Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 67.3 | ||
Character | \(\chi\) | \(=\) | 210.67 |
Dual form | 210.3.v.a.163.3 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.183013 | − | 0.683013i | ||||
\(3\) | −0.448288 | − | 1.67303i | −0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0.626586 | − | 4.96058i | 0.125317 | − | 0.992117i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −6.84672 | − | 1.45688i | −0.978102 | − | 0.208125i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −6.54694 | − | 2.67163i | −0.654694 | − | 0.267163i | ||||
\(11\) | −6.59836 | + | 11.4287i | −0.599851 | + | 1.03897i | 0.392992 | + | 0.919542i | \(0.371440\pi\) |
−0.992843 | + | 0.119430i | \(0.961893\pi\) | |||||||
\(12\) | −0.896575 | + | 3.34607i | −0.0747146 | + | 0.278839i | ||||
\(13\) | 10.7755 | − | 10.7755i | 0.828886 | − | 0.828886i | −0.158476 | − | 0.987363i | \(-0.550658\pi\) |
0.987363 | + | 0.158476i | \(0.0506582\pi\) | |||||||
\(14\) | −4.49620 | + | 8.81953i | −0.321157 | + | 0.629967i | ||||
\(15\) | −8.58011 | + | 1.17547i | −0.572007 | + | 0.0783647i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −7.85475 | + | 2.10467i | −0.462044 | + | 0.123804i | −0.482329 | − | 0.875990i | \(-0.660209\pi\) |
0.0202855 | + | 0.999794i | \(0.493542\pi\) | |||||||
\(18\) | 1.09808 | + | 4.09808i | 0.0610042 | + | 0.227671i | ||||
\(19\) | 8.35848 | − | 4.82577i | 0.439920 | − | 0.253988i | −0.263644 | − | 0.964620i | \(-0.584924\pi\) |
0.703564 | + | 0.710632i | \(0.251591\pi\) | |||||||
\(20\) | −6.04586 | + | 7.96540i | −0.302293 | + | 0.398270i | ||||
\(21\) | 0.631897 | + | 12.1079i | 0.0300903 | + | 0.576566i | ||||
\(22\) | 13.1967 | + | 13.1967i | 0.599851 | + | 0.599851i | ||||
\(23\) | −22.6417 | − | 6.06684i | −0.984424 | − | 0.263776i | −0.269517 | − | 0.962996i | \(-0.586864\pi\) |
−0.714907 | + | 0.699220i | \(0.753531\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | −24.2148 | − | 6.21646i | −0.968591 | − | 0.248658i | ||||
\(26\) | −10.7755 | − | 18.6638i | −0.414443 | − | 0.717837i | ||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 10.4020 | + | 9.37010i | 0.371499 | + | 0.334646i | ||||
\(29\) | − | 41.4745i | − | 1.43015i | −0.699046 | − | 0.715077i | \(-0.746392\pi\) | ||
0.699046 | − | 0.715077i | \(-0.253608\pi\) | |||||||
\(30\) | −1.53482 | + | 12.1509i | −0.0511605 | + | 0.405030i | ||||
\(31\) | −18.0882 | + | 31.3297i | −0.583490 | + | 1.01063i | 0.411572 | + | 0.911377i | \(0.364980\pi\) |
−0.995062 | + | 0.0992569i | \(0.968353\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 22.0785 | + | 5.91593i | 0.669047 | + | 0.179271i | ||||
\(34\) | 11.5001i | 0.338240i | ||||||||
\(35\) | −11.5170 | + | 33.0508i | −0.329057 | + | 0.944310i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 1.25630 | − | 4.68858i | 0.0339541 | − | 0.126718i | −0.946869 | − | 0.321621i | \(-0.895772\pi\) |
0.980823 | + | 0.194902i | \(0.0624390\pi\) | |||||||
\(38\) | −3.53271 | − | 13.1843i | −0.0929661 | − | 0.346954i | ||||
\(39\) | −22.8583 | − | 13.1973i | −0.586111 | − | 0.338391i | ||||
\(40\) | 8.66800 | + | 11.1743i | 0.216700 | + | 0.279358i | ||||
\(41\) | −7.31247 | −0.178353 | −0.0891764 | − | 0.996016i | \(-0.528424\pi\) | ||||
−0.0891764 | + | 0.996016i | \(0.528424\pi\) | |||||||
\(42\) | 16.7710 | + | 3.56860i | 0.399309 | + | 0.0849668i | ||||
\(43\) | 48.7061 | − | 48.7061i | 1.13270 | − | 1.13270i | 0.142972 | − | 0.989727i | \(-0.454334\pi\) |
0.989727 | − | 0.142972i | \(-0.0456660\pi\) | |||||||
\(44\) | 22.8574 | − | 13.1967i | 0.519486 | − | 0.299925i | ||||
\(45\) | 5.81296 | + | 13.8279i | 0.129177 | + | 0.307286i | ||||
\(46\) | −16.5749 | + | 28.7086i | −0.360324 | + | 0.624100i | ||||
\(47\) | 13.9237 | − | 51.9641i | 0.296250 | − | 1.10562i | −0.643970 | − | 0.765051i | \(-0.722714\pi\) |
0.940220 | − | 0.340568i | \(-0.110619\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 44.7550 | + | 19.9496i | 0.913368 | + | 0.407135i | ||||
\(50\) | −17.3551 | + | 30.8026i | −0.347101 | + | 0.616052i | ||||
\(51\) | 7.04237 | + | 12.1977i | 0.138086 | + | 0.239172i | ||||
\(52\) | −29.4393 | + | 7.88823i | −0.566140 | + | 0.151697i | ||||
\(53\) | −12.1809 | − | 45.4596i | −0.229827 | − | 0.857728i | −0.980413 | − | 0.196954i | \(-0.936895\pi\) |
0.750585 | − | 0.660774i | \(-0.229772\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 52.5586 | + | 39.8928i | 0.955610 | + | 0.725323i | ||||
\(56\) | 16.6072 | − | 10.7797i | 0.296557 | − | 0.192494i | ||||
\(57\) | −11.8207 | − | 11.8207i | −0.207380 | − | 0.207380i | ||||
\(58\) | −56.6552 | − | 15.1807i | −0.976813 | − | 0.261736i | ||||
\(59\) | 1.15330 | + | 0.665857i | 0.0195474 | + | 0.0112857i | 0.509742 | − | 0.860327i | \(-0.329741\pi\) |
−0.490194 | + | 0.871613i | \(0.663074\pi\) | |||||||
\(60\) | 16.0367 | + | 6.54413i | 0.267278 | + | 0.109069i | ||||
\(61\) | −29.7996 | − | 51.6144i | −0.488518 | − | 0.846138i | 0.511395 | − | 0.859346i | \(-0.329129\pi\) |
−0.999913 | + | 0.0132077i | \(0.995796\pi\) | |||||||
\(62\) | 36.1764 | + | 36.1764i | 0.583490 | + | 0.583490i | ||||
\(63\) | 19.9736 | − | 6.48500i | 0.317041 | − | 0.102936i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −46.7011 | − | 60.2047i | −0.718478 | − | 0.926226i | ||||
\(66\) | 16.1626 | − | 27.9945i | 0.244888 | − | 0.424159i | ||||
\(67\) | 117.692 | − | 31.5356i | 1.75660 | − | 0.470680i | 0.770587 | − | 0.637335i | \(-0.219963\pi\) |
0.986015 | + | 0.166654i | \(0.0532964\pi\) | |||||||
\(68\) | 15.7095 | + | 4.20935i | 0.231022 | + | 0.0619021i | ||||
\(69\) | 40.6001i | 0.588407i | ||||||||
\(70\) | 40.9328 | + | 27.8300i | 0.584754 | + | 0.397571i | ||||
\(71\) | −82.6803 | −1.16451 | −0.582256 | − | 0.813006i | \(-0.697830\pi\) | ||||
−0.582256 | + | 0.813006i | \(0.697830\pi\) | |||||||
\(72\) | 2.19615 | − | 8.19615i | 0.0305021 | − | 0.113835i | ||||
\(73\) | −13.2814 | − | 49.5667i | −0.181936 | − | 0.678996i | −0.995266 | − | 0.0971923i | \(-0.969014\pi\) |
0.813329 | − | 0.581804i | \(-0.197653\pi\) | |||||||
\(74\) | −5.94488 | − | 3.43228i | −0.0803362 | − | 0.0463821i | ||||
\(75\) | 0.454846 | + | 43.2989i | 0.00606461 | + | 0.577318i | ||||
\(76\) | −19.3031 | −0.253988 | ||||||||
\(77\) | 61.8273 | − | 68.6360i | 0.802952 | − | 0.891377i | ||||
\(78\) | −26.3945 | + | 26.3945i | −0.338391 | + | 0.338391i | ||||
\(79\) | 26.3388 | − | 15.2067i | 0.333403 | − | 0.192490i | −0.323948 | − | 0.946075i | \(-0.605010\pi\) |
0.657351 | + | 0.753585i | \(0.271677\pi\) | |||||||
\(80\) | 18.4371 | − | 7.75061i | 0.230464 | − | 0.0968826i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.67655 | + | 9.98902i | −0.0326408 | + | 0.121817i | ||||
\(83\) | −32.2690 | + | 32.2690i | −0.388784 | + | 0.388784i | −0.874253 | − | 0.485470i | \(-0.838649\pi\) |
0.485470 | + | 0.874253i | \(0.338649\pi\) | |||||||
\(84\) | 11.0134 | − | 21.6034i | 0.131112 | − | 0.257183i | ||||
\(85\) | 5.51873 | + | 40.2829i | 0.0649263 | + | 0.473916i | ||||
\(86\) | −48.7061 | − | 84.3614i | −0.566350 | − | 0.980946i | ||||
\(87\) | −69.3881 | + | 18.5925i | −0.797565 | + | 0.213707i | ||||
\(88\) | −9.66067 | − | 36.0541i | −0.109780 | − | 0.409706i | ||||
\(89\) | 19.1540 | − | 11.0586i | 0.215214 | − | 0.124254i | −0.388518 | − | 0.921441i | \(-0.627013\pi\) |
0.603732 | + | 0.797187i | \(0.293680\pi\) | |||||||
\(90\) | 21.0169 | − | 2.87930i | 0.233521 | − | 0.0319923i | ||||
\(91\) | −89.4755 | + | 58.0783i | −0.983248 | + | 0.638223i | ||||
\(92\) | 33.1498 | + | 33.1498i | 0.360324 | + | 0.360324i | ||||
\(93\) | 60.5243 | + | 16.2174i | 0.650798 | + | 0.174381i | ||||
\(94\) | −65.8878 | − | 38.0403i | −0.700934 | − | 0.404685i | ||||
\(95\) | −18.7013 | − | 44.4867i | −0.196856 | − | 0.468281i | ||||
\(96\) | −4.89898 | − | 8.48528i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 128.645 | + | 128.645i | 1.32623 | + | 1.32623i | 0.908630 | + | 0.417603i | \(0.137130\pi\) |
0.417603 | + | 0.908630i | \(0.362870\pi\) | |||||||
\(98\) | 43.6332 | − | 53.8344i | 0.445237 | − | 0.549331i | ||||
\(99\) | − | 39.5902i | − | 0.399901i | ||||||
\(100\) | 35.7248 | + | 34.9820i | 0.357248 | + | 0.349820i | ||||
\(101\) | 25.4347 | − | 44.0541i | 0.251828 | − | 0.436179i | −0.712201 | − | 0.701976i | \(-0.752302\pi\) |
0.964029 | + | 0.265796i | \(0.0856348\pi\) | |||||||
\(102\) | 19.2401 | − | 5.15537i | 0.188629 | − | 0.0505429i | ||||
\(103\) | 118.462 | + | 31.7417i | 1.15011 | + | 0.308172i | 0.783010 | − | 0.622009i | \(-0.213683\pi\) |
0.367102 | + | 0.930181i | \(0.380350\pi\) | |||||||
\(104\) | 43.1021i | 0.414443i | ||||||||
\(105\) | 60.4581 | + | 4.45205i | 0.575791 | + | 0.0424004i | ||||
\(106\) | −66.5574 | −0.627900 | ||||||||
\(107\) | −50.1735 | + | 187.250i | −0.468912 | + | 1.75000i | 0.174673 | + | 0.984627i | \(0.444113\pi\) |
−0.643584 | + | 0.765375i | \(0.722553\pi\) | |||||||
\(108\) | −2.68973 | − | 10.0382i | −0.0249049 | − | 0.0929463i | ||||
\(109\) | −58.3978 | − | 33.7160i | −0.535760 | − | 0.309321i | 0.207599 | − | 0.978214i | \(-0.433435\pi\) |
−0.743359 | + | 0.668893i | \(0.766768\pi\) | |||||||
\(110\) | 73.7323 | − | 57.1946i | 0.670294 | − | 0.519951i | ||||
\(111\) | −8.40733 | −0.0757417 | ||||||||
\(112\) | −8.64666 | − | 26.6315i | −0.0772023 | − | 0.237781i | ||||
\(113\) | 85.9828 | − | 85.9828i | 0.760910 | − | 0.760910i | −0.215577 | − | 0.976487i | \(-0.569163\pi\) |
0.976487 | + | 0.215577i | \(0.0691632\pi\) | |||||||
\(114\) | −20.4740 | + | 11.8207i | −0.179597 | + | 0.103690i | ||||
\(115\) | −44.2820 | + | 108.515i | −0.385061 | + | 0.943608i | ||||
\(116\) | −41.4745 | + | 71.8359i | −0.357538 | + | 0.619275i | ||||
\(117\) | −11.8323 | + | 44.1589i | −0.101131 | + | 0.377427i | ||||
\(118\) | 1.33171 | − | 1.33171i | 0.0112857 | − | 0.0112857i | ||||
\(119\) | 56.8455 | − | 2.96670i | 0.477693 | − | 0.0249303i | ||||
\(120\) | 14.8093 | − | 19.5112i | 0.123411 | − | 0.162593i | ||||
\(121\) | −26.5767 | − | 46.0322i | −0.219642 | − | 0.380432i | ||||
\(122\) | −81.4140 | + | 21.8148i | −0.667328 | + | 0.178810i | ||||
\(123\) | 3.27809 | + | 12.2340i | 0.0266511 | + | 0.0994634i | ||||
\(124\) | 62.6593 | − | 36.1764i | 0.505317 | − | 0.291745i | ||||
\(125\) | −46.0099 | + | 116.224i | −0.368079 | + | 0.929794i | ||||
\(126\) | −1.54783 | − | 29.6581i | −0.0122843 | − | 0.235382i | ||||
\(127\) | −111.649 | − | 111.649i | −0.879125 | − | 0.879125i | 0.114319 | − | 0.993444i | \(-0.463531\pi\) |
−0.993444 | + | 0.114319i | \(0.963531\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | −103.321 | − | 59.6525i | −0.800939 | − | 0.462422i | ||||
\(130\) | −99.3349 | + | 41.7584i | −0.764115 | + | 0.321219i | ||||
\(131\) | 36.8045 | + | 63.7473i | 0.280951 | + | 0.486621i | 0.971619 | − | 0.236551i | \(-0.0760170\pi\) |
−0.690669 | + | 0.723171i | \(0.742684\pi\) | |||||||
\(132\) | −32.3252 | − | 32.3252i | −0.244888 | − | 0.244888i | ||||
\(133\) | −64.2587 | + | 20.8634i | −0.483148 | + | 0.156868i | ||||
\(134\) | − | 172.314i | − | 1.28592i | ||||||
\(135\) | 20.5286 | − | 15.9241i | 0.152063 | − | 0.117956i | ||||
\(136\) | 11.5001 | − | 19.9188i | 0.0845599 | − | 0.146462i | ||||
\(137\) | −230.343 | + | 61.7203i | −1.68134 | + | 0.450513i | −0.968132 | − | 0.250440i | \(-0.919425\pi\) |
−0.713207 | + | 0.700953i | \(0.752758\pi\) | |||||||
\(138\) | 55.4607 | + | 14.8607i | 0.401889 | + | 0.107686i | ||||
\(139\) | 185.128i | 1.33186i | 0.746015 | + | 0.665930i | \(0.231965\pi\) | ||||
−0.746015 | + | 0.665930i | \(0.768035\pi\) | |||||||
\(140\) | 52.9989 | − | 45.7287i | 0.378564 | − | 0.326634i | ||||
\(141\) | −93.1794 | −0.660847 | ||||||||
\(142\) | −30.2631 | + | 112.943i | −0.213120 | + | 0.795376i | ||||
\(143\) | 52.0494 | + | 194.251i | 0.363982 | + | 1.35840i | ||||
\(144\) | −10.3923 | − | 6.00000i | −0.0721688 | − | 0.0416667i | ||||
\(145\) | −205.738 | − | 25.9873i | −1.41888 | − | 0.179223i | ||||
\(146\) | −72.5707 | −0.497060 | ||||||||
\(147\) | 13.3133 | − | 83.8198i | 0.0905664 | − | 0.570203i | ||||
\(148\) | −6.86455 | + | 6.86455i | −0.0463821 | + | 0.0463821i | ||||
\(149\) | 43.7077 | − | 25.2346i | 0.293340 | − | 0.169360i | −0.346107 | − | 0.938195i | \(-0.612497\pi\) |
0.639447 | + | 0.768835i | \(0.279163\pi\) | |||||||
\(150\) | 59.3139 | + | 15.2272i | 0.395426 | + | 0.101514i | ||||
\(151\) | −16.5824 | + | 28.7216i | −0.109817 | + | 0.190209i | −0.915696 | − | 0.401871i | \(-0.868360\pi\) |
0.805879 | + | 0.592080i | \(0.201693\pi\) | |||||||
\(152\) | −7.06542 | + | 26.3685i | −0.0464830 | + | 0.173477i | ||||
\(153\) | 17.2502 | − | 17.2502i | 0.112747 | − | 0.112747i | ||||
\(154\) | −71.1282 | − | 109.580i | −0.461871 | − | 0.711560i | ||||
\(155\) | 144.080 | + | 109.359i | 0.929546 | + | 0.705540i | ||||
\(156\) | 26.3945 | + | 45.7167i | 0.169196 | + | 0.293056i | ||||
\(157\) | 218.642 | − | 58.5850i | 1.39262 | − | 0.373153i | 0.516934 | − | 0.856025i | \(-0.327073\pi\) |
0.875690 | + | 0.482873i | \(0.160407\pi\) | |||||||
\(158\) | −11.1321 | − | 41.5456i | −0.0704564 | − | 0.262947i | ||||
\(159\) | −70.5948 | + | 40.7579i | −0.443992 | + | 0.256339i | ||||
\(160\) | −3.83907 | − | 28.0225i | −0.0239942 | − | 0.175141i | ||||
\(161\) | 146.183 | + | 74.5241i | 0.907969 | + | 0.462883i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −166.784 | − | 44.6896i | −1.02321 | − | 0.274169i | −0.292073 | − | 0.956396i | \(-0.594345\pi\) |
−0.731141 | + | 0.682227i | \(0.761012\pi\) | |||||||
\(164\) | 12.6656 | + | 7.31247i | 0.0772291 | + | 0.0445882i | ||||
\(165\) | 43.1806 | − | 105.816i | 0.261700 | − | 0.641307i | ||||
\(166\) | 32.2690 | + | 55.8916i | 0.194392 | + | 0.336697i | ||||
\(167\) | −158.459 | − | 158.459i | −0.948854 | − | 0.948854i | 0.0498998 | − | 0.998754i | \(-0.484110\pi\) |
−0.998754 | + | 0.0498998i | \(0.984110\pi\) | |||||||
\(168\) | −25.4795 | − | 22.9520i | −0.151664 | − | 0.136619i | ||||
\(169\) | − | 63.2238i | − | 0.374105i | ||||||
\(170\) | 57.0474 | + | 7.20583i | 0.335573 | + | 0.0423872i | ||||
\(171\) | −14.4773 | + | 25.0755i | −0.0846627 | + | 0.146640i | ||||
\(172\) | −133.067 | + | 35.6553i | −0.773648 | + | 0.207298i | ||||
\(173\) | 40.8069 | + | 10.9342i | 0.235878 | + | 0.0632033i | 0.374822 | − | 0.927097i | \(-0.377704\pi\) |
−0.138944 | + | 0.990300i | \(0.544371\pi\) | |||||||
\(174\) | 101.591i | 0.583858i | ||||||||
\(175\) | 156.735 | + | 77.8403i | 0.895629 | + | 0.444802i | ||||
\(176\) | −52.7869 | −0.299925 | ||||||||
\(177\) | 0.596991 | − | 2.22800i | 0.00337283 | − | 0.0125876i | ||||
\(178\) | −8.09545 | − | 30.2126i | −0.0454800 | − | 0.169734i | ||||
\(179\) | −294.348 | − | 169.942i | −1.64440 | − | 0.949398i | −0.979241 | − | 0.202700i | \(-0.935028\pi\) |
−0.665164 | − | 0.746697i | \(-0.731638\pi\) | |||||||
\(180\) | 3.75951 | − | 29.7635i | 0.0208862 | − | 0.165353i | ||||
\(181\) | 37.6015 | 0.207743 | 0.103871 | − | 0.994591i | \(-0.466877\pi\) | ||||
0.103871 | + | 0.994591i | \(0.466877\pi\) | |||||||
\(182\) | 46.5862 | + | 143.484i | 0.255968 | + | 0.788374i | ||||
\(183\) | −72.9938 | + | 72.9938i | −0.398873 | + | 0.398873i | ||||
\(184\) | 57.4172 | − | 33.1498i | 0.312050 | − | 0.180162i | ||||
\(185\) | −22.4709 | − | 9.16978i | −0.121464 | − | 0.0495664i | ||||
\(186\) | 44.3068 | − | 76.7417i | 0.238209 | − | 0.412590i | ||||
\(187\) | 27.7748 | − | 103.657i | 0.148528 | − | 0.554315i | ||||
\(188\) | −76.0807 | + | 76.0807i | −0.404685 | + | 0.404685i | ||||
\(189\) | −19.8035 | − | 30.5093i | −0.104781 | − | 0.161425i | ||||
\(190\) | −67.6152 | + | 9.26324i | −0.355869 | + | 0.0487539i | ||||
\(191\) | 141.603 | + | 245.263i | 0.741375 | + | 1.28410i | 0.951870 | + | 0.306503i | \(0.0991591\pi\) |
−0.210495 | + | 0.977595i | \(0.567508\pi\) | |||||||
\(192\) | −13.3843 | + | 3.58630i | −0.0697097 | + | 0.0186787i | ||||
\(193\) | −40.9517 | − | 152.834i | −0.212185 | − | 0.791885i | −0.987139 | − | 0.159867i | \(-0.948894\pi\) |
0.774954 | − | 0.632018i | \(-0.217773\pi\) | |||||||
\(194\) | 222.819 | − | 128.645i | 1.14855 | − | 0.663116i | ||||
\(195\) | −79.7889 | + | 105.121i | −0.409174 | + | 0.539084i | ||||
\(196\) | −57.5683 | − | 79.3088i | −0.293716 | − | 0.404637i | ||||
\(197\) | 188.004 | + | 188.004i | 0.954337 | + | 0.954337i | 0.999002 | − | 0.0446654i | \(-0.0142222\pi\) |
−0.0446654 | + | 0.999002i | \(0.514222\pi\) | |||||||
\(198\) | −54.0812 | − | 14.4910i | −0.273137 | − | 0.0731869i | ||||
\(199\) | −4.52064 | − | 2.60999i | −0.0227168 | − | 0.0131155i | 0.488599 | − | 0.872509i | \(-0.337508\pi\) |
−0.511315 | + | 0.859393i | \(0.670842\pi\) | |||||||
\(200\) | 60.8625 | − | 35.9966i | 0.304312 | − | 0.179983i | ||||
\(201\) | −105.520 | − | 182.766i | −0.524976 | − | 0.909284i | ||||
\(202\) | −50.8693 | − | 50.8693i | −0.251828 | − | 0.251828i | ||||
\(203\) | −60.4232 | + | 283.964i | −0.297651 | + | 1.39884i | ||||
\(204\) | − | 28.1695i | − | 0.138086i | ||||||
\(205\) | −4.58189 | + | 36.2741i | −0.0223507 | + | 0.176947i | ||||
\(206\) | 86.7199 | − | 150.203i | 0.420970 | − | 0.729142i | ||||
\(207\) | 67.9252 | − | 18.2005i | 0.328141 | − | 0.0879252i | ||||
\(208\) | 58.8786 | + | 15.7765i | 0.283070 | + | 0.0758484i | ||||
\(209\) | 127.369i | 0.609420i | ||||||||
\(210\) | 28.2108 | − | 80.9577i | 0.134337 | − | 0.385513i | ||||
\(211\) | 49.9660 | 0.236806 | 0.118403 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118403 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(212\) | −24.3617 | + | 90.9191i | −0.114914 | + | 0.428864i | ||||
\(213\) | 37.0646 | + | 138.327i | 0.174012 | + | 0.649422i | ||||
\(214\) | 237.424 | + | 137.077i | 1.10946 | + | 0.640545i | ||||
\(215\) | −211.092 | − | 272.129i | −0.981823 | − | 1.26572i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 169.488 | − | 188.153i | 0.781051 | − | 0.867065i | ||||
\(218\) | −67.4320 | + | 67.4320i | −0.309321 | + | 0.309321i | ||||
\(219\) | −76.9729 | + | 44.4403i | −0.351474 | + | 0.202924i | ||||
\(220\) | −51.1413 | − | 121.655i | −0.232461 | − | 0.552977i | ||||
\(221\) | −61.9601 | + | 107.318i | −0.280362 | + | 0.485602i | ||||
\(222\) | −3.07730 | + | 11.4846i | −0.0138617 | + | 0.0517325i | ||||
\(223\) | 211.407 | − | 211.407i | 0.948013 | − | 0.948013i | −0.0507005 | − | 0.998714i | \(-0.516145\pi\) |
0.998714 | + | 0.0507005i | \(0.0161454\pi\) | |||||||
\(224\) | −39.5442 | + | 2.06377i | −0.176536 | + | 0.00921324i | ||||
\(225\) | 72.2365 | − | 20.1713i | 0.321051 | − | 0.0896504i | ||||
\(226\) | −85.9828 | − | 148.927i | −0.380455 | − | 0.658967i | ||||
\(227\) | −43.7476 | + | 11.7221i | −0.192721 | + | 0.0516393i | −0.353888 | − | 0.935288i | \(-0.615141\pi\) |
0.161168 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(228\) | 8.65334 | + | 32.2947i | 0.0379532 | + | 0.141643i | ||||
\(229\) | 84.7804 | − | 48.9480i | 0.370220 | − | 0.213747i | −0.303335 | − | 0.952884i | \(-0.598100\pi\) |
0.673555 | + | 0.739138i | \(0.264767\pi\) | |||||||
\(230\) | 132.026 | + | 100.210i | 0.574025 | + | 0.435694i | ||||
\(231\) | −142.547 | − | 72.6704i | −0.617085 | − | 0.314590i | ||||
\(232\) | 82.9489 | + | 82.9489i | 0.357538 | + | 0.357538i | ||||
\(233\) | 176.069 | + | 47.1774i | 0.755659 | + | 0.202478i | 0.616027 | − | 0.787725i | \(-0.288741\pi\) |
0.139632 | + | 0.990203i | \(0.455408\pi\) | |||||||
\(234\) | 55.9913 | + | 32.3266i | 0.239279 | + | 0.138148i | ||||
\(235\) | −249.048 | − | 101.630i | −1.05978 | − | 0.432467i | ||||
\(236\) | −1.33171 | − | 2.30660i | −0.00564286 | − | 0.00977372i | ||||
\(237\) | −37.2488 | − | 37.2488i | −0.157168 | − | 0.157168i | ||||
\(238\) | 16.7543 | − | 78.7382i | 0.0703962 | − | 0.330833i | ||||
\(239\) | − | 68.1419i | − | 0.285112i | −0.989787 | − | 0.142556i | \(-0.954468\pi\) | ||
0.989787 | − | 0.142556i | \(-0.0455322\pi\) | |||||||
\(240\) | −21.2322 | − | 27.3714i | −0.0884674 | − | 0.114048i | ||||
\(241\) | 136.691 | − | 236.756i | 0.567183 | − | 0.982389i | −0.429660 | − | 0.902991i | \(-0.641367\pi\) |
0.996843 | − | 0.0793984i | \(-0.0252999\pi\) | |||||||
\(242\) | −72.6089 | + | 19.4555i | −0.300037 | + | 0.0803946i | ||||
\(243\) | −15.0573 | − | 4.03459i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 119.198i | 0.488518i | ||||||||
\(245\) | 127.005 | − | 209.511i | 0.518387 | − | 0.855146i | ||||
\(246\) | 17.9118 | 0.0728123 | ||||||||
\(247\) | 38.0668 | − | 142.067i | 0.154117 | − | 0.575171i | ||||
\(248\) | −26.4829 | − | 98.8357i | −0.106786 | − | 0.398531i | ||||
\(249\) | 68.4530 | + | 39.5214i | 0.274912 | + | 0.158720i | ||||
\(250\) | 141.925 | + | 105.392i | 0.567698 | + | 0.421567i | ||||
\(251\) | 102.144 | 0.406947 | 0.203473 | − | 0.979081i | \(-0.434777\pi\) | ||||
0.203473 | + | 0.979081i | \(0.434777\pi\) | |||||||
\(252\) | −41.0803 | − | 8.74126i | −0.163017 | − | 0.0346875i | ||||
\(253\) | 218.734 | − | 218.734i | 0.864563 | − | 0.864563i | ||||
\(254\) | −193.381 | + | 111.649i | −0.761344 | + | 0.439562i | ||||
\(255\) | 64.9206 | − | 27.2913i | 0.254591 | − | 0.107025i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 92.3792 | − | 344.764i | 0.359452 | − | 1.34149i | −0.515336 | − | 0.856988i | \(-0.672333\pi\) |
0.874788 | − | 0.484506i | \(-0.161000\pi\) | |||||||
\(258\) | −119.305 | + | 119.305i | −0.462422 | + | 0.462422i | ||||
\(259\) | −15.4322 | + | 30.2711i | −0.0595838 | + | 0.116877i | ||||
\(260\) | 20.6840 | + | 150.979i | 0.0795538 | + | 0.580687i | ||||
\(261\) | 62.2117 | + | 107.754i | 0.238359 | + | 0.412850i | ||||
\(262\) | 100.552 | − | 26.9428i | 0.383786 | − | 0.102835i | ||||
\(263\) | 50.0033 | + | 186.615i | 0.190126 | + | 0.709562i | 0.993475 | + | 0.114052i | \(0.0363831\pi\) |
−0.803348 | + | 0.595509i | \(0.796950\pi\) | |||||||
\(264\) | −55.9889 | + | 32.3252i | −0.212079 | + | 0.122444i | ||||
\(265\) | −233.138 | + | 31.9398i | −0.879767 | + | 0.120528i | ||||
\(266\) | 4.97963 | + | 95.4156i | 0.0187204 | + | 0.358705i | ||||
\(267\) | −27.0879 | − | 27.0879i | −0.101453 | − | 0.101453i | ||||
\(268\) | −235.385 | − | 63.0712i | −0.878301 | − | 0.235340i | ||||
\(269\) | 244.880 | + | 141.381i | 0.910334 | + | 0.525582i | 0.880539 | − | 0.473974i | \(-0.157181\pi\) |
0.0297956 | + | 0.999556i | \(0.490514\pi\) | |||||||
\(270\) | −14.2388 | − | 33.8712i | −0.0527362 | − | 0.125449i | ||||
\(271\) | 256.230 | + | 443.803i | 0.945497 | + | 1.63765i | 0.754752 | + | 0.656010i | \(0.227757\pi\) |
0.190745 | + | 0.981640i | \(0.438910\pi\) | |||||||
\(272\) | −23.0003 | − | 23.0003i | −0.0845599 | − | 0.0845599i | ||||
\(273\) | 137.278 | + | 123.660i | 0.502849 | + | 0.452966i | ||||
\(274\) | 337.246i | 1.23083i | ||||||||
\(275\) | 230.824 | − | 235.725i | 0.839360 | − | 0.857181i | ||||
\(276\) | 40.6001 | − | 70.3214i | 0.147102 | − | 0.254788i | ||||
\(277\) | 128.464 | − | 34.4217i | 0.463767 | − | 0.124266i | −0.0193668 | − | 0.999812i | \(-0.506165\pi\) |
0.483134 | + | 0.875546i | \(0.339498\pi\) | |||||||
\(278\) | 252.890 | + | 67.7617i | 0.909677 | + | 0.243747i | ||||
\(279\) | − | 108.529i | − | 0.388993i | ||||||
\(280\) | −43.0677 | − | 89.1357i | −0.153813 | − | 0.318342i | ||||
\(281\) | 456.720 | 1.62534 | 0.812670 | − | 0.582724i | \(-0.198013\pi\) | ||||
0.812670 | + | 0.582724i | \(0.198013\pi\) | |||||||
\(282\) | −34.1060 | + | 127.285i | −0.120943 | + | 0.451367i | ||||
\(283\) | 24.2323 | + | 90.4360i | 0.0856264 | + | 0.319562i | 0.995432 | − | 0.0954725i | \(-0.0304362\pi\) |
−0.909806 | + | 0.415034i | \(0.863770\pi\) | |||||||
\(284\) | 143.207 | + | 82.6803i | 0.504248 | + | 0.291128i | ||||
\(285\) | −66.0441 | + | 51.2308i | −0.231734 | + | 0.179757i | ||||
\(286\) | 284.403 | 0.994417 | ||||||||
\(287\) | 50.0664 | + | 10.6534i | 0.174447 | + | 0.0371197i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | −193.014 | + | 111.437i | −0.667868 | + | 0.385594i | ||||
\(290\) | −110.804 | + | 271.531i | −0.382084 | + | 0.936313i | ||||
\(291\) | 157.557 | − | 272.896i | 0.541432 | − | 0.937788i | ||||
\(292\) | −26.5627 | + | 99.1334i | −0.0909682 | + | 0.339498i | ||||
\(293\) | 41.1011 | − | 41.1011i | 0.140277 | − | 0.140277i | −0.633481 | − | 0.773758i | \(-0.718375\pi\) |
0.773758 | + | 0.633481i | \(0.218375\pi\) | |||||||
\(294\) | −109.627 | − | 48.8664i | −0.372881 | − | 0.166212i | ||||
\(295\) | 4.02568 | − | 5.30382i | 0.0136464 | − | 0.0179790i | ||||
\(296\) | 6.86455 | + | 11.8898i | 0.0231911 | + | 0.0401681i | ||||
\(297\) | −66.2356 | + | 17.7478i | −0.223016 | + | 0.0597568i | ||||
\(298\) | −18.4730 | − | 68.9423i | −0.0619900 | − | 0.231350i | ||||
\(299\) | −309.350 | + | 178.603i | −1.03462 | + | 0.597335i | ||||
\(300\) | 42.5111 | − | 75.4507i | 0.141704 | − | 0.251502i | ||||
\(301\) | −404.435 | + | 262.518i | −1.34364 | + | 0.872152i | ||||
\(302\) | 33.1648 | + | 33.1648i | 0.109817 | + | 0.109817i | ||||
\(303\) | −85.1060 | − | 22.8041i | −0.280878 | − | 0.0752610i | ||||
\(304\) | 33.4339 | + | 19.3031i | 0.109980 | + | 0.0634970i | ||||
\(305\) | −274.710 | + | 115.483i | −0.900688 | + | 0.378631i | ||||
\(306\) | −17.2502 | − | 29.8783i | −0.0563733 | − | 0.0976414i | ||||
\(307\) | −219.450 | − | 219.450i | −0.714822 | − | 0.714822i | 0.252718 | − | 0.967540i | \(-0.418676\pi\) |
−0.967540 | + | 0.252718i | \(0.918676\pi\) | |||||||
\(308\) | −175.724 | + | 57.0538i | −0.570533 | + | 0.185240i | ||||
\(309\) | − | 212.419i | − | 0.687442i | ||||||
\(310\) | 202.124 | − | 156.788i | 0.652011 | − | 0.505769i | ||||
\(311\) | 239.292 | − | 414.465i | 0.769427 | − | 1.33269i | −0.168447 | − | 0.985711i | \(-0.553875\pi\) |
0.937874 | − | 0.346976i | \(-0.112791\pi\) | |||||||
\(312\) | 72.1112 | − | 19.3221i | 0.231126 | − | 0.0619299i | ||||
\(313\) | −370.684 | − | 99.3245i | −1.18429 | − | 0.317331i | −0.387666 | − | 0.921800i | \(-0.626718\pi\) |
−0.796628 | + | 0.604470i | \(0.793385\pi\) | |||||||
\(314\) | − | 320.114i | − | 1.01947i | ||||||
\(315\) | −19.6542 | − | 103.144i | −0.0623943 | − | 0.327442i | ||||
\(316\) | −60.8270 | −0.192490 | ||||||||
\(317\) | −37.9902 | + | 141.782i | −0.119843 | + | 0.447260i | −0.999604 | − | 0.0281569i | \(-0.991036\pi\) |
0.879760 | + | 0.475417i | \(0.157703\pi\) | |||||||
\(318\) | 29.8369 | + | 111.353i | 0.0938267 | + | 0.350166i | ||||
\(319\) | 473.999 | + | 273.663i | 1.48589 | + | 0.857879i | ||||
\(320\) | −39.6847 | − | 5.01269i | −0.124015 | − | 0.0156646i | ||||
\(321\) | 335.768 | 1.04601 | ||||||||
\(322\) | 155.309 | − | 172.412i | 0.482325 | − | 0.535441i | ||||
\(323\) | −55.4971 | + | 55.4971i | −0.171818 | + | 0.171818i | ||||
\(324\) | −15.5885 | + | 9.00000i | −0.0481125 | + | 0.0277778i | ||||
\(325\) | −327.913 | + | 193.941i | −1.00896 | + | 0.596742i | ||||
\(326\) | −122.094 | + | 211.473i | −0.374522 | + | 0.648692i | ||||
\(327\) | −30.2289 | + | 112.816i | −0.0924432 | + | 0.345003i | ||||
\(328\) | 14.6249 | − | 14.6249i | 0.0445882 | − | 0.0445882i | ||||
\(329\) | −171.037 | + | 335.498i | −0.519870 | + | 1.01975i | ||||
\(330\) | −128.742 | − | 97.7169i | −0.390126 | − | 0.296112i | ||||
\(331\) | 29.0788 | + | 50.3660i | 0.0878515 | + | 0.152163i | 0.906603 | − | 0.421985i | \(-0.138667\pi\) |
−0.818751 | + | 0.574148i | \(0.805333\pi\) | |||||||
\(332\) | 88.1607 | − | 23.6226i | 0.265544 | − | 0.0711524i | ||||
\(333\) | 3.76890 | + | 14.0657i | 0.0113180 | + | 0.0422394i | ||||
\(334\) | −274.459 | + | 158.459i | −0.821732 | + | 0.474427i | ||||
\(335\) | −82.6905 | − | 603.583i | −0.246837 | − | 1.80174i | ||||
\(336\) | −40.6791 | + | 26.4047i | −0.121069 | + | 0.0785854i | ||||
\(337\) | −296.066 | − | 296.066i | −0.878534 | − | 0.878534i | 0.114849 | − | 0.993383i | \(-0.463362\pi\) |
−0.993383 | + | 0.114849i | \(0.963362\pi\) | |||||||
\(338\) | −86.3653 | − | 23.1415i | −0.255519 | − | 0.0684660i | ||||
\(339\) | −182.397 | − | 105.307i | −0.538045 | − | 0.310640i | ||||
\(340\) | 30.7242 | − | 75.2907i | 0.0903652 | − | 0.221443i | ||||
\(341\) | −238.705 | − | 413.449i | −0.700014 | − | 1.21246i | ||||
\(342\) | 28.9546 | + | 28.9546i | 0.0846627 | + | 0.0846627i | ||||
\(343\) | −277.361 | − | 201.792i | −0.808632 | − | 0.588315i | ||||
\(344\) | 194.824i | 0.566350i | ||||||||
\(345\) | 201.400 | + | 25.4394i | 0.583768 | + | 0.0737375i | ||||
\(346\) | 29.8727 | − | 51.7411i | 0.0863373 | − | 0.149541i | ||||
\(347\) | 124.162 | − | 33.2690i | 0.357814 | − | 0.0958760i | −0.0754337 | − | 0.997151i | \(-0.524034\pi\) |
0.433248 | + | 0.901275i | \(0.357367\pi\) | |||||||
\(348\) | 138.776 | + | 37.1850i | 0.398782 | + | 0.106853i | ||||
\(349\) | 335.241i | 0.960576i | 0.877111 | + | 0.480288i | \(0.159468\pi\) | ||||
−0.877111 | + | 0.480288i | \(0.840532\pi\) | |||||||
\(350\) | 163.701 | − | 185.613i | 0.467717 | − | 0.530322i | ||||
\(351\) | 79.1836 | 0.225594 | ||||||||
\(352\) | −19.3213 | + | 72.1082i | −0.0548902 | + | 0.204853i | ||||
\(353\) | 7.50598 | + | 28.0127i | 0.0212634 | + | 0.0793561i | 0.975742 | − | 0.218923i | \(-0.0702542\pi\) |
−0.954479 | + | 0.298279i | \(0.903588\pi\) | |||||||
\(354\) | −2.82499 | − | 1.63101i | −0.00798021 | − | 0.00460737i | ||||
\(355\) | −51.8063 | + | 410.143i | −0.145933 | + | 1.15533i | ||||
\(356\) | −44.2343 | −0.124254 | ||||||||
\(357\) | −30.4465 | − | 93.7744i | −0.0852844 | − | 0.262673i | ||||
\(358\) | −339.884 | + | 339.884i | −0.949398 | + | 0.949398i | ||||
\(359\) | 237.071 | − | 136.873i | 0.660366 | − | 0.381262i | −0.132050 | − | 0.991243i | \(-0.542156\pi\) |
0.792416 | + | 0.609981i | \(0.208823\pi\) | |||||||
\(360\) | −39.2816 | − | 16.0298i | −0.109116 | − | 0.0445272i | ||||
\(361\) | −133.924 | + | 231.963i | −0.370980 | + | 0.642556i | ||||
\(362\) | 13.7631 | − | 51.3646i | 0.0380196 | − | 0.141891i | ||||
\(363\) | −65.0994 | + | 65.0994i | −0.179337 | + | 0.179337i | ||||
\(364\) | 213.055 | − | 11.1191i | 0.585315 | − | 0.0305469i | ||||
\(365\) | −254.202 | + | 34.8255i | −0.696443 | + | 0.0954123i | ||||
\(366\) | 72.9938 | + | 126.429i | 0.199437 | + | 0.345434i | ||||
\(367\) | −273.270 | + | 73.2224i | −0.744604 | + | 0.199516i | −0.611123 | − | 0.791535i | \(-0.709282\pi\) |
−0.133481 | + | 0.991051i | \(0.542615\pi\) | |||||||
\(368\) | −24.2673 | − | 90.5670i | −0.0659439 | − | 0.246106i | ||||
\(369\) | 18.9984 | − | 10.9687i | 0.0514860 | − | 0.0297255i | ||||
\(370\) | −20.7511 | + | 27.3394i | −0.0560840 | + | 0.0738904i | ||||
\(371\) | 17.1699 | + | 328.995i | 0.0462800 | + | 0.886778i | ||||
\(372\) | −88.6137 | − | 88.6137i | −0.238209 | − | 0.238209i | ||||
\(373\) | −324.416 | − | 86.9270i | −0.869747 | − | 0.233048i | −0.203769 | − | 0.979019i | \(-0.565319\pi\) |
−0.665979 | + | 0.745971i | \(0.731986\pi\) | |||||||
\(374\) | −131.432 | − | 75.8821i | −0.351422 | − | 0.202893i | ||||
\(375\) | 215.073 | + | 24.8742i | 0.573527 | + | 0.0663311i | ||||
\(376\) | 76.0807 | + | 131.776i | 0.202342 | + | 0.350467i | ||||
\(377\) | −446.909 | − | 446.909i | −1.18544 | − | 1.18544i | ||||
\(378\) | −48.9251 | + | 15.8849i | −0.129432 | + | 0.0420236i | ||||
\(379\) | − | 479.313i | − | 1.26468i | −0.774692 | − | 0.632339i | \(-0.782095\pi\) | ||
0.774692 | − | 0.632339i | \(-0.217905\pi\) | |||||||
\(380\) | −12.0950 | + | 95.7546i | −0.0318291 | + | 0.251986i | ||||
\(381\) | −136.741 | + | 236.843i | −0.358901 | + | 0.621635i | ||||
\(382\) | 386.865 | − | 103.660i | 1.01274 | − | 0.271362i | ||||
\(383\) | −394.771 | − | 105.779i | −1.03073 | − | 0.276184i | −0.296465 | − | 0.955044i | \(-0.595808\pi\) |
−0.734268 | + | 0.678859i | \(0.762475\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −301.735 | − | 349.706i | −0.783726 | − | 0.908327i | ||||
\(386\) | −223.764 | −0.579700 | ||||||||
\(387\) | −53.4830 | + | 199.601i | −0.138199 | + | 0.515765i | ||||
\(388\) | −94.1744 | − | 351.464i | −0.242717 | − | 0.905834i | ||||
\(389\) | −427.944 | − | 247.074i | −1.10011 | − | 0.635151i | −0.163863 | − | 0.986483i | \(-0.552395\pi\) |
−0.936251 | + | 0.351332i | \(0.885729\pi\) | |||||||
\(390\) | 114.394 | + | 147.471i | 0.293318 | + | 0.378130i | ||||
\(391\) | 190.614 | 0.487504 | ||||||||
\(392\) | −129.409 | + | 49.6108i | −0.330126 | + | 0.126558i | ||||
\(393\) | 90.1523 | − | 90.1523i | 0.229395 | − | 0.229395i | ||||
\(394\) | 325.633 | − | 188.004i | 0.826480 | − | 0.477168i | ||||
\(395\) | −58.9308 | − | 140.184i | −0.149192 | − | 0.354897i | ||||
\(396\) | −39.5902 | + | 68.5722i | −0.0999752 | + | 0.173162i | ||||
\(397\) | −149.301 | + | 557.198i | −0.376073 | + | 1.40352i | 0.475699 | + | 0.879608i | \(0.342195\pi\) |
−0.851771 | + | 0.523914i | \(0.824471\pi\) | |||||||
\(398\) | −5.21998 | + | 5.21998i | −0.0131155 | + | 0.0131155i | ||||
\(399\) | 63.7116 | + | 98.1541i | 0.159678 | + | 0.246000i | ||||
\(400\) | −26.8951 | − | 96.3154i | −0.0672378 | − | 0.240788i | ||||
\(401\) | −200.253 | − | 346.849i | −0.499384 | − | 0.864959i | 0.500615 | − | 0.865670i | \(-0.333107\pi\) |
−1.00000 | 0.000710769i | \(0.999774\pi\) | ||||||||
\(402\) | −288.286 | + | 77.2461i | −0.717130 | + | 0.192154i | ||||
\(403\) | 142.684 | + | 532.503i | 0.354054 | + | 1.32135i | ||||
\(404\) | −88.1083 | + | 50.8693i | −0.218090 | + | 0.125914i | ||||
\(405\) | −35.8443 | − | 27.2064i | −0.0885044 | − | 0.0671762i | ||||
\(406\) | 365.785 | + | 186.478i | 0.900949 | + | 0.459304i | ||||
\(407\) | 45.2948 | + | 45.2948i | 0.111289 | + | 0.111289i | ||||
\(408\) | −38.4802 | − | 10.3107i | −0.0943143 | − | 0.0252714i | ||||
\(409\) | 579.420 | + | 334.528i | 1.41667 | + | 0.817917i | 0.996005 | − | 0.0892974i | \(-0.0284621\pi\) |
0.420669 | + | 0.907214i | \(0.361795\pi\) | |||||||
\(410\) | 47.8743 | + | 19.5362i | 0.116767 | + | 0.0476493i | ||||
\(411\) | 206.520 | + | 357.704i | 0.502482 | + | 0.870325i | ||||
\(412\) | −173.440 | − | 173.440i | −0.420970 | − | 0.420970i | ||||
\(413\) | −6.92624 | − | 6.23915i | −0.0167705 | − | 0.0151069i | ||||
\(414\) | − | 99.4494i | − | 0.240216i | ||||||
\(415\) | 139.854 | + | 180.293i | 0.336998 | + | 0.434440i | ||||
\(416\) | 43.1021 | − | 74.6550i | 0.103611 | − | 0.179459i | ||||
\(417\) | 309.726 | − | 82.9908i | 0.742748 | − | 0.199019i | ||||
\(418\) | 173.989 | + | 46.6202i | 0.416241 | + | 0.111532i | ||||
\(419\) | − | 19.3686i | − | 0.0462258i | −0.999733 | − | 0.0231129i | \(-0.992642\pi\) | ||
0.999733 | − | 0.0231129i | \(-0.00735772\pi\) | |||||||
\(420\) | −100.264 | − | 68.1692i | −0.238725 | − | 0.162308i | ||||
\(421\) | −337.581 | −0.801854 | −0.400927 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400927 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(422\) | 18.2888 | − | 68.2548i | 0.0433384 | − | 0.161741i | ||||
\(423\) | 41.7712 | + | 155.892i | 0.0987499 | + | 0.368540i | ||||
\(424\) | 115.281 | + | 66.5574i | 0.271889 | + | 0.156975i | ||||
\(425\) | 203.285 | − | 2.13546i | 0.478317 | − | 0.00502462i | ||||
\(426\) | 202.525 | 0.475410 | ||||||||
\(427\) | 128.834 | + | 396.804i | 0.301718 | + | 0.929283i | ||||
\(428\) | 274.153 | − | 274.153i | 0.640545 | − | 0.640545i | ||||
\(429\) | 301.655 | − | 174.161i | 0.703159 | − | 0.405969i | ||||
\(430\) | −449.000 | + | 188.751i | −1.04419 | + | 0.438956i | ||||
\(431\) | 123.164 | − | 213.326i | 0.285763 | − | 0.494955i | −0.687031 | − | 0.726628i | \(-0.741086\pi\) |
0.972794 | + | 0.231673i | \(0.0744198\pi\) | |||||||
\(432\) | −5.37945 | + | 20.0764i | −0.0124524 | + | 0.0464731i | ||||
\(433\) | 480.212 | − | 480.212i | 1.10904 | − | 1.10904i | 0.115758 | − | 0.993277i | \(-0.463070\pi\) |
0.993277 | − | 0.115758i | \(-0.0369298\pi\) | |||||||
\(434\) | −194.985 | − | 300.394i | −0.449274 | − | 0.692152i | ||||
\(435\) | 48.7520 | + | 355.855i | 0.112074 | + | 0.818058i | ||||
\(436\) | 67.4320 | + | 116.796i | 0.154661 | + | 0.267880i | ||||
\(437\) | −218.528 | + | 58.5544i | −0.500064 | + | 0.133992i | ||||
\(438\) | 32.5326 | + | 121.413i | 0.0742752 | + | 0.277199i | ||||
\(439\) | 309.357 | − | 178.607i | 0.704685 | − | 0.406850i | −0.104405 | − | 0.994535i | \(-0.533294\pi\) |
0.809090 | + | 0.587685i | \(0.199960\pi\) | |||||||
\(440\) | −184.903 | + | 25.3316i | −0.420233 | + | 0.0575717i | ||||
\(441\) | −146.201 | + | 15.3019i | −0.331522 | + | 0.0346981i | ||||
\(442\) | 123.920 | + | 123.920i | 0.280362 | + | 0.280362i | ||||
\(443\) | −769.781 | − | 206.262i | −1.73765 | − | 0.465603i | −0.755731 | − | 0.654883i | \(-0.772718\pi\) |
−0.981923 | + | 0.189280i | \(0.939385\pi\) | |||||||
\(444\) | 14.5619 | + | 8.40733i | 0.0327971 | + | 0.0189354i | ||||
\(445\) | −42.8554 | − | 101.944i | −0.0963043 | − | 0.229088i | ||||
\(446\) | −211.407 | − | 366.168i | −0.474007 | − | 0.821004i | ||||
\(447\) | −61.8120 | − | 61.8120i | −0.138282 | − | 0.138282i | ||||
\(448\) | −11.6550 | + | 54.7737i | −0.0260156 | + | 0.122263i | ||||
\(449\) | 838.986i | 1.86857i | 0.356531 | + | 0.934283i | \(0.383959\pi\) | ||||
−0.356531 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(450\) | −1.11414 | − | 106.060i | −0.00247587 | − | 0.235689i | ||||
\(451\) | 48.2503 | − | 83.5720i | 0.106985 | − | 0.185304i | ||||
\(452\) | −234.909 | + | 62.9438i | −0.519711 | + | 0.139256i | ||||
\(453\) | 55.4858 | + | 14.8674i | 0.122485 | + | 0.0328198i | ||||
\(454\) | 64.0509i | 0.141081i | ||||||||
\(455\) | 232.038 | + | 480.242i | 0.509974 | + | 1.05548i | ||||
\(456\) | 47.2827 | 0.103690 | ||||||||
\(457\) | −119.305 | + | 445.251i | −0.261060 | + | 0.974291i | 0.703557 | + | 0.710638i | \(0.251594\pi\) |
−0.964618 | + | 0.263652i | \(0.915073\pi\) | |||||||
\(458\) | −35.8324 | − | 133.728i | −0.0782367 | − | 0.291983i | ||||
\(459\) | −36.5932 | − | 21.1271i | −0.0797238 | − | 0.0460286i | ||||
\(460\) | 185.214 | − | 143.671i | 0.402638 | − | 0.312329i | ||||
\(461\) | 583.525 | 1.26578 | 0.632890 | − | 0.774241i | \(-0.281868\pi\) | ||||
0.632890 | + | 0.774241i | \(0.281868\pi\) | |||||||
\(462\) | −151.445 | + | 168.123i | −0.327804 | + | 0.363903i | ||||
\(463\) | 235.910 | − | 235.910i | 0.509525 | − | 0.509525i | −0.404856 | − | 0.914381i | \(-0.632678\pi\) |
0.914381 | + | 0.404856i | \(0.132678\pi\) | |||||||
\(464\) | 143.672 | − | 82.9489i | 0.309637 | − | 0.178769i | ||||
\(465\) | 118.372 | − | 290.074i | 0.254562 | − | 0.623815i | ||||
\(466\) | 128.891 | − | 223.246i | 0.276591 | − | 0.479069i | ||||
\(467\) | 59.7647 | − | 223.045i | 0.127976 | − | 0.477612i | −0.871952 | − | 0.489590i | \(-0.837146\pi\) |
0.999928 | + | 0.0119785i | \(0.00381295\pi\) | |||||||
\(468\) | 64.6531 | − | 64.6531i | 0.138148 | − | 0.138148i | ||||
\(469\) | −851.750 | + | 44.4519i | −1.81610 | + | 0.0947801i | ||||
\(470\) | −229.987 | + | 303.006i | −0.489333 | + | 0.644695i | ||||
\(471\) | −196.029 | − | 339.532i | −0.416198 | − | 0.720875i | ||||
\(472\) | −3.63831 | + | 0.974883i | −0.00770829 | + | 0.00206543i | ||||
\(473\) | 235.267 | + | 878.027i | 0.497392 | + | 1.85629i | ||||
\(474\) | −64.5167 | + | 37.2488i | −0.136111 | + | 0.0785839i | ||||
\(475\) | −232.398 | + | 64.8948i | −0.489259 | + | 0.136621i | ||||
\(476\) | −101.426 | − | 51.7070i | −0.213080 | − | 0.108628i | ||||
\(477\) | 99.8361 | + | 99.8361i | 0.209300 | + | 0.209300i | ||||
\(478\) | −93.0835 | − | 24.9416i | −0.194735 | − | 0.0521792i | ||||
\(479\) | 497.384 | + | 287.165i | 1.03838 | + | 0.599509i | 0.919374 | − | 0.393385i | \(-0.128696\pi\) |
0.119006 | + | 0.992894i | \(0.462029\pi\) | |||||||
\(480\) | −45.1616 | + | 18.9850i | −0.0940866 | + | 0.0395522i | ||||
\(481\) | −36.9846 | − | 64.0592i | −0.0768910 | − | 0.133179i | ||||
\(482\) | −273.382 | − | 273.382i | −0.567183 | − | 0.567183i | ||||
\(483\) | 59.1493 | − | 277.977i | 0.122462 | − | 0.575522i | ||||
\(484\) | 106.307i | 0.219642i | ||||||||
\(485\) | 718.759 | − | 557.545i | 1.48198 | − | 1.14958i | ||||
\(486\) | −11.0227 | + | 19.0919i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 737.079 | − | 197.500i | 1.51351 | − | 0.405544i | 0.595911 | − | 0.803051i | \(-0.296791\pi\) |
0.917599 | + | 0.397507i | \(0.130125\pi\) | |||||||
\(488\) | 162.828 | + | 43.6297i | 0.333664 | + | 0.0894050i | ||||
\(489\) | 299.069i | 0.611592i | ||||||||
\(490\) | −239.710 | − | 250.178i | −0.489205 | − | 0.510567i | ||||
\(491\) | 267.633 | 0.545077 | 0.272538 | − | 0.962145i | \(-0.412137\pi\) | ||||
0.272538 | + | 0.962145i | \(0.412137\pi\) | |||||||
\(492\) | 6.55618 | − | 24.4680i | 0.0133256 | − | 0.0497317i | ||||
\(493\) | 87.2902 | + | 325.771i | 0.177059 | + | 0.660794i | ||||
\(494\) | −180.134 | − | 104.000i | −0.364644 | − | 0.210527i | ||||
\(495\) | −196.390 | − | 24.8066i | −0.396748 | − | 0.0501144i | ||||
\(496\) | −144.705 | −0.291745 | ||||||||
\(497\) | 566.089 | + | 120.455i | 1.13901 | + | 0.242364i | ||||
\(498\) | 79.0427 | − | 79.0427i | 0.158720 | − | 0.158720i | ||||
\(499\) | 328.627 | − | 189.733i | 0.658572 | − | 0.380227i | −0.133161 | − | 0.991094i | \(-0.542513\pi\) |
0.791733 | + | 0.610868i | \(0.209179\pi\) | |||||||
\(500\) | 195.916 | − | 155.296i | 0.391832 | − | 0.310593i | ||||
\(501\) | −194.071 | + | 336.142i | −0.387368 | + | 0.670941i | ||||
\(502\) | 37.3871 | − | 139.531i | 0.0744764 | − | 0.277950i | ||||
\(503\) | −344.318 | + | 344.318i | −0.684530 | + | 0.684530i | −0.961017 | − | 0.276488i | \(-0.910829\pi\) |
0.276488 | + | 0.961017i | \(0.410829\pi\) | |||||||
\(504\) | −26.9772 | + | 52.9172i | −0.0535262 | + | 0.104994i | ||||
\(505\) | −202.597 | − | 153.774i | −0.401183 | − | 0.304504i | ||||
\(506\) | −218.734 | − | 378.859i | −0.432281 | − | 0.748733i | ||||
\(507\) | −105.776 | + | 28.3425i | −0.208630 | + | 0.0559023i | ||||
\(508\) | 81.7326 | + | 305.030i | 0.160891 | + | 0.600453i | ||||
\(509\) | 217.653 | − | 125.662i | 0.427608 | − | 0.246880i | −0.270719 | − | 0.962658i | \(-0.587261\pi\) |
0.698327 | + | 0.715779i | \(0.253928\pi\) | |||||||
\(510\) | −13.5181 | − | 98.6725i | −0.0265060 | − | 0.193476i | ||||
\(511\) | 18.7211 | + | 358.718i | 0.0366363 | + | 0.701993i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 48.4421 | + | 12.9800i | 0.0944290 | + | 0.0253022i | ||||
\(514\) | −437.143 | − | 252.385i | −0.850473 | − | 0.491021i | ||||
\(515\) | 231.684 | − | 567.750i | 0.449871 | − | 1.10243i | ||||
\(516\) | 119.305 | + | 206.642i | 0.231211 | + | 0.400470i | ||||
\(517\) | 502.008 | + | 502.008i | 0.971002 | + | 0.971002i | ||||
\(518\) | 35.7025 | + | 32.1608i | 0.0689237 | + | 0.0620864i | ||||
\(519\) | − | 73.1729i | − | 0.140988i | ||||||
\(520\) | 213.812 | + | 27.0072i | 0.411176 | + | 0.0519368i | ||||
\(521\) | −146.018 | + | 252.911i | −0.280266 | + | 0.485434i | −0.971450 | − | 0.237244i | \(-0.923756\pi\) |
0.691184 | + | 0.722678i | \(0.257089\pi\) | |||||||
\(522\) | 169.966 | − | 45.5421i | 0.325604 | − | 0.0872454i | ||||
\(523\) | −743.873 | − | 199.320i | −1.42232 | − | 0.381109i | −0.536014 | − | 0.844209i | \(-0.680070\pi\) |
−0.886306 | + | 0.463100i | \(0.846737\pi\) | |||||||
\(524\) | − | 147.218i | − | 0.280951i | ||||||
\(525\) | 59.9669 | − | 297.118i | 0.114223 | − | 0.565939i | ||||
\(526\) | 273.223 | 0.519435 | ||||||||
\(527\) | 76.1394 | − | 284.156i | 0.144477 | − | 0.539196i | ||||
\(528\) | 23.6637 | + | 88.3142i | 0.0448176 | + | 0.167262i | ||||
\(529\) | 17.7146 | + | 10.2276i | 0.0334870 | + | 0.0193337i | ||||
\(530\) | −41.7039 | + | 330.164i | −0.0786867 | + | 0.622950i | ||||
\(531\) | −3.99514 | −0.00752381 | ||||||||
\(532\) | 132.163 | + | 28.1222i | 0.248426 | + | 0.0528613i | ||||
\(533\) | −78.7957 | + | 78.7957i | −0.147834 | + | 0.147834i | ||||
\(534\) | −46.9176 | + | 27.0879i | −0.0878607 | + | 0.0507264i | ||||
\(535\) | 897.432 | + | 366.218i | 1.67744 | + | 0.684520i | ||||
\(536\) | −172.314 | + | 298.456i | −0.321481 | + | 0.556821i | ||||
\(537\) | −152.366 | + | 568.638i | −0.283736 | + | 1.05892i | ||||
\(538\) | 282.763 | − | 282.763i | 0.525582 | − | 0.525582i | ||||
\(539\) | −523.308 | + | 379.857i | −0.970887 | + | 0.704743i | ||||
\(540\) | −51.4807 | + | 7.05282i | −0.0953345 | + | 0.0130608i | ||||
\(541\) | 82.6003 | + | 143.068i | 0.152681 | + | 0.264451i | 0.932212 | − | 0.361912i | \(-0.117876\pi\) |
−0.779531 | + | 0.626363i | \(0.784543\pi\) | |||||||
\(542\) | 700.033 | − | 187.573i | 1.29157 | − | 0.346076i | ||||
\(543\) | −16.8563 | − | 62.9085i | −0.0310429 | − | 0.115854i | ||||
\(544\) | −39.8377 | + | 23.0003i | −0.0732310 | + | 0.0422800i | ||||
\(545\) | −203.842 | + | 268.561i | −0.374022 | + | 0.492773i | ||||
\(546\) | 219.169 | − | 142.262i | 0.401409 | − | 0.260554i | ||||
\(547\) | 172.204 | + | 172.204i | 0.314815 | + | 0.314815i | 0.846772 | − | 0.531956i | \(-0.178543\pi\) |
−0.531956 | + | 0.846772i | \(0.678543\pi\) | |||||||
\(548\) | 460.687 | + | 123.441i | 0.840670 | + | 0.225257i | ||||
\(549\) | 154.843 | + | 89.3988i | 0.282046 | + | 0.162839i | ||||
\(550\) | −237.519 | − | 401.593i | −0.431852 | − | 0.730168i | ||||
\(551\) | −200.146 | − | 346.664i | −0.363242 | − | 0.629154i | ||||
\(552\) | −81.2001 | − | 81.2001i | −0.147102 | − | 0.147102i | ||||
\(553\) | −202.489 | + | 65.7438i | −0.366164 | + | 0.118886i | ||||
\(554\) | − | 188.084i | − | 0.339501i | ||||||
\(555\) | −5.26791 | + | 41.7052i | −0.00949173 | + | 0.0751446i | ||||
\(556\) | 185.128 | − | 320.652i | 0.332965 | − | 0.576712i | ||||
\(557\) | 24.8018 | − | 6.64563i | 0.0445275 | − | 0.0119311i | −0.236487 | − | 0.971635i | \(-0.575996\pi\) |
0.281014 | + | 0.959704i | \(0.409329\pi\) | |||||||
\(558\) | −148.254 | − | 39.7244i | −0.265687 | − | 0.0711907i | ||||
\(559\) | − | 1049.67i | − | 1.87776i | ||||||
\(560\) | −137.526 | + | 26.2056i | −0.245581 | + | 0.0467957i | ||||
\(561\) | −185.872 | −0.331323 | ||||||||
\(562\) | 167.171 | − | 623.892i | 0.297458 | − | 1.11013i | ||||
\(563\) | −217.937 | − | 813.352i | −0.387100 | − | 1.44468i | −0.834831 | − | 0.550507i | \(-0.814434\pi\) |
0.447731 | − | 0.894168i | \(-0.352232\pi\) | |||||||
\(564\) | 161.392 | + | 93.1794i | 0.286155 | + | 0.165212i | ||||
\(565\) | −372.649 | − | 480.401i | −0.659557 | − | 0.850267i | ||||
\(566\) | 132.408 | 0.233936 | ||||||||
\(567\) | −42.1654 | + | 46.8089i | −0.0743659 | + | 0.0825554i | ||||
\(568\) | 165.361 | − | 165.361i | 0.291128 | − | 0.291128i | ||||
\(569\) | 88.8020 | − | 51.2699i | 0.156067 | − | 0.0901052i | −0.419933 | − | 0.907555i | \(-0.637946\pi\) |
0.576000 | + | 0.817450i | \(0.304613\pi\) | |||||||
\(570\) | 45.8087 | + | 108.970i | 0.0803662 | + | 0.191175i | ||||
\(571\) | 313.449 | − | 542.910i | 0.548947 | − | 0.950805i | −0.449400 | − | 0.893331i | \(-0.648362\pi\) |
0.998347 | − | 0.0574739i | \(-0.0183046\pi\) | |||||||
\(572\) | 104.099 | − | 388.502i | 0.181991 | − | 0.679199i | ||||
\(573\) | 346.854 | − | 346.854i | 0.605330 | − | 0.605330i | ||||
\(574\) | 32.8783 | − | 64.4926i | 0.0572793 | − | 0.112356i | ||||
\(575\) | 510.551 | + | 287.659i | 0.887914 | + | 0.500276i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −957.078 | + | 256.448i | −1.65871 | + | 0.444451i | −0.962034 | − | 0.272930i | \(-0.912007\pi\) |
−0.696681 | + | 0.717381i | \(0.745341\pi\) | |||||||
\(578\) | 81.5773 | + | 304.451i | 0.141137 | + | 0.526731i | ||||
\(579\) | −237.338 | + | 137.027i | −0.409910 | + | 0.236661i | ||||
\(580\) | 330.361 | + | 250.749i | 0.569587 | + | 0.432326i | ||||
\(581\) | 267.949 | − | 173.925i | 0.461186 | − | 0.299355i | ||||
\(582\) | −315.114 | − | 315.114i | −0.541432 | − | 0.541432i | ||||
\(583\) | 599.917 | + | 160.747i | 1.02902 | + | 0.275724i | ||||
\(584\) | 125.696 | + | 72.5707i | 0.215233 | + | 0.124265i | ||||
\(585\) | 211.640 | + | 86.3647i | 0.361778 | + | 0.147632i | ||||
\(586\) | −41.1011 | − | 71.1892i | −0.0701384 | − | 0.121483i | ||||
\(587\) | −625.656 | − | 625.656i | −1.06585 | − | 1.06585i | −0.997673 | − | 0.0681813i | \(-0.978280\pi\) |
−0.0681813 | − | 0.997673i | \(-0.521720\pi\) | |||||||
\(588\) | −106.879 | + | 131.867i | −0.181767 | + | 0.224263i | ||||
\(589\) | 349.158i | 0.592798i | ||||||||
\(590\) | −5.77165 | − | 7.44051i | −0.00978245 | − | 0.0126110i | ||||
\(591\) | 230.257 | − | 398.817i | 0.389606 | − | 0.674818i | ||||
\(592\) | 18.7543 | − | 5.02520i | 0.0316796 | − | 0.00848852i | ||||
\(593\) | 537.263 | + | 143.959i | 0.906009 | + | 0.242764i | 0.681595 | − | 0.731730i | \(-0.261287\pi\) |
0.224414 | + | 0.974494i | \(0.427953\pi\) | |||||||
\(594\) | 96.9757i | 0.163259i | ||||||||
\(595\) | 20.9020 | − | 283.846i | 0.0351294 | − | 0.477051i | ||||
\(596\) | −100.938 | −0.169360 | ||||||||
\(597\) | −2.34005 | + | 8.73320i | −0.00391969 | + | 0.0146285i | ||||
\(598\) | 130.747 | + | 487.953i | 0.218640 | + | 0.815975i | ||||
\(599\) | −179.972 | − | 103.907i | −0.300454 | − | 0.173467i | 0.342193 | − | 0.939630i | \(-0.388830\pi\) |
−0.642647 | + | 0.766163i | \(0.722164\pi\) | |||||||
\(600\) | −87.5075 | − | 85.6881i | −0.145846 | − | 0.142813i | ||||
\(601\) | −803.576 | −1.33707 | −0.668533 | − | 0.743683i | \(-0.733077\pi\) | ||||
−0.668533 | + | 0.743683i | \(0.733077\pi\) | |||||||
\(602\) | 210.572 | + | 648.557i | 0.349788 | + | 1.07734i | ||||
\(603\) | −258.470 | + | 258.470i | −0.428641 | + | 0.428641i | ||||
\(604\) | 57.4431 | − | 33.1648i | 0.0951045 | − | 0.0549086i | ||||
\(605\) | −244.999 | + | 102.993i | −0.404957 | + | 0.170236i | ||||
\(606\) | −62.3019 | + | 107.910i | −0.102808 | + | 0.178070i | ||||
\(607\) | 64.7010 | − | 241.467i | 0.106591 | − | 0.397805i | −0.891929 | − | 0.452175i | \(-0.850648\pi\) |
0.998521 | + | 0.0543700i | \(0.0173151\pi\) | |||||||
\(608\) | 38.6062 | − | 38.6062i | 0.0634970 | − | 0.0634970i | ||||
\(609\) | 502.168 | − | 26.2076i | 0.824578 | − | 0.0430338i | ||||
\(610\) | 57.2014 | + | 417.530i | 0.0937728 | + | 0.684475i | ||||
\(611\) | −409.905 | − | 709.976i | −0.670875 | − | 1.16199i | ||||
\(612\) | −47.1285 | + | 12.6280i | −0.0770073 | + | 0.0206340i | ||||
\(613\) | −136.336 | − | 508.814i | −0.222408 | − | 0.830039i | −0.983426 | − | 0.181308i | \(-0.941967\pi\) |
0.761018 | − | 0.648731i | \(-0.224700\pi\) | |||||||
\(614\) | −380.099 | + | 219.450i | −0.619054 | + | 0.357411i | ||||
\(615\) | 62.7418 | − | 8.59559i | 0.102019 | − | 0.0139766i | ||||
\(616\) | 13.6175 | + | 260.927i | 0.0221063 | + | 0.423582i | ||||
\(617\) | −188.817 | − | 188.817i | −0.306025 | − | 0.306025i | 0.537340 | − | 0.843365i | \(-0.319429\pi\) |
−0.843365 | + | 0.537340i | \(0.819429\pi\) | |||||||
\(618\) | −290.170 | − | 77.7509i | −0.469531 | − | 0.125811i | ||||
\(619\) | −93.0351 | − | 53.7139i | −0.150299 | − | 0.0867752i | 0.422964 | − | 0.906146i | \(-0.360990\pi\) |
−0.573263 | + | 0.819371i | \(0.694323\pi\) | |||||||
\(620\) | −140.194 | − | 333.494i | −0.226120 | − | 0.537894i | ||||
\(621\) | −60.9001 | − | 105.482i | −0.0980678 | − | 0.169858i | ||||
\(622\) | −478.584 | − | 478.584i | −0.769427 | − | 0.769427i | ||||
\(623\) | −147.253 | + | 47.8099i | −0.236361 | + | 0.0767415i | ||||
\(624\) | − | 105.578i | − | 0.169196i | ||||||
\(625\) | 547.711 | + | 301.061i | 0.876338 | + | 0.481697i | ||||
\(626\) | −271.359 | + | 470.008i | −0.433482 | + | 0.750812i | ||||
\(627\) | 213.092 | − | 57.0978i | 0.339860 | − | 0.0910651i | ||||
\(628\) | −437.284 | − | 117.170i | −0.696312 | − | 0.186576i | ||||
\(629\) | 39.4717i | 0.0627531i | ||||||||
\(630\) | −148.091 | − | 10.9052i | −0.235066 | − | 0.0173099i | ||||
\(631\) | −494.190 | −0.783185 | −0.391593 | − | 0.920139i | \(-0.628076\pi\) | ||||
−0.391593 | + | 0.920139i | \(0.628076\pi\) | |||||||
\(632\) | −22.2642 | + | 83.0912i | −0.0352282 | + | 0.131473i | ||||
\(633\) | −22.3991 | − | 83.5947i | −0.0353857 | − | 0.132061i | ||||
\(634\) | 179.772 | + | 103.791i | 0.283552 | + | 0.163709i | ||||
\(635\) | −623.801 | + | 483.886i | −0.982364 | + | 0.762025i | ||||
\(636\) | 163.032 | 0.256339 | ||||||||
\(637\) | 697.227 | − | 267.291i | 1.09455 | − | 0.419609i | ||||
\(638\) | 547.327 | − | 547.327i | 0.857879 | − | 0.857879i | ||||
\(639\) | 214.810 | − | 124.021i | 0.336166 | − | 0.194085i | ||||
\(640\) | −21.3731 | + | 52.3755i | −0.0333954 | + | 0.0818367i | ||||
\(641\) | −209.798 | + | 363.381i | −0.327298 | + | 0.566897i | −0.981975 | − | 0.189012i | \(-0.939471\pi\) |
0.654677 | + | 0.755909i | \(0.272805\pi\) | |||||||
\(642\) | 122.900 | − | 458.667i | 0.191432 | − | 0.714435i | ||||
\(643\) | −192.944 | + | 192.944i | −0.300069 | + | 0.300069i | −0.841041 | − | 0.540972i | \(-0.818057\pi\) |
0.540972 | + | 0.841041i | \(0.318057\pi\) | |||||||
\(644\) | −178.672 | − | 275.263i | −0.277441 | − | 0.427426i | ||||
\(645\) | −360.651 | + | 475.156i | −0.559149 | + | 0.736676i | ||||
\(646\) | 55.4971 | + | 96.1238i | 0.0859088 | + | 0.148798i | ||||
\(647\) | −342.959 | + | 91.8957i | −0.530076 | + | 0.142033i | −0.513923 | − | 0.857836i | \(-0.671808\pi\) |
−0.0161528 | + | 0.999870i | \(0.505142\pi\) | |||||||
\(648\) | 6.58846 | + | 24.5885i | 0.0101674 | + | 0.0379452i | ||||
\(649\) | −15.2198 | + | 8.78713i | −0.0234511 | + | 0.0135395i | ||||
\(650\) | 144.904 | + | 518.924i | 0.222930 | + | 0.798345i | ||||
\(651\) | −390.766 | − | 199.212i | −0.600254 | − | 0.306010i | ||||
\(652\) | 244.189 | + | 244.189i | 0.374522 | + | 0.374522i | ||||
\(653\) | 377.692 | + | 101.202i | 0.578395 | + | 0.154981i | 0.536144 | − | 0.844126i | \(-0.319880\pi\) |
0.0422513 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(654\) | 143.045 | + | 82.5870i | 0.218723 | + | 0.126280i | ||||
\(655\) | 339.285 | − | 142.629i | 0.517992 | − | 0.217754i | ||||
\(656\) | −14.6249 | − | 25.3311i | −0.0222941 | − | 0.0386145i | ||||
\(657\) | 108.856 | + | 108.856i | 0.165687 | + | 0.165687i | ||||
\(658\) | 395.695 | + | 356.442i | 0.601360 | + | 0.541705i | ||||
\(659\) | 325.611i | 0.494099i | 0.969003 | + | 0.247050i | \(0.0794610\pi\) | ||||
−0.969003 | + | 0.247050i | \(0.920539\pi\) | |||||||
\(660\) | −180.607 | + | 140.097i | −0.273646 | + | 0.212269i | ||||
\(661\) | −127.822 | + | 221.394i | −0.193377 | + | 0.334938i | −0.946367 | − | 0.323093i | \(-0.895277\pi\) |
0.752990 | + | 0.658032i | \(0.228611\pi\) | |||||||
\(662\) | 79.4448 | − | 21.2872i | 0.120007 | − | 0.0321559i | ||||
\(663\) | 207.322 | + | 55.5519i | 0.312703 | + | 0.0837886i | ||||
\(664\) | − | 129.076i | − | 0.194392i | ||||||
\(665\) | 63.2311 | + | 331.833i | 0.0950844 | + | 0.498998i | ||||
\(666\) | 20.5937 | 0.0309214 | ||||||||
\(667\) | −251.619 | + | 939.054i | −0.377240 | + | 1.40788i | ||||
\(668\) | 116.000 | + | 432.917i | 0.173652 | + | 0.648080i | ||||
\(669\) | −448.462 | − | 258.920i | −0.670347 | − | 0.387025i | ||||
\(670\) | −854.776 | − | 107.969i | −1.27579 | − | 0.161148i | ||||
\(671\) | 786.514 | 1.17215 | ||||||||
\(672\) | 21.1799 | + | 65.2335i | 0.0315177 | + | 0.0970737i | ||||
\(673\) | 74.4755 | − | 74.4755i | 0.110662 | − | 0.110662i | −0.649608 | − | 0.760270i | \(-0.725067\pi\) |
0.760270 | + | 0.649608i | \(0.225067\pi\) | |||||||
\(674\) | −512.801 | + | 296.066i | −0.760833 | + | 0.439267i | ||||
\(675\) | −66.1300 | − | 111.812i | −0.0979704 | − | 0.165647i | ||||
\(676\) | −63.2238 | + | 109.507i | −0.0935264 | + | 0.161992i | ||||
\(677\) | −77.9835 | + | 291.039i | −0.115190 | + | 0.429894i | −0.999301 | − | 0.0373822i | \(-0.988098\pi\) |
0.884111 | + | 0.467277i | \(0.154765\pi\) | |||||||
\(678\) | −210.614 | + | 210.614i | −0.310640 | + | 0.310640i | ||||
\(679\) | −693.374 | − | 1068.21i | −1.02117 | − | 1.57321i | ||||
\(680\) | −91.6032 | − | 69.5283i | −0.134711 | − | 0.102248i | ||||
\(681\) | 39.2230 | + | 67.9362i | 0.0575962 | + | 0.0997595i | ||||
\(682\) | −652.153 | + | 174.744i | −0.956237 | + | 0.256223i | ||||
\(683\) | 182.816 | + | 682.280i | 0.267667 | + | 0.998945i | 0.960598 | + | 0.277942i | \(0.0896523\pi\) |
−0.692931 | + | 0.721004i | \(0.743681\pi\) | |||||||
\(684\) | 50.1509 | − | 28.9546i | 0.0733200 | − | 0.0423313i | ||||
\(685\) | 161.839 | + | 1181.31i | 0.236261 | + | 1.72454i | ||||
\(686\) | −377.174 | + | 305.021i | −0.549816 | + | 0.444637i | ||||
\(687\) | −119.898 | − | 119.898i | −0.174523 | − | 0.174523i | ||||
\(688\) | 266.135 | + | 71.3106i | 0.386824 | + | 0.103649i | ||||
\(689\) | −621.106 | − | 358.596i | −0.901460 | − | 0.520458i | ||||
\(690\) | 108.468 | − | 265.806i | 0.157201 | − | 0.385226i | ||||
\(691\) | 363.308 | + | 629.267i | 0.525771 | + | 0.910662i | 0.999549 | + | 0.0300178i | \(0.00955639\pi\) |
−0.473779 | + | 0.880644i | \(0.657110\pi\) | |||||||
\(692\) | −59.7454 | − | 59.7454i | −0.0863373 | − | 0.0863373i | ||||
\(693\) | −57.6780 | + | 271.063i | −0.0832294 | + | 0.391144i | ||||
\(694\) | − | 181.785i | − | 0.261938i | ||||||
\(695\) | 918.345 | + | 115.999i | 1.32136 | + | 0.166905i | ||||
\(696\) | 101.591 | − | 175.961i | 0.145964 | − | 0.252818i | ||||
\(697\) | 57.4376 | − | 15.3904i | 0.0824069 | − | 0.0220809i | ||||
\(698\) | 457.948 | + | 122.707i | 0.656086 | + | 0.175798i | ||||
\(699\) | − | 315.718i | − | 0.451670i | ||||||
\(700\) | −193.633 | − | 291.558i | −0.276618 | − | 0.416512i | ||||
\(701\) | −693.038 | −0.988642 | −0.494321 | − | 0.869279i | \(-0.664583\pi\) | ||||
−0.494321 | + | 0.869279i | \(0.664583\pi\) | |||||||
\(702\) | 28.9832 | − | 108.167i | 0.0412866 | − | 0.154084i | ||||
\(703\) | −12.1252 | − | 45.2520i | −0.0172479 | − | 0.0643699i | ||||
\(704\) | 91.4296 | + | 52.7869i | 0.129872 | + | 0.0749814i | ||||
\(705\) | −58.3849 | + | 462.224i | −0.0828155 | + | 0.655637i | ||||
\(706\) | 41.0134 | 0.0580927 | ||||||||
\(707\) | −238.325 | + | 264.571i | −0.337094 | + | 0.374216i | ||||
\(708\) | −3.26202 | + | 3.26202i | −0.00460737 | + | 0.00460737i | ||||
\(709\) | 222.013 | − | 128.179i | 0.313135 | − | 0.180789i | −0.335193 | − | 0.942149i | \(-0.608802\pi\) |
0.648329 | + | 0.761361i | \(0.275468\pi\) | |||||||
\(710\) | 541.303 | + | 220.891i | 0.762399 | + | 0.311115i | ||||
\(711\) | −45.6202 | + | 79.0165i | −0.0641635 | + | 0.111134i | ||||
\(712\) | −16.1909 | + | 60.4252i | −0.0227400 | + | 0.0848669i | ||||
\(713\) | 599.620 | − | 599.620i | 0.840982 | − | 0.840982i | ||||
\(714\) | −139.242 | + | 7.26691i | −0.195017 | + | 0.0101777i | ||||
\(715\) | 996.212 | − | 136.480i | 1.39330 | − | 0.190882i | ||||
\(716\) | 339.884 | + | 588.697i | 0.474699 | + | 0.822202i | ||||
\(717\) | −114.004 | + | 30.5472i | −0.159001 | + | 0.0426041i | ||||
\(718\) | −100.198 | − | 373.945i | −0.139552 | − | 0.520814i | ||||
\(719\) | 527.096 | − | 304.319i | 0.733096 | − | 0.423253i | −0.0864576 | − | 0.996256i | \(-0.527555\pi\) |
0.819554 | + | 0.573002i | \(0.194221\pi\) | |||||||
\(720\) | −36.2752 | + | 47.7924i | −0.0503822 | + | 0.0663783i | ||||
\(721\) | −764.829 | − | 389.910i | −1.06079 | − | 0.540791i | ||||
\(722\) | 267.848 | + | 267.848i | 0.370980 | + | 0.370980i | ||||
\(723\) | −457.377 | − | 122.554i | −0.632610 | − | 0.169507i | ||||
\(724\) | −65.1277 | − | 37.6015i | −0.0899553 | − | 0.0519357i | ||||
\(725\) | −257.824 | + | 1004.29i | −0.355620 | + | 1.38523i | ||||
\(726\) | 65.0994 | + | 112.755i | 0.0896686 | + | 0.155311i | ||||
\(727\) | −549.001 | − | 549.001i | −0.755160 | − | 0.755160i | 0.220278 | − | 0.975437i | \(-0.429304\pi\) |
−0.975437 | + | 0.220278i | \(0.929304\pi\) | |||||||
\(728\) | 62.7944 | − | 295.108i | 0.0862561 | − | 0.405368i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −45.4718 | + | 359.993i | −0.0622901 | + | 0.493141i | ||||
\(731\) | −280.063 | + | 485.084i | −0.383124 | + | 0.663590i | ||||
\(732\) | 199.423 | − | 53.4352i | 0.272436 | − | 0.0729989i | ||||
\(733\) | 583.723 | + | 156.408i | 0.796347 | + | 0.213381i | 0.633980 | − | 0.773350i | \(-0.281420\pi\) |
0.162368 | + | 0.986730i | \(0.448087\pi\) | |||||||
\(734\) | 400.095i | 0.545088i | ||||||||
\(735\) | −407.453 | − | 118.562i | −0.554358 | − | 0.161309i | ||||
\(736\) | −132.599 | −0.180162 | ||||||||
\(737\) | −416.166 | + | 1553.15i | −0.564676 | + | 2.10740i | ||||
\(738\) | −8.02965 | − | 29.9671i | −0.0108803 | − | 0.0406058i | ||||
\(739\) | −532.900 | − | 307.670i | −0.721109 | − | 0.416333i | 0.0940517 | − | 0.995567i | \(-0.470018\pi\) |
−0.815161 | + | 0.579235i | \(0.803351\pi\) | |||||||
\(740\) | 29.7510 | + | 38.3534i | 0.0402040 | + | 0.0518290i | ||||
\(741\) | −254.748 | −0.343790 | ||||||||
\(742\) | 455.700 | + | 96.9659i | 0.614151 | + | 0.130682i | ||||
\(743\) | 236.059 | − | 236.059i | 0.317710 | − | 0.317710i | −0.530177 | − | 0.847887i | \(-0.677874\pi\) |
0.847887 | + | 0.530177i | \(0.177874\pi\) | |||||||
\(744\) | −153.483 | + | 88.6137i | −0.206295 | + | 0.119104i | ||||
\(745\) | −97.7919 | − | 232.627i | −0.131264 | − | 0.312251i | ||||
\(746\) | −237.489 | + | 411.343i | −0.318350 | + | 0.551398i | ||||
\(747\) | 35.4339 | − | 132.241i | 0.0474349 | − | 0.177029i | ||||
\(748\) | −151.764 | + | 151.764i | −0.202893 | + | 0.202893i | ||||
\(749\) | 616.324 | − | 1208.95i | 0.822863 | − | 1.61409i | ||||
\(750\) | 112.701 | − | 284.690i | 0.150268 | − | 0.379587i | ||||
\(751\) | −676.879 | − | 1172.39i | −0.901303 | − | 1.56110i | −0.825804 | − | 0.563957i | \(-0.809279\pi\) |
−0.0754985 | − | 0.997146i | \(-0.524055\pi\) | |||||||
\(752\) | 207.856 | − | 55.6949i | 0.276405 | − | 0.0740624i | ||||
\(753\) | −45.7897 | − | 170.890i | −0.0608097 | − | 0.226945i | ||||
\(754\) | −774.069 | + | 446.909i | −1.02662 | + | 0.592718i | ||||
\(755\) | 132.085 | + | 100.255i | 0.174948 | + | 0.132788i | ||||
\(756\) | 3.79138 | + | 72.6473i | 0.00501506 | + | 0.0960943i | ||||
\(757\) | −435.838 | − | 435.838i | −0.575744 | − | 0.575744i | 0.357984 | − | 0.933728i | \(-0.383464\pi\) |
−0.933728 | + | 0.357984i | \(0.883464\pi\) | |||||||
\(758\) | −654.753 | − | 175.441i | −0.863791 | − | 0.231452i | ||||
\(759\) | −464.006 | − | 267.894i | −0.611338 | − | 0.352956i | ||||
\(760\) | 126.376 | + | 51.5707i | 0.166284 | + | 0.0678562i | ||||
\(761\) | 560.575 | + | 970.944i | 0.736629 | + | 1.27588i | 0.954005 | + | 0.299792i | \(0.0969171\pi\) |
−0.217375 | + | 0.976088i | \(0.569750\pi\) | |||||||
\(762\) | 273.483 | + | 273.483i | 0.358901 | + | 0.358901i | ||||
\(763\) | 350.713 | + | 315.922i | 0.459650 | + | 0.414053i | ||||
\(764\) | − | 566.410i | − | 0.741375i | ||||||
\(765\) | −74.7624 | − | 96.3799i | −0.0977287 | − | 0.125987i | ||||
\(766\) | −288.992 | + | 500.550i | −0.377275 | + | 0.653459i | ||||
\(767\) | 19.6024 | − | 5.25244i | 0.0255572 | − | 0.00684803i | ||||
\(768\) | 26.7685 | + | 7.17260i | 0.0348548 | + | 0.00933933i | ||||
\(769\) | 103.197i | 0.134196i | 0.997746 | + | 0.0670980i | \(0.0213740\pi\) | ||||
−0.997746 | + | 0.0670980i | \(0.978626\pi\) | |||||||
\(770\) | −588.150 | + | 284.176i | −0.763831 | + | 0.369060i | ||||
\(771\) | −618.214 | −0.801834 | ||||||||
\(772\) | −81.9034 | + | 305.667i | −0.106092 | + | 0.395942i | ||||
\(773\) | −274.026 | − | 1022.68i | −0.354496 | − | 1.32300i | −0.881117 | − | 0.472898i | \(-0.843208\pi\) |
0.526621 | − | 0.850100i | \(-0.323459\pi\) | |||||||
\(774\) | 253.084 | + | 146.118i | 0.326982 | + | 0.188783i | ||||
\(775\) | 632.761 | − | 646.196i | 0.816466 | − | 0.833802i | ||||
\(776\) | −514.578 | −0.663116 | ||||||||
\(777\) | 57.5626 | + | 12.2484i | 0.0740831 | + | 0.0157638i | ||||
\(778\) | −494.148 | + | 494.148i | −0.635151 | + | 0.635151i | ||||
\(779\) | −61.1211 | + | 35.2883i | −0.0784610 | + | 0.0452995i | ||||
\(780\) | 243.320 | − | 102.287i | 0.311949 | − | 0.131137i | ||||
\(781\) | 545.555 | − | 944.928i | 0.698534 | − | 1.20990i | ||||
\(782\) | 69.7695 | − | 260.383i | 0.0892193 | − | 0.332971i | ||||
\(783\) | 152.387 | − | 152.387i | 0.194619 | − | 0.194619i | ||||
\(784\) | 20.4025 | + | 194.935i | 0.0260236 | + | 0.248642i | ||||
\(785\) | −153.618 | − | 1121.30i | −0.195691 | − | 1.42841i | ||||
\(786\) | −90.1523 | − | 156.148i | −0.114698 | − | 0.198662i | ||||
\(787\) | 63.4609 | − | 17.0043i | 0.0806365 | − | 0.0216065i | −0.218275 | − | 0.975887i | \(-0.570043\pi\) |
0.298912 | + | 0.954281i | \(0.403376\pi\) | |||||||
\(788\) | −137.629 | − | 513.637i | −0.174656 | − | 0.651824i | ||||
\(789\) | 289.797 | − | 167.314i | 0.367296 | − | 0.212059i | ||||
\(790\) | −213.066 | + | 29.1899i | −0.269703 | + | 0.0369492i | ||||
\(791\) | −713.966 | + | 463.434i | −0.902612 | + | 0.585883i | ||||
\(792\) | 79.1803 | + | 79.1803i | 0.0999752 | + | 0.0999752i | ||||
\(793\) | −877.279 | − | 235.066i | −1.10628 | − | 0.296426i | ||||
\(794\) | 706.499 | + | 407.898i | 0.889798 | + | 0.513725i | ||||
\(795\) | 157.949 | + | 375.730i | 0.198679 | + | 0.472616i | ||||
\(796\) | 5.21998 | + | 9.04127i | 0.00655776 | + | 0.0113584i | ||||
\(797\) | 376.938 | + | 376.938i | 0.472946 | + | 0.472946i | 0.902867 | − | 0.429921i | \(-0.141458\pi\) |
−0.429921 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(798\) | 157.401 | − | 51.1047i | 0.197244 | − | 0.0640410i | ||||
\(799\) | 437.470i | 0.547521i | ||||||||
\(800\) | −141.414 | + | 1.48552i | −0.176767 | + | 0.00185690i | ||||
\(801\) | −33.1758 | + | 57.4621i | −0.0414179 | + | 0.0717380i | ||||
\(802\) | −547.102 | + | 146.595i | −0.682172 | + | 0.182787i | ||||
\(803\) | 654.118 | + | 175.270i | 0.814593 | + | 0.218269i | ||||
\(804\) | 422.080i | 0.524976i | ||||||||
\(805\) | 461.279 | − | 678.457i | 0.573018 | − | 0.842804i | ||||
\(806\) | 779.639 | 0.967294 | ||||||||
\(807\) | 126.759 | − | 473.072i | 0.157075 | − | 0.586210i | ||||
\(808\) | 37.2389 | + | 138.978i | 0.0460878 | + | 0.172002i | ||||
\(809\) | −936.058 | − | 540.433i | −1.15706 | − | 0.668026i | −0.206459 | − | 0.978455i | \(-0.566194\pi\) |
−0.950597 | + | 0.310429i | \(0.899527\pi\) | |||||||
\(810\) | −50.2845 | + | 39.0060i | −0.0620797 | + | 0.0481555i | ||||
\(811\) | −588.576 | −0.725741 | −0.362870 | − | 0.931840i | \(-0.618203\pi\) | ||||
−0.362870 | + | 0.931840i | \(0.618203\pi\) | |||||||
\(812\) | 388.620 | − | 431.417i | 0.478596 | − | 0.531301i | ||||
\(813\) | 627.632 | − | 627.632i | 0.771995 | − | 0.771995i | ||||
\(814\) | 78.4529 | − | 45.2948i | 0.0963795 | − | 0.0556447i | ||||
\(815\) | −326.191 | + | 799.344i | −0.400234 | + | 0.980790i | ||||
\(816\) | −28.1695 | + | 48.7910i | −0.0345214 | + | 0.0597929i | ||||
\(817\) | 172.064 | − | 642.153i | 0.210605 | − | 0.785989i | ||||
\(818\) | 669.056 | − | 669.056i | 0.817917 | − | 0.817917i | ||||
\(819\) | 145.347 | − | 285.105i | 0.177469 | − | 0.348114i | ||||
\(820\) | 44.2102 | − | 58.2467i | 0.0539148 | − | 0.0710326i | ||||
\(821\) | −291.956 | − | 505.682i | −0.355610 | − | 0.615934i | 0.631612 | − | 0.775284i | \(-0.282393\pi\) |
−0.987222 | + | 0.159350i | \(0.949060\pi\) | |||||||
\(822\) | 564.224 | − | 151.183i | 0.686404 | − | 0.183921i | ||||
\(823\) | 325.609 | + | 1215.19i | 0.395637 | + | 1.47654i | 0.820693 | + | 0.571370i | \(0.193588\pi\) |
−0.425056 | + | 0.905167i | \(0.639745\pi\) | |||||||
\(824\) | −300.407 | + | 173.440i | −0.364571 | + | 0.210485i | ||||
\(825\) | −497.851 | − | 280.503i | −0.603456 | − | 0.340004i | ||||
\(826\) | −11.0580 | + | 7.17773i | −0.0133874 | + | 0.00868974i | ||||
\(827\) | 613.456 | + | 613.456i | 0.741784 | + | 0.741784i | 0.972921 | − | 0.231137i | \(-0.0742445\pi\) |
−0.231137 | + | 0.972921i | \(0.574245\pi\) | |||||||
\(828\) | −135.850 | − | 36.4010i | −0.164071 | − | 0.0439626i | ||||
\(829\) | 721.377 | + | 416.487i | 0.870177 | + | 0.502397i | 0.867407 | − | 0.497599i | \(-0.165785\pi\) |
0.00276996 | + | 0.999996i | \(0.499118\pi\) | |||||||
\(830\) | 297.474 | − | 125.052i | 0.358403 | − | 0.150666i | ||||
\(831\) | −115.177 | − | 199.493i | −0.138601 | − | 0.240064i | ||||
\(832\) | −86.2042 | − | 86.2042i | −0.103611 | − | 0.103611i | ||||
\(833\) | −393.527 | − | 62.5046i | −0.472421 | − | 0.0750356i | ||||
\(834\) | − | 453.470i | − | 0.543729i | ||||||
\(835\) | −885.336 | + | 686.760i | −1.06028 | + | 0.822467i | ||||
\(836\) | 127.369 | − | 220.609i | 0.152355 | − | 0.263887i | ||||
\(837\) | −181.573 | + | 48.6523i | −0.216933 | + | 0.0581270i | ||||
\(838\) | −26.4580 | − | 7.08941i | −0.0315728 | − | 0.00845991i | ||||
\(839\) | − | 553.700i | − | 0.659953i | −0.943989 | − | 0.329976i | \(-0.892959\pi\) | ||
0.943989 | − | 0.329976i | \(-0.107041\pi\) | |||||||
\(840\) | −129.820 | + | 112.012i | −0.154548 | + | 0.133348i | ||||
\(841\) | −879.131 | −1.04534 | ||||||||
\(842\) | −123.563 | + | 461.144i | −0.146749 | + | 0.547676i | ||||
\(843\) | −204.742 | − | 764.108i | −0.242873 | − | 0.906415i | ||||
\(844\) | −86.5436 | − | 49.9660i | −0.102540 | − | 0.0592014i | ||||
\(845\) | −313.627 | − | 39.6151i | −0.371156 | − | 0.0468818i | ||||
\(846\) | 228.242 | 0.269790 | ||||||||
\(847\) | 114.900 | + | 353.888i | 0.135655 | + | 0.417814i | ||||
\(848\) | 133.115 | − | 133.115i | 0.156975 | − | 0.156975i | ||||
\(849\) | 140.439 | − | 81.0827i | 0.165417 | − | 0.0955038i | ||||
\(850\) | 71.4902 | − | 278.474i | 0.0841062 | − | 0.327616i | ||||
\(851\) | −56.8897 | + | 98.5358i | −0.0668504 | + | 0.115788i | ||||
\(852\) | 74.1292 | − | 276.654i | 0.0870061 | − | 0.324711i | ||||
\(853\) | 299.589 | − | 299.589i | 0.351218 | − | 0.351218i | −0.509344 | − | 0.860563i | \(-0.670112\pi\) |
0.860563 | + | 0.509344i | \(0.170112\pi\) | |||||||
\(854\) | 589.200 | − | 30.7497i | 0.689930 | − | 0.0360067i | ||||
\(855\) | 115.318 | + | 87.5279i | 0.134874 | + | 0.102372i | ||||
\(856\) | −274.153 | − | 474.847i | −0.320273 | − | 0.554728i | ||||
\(857\) | 1332.19 | − | 356.960i | 1.55448 | − | 0.416523i | 0.623572 | − | 0.781766i | \(-0.285681\pi\) |
0.930912 | + | 0.365243i | \(0.119014\pi\) | |||||||
\(858\) | −127.494 | − | 475.816i | −0.148595 | − | 0.554564i | ||||
\(859\) | 284.064 | − | 164.005i | 0.330692 | − | 0.190925i | −0.325456 | − | 0.945557i | \(-0.605518\pi\) |
0.656148 | + | 0.754632i | \(0.272185\pi\) | |||||||
\(860\) | 93.4930 | + | 682.433i | 0.108713 | + | 0.793527i | ||||
\(861\) | −4.62073 | − | 88.5385i | −0.00536670 | − | 0.102832i | ||||
\(862\) | −246.327 | − | 246.327i | −0.285763 | − | 0.285763i | ||||
\(863\) | −340.102 | − | 91.1301i | −0.394093 | − | 0.105597i | 0.0563301 | − | 0.998412i | \(-0.482060\pi\) |
−0.450423 | + | 0.892815i | \(0.648727\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 79.8089 | − | 195.575i | 0.0922646 | − | 0.226098i | ||||
\(866\) | −480.212 | − | 831.752i | −0.554518 | − | 0.960453i | ||||
\(867\) | 272.963 | + | 272.963i | 0.314836 | + | 0.314836i | ||||
\(868\) | −481.715 | + | 156.402i | −0.554971 | + | 0.180187i | ||||
\(869\) | 401.358i | 0.461862i | ||||||||
\(870\) | 503.952 | + | 63.6556i | 0.579255 | + | 0.0731674i | ||||
\(871\) | 928.385 | − | 1608.01i | 1.06588 | − | 1.84616i | ||||
\(872\) | 184.228 | − | 49.3636i | 0.211270 | − | 0.0566097i | ||||
\(873\) | −527.195 | − | 141.262i | −0.603889 | − | 0.161812i | ||||
\(874\) | 319.947i | 0.366072i | ||||||||
\(875\) | 484.341 | − | 728.724i | 0.553533 | − | 0.832827i | ||||
\(876\) | 177.761 | 0.202924 | ||||||||
\(877\) | −308.205 | + | 1150.23i | −0.351430 | + | 1.31156i | 0.533487 | + | 0.845808i | \(0.320881\pi\) |
−0.884917 | + | 0.465748i | \(0.845785\pi\) | |||||||
\(878\) | −130.750 | − | 487.964i | −0.148917 | − | 0.555767i | ||||
\(879\) | −87.1886 | − | 50.3384i | −0.0991907 | − | 0.0572678i | ||||
\(880\) | −33.0755 | + | 261.854i | −0.0375858 | + | 0.297561i | ||||
\(881\) | 804.709 | 0.913404 | 0.456702 | − | 0.889620i | \(-0.349031\pi\) | ||||
0.456702 | + | 0.889620i | \(0.349031\pi\) | |||||||
\(882\) | −32.6107 | + | 205.316i | −0.0369736 | + | 0.232784i | ||||
\(883\) | 3.52555 | − | 3.52555i | 0.00399269 | − | 0.00399269i | −0.705108 | − | 0.709100i | \(-0.749101\pi\) |
0.709100 | + | 0.705108i | \(0.249101\pi\) | |||||||
\(884\) | 214.636 | − | 123.920i | 0.242801 | − | 0.140181i | ||||
\(885\) | −10.6781 | − | 4.35746i | −0.0120657 | − | 0.00492368i | ||||
\(886\) | −563.519 | + | 976.043i | −0.636025 | + | 1.10163i | ||||
\(887\) | −126.111 | + | 470.654i | −0.142177 | + | 0.530613i | 0.857688 | + | 0.514171i | \(0.171900\pi\) |
−0.999865 | + | 0.0164416i | \(0.994766\pi\) | |||||||
\(888\) | 16.8147 | − | 16.8147i | 0.0189354 | − | 0.0189354i | ||||
\(889\) | 601.769 | + | 927.086i | 0.676906 | + | 1.04284i | ||||
\(890\) | −154.945 | + | 21.2273i | −0.174095 | + | 0.0238510i | ||||
\(891\) | 59.3852 | + | 102.858i | 0.0666501 | + | 0.115441i | ||||
\(892\) | −577.575 | + | 154.761i | −0.647505 | + | 0.173499i | ||||
\(893\) | −134.386 | − | 501.534i | −0.150488 | − | 0.561628i | ||||
\(894\) | −107.061 | + | 61.8120i | −0.119756 | + | 0.0691409i | ||||
\(895\) | −1027.45 | + | 1353.66i | −1.14799 | + | 1.51247i | ||||
\(896\) | 70.5563 | + | 35.9696i | 0.0787458 | + | 0.0401447i | ||||
\(897\) | 437.487 | + | 437.487i | 0.487722 | + | 0.487722i | ||||
\(898\) | 1146.08 | + | 307.090i | 1.27625 | + | 0.341971i | ||||
\(899\) | 1299.38 | + | 750.198i | 1.44536 | + | 0.834480i | ||||
\(900\) | −145.289 | − | 37.2988i | −0.161432 | − | 0.0414431i | ||||
\(901\) | 191.355 | + | 331.437i | 0.212381 | + | 0.367854i | ||||
\(902\) | −96.5006 | − | 96.5006i | −0.106985 | − | 0.106985i | ||||
\(903\) | 620.504 | + | 558.950i | 0.687159 | + | 0.618992i | ||||
\(904\) | 343.931i | 0.380455i | ||||||||
\(905\) | 23.5605 | − | 186.525i | 0.0260337 | − | 0.206105i | ||||
\(906\) | 40.6184 | − | 70.3532i | 0.0448327 | − | 0.0776525i | ||||
\(907\) | 160.022 | − | 42.8777i | 0.176430 | − | 0.0472742i | −0.169523 | − | 0.985526i | \(-0.554223\pi\) |
0.345952 | + | 0.938252i | \(0.387556\pi\) | |||||||
\(908\) | 87.4951 | + | 23.4442i | 0.0963603 | + | 0.0258197i | ||||
\(909\) | 152.608i | 0.167886i | ||||||||
\(910\) | 740.955 | − | 141.190i | 0.814236 | − | 0.155153i | ||||
\(911\) | −6.95825 | −0.00763803 | −0.00381902 | − | 0.999993i | \(-0.501216\pi\) | ||||
−0.00381902 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(912\) | 17.3067 | − | 64.5894i | 0.0189766 | − | 0.0708217i | ||||
\(913\) | −155.870 | − | 581.716i | −0.170723 | − | 0.637148i | ||||
\(914\) | 564.555 | + | 325.946i | 0.617676 | + | 0.356615i | ||||
\(915\) | 316.355 | + | 407.829i | 0.345743 | + | 0.445715i | ||||
\(916\) | −195.792 | −0.213747 | ||||||||
\(917\) | −159.118 | − | 490.079i | −0.173520 | − | 0.534438i | ||||
\(918\) | −42.2542 | + | 42.2542i | −0.0460286 | + | 0.0460286i | ||||
\(919\) | 161.798 | − | 93.4143i | 0.176059 | − | 0.101648i | −0.409381 | − | 0.912364i | \(-0.634255\pi\) |
0.585440 | + | 0.810716i | \(0.300922\pi\) | |||||||
\(920\) | −128.466 | − | 305.594i | −0.139637 | − | 0.332167i | ||||
\(921\) | −268.771 | + | 465.525i | −0.291825 | + | 0.505456i | ||||
\(922\) | 213.585 | − | 797.110i | 0.231654 | − | 0.864544i | ||||
\(923\) | −890.924 | + | 890.924i | −0.965248 | + | 0.965248i | ||||
\(924\) | 174.228 | + | 268.416i | 0.188558 | + | 0.290493i | ||||
\(925\) | −59.5674 | + | 105.723i | −0.0643972 | + | 0.114295i | ||||
\(926\) | −235.910 | − | 408.608i | −0.254762 | − | 0.441261i | ||||
\(927\) | −355.385 | + | 95.2250i | −0.383371 | + | 0.102724i | ||||
\(928\) | −60.7228 | − | 226.621i | −0.0654341 | − | 0.244203i | ||||
\(929\) | 938.697 | − | 541.957i | 1.01044 | − | 0.583377i | 0.0991182 | − | 0.995076i | \(-0.468398\pi\) |
0.911320 | + | 0.411699i | \(0.135064\pi\) | |||||||
\(930\) | −352.921 | − | 267.873i | −0.379485 | − | 0.288035i | ||||
\(931\) | 470.357 | − | 49.2289i | 0.505216 | − | 0.0528774i | ||||
\(932\) | −257.782 | − | 257.782i | −0.276591 | − | 0.276591i | ||||
\(933\) | −800.686 | − | 214.543i | −0.858184 | − | 0.229950i | ||||
\(934\) | −282.809 | − | 163.280i | −0.302794 | − | 0.174818i | ||||
\(935\) | −496.795 | − | 202.729i | −0.531332 | − | 0.216823i | ||||
\(936\) | −64.6531 | − | 111.983i | −0.0690739 | − | 0.119639i | ||||
\(937\) | 790.801 | + | 790.801i | 0.843971 | + | 0.843971i | 0.989373 | − | 0.145401i | \(-0.0464474\pi\) |
−0.145401 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(938\) | −251.040 | + | 1179.78i | −0.267633 | + | 1.25776i | ||||
\(939\) | 664.692i | 0.707872i | ||||||||
\(940\) | 329.734 | + | 425.076i | 0.350780 | + | 0.452208i | ||||
\(941\) | −33.5626 | + | 58.1322i | −0.0356670 | + | 0.0617770i | −0.883308 | − | 0.468793i | \(-0.844689\pi\) |
0.847641 | + | 0.530570i | \(0.178022\pi\) | |||||||
\(942\) | −535.561 | + | 143.503i | −0.568536 | + | 0.152339i | ||||
\(943\) | 165.567 | + | 44.3636i | 0.175575 | + | 0.0470451i | ||||
\(944\) | 5.32686i | 0.00564286i | ||||||||
\(945\) | −163.753 | + | 79.1204i | −0.173283 | + | 0.0837253i | ||||
\(946\) | 1285.52 | 1.35890 | ||||||||
\(947\) | −38.7341 | + | 144.558i | −0.0409019 | + | 0.152648i | −0.983357 | − | 0.181686i | \(-0.941845\pi\) |
0.942455 | + | 0.334334i | \(0.108511\pi\) | |||||||
\(948\) | 27.2680 | + | 101.765i | 0.0287637 | + | 0.107348i | ||||
\(949\) | −677.221 | − | 390.994i | −0.713615 | − | 0.412006i | ||||
\(950\) | 3.58439 | + | 341.215i | 0.00377304 | + | 0.359174i | ||||
\(951\) | 254.236 | 0.267335 | ||||||||
\(952\) | −107.758 | + | 119.624i | −0.113191 | + | 0.125656i | ||||
\(953\) | −778.354 | + | 778.354i | −0.816741 | + | 0.816741i | −0.985634 | − | 0.168893i | \(-0.945981\pi\) |
0.168893 | + | 0.985634i | \(0.445981\pi\) | |||||||
\(954\) | 172.921 | − | 99.8361i | 0.181259 | − | 0.104650i | ||||
\(955\) | 1305.37 | − | 548.753i | 1.36688 | − | 0.574611i | ||||
\(956\) | −68.1419 | + | 118.025i | −0.0712781 | + | 0.123457i | ||||
\(957\) | 245.360 | − | 915.696i | 0.256384 | − | 0.956840i | ||||
\(958\) | 574.329 | − | 574.329i | 0.599509 | − | 0.599509i | ||||
\(959\) | 1667.02 | − | 86.9997i | 1.73828 | − | 0.0907192i | ||||
\(960\) | 9.40376 | + | 68.6409i | 0.00979559 | + | 0.0715009i | ||||
\(961\) | −173.865 | − | 301.143i | −0.180921 | − | 0.313364i | ||||
\(962\) | −101.044 | + | 27.0746i | −0.105035 | + | 0.0281441i | ||||
\(963\) | −150.521 | − | 561.751i | −0.156304 | − | 0.583334i | ||||
\(964\) | −473.511 | + | 273.382i | −0.491194 | + | 0.283591i | ||||
\(965\) | −783.804 | + | 107.381i | −0.812232 | + | 0.111275i | ||||
\(966\) | −358.074 | − | 182.546i | −0.370677 | − | 0.188971i | ||||
\(967\) | −959.028 | − | 959.028i | −0.991756 | − | 0.991756i | 0.00821072 | − | 0.999966i | \(-0.497386\pi\) |
−0.999966 | + | 0.00821072i | \(0.997386\pi\) | |||||||
\(968\) | 145.218 | + | 38.9110i | 0.150018 | + | 0.0401973i | ||||
\(969\) | 117.727 | + | 67.9698i | 0.121493 | + | 0.0701443i | ||||
\(970\) | −498.537 | − | 1185.92i | −0.513956 | − | 1.22260i | ||||
\(971\) | 417.900 | + | 723.824i | 0.430381 | + | 0.745442i | 0.996906 | − | 0.0786028i | \(-0.0250459\pi\) |
−0.566525 | + | 0.824045i | \(0.691713\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 269.709 | − | 1267.52i | 0.277193 | − | 1.30269i | ||||
\(974\) | − | 1079.16i | − | 1.10797i | ||||||
\(975\) | 471.469 | + | 461.667i | 0.483558 | + | 0.473505i | ||||
\(976\) | 119.198 | − | 206.458i | 0.122130 | − | 0.211535i | ||||
\(977\) | 958.504 | − | 256.830i | 0.981069 | − | 0.262877i | 0.267574 | − | 0.963537i | \(-0.413778\pi\) |
0.713495 | + | 0.700661i | \(0.247111\pi\) | |||||||
\(978\) | 408.535 | + | 109.467i | 0.417725 | + | 0.111929i | ||||
\(979\) | 291.874i | 0.298135i | ||||||||
\(980\) | −429.489 | + | 235.879i | −0.438255 | + | 0.240693i | ||||
\(981\) | 202.296 | 0.206214 | ||||||||
\(982\) | 97.9603 | − | 365.593i | 0.0997559 | − | 0.372294i | ||||
\(983\) | −310.936 | − | 1160.43i | −0.316313 | − | 1.18050i | −0.922761 | − | 0.385373i | \(-0.874073\pi\) |
0.606447 | − | 0.795124i | \(-0.292594\pi\) | |||||||
\(984\) | −31.0242 | − | 17.9118i | −0.0315286 | − | 0.0182031i | ||||
\(985\) | 1050.41 | − | 814.810i | 1.06641 | − | 0.827219i | ||||
\(986\) | 476.962 | 0.483735 | ||||||||
\(987\) | 637.973 | + | 135.751i | 0.646376 | + | 0.137539i | ||||
\(988\) | −208.001 | + | 208.001i | −0.210527 | + | 0.210527i | ||||
\(989\) | −1398.28 | + | 807.298i | −1.41383 | + | 0.816278i | ||||
\(990\) | −105.770 | + | 259.194i | −0.106839 | + | 0.261812i | ||||
\(991\) | −134.710 | + | 233.324i | −0.135933 | + | 0.235443i | −0.925954 | − | 0.377637i | \(-0.876737\pi\) |
0.790020 | + | 0.613081i | \(0.210070\pi\) | |||||||
\(992\) | −52.9659 | + | 197.671i | −0.0533930 | + | 0.199266i | ||||
\(993\) | 71.2283 | − | 71.2283i | 0.0717304 | − | 0.0717304i | ||||
\(994\) | 371.748 | − | 729.202i | 0.373991 | − | 0.733604i | ||||
\(995\) | −15.7796 | + | 20.7896i | −0.0158589 | + | 0.0208941i | ||||
\(996\) | −79.0427 | − | 136.906i | −0.0793601 | − | 0.137456i | ||||
\(997\) | 725.514 | − | 194.401i | 0.727697 | − | 0.194986i | 0.124093 | − | 0.992271i | \(-0.460398\pi\) |
0.603603 | + | 0.797285i | \(0.293731\pi\) | |||||||
\(998\) | −138.894 | − | 518.360i | −0.139173 | − | 0.519399i | ||||
\(999\) | 21.8429 | − | 12.6110i | 0.0218647 | − | 0.0126236i |
(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 | 210.3.v.a.67.3 | yes | 32 | |
5.3 | odd | 4 | inner | 210.3.v.a.193.5 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.a.37.5 | ✓ | 32 | |
35.23 | odd | 12 | inner | 210.3.v.a.163.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.a.37.5 | ✓ | 32 | 7.2 | even | 3 | inner | |
210.3.v.a.67.3 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.a.163.3 | yes | 32 | 35.23 | odd | 12 | inner | |
210.3.v.a.193.5 | yes | 32 | 5.3 | odd | 4 | inner |