566201\pi\) |
0.310409 | + | 0.950603i | \(0.399534\pi\) | |||||||
\(164\) | 18001.2 | + | 18001.2i | 0.669288 | + | 0.669288i | ||||
\(165\) | −16037.2 | + | 27777.3i | −0.589063 | + | 1.02029i | ||||
\(166\) | −11152.2 | + | 6438.70i | −0.404709 | + | 0.233659i | ||||
\(167\) | 6856.78 | − | 25589.9i | 0.245860 | − | 0.917561i | −0.727090 | − | 0.686543i | \(-0.759127\pi\) |
0.972949 | − | 0.231019i | \(-0.0742058\pi\) | |||||||
\(168\) | − | 23455.4i | − | 0.831044i | ||||||
\(169\) | 24047.0 | − | 15410.2i | 0.841951 | − | 0.539554i | ||||
\(170\) | 26076.4 | 0.902299 | ||||||||
\(171\) | −28387.0 | − | 7606.27i | −0.970793 | − | 0.260123i | ||||
\(172\) | −33139.7 | − | 57399.6i | −1.12019 | − | 1.94023i | ||||
\(173\) | 45826.6 | + | 26458.0i | 1.53118 | + | 0.884026i | 0.999308 | + | 0.0371990i | \(0.0118436\pi\) |
0.531869 | + | 0.846826i | \(0.321490\pi\) | |||||||
\(174\) | −55014.6 | + | 55014.6i | −1.81710 | + | 1.81710i | ||||
\(175\) | −1128.90 | − | 4213.10i | −0.0368620 | − | 0.137571i | ||||
\(176\) | 3323.57 | − | 890.547i | 0.107295 | − | 0.0287496i | ||||
\(177\) | −36455.3 | − | 36455.3i | −1.16363 | − | 1.16363i | ||||
\(178\) | −30384.2 | + | 52627.0i | −0.958976 | + | 1.66100i | ||||
\(179\) | −33039.9 | + | 19075.6i | −1.03118 | + | 0.595349i | −0.917321 | − | 0.398148i | \(-0.869653\pi\) |
−0.113854 | + | 0.993497i | \(0.536320\pi\) | |||||||
\(180\) | 26430.4 | − | 98639.7i | 0.815754 | − | 3.04444i | ||||
\(181\) | 23773.2i | 0.725656i | 0.931856 | + | 0.362828i | \(0.118189\pi\) | ||||
−0.931856 | + | 0.362828i | \(0.881811\pi\) | |||||||
\(182\) | −23514.6 | + | 6888.01i | −0.709895 | + | 0.207946i | ||||
\(183\) | 82080.9 | 2.45098 | ||||||||
\(184\) | −39959.6 | − | 10707.1i | −1.18028 | − | 0.316255i | ||||
\(185\) | 23818.6 | + | 41255.0i | 0.695941 | + | 1.20541i | ||||
\(186\) | 78069.1 | + | 45073.2i | 2.25659 | + | 1.30285i | ||||
\(187\) | 7515.31 | − | 7515.31i | 0.214913 | − | 0.214913i | ||||
\(188\) | 9008.27 | + | 33619.3i | 0.254874 | + | 0.951204i | ||||
\(189\) | −15664.9 | + | 4197.40i | −0.438535 | + | 0.117505i | ||||
\(190\) | 29779.2 | + | 29779.2i | 0.824908 | + | 0.824908i | ||||
\(191\) | 7556.32 | − | 13087.9i | 0.207130 | − | 0.358760i | −0.743679 | − | 0.668537i | \(-0.766921\pi\) |
0.950809 | + | 0.309777i | \(0.100254\pi\) | |||||||
\(192\) | 81280.5 | − | 46927.3i | 2.20487 | − | 1.27298i | ||||
\(193\) | 15078.6 | − | 56274.0i | 0.404805 | − | 1.51075i | −0.399610 | − | 0.916685i | \(-0.630855\pi\) |
0.804415 | − | 0.594067i | \(-0.202479\pi\) | |||||||
\(194\) | − | 19050.6i | − | 0.506181i | ||||||
\(195\) | −70616.3 | + | 1635.36i | −1.85710 | + | 0.0430076i | ||||
\(196\) | −51851.3 | −1.34973 | ||||||||
\(197\) | −24810.2 | − | 6647.88i | −0.639291 | − | 0.171297i | −0.0754087 | − | 0.997153i | \(-0.524026\pi\) |
−0.563882 | + | 0.825855i | \(0.690693\pi\) | |||||||
\(198\) | −33097.5 | − | 57326.6i | −0.844239 | − | 1.46226i | ||||
\(199\) | −57761.4 | − | 33348.6i | −1.45859 | − | 0.842115i | −0.459644 | − | 0.888103i | \(-0.652023\pi\) |
−0.998942 | + | 0.0459886i | \(0.985356\pi\) | |||||||
\(200\) | −10177.8 | + | 10177.8i | −0.254444 | + | 0.254444i | ||||
\(201\) | −12805.3 | − | 47790.1i | −0.316956 | − | 1.18289i | ||||
\(202\) | −18195.7 | + | 4875.52i | −0.445929 | + | 0.119486i | ||||
\(203\) | −12698.5 | − | 12698.5i | −0.308150 | − | 0.308150i | ||||
\(204\) | −27349.8 | + | 47371.2i | −0.657193 | + | 1.13829i | ||||
\(205\) | −23331.1 | + | 13470.2i | −0.555171 | + | 0.320528i | ||||
\(206\) | 9287.08 | − | 34659.8i | 0.218849 | − | 0.816756i | ||||
\(207\) | 74583.5i | 1.74061i | ||||||||
\(208\) | 5480.67 | + | 5232.57i | 0.126680 | + | 0.120945i | ||||
\(209\) | 17164.9 | 0.392960 | ||||||||
\(210\) | 58533.5 | + | 15684.0i | 1.32729 | + | 0.355646i | ||||
\(211\) | 14547.1 | + | 25196.3i | 0.326747 | + | 0.565942i | 0.981864 | − | 0.189585i | \(-0.0607142\pi\) |
−0.655117 | + | 0.755527i | \(0.727381\pi\) | |||||||
\(212\) | 49320.6 | + | 28475.3i | 1.09738 | + | 0.633572i | ||||
\(213\) | 75830.3 | − | 75830.3i | 1.67141 | − | 1.67141i | ||||
\(214\) | 996.408 | + | 3718.65i | 0.0217575 | + | 0.0812002i | ||||
\(215\) | 67750.2 | − | 18153.6i | 1.46566 | − | 0.392723i | ||||
\(216\) | 37842.4 | + | 37842.4i | 0.811093 | + | 0.811093i | ||||
\(217\) | −10403.9 | + | 18020.0i | −0.220940 | + | 0.382680i | ||||
\(218\) | −42278.8 | + | 24409.7i | −0.889631 | + | 0.513628i | ||||
\(219\) | −22363.5 | + | 83461.7i | −0.466285 | + | 1.74020i | ||||
\(220\) | 59645.0i | 1.23234i | ||||||||
\(221\) | 22742.5 | + | 5532.81i | 0.465643 | + | 0.113282i | ||||
\(222\) | −158922. | −3.22462 | ||||||||
\(223\) | −20898.8 | − | 5599.80i | −0.420253 | − | 0.112606i | 0.0424944 | − | 0.999097i | \(-0.486470\pi\) |
−0.462747 | + | 0.886490i | \(0.653136\pi\) | |||||||
\(224\) | 9625.21 | + | 16671.4i | 0.191829 | + | 0.332257i | ||||
\(225\) | 22473.1 | + | 12974.9i | 0.443914 | + | 0.256294i | ||||
\(226\) | 94584.0 | − | 94584.0i | 1.85183 | − | 1.85183i | ||||
\(227\) | 18887.8 | + | 70490.2i | 0.366547 | + | 1.36797i | 0.865312 | + | 0.501234i | \(0.167120\pi\) |
−0.498765 | + | 0.866737i | \(0.666213\pi\) | |||||||
\(228\) | −85331.0 | + | 22864.4i | −1.64149 | + | 0.439835i | ||||
\(229\) | 13183.8 | + | 13183.8i | 0.251403 | + | 0.251403i | 0.821546 | − | 0.570143i | \(-0.193112\pi\) |
−0.570143 | + | 0.821546i | \(0.693112\pi\) | |||||||
\(230\) | 53439.8 | − | 92560.5i | 1.01020 | − | 1.74973i | ||||
\(231\) | 21389.7 | − | 12349.4i | 0.400849 | − | 0.231430i | ||||
\(232\) | −15338.2 | + | 57242.9i | −0.284969 | + | 1.06352i | ||||
\(233\) | − | 2695.47i | − | 0.0496503i | −0.999692 | − | 0.0248251i | \(-0.992097\pi\) | ||
0.999692 | − | 0.0248251i | \(-0.00790290\pi\) | |||||||
\(234\) | 69945.8 | − | 127900.i | 1.27741 | − | 2.33581i | ||||
\(235\) | −36832.7 | −0.666957 | ||||||||
\(236\) | −92604.9 | − | 24813.4i | −1.66269 | − | 0.445515i | ||||
\(237\) | −28833.8 | − | 49941.6i | −0.513340 | − | 0.889131i | ||||
\(238\) | −17389.8 | − | 10040.0i | −0.307001 | − | 0.177247i | ||||
\(239\) | −60150.4 | + | 60150.4i | −1.05303 | + | 1.05303i | −0.0545214 | + | 0.998513i | \(0.517363\pi\) |
−0.998513 | + | 0.0545214i | \(0.982637\pi\) | |||||||
\(240\) | −4850.28 | − | 18101.5i | −0.0842062 | − | 0.314262i | ||||
\(241\) | −50325.8 | + | 13484.7i | −0.866475 | + | 0.232171i | −0.664563 | − | 0.747232i | \(-0.731382\pi\) |
−0.201912 | + | 0.979404i | \(0.564716\pi\) | |||||||
\(242\) | −40628.3 | − | 40628.3i | −0.693743 | − | 0.693743i | ||||
\(243\) | −29307.2 | + | 50761.5i | −0.496319 | + | 0.859651i | ||||
\(244\) | 132187. | − | 76317.9i | 2.22028 | − | 1.28188i | ||||
\(245\) | 14201.8 | − | 53002.0i | 0.236599 | − | 0.882998i | ||||
\(246\) | − | 89875.8i | − | 1.48516i | ||||||
\(247\) | 19653.4 | + | 32290.3i | 0.322139 | + | 0.529271i | ||||
\(248\) | 68664.7 | 1.11643 | ||||||||
\(249\) | 27611.9 | + | 7398.58i | 0.445346 | + | 0.119330i | ||||
\(250\) | 40245.2 | + | 69706.7i | 0.643923 | + | 1.11531i | ||||
\(251\) | −32906.3 | − | 18998.4i | −0.522313 | − | 0.301558i | 0.215567 | − | 0.976489i | \(-0.430840\pi\) |
−0.737881 | + | 0.674931i | \(0.764173\pi\) | |||||||
\(252\) | −55604.2 | + | 55604.2i | −0.875602 | + | 0.875602i | ||||
\(253\) | −11274.7 | − | 42077.8i | −0.176142 | − | 0.657373i | ||||
\(254\) | 29055.9 | − | 7785.51i | 0.450368 | − | 0.120676i | ||||
\(255\) | −40931.4 | − | 40931.4i | −0.629472 | − | 0.629472i | ||||
\(256\) | 41483.7 | − | 71851.9i | 0.632991 | − | 1.09637i | ||||
\(257\) | 3349.07 | − | 1933.59i | 0.0507058 | − | 0.0292750i | −0.474433 | − | 0.880292i | \(-0.657347\pi\) |
0.525139 | + | 0.851017i | \(0.324013\pi\) | |||||||
\(258\) | −60562.3 | + | 226021.i | −0.909835 | + | 3.39555i | ||||
\(259\) | − | 36682.7i | − | 0.546841i | ||||||
\(260\) | −112203. | + | 68292.0i | −1.65981 | + | 1.01024i | ||||
\(261\) | 106842. | 1.56842 | ||||||||
\(262\) | 179291. | + | 48040.9i | 2.61190 | + | 0.699856i | ||||
\(263\) | −1730.83 | − | 2997.89i | −0.0250232 | − | 0.0433415i | 0.853243 | − | 0.521514i | \(-0.174633\pi\) |
−0.878266 | + | 0.478173i | \(0.841299\pi\) | |||||||
\(264\) | −70585.3 | − | 40752.4i | −1.01276 | − | 0.584717i | ||||
\(265\) | −42615.8 | + | 42615.8i | −0.606847 | + | 0.606847i | ||||
\(266\) | −8393.42 | − | 31324.7i | −0.118625 | − | 0.442714i | ||||
\(267\) | 130300. | − | 34913.9i | 1.82778 | − | 0.489751i | ||||
\(268\) | −65057.0 | − | 65057.0i | −0.905783 | − | 0.905783i | ||||
\(269\) | −35350.0 | + | 61227.9i | −0.488522 | + | 0.846146i | −0.999913 | − | 0.0132029i | \(-0.995797\pi\) |
0.511390 | + | 0.859348i | \(0.329131\pi\) | |||||||
\(270\) | −119741. | + | 69132.4i | −1.64253 | + | 0.948318i | ||||
\(271\) | −3225.01 | + | 12035.9i | −0.0439129 | + | 0.163885i | −0.984400 | − | 0.175944i | \(-0.943702\pi\) |
0.940487 | + | 0.339829i | \(0.110369\pi\) | |||||||
\(272\) | 6209.73i | 0.0839334i | ||||||||
\(273\) | 47722.0 | + | 26098.2i | 0.640315 | + | 0.350175i | ||||
\(274\) | 48023.3 | 0.639663 | ||||||||
\(275\) | −14640.1 | − | 3922.79i | −0.193588 | − | 0.0518717i | ||||
\(276\) | 112099. | + | 194161.i | 1.47157 | + | 2.54884i | ||||
\(277\) | −49200.6 | − | 28406.0i | −0.641225 | − | 0.370212i | 0.143861 | − | 0.989598i | \(-0.454048\pi\) |
−0.785086 | + | 0.619386i | \(0.787381\pi\) | |||||||
\(278\) | −96557.6 | + | 96557.6i | −1.24939 | + | 1.24939i | ||||
\(279\) | −32040.2 | − | 119576.i | −0.411611 | − | 1.53615i | ||||
\(280\) | 44585.0 | − | 11946.5i | 0.568687 | − | 0.152379i | ||||
\(281\) | 28752.4 | + | 28752.4i | 0.364135 | + | 0.364135i | 0.865333 | − | 0.501198i | \(-0.167107\pi\) |
−0.501198 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(282\) | 61438.8 | − | 106415.i | 0.772582 | − | 1.33815i | ||||
\(283\) | 35550.4 | − | 20525.0i | 0.443886 | − | 0.256278i | −0.261358 | − | 0.965242i | \(-0.584170\pi\) |
0.705245 | + | 0.708964i | \(0.250837\pi\) | |||||||
\(284\) | 51614.1 | − | 192626.i | 0.639929 | − | 2.38825i | ||||
\(285\) | − | 93487.0i | − | 1.15096i | ||||||
\(286\) | −20126.9 | + | 82730.9i | −0.246062 | + | 1.01143i | ||||
\(287\) | 20745.2 | 0.251857 | ||||||||
\(288\) | −110626. | − | 29642.3i | −1.33375 | − | 0.357377i | ||||
\(289\) | −32169.9 | − | 55720.0i | −0.385172 | − | 0.667137i | ||||
\(290\) | −132595. | − | 76553.7i | −1.57663 | − | 0.910270i | ||||
\(291\) | −29903.2 | + | 29903.2i | −0.353128 | + | 0.353128i | ||||
\(292\) | 41586.7 | + | 155204.i | 0.487741 | + | 1.82027i | ||||
\(293\) | −16479.2 | + | 4415.59i | −0.191956 | + | 0.0514344i | −0.353516 | − | 0.935428i | \(-0.615014\pi\) |
0.161560 | + | 0.986863i | \(0.448347\pi\) | |||||||
\(294\) | 129441. | + | 129441.i | 1.49754 | + | 1.49754i | ||||
\(295\) | 50728.1 | − | 87863.7i | 0.582914 | − | 1.00964i | ||||
\(296\) | −104834. | + | 60525.7i | −1.19651 | + | 0.690806i | ||||
\(297\) | −14585.5 | + | 54433.8i | −0.165352 | + | 0.617101i | ||||
\(298\) | − | 1422.14i | − | 0.0160144i | ||||||
\(299\) | 66246.6 | − | 69387.7i | 0.741005 | − | 0.776140i | ||||
\(300\) | 78004.7 | 0.866719 | ||||||||
\(301\) | −52170.5 | − | 13979.1i | −0.575827 | − | 0.154293i | ||||
\(302\) | −98767.9 | − | 171071.i | −1.08293 | − | 1.87570i | ||||
\(303\) | 36214.2 | + | 20908.3i | 0.394452 | + | 0.227737i | ||||
\(304\) | −7091.49 | + | 7091.49i | −0.0767344 | + | 0.0767344i | ||||
\(305\) | 41806.2 | + | 156023.i | 0.449409 | + | 1.67722i | ||||
\(306\) | 115394. | − | 30919.6i | 1.23236 | − | 0.330211i | ||||
\(307\) | −33947.8 | − | 33947.8i | −0.360193 | − | 0.360193i | 0.503691 | − | 0.863884i | \(-0.331975\pi\) |
−0.863884 | + | 0.503691i | \(0.831975\pi\) | |||||||
\(308\) | 22964.6 | − | 39775.9i | 0.242079 | − | 0.419294i | ||||
\(309\) | −68982.2 | + | 39826.9i | −0.722471 | + | 0.417119i | ||||
\(310\) | −45914.3 | + | 171354.i | −0.477776 | + | 1.78308i | ||||
\(311\) | 30532.2i | 0.315673i | 0.987465 | + | 0.157836i | \(0.0504518\pi\) | ||||
−0.987465 | + | 0.157836i | \(0.949548\pi\) | |||||||
\(312\) | −4155.64 | − | 179444.i | −0.0426903 | − | 1.84340i | ||||
\(313\) | −10587.5 | −0.108070 | −0.0540350 | − | 0.998539i | \(-0.517208\pi\) | ||||
−0.0540350 | + | 0.998539i | \(0.517208\pi\) | |||||||
\(314\) | 99870.1 | + | 26760.1i | 1.01292 | + | 0.271412i | ||||
\(315\) | −41608.4 | − | 72067.9i | −0.419334 | − | 0.726308i | ||||
\(316\) | −92870.3 | − | 53618.7i | −0.930043 | − | 0.536960i | ||||
\(317\) | 14491.7 | − | 14491.7i | 0.144212 | − | 0.144212i | −0.631315 | − | 0.775527i | \(-0.717484\pi\) |
0.775527 | + | 0.631315i | \(0.217484\pi\) | |||||||
\(318\) | −52038.1 | − | 194209.i | −0.514597 | − | 1.92050i | ||||
\(319\) | −60277.3 | + | 16151.3i | −0.592342 | + | 0.158717i | ||||
\(320\) | 130600. | + | 130600.i | 1.27539 | + | 1.27539i | ||||
\(321\) | 4273.02 | − | 7401.09i | 0.0414691 | − | 0.0718266i | ||||
\(322\) | −71275.6 | + | 41151.0i | −0.687431 | + | 0.396888i | ||||
\(323\) | −8017.70 | + | 29922.5i | −0.0768502 | + | 0.286809i | ||||
\(324\) | − | 1613.47i | − | 0.0153699i | ||||||
\(325\) | −9383.01 | − | 32032.1i | −0.0888332 | − | 0.303262i | ||||
\(326\) | −18767.6 | −0.176593 | ||||||||
\(327\) | 104679. | + | 28048.7i | 0.978958 | + | 0.262311i | ||||
\(328\) | −34229.3 | − | 59286.8i | −0.318163 | − | 0.551075i | ||||
\(329\) | 24562.9 | + | 14181.4i | 0.226928 | + | 0.131017i | ||||
\(330\) | 148897. | − | 148897.i | 1.36728 | − | 1.36728i | ||||
\(331\) | 9079.85 | + | 33886.5i | 0.0828749 | + | 0.309293i | 0.994903 | − | 0.100834i | \(-0.0321510\pi\) |
−0.912028 | + | 0.410127i | \(0.865484\pi\) | |||||||
\(332\) | 51346.5 | − | 13758.2i | 0.465838 | − | 0.124821i | ||||
\(333\) | 154319. | + | 154319.i | 1.39166 | + | 1.39166i | ||||
\(334\) | −86963.4 | + | 150625.i | −0.779549 | + | 1.35022i | ||||
\(335\) | 84319.5 | − | 48681.9i | 0.751343 | − | 0.433788i | ||||
\(336\) | −3734.92 | + | 13938.9i | −0.0330829 | + | 0.123467i | ||||
\(337\) | 68997.6i | 0.607539i | 0.952746 | + | 0.303769i | \(0.0982452\pi\) | ||||
−0.952746 | + | 0.303769i | \(0.901755\pi\) | |||||||
\(338\) | −178676. | + | 56862.4i | −1.56399 | + | 0.497728i | ||||
\(339\) | −296932. | −2.58379 | ||||||||
\(340\) | −103975. | − | 27860.1i | −0.899440 | − | 0.241004i | ||||
\(341\) | 36152.3 | + | 62617.5i | 0.310904 | + | 0.538502i | ||||
\(342\) | 167089. | + | 96468.9i | 1.42855 | + | 0.824774i | ||||
\(343\) | −67371.7 | + | 67371.7i | −0.572650 | + | 0.572650i | ||||
\(344\) | 46130.4 | + | 172161.i | 0.389825 | + | 1.45485i | ||||
\(345\) | −229173. | + | 61406.6i | −1.92542 | + | 0.515913i | ||||
\(346\) | −245649. | − | 245649.i | −2.05193 | − | 2.05193i | ||||
\(347\) | 67786.7 | − | 117410.i | 0.562971 | − | 0.975094i | −0.434265 | − | 0.900785i | \(-0.642992\pi\) |
0.997235 | − | 0.0743084i | \(-0.0236749\pi\) | |||||||
\(348\) | 278139. | − | 160584.i | 2.29670 | − | 1.32600i | ||||
\(349\) | 35819.2 | − | 133679.i | 0.294080 | − | 1.09752i | −0.647865 | − | 0.761755i | \(-0.724338\pi\) |
0.941945 | − | 0.335767i | \(-0.108995\pi\) | |||||||
\(350\) | 28635.2i | 0.233757i | ||||||||
\(351\) | −119100. | + | 34887.4i | −0.966712 | + | 0.283174i | ||||
\(352\) | 66893.1 | 0.539878 | ||||||||
\(353\) | 38151.7 | + | 10222.7i | 0.306171 | + | 0.0820383i | 0.408633 | − | 0.912699i | \(-0.366005\pi\) |
−0.102462 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(354\) | 169234. | + | 293122.i | 1.35046 | + | 2.33906i | ||||
\(355\) | 182764. | + | 105519.i | 1.45022 | + | 0.837286i | ||||
\(356\) | 177379. | − | 177379.i | 1.39959 | − | 1.39959i | ||||
\(357\) | 11536.7 | + | 43055.7i | 0.0905204 | + | 0.337827i | ||||
\(358\) | 241932. | − | 64825.6i | 1.88768 | − | 0.505802i | ||||
\(359\) | −17939.3 | − | 17939.3i | −0.139193 | − | 0.139193i | 0.634077 | − | 0.773270i | \(-0.281380\pi\) |
−0.773270 | + | 0.634077i | \(0.781380\pi\) | |||||||
\(360\) | −137306. | + | 237821.i | −1.05946 | + | 1.83504i | ||||
\(361\) | 69533.8 | − | 40145.3i | 0.533558 | − | 0.308050i | ||||
\(362\) | 40394.9 | − | 150756.i | 0.308255 | − | 1.15042i | ||||
\(363\) | 127546.i | 0.967954i | ||||||||
\(364\) | 101119. | − | 2341.77i | 0.763189 | − | 0.0176743i | ||||
\(365\) | −170038. | −1.27632 | ||||||||
\(366\) | −520508. | − | 139470.i | −3.88567 | − | 1.04116i | ||||
\(367\) | 109265. | + | 189253.i | 0.811242 | + | 1.40511i | 0.911995 | + | 0.410201i | \(0.134541\pi\) |
−0.100753 | + | 0.994911i | \(0.532125\pi\) | |||||||
\(368\) | 22042.0 | + | 12725.9i | 0.162763 | + | 0.0939711i | ||||
\(369\) | −87272.7 | + | 87272.7i | −0.640952 | + | 0.640952i | ||||
\(370\) | −80943.9 | − | 302087.i | −0.591263 | − | 2.20662i | ||||
\(371\) | 44827.5 | − | 12011.5i | 0.325684 | − | 0.0872669i | ||||
\(372\) | −263131. | − | 263131.i | −1.90146 | − | 1.90146i | ||||
\(373\) | 97162.0 | − | 168290.i | 0.698359 | − | 1.20959i | −0.270676 | − | 0.962671i | \(-0.587247\pi\) |
0.969035 | − | 0.246923i | \(-0.0794195\pi\) | |||||||
\(374\) | −60427.5 | + | 34887.8i | −0.432008 | + | 0.249420i | ||||
\(375\) | 46244.9 | − | 172588.i | 0.328852 | − | 1.22729i | ||||
\(376\) | − | 93596.0i | − | 0.662036i | ||||||
\(377\) | −99399.3 | − | 94899.6i | −0.699360 | − | 0.667701i | ||||
\(378\) | 106470. | 0.745149 | ||||||||
\(379\) | 188740. | + | 50572.7i | 1.31397 | + | 0.352077i | 0.846715 | − | 0.532047i | \(-0.178577\pi\) |
0.467254 | + | 0.884123i | \(0.345244\pi\) | |||||||
\(380\) | −86923.3 | − | 150556.i | −0.601962 | − | 1.04263i | ||||
\(381\) | −57829.0 | − | 33387.6i | −0.398378 | − | 0.230004i | ||||
\(382\) | −70156.4 | + | 70156.4i | −0.480774 | + | 0.480774i | ||||
\(383\) | −31354.7 | − | 117017.i | −0.213749 | − | 0.797723i | −0.986603 | − | 0.163139i | \(-0.947838\pi\) |
0.772854 | − | 0.634584i | \(-0.218829\pi\) | |||||||
\(384\) | −398841. | + | 106869.i | −2.70481 | + | 0.724753i | ||||
\(385\) | 34368.6 | + | 34368.6i | 0.231868 | + | 0.231868i | ||||
\(386\) | −191239. | + | 331236.i | −1.28352 | + | 2.22312i | ||||
\(387\) | 278283. | − | 160667.i | 1.85808 | − | 1.07276i | ||||
\(388\) | −20353.7 | + | 75961.2i | −0.135201 | + | 0.504578i | ||||
\(389\) | 3999.65i | 0.0264316i | 0.999913 | + | 0.0132158i | \(0.00420684\pi\) | ||||
−0.999913 | + | 0.0132158i | \(0.995793\pi\) | |||||||
\(390\) | 450586. | + | 109619.i | 2.96243 | + | 0.720704i | ||||
\(391\) | 78617.8 | 0.514242 | ||||||||
\(392\) | 134684. | + | 36088.5i | 0.876483 | + | 0.234853i | ||||
\(393\) | −206020. | − | 356837.i | −1.33390 | − | 2.31038i | ||||
\(394\) | 146036. | + | 84313.9i | 0.940736 | + | 0.543134i | ||||
\(395\) | 80245.3 | − | 80245.3i | 0.514311 | − | 0.514311i | ||||
\(396\) | 70722.9 | + | 263942.i | 0.450993 | + | 1.68313i | ||||
\(397\) | −177669. | + | 47606.1i | −1.12727 | + | 0.302052i | −0.773824 | − | 0.633401i | \(-0.781658\pi\) |
−0.353450 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(398\) | 309624. | + | 309624.i | 1.95465 | + | 1.95465i | ||||
\(399\) | −35994.5 | + | 62344.3i | −0.226095 | + | 0.391608i | ||||
\(400\) | 7669.04 | − | 4427.72i | 0.0479315 | − | 0.0276733i | ||||
\(401\) | −80819.4 | + | 301622.i | −0.502605 | + | 1.87575i | −0.0202056 | + | 0.999796i | \(0.506432\pi\) |
−0.482399 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(402\) | 324815.i | 2.00995i | ||||||||
\(403\) | −76401.4 | + | 139704.i | −0.470426 | + | 0.860200i | ||||
\(404\) | 77761.3 | 0.476432 | ||||||||
\(405\) | 1649.28 | + | 441.922i | 0.0100550 | + | 0.00269424i | ||||
\(406\) | 58949.6 | + | 102104.i | 0.357626 | + | 0.619426i | ||||
\(407\) | −110391. | − | 63734.1i | −0.666413 | − | 0.384754i | ||||
\(408\) | 104011. | − | 104011.i | 0.624828 | − | 0.624828i | ||||
\(409\) | −42559.5 | − | 158834.i | −0.254419 | − | 0.949505i | −0.968413 | − | 0.249353i | \(-0.919782\pi\) |
0.713994 | − | 0.700152i | \(-0.246885\pi\) | |||||||
\(410\) | 170840. | − | 45776.4i | 1.01630 | − | 0.272317i | ||||
\(411\) | −75380.9 | − | 75380.9i | −0.446249 | − | 0.446249i | ||||
\(412\) | −74061.3 | + | 128278.i | −0.436312 | + | 0.755714i | ||||
\(413\) | −67658.8 | + | 39062.8i | −0.396665 | + | 0.229015i | ||||
\(414\) | 126730. | − | 472965.i | 0.739402 | − | 2.75948i | ||||
\(415\) | 56254.2i | 0.326632i | ||||||||
\(416\) | 76590.8 | + | 125838.i | 0.442578 | + | 0.727151i | ||||
\(417\) | 303127. | 1.74322 | ||||||||
\(418\) | −108850. | − | 29166.2i | −0.622981 | − | 0.166927i | ||||
\(419\) | −133921. | − | 231958.i | −0.762817 | − | 1.32124i | −0.941393 | − | 0.337311i | \(-0.890483\pi\) |
0.178577 | − | 0.983926i | \(-0.442851\pi\) | |||||||
\(420\) | −216636. | − | 125075.i | −1.22809 | − | 0.709040i | ||||
\(421\) | −10736.2 | + | 10736.2i | −0.0605743 | + | 0.0605743i | −0.736745 | − | 0.676171i | \(-0.763638\pi\) |
0.676171 | + | 0.736745i | \(0.263638\pi\) | |||||||
\(422\) | −49436.2 | − | 184498.i | −0.277600 | − | 1.03602i | ||||
\(423\) | −162992. | + | 43673.7i | −0.910933 | + | 0.244084i | ||||
\(424\) | −108292. | − | 108292.i | −0.602370 | − | 0.602370i | ||||
\(425\) | 13676.7 | − | 23688.8i | 0.0757188 | − | 0.131149i | ||||
\(426\) | −609720. | + | 352022.i | −3.35978 | + | 1.93977i | ||||
\(427\) | 32192.6 | − | 120144.i | 0.176563 | − | 0.658943i | ||||
\(428\) | − | 15892.0i | − | 0.0867545i | ||||||
\(429\) | 161453. | − | 98267.7i | 0.877266 | − | 0.533945i | ||||
\(430\) | −460478. | −2.49042 | ||||||||
\(431\) | 73459.2 | + | 19683.3i | 0.395450 | + | 0.105960i | 0.451063 | − | 0.892492i | \(-0.351045\pi\) |
−0.0556136 | + | 0.998452i | \(0.517711\pi\) | |||||||
\(432\) | −16462.9 | − | 28514.6i | −0.0882142 | − | 0.152792i | ||||
\(433\) | 287163. | + | 165794.i | 1.53163 | + | 0.884286i | 0.999287 | + | 0.0377562i | \(0.0120210\pi\) |
0.532341 | + | 0.846530i | \(0.321312\pi\) | |||||||
\(434\) | 96594.3 | − | 96594.3i | 0.512828 | − | 0.512828i | ||||
\(435\) | 87966.3 | + | 328295.i | 0.464876 | + | 1.73494i | ||||
\(436\) | 194659. | − | 52158.7i | 1.02400 | − | 0.274381i | ||||
\(437\) | 89781.3 | + | 89781.3i | 0.470135 | + | 0.470135i | ||||
\(438\) | 283632. | − | 491266.i | 1.47845 | − | 2.56076i | ||||
\(439\) | −230242. | + | 132931.i | −1.19469 | + | 0.689756i | −0.959367 | − | 0.282160i | \(-0.908949\pi\) |
−0.235326 | + | 0.971917i | \(0.575616\pi\) | |||||||
\(440\) | 41512.9 | − | 154928.i | 0.214426 | − | 0.800248i | ||||
\(441\) | − | 251384.i | − | 1.29259i | ||||||
\(442\) | −134818. | − | 73729.3i | −0.690087 | − | 0.377395i | ||||
\(443\) | 422.417 | 0.00215246 | 0.00107623 | − | 0.999999i | \(-0.499657\pi\) | ||||
0.00107623 | + | 0.999999i | \(0.499657\pi\) | |||||||
\(444\) | 633676. | + | 169793.i | 3.21441 | + | 0.861299i | ||||
\(445\) | 132732. | + | 229898.i | 0.670277 | + | 1.16095i | ||||
\(446\) | 123013. | + | 71021.3i | 0.618415 | + | 0.357042i | ||||
\(447\) | −2232.30 | + | 2232.30i | −0.0111722 | + | 0.0111722i | ||||
\(448\) | −36810.3 | − | 137378.i | −0.183406 | − | 0.684481i | ||||
\(449\) | 136854. | − | 36669.8i | 0.678834 | − | 0.181893i | 0.0971032 | − | 0.995274i | \(-0.469042\pi\) |
0.581731 | + | 0.813381i | \(0.302376\pi\) | |||||||
\(450\) | −120465. | − | 120465.i | −0.594888 | − | 0.594888i | ||||
\(451\) | 36043.7 | − | 62429.6i | 0.177205 | − | 0.306928i | ||||
\(452\) | −478191. | + | 276084.i | −2.34059 | + | 1.35134i | ||||
\(453\) | −113492. | + | 423558.i | −0.553056 | + | 2.06403i | ||||
\(454\) | − | 479101.i | − | 2.32442i | ||||||
\(455\) | −25302.4 | + | 104005.i | −0.122219 | + | 0.502378i | ||||
\(456\) | 237561. | 1.14247 | ||||||||
\(457\) | −134308. | − | 35987.8i | −0.643088 | − | 0.172315i | −0.0774862 | − | 0.996993i | \(-0.524689\pi\) |
−0.565602 | + | 0.824679i | \(0.691356\pi\) | |||||||
\(458\) | −61202.4 | − | 106006.i | −0.291768 | − | 0.505357i | ||||
\(459\) | −88078.1 | − | 50851.9i | −0.418064 | − | 0.241369i | ||||
\(460\) | −311974. | + | 311974.i | −1.47436 | + | 1.47436i | ||||
\(461\) | 4115.18 | + | 15358.1i | 0.0193636 | + | 0.0722660i | 0.974932 | − | 0.222505i | \(-0.0714233\pi\) |
−0.955568 | + | 0.294771i | \(0.904757\pi\) | |||||||
\(462\) | −156625. | + | 41967.5i | −0.733798 | + | 0.196621i | ||||
\(463\) | −146640. | − | 146640.i | −0.684055 | − | 0.684055i | 0.276856 | − | 0.960911i | \(-0.410707\pi\) |
−0.960911 | + | 0.276856i | \(0.910707\pi\) | |||||||
\(464\) | 18230.2 | − | 31575.6i | 0.0846749 | − | 0.146661i | ||||
\(465\) | 341040. | − | 196900.i | 1.57725 | − | 0.910625i | ||||
\(466\) | −4580.07 | + | 17093.1i | −0.0210912 | + | 0.0787132i | ||||
\(467\) | − | 229929.i | − | 1.05429i | −0.849775 | − | 0.527146i | \(-0.823262\pi\) | ||
0.849775 | − | 0.527146i | \(-0.176738\pi\) | |||||||
\(468\) | −415545. | + | 435249.i | −1.89726 | + | 1.98722i | ||||
\(469\) | −74974.3 | −0.340852 | ||||||||
\(470\) | 233571. | + | 62585.3i | 1.05736 | + | 0.283319i | ||||
\(471\) | −114759. | − | 198768.i | −0.517301 | − | 0.895992i | ||||
\(472\) | 223271. | + | 128906.i | 1.00219 | + | 0.578613i | ||||
\(473\) | −132711. | + | 132711.i | −0.593178 | + | 0.593178i | ||||
\(474\) | 97987.4 | + | 365694.i | 0.436127 | + | 1.62765i | ||||
\(475\) | 42671.2 | − | 11433.7i | 0.189124 | − | 0.0506758i | ||||
\(476\) | 58612.0 | + | 58612.0i | 0.258686 | + | 0.258686i | ||||
\(477\) | −138053. | + | 239115.i | −0.606749 | + | 1.05092i | ||||
\(478\) | 483644. | − | 279232.i | 2.11675 | − | 1.22211i | ||||
\(479\) | 36794.2 | − | 137318.i | 0.160364 | − | 0.598488i | −0.838222 | − | 0.545330i | \(-0.816404\pi\) |
0.998586 | − | 0.0531586i | \(-0.0169289\pi\) | |||||||
\(480\) | − | 364327.i | − | 1.58128i | ||||||
\(481\) | −6499.15 | − | 280639.i | −0.0280910 | − | 1.21299i | ||||
\(482\) | 342049. | 1.47229 | ||||||||
\(483\) | 176473. | + | 47285.7i | 0.756455 | + | 0.202692i | ||||
\(484\) | 118591. | + | 205406.i | 0.506246 | + | 0.876844i | ||||
\(485\) | −72072.0 | − | 41610.8i | −0.306396 | − | 0.176898i | ||||
\(486\) | 272102. | − | 272102.i | 1.15202 | − | 1.15202i | ||||
\(487\) | 66412.1 | + | 247853.i | 0.280020 | + | 1.04505i | 0.952402 | + | 0.304845i | \(0.0986045\pi\) |
−0.672382 | + | 0.740204i | \(0.734729\pi\) | |||||||
\(488\) | −396472. | + | 106234.i | −1.66484 | + | 0.446093i | ||||
\(489\) | 29459.0 | + | 29459.0i | 0.123197 | + | 0.123197i | ||||
\(490\) | −180119. | + | 311976.i | −0.750185 | + | 1.29936i | ||||
\(491\) | −246510. | + | 142323.i | −1.02252 | + | 0.590352i | −0.914833 | − | 0.403833i | \(-0.867678\pi\) |
−0.107687 | + | 0.994185i | \(0.534344\pi\) | |||||||
\(492\) | −96023.5 | + | 358365.i | −0.396686 | + | 1.48045i | ||||
\(493\) | − | 112622.i | − | 0.463370i | ||||||
\(494\) | −69763.2 | − | 238160.i | −0.285873 | − | 0.975923i | ||||
\(495\) | −289169. | −1.18016 | ||||||||
\(496\) | −40805.6 | − | 10933.8i | −0.165866 | − | 0.0444436i | ||||
\(497\) | −81254.1 | − | 140736.i | −0.328952 | − | 0.569762i | ||||
\(498\) | −162527. | − | 93834.9i | −0.655339 | − | 0.378360i | ||||
\(499\) | −119045. | + | 119045.i | −0.478089 | + | 0.478089i | −0.904520 | − | 0.426431i | \(-0.859771\pi\) |
0.426431 | + | 0.904520i | \(0.359771\pi\) | |||||||
\(500\) | −85996.0 | − | 320942.i | −0.343984 | − | 1.28377i | ||||
\(501\) | 372936. | − | 99927.8i | 1.48579 | − | 0.398117i | ||||
\(502\) | 176390. | + | 176390.i | 0.699951 | + | 0.699951i | ||||
\(503\) | −7841.79 | + | 13582.4i | −0.0309941 | + | 0.0536834i | −0.881106 | − | 0.472918i | \(-0.843201\pi\) |
0.850112 | + | 0.526601i | \(0.176534\pi\) | |||||||
\(504\) | 183133. | − | 105732.i | 0.720949 | − | 0.416240i | ||||
\(505\) | −21298.4 | + | 79486.9i | −0.0835151 | + | 0.311683i | ||||
\(506\) | 285990.i | 1.11699i | ||||||||
\(507\) | 369718. | + | 191208.i | 1.43832 | + | 0.743857i | ||||
\(508\) | −124174. | −0.481174 | ||||||||
\(509\) | −339655. | − | 91010.2i | −1.31100 | − | 0.351281i | −0.465400 | − | 0.885101i | \(-0.654089\pi\) |
−0.845598 | + | 0.533820i | \(0.820756\pi\) | |||||||
\(510\) | 190013. | + | 329113.i | 0.730539 | + | 1.26533i | ||||
\(511\) | 113395. | + | 65468.4i | 0.434261 | + | 0.250720i | ||||
\(512\) | −64604.8 | + | 64604.8i | −0.246448 | + | 0.246448i | ||||
\(513\) | −42512.2 | − | 158658.i | −0.161539 | − | 0.602873i | ||||
\(514\) | −24523.3 | + | 6571.00i | −0.0928225 | + | 0.0248717i | ||||
\(515\) | −110839. | − | 110839.i | −0.417907 | − | 0.417907i | ||||
\(516\) | 482963. | − | 836517.i | 1.81391 | − | 3.14178i | ||||
\(517\) | 85353.3 | − | 49278.7i | 0.319330 | − | 0.184365i | ||||
\(518\) | −62330.3 | + | 232620.i | −0.232295 | + | 0.866937i | ||||
\(519\) | 771175.i | 2.86298i | ||||||||
\(520\) | 338979. | − | 99295.4i | 1.25362 | − | 0.367217i | ||||
\(521\) | 393166. | 1.44844 | 0.724220 | − | 0.689569i | \(-0.242200\pi\) | ||||
0.724220 | + | 0.689569i | \(0.242200\pi\) | |||||||
\(522\) | −677532. | − | 181544.i | −2.48650 | − | 0.666256i | ||||
\(523\) | −105537. | − | 182796.i | −0.385836 | − | 0.668287i | 0.606049 | − | 0.795427i | \(-0.292754\pi\) |
−0.991885 | + | 0.127140i | \(0.959420\pi\) | |||||||
\(524\) | −663566. | − | 383110.i | −2.41669 | − | 1.39528i | ||||
\(525\) | 44947.9 | − | 44947.9i | 0.163076 | − | 0.163076i | ||||
\(526\) | 5881.98 | + | 21951.8i | 0.0212595 | + | 0.0793414i | ||||
\(527\) | −126044. | + | 33773.3i | −0.453837 | + | 0.121605i | ||||
\(528\) | 35457.8 | + | 35457.8i | 0.127187 | + | 0.127187i | ||||
\(529\) | 21195.3 | − | 36711.4i | 0.0757406 | − | 0.131187i | ||||
\(530\) | 342656. | − | 197833.i | 1.21985 | − | 0.704282i | ||||
\(531\) | 120300. | − | 448965.i | 0.426654 | − | 1.59229i | ||||
\(532\) | 133869.i | 0.472996i | ||||||||
\(533\) | 158710. | − | 3675.48i | 0.558664 | − | 0.0129378i | ||||
\(534\) | −885612. | −3.10571 | ||||||||
\(535\) | 16244.7 | + | 4352.75i | 0.0567550 | + | 0.0152075i | ||||
\(536\) | 123706. | + | 214265.i | 0.430588 | + | 0.745800i | ||||
\(537\) | −481509. | − | 277999.i | −1.66977 | − | 0.964041i | ||||
\(538\) | 328206. | − | 328206.i | 1.13392 | − | 1.13392i | ||||
\(539\) | 38001.5 | + | 141823.i | 0.130805 | + | 0.488169i | ||||
\(540\) | 551307. | − | 147722.i | 1.89063 | − | 0.506592i | ||||
\(541\) | −153707. | − | 153707.i | −0.525169 | − | 0.525169i | 0.393959 | − | 0.919128i | \(-0.371105\pi\) |
−0.919128 | + | 0.393959i | \(0.871105\pi\) | |||||||
\(542\) | 40902.2 | − | 70844.6i | 0.139235 | − | 0.241162i | ||||
\(543\) | −300044. | + | 173230.i | −1.01762 | + | 0.587522i | ||||
\(544\) | −31245.7 | + | 116610.i | −0.105582 | + | 0.394039i | ||||
\(545\) | 213265.i | 0.718002i | ||||||||
\(546\) | −258280. | − | 246588.i | −0.866373 | − | 0.827153i | ||||
\(547\) | 555728. | 1.85732 | 0.928662 | − | 0.370926i | \(-0.120960\pi\) | ||||
0.928662 | + | 0.370926i | \(0.120960\pi\) | |||||||
\(548\) | −191485. | − | 51308.2i | −0.637637 | − | 0.170854i | ||||
\(549\) | 370002. | + | 640863.i | 1.22761 | + | 2.12628i | ||||
\(550\) | 86173.2 | + | 49752.1i | 0.284870 | + | 0.164470i | ||||
\(551\) | 128614. | − | 128614.i | 0.423627 | − | 0.423627i | ||||
\(552\) | −156041. | − | 582353.i | −0.512107 | − | 1.91121i | ||||
\(553\) | −84409.9 | + | 22617.6i | −0.276022 | + | 0.0739598i | ||||
\(554\) | 263734. | + | 263734.i | 0.859305 | + | 0.859305i | ||||
\(555\) | −347122. | + | 601232.i | −1.12693 | + | 1.95190i | ||||
\(556\) | 488169. | − | 281845.i | 1.57914 | − | 0.911717i | ||||
\(557\) | 5258.75 | − | 19625.9i | 0.0169501 | − | 0.0632586i | −0.956933 | − | 0.290310i | \(-0.906242\pi\) |
0.973883 | + | 0.227051i | \(0.0729084\pi\) | |||||||
\(558\) | 812721.i | 2.61019i | ||||||||
\(559\) | −401604. | − | 97702.8i | −1.28521 | − | 0.312668i | ||||
\(560\) | −28398.0 | −0.0905550 | ||||||||
\(561\) | 149614. | + | 40088.9i | 0.475385 | + | 0.127379i | ||||
\(562\) | −133476. | − | 231187.i | −0.422600 | − | 0.731964i | ||||
\(563\) | 172856. | + | 99798.3i | 0.545340 | + | 0.314852i | 0.747240 | − | 0.664554i | \(-0.231378\pi\) |
−0.201901 | + | 0.979406i | \(0.564712\pi\) | |||||||
\(564\) | −358671. | + | 358671.i | −1.12756 | + | 1.12756i | ||||
\(565\) | −151236. | − | 564421.i | −0.473760 | − | 1.76810i | ||||
\(566\) | −260315. | + | 69751.3i | −0.812582 | + | 0.217731i | ||||
\(567\) | −929.715 | − | 929.715i | −0.00289190 | − | 0.00289190i | ||||
\(568\) | −268136. | + | 464424.i | −0.831108 | + | 1.43952i | ||||
\(569\) | 281029. | − | 162252.i | 0.868015 | − | 0.501149i | 0.00132689 | − | 0.999999i | \(-0.499578\pi\) |
0.866688 | + | 0.498850i | \(0.166244\pi\) | |||||||
\(570\) | −158851. | + | 592840.i | −0.488923 | + | 1.82468i | ||||
\(571\) | 478957.i | 1.46901i | 0.678605 | + | 0.734504i | \(0.262585\pi\) | ||||
−0.678605 | + | 0.734504i | \(0.737415\pi\) | |||||||
\(572\) | 168642. | − | 308372.i | 0.515436 | − | 0.942502i | ||||
\(573\) | 220245. | 0.670806 | ||||||||
\(574\) | −131554. | − | 35249.8i | −0.399283 | − | 0.106988i | ||||
\(575\) | −56056.8 | − | 97093.3i | −0.169548 | − | 0.293666i | ||||
\(576\) | 732789. | + | 423076.i | 2.20869 | + | 1.27519i | ||||
\(577\) | −178299. | + | 178299.i | −0.535547 | + | 0.535547i | −0.922218 | − | 0.386671i | \(-0.873625\pi\) |
0.386671 | + | 0.922218i | \(0.373625\pi\) | |||||||
\(578\) | 109325. | + | 408006.i | 0.327237 | + | 1.22127i | ||||
\(579\) | 820113. | − | 219749.i | 2.44634 | − | 0.655495i | ||||
\(580\) | 446909. | + | 446909.i | 1.32851 | + | 1.32851i | ||||
\(581\) | 21659.1 | − | 37514.6i | 0.0641635 | − | 0.111134i | ||||
\(582\) | 240440. | − | 138818.i | 0.709839 | − | 0.409826i | ||||
\(583\) | 41738.6 | − | 155771.i | 0.122801 | − | 0.458299i | ||||
\(584\) | − | 432086.i | − | 1.26691i | ||||||
\(585\) | −331091. | − | 543979.i | −0.967466 | − | 1.58954i | ||||
\(586\) | 112004. | 0.326167 | ||||||||
\(587\) | −208395. | − | 55839.4i | −0.604800 | − | 0.162056i | −0.0565918 | − | 0.998397i | \(-0.518023\pi\) |
−0.548209 | + | 0.836342i | \(0.684690\pi\) | |||||||
\(588\) | −377829. | − | 654420.i | −1.09280 | − | 1.89279i | ||||
\(589\) | −182511. | − | 105372.i | −0.526087 | − | 0.303736i | ||||
\(590\) | −470984. | + | 470984.i | −1.35301 | + | 1.35301i | ||||
\(591\) | −96883.4 | − | 361574.i | −0.277379 | − | 1.03519i | ||||
\(592\) | 71937.7 | − | 19275.7i | 0.205264 | − | 0.0550004i | ||||
\(593\) | −151916. | − | 151916.i | −0.432011 | − | 0.432011i | 0.457301 | − | 0.889312i | \(-0.348816\pi\) |
−0.889312 | + | 0.457301i | \(0.848816\pi\) | |||||||
\(594\) | 184985. | − | 320404.i | 0.524282 | − | 0.908082i | ||||
\(595\) | −75966.2 | + | 43859.1i | −0.214579 | + | 0.123887i | ||||
\(596\) | −1519.42 | + | 5670.55i | −0.00427745 | + | 0.0159637i | ||||
\(597\) | − | 972016.i | − | 2.72725i | ||||||
\(598\) | −537999. | + | 327451.i | −1.50445 | + | 0.915681i | ||||
\(599\) | −544593. | −1.51781 | −0.758907 | − | 0.651199i | \(-0.774266\pi\) | ||||
−0.758907 | + | 0.651199i | \(0.774266\pi\) | |||||||
\(600\) | −202617. | − | 54291.2i | −0.562826 | − | 0.150809i | ||||
\(601\) | 317137. | + | 549298.i | 0.878008 | + | 1.52075i | 0.853524 | + | 0.521054i | \(0.174461\pi\) |
0.0244843 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(602\) | 307082. | + | 177294.i | 0.847347 | + | 0.489216i | ||||
\(603\) | 315407. | − | 315407.i | 0.867436 | − | 0.867436i | ||||
\(604\) | 211048. | + | 787640.i | 0.578504 | + | 2.15901i | ||||
\(605\) | −242446. | + | 64963.1i | −0.662375 | + | 0.177483i | ||||
\(606\) | −194123. | − | 194123.i | −0.528604 | − | 0.528604i | ||||
\(607\) | 95785.7 | − | 165906.i | 0.259970 | − | 0.450281i | −0.706264 | − | 0.707949i | \(-0.749621\pi\) |
0.966234 | + | 0.257668i | \(0.0829540\pi\) | |||||||
\(608\) | −168851. | + | 97486.2i | −0.456769 | + | 0.263716i | ||||
\(609\) | 67737.8 | − | 252801.i | 0.182640 | − | 0.681623i | ||||
\(610\) | − | 1.06044e6i | − | 2.84989i | ||||||
\(611\) | 190429. | + | 104142.i | 0.510096 | + | 0.278961i | ||||
\(612\) | −493147. | −1.31666 | ||||||||
\(613\) | −184028. | − | 49310.1i | −0.489736 | − | 0.131224i | 0.00549620 | − | 0.999985i | \(-0.498250\pi\) |
−0.495233 | + | 0.868760i | \(0.664917\pi\) | |||||||
\(614\) | 157594. | + | 272960.i | 0.418025 | + | 0.724041i | ||||
\(615\) | −340017. | − | 196309.i | −0.898980 | − | 0.519026i | ||||
\(616\) | −87334.6 | + | 87334.6i | −0.230157 | + | 0.230157i | ||||
\(617\) | 179296. | + | 669141.i | 0.470977 | + | 1.75771i | 0.636271 | + | 0.771465i | \(0.280476\pi\) |
−0.165294 | + | 0.986244i | \(0.552857\pi\) | |||||||
\(618\) | 505118. | − | 135346.i | 1.32256 | − | 0.354379i | ||||
\(619\) | −103746. | − | 103746.i | −0.270763 | − | 0.270763i | 0.558644 | − | 0.829407i | \(-0.311322\pi\) |
−0.829407 | + | 0.558644i | \(0.811322\pi\) | |||||||
\(620\) | 366151. | − | 634192.i | 0.952526 | − | 1.64982i | ||||
\(621\) | −361007. | + | 208427.i | −0.936121 | + | 0.540470i | ||||
\(622\) | 51879.6 | − | 193617.i | 0.134096 | − | 0.500453i | ||||
\(623\) | − | 204418.i | − | 0.526676i | ||||||
\(624\) | −26104.2 | + | 107301.i | −0.0670412 | + | 0.275571i | ||||
\(625\) | 475057. | 1.21615 | ||||||||
\(626\) | 67139.8 | + | 17990.1i | 0.171329 | + | 0.0459075i | ||||
\(627\) | 125077. | + | 216640.i | 0.318158 | + | 0.551065i | ||||
\(628\) | −369625. | − | 213403.i | −0.937220 | − | 0.541104i | ||||
\(629\) | 162667. | − | 162667.i | 0.411148 | − | 0.411148i | ||||
\(630\) | 141400. | + | 527712.i | 0.356261 | + | 1.32958i | ||||
\(631\) | −484445. | + | 129807.i | −1.21671 | + | 0.326015i | −0.809389 | − | 0.587272i | \(-0.800202\pi\) |
−0.407316 | + | 0.913287i | \(0.633535\pi\) | |||||||
\(632\) | 203912. | + | 203912.i | 0.510516 | + | 0.510516i | ||||
\(633\) | −212003. | + | 367200.i | −0.529097 | + | 0.916422i | ||||
\(634\) | −116522. | + | 67274.1i | −0.289888 | + | 0.167367i | ||||
\(635\) | 34010.6 | − | 126929.i | 0.0843464 | − | 0.314785i | ||||
\(636\) | 829973.i | 2.05187i | ||||||||
\(637\) | −223285. | + | 233872.i | −0.550275 | + | 0.576366i | ||||
\(638\) | 409687. | 1.00649 | ||||||||
\(639\) | 933886. | + | 250234.i | 2.28714 | + | 0.612837i | ||||
\(640\) | −406284. | − | 703704.i | −0.991903 | − | 1.71803i | ||||
\(641\) | 411467. | + | 237561.i | 1.00143 | + | 0.578174i | 0.908670 | − | 0.417515i | \(-0.137099\pi\) |
0.0927567 | + | 0.995689i | \(0.470432\pi\) | |||||||
\(642\) | −39672.7 | + | 39672.7i | −0.0962547 | + | 0.0962547i | ||||
\(643\) | −73868.4 | − | 275681.i | −0.178664 | − | 0.666783i | −0.995898 | − | 0.0904777i | \(-0.971161\pi\) |
0.817235 | − | 0.576305i | \(-0.195506\pi\) | |||||||
\(644\) | 328165. | − | 87931.5i | 0.791262 | − | 0.212018i | ||||
\(645\) | 722799. | + | 722799.i | 1.73739 | + | 1.73739i | ||||
\(646\) | 101687. | − | 176127.i | 0.243669 | − | 0.422048i | ||||
\(647\) | −90764.9 | + | 52403.1i | −0.216825 | + | 0.125184i | −0.604479 | − | 0.796621i | \(-0.706619\pi\) |
0.387654 | + | 0.921805i | \(0.373285\pi\) | |||||||
\(648\) | −1122.97 | + | 4191.00i | −0.00267436 | + | 0.00998085i | ||||
\(649\) | 271478.i | 0.644533i | ||||||||
\(650\) | 5073.37 | + | 219072.i | 0.0120080 | + | 0.518514i | ||||
\(651\) | −303243. | −0.715531 | ||||||||
\(652\) | 74832.6 | + | 20051.3i | 0.176034 | + | 0.0471681i | ||||
\(653\) | 95438.9 | + | 165305.i | 0.223820 | + | 0.387668i | 0.955965 | − | 0.293481i | \(-0.0948139\pi\) |
−0.732145 | + | 0.681149i | \(0.761481\pi\) | |||||||
\(654\) | −616153. | − | 355736.i | −1.44057 | − | 0.831711i | ||||
\(655\) | 573359. | − | 573359.i | 1.33642 | − | 1.33642i | ||||
\(656\) | 10901.0 | + | 40683.1i | 0.0253314 | + | 0.0945381i | ||||
\(657\) | −752454. | + | 201620.i | −1.74321 | + | 0.467091i | ||||
\(658\) | −131667. | − | 131667.i | −0.304105 | − | 0.304105i | ||||
\(659\) | 184755. | − | 320004.i | 0.425426 | − | 0.736860i | −0.571034 | − | 0.820927i | \(-0.693457\pi\) |
0.996460 | + | 0.0840664i | \(0.0267908\pi\) | |||||||
\(660\) | −752785. | + | 434620.i | −1.72816 | + | 0.997751i | ||||
\(661\) | −167346. | + | 624543.i | −0.383011 | + | 1.42942i | 0.458266 | + | 0.888815i | \(0.348471\pi\) |
−0.841278 | + | 0.540603i | \(0.818196\pi\) | |||||||
\(662\) | − | 230316.i | − | 0.525544i | ||||||
\(663\) | 95889.4 | + | 327351.i | 0.218144 | + | 0.744709i | ||||
\(664\) | −142948. | −0.324222 | ||||||||
\(665\) | −136840. | − | 36666.2i | −0.309435 | − | 0.0829129i | ||||
\(666\) | −716387. | − | 1.24082e6i | −1.61510 | − | 2.79744i | ||||
\(667\) | −399760. | − | 230802.i | −0.898562 | − | 0.518785i | ||||
\(668\) | 507680. | − | 507680.i | 1.13772 | − | 1.13772i | ||||
\(669\) | −81609.1 | − | 304569.i | −0.182342 | − | 0.680509i | ||||
\(670\) | −617424. | + | 165438.i | −1.37541 | + | 0.368541i | ||||
\(671\) | −305623. | − | 305623.i | −0.678798 | − | 0.678798i | ||||
\(672\) | −140274. | + | 242961.i | −0.310626 | + | 0.538020i | ||||
\(673\) | −438672. | + | 253268.i | −0.968523 | + | 0.559177i | −0.898786 | − | 0.438388i | \(-0.855549\pi\) |
−0.0697375 | + | 0.997565i | \(0.522216\pi\) | |||||||
\(674\) | 117239. | − | 437542.i | 0.258079 | − | 0.963163i | ||||
\(675\) | 145036.i | 0.318323i | ||||||||
\(676\) | 773193. | − | 35831.1i | 1.69198 | − | 0.0784092i | ||||
\(677\) | 125231. | 0.273234 | 0.136617 | − | 0.990624i | \(-0.456377\pi\) | ||||
0.136617 | + | 0.990624i | \(0.456377\pi\) | |||||||
\(678\) | 1.88297e6 | + | 504539.i | 4.09622 | + | 1.09758i | ||||
\(679\) | 32042.1 | + | 55498.6i | 0.0694995 | + | 0.120377i | ||||
\(680\) | 250686. | + | 144733.i | 0.542140 | + | 0.313005i | ||||
\(681\) | −752031. | + | 752031.i | −1.62159 | + | 1.62159i | ||||
\(682\) | −122858. | − | 458513.i | −0.264141 | − | 0.985786i | ||||
\(683\) | 236156. | − | 63277.9i | 0.506242 | − | 0.135647i | 0.00334667 | − | 0.999994i | \(-0.498935\pi\) |
0.502896 | + | 0.864347i | \(0.332268\pi\) | |||||||
\(684\) | −563172. | − | 563172.i | −1.20373 | − | 1.20373i | ||||
\(685\) | 104894. | − | 181681.i | 0.223547 | − | 0.387194i | ||||
\(686\) | 541708. | − | 312755.i | 1.15111 | − | 0.664594i | ||||
\(687\) | −70326.4 | + | 262462.i | −0.149006 | + | 0.556100i | ||||
\(688\) | − | 109656.i | − | 0.231663i | ||||||
\(689\) | 340822. | − | 99835.5i | 0.717942 | − | 0.210303i | ||||
\(690\) | 1.55762e6 | 3.27162 | ||||||||
\(691\) | −483617. | − | 129585.i | −1.01285 | − | 0.271393i | −0.286031 | − | 0.958220i | \(-0.592336\pi\) |
−0.726820 | + | 0.686827i | \(0.759003\pi\) | |||||||
\(692\) | 717030. | + | 1.24193e6i | 1.49736 | + | 2.59350i | ||||
\(693\) | 192840. | + | 111336.i | 0.401542 | + | 0.231831i | ||||
\(694\) | −629364. | + | 629364.i | −1.30672 | + | 1.30672i | ||||
\(695\) | 154392. | + | 576198.i | 0.319635 | + | 1.19289i | ||||
\(696\) | −834233. | + | 223532.i | −1.72214 | + | 0.461447i | ||||
\(697\) | 91993.4 | + | 91993.4i | 0.189361 | + | 0.189361i | ||||
\(698\) | −454289. | + | 786852.i | −0.932441 | + | 1.61504i | ||||
\(699\) | 34019.7 | − | 19641.3i | 0.0696267 | − | 0.0401990i | ||||
\(700\) | 30593.9 | − | 114178.i | 0.0624366 | − | 0.233016i | ||||
\(701\) | − | 790148.i | − | 1.60795i | −0.594663 | − | 0.803975i | \(-0.702715\pi\) | ||
0.594663 | − | 0.803975i | \(-0.297285\pi\) | |||||||
\(702\) | 814541. | − | 18863.5i | 1.65287 | − | 0.0382779i | ||||
\(703\) | 371530. | 0.751767 | ||||||||
\(704\) | −477374. | − | 127912.i | −0.963192 | − | 0.258087i | ||||
\(705\) | −268392. | − | 464869.i | −0.539997 | − | 0.935302i | ||||
\(706\) | −224565. | − | 129653.i | −0.450540 | − | 0.260119i | ||||
\(707\) | 44807.6 | − | 44807.6i | 0.0896423 | − | 0.0896423i | ||||
\(708\) | −361620. | − | 1.34958e6i | −0.721416 | − | 2.69236i | ||||
\(709\) | 863561. | − | 231390.i | 1.71791 | − | 0.460313i | 0.740569 | − | 0.671981i | \(-0.234556\pi\) |
0.977342 | + | 0.211668i | \(0.0678895\pi\) | |||||||
\(710\) | −979688. | − | 979688.i | −1.94344 | − | 1.94344i | ||||
\(711\) | 259953. | − | 450251.i | 0.514227 | − | 0.890668i | ||||
\(712\) | −584197. | + | 337286.i | −1.15239 | + | 0.665332i | ||||
\(713\) | −138427. | + | 516617.i | −0.272296 | + | 1.01622i | ||||
\(714\) | − | 292637.i | − | 0.574027i | ||||||
\(715\) | 269024. | + | 256846.i | 0.526235 | + | 0.502413i | ||||
\(716\) | −1.03392e6 | −2.01680 | ||||||||
\(717\) | −1.19747e6 | − | 320860.i | −2.32930 | − | 0.624133i | ||||
\(718\) | 83278.6 | + | 144243.i | 0.161542 | + | 0.279798i | ||||
\(719\) | 689802. | + | 398258.i | 1.33434 | + | 0.770382i | 0.985962 | − | 0.166971i | \(-0.0533987\pi\) |
0.348380 | + | 0.937354i | \(0.386732\pi\) | |||||||
\(720\) | 119467. | − | 119467.i | 0.230453 | − | 0.230453i | ||||
\(721\) | 31240.7 | + | 116592.i | 0.0600966 | + | 0.224284i | ||||
\(722\) | −509156. | + | 136428.i | −0.976735 | + | 0.261715i | ||||
\(723\) | −536905. | − | 536905.i | −1.02712 | − | 1.02712i | ||||
\(724\) | −322136. | + | 557955.i | −0.614556 | + | 1.06444i | ||||
\(725\) | −139088. | + | 80302.6i | −0.264615 | + | 0.152775i | ||||
\(726\) | 216724. | − | 808823.i | 0.411181 | − | 1.53455i | ||||
\(727\) | 60581.5i | 0.114623i | 0.998356 | + | 0.0573114i | \(0.0182528\pi\) | ||||
−0.998356 | + | 0.0573114i | \(0.981747\pi\) | |||||||
\(728\) | −264288. | − | 64296.2i | −0.498671 | − | 0.121317i | ||||
\(729\) | −859042. | −1.61644 | ||||||||
\(730\) | 1.07828e6 | + | 288925.i | 2.02342 | + | 0.542175i | ||||
\(731\) | −169358. | − | 293336.i | −0.316935 | − | 0.548947i | ||||
\(732\) | 1.92643e6 | + | 1.11222e6i | 3.59526 | + | 2.07573i | ||||
\(733\) | 572778. | − | 572778.i | 1.06605 | − | 1.06605i | 0.0683928 | − | 0.997658i | \(-0.478213\pi\) |
0.997658 | − | 0.0683928i | \(-0.0217871\pi\) | |||||||
\(734\) | −371322. | − | 1.38579e6i | −0.689222 | − | 2.57221i | ||||
\(735\) | 772428. | − | 206971.i | 1.42983 | − | 0.383121i | ||||
\(736\) | 349885. | + | 349885.i | 0.645907 | + | 0.645907i | ||||
\(737\) | −130264. | + | 225623.i | −0.239822 | + | 0.415383i | ||||
\(738\) | 701724. | − | 405140.i | 1.28841 | − | 0.743863i | ||||
\(739\) | 40364.3 | − | 150642.i | 0.0739110 | − | 0.275839i | −0.919073 | − | 0.394087i | \(-0.871061\pi\) |
0.992984 | + | 0.118247i | \(0.0377276\pi\) | |||||||
\(740\) | 1.29100e6i | 2.35756i | ||||||||
\(741\) | −264328. | + | 483339.i | −0.481401 | + | 0.880269i | ||||
\(742\) | −304680. | −0.553395 | ||||||||
\(743\) | 96406.5 | + | 25832.0i | 0.174634 | + | 0.0467930i | 0.345076 | − | 0.938575i | \(-0.387853\pi\) |
−0.170442 | + | 0.985368i | \(0.554520\pi\) | |||||||
\(744\) | 500345. | + | 866622.i | 0.903906 | + | 1.56561i | ||||
\(745\) | −5380.23 | − | 3106.27i | −0.00969366 | − | 0.00559664i | ||||
\(746\) | −902098. | + | 902098.i | −1.62097 | + | 1.62097i | ||||
\(747\) | 66702.3 | + | 248937.i | 0.119536 | + | 0.446116i | ||||
\(748\) | 278219. | − | 74548.5i | 0.497259 | − | 0.133240i | ||||
\(749\) | −9157.31 | − | 9157.31i | −0.0163232 | − | 0.0163232i | ||||
\(750\) | −586516. | + | 1.01587e6i | −1.04269 | + | 1.80600i | ||||
\(751\) | 521537. | − | 301110.i | 0.924710 | − | 0.533882i | 0.0395753 | − | 0.999217i | \(-0.487399\pi\) |
0.885135 | + | 0.465335i | \(0.154066\pi\) | |||||||
\(752\) | −14903.8 | + | 55621.7i | −0.0263549 | + | 0.0983578i | ||||
\(753\) | − | 553750.i | − | 0.976616i | ||||||
\(754\) | 469081. | + | 770695.i | 0.825097 | + | 1.35563i | ||||
\(755\) | −862924. | −1.51383 | ||||||||
\(756\) | −424530. | − | 113753.i | −0.742788 | − | 0.199030i | ||||
\(757\) | −96392.8 | − | 166957.i | −0.168210 | − | 0.291349i | 0.769580 | − | 0.638550i | \(-0.220465\pi\) |
−0.937791 | + | 0.347201i | \(0.887132\pi\) | |||||||
\(758\) | −1.11094e6 | − | 641404.i | −1.93354 | − | 1.11633i | ||||
\(759\) | 448910. | − | 448910.i | 0.779249 | − | 0.779249i | ||||
\(760\) | 120997. | + | 451567.i | 0.209482 | + | 0.781799i | ||||
\(761\) | 86176.8 | − | 23091.0i | 0.148806 | − | 0.0398725i | −0.183647 | − | 0.982992i | \(-0.558790\pi\) |
0.332453 | + | 0.943120i | \(0.392124\pi\) | |||||||
\(762\) | 309986. | + | 309986.i | 0.533866 | + | 0.533866i | ||||
\(763\) | 82111.4 | − | 142221.i | 0.141044 | − | 0.244295i | ||||
\(764\) | 354692. | − | 204782.i | 0.607666 | − | 0.350836i | ||||
\(765\) | 135071. | − | 504090.i | 0.230801 | − | 0.861361i | ||||
\(766\) | 795331.i | 1.35547i | ||||||||
\(767\) | −510699. | + | 310835.i | −0.868109 | + | 0.528371i | ||||
\(768\) | 1.20913e6 | 2.04999 | ||||||||
\(769\) | 1.06047e6 | + | 284153.i | 1.79327 | + | 0.480507i | 0.992896 | − | 0.118988i | \(-0.0379650\pi\) |
0.800379 | + | 0.599494i | \(0.204632\pi\) | |||||||
\(770\) | −159547. | − | 276344.i | −0.269097 | − | 0.466089i | ||||
\(771\) | 48807.9 | + | 28179.2i | 0.0821072 | + | 0.0474046i | ||||
\(772\) | 1.11643e6 | − | 1.11643e6i | 1.87325 | − | 1.87325i | ||||
\(773\) | −25594.4 | − | 95519.7i | −0.0428338 | − | 0.159858i | 0.941196 | − | 0.337860i | \(-0.109703\pi\) |
−0.984030 | + | 0.178003i | \(0.943036\pi\) | |||||||
\(774\) | −2.03771e6 | + | 546003.i | −3.40142 | + | 0.911408i | ||||
\(775\) | 131583. | + | 131583.i | 0.219077 | + | 0.219077i | ||||
\(776\) | 105738. | − | 183143.i | 0.175593 | − | 0.304136i | ||||
\(777\) | 462975. | − | 267299.i | 0.766859 | − | 0.442746i | ||||
\(778\) | 6796.11 | − | 25363.4i | 0.0112280 | − | 0.0419034i | ||||
\(779\) | 210112.i | 0.346239i | ||||||||
\(780\) | −1.67952e6 | − | 918494.i | −2.76055 | − | 1.50969i | ||||
\(781\) | −564698. | −0.925794 | ||||||||
\(782\) | −498548. | − | 133586.i | −0.815255 | − | 0.218447i | ||||
\(783\) | 298576. | + | 517150.i | 0.487003 | + | 0.843515i | ||||
\(784\) | −74292.6 | − | 42892.9i | −0.120869 | − | 0.0697835i | ||||
\(785\) | 319377. | − | 319377.i | 0.518280 | − | 0.518280i | ||||
\(786\) | 700128. | + | 2.61291e6i | 1.13327 | + | 4.22941i | ||||
\(787\) | −562536. | + | 150731.i | −0.908241 | + | 0.243362i | −0.682552 | − | 0.730837i | \(-0.739130\pi\) |
−0.225689 | + | 0.974199i | \(0.572463\pi\) | |||||||
\(788\) | −492213. | − | 492213.i | −0.792684 | − | 0.792684i | ||||
\(789\) | 25224.4 | − | 43690.0i | 0.0405198 | − | 0.0701823i | ||||
\(790\) | −645219. | + | 372518.i | −1.03384 | + | 0.596888i | ||||
\(791\) | −116458. | + | 434629.i | −0.186131 | + | 0.694649i | ||||
\(792\) | − | 734812.i | − | 1.17146i | ||||||
\(793\) | 225001. | − | 924861.i | 0.357799 | − | 1.47072i | ||||
\(794\) | 1.20756e6 | 1.91544 | ||||||||
\(795\) | −848390. | − | 227326.i | −1.34234 | − | 0.359678i | ||||
\(796\) | −903770. | − | 1.56538e6i | −1.42637 | − | 2.47054i | ||||
\(797\) | 432314. | + | 249597.i | 0.680586 | + | 0.392936i | 0.800076 | − | 0.599899i | \(-0.204793\pi\) |
−0.119490 | + | 0.992835i | \(0.538126\pi\) | |||||||
\(798\) | 334190. | − | 334190.i | 0.524793 | − | 0.524793i | ||||
\(799\) | 46036.1 | + | 171809.i | 0.0721115 | + | 0.269124i | ||||
\(800\) | 166293. | − | 44558.2i | 0.259833 | − | 0.0696221i | ||||
\(801\) | 859962. | + | 859962.i | 1.34034 | + | 1.34034i | ||||
\(802\) | 1.02502e6 | − | 1.77538e6i | 1.59361 | − | 2.76022i | ||||
\(803\) | 394034. | − | 227495.i | 0.611086 | − | 0.352810i | ||||
\(804\) | 347033. | − | 1.29515e6i | 0.536857 | − | 2.00358i | ||||
\(805\) | 359531.i | 0.554811i | ||||||||
\(806\) | 721875. | − | 756103.i | 1.11120 | − | 1.16389i | ||||
\(807\) | −1.03035e6 | −1.58211 | ||||||||
\(808\) | −201985. | − | 54121.7i | −0.309383 | − | 0.0828990i | ||||
\(809\) | −434066. | − | 751824.i | −0.663222 | − | 1.14873i | −0.979764 | − | 0.200155i | \(-0.935855\pi\) |
0.316542 | − | 0.948578i | \(-0.397478\pi\) | |||||||
\(810\) | −9707.84 | − | 5604.82i | −0.0147963 | − | 0.00854264i | ||||
\(811\) | −607624. | + | 607624.i | −0.923833 | + | 0.923833i | −0.997298 | − | 0.0734651i | \(-0.976594\pi\) |
0.0734651 | + | 0.997298i | \(0.476594\pi\) | |||||||
\(812\) | −125964. | − | 470103.i | −0.191044 | − | 0.712986i | ||||
\(813\) | −175406. | + | 46999.8i | −0.265377 | + | 0.0711075i | ||||
\(814\) | 591737. | + | 591737.i | 0.893059 | + | 0.893059i | ||||
\(815\) | −40992.6 | + | 71001.3i | −0.0617149 | + | 0.106893i | ||||
\(816\) | −78373.5 | + | 45249.0i | −0.117703 | + | 0.0679561i | ||||
\(817\) | 141583. | − | 528394.i | 0.212113 | − | 0.791615i | ||||
\(818\) | 1.07955e6i | 1.61338i | ||||||||
\(819\) | 11353.3 | + | 490244.i | 0.0169260 | + | 0.730878i | ||||
\(820\) | −730103. | −1.08582 | ||||||||
\(821\) | −255430. | − | 68442.2i | −0.378953 | − | 0.101540i | 0.0643141 | − | 0.997930i | \(-0.479514\pi\) |
−0.443267 | + | 0.896390i | \(0.646181\pi\) | |||||||
\(822\) | 349936. | + | 606106.i | 0.517898 | + | 0.897026i | ||||
\(823\) | −558509. | − | 322455.i | −0.824575 | − | 0.476069i | 0.0274163 | − | 0.999624i | \(-0.491272\pi\) |
−0.851992 | + | 0.523555i | \(0.824605\pi\) | |||||||
\(824\) | 281656. | − | 281656.i | 0.414824 | − | 0.414824i | ||||
\(825\) | −57169.1 | − | 213358.i | −0.0839950 | − | 0.313474i | ||||
\(826\) | 495427. | − | 132749.i | 0.726138 | − | 0.194568i | ||||
\(827\) | 820167. | + | 820167.i | 1.19920 | + | 1.19920i | 0.974407 | + | 0.224792i | \(0.0721702\pi\) |
0.224792 | + | 0.974407i | \(0.427830\pi\) | |||||||
\(828\) | −1.01063e6 | + | 1.75047e6i | −1.47412 | + | 2.55325i | ||||
\(829\) | −1.17667e6 | + | 679351.i | −1.71217 | + | 0.988519i | −0.780535 | + | 0.625113i | \(0.785053\pi\) |
−0.931631 | + | 0.363406i | \(0.881614\pi\) | |||||||
\(830\) | 95585.8 | − | 356731.i | 0.138751 | − | 0.517827i | ||||
\(831\) | − | 827953.i | − | 1.19896i | ||||||
\(832\) | −305955. | − | 1.04448e6i | −0.441988 | − | 1.50888i | ||||
\(833\) | −264982. | −0.381879 | ||||||||
\(834\) | −1.92225e6 | − | 515067.i | −2.76362 | − | 0.740511i | ||||
\(835\) | 379895. | + | 657997.i | 0.544867 | + | 0.943737i | ||||
\(836\) | 402859. | + | 232591.i | 0.576421 | + | 0.332797i | ||||
\(837\) | 489245. | − | 489245.i | 0.698353 | − | 0.698353i | ||||
\(838\) | 455110. | + | 1.69849e6i | 0.648080 | + | 2.41867i | ||||
\(839\) | 490865. | − | 131527.i | 0.697330 | − | 0.186849i | 0.107295 | − | 0.994227i | \(-0.465781\pi\) |
0.590034 | + | 0.807378i | \(0.299114\pi\) | |||||||
\(840\) | 475660. | + | 475660.i | 0.674121 | + | 0.674121i | ||||
\(841\) | 23012.0 | − | 39858.0i | 0.0325359 | − | 0.0563538i | ||||
\(842\) | 86325.7 | − | 49840.2i | 0.121763 | − | 0.0703000i | ||||
\(843\) | −153374. | + | 572400.i | −0.215823 | + | 0.805461i | ||||
\(844\) | 788474.i | 1.10688i | ||||||||
\(845\) | −175148. | + | 800165.i | −0.245296 | + | 1.12064i | ||||
\(846\) | 1.10781e6 | 1.54784 | ||||||||
\(847\) | 186694. | + | 50024.4i | 0.260233 | + | 0.0697293i | ||||
\(848\) | 47111.1 | + | 81598.8i | 0.0655136 | + | 0.113473i | ||||
\(849\) | 518096. | + | 299123.i | 0.718778 | + | 0.414987i | ||||
\(850\) | −126981. | + | 126981.i | −0.175752 | + | 0.175752i | ||||
\(851\) | −244038. | − | 910762.i | −0.336975 | − | 1.25761i | ||||
\(852\) | 2.80725e6 | − | 752202.i | 3.86725 | − | 1.03623i | ||||
\(853\) | 572753. | + | 572753.i | 0.787171 | + | 0.787171i | 0.981029 | − | 0.193859i | \(-0.0621003\pi\) |
−0.193859 | + | 0.981029i | \(0.562100\pi\) | |||||||
\(854\) | −408293. | + | 707184.i | −0.559830 | + | 0.969654i | ||||
\(855\) | 729919. | − | 421419.i | 0.998487 | − | 0.576477i | ||||
\(856\) | −11060.8 | + | 41279.6i | −0.0150953 | + | 0.0563362i | ||||
\(857\) | − | 68607.9i | − | 0.0934141i | −0.998909 | − | 0.0467071i | \(-0.985127\pi\) | ||
0.998909 | − | 0.0467071i | \(-0.0148727\pi\) | |||||||
\(858\) | −1.19081e6 | + | 348819.i | −1.61759 | + | 0.473834i | ||||
\(859\) | 507339. | 0.687563 | 0.343781 | − | 0.939050i | \(-0.388292\pi\) | ||||
0.343781 | + | 0.939050i | \(0.388292\pi\) | |||||||
\(860\) | 1.83608e6 | + | 491975.i | 2.48253 | + | 0.665191i | ||||
\(861\) | 151166. | + | 261827.i | 0.203915 | + | 0.353190i | ||||
\(862\) | −432389. | − | 249640.i | −0.581916 | − | 0.335970i | ||||
\(863\) | −722013. | + | 722013.i | −0.969445 | + | 0.969445i | −0.999547 | − | 0.0301019i | \(-0.990417\pi\) |
0.0301019 | + | 0.999547i | \(0.490417\pi\) | |||||||
\(864\) | −165674. | − | 618302.i | −0.221935 | − | 0.828272i | ||||
\(865\) | −1.46588e6 | + | 392782.i | −1.95915 | + | 0.524952i | ||||
\(866\) | −1.53931e6 | − | 1.53931e6i | −2.05253 | − | 2.05253i | ||||
\(867\) | 468831. | − | 812039.i | 0.623703 | − | 1.08029i | ||||
\(868\) | −488355. | + | 281952.i | −0.648181 | + | 0.374227i | ||||
\(869\) | −78593.5 | + | 293315.i | −0.104075 | + | 0.388414i | ||||
\(870\) | − | 2.23132e6i | − | 2.94797i | ||||||
\(871\) | −573586. | + | 13283.4i | −0.756071 | + | 0.0175094i | ||||
\(872\) | −541929. | −0.712705 | ||||||||
\(873\) | −368273. | − | 98678.4i | −0.483216 | − | 0.129477i | ||||
\(874\) | −416786. | − | 721894.i | −0.545620 | − | 0.945041i | ||||
\(875\) | −234485. | − | 135380.i | −0.306267 | − | 0.176823i | ||||
\(876\) | −1.65581e6 | + | 1.65581e6i | −2.15775 | + | 2.15775i | ||||
\(877\) | −238238. | − | 889116.i | −0.309750 | − | 1.15600i | −0.928779 | − | 0.370635i | \(-0.879140\pi\) |
0.619028 | − | 0.785369i | \(-0.287527\pi\) | |||||||
\(878\) | 1.68593e6 | − | 451745.i | 2.18701 | − | 0.586009i | ||||
\(879\) | −175810. | − | 175810.i | −0.227544 | − | 0.227544i | ||||
\(880\) | −49340.0 | + | 85459.4i | −0.0637139 | + | 0.110356i | ||||
\(881\) | 789311. | − | 455709.i | 1.01694 | − | 0.587132i | 0.103725 | − | 0.994606i | \(-0.466924\pi\) |
0.913217 | + | 0.407474i | \(0.133590\pi\) | |||||||
\(882\) | −427146. | + | 1.59413e6i | −0.549084 | + | 2.04921i | ||||
\(883\) | 761482.i | 0.976648i | 0.872662 | + | 0.488324i | \(0.162392\pi\) | ||||
−0.872662 | + | 0.488324i | \(0.837608\pi\) | |||||||
\(884\) | 458792. | + | 438023.i | 0.587099 | + | 0.560522i | ||||
\(885\) | 1.47858e6 | 1.88781 | ||||||||
\(886\) | −2678.72 | − | 717.761i | −0.00341240 | − | 0.000914351i | ||||
\(887\) | 221118. | + | 382987.i | 0.281045 | + | 0.486785i | 0.971642 | − | 0.236455i | \(-0.0759856\pi\) |
−0.690597 | + | 0.723240i | \(0.742652\pi\) | |||||||
\(888\) | −1.52780e6 | − | 882075.i | −1.93749 | − | 1.11861i | ||||
\(889\) | −71551.3 | + | 71551.3i | −0.0905345 | + | 0.0905345i | ||||
\(890\) | −451069. | − | 1.68341e6i | −0.569460 | − | 2.12525i | ||||
\(891\) | −4413.16 | + | 1182.50i | −0.00555897 | + | 0.00148952i | ||||
\(892\) | −414612. | − | 414612.i | −0.521090 | − | 0.521090i | ||||
\(893\) | −143632. | + | 248778.i | −0.180114 | + | 0.311967i | ||||
\(894\) | 17949.0 | − | 10362.8i | 0.0224577 | − | 0.0129659i | ||||
\(895\) | 283187. | − | 1.05687e6i | 0.353531 | − | 1.31939i | ||||
\(896\) | 625712.i | 0.779396i | ||||||||
\(897\) | 1.35847e6 | + | 330491.i | 1.68836 | + | 0.410747i | ||||
\(898\) | −930154. | −1.15346 | ||||||||
\(899\) | 740064. | + | 198300.i | 0.915693 | + | 0.245359i | ||||
\(900\) | 351628. | + | 609038.i | 0.434109 | + | 0.751899i | ||||
\(901\) | 252049. | + | 145521.i | 0.310481 | + | 0.179256i | ||||
\(902\) | −334647. | + | 334647.i | −0.411314 | + | 0.411314i | ||||
\(903\) | −203725. | − | 760311.i | −0.249844 | − | 0.932429i | ||||
\(904\) | 1.43426e6 | − | 384308.i | 1.75505 | − | 0.470265i | ||||
\(905\) | −482105. | − | 482105.i | −0.588633 | − | 0.588633i | ||||
\(906\) | 1.43940e6 | − | 2.49311e6i | 1.75358 | − | 3.03729i | ||||
\(907\) | −1.15076e6 | + | 664392.i | −1.39885 | + | 0.807625i | −0.994272 | − | 0.106880i | \(-0.965914\pi\) |
−0.404575 | + | 0.914505i | \(0.632581\pi\) | |||||||
\(908\) | −511873. | + | 1.91033e6i | −0.620855 | + | 2.31706i | ||||
\(909\) | 377000.i | 0.456261i | ||||||||
\(910\) | 337175. | − | 616544.i | 0.407167 | − | 0.744528i | ||||
\(911\) | −77944.7 | −0.0939183 | −0.0469591 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469591 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(912\) | −141176. | − | 37828.1i | −0.169735 | − | 0.0454805i | ||||
\(913\) | −75262.9 | − | 130359.i | −0.0902900 | − | 0.156387i | ||||
\(914\) | 790554. | + | 456427.i | 0.946323 | + | 0.546360i | ||||
\(915\) | −1.66455e6 | + | 1.66455e6i | −1.98817 | + | 1.98817i | ||||
\(916\) | 130778. | + | 488069.i | 0.155863 | + | 0.581688i | ||||
\(917\) | −603116. | + | 161604.i | −0.717236 | + | 0.192183i | ||||
\(918\) | 472133. | + | 472133.i | 0.560247 | + | 0.560247i | ||||
\(919\) | 221789. | − | 384149.i | 0.262608 | − | 0.454851i | −0.704326 | − | 0.709877i | \(-0.748751\pi\) |
0.966934 | + | 0.255026i | \(0.0820840\pi\) | |||||||
\(920\) | 1.02749e6 | − | 593220.i | 1.21395 | − | 0.700874i | ||||
\(921\) | 181088. | − | 675829.i | 0.213486 | − | 0.796741i | ||||
\(922\) | − | 104384.i | − | 0.122793i | ||||||
\(923\) | −646564. | − | 1.06230e6i | −0.758942 | − | 1.24693i | ||||
\(924\) | 669353. | 0.783991 | ||||||||
\(925\) | −316880. | − | 84907.9i | −0.370350 | − | 0.0992349i | ||||
\(926\) | 680739. | + | 1.17907e6i | 0.793887 | + | 1.37505i | ||||
\(927\) | −621913. | − | 359062.i | −0.723720 | − | 0.417840i | ||||
\(928\) | 501218. | − | 501218.i | 0.582010 | − | 0.582010i | ||||
\(929\) | 53117.1 | + | 198236.i | 0.0615464 | + | 0.229694i | 0.989847 | − | 0.142136i | \(-0.0453970\pi\) |
−0.928301 | + | 0.371830i | \(0.878730\pi\) | |||||||
\(930\) | −2.49725e6 | + | 669135.i | −2.88732 | + | 0.773656i | ||||
\(931\) | −302608. | − | 302608.i | −0.349126 | − | 0.349126i | ||||
\(932\) | 36524.5 | − | 63262.3i | 0.0420487 | − | 0.0728305i | ||||
\(933\) | −385349. | + | 222481.i | −0.442681 | + | 0.255582i | ||||
\(934\) | −390691. | + | 1.45808e6i | −0.447857 | + | 1.67142i | ||||
\(935\) | 304811.i | 0.348664i | ||||||||
\(936\) | 1.38231e6 | − | 841340.i | 1.57781 | − | 0.960329i | ||||
\(937\) | 774009. | 0.881590 | 0.440795 | − | 0.897608i | \(-0.354697\pi\) | ||||
0.440795 | + | 0.897608i | \(0.354697\pi\) | |||||||
\(938\) | 475443. | + | 127394.i | 0.540372 | + | 0.144792i | ||||
\(939\) | −77149.0 | − | 133626.i | −0.0874982 | − | 0.151551i | ||||
\(940\) | −864460. | − | 499096.i | −0.978338 | − | 0.564844i | ||||
\(941\) | 828766. | − | 828766.i | 0.935950 | − | 0.935950i | −0.0621190 | − | 0.998069i | \(-0.519786\pi\) |
0.998069 | + | 0.0621190i | \(0.0197858\pi\) | |||||||
\(942\) | 389990. | + | 1.45546e6i | 0.439493 | + | 1.64021i | ||||
\(943\) | 515066. | − | 138011.i | 0.579214 | − | 0.155200i | ||||
\(944\) | −112158. | − | 112158.i | −0.125860 | − | 0.125860i | ||||
\(945\) | 232554. | − | 402795.i | 0.260411 | − | 0.451045i | ||||
\(946\) | 1.06708e6 | − | 616077.i | 1.19238 | − | 0.688418i | ||||
\(947\) | −17653.9 | + | 65885.2i | −0.0196852 | + | 0.0734663i | −0.975070 | − | 0.221899i | \(-0.928775\pi\) |
0.955384 | + | 0.295365i | \(0.0954412\pi\) | |||||||
\(948\) | − | 1.56283e6i | − | 1.73898i | ||||||
\(949\) | 879118. | + | 480772.i | 0.976145 | + | 0.533834i | ||||
\(950\) | −290024. | −0.321356 | ||||||||
\(951\) | 288500. | + | 77303.2i | 0.318995 | + | 0.0854745i | ||||
\(952\) | −111451. | − | 193039.i | −0.122973 | − | 0.212995i | ||||
\(953\) | −1.43168e6 | − | 826582.i | −1.57638 | − | 0.910123i | −0.995359 | − | 0.0962331i | \(-0.969321\pi\) |
−0.581020 | − | 0.813889i | \(-0.697346\pi\) | |||||||
\(954\) | 1.28175e6 | − | 1.28175e6i | 1.40834 | − | 1.40834i | ||||
\(955\) | 112177. | + | 418652.i | 0.122998 | + | 0.459035i | ||||
\(956\) | −2.22678e6 | + | 596664.i | −2.43647 | + | 0.652851i | ||||
\(957\) | −643074. | − | 643074.i | −0.702161 | − | 0.702161i | ||||
\(958\) | −466654. | + | 808269.i | −0.508469 | + | 0.880693i | ||||
\(959\) | −139902. | + | 80772.6i | −0.152120 | + | 0.0878267i | ||||
\(960\) | −696660. | + | 2.59997e6i | −0.755924 | + | 2.82115i | ||||
\(961\) | 35790.5i | 0.0387544i | ||||||||
\(962\) | −435641. | + | 1.79069e6i | −0.470737 | + | 1.93495i | ||||
\(963\) | 77047.3 | 0.0830816 | ||||||||
\(964\) | −1.36386e6 | − | 365446.i | −1.46763 | − | 0.393250i | ||||
\(965\) | 835416. | + | 1.44698e6i | 0.897115 | + | 1.55385i | ||||
\(966\) | −1.03874e6 | − | 599716.i | −1.11315 | − | 0.642675i | ||||
\(967\) | 264009. | − | 264009.i | 0.282335 | − | 0.282335i | −0.551704 | − | 0.834040i | \(-0.686022\pi\) |
0.834040 | + | 0.551704i | \(0.186022\pi\) | |||||||
\(968\) | −165079. | − | 616082.i | −0.176173 | − | 0.657488i | ||||
\(969\) | −436077. | + | 116847.i | −0.464425 | + | 0.124442i | ||||
\(970\) | 386334. | + | 386334.i | 0.410601 | + | 0.410601i | ||||
\(971\) | −82653.0 | + | 143159.i | −0.0876637 | + | 0.151838i | −0.906523 | − | 0.422156i | \(-0.861273\pi\) |
0.818859 | + | 0.573994i | \(0.194607\pi\) | |||||||
\(972\) | −1.37567e6 | + | 794245.i | −1.45607 | + | 0.840663i | ||||
\(973\) | 118888. | − | 443697.i | 0.125578 | − | 0.468663i | ||||
\(974\) | − | 1.68458e6i | − | 1.77572i | ||||||
\(975\) | 335908. | − | 351835.i | 0.353354 | − | 0.370109i | ||||
\(976\) | 252529. | 0.265101 | ||||||||
\(977\) | 1.60136e6 | + | 429084.i | 1.67765 | + | 0.449525i | 0.967157 | − | 0.254181i | \(-0.0818058\pi\) |
0.710492 | + | 0.703705i | \(0.248473\pi\) | |||||||
\(978\) | −136755. | − | 236867.i | −0.142977 | − | 0.247644i | ||||
\(979\) | −615164. | − | 355165.i | −0.641838 | − | 0.370566i | ||||
\(980\) | 1.05151e6 | − | 1.05151e6i | 1.09487 | − | 1.09487i | ||||
\(981\) | 252874. | + | 943740.i | 0.262764 | + | 0.980650i | ||||
\(982\) | 1.80505e6 | − | 483662.i | 1.87183 | − | 0.501556i | ||||
\(983\) | 1.27109e6 | + | 1.27109e6i | 1.31544 | + | 1.31544i | 0.917347 | + | 0.398089i | \(0.130326\pi\) |
0.398089 | + | 0.917347i | \(0.369674\pi\) | |||||||
\(984\) | 498843. | − | 864021.i | 0.515197 | − | 0.892347i | ||||
\(985\) | 637950. | − | 368321.i | 0.657528 | − | 0.379624i | ||||
\(986\) | −191364. | + | 714181.i | −0.196837 | + | 0.734606i | ||||
\(987\) | 413347.i | 0.424307i | ||||||||
\(988\) | 23717.9 | + | 1.02416e6i | 0.0242976 | + | 1.04919i | ||||
\(989\) | −1.38830e6 | −1.41935 | ||||||||
\(990\) | 1.83374e6 | + | 491350.i | 1.87097 | + | 0.501326i | ||||
\(991\) | −21120.3 | − | 36581.5i | −0.0215057 | − | 0.0372490i | 0.855072 | − | 0.518509i | \(-0.173513\pi\) |
−0.876578 | + | 0.481260i | \(0.840179\pi\) | |||||||
\(992\) | −711259. | − | 410645.i | −0.722777 | − | 0.417295i | ||||
\(993\) | −361521. | + | 361521.i | −0.366636 | + | 0.366636i | ||||
\(994\) | 276130. | + | 1.03053e6i | 0.279474 | + | 1.04301i | ||||
\(995\) | 1.84765e6 | − | 495077.i | 1.86627 | − | 0.500065i | ||||
\(996\) | 547795. | + | 547795.i | 0.552203 | + | 0.552203i | ||||
\(997\) | 92901.4 | − | 160910.i | 0.0934613 | − | 0.161880i | −0.815504 | − | 0.578751i | \(-0.803540\pi\) |
0.908965 | + | 0.416872i | \(0.136874\pi\) | |||||||
\(998\) | 957189. | − | 552633.i | 0.961029 | − | 0.554850i | ||||
\(999\) | −315699. | + | 1.17821e6i | −0.316332 | + | 1.18057i |
(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 | 13.5.f.a.2.1 | ✓ | 16 | |
3.2 | odd | 2 | 117.5.bd.c.28.4 | 16 | |||
13.2 | odd | 12 | 169.5.d.c.99.1 | 16 | |||
13.3 | even | 3 | 169.5.d.d.70.8 | 16 | |||
13.7 | odd | 12 | inner | 13.5.f.a.7.1 | yes | 16 | |
13.10 | even | 6 | 169.5.d.c.70.1 | 16 | |||
13.11 | odd | 12 | 169.5.d.d.99.8 | 16 | |||
39.20 | even | 12 | 117.5.bd.c.46.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.5.f.a.2.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
13.5.f.a.7.1 | yes | 16 | 13.7 | odd | 12 | inner | |
117.5.bd.c.28.4 | 16 | 3.2 | odd | 2 | |||
117.5.bd.c.46.4 | 16 | 39.20 | even | 12 | |||
169.5.d.c.70.1 | 16 | 13.10 | even | 6 | |||
169.5.d.c.99.1 | 16 | 13.2 | odd | 12 | |||
169.5.d.d.70.8 | 16 | 13.3 | even | 3 | |||
169.5.d.d.99.8 | 16 | 13.11 | odd | 12 |