Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 2 x^{10} - x^{9} - 4 x^{8} + 20 x^{7} - 38 x^{6} + 60 x^{5} - 36 x^{4} - 27 x^{3} + 162 x^{2} - 243 x + 729 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(1.24736 - 1.20170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.211 |
Dual form | 315.2.i.e.106.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35359 | − | 2.34448i | −0.957129 | − | 1.65780i | −0.729419 | − | 0.684067i | \(-0.760209\pi\) |
−0.227710 | − | 0.973729i | \(-0.573124\pi\) | |||||||
\(3\) | 1.24736 | + | 1.20170i | 0.720166 | + | 0.693802i | ||||
\(4\) | −2.66438 | + | 4.61485i | −1.33219 | + | 2.30742i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 1.12895 | − | 4.55102i | 0.460890 | − | 1.85795i | ||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 9.01155 | 3.18606 | ||||||||
\(9\) | 0.111834 | + | 2.99791i | 0.0372781 | + | 0.999305i | ||||
\(10\) | −2.70717 | −0.856082 | ||||||||
\(11\) | 2.08384 | + | 3.60931i | 0.628301 | + | 1.08825i | 0.987893 | + | 0.155139i | \(0.0495825\pi\) |
−0.359592 | + | 0.933110i | \(0.617084\pi\) | |||||||
\(12\) | −8.86912 | + | 2.55461i | −2.56030 | + | 0.737451i | ||||
\(13\) | −1.08055 | + | 1.87156i | −0.299690 | + | 0.519078i | −0.976065 | − | 0.217479i | \(-0.930217\pi\) |
0.676375 | + | 0.736557i | \(0.263550\pi\) | |||||||
\(14\) | −1.35359 | + | 2.34448i | −0.361761 | + | 0.626588i | ||||
\(15\) | 1.66438 | − | 0.479399i | 0.429742 | − | 0.123780i | ||||
\(16\) | −6.86912 | − | 11.8977i | −1.71728 | − | 2.97442i | ||||
\(17\) | 6.91475 | 1.67707 | 0.838536 | − | 0.544846i | \(-0.183412\pi\) | ||||
0.838536 | + | 0.544846i | \(0.183412\pi\) | |||||||
\(18\) | 6.87717 | − | 4.32013i | 1.62096 | − | 1.01826i | ||||
\(19\) | 2.44928 | 0.561903 | 0.280951 | − | 0.959722i | \(-0.409350\pi\) | ||||
0.280951 | + | 0.959722i | \(0.409350\pi\) | |||||||
\(20\) | 2.66438 | + | 4.61485i | 0.595775 | + | 1.03191i | ||||
\(21\) | 0.417021 | − | 1.68110i | 0.0910014 | − | 0.366846i | ||||
\(22\) | 5.64130 | − | 9.77102i | 1.20273 | − | 2.08319i | ||||
\(23\) | 3.23517 | − | 5.60347i | 0.674579 | − | 1.16840i | −0.302013 | − | 0.953304i | \(-0.597659\pi\) |
0.976592 | − | 0.215101i | \(-0.0690081\pi\) | |||||||
\(24\) | 11.2407 | + | 10.8292i | 2.29449 | + | 2.21050i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 5.85045 | 1.14737 | ||||||||
\(27\) | −3.46310 | + | 3.87388i | −0.666473 | + | 0.745529i | ||||
\(28\) | 5.32877 | 1.00704 | ||||||||
\(29\) | −2.24736 | − | 3.89255i | −0.417325 | − | 0.722828i | 0.578344 | − | 0.815793i | \(-0.303699\pi\) |
−0.995669 | + | 0.0929646i | \(0.970366\pi\) | |||||||
\(30\) | −3.37683 | − | 3.25321i | −0.616521 | − | 0.593951i | ||||
\(31\) | −2.65462 | + | 4.59794i | −0.476784 | + | 0.825814i | −0.999646 | − | 0.0266035i | \(-0.991531\pi\) |
0.522862 | + | 0.852417i | \(0.324864\pi\) | |||||||
\(32\) | −9.58434 | + | 16.6006i | −1.69429 | + | 2.93459i | ||||
\(33\) | −1.73801 | + | 7.00627i | −0.302548 | + | 1.21964i | ||||
\(34\) | −9.35970 | − | 16.2115i | −1.60518 | − | 2.78024i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −14.1329 | − | 7.47150i | −2.35548 | − | 1.24525i | ||||
\(37\) | 3.98774 | 0.655580 | 0.327790 | − | 0.944751i | \(-0.393696\pi\) | ||||
0.327790 | + | 0.944751i | \(0.393696\pi\) | |||||||
\(38\) | −3.31531 | − | 5.74228i | −0.537814 | − | 0.931521i | ||||
\(39\) | −3.59689 | + | 1.03603i | −0.575964 | + | 0.165897i | ||||
\(40\) | 4.50577 | − | 7.80423i | 0.712425 | − | 1.23396i | ||||
\(41\) | −1.13553 | + | 1.96680i | −0.177340 | + | 0.307162i | −0.940969 | − | 0.338494i | \(-0.890083\pi\) |
0.763629 | + | 0.645656i | \(0.223416\pi\) | |||||||
\(42\) | −4.50577 | + | 1.29781i | −0.695256 | + | 0.200257i | ||||
\(43\) | 2.98010 | + | 5.16168i | 0.454461 | + | 0.787149i | 0.998657 | − | 0.0518088i | \(-0.0164986\pi\) |
−0.544196 | + | 0.838958i | \(0.683165\pi\) | |||||||
\(44\) | −22.2086 | −3.34807 | ||||||||
\(45\) | 2.65219 | + | 1.40211i | 0.395365 | + | 0.209014i | ||||
\(46\) | −17.5163 | −2.58264 | ||||||||
\(47\) | −1.41418 | − | 2.44943i | −0.206279 | − | 0.357287i | 0.744260 | − | 0.667890i | \(-0.232802\pi\) |
−0.950540 | + | 0.310603i | \(0.899469\pi\) | |||||||
\(48\) | 5.72913 | − | 23.0954i | 0.826929 | − | 3.33353i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −1.35359 | + | 2.34448i | −0.191426 | + | 0.331559i | ||||
\(51\) | 8.62521 | + | 8.30945i | 1.20777 | + | 1.16356i | ||||
\(52\) | −5.75799 | − | 9.97313i | −0.798489 | − | 1.38302i | ||||
\(53\) | −1.20654 | −0.165732 | −0.0828658 | − | 0.996561i | \(-0.526407\pi\) | ||||
−0.0828658 | + | 0.996561i | \(0.526407\pi\) | |||||||
\(54\) | 13.7698 | + | 2.87552i | 1.87384 | + | 0.391309i | ||||
\(55\) | 4.16767 | 0.561969 | ||||||||
\(56\) | −4.50577 | − | 7.80423i | −0.602109 | − | 1.04288i | ||||
\(57\) | 3.05514 | + | 2.94330i | 0.404663 | + | 0.389849i | ||||
\(58\) | −6.08400 | + | 10.5378i | −0.798868 | + | 1.38368i | ||||
\(59\) | 4.59534 | − | 7.95935i | 0.598262 | − | 1.03622i | −0.394816 | − | 0.918760i | \(-0.629192\pi\) |
0.993078 | − | 0.117460i | \(-0.0374750\pi\) | |||||||
\(60\) | −2.22221 | + | 8.95819i | −0.286886 | + | 1.15650i | ||||
\(61\) | −3.98623 | − | 6.90435i | −0.510384 | − | 0.884012i | −0.999928 | − | 0.0120326i | \(-0.996170\pi\) |
0.489543 | − | 0.871979i | \(-0.337164\pi\) | |||||||
\(62\) | 14.3730 | 1.82537 | ||||||||
\(63\) | 2.54035 | − | 1.59581i | 0.320054 | − | 0.201053i | ||||
\(64\) | 24.4164 | 3.05205 | ||||||||
\(65\) | 1.08055 | + | 1.87156i | 0.134025 | + | 0.232139i | ||||
\(66\) | 18.7786 | − | 5.40887i | 2.31149 | − | 0.665786i | ||||
\(67\) | −2.89263 | + | 5.01018i | −0.353391 | + | 0.612090i | −0.986841 | − | 0.161693i | \(-0.948305\pi\) |
0.633451 | + | 0.773783i | \(0.281638\pi\) | |||||||
\(68\) | −18.4235 | + | 31.9105i | −2.23418 | + | 3.86972i | ||||
\(69\) | 10.7691 | − | 3.10187i | 1.29645 | − | 0.373421i | ||||
\(70\) | 1.35359 | + | 2.34448i | 0.161784 | + | 0.280219i | ||||
\(71\) | −15.4161 | −1.82955 | −0.914775 | − | 0.403965i | \(-0.867632\pi\) | ||||
−0.914775 | + | 0.403965i | \(0.867632\pi\) | |||||||
\(72\) | 1.00780 | + | 27.0158i | 0.118770 | + | 3.18385i | ||||
\(73\) | −6.40221 | −0.749321 | −0.374661 | − | 0.927162i | \(-0.622241\pi\) | ||||
−0.374661 | + | 0.927162i | \(0.622241\pi\) | |||||||
\(74\) | −5.39775 | − | 9.34917i | −0.627475 | − | 1.08682i | ||||
\(75\) | 0.417021 | − | 1.68110i | 0.0481534 | − | 0.194117i | ||||
\(76\) | −6.52582 | + | 11.3031i | −0.748563 | + | 1.29655i | ||||
\(77\) | 2.08384 | − | 3.60931i | 0.237475 | − | 0.411319i | ||||
\(78\) | 7.29764 | + | 7.03049i | 0.826295 | + | 0.796046i | ||||
\(79\) | 5.67491 | + | 9.82924i | 0.638478 | + | 1.10588i | 0.985767 | + | 0.168118i | \(0.0537688\pi\) |
−0.347289 | + | 0.937758i | \(0.612898\pi\) | |||||||
\(80\) | −13.7382 | −1.53598 | ||||||||
\(81\) | −8.97499 | + | 0.670539i | −0.997221 | + | 0.0745044i | ||||
\(82\) | 6.14814 | 0.678949 | ||||||||
\(83\) | 5.11199 | + | 8.85423i | 0.561114 | + | 0.971878i | 0.997400 | + | 0.0720699i | \(0.0229605\pi\) |
−0.436285 | + | 0.899808i | \(0.643706\pi\) | |||||||
\(84\) | 6.64692 | + | 6.40358i | 0.725238 | + | 0.698688i | ||||
\(85\) | 3.45737 | − | 5.98835i | 0.375005 | − | 0.649527i | ||||
\(86\) | 8.06763 | − | 13.9736i | 0.869955 | − | 1.50681i | ||||
\(87\) | 1.87439 | − | 7.55608i | 0.200956 | − | 0.810097i | ||||
\(88\) | 18.7786 | + | 32.5255i | 2.00180 | + | 3.46723i | ||||
\(89\) | −1.00740 | −0.106784 | −0.0533919 | − | 0.998574i | \(-0.517003\pi\) | ||||
−0.0533919 | + | 0.998574i | \(0.517003\pi\) | |||||||
\(90\) | −0.302754 | − | 8.11587i | −0.0319131 | − | 0.855487i | ||||
\(91\) | 2.16109 | 0.226544 | ||||||||
\(92\) | 17.2395 | + | 29.8596i | 1.79734 | + | 3.11308i | ||||
\(93\) | −8.83662 | + | 2.54524i | −0.916314 | + | 0.263929i | ||||
\(94\) | −3.82843 | + | 6.63103i | −0.394872 | + | 0.683939i | ||||
\(95\) | 1.22464 | − | 2.12114i | 0.125645 | − | 0.217624i | ||||
\(96\) | −31.9041 | + | 9.18944i | −3.25619 | + | 0.937894i | ||||
\(97\) | −4.43975 | − | 7.68987i | −0.450788 | − | 0.780787i | 0.547647 | − | 0.836709i | \(-0.315524\pi\) |
−0.998435 | + | 0.0559218i | \(0.982190\pi\) | |||||||
\(98\) | 2.70717 | 0.273465 | ||||||||
\(99\) | −10.5874 | + | 6.65081i | −1.06407 | + | 0.668432i | ||||
\(100\) | 5.32877 | 0.532877 | ||||||||
\(101\) | 0.124032 | + | 0.214829i | 0.0123416 | + | 0.0213763i | 0.872130 | − | 0.489274i | \(-0.162738\pi\) |
−0.859789 | + | 0.510650i | \(0.829405\pi\) | |||||||
\(102\) | 7.80638 | − | 31.4692i | 0.772946 | − | 3.11591i | ||||
\(103\) | 1.98623 | − | 3.44025i | 0.195709 | − | 0.338978i | −0.751424 | − | 0.659820i | \(-0.770633\pi\) |
0.947133 | + | 0.320842i | \(0.103966\pi\) | |||||||
\(104\) | −9.73740 | + | 16.8657i | −0.954831 | + | 1.65382i | ||||
\(105\) | −1.24736 | − | 1.20170i | −0.121730 | − | 0.117274i | ||||
\(106\) | 1.63316 | + | 2.82872i | 0.158627 | + | 0.274749i | ||||
\(107\) | 4.46799 | 0.431937 | 0.215969 | − | 0.976400i | \(-0.430709\pi\) | ||||
0.215969 | + | 0.976400i | \(0.430709\pi\) | |||||||
\(108\) | −8.65037 | − | 26.3032i | −0.832382 | − | 2.53102i | ||||
\(109\) | −5.57683 | −0.534164 | −0.267082 | − | 0.963674i | \(-0.586059\pi\) | ||||
−0.267082 | + | 0.963674i | \(0.586059\pi\) | |||||||
\(110\) | −5.64130 | − | 9.77102i | −0.537877 | − | 0.931630i | ||||
\(111\) | 4.97416 | + | 4.79207i | 0.472127 | + | 0.454843i | ||||
\(112\) | −6.86912 | + | 11.8977i | −0.649071 | + | 1.12422i | ||||
\(113\) | 6.32523 | − | 10.9556i | 0.595028 | − | 1.03062i | −0.398515 | − | 0.917162i | \(-0.630474\pi\) |
0.993543 | − | 0.113456i | \(-0.0361922\pi\) | |||||||
\(114\) | 2.76510 | − | 11.1467i | 0.258976 | − | 1.04399i | ||||
\(115\) | −3.23517 | − | 5.60347i | −0.301681 | − | 0.522527i | ||||
\(116\) | 23.9514 | 2.22383 | ||||||||
\(117\) | −5.73163 | − | 3.03008i | −0.529889 | − | 0.280131i | ||||
\(118\) | −24.8807 | −2.29046 | ||||||||
\(119\) | −3.45737 | − | 5.98835i | −0.316937 | − | 0.548951i | ||||
\(120\) | 14.9987 | − | 4.32013i | 1.36919 | − | 0.394372i | ||||
\(121\) | −3.18476 | + | 5.51616i | −0.289523 | + | 0.501469i | ||||
\(122\) | −10.7914 | + | 18.6913i | −0.977007 | + | 1.69223i | ||||
\(123\) | −3.77992 | + | 1.08874i | −0.340824 | + | 0.0981687i | ||||
\(124\) | −14.1459 | − | 24.5013i | −1.27034 | − | 2.20029i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.17992 | − | 3.79574i | −0.639638 | − | 0.338151i | ||||
\(127\) | −9.68630 | −0.859520 | −0.429760 | − | 0.902943i | \(-0.641402\pi\) | ||||
−0.429760 | + | 0.902943i | \(0.641402\pi\) | |||||||
\(128\) | −13.8810 | − | 24.0425i | −1.22692 | − | 2.12508i | ||||
\(129\) | −2.48553 | + | 10.0197i | −0.218838 | + | 0.882184i | ||||
\(130\) | 2.92523 | − | 5.06664i | 0.256559 | − | 0.444374i | ||||
\(131\) | 3.31847 | − | 5.74777i | 0.289936 | − | 0.502185i | −0.683858 | − | 0.729615i | \(-0.739699\pi\) |
0.973794 | + | 0.227431i | \(0.0730325\pi\) | |||||||
\(132\) | −27.7022 | − | 26.6880i | −2.41117 | − | 2.32290i | ||||
\(133\) | −1.22464 | − | 2.12114i | −0.106190 | − | 0.183926i | ||||
\(134\) | 15.6617 | 1.35296 | ||||||||
\(135\) | 1.62333 | + | 4.93607i | 0.139714 | + | 0.424829i | ||||
\(136\) | 62.3126 | 5.34326 | ||||||||
\(137\) | −10.2885 | − | 17.8201i | −0.879003 | − | 1.52248i | −0.852437 | − | 0.522830i | \(-0.824876\pi\) |
−0.0265659 | − | 0.999647i | \(-0.508457\pi\) | |||||||
\(138\) | −21.8492 | − | 21.0493i | −1.85993 | − | 1.79184i | ||||
\(139\) | −4.57816 | + | 7.92960i | −0.388314 | + | 0.672580i | −0.992223 | − | 0.124473i | \(-0.960276\pi\) |
0.603909 | + | 0.797054i | \(0.293609\pi\) | |||||||
\(140\) | 2.66438 | − | 4.61485i | 0.225182 | − | 0.390026i | ||||
\(141\) | 1.17949 | − | 4.75476i | 0.0993306 | − | 0.400423i | ||||
\(142\) | 20.8669 | + | 36.1426i | 1.75111 | + | 3.03302i | ||||
\(143\) | −9.00674 | −0.753181 | ||||||||
\(144\) | 34.9000 | − | 21.9236i | 2.90833 | − | 1.82697i | ||||
\(145\) | −4.49473 | −0.373267 | ||||||||
\(146\) | 8.66593 | + | 15.0098i | 0.717197 | + | 1.24222i | ||||
\(147\) | −1.66438 | + | 0.479399i | −0.137276 | + | 0.0395402i | ||||
\(148\) | −10.6249 | + | 18.4028i | −0.873359 | + | 1.51270i | ||||
\(149\) | −11.2617 | + | 19.5058i | −0.922592 | + | 1.59798i | −0.127203 | + | 0.991877i | \(0.540600\pi\) |
−0.795389 | + | 0.606099i | \(0.792733\pi\) | |||||||
\(150\) | −4.50577 | + | 1.29781i | −0.367895 | + | 0.105966i | ||||
\(151\) | −0.275128 | − | 0.476536i | −0.0223896 | − | 0.0387800i | 0.854613 | − | 0.519265i | \(-0.173794\pi\) |
−0.877003 | + | 0.480485i | \(0.840461\pi\) | |||||||
\(152\) | 22.0718 | 1.79026 | ||||||||
\(153\) | 0.773306 | + | 20.7298i | 0.0625181 | + | 1.67591i | ||||
\(154\) | −11.2826 | −0.909178 | ||||||||
\(155\) | 2.65462 | + | 4.59794i | 0.213224 | + | 0.369315i | ||||
\(156\) | 4.80240 | − | 19.3595i | 0.384500 | − | 1.55000i | ||||
\(157\) | 8.65486 | − | 14.9907i | 0.690733 | − | 1.19638i | −0.280865 | − | 0.959747i | \(-0.590621\pi\) |
0.971598 | − | 0.236637i | \(-0.0760453\pi\) | |||||||
\(158\) | 15.3630 | − | 26.6094i | 1.22221 | − | 2.11693i | ||||
\(159\) | −1.50500 | − | 1.44990i | −0.119354 | − | 0.114985i | ||||
\(160\) | 9.58434 | + | 16.6006i | 0.757708 | + | 1.31239i | ||||
\(161\) | −6.47033 | −0.509934 | ||||||||
\(162\) | 13.7205 | + | 20.1340i | 1.07798 | + | 1.58188i | ||||
\(163\) | −9.60379 | −0.752227 | −0.376114 | − | 0.926574i | \(-0.622740\pi\) | ||||
−0.376114 | + | 0.926574i | \(0.622740\pi\) | |||||||
\(164\) | −6.05098 | − | 10.4806i | −0.472502 | − | 0.818397i | ||||
\(165\) | 5.19861 | + | 5.00829i | 0.404711 | + | 0.389895i | ||||
\(166\) | 13.8390 | − | 23.9699i | 1.07412 | − | 1.86043i | ||||
\(167\) | 11.7916 | − | 20.4236i | 0.912458 | − | 1.58042i | 0.101878 | − | 0.994797i | \(-0.467515\pi\) |
0.810581 | − | 0.585627i | \(-0.199152\pi\) | |||||||
\(168\) | 3.75800 | − | 15.1493i | 0.289936 | − | 1.16879i | ||||
\(169\) | 4.16484 | + | 7.21371i | 0.320372 | + | 0.554900i | ||||
\(170\) | −18.7194 | −1.43571 | ||||||||
\(171\) | 0.273913 | + | 7.34273i | 0.0209467 | + | 0.561512i | ||||
\(172\) | −31.7605 | −2.42172 | ||||||||
\(173\) | −7.63921 | − | 13.2315i | −0.580799 | − | 1.00597i | −0.995385 | − | 0.0959626i | \(-0.969407\pi\) |
0.414586 | − | 0.910010i | \(-0.363926\pi\) | |||||||
\(174\) | −20.2522 | + | 5.83332i | −1.53532 | + | 0.442223i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 28.6283 | − | 49.5856i | 2.15794 | − | 3.73766i | ||||
\(177\) | 15.2968 | − | 4.40600i | 1.14978 | − | 0.331175i | ||||
\(178\) | 1.36360 | + | 2.36182i | 0.102206 | + | 0.177026i | ||||
\(179\) | 1.93428 | 0.144575 | 0.0722874 | − | 0.997384i | \(-0.476970\pi\) | ||||
0.0722874 | + | 0.997384i | \(0.476970\pi\) | |||||||
\(180\) | −13.5370 | + | 8.50370i | −1.00899 | + | 0.633828i | ||||
\(181\) | −6.95394 | −0.516882 | −0.258441 | − | 0.966027i | \(-0.583209\pi\) | ||||
−0.258441 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(182\) | −2.92523 | − | 5.06664i | −0.216832 | − | 0.375564i | ||||
\(183\) | 3.32468 | − | 13.4025i | 0.245767 | − | 0.990741i | ||||
\(184\) | 29.1539 | − | 50.4960i | 2.14925 | − | 3.72261i | ||||
\(185\) | 1.99387 | − | 3.45348i | 0.146592 | − | 0.253905i | ||||
\(186\) | 17.9284 | + | 17.2720i | 1.31457 | + | 1.26645i | ||||
\(187\) | 14.4092 | + | 24.9575i | 1.05371 | + | 1.82507i | ||||
\(188\) | 15.0717 | 1.09922 | ||||||||
\(189\) | 5.08643 | + | 1.06219i | 0.369983 | + | 0.0772628i | ||||
\(190\) | −6.63061 | −0.481035 | ||||||||
\(191\) | 0.318146 | + | 0.551045i | 0.0230202 | + | 0.0398722i | 0.877306 | − | 0.479931i | \(-0.159338\pi\) |
−0.854286 | + | 0.519804i | \(0.826005\pi\) | |||||||
\(192\) | 30.4561 | + | 29.3412i | 2.19798 | + | 2.11752i | ||||
\(193\) | 3.59304 | − | 6.22333i | 0.258633 | − | 0.447965i | −0.707243 | − | 0.706970i | \(-0.750061\pi\) |
0.965876 | + | 0.259005i | \(0.0833947\pi\) | |||||||
\(194\) | −12.0191 | + | 20.8178i | −0.862924 | + | 1.49463i | ||||
\(195\) | −0.901221 | + | 3.63301i | −0.0645378 | + | 0.260166i | ||||
\(196\) | −2.66438 | − | 4.61485i | −0.190313 | − | 0.329632i | ||||
\(197\) | −16.2961 | −1.16105 | −0.580524 | − | 0.814243i | \(-0.697152\pi\) | ||||
−0.580524 | + | 0.814243i | \(0.697152\pi\) | |||||||
\(198\) | 29.9236 | + | 15.8194i | 2.12658 | + | 1.12424i | ||||
\(199\) | 10.0816 | 0.714666 | 0.357333 | − | 0.933977i | \(-0.383686\pi\) | ||||
0.357333 | + | 0.933977i | \(0.383686\pi\) | |||||||
\(200\) | −4.50577 | − | 7.80423i | −0.318606 | − | 0.551842i | ||||
\(201\) | −9.62889 | + | 2.77344i | −0.679169 | + | 0.195624i | ||||
\(202\) | 0.335774 | − | 0.581578i | 0.0236250 | − | 0.0409197i | ||||
\(203\) | −2.24736 | + | 3.89255i | −0.157734 | + | 0.273203i | ||||
\(204\) | −61.3277 | + | 17.6645i | −4.29380 | + | 1.23676i | ||||
\(205\) | 1.13553 | + | 1.96680i | 0.0793088 | + | 0.137367i | ||||
\(206\) | −10.7541 | −0.749275 | ||||||||
\(207\) | 17.1605 | + | 9.07209i | 1.19274 | + | 0.630554i | ||||
\(208\) | 29.6896 | 2.05861 | ||||||||
\(209\) | 5.10390 | + | 8.84021i | 0.353044 | + | 0.611490i | ||||
\(210\) | −1.12895 | + | 4.55102i | −0.0779047 | + | 0.314050i | ||||
\(211\) | 3.56402 | − | 6.17306i | 0.245357 | − | 0.424971i | −0.716875 | − | 0.697202i | \(-0.754428\pi\) |
0.962232 | + | 0.272231i | \(0.0877615\pi\) | |||||||
\(212\) | 3.21470 | − | 5.56802i | 0.220786 | − | 0.382413i | ||||
\(213\) | −19.2294 | − | 18.5255i | −1.31758 | − | 1.26934i | ||||
\(214\) | −6.04781 | − | 10.4751i | −0.413420 | − | 0.716064i | ||||
\(215\) | 5.96020 | 0.406482 | ||||||||
\(216\) | −31.2078 | + | 34.9097i | −2.12343 | + | 2.37530i | ||||
\(217\) | 5.30924 | 0.360415 | ||||||||
\(218\) | 7.54872 | + | 13.0748i | 0.511264 | + | 0.885535i | ||||
\(219\) | −7.98588 | − | 7.69353i | −0.539636 | − | 0.519881i | ||||
\(220\) | −11.1043 | + | 19.2332i | −0.748651 | + | 1.29670i | ||||
\(221\) | −7.47171 | + | 12.9414i | −0.502602 | + | 0.870532i | ||||
\(222\) | 4.50194 | − | 18.1483i | 0.302151 | − | 1.21803i | ||||
\(223\) | −7.95304 | − | 13.7751i | −0.532575 | − | 0.922447i | −0.999277 | − | 0.0380320i | \(-0.987891\pi\) |
0.466702 | − | 0.884415i | \(-0.345442\pi\) | |||||||
\(224\) | 19.1687 | 1.28076 | ||||||||
\(225\) | 2.54035 | − | 1.59581i | 0.169357 | − | 0.106387i | ||||
\(226\) | −34.2469 | −2.27807 | ||||||||
\(227\) | −0.267906 | − | 0.464026i | −0.0177815 | − | 0.0307985i | 0.856998 | − | 0.515320i | \(-0.172327\pi\) |
−0.874779 | + | 0.484522i | \(0.838994\pi\) | |||||||
\(228\) | −21.7229 | + | 6.25694i | −1.43864 | + | 0.414376i | ||||
\(229\) | 0.653745 | − | 1.13232i | 0.0432007 | − | 0.0748257i | −0.843617 | − | 0.536946i | \(-0.819578\pi\) |
0.886817 | + | 0.462120i | \(0.152911\pi\) | |||||||
\(230\) | −8.75815 | + | 15.1696i | −0.577495 | + | 1.00025i | ||||
\(231\) | 6.93661 | − | 1.99798i | 0.456396 | − | 0.131457i | ||||
\(232\) | −20.2522 | − | 35.0779i | −1.32962 | − | 2.30298i | ||||
\(233\) | −23.6393 | −1.54866 | −0.774331 | − | 0.632781i | \(-0.781913\pi\) | ||||
−0.774331 | + | 0.632781i | \(0.781913\pi\) | |||||||
\(234\) | 0.654281 | + | 17.5392i | 0.0427717 | + | 1.14657i | ||||
\(235\) | −2.82836 | −0.184502 | ||||||||
\(236\) | 24.4875 | + | 42.4136i | 1.59400 | + | 2.76089i | ||||
\(237\) | −4.73311 | + | 19.0802i | −0.307449 | + | 1.23939i | ||||
\(238\) | −9.35970 | + | 16.2115i | −0.606699 | + | 1.05083i | ||||
\(239\) | 0.230521 | − | 0.399273i | 0.0149111 | − | 0.0258268i | −0.858474 | − | 0.512858i | \(-0.828587\pi\) |
0.873385 | + | 0.487031i | \(0.161920\pi\) | |||||||
\(240\) | −17.1366 | − | 16.5092i | −1.10616 | − | 1.06567i | ||||
\(241\) | −12.3586 | − | 21.4058i | −0.796090 | − | 1.37887i | −0.922145 | − | 0.386845i | \(-0.873565\pi\) |
0.126055 | − | 0.992023i | \(-0.459769\pi\) | |||||||
\(242\) | 17.2434 | 1.10845 | ||||||||
\(243\) | −12.0009 | − | 9.94883i | −0.769856 | − | 0.638218i | ||||
\(244\) | 42.4834 | 2.71972 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 7.66897 | + | 7.38823i | 0.488956 | + | 0.471056i | ||||
\(247\) | −2.64656 | + | 4.58398i | −0.168397 | + | 0.291672i | ||||
\(248\) | −23.9222 | + | 41.4345i | −1.51906 | + | 2.63109i | ||||
\(249\) | −4.26361 | + | 17.1875i | −0.270196 | + | 1.08922i | ||||
\(250\) | 1.35359 | + | 2.34448i | 0.0856082 | + | 0.148278i | ||||
\(251\) | 9.94783 | 0.627901 | 0.313951 | − | 0.949439i | \(-0.398347\pi\) | ||||
0.313951 | + | 0.949439i | \(0.398347\pi\) | |||||||
\(252\) | 0.595939 | + | 15.9752i | 0.0375406 | + | 1.00634i | ||||
\(253\) | 26.9662 | 1.69535 | ||||||||
\(254\) | 13.1112 | + | 22.7093i | 0.822672 | + | 1.42491i | ||||
\(255\) | 11.5088 | − | 3.31492i | 0.720709 | − | 0.207589i | ||||
\(256\) | −13.1618 | + | 22.7968i | −0.822609 | + | 1.42480i | ||||
\(257\) | 11.2625 | − | 19.5073i | 0.702538 | − | 1.21683i | −0.265034 | − | 0.964239i | \(-0.585383\pi\) |
0.967573 | − | 0.252593i | \(-0.0812833\pi\) | |||||||
\(258\) | 26.8553 | − | 7.73523i | 1.67194 | − | 0.481574i | ||||
\(259\) | −1.99387 | − | 3.45348i | −0.123893 | − | 0.214589i | ||||
\(260\) | −11.5160 | −0.714190 | ||||||||
\(261\) | 11.4182 | − | 7.17273i | 0.706769 | − | 0.443981i | ||||
\(262\) | −17.9673 | −1.11003 | ||||||||
\(263\) | 6.02991 | + | 10.4441i | 0.371820 | + | 0.644011i | 0.989846 | − | 0.142147i | \(-0.0454006\pi\) |
−0.618026 | + | 0.786158i | \(0.712067\pi\) | |||||||
\(264\) | −15.6621 | + | 63.1374i | −0.963937 | + | 3.88584i | ||||
\(265\) | −0.603272 | + | 1.04490i | −0.0370587 | + | 0.0641876i | ||||
\(266\) | −3.31531 | + | 5.74228i | −0.203274 | + | 0.352082i | ||||
\(267\) | −1.25659 | − | 1.21059i | −0.0769020 | − | 0.0740868i | ||||
\(268\) | −15.4141 | − | 26.6981i | −0.941568 | − | 1.63084i | ||||
\(269\) | −4.28838 | −0.261467 | −0.130733 | − | 0.991418i | \(-0.541733\pi\) | ||||
−0.130733 | + | 0.991418i | \(0.541733\pi\) | |||||||
\(270\) | 9.37519 | − | 10.4873i | 0.570556 | − | 0.638234i | ||||
\(271\) | 4.49009 | 0.272753 | 0.136377 | − | 0.990657i | \(-0.456454\pi\) | ||||
0.136377 | + | 0.990657i | \(0.456454\pi\) | |||||||
\(272\) | −47.4983 | − | 82.2694i | −2.88000 | − | 4.98831i | ||||
\(273\) | 2.69567 | + | 2.59699i | 0.163149 | + | 0.157177i | ||||
\(274\) | −27.8526 | + | 48.2422i | −1.68264 | + | 2.91441i | ||||
\(275\) | 2.08384 | − | 3.60931i | 0.125660 | − | 0.217650i | ||||
\(276\) | −14.3784 | + | 57.9625i | −0.865479 | + | 3.48893i | ||||
\(277\) | 0.839410 | + | 1.45390i | 0.0504352 | + | 0.0873564i | 0.890141 | − | 0.455685i | \(-0.150606\pi\) |
−0.839706 | + | 0.543042i | \(0.817272\pi\) | |||||||
\(278\) | 24.7877 | 1.48667 | ||||||||
\(279\) | −14.0811 | − | 7.44412i | −0.843013 | − | 0.445668i | ||||
\(280\) | −9.01155 | −0.538543 | ||||||||
\(281\) | 8.87866 | + | 15.3783i | 0.529656 | + | 0.917391i | 0.999402 | + | 0.0345895i | \(0.0110124\pi\) |
−0.469745 | + | 0.882802i | \(0.655654\pi\) | |||||||
\(282\) | −12.7440 | + | 3.67069i | −0.758891 | + | 0.218586i | ||||
\(283\) | −1.17892 | + | 2.04195i | −0.0700794 | + | 0.121381i | −0.898936 | − | 0.438080i | \(-0.855659\pi\) |
0.828856 | + | 0.559461i | \(0.188992\pi\) | |||||||
\(284\) | 41.0743 | − | 71.1428i | 2.43731 | − | 4.22155i | ||||
\(285\) | 4.07654 | − | 1.17418i | 0.241473 | − | 0.0695525i | ||||
\(286\) | 12.1914 | + | 21.1161i | 0.720892 | + | 1.24862i | ||||
\(287\) | 2.27106 | 0.134056 | ||||||||
\(288\) | −50.8389 | − | 26.8765i | −2.99571 | − | 1.58371i | ||||
\(289\) | 30.8137 | 1.81257 | ||||||||
\(290\) | 6.08400 | + | 10.5378i | 0.357265 | + | 0.618800i | ||||
\(291\) | 3.70293 | − | 14.9273i | 0.217070 | − | 0.875054i | ||||
\(292\) | 17.0579 | − | 29.5452i | 0.998240 | − | 1.72900i | ||||
\(293\) | 5.54018 | − | 9.59587i | 0.323661 | − | 0.560597i | −0.657580 | − | 0.753385i | \(-0.728420\pi\) |
0.981240 | + | 0.192788i | \(0.0617530\pi\) | |||||||
\(294\) | 3.37683 | + | 3.25321i | 0.196941 | + | 0.189731i | ||||
\(295\) | −4.59534 | − | 7.95935i | −0.267551 | − | 0.463412i | ||||
\(296\) | 35.9357 | 2.08872 | ||||||||
\(297\) | −21.1986 | − | 4.42685i | −1.23007 | − | 0.256872i | ||||
\(298\) | 60.9745 | 3.53216 | ||||||||
\(299\) | 6.99150 | + | 12.1096i | 0.404329 | + | 0.700318i | ||||
\(300\) | 6.64692 | + | 6.40358i | 0.383760 | + | 0.369711i | ||||
\(301\) | 2.98010 | − | 5.16168i | 0.171770 | − | 0.297514i | ||||
\(302\) | −0.744819 | + | 1.29006i | −0.0428595 | + | 0.0742349i | ||||
\(303\) | −0.103447 | + | 0.417019i | −0.00594290 | + | 0.0239571i | ||||
\(304\) | −16.8244 | − | 29.1407i | −0.964945 | − | 1.67133i | ||||
\(305\) | −7.97246 | −0.456502 | ||||||||
\(306\) | 47.5539 | − | 29.8726i | 2.71847 | − | 1.70770i | ||||
\(307\) | 25.0379 | 1.42899 | 0.714494 | − | 0.699642i | \(-0.246657\pi\) | ||||
0.714494 | + | 0.699642i | \(0.246657\pi\) | |||||||
\(308\) | 11.1043 | + | 19.2332i | 0.632726 | + | 1.09591i | ||||
\(309\) | 6.61170 | − | 1.90439i | 0.376126 | − | 0.108337i | ||||
\(310\) | 7.18651 | − | 12.4474i | 0.408166 | − | 0.706964i | ||||
\(311\) | 3.94817 | − | 6.83843i | 0.223880 | − | 0.387772i | −0.732103 | − | 0.681194i | \(-0.761461\pi\) |
0.955983 | + | 0.293422i | \(0.0947942\pi\) | |||||||
\(312\) | −32.4136 | + | 9.33620i | −1.83506 | + | 0.528558i | ||||
\(313\) | 0.416010 | + | 0.720550i | 0.0235143 | + | 0.0407279i | 0.877543 | − | 0.479498i | \(-0.159181\pi\) |
−0.854029 | + | 0.520226i | \(0.825848\pi\) | |||||||
\(314\) | −46.8603 | −2.64448 | ||||||||
\(315\) | −0.111834 | − | 2.99791i | −0.00630115 | − | 0.168913i | ||||
\(316\) | −60.4806 | −3.40230 | ||||||||
\(317\) | −9.22282 | − | 15.9744i | −0.518005 | − | 0.897211i | −0.999781 | − | 0.0209167i | \(-0.993342\pi\) |
0.481776 | − | 0.876294i | \(-0.339992\pi\) | |||||||
\(318\) | −1.36212 | + | 5.49101i | −0.0763841 | + | 0.307920i | ||||
\(319\) | 9.36628 | − | 16.2229i | 0.524411 | − | 0.908307i | ||||
\(320\) | 12.2082 | − | 21.1452i | 0.682458 | − | 1.18205i | ||||
\(321\) | 5.57321 | + | 5.36919i | 0.311066 | + | 0.299679i | ||||
\(322\) | 8.75815 | + | 15.1696i | 0.488072 | + | 0.845366i | ||||
\(323\) | 16.9361 | 0.942352 | ||||||||
\(324\) | 20.8184 | − | 43.2048i | 1.15658 | − | 2.40027i | ||||
\(325\) | 2.16109 | 0.119876 | ||||||||
\(326\) | 12.9995 | + | 22.5159i | 0.719978 | + | 1.24704i | ||||
\(327\) | −6.95634 | − | 6.70168i | −0.384687 | − | 0.370604i | ||||
\(328\) | −10.2329 | + | 17.7239i | −0.565016 | + | 0.978637i | ||||
\(329\) | −1.41418 | + | 2.44943i | −0.0779663 | + | 0.135042i | ||||
\(330\) | 4.70508 | − | 18.9672i | 0.259006 | − | 1.04411i | ||||
\(331\) | −4.70826 | − | 8.15495i | −0.258789 | − | 0.448236i | 0.707128 | − | 0.707085i | \(-0.249990\pi\) |
−0.965918 | + | 0.258849i | \(0.916657\pi\) | |||||||
\(332\) | −54.4813 | −2.99005 | ||||||||
\(333\) | 0.445966 | + | 11.9549i | 0.0244388 | + | 0.655125i | ||||
\(334\) | −63.8435 | −3.49336 | ||||||||
\(335\) | 2.89263 | + | 5.01018i | 0.158041 | + | 0.273735i | ||||
\(336\) | −22.8657 | + | 6.58610i | −1.24743 | + | 0.359301i | ||||
\(337\) | −4.51261 | + | 7.81606i | −0.245817 | + | 0.425768i | −0.962361 | − | 0.271774i | \(-0.912390\pi\) |
0.716544 | + | 0.697542i | \(0.245723\pi\) | |||||||
\(338\) | 11.2749 | − | 19.5287i | 0.613275 | − | 1.06222i | ||||
\(339\) | 21.0552 | − | 6.06462i | 1.14356 | − | 0.329385i | ||||
\(340\) | 18.4235 | + | 31.9105i | 0.999157 | + | 1.73059i | ||||
\(341\) | −22.1272 | −1.19825 | ||||||||
\(342\) | 16.8441 | − | 10.5812i | 0.910825 | − | 0.572165i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 26.8553 | + | 46.5147i | 1.44794 | + | 2.50791i | ||||
\(345\) | 2.69826 | − | 10.8773i | 0.145270 | − | 0.585613i | ||||
\(346\) | −20.6806 | + | 35.8199i | −1.11180 | + | 1.92569i | ||||
\(347\) | 3.76937 | − | 6.52875i | 0.202351 | − | 0.350481i | −0.746935 | − | 0.664897i | \(-0.768475\pi\) |
0.949285 | + | 0.314416i | \(0.101809\pi\) | |||||||
\(348\) | 29.8761 | + | 28.7824i | 1.60153 | + | 1.54290i | ||||
\(349\) | −2.51662 | − | 4.35891i | −0.134711 | − | 0.233327i | 0.790776 | − | 0.612106i | \(-0.209677\pi\) |
−0.925487 | + | 0.378779i | \(0.876344\pi\) | |||||||
\(350\) | 2.70717 | 0.144704 | ||||||||
\(351\) | −3.50818 | − | 10.6673i | −0.187253 | − | 0.569379i | ||||
\(352\) | −79.8888 | −4.25809 | ||||||||
\(353\) | 1.26788 | + | 2.19603i | 0.0674824 | + | 0.116883i | 0.897792 | − | 0.440419i | \(-0.145170\pi\) |
−0.830310 | + | 0.557302i | \(0.811837\pi\) | |||||||
\(354\) | −31.0353 | − | 29.8991i | −1.64951 | − | 1.58912i | ||||
\(355\) | −7.70803 | + | 13.3507i | −0.409100 | + | 0.708581i | ||||
\(356\) | 2.68409 | − | 4.64898i | 0.142257 | − | 0.246395i | ||||
\(357\) | 2.88359 | − | 11.6244i | 0.152616 | − | 0.615227i | ||||
\(358\) | −2.61821 | − | 4.53487i | −0.138377 | − | 0.239675i | ||||
\(359\) | 24.3845 | 1.28696 | 0.643481 | − | 0.765462i | \(-0.277489\pi\) | ||||
0.643481 | + | 0.765462i | \(0.277489\pi\) | |||||||
\(360\) | 23.9003 | + | 12.6351i | 1.25966 | + | 0.665930i | ||||
\(361\) | −13.0010 | −0.684265 | ||||||||
\(362\) | 9.41274 | + | 16.3033i | 0.494723 | + | 0.856885i | ||||
\(363\) | −10.6013 | + | 3.05354i | −0.556425 | + | 0.160269i | ||||
\(364\) | −5.75799 | + | 9.97313i | −0.301801 | + | 0.522734i | ||||
\(365\) | −3.20110 | + | 5.54447i | −0.167553 | + | 0.290211i | ||||
\(366\) | −35.9221 | + | 10.3468i | −1.87768 | + | 0.540834i | ||||
\(367\) | 13.7397 | + | 23.7978i | 0.717204 | + | 1.24223i | 0.962103 | + | 0.272685i | \(0.0879117\pi\) |
−0.244899 | + | 0.969548i | \(0.578755\pi\) | |||||||
\(368\) | −88.8910 | −4.63377 | ||||||||
\(369\) | −6.02328 | − | 3.18427i | −0.313559 | − | 0.165766i | ||||
\(370\) | −10.7955 | −0.561231 | ||||||||
\(371\) | 0.603272 | + | 1.04490i | 0.0313203 | + | 0.0542484i | ||||
\(372\) | 11.7982 | − | 47.5612i | 0.611710 | − | 2.46593i | ||||
\(373\) | −18.5770 | + | 32.1763i | −0.961880 | + | 1.66603i | −0.244108 | + | 0.969748i | \(0.578495\pi\) |
−0.717772 | + | 0.696278i | \(0.754838\pi\) | |||||||
\(374\) | 39.0082 | − | 67.5642i | 2.01707 | − | 3.49366i | ||||
\(375\) | −1.24736 | − | 1.20170i | −0.0644136 | − | 0.0620555i | ||||
\(376\) | −12.7440 | − | 22.0732i | −0.657219 | − | 1.13834i | ||||
\(377\) | 9.71353 | 0.500272 | ||||||||
\(378\) | −4.39464 | − | 13.3628i | −0.226036 | − | 0.687307i | ||||
\(379\) | 34.3188 | 1.76284 | 0.881420 | − | 0.472333i | \(-0.156588\pi\) | ||||
0.881420 | + | 0.472333i | \(0.156588\pi\) | |||||||
\(380\) | 6.52582 | + | 11.3031i | 0.334767 | + | 0.579834i | ||||
\(381\) | −12.0823 | − | 11.6400i | −0.618997 | − | 0.596337i | ||||
\(382\) | 0.861276 | − | 1.49177i | 0.0440667 | − | 0.0763258i | ||||
\(383\) | −15.7901 | + | 27.3492i | −0.806835 | + | 1.39748i | 0.108210 | + | 0.994128i | \(0.465488\pi\) |
−0.915045 | + | 0.403351i | \(0.867845\pi\) | |||||||
\(384\) | 11.5773 | − | 46.6705i | 0.590801 | − | 2.38165i | ||||
\(385\) | −2.08384 | − | 3.60931i | −0.106202 | − | 0.183948i | ||||
\(386\) | −19.4539 | −0.990179 | ||||||||
\(387\) | −15.1410 | + | 9.51134i | −0.769661 | + | 0.483488i | ||||
\(388\) | 47.3168 | 2.40214 | ||||||||
\(389\) | 2.12369 | + | 3.67833i | 0.107675 | + | 0.186499i | 0.914828 | − | 0.403844i | \(-0.132326\pi\) |
−0.807153 | + | 0.590343i | \(0.798993\pi\) | |||||||
\(390\) | 9.73740 | − | 2.80470i | 0.493072 | − | 0.142022i | ||||
\(391\) | 22.3704 | − | 38.7466i | 1.13132 | − | 1.95950i | ||||
\(392\) | −4.50577 | + | 7.80423i | −0.227576 | + | 0.394173i | ||||
\(393\) | 11.0464 | − | 3.18175i | 0.557219 | − | 0.160498i | ||||
\(394\) | 22.0581 | + | 38.2058i | 1.11127 | + | 1.92478i | ||||
\(395\) | 11.3498 | 0.571072 | ||||||||
\(396\) | −2.48368 | − | 66.5794i | −0.124810 | − | 3.34574i | ||||
\(397\) | −12.5714 | −0.630940 | −0.315470 | − | 0.948936i | \(-0.602162\pi\) | ||||
−0.315470 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(398\) | −13.6463 | − | 23.6361i | −0.684028 | − | 1.18477i | ||||
\(399\) | 1.02140 | − | 4.11748i | 0.0511339 | − | 0.206132i | ||||
\(400\) | −6.86912 | + | 11.8977i | −0.343456 | + | 0.594883i | ||||
\(401\) | −18.6480 | + | 32.2992i | −0.931236 | + | 1.61295i | −0.150023 | + | 0.988683i | \(0.547935\pi\) |
−0.781213 | + | 0.624265i | \(0.785399\pi\) | |||||||
\(402\) | 19.5358 | + | 18.8206i | 0.974357 | + | 0.938687i | ||||
\(403\) | −5.73688 | − | 9.93657i | −0.285775 | − | 0.494976i | ||||
\(404\) | −1.32187 | −0.0657655 | ||||||||
\(405\) | −3.90679 | + | 8.10784i | −0.194130 | + | 0.402882i | ||||
\(406\) | 12.1680 | 0.603887 | ||||||||
\(407\) | 8.30980 | + | 14.3930i | 0.411902 | + | 0.713434i | ||||
\(408\) | 77.7265 | + | 74.8810i | 3.84803 | + | 3.70716i | ||||
\(409\) | 2.27904 | − | 3.94742i | 0.112691 | − | 0.195187i | −0.804163 | − | 0.594409i | \(-0.797386\pi\) |
0.916855 | + | 0.399221i | \(0.130720\pi\) | |||||||
\(410\) | 3.07407 | − | 5.32445i | 0.151818 | − | 0.262956i | ||||
\(411\) | 8.58100 | − | 34.5918i | 0.423270 | − | 1.70629i | ||||
\(412\) | 10.5842 | + | 18.3323i | 0.521444 | + | 0.903167i | ||||
\(413\) | −9.19067 | −0.452243 | ||||||||
\(414\) | −1.95892 | − | 52.5124i | −0.0962758 | − | 2.58084i | ||||
\(415\) | 10.2240 | 0.501876 | ||||||||
\(416\) | −20.7127 | − | 35.8754i | −1.01552 | − | 1.75894i | ||||
\(417\) | −15.2396 | + | 4.38953i | −0.746288 | + | 0.214956i | ||||
\(418\) | 13.8171 | − | 23.9320i | 0.675817 | − | 1.17055i | ||||
\(419\) | 8.36903 | − | 14.4956i | 0.408854 | − | 0.708155i | −0.585908 | − | 0.810378i | \(-0.699262\pi\) |
0.994762 | + | 0.102222i | \(0.0325953\pi\) | |||||||
\(420\) | 8.86912 | − | 2.55461i | 0.432769 | − | 0.124652i | ||||
\(421\) | 12.0704 | + | 20.9065i | 0.588275 | + | 1.01892i | 0.994458 | + | 0.105130i | \(0.0335259\pi\) |
−0.406184 | + | 0.913791i | \(0.633141\pi\) | |||||||
\(422\) | −19.2968 | −0.939353 | ||||||||
\(423\) | 7.18504 | − | 4.51352i | 0.349348 | − | 0.219455i | ||||
\(424\) | −10.8728 | −0.528031 | ||||||||
\(425\) | −3.45737 | − | 5.98835i | −0.167707 | − | 0.290478i | ||||
\(426\) | −17.4039 | + | 70.1588i | −0.843221 | + | 3.39920i | ||||
\(427\) | −3.98623 | + | 6.90435i | −0.192907 | + | 0.334125i | ||||
\(428\) | −11.9045 | + | 20.6191i | −0.575423 | + | 0.996663i | ||||
\(429\) | −11.2347 | − | 10.8234i | −0.542416 | − | 0.522559i | ||||
\(430\) | −8.06763 | − | 13.9736i | −0.389056 | − | 0.673865i | ||||
\(431\) | −19.9625 | −0.961562 | −0.480781 | − | 0.876841i | \(-0.659647\pi\) | ||||
−0.480781 | + | 0.876841i | \(0.659647\pi\) | |||||||
\(432\) | 69.8786 | + | 14.5926i | 3.36204 | + | 0.702087i | ||||
\(433\) | 7.61796 | 0.366096 | 0.183048 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183048 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(434\) | −7.18651 | − | 12.4474i | −0.344963 | − | 0.597494i | ||||
\(435\) | −5.60656 | − | 5.40131i | −0.268814 | − | 0.258973i | ||||
\(436\) | 14.8588 | − | 25.7362i | 0.711609 | − | 1.23254i | ||||
\(437\) | 7.92382 | − | 13.7245i | 0.379048 | − | 0.656530i | ||||
\(438\) | −7.22774 | + | 29.1366i | −0.345355 | + | 1.39220i | ||||
\(439\) | 4.91263 | + | 8.50892i | 0.234467 | + | 0.406109i | 0.959118 | − | 0.283008i | \(-0.0913322\pi\) |
−0.724651 | + | 0.689116i | \(0.757999\pi\) | |||||||
\(440\) | 37.5572 | 1.79047 | ||||||||
\(441\) | −2.65219 | − | 1.40211i | −0.126295 | − | 0.0667670i | ||||
\(442\) | 40.4544 | 1.92422 | ||||||||
\(443\) | −0.208919 | − | 0.361858i | −0.00992605 | − | 0.0171924i | 0.861020 | − | 0.508572i | \(-0.169826\pi\) |
−0.870946 | + | 0.491379i | \(0.836493\pi\) | |||||||
\(444\) | −35.3678 | + | 10.1871i | −1.67848 | + | 0.483459i | ||||
\(445\) | −0.503698 | + | 0.872430i | −0.0238776 | + | 0.0413572i | ||||
\(446\) | −21.5302 | + | 37.2915i | −1.01949 | + | 1.76580i | ||||
\(447\) | −37.4875 | + | 10.7977i | −1.77310 | + | 0.510712i | ||||
\(448\) | −12.2082 | − | 21.1452i | −0.576783 | − | 0.999017i | ||||
\(449\) | −30.5529 | −1.44188 | −0.720941 | − | 0.692996i | \(-0.756290\pi\) | ||||
−0.720941 | + | 0.692996i | \(0.756290\pi\) | |||||||
\(450\) | −7.17992 | − | 3.79574i | −0.338465 | − | 0.178933i | ||||
\(451\) | −9.46504 | −0.445691 | ||||||||
\(452\) | 33.7057 | + | 58.3800i | 1.58538 | + | 2.74596i | ||||
\(453\) | 0.229468 | − | 0.925036i | 0.0107814 | − | 0.0434620i | ||||
\(454\) | −0.725266 | + | 1.25620i | −0.0340384 | + | 0.0589563i | ||||
\(455\) | 1.08055 | − | 1.87156i | 0.0506568 | − | 0.0877402i | ||||
\(456\) | 27.5315 | + | 26.5237i | 1.28928 | + | 1.24208i | ||||
\(457\) | −2.53414 | − | 4.38927i | −0.118542 | − | 0.205321i | 0.800648 | − | 0.599135i | \(-0.204489\pi\) |
−0.919190 | + | 0.393814i | \(0.871155\pi\) | |||||||
\(458\) | −3.53960 | −0.165394 | ||||||||
\(459\) | −23.9464 | + | 26.7869i | −1.11772 | + | 1.25031i | ||||
\(460\) | 34.4789 | 1.60759 | ||||||||
\(461\) | 2.69575 | + | 4.66918i | 0.125554 | + | 0.217465i | 0.921949 | − | 0.387311i | \(-0.126596\pi\) |
−0.796396 | + | 0.604776i | \(0.793263\pi\) | |||||||
\(462\) | −14.0735 | − | 13.5583i | −0.654759 | − | 0.630789i | ||||
\(463\) | −3.15089 | + | 5.45749i | −0.146434 | + | 0.253631i | −0.929907 | − | 0.367795i | \(-0.880113\pi\) |
0.783473 | + | 0.621426i | \(0.213446\pi\) | |||||||
\(464\) | −30.8748 | + | 53.4768i | −1.43333 | + | 2.48260i | ||||
\(465\) | −2.21406 | + | 8.92536i | −0.102675 | + | 0.413903i | ||||
\(466\) | 31.9978 | + | 55.4218i | 1.48227 | + | 2.56737i | ||||
\(467\) | −3.84708 | −0.178022 | −0.0890109 | − | 0.996031i | \(-0.528371\pi\) | ||||
−0.0890109 | + | 0.996031i | \(0.528371\pi\) | |||||||
\(468\) | 29.2546 | − | 18.3773i | 1.35230 | − | 0.849491i | ||||
\(469\) | 5.78525 | 0.267138 | ||||||||
\(470\) | 3.82843 | + | 6.63103i | 0.176592 | + | 0.305867i | ||||
\(471\) | 28.8100 | − | 8.29826i | 1.32750 | − | 0.382364i | ||||
\(472\) | 41.4111 | − | 71.7261i | 1.90610 | − | 3.30146i | ||||
\(473\) | −12.4201 | + | 21.5122i | −0.571076 | + | 0.989133i | ||||
\(474\) | 51.1397 | − | 14.7300i | 2.34893 | − | 0.676570i | ||||
\(475\) | −1.22464 | − | 2.12114i | −0.0561903 | − | 0.0973244i | ||||
\(476\) | 36.8471 | 1.68888 | ||||||||
\(477\) | −0.134933 | − | 3.61712i | −0.00617816 | − | 0.165616i | ||||
\(478\) | −1.24812 | −0.0570875 | ||||||||
\(479\) | 10.0389 | + | 17.3879i | 0.458690 | + | 0.794474i | 0.998892 | − | 0.0470609i | \(-0.0149855\pi\) |
−0.540202 | + | 0.841535i | \(0.681652\pi\) | |||||||
\(480\) | −7.99373 | + | 32.2244i | −0.364862 | + | 1.47084i | ||||
\(481\) | −4.30894 | + | 7.46331i | −0.196471 | + | 0.340297i | ||||
\(482\) | −33.4569 | + | 57.9491i | −1.52392 | + | 2.63951i | ||||
\(483\) | −8.07086 | − | 7.77540i | −0.367237 | − | 0.353793i | ||||
\(484\) | −16.9708 | − | 29.3944i | −0.771402 | − | 1.33611i | ||||
\(485\) | −8.87949 | −0.403197 | ||||||||
\(486\) | −7.08064 | + | 41.6024i | −0.321184 | + | 1.88712i | ||||
\(487\) | −22.0173 | −0.997699 | −0.498849 | − | 0.866689i | \(-0.666244\pi\) | ||||
−0.498849 | + | 0.866689i | \(0.666244\pi\) | |||||||
\(488\) | −35.9221 | − | 62.2189i | −1.62612 | − | 2.81652i | ||||
\(489\) | −11.9794 | − | 11.5409i | −0.541728 | − | 0.521897i | ||||
\(490\) | 1.35359 | − | 2.34448i | 0.0611487 | − | 0.105913i | ||||
\(491\) | −4.89080 | + | 8.47111i | −0.220719 | + | 0.382296i | −0.955026 | − | 0.296521i | \(-0.904174\pi\) |
0.734308 | + | 0.678817i | \(0.237507\pi\) | |||||||
\(492\) | 5.04676 | − | 20.3446i | 0.227526 | − | 0.917205i | ||||
\(493\) | −15.5400 | − | 26.9160i | −0.699884 | − | 1.21224i | ||||
\(494\) | 14.3294 | 0.644709 | ||||||||
\(495\) | 0.466089 | + | 12.4943i | 0.0209491 | + | 0.561579i | ||||
\(496\) | 72.9396 | 3.27509 | ||||||||
\(497\) | 7.70803 | + | 13.3507i | 0.345752 | + | 0.598861i | ||||
\(498\) | 46.0670 | − | 13.2688i | 2.06431 | − | 0.594591i | ||||
\(499\) | −7.01594 | + | 12.1520i | −0.314077 | + | 0.543997i | −0.979241 | − | 0.202700i | \(-0.935028\pi\) |
0.665164 | + | 0.746697i | \(0.268362\pi\) | |||||||
\(500\) | 2.66438 | − | 4.61485i | 0.119155 | − | 0.206382i | ||||
\(501\) | 39.2514 | − | 11.3057i | 1.75362 | − | 0.505102i | ||||
\(502\) | −13.4652 | − | 23.3225i | −0.600983 | − | 1.04093i | ||||
\(503\) | 17.7596 | 0.791862 | 0.395931 | − | 0.918280i | \(-0.370422\pi\) | ||||
0.395931 | + | 0.918280i | \(0.370422\pi\) | |||||||
\(504\) | 22.8925 | − | 14.3807i | 1.01971 | − | 0.640567i | ||||
\(505\) | 0.248063 | 0.0110387 | ||||||||
\(506\) | −36.5011 | − | 63.2218i | −1.62267 | − | 2.81055i | ||||
\(507\) | −3.47364 | + | 14.0030i | −0.154270 | + | 0.621895i | ||||
\(508\) | 25.8080 | − | 44.7008i | 1.14505 | − | 1.98328i | ||||
\(509\) | 16.5982 | − | 28.7489i | 0.735700 | − | 1.27427i | −0.218715 | − | 0.975789i | \(-0.570186\pi\) |
0.954415 | − | 0.298482i | \(-0.0964802\pi\) | |||||||
\(510\) | −23.3499 | − | 22.4951i | −1.03395 | − | 0.996100i | ||||
\(511\) | 3.20110 | + | 5.54447i | 0.141608 | + | 0.245273i | ||||
\(512\) | 15.7383 | 0.695543 | ||||||||
\(513\) | −8.48209 | + | 9.48822i | −0.374493 | + | 0.418915i | ||||
\(514\) | −60.9792 | −2.68968 | ||||||||
\(515\) | −1.98623 | − | 3.44025i | −0.0875237 | − | 0.151595i | ||||
\(516\) | −39.6169 | − | 38.1666i | −1.74404 | − | 1.68019i | ||||
\(517\) | 5.89385 | − | 10.2084i | 0.259211 | − | 0.448967i | ||||
\(518\) | −5.39775 | + | 9.34917i | −0.237163 | + | 0.410779i | ||||
\(519\) | 6.37142 | − | 25.6845i | 0.279674 | − | 1.12743i | ||||
\(520\) | 9.73740 | + | 16.8657i | 0.427013 | + | 0.739609i | ||||
\(521\) | −42.7520 | −1.87300 | −0.936500 | − | 0.350668i | \(-0.885955\pi\) | ||||
−0.936500 | + | 0.350668i | \(0.885955\pi\) | |||||||
\(522\) | −32.2718 | − | 17.0608i | −1.41250 | − | 0.746732i | ||||
\(523\) | 24.9327 | 1.09023 | 0.545114 | − | 0.838362i | \(-0.316486\pi\) | ||||
0.545114 | + | 0.838362i | \(0.316486\pi\) | |||||||
\(524\) | 17.6834 | + | 30.6285i | 0.772502 | + | 1.33801i | ||||
\(525\) | −1.66438 | + | 0.479399i | −0.0726397 | + | 0.0209227i | ||||
\(526\) | 16.3240 | − | 28.2740i | 0.711759 | − | 1.23280i | ||||
\(527\) | −18.3560 | + | 31.7936i | −0.799601 | + | 1.38495i | ||||
\(528\) | 95.2969 | − | 27.4487i | 4.14727 | − | 1.19455i | ||||
\(529\) | −9.43261 | − | 16.3378i | −0.410113 | − | 0.710337i | ||||
\(530\) | 3.26632 | 0.141880 | ||||||||
\(531\) | 24.3754 | + | 12.8863i | 1.05780 | + | 0.559218i | ||||
\(532\) | 13.0516 | 0.565860 | ||||||||
\(533\) | −2.45399 | − | 4.25043i | −0.106294 | − | 0.184107i | ||||
\(534\) | −1.13730 | + | 4.58468i | −0.0492156 | + | 0.198398i | ||||
\(535\) | 2.23400 | − | 3.86940i | 0.0965841 | − | 0.167289i | ||||
\(536\) | −26.0670 | + | 45.1494i | −1.12592 | + | 1.95016i | ||||
\(537\) | 2.41275 | + | 2.32442i | 0.104118 | + | 0.100306i | ||||
\(538\) | 5.80468 | + | 10.0540i | 0.250258 | + | 0.433459i | ||||
\(539\) | −4.16767 | −0.179514 | ||||||||
\(540\) | −27.1044 | − | 5.66015i | −1.16639 | − | 0.243574i | ||||
\(541\) | 17.2838 | 0.743090 | 0.371545 | − | 0.928415i | \(-0.378828\pi\) | ||||
0.371545 | + | 0.928415i | \(0.378828\pi\) | |||||||
\(542\) | −6.07772 | − | 10.5269i | −0.261060 | − | 0.452170i | ||||
\(543\) | −8.67409 | − | 8.35654i | −0.372241 | − | 0.358614i | ||||
\(544\) | −66.2733 | + | 114.789i | −2.84144 | + | 4.92152i | ||||
\(545\) | −2.78842 | + | 4.82968i | −0.119443 | + | 0.206881i | ||||
\(546\) | 2.43976 | − | 9.83519i | 0.104412 | − | 0.420907i | ||||
\(547\) | 12.5504 | + | 21.7379i | 0.536616 | + | 0.929446i | 0.999083 | + | 0.0428094i | \(0.0136308\pi\) |
−0.462468 | + | 0.886636i | \(0.653036\pi\) | |||||||
\(548\) | 109.650 | 4.68400 | ||||||||
\(549\) | 20.2529 | − | 12.7225i | 0.864371 | − | 0.542984i | ||||
\(550\) | −11.2826 | −0.481092 | ||||||||
\(551\) | −5.50442 | − | 9.53394i | −0.234496 | − | 0.406159i | ||||
\(552\) | 97.0465 | − | 27.9527i | 4.13057 | − | 1.18974i | ||||
\(553\) | 5.67491 | − | 9.82924i | 0.241322 | − | 0.417982i | ||||
\(554\) | 2.27242 | − | 3.93595i | 0.0965461 | − | 0.167223i | ||||
\(555\) | 6.63713 | − | 1.91172i | 0.281731 | − | 0.0811479i | ||||
\(556\) | −24.3959 | − | 42.2550i | −1.03462 | − | 1.79201i | ||||
\(557\) | 33.9496 | 1.43849 | 0.719245 | − | 0.694756i | \(-0.244488\pi\) | ||||
0.719245 | + | 0.694756i | \(0.244488\pi\) | |||||||
\(558\) | 1.60740 | + | 43.0891i | 0.0680465 | + | 1.82411i | ||||
\(559\) | −12.8806 | −0.544789 | ||||||||
\(560\) | 6.86912 | + | 11.8977i | 0.290273 | + | 0.502768i | ||||
\(561\) | −12.0179 | + | 48.4466i | −0.507395 | + | 2.04542i | ||||
\(562\) | 24.0360 | − | 41.6316i | 1.01390 | − | 1.75612i | ||||
\(563\) | −0.0831908 | + | 0.144091i | −0.00350608 | + | 0.00607270i | −0.867773 | − | 0.496961i | \(-0.834449\pi\) |
0.864267 | + | 0.503033i | \(0.167783\pi\) | |||||||
\(564\) | 18.7999 | + | 18.1116i | 0.791618 | + | 0.762638i | ||||
\(565\) | −6.32523 | − | 10.9556i | −0.266104 | − | 0.460906i | ||||
\(566\) | 6.38306 | 0.268300 | ||||||||
\(567\) | 5.06820 | + | 7.43730i | 0.212844 | + | 0.312337i | ||||
\(568\) | −138.922 | −5.82906 | ||||||||
\(569\) | 0.808497 | + | 1.40036i | 0.0338939 | + | 0.0587060i | 0.882475 | − | 0.470360i | \(-0.155876\pi\) |
−0.848581 | + | 0.529066i | \(0.822542\pi\) | |||||||
\(570\) | −8.27079 | − | 7.96801i | −0.346425 | − | 0.333743i | ||||
\(571\) | 0.582809 | − | 1.00946i | 0.0243898 | − | 0.0422444i | −0.853573 | − | 0.520973i | \(-0.825569\pi\) |
0.877963 | + | 0.478729i | \(0.158902\pi\) | |||||||
\(572\) | 23.9974 | − | 41.5648i | 1.00338 | − | 1.73791i | ||||
\(573\) | −0.265347 | + | 1.06967i | −0.0110850 | + | 0.0446861i | ||||
\(574\) | −3.07407 | − | 5.32445i | −0.128309 | − | 0.222238i | ||||
\(575\) | −6.47033 | −0.269832 | ||||||||
\(576\) | 2.73059 | + | 73.1982i | 0.113774 | + | 3.04993i | ||||
\(577\) | −21.5482 | −0.897062 | −0.448531 | − | 0.893767i | \(-0.648053\pi\) | ||||
−0.448531 | + | 0.893767i | \(0.648053\pi\) | |||||||
\(578\) | −41.7090 | − | 72.2421i | −1.73487 | − | 3.00488i | ||||
\(579\) | 11.9604 | − | 3.44500i | 0.497057 | − | 0.143169i | ||||
\(580\) | 11.9757 | − | 20.7425i | 0.497263 | − | 0.861285i | ||||
\(581\) | 5.11199 | − | 8.85423i | 0.212081 | − | 0.367335i | ||||
\(582\) | −40.0090 | + | 11.5239i | −1.65843 | + | 0.477682i | ||||
\(583\) | −2.51424 | − | 4.35480i | −0.104129 | − | 0.180357i | ||||
\(584\) | −57.6938 | −2.38738 | ||||||||
\(585\) | −5.48994 | + | 3.44869i | −0.226981 | + | 0.142586i | ||||
\(586\) | −29.9964 | −1.23914 | ||||||||
\(587\) | −17.5719 | − | 30.4354i | −0.725268 | − | 1.25620i | −0.958863 | − | 0.283868i | \(-0.908382\pi\) |
0.233595 | − | 0.972334i | \(-0.424951\pi\) | |||||||
\(588\) | 2.22221 | − | 8.95819i | 0.0916423 | − | 0.369429i | ||||
\(589\) | −6.50190 | + | 11.2616i | −0.267906 | + | 0.464027i | ||||
\(590\) | −12.4404 | + | 21.5473i | −0.512161 | + | 0.887089i | ||||
\(591\) | −20.3272 | − | 19.5830i | −0.836148 | − | 0.805537i | ||||
\(592\) | −27.3923 | − | 47.4448i | −1.12582 | − | 1.94997i | ||||
\(593\) | −37.2623 | −1.53018 | −0.765090 | − | 0.643923i | \(-0.777306\pi\) | ||||
−0.765090 | + | 0.643923i | \(0.777306\pi\) | |||||||
\(594\) | 18.3154 | + | 55.6917i | 0.751491 | + | 2.28506i | ||||
\(595\) | −6.91475 | −0.283477 | ||||||||
\(596\) | −60.0108 | − | 103.942i | −2.45814 | − | 4.25762i | ||||
\(597\) | 12.5754 | + | 12.1151i | 0.514678 | + | 0.495837i | ||||
\(598\) | 18.9272 | − | 32.7828i | 0.773990 | − | 1.34059i | ||||
\(599\) | −17.4631 | + | 30.2470i | −0.713522 | + | 1.23586i | 0.250004 | + | 0.968245i | \(0.419568\pi\) |
−0.963527 | + | 0.267612i | \(0.913765\pi\) | |||||||
\(600\) | 3.75800 | − | 15.1493i | 0.153420 | − | 0.618468i | ||||
\(601\) | −4.96606 | − | 8.60146i | −0.202570 | − | 0.350861i | 0.746786 | − | 0.665064i | \(-0.231596\pi\) |
−0.949356 | + | 0.314203i | \(0.898263\pi\) | |||||||
\(602\) | −16.1353 | −0.657624 | ||||||||
\(603\) | −15.3436 | − | 8.11154i | −0.624839 | − | 0.330327i | ||||
\(604\) | 2.93219 | 0.119309 | ||||||||
\(605\) | 3.18476 | + | 5.51616i | 0.129479 | + | 0.224264i | ||||
\(606\) | 1.11772 | − | 0.321940i | 0.0454041 | − | 0.0130779i | ||||
\(607\) | −14.4965 | + | 25.1087i | −0.588394 | + | 1.01913i | 0.406048 | + | 0.913852i | \(0.366906\pi\) |
−0.994443 | + | 0.105277i | \(0.966427\pi\) | |||||||
\(608\) | −23.4747 | + | 40.6594i | −0.952025 | + | 1.64896i | ||||
\(609\) | −7.48096 | + | 2.15477i | −0.303144 | + | 0.0873156i | ||||
\(610\) | 10.7914 | + | 18.6913i | 0.436931 | + | 0.756787i | ||||
\(611\) | 6.11236 | 0.247280 | ||||||||
\(612\) | −97.7254 | − | 51.6635i | −3.95032 | − | 2.08837i | ||||
\(613\) | 37.4502 | 1.51260 | 0.756299 | − | 0.654226i | \(-0.227006\pi\) | ||||
0.756299 | + | 0.654226i | \(0.227006\pi\) | |||||||
\(614\) | −33.8909 | − | 58.7008i | −1.36773 | − | 2.36897i | ||||
\(615\) | −0.947079 | + | 3.81788i | −0.0381899 | + | 0.153952i | ||||
\(616\) | 18.7786 | − | 32.5255i | 0.756611 | − | 1.31049i | ||||
\(617\) | 18.4575 | − | 31.9694i | 0.743072 | − | 1.28704i | −0.208018 | − | 0.978125i | \(-0.566701\pi\) |
0.951090 | − | 0.308913i | \(-0.0999653\pi\) | |||||||
\(618\) | −13.4143 | − | 12.9232i | −0.539602 | − | 0.519848i | ||||
\(619\) | 15.0361 | + | 26.0434i | 0.604353 | + | 1.04677i | 0.992153 | + | 0.125027i | \(0.0399018\pi\) |
−0.387800 | + | 0.921744i | \(0.626765\pi\) | |||||||
\(620\) | −28.2917 | −1.13622 | ||||||||
\(621\) | 10.5035 | + | 31.9380i | 0.421491 | + | 1.28163i | ||||
\(622\) | −21.3767 | −0.857129 | ||||||||
\(623\) | 0.503698 | + | 0.872430i | 0.0201802 | + | 0.0349532i | ||||
\(624\) | 37.0338 | + | 35.6780i | 1.48254 | + | 1.42827i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1.12621 | − | 1.95065i | 0.0450124 | − | 0.0779637i | ||||
\(627\) | −4.25686 | + | 17.1603i | −0.170003 | + | 0.685317i | ||||
\(628\) | 46.1197 | + | 79.8817i | 1.84038 | + | 3.18763i | ||||
\(629\) | 27.5742 | 1.09946 | ||||||||
\(630\) | −6.87717 | + | 4.32013i | −0.273993 | + | 0.172118i | ||||
\(631\) | −23.0115 | −0.916074 | −0.458037 | − | 0.888933i | \(-0.651447\pi\) | ||||
−0.458037 | + | 0.888933i | \(0.651447\pi\) | |||||||
\(632\) | 51.1397 | + | 88.5766i | 2.03423 | + | 3.52339i | ||||
\(633\) | 11.8638 | − | 3.41717i | 0.471543 | − | 0.135820i | ||||
\(634\) | −24.9677 | + | 43.2454i | −0.991595 | + | 1.71749i | ||||
\(635\) | −4.84315 | + | 8.38858i | −0.192195 | + | 0.332891i | ||||
\(636\) | 10.7010 | − | 3.08225i | 0.424322 | − | 0.122219i | ||||
\(637\) | −1.08055 | − | 1.87156i | −0.0428128 | − | 0.0741540i | ||||
\(638\) | −50.7122 | −2.00772 | ||||||||
\(639\) | −1.72404 | − | 46.2160i | −0.0682021 | − | 1.82828i | ||||
\(640\) | −27.7619 | −1.09739 | ||||||||
\(641\) | 14.8746 | + | 25.7635i | 0.587510 | + | 1.01760i | 0.994557 | + | 0.104190i | \(0.0332249\pi\) |
−0.407048 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(642\) | 5.04412 | − | 20.3339i | 0.199076 | − | 0.802516i | ||||
\(643\) | −16.7292 | + | 28.9758i | −0.659735 | + | 1.14269i | 0.320950 | + | 0.947096i | \(0.395998\pi\) |
−0.980684 | + | 0.195598i | \(0.937335\pi\) | |||||||
\(644\) | 17.2395 | − | 29.8596i | 0.679330 | − | 1.17663i | ||||
\(645\) | 7.43454 | + | 7.16237i | 0.292735 | + | 0.282018i | ||||
\(646\) | −22.9245 | − | 39.7064i | −0.901953 | − | 1.56223i | ||||
\(647\) | 32.8534 | 1.29160 | 0.645799 | − | 0.763507i | \(-0.276524\pi\) | ||||
0.645799 | + | 0.763507i | \(0.276524\pi\) | |||||||
\(648\) | −80.8785 | + | 6.04259i | −3.17721 | + | 0.237376i | ||||
\(649\) | 38.3037 | 1.50355 | ||||||||
\(650\) | −2.92523 | − | 5.06664i | −0.114737 | − | 0.198730i | ||||
\(651\) | 6.62255 | + | 6.38011i | 0.259558 | + | 0.250056i | ||||
\(652\) | 25.5882 | − | 44.3201i | 1.00211 | − | 1.73571i | ||||
\(653\) | 6.20437 | − | 10.7463i | 0.242796 | − | 0.420534i | −0.718714 | − | 0.695306i | \(-0.755269\pi\) |
0.961510 | + | 0.274772i | \(0.0886022\pi\) | |||||||
\(654\) | −6.29594 | + | 25.3803i | −0.246191 | + | 0.992448i | ||||
\(655\) | −3.31847 | − | 5.74777i | −0.129664 | − | 0.224584i | ||||
\(656\) | 31.2004 | 1.21817 | ||||||||
\(657\) | −0.715986 | − | 19.1933i | −0.0279333 | − | 0.748801i | ||||
\(658\) | 7.65686 | 0.298495 | ||||||||
\(659\) | −21.7394 | − | 37.6537i | −0.846847 | − | 1.46678i | −0.884008 | − | 0.467472i | \(-0.845165\pi\) |
0.0371610 | − | 0.999309i | \(-0.488169\pi\) | |||||||
\(660\) | −36.9636 | + | 10.6468i | −1.43881 | + | 0.414425i | ||||
\(661\) | 14.6646 | − | 25.3998i | 0.570386 | − | 0.987938i | −0.426140 | − | 0.904657i | \(-0.640127\pi\) |
0.996526 | − | 0.0832809i | \(-0.0265399\pi\) | |||||||
\(662\) | −12.7461 | + | 22.0768i | −0.495390 | + | 0.858040i | ||||
\(663\) | −24.8716 | + | 7.16386i | −0.965933 | + | 0.278221i | ||||
\(664\) | 46.0670 | + | 79.7903i | 1.78774 | + | 3.09646i | ||||
\(665\) | −2.44928 | −0.0949789 | ||||||||
\(666\) | 27.4244 | − | 17.2275i | 1.06267 | − | 0.667554i | ||||
\(667\) | −29.0824 | −1.12607 | ||||||||
\(668\) | 62.8345 | + | 108.833i | 2.43114 | + | 4.21086i | ||||
\(669\) | 6.63316 | − | 26.7397i | 0.256453 | − | 1.03382i | ||||
\(670\) | 7.83083 | − | 13.5634i | 0.302531 | − | 0.524000i | ||||
\(671\) | 16.6133 | − | 28.7751i | 0.641350 | − | 1.11085i | ||||
\(672\) | 23.9103 | + | 23.0350i | 0.922361 | + | 0.888594i | ||||
\(673\) | −3.89576 | − | 6.74766i | −0.150171 | − | 0.260103i | 0.781119 | − | 0.624382i | \(-0.214649\pi\) |
−0.931290 | + | 0.364278i | \(0.881316\pi\) | |||||||
\(674\) | 24.4328 | 0.941115 | ||||||||
\(675\) | 5.08643 | + | 1.06219i | 0.195777 | + | 0.0408836i | ||||
\(676\) | −44.3869 | −1.70719 | ||||||||
\(677\) | 11.3246 | + | 19.6148i | 0.435240 | + | 0.753858i | 0.997315 | − | 0.0732280i | \(-0.0233301\pi\) |
−0.562075 | + | 0.827086i | \(0.689997\pi\) | |||||||
\(678\) | −42.7184 | − | 41.1546i | −1.64059 | − | 1.58053i | ||||
\(679\) | −4.43975 | + | 7.68987i | −0.170382 | + | 0.295110i | ||||
\(680\) | 31.1563 | − | 53.9643i | 1.19479 | − | 2.06943i | ||||
\(681\) | 0.223444 | − | 0.900752i | 0.00856241 | − | 0.0345169i | ||||
\(682\) | 29.9510 | + | 51.8767i | 1.14688 | + | 1.98646i | ||||
\(683\) | 22.0281 | 0.842880 | 0.421440 | − | 0.906856i | \(-0.361525\pi\) | ||||
0.421440 | + | 0.906856i | \(0.361525\pi\) | |||||||
\(684\) | −34.6154 | − | 18.2998i | −1.32355 | − | 0.699710i | ||||
\(685\) | −20.5769 | −0.786204 | ||||||||
\(686\) | −1.35359 | − | 2.34448i | −0.0516801 | − | 0.0895126i | ||||
\(687\) | 2.17617 | − | 0.626809i | 0.0830259 | − | 0.0239143i | ||||
\(688\) | 40.9413 | − | 70.9125i | 1.56087 | − | 2.70351i | ||||
\(689\) | 1.30373 | − | 2.25812i | 0.0496681 | − | 0.0860277i | ||||
\(690\) | −29.1539 | + | 8.39729i | −1.10987 | + | 0.319679i | ||||
\(691\) | 14.8236 | + | 25.6752i | 0.563915 | + | 0.976729i | 0.997150 | + | 0.0754481i | \(0.0240387\pi\) |
−0.433235 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(692\) | 81.4152 | 3.09494 | ||||||||
\(693\) | 11.0535 | + | 5.84352i | 0.419886 | + | 0.221977i | ||||
\(694\) | −20.4087 | −0.774702 | ||||||||
\(695\) | 4.57816 | + | 7.92960i | 0.173659 | + | 0.300787i | ||||
\(696\) | 16.8912 | − | 68.0920i | 0.640259 | − | 2.58102i | ||||
\(697\) | −7.85190 | + | 13.5999i | −0.297412 | + | 0.515133i | ||||
\(698\) | −6.81291 | + | 11.8003i | −0.257872 | + | 0.446648i | ||||
\(699\) | −29.4868 | − | 28.4073i | −1.11529 | − | 1.07446i | ||||
\(700\) | −2.66438 | − | 4.61485i | −0.100704 | − | 0.174425i | ||||
\(701\) | 32.4868 | 1.22701 | 0.613505 | − | 0.789691i | \(-0.289759\pi\) | ||||
0.613505 | + | 0.789691i | \(0.289759\pi\) | |||||||
\(702\) | −20.2607 | + | 22.6640i | −0.764690 | + | 0.855396i | ||||
\(703\) | 9.76708 | 0.368373 | ||||||||
\(704\) | 50.8798 | + | 88.1263i | 1.91760 | + | 3.32139i | ||||
\(705\) | −3.52800 | − | 3.39884i | −0.132872 | − | 0.128008i | ||||
\(706\) | 3.43236 | − | 5.94503i | 0.129179 | − | 0.223744i | ||||
\(707\) | 0.124032 | − | 0.214829i | 0.00466469 | − | 0.00807947i | ||||
\(708\) | −20.4236 | + | 82.3318i | −0.767565 | + | 3.09422i | ||||
\(709\) | 4.59556 | + | 7.95974i | 0.172590 | + | 0.298934i | 0.939325 | − | 0.343030i | \(-0.111453\pi\) |
−0.766735 | + | 0.641964i | \(0.778120\pi\) | |||||||
\(710\) | 41.7339 | 1.56624 | ||||||||
\(711\) | −28.8326 | + | 18.1121i | −1.08131 | + | 0.679259i | ||||
\(712\) | −9.07819 | −0.340220 | ||||||||
\(713\) | 17.1763 | + | 29.7502i | 0.643257 | + | 1.11415i | ||||
\(714\) | −31.1563 | + | 8.97406i | −1.16599 | + | 0.335846i | ||||
\(715\) | −4.50337 | + | 7.80007i | −0.168416 | + | 0.291706i | ||||
\(716\) | −5.15366 | + | 8.92640i | −0.192601 | + | 0.333595i | ||||
\(717\) | 0.767350 | − | 0.221023i | 0.0286572 | − | 0.00825424i | ||||
\(718\) | −33.0064 | − | 57.1688i | −1.23179 | − | 2.13352i | ||||
\(719\) | 32.0782 | 1.19632 | 0.598158 | − | 0.801378i | \(-0.295900\pi\) | ||||
0.598158 | + | 0.801378i | \(0.295900\pi\) | |||||||
\(720\) | −1.53641 | − | 41.1861i | −0.0572585 | − | 1.53491i | ||||
\(721\) | −3.97246 | −0.147942 | ||||||||
\(722\) | 17.5980 | + | 30.4806i | 0.654930 | + | 1.13437i | ||||
\(723\) | 10.3076 | − | 41.5522i | 0.383344 | − | 1.54534i | ||||
\(724\) | 18.5280 | − | 32.0914i | 0.688586 | − | 1.19267i | ||||
\(725\) | −2.24736 | + | 3.89255i | −0.0834650 | + | 0.144566i | ||||
\(726\) | 21.5087 | + | 20.7213i | 0.798264 | + | 0.769041i | ||||
\(727\) | −26.5430 | − | 45.9738i | −0.984425 | − | 1.70507i | −0.644463 | − | 0.764636i | \(-0.722919\pi\) |
−0.339963 | − | 0.940439i | \(-0.610414\pi\) | |||||||
\(728\) | 19.4748 | 0.721784 | ||||||||
\(729\) | −3.01393 | − | 26.8313i | −0.111627 | − | 0.993750i | ||||
\(730\) | 17.3319 | 0.641481 | ||||||||
\(731\) | 20.6066 | + | 35.6917i | 0.762164 | + | 1.32011i | ||||
\(732\) | 52.9923 | + | 51.0523i | 1.95865 | + | 1.88695i | ||||
\(733\) | −6.72493 | + | 11.6479i | −0.248391 | + | 0.430226i | −0.963080 | − | 0.269217i | \(-0.913235\pi\) |
0.714689 | + | 0.699443i | \(0.246568\pi\) | |||||||
\(734\) | 37.1956 | − | 64.4246i | 1.37291 | − | 2.37796i | ||||
\(735\) | −0.417021 | + | 1.68110i | −0.0153820 | + | 0.0620083i | ||||
\(736\) | 62.0139 | + | 107.411i | 2.28586 | + | 3.95923i | ||||
\(737\) | −24.1111 | −0.888142 | ||||||||
\(738\) | 0.687573 | + | 18.4316i | 0.0253099 | + | 0.678477i | ||||
\(739\) | −44.5198 | −1.63769 | −0.818844 | − | 0.574016i | \(-0.805385\pi\) | ||||
−0.818844 | + | 0.574016i | \(0.805385\pi\) | |||||||
\(740\) | 10.6249 | + | 18.4028i | 0.390578 | + | 0.676501i | ||||
\(741\) | −8.80979 | + | 2.53752i | −0.323636 | + | 0.0932180i | ||||
\(742\) | 1.63316 | − | 2.82872i | 0.0599552 | − | 0.103845i | ||||
\(743\) | 9.34029 | − | 16.1779i | 0.342662 | − | 0.593508i | −0.642264 | − | 0.766483i | \(-0.722005\pi\) |
0.984926 | + | 0.172975i | \(0.0553381\pi\) | |||||||
\(744\) | −79.6316 | + | 22.9366i | −2.91943 | + | 0.840896i | ||||
\(745\) | 11.2617 | + | 19.5058i | 0.412596 | + | 0.714637i | ||||
\(746\) | 100.582 | 3.68258 | ||||||||
\(747\) | −25.9725 | + | 16.3155i | −0.950285 | + | 0.596954i | ||||
\(748\) | −153.567 | −5.61496 | ||||||||
\(749\) | −2.23400 | − | 3.86940i | −0.0816285 | − | 0.141385i | ||||
\(750\) | −1.12895 | + | 4.55102i | −0.0412233 | + | 0.166180i | ||||
\(751\) | −14.6884 | + | 25.4410i | −0.535986 | + | 0.928355i | 0.463129 | + | 0.886291i | \(0.346727\pi\) |
−0.999115 | + | 0.0420642i | \(0.986607\pi\) | |||||||
\(752\) | −19.4284 | + | 33.6509i | −0.708480 | + | 1.22712i | ||||
\(753\) | 12.4086 | + | 11.9543i | 0.452193 | + | 0.435639i | ||||
\(754\) | −13.1481 | − | 22.7732i | −0.478825 | − | 0.829350i | ||||
\(755\) | −0.550257 | −0.0200259 | ||||||||
\(756\) | −18.4540 | + | 20.6430i | −0.671167 | + | 0.750780i | ||||
\(757\) | 22.3860 | 0.813631 | 0.406816 | − | 0.913510i | \(-0.366639\pi\) | ||||
0.406816 | + | 0.913510i | \(0.366639\pi\) | |||||||
\(758\) | −46.4535 | − | 80.4597i | −1.68727 | − | 2.92243i | ||||
\(759\) | 33.6367 | + | 32.4053i | 1.22094 | + | 1.17624i | ||||
\(760\) | 11.0359 | − | 19.1147i | 0.400314 | − | 0.693364i | ||||
\(761\) | −22.1153 | + | 38.3049i | −0.801680 | + | 1.38855i | 0.116830 | + | 0.993152i | \(0.462727\pi\) |
−0.918510 | + | 0.395399i | \(0.870606\pi\) | |||||||
\(762\) | −10.9353 | + | 44.0826i | −0.396144 | + | 1.59694i | ||||
\(763\) | 2.78842 | + | 4.82968i | 0.100947 | + | 0.174846i | ||||
\(764\) | −3.39065 | −0.122670 | ||||||||
\(765\) | 18.3392 | + | 9.69521i | 0.663055 | + | 0.350531i | ||||
\(766\) | 85.4928 | 3.08898 | ||||||||
\(767\) | 9.93096 | + | 17.2009i | 0.358586 | + | 0.621089i | ||||
\(768\) | −43.8124 | + | 12.6195i | −1.58095 | + | 0.455366i | ||||
\(769\) | 10.2249 | − | 17.7101i | 0.368719 | − | 0.638641i | −0.620646 | − | 0.784091i | \(-0.713130\pi\) |
0.989366 | + | 0.145450i | \(0.0464630\pi\) | |||||||
\(770\) | −5.64130 | + | 9.77102i | −0.203298 | + | 0.352123i | ||||
\(771\) | 37.4904 | − | 10.7985i | 1.35018 | − | 0.388899i | ||||
\(772\) | 19.1465 | + | 33.1627i | 0.689097 | + | 1.19355i | ||||
\(773\) | 4.80680 | 0.172889 | 0.0864444 | − | 0.996257i | \(-0.472450\pi\) | ||||
0.0864444 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(774\) | 42.7938 | + | 22.6234i | 1.53819 | + | 0.813180i | ||||
\(775\) | 5.30924 | 0.190713 | ||||||||
\(776\) | −40.0090 | − | 69.2976i | −1.43624 | − | 2.48764i | ||||
\(777\) | 1.66297 | − | 6.70379i | 0.0596587 | − | 0.240497i | ||||
\(778\) | 5.74918 | − | 9.95787i | 0.206118 | − | 0.357007i | ||||
\(779\) | −2.78123 | + | 4.81723i | −0.0996479 | + | 0.172595i | ||||
\(780\) | −14.3646 | − | 13.8387i | −0.514336 | − | 0.495507i | ||||
\(781\) | −32.1246 | − | 55.6414i | −1.14951 | − | 1.99100i | ||||
\(782\) | −121.121 | −4.33127 | ||||||||
\(783\) | 22.8621 | + | 4.77425i | 0.817025 | + | 0.170618i | ||||
\(784\) | 13.7382 | 0.490652 | ||||||||
\(785\) | −8.65486 | − | 14.9907i | −0.308905 | − | 0.535039i | ||||
\(786\) | −22.4118 | − | 21.5914i | −0.799403 | − | 0.770138i | ||||
\(787\) | −19.4794 | + | 33.7394i | −0.694367 | + | 1.20268i | 0.276026 | + | 0.961150i | \(0.410982\pi\) |
−0.970394 | + | 0.241529i | \(0.922351\pi\) | |||||||
\(788\) | 43.4191 | − | 75.2040i | 1.54674 | − | 2.67903i | ||||
\(789\) | −5.02919 | + | 20.2737i | −0.179044 | + | 0.721764i | ||||
\(790\) | −15.3630 | − | 26.6094i | −0.546589 | − | 0.946720i | ||||
\(791\) | −12.6505 | −0.449799 | ||||||||
\(792\) | −95.4085 | + | 59.9341i | −3.39019 | + | 2.12967i | ||||
\(793\) | 17.2292 | 0.611828 | ||||||||
\(794\) | 17.0164 | + | 29.4733i | 0.603891 | + | 1.04597i | ||||
\(795\) | −2.00815 | + | 0.578416i | −0.0712219 | + | 0.0205143i | ||||
\(796\) | −26.8613 | + | 46.5251i | −0.952073 | + | 1.64904i | ||||
\(797\) | −9.44776 | + | 16.3640i | −0.334657 | + | 0.579643i | −0.983419 | − | 0.181349i | \(-0.941954\pi\) |
0.648762 | + | 0.760991i | \(0.275287\pi\) | |||||||
\(798\) | −11.0359 | + | 3.17871i | −0.390666 | + | 0.112525i | ||||
\(799\) | −9.77870 | − | 16.9372i | −0.345946 | − | 0.599195i | ||||
\(800\) | 19.1687 | 0.677715 | ||||||||
\(801\) | −0.112661 | − | 3.02009i | −0.00398069 | − | 0.106710i | ||||
\(802\) | 100.967 | 3.56525 | ||||||||
\(803\) | −13.3412 | − | 23.1076i | −0.470799 | − | 0.815448i | ||||
\(804\) | 12.8560 | − | 51.8254i | 0.453397 | − | 1.82774i | ||||
\(805\) | −3.23517 | + | 5.60347i | −0.114025 | + | 0.197496i | ||||
\(806\) | −15.5307 | + | 26.9000i | −0.547046 | + | 0.947512i | ||||
\(807\) | −5.34917 | − | 5.15334i | −0.188300 | − | 0.181406i | ||||
\(808\) | 1.11772 | + | 1.93594i | 0.0393211 | + | 0.0681061i | ||||
\(809\) | 1.94753 | 0.0684716 | 0.0342358 | − | 0.999414i | \(-0.489100\pi\) | ||||
0.0342358 | + | 0.999414i | \(0.489100\pi\) | |||||||
\(810\) | 24.2968 | − | 1.81526i | 0.853703 | − | 0.0637819i | ||||
\(811\) | −51.0182 | −1.79149 | −0.895746 | − | 0.444565i | \(-0.853358\pi\) | ||||
−0.895746 | + | 0.444565i | \(0.853358\pi\) | |||||||
\(812\) | −11.9757 | − | 20.7425i | −0.420264 | − | 0.727919i | ||||
\(813\) | 5.60078 | + | 5.39574i | 0.196428 | + | 0.189237i | ||||
\(814\) | 22.4960 | − | 38.9643i | 0.788486 | − | 1.36570i | ||||
\(815\) | −4.80190 | + | 8.31713i | −0.168203 | + | 0.291336i | ||||
\(816\) | 39.6155 | − | 159.699i | 1.38682 | − | 5.59057i | ||||
\(817\) | 7.29909 | + | 12.6424i | 0.255363 | + | 0.442301i | ||||
\(818\) | −12.3395 | −0.431441 | ||||||||
\(819\) | 0.241684 | + | 6.47878i | 0.00844514 | + | 0.226387i | ||||
\(820\) | −12.1020 | −0.422619 | ||||||||
\(821\) | 8.23988 | + | 14.2719i | 0.287574 | + | 0.498093i | 0.973230 | − | 0.229833i | \(-0.0738180\pi\) |
−0.685656 | + | 0.727926i | \(0.740485\pi\) | |||||||
\(822\) | −92.7149 | + | 26.7050i | −3.23381 | + | 0.931445i | ||||
\(823\) | −11.7457 | + | 20.3442i | −0.409429 | + | 0.709153i | −0.994826 | − | 0.101595i | \(-0.967606\pi\) |
0.585396 | + | 0.810747i | \(0.300939\pi\) | |||||||
\(824\) | 17.8990 | − | 31.0020i | 0.623541 | − | 1.08000i | ||||
\(825\) | 6.93661 | − | 1.99798i | 0.241502 | − | 0.0695607i | ||||
\(826\) | 12.4404 | + | 21.5473i | 0.432855 | + | 0.749727i | ||||
\(827\) | −18.7714 | −0.652744 | −0.326372 | − | 0.945241i | \(-0.605826\pi\) | ||||
−0.326372 | + | 0.945241i | \(0.605826\pi\) | |||||||
\(828\) | −87.5886 | + | 55.0218i | −3.04392 | + | 1.91214i | ||||
\(829\) | 40.9504 | 1.42227 | 0.711134 | − | 0.703057i | \(-0.248182\pi\) | ||||
0.711134 | + | 0.703057i | \(0.248182\pi\) | |||||||
\(830\) | −13.8390 | − | 23.9699i | −0.480360 | − | 0.832008i | ||||
\(831\) | −0.700102 | + | 2.82226i | −0.0242863 | + | 0.0979032i | ||||
\(832\) | −26.3830 | + | 45.6968i | −0.914668 | + | 1.58425i | ||||
\(833\) | −3.45737 | + | 5.98835i | −0.119791 | + | 0.207484i | ||||
\(834\) | 30.9193 | + | 29.7874i | 1.07065 | + | 1.03145i | ||||
\(835\) | −11.7916 | − | 20.4236i | −0.408064 | − | 0.706787i | ||||
\(836\) | −54.3950 | −1.88129 | ||||||||
\(837\) | −8.61866 | − | 26.2068i | −0.297904 | − | 0.905839i | ||||
\(838\) | −45.3128 | −1.56530 | ||||||||
\(839\) | 4.06342 | + | 7.03805i | 0.140285 | + | 0.242981i | 0.927604 | − | 0.373565i | \(-0.121865\pi\) |
−0.787319 | + | 0.616546i | \(0.788531\pi\) | |||||||
\(840\) | −11.2407 | − | 10.8292i | −0.387840 | − | 0.373642i | ||||
\(841\) | 4.39871 | − | 7.61879i | 0.151680 | − | 0.262717i | ||||
\(842\) | 32.6766 | − | 56.5975i | 1.12611 | − | 1.95048i | ||||
\(843\) | −7.40517 | + | 29.8518i | −0.255047 | + | 1.02815i | ||||
\(844\) | 18.9918 | + | 32.8948i | 0.653725 | + | 1.13229i | ||||
\(845\) | 8.32967 | 0.286549 | ||||||||
\(846\) | −20.3074 | − | 10.7357i | −0.698183 | − | 0.369102i | ||||
\(847\) | 6.36951 | 0.218859 | ||||||||
\(848\) | 8.28790 | + | 14.3551i | 0.284608 | + | 0.492955i | ||||
\(849\) | −3.92435 | + | 1.13034i | −0.134683 | + | 0.0387933i | ||||
\(850\) | −9.35970 | + | 16.2115i | −0.321035 | + | 0.556049i | ||||
\(851\) | 12.9010 | − | 22.3452i | 0.442241 | − | 0.765983i | ||||
\(852\) | 136.727 | − | 39.3820i | 4.68419 | − | 1.34920i | ||||
\(853\) | −12.1844 | − | 21.1039i | −0.417185 | − | 0.722585i | 0.578470 | − | 0.815703i | \(-0.303650\pi\) |
−0.995655 | + | 0.0931183i | \(0.970317\pi\) | |||||||
\(854\) | 21.5828 | 0.738548 | ||||||||
\(855\) | 6.49595 | + | 3.43415i | 0.222157 | + | 0.117445i | ||||
\(856\) | 40.2635 | 1.37618 | ||||||||
\(857\) | −6.52746 | − | 11.3059i | −0.222974 | − | 0.386202i | 0.732736 | − | 0.680513i | \(-0.238243\pi\) |
−0.955710 | + | 0.294311i | \(0.904910\pi\) | |||||||
\(858\) | −10.1681 | + | 40.9899i | −0.347134 | + | 1.39937i | ||||
\(859\) | −4.02025 | + | 6.96328i | −0.137169 | + | 0.237584i | −0.926424 | − | 0.376482i | \(-0.877134\pi\) |
0.789255 | + | 0.614066i | \(0.210467\pi\) | |||||||
\(860\) | −15.8803 | + | 27.5054i | −0.541512 | + | 0.937927i | ||||
\(861\) | 2.83284 | + | 2.72913i | 0.0965429 | + | 0.0930086i | ||||
\(862\) | 27.0210 | + | 46.8017i | 0.920339 | + | 1.59407i | ||||
\(863\) | −34.8130 | −1.18505 | −0.592523 | − | 0.805553i | \(-0.701868\pi\) | ||||
−0.592523 | + | 0.805553i | \(0.701868\pi\) | |||||||
\(864\) | −31.1171 | − | 94.6179i | −1.05863 | − | 3.21897i | ||||
\(865\) | −15.2784 | −0.519482 | ||||||||
\(866\) | −10.3116 | − | 17.8601i | −0.350401 | − | 0.606912i | ||||
\(867\) | 38.4359 | + | 37.0289i | 1.30535 | + | 1.25757i | ||||
\(868\) | −14.1459 | + | 24.5013i | −0.480142 | + | 0.831630i | ||||
\(869\) | −23.6512 | + | 40.9651i | −0.802312 | + | 1.38964i | ||||
\(870\) | −5.07430 | + | 20.4556i | −0.172035 | + | 0.693510i | ||||
\(871\) | −6.25124 | − | 10.8275i | −0.211815 | − | 0.366875i | ||||
\(872\) | −50.2559 | −1.70188 | ||||||||
\(873\) | 22.5570 | − | 14.1700i | 0.763440 | − | 0.479581i | ||||
\(874\) | −42.9023 | −1.45119 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | 56.7819 | − | 16.3551i | 1.91848 | − | 0.552588i | ||||
\(877\) | 20.1118 | − | 34.8347i | 0.679127 | − | 1.17628i | −0.296117 | − | 0.955152i | \(-0.595692\pi\) |
0.975244 | − | 0.221131i | \(-0.0709750\pi\) | |||||||
\(878\) | 13.2993 | − | 23.0351i | 0.448830 | − | 0.777397i | ||||
\(879\) | 18.4420 | − | 5.31191i | 0.622032 | − | 0.179166i | ||||
\(880\) | −28.6283 | − | 49.5856i | −0.965059 | − | 1.67153i | ||||
\(881\) | 25.8229 | 0.869995 | 0.434998 | − | 0.900432i | \(-0.356749\pi\) | ||||
0.434998 | + | 0.900432i | \(0.356749\pi\) | |||||||
\(882\) | 0.302754 | + | 8.11587i | 0.0101943 | + | 0.273275i | ||||
\(883\) | −25.4291 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(884\) | −39.8150 | − | 68.9617i | −1.33912 | − | 2.31943i | ||||
\(885\) | 3.83270 | − | 15.4504i | 0.128835 | − | 0.519360i | ||||
\(886\) | −0.565579 | + | 0.979612i | −0.0190010 | + | 0.0329107i | ||||
\(887\) | −6.63820 | + | 11.4977i | −0.222889 | + | 0.386055i | −0.955684 | − | 0.294394i | \(-0.904882\pi\) |
0.732795 | + | 0.680449i | \(0.238215\pi\) | |||||||
\(888\) | 44.8249 | + | 43.1839i | 1.50423 | + | 1.44916i | ||||
\(889\) | 4.84315 | + | 8.38858i | 0.162434 | + | 0.281344i | ||||
\(890\) | 2.72719 | 0.0914157 | ||||||||
\(891\) | −21.1226 | − | 30.9962i | −0.707634 | − | 1.03841i | ||||
\(892\) | 84.7598 | 2.83797 | ||||||||
\(893\) | −3.46372 | − | 5.99934i | −0.115909 | − | 0.200760i | ||||
\(894\) | 76.0574 | + | 73.2731i | 2.54374 | + | 2.45062i | ||||
\(895\) | 0.967139 | − | 1.67513i | 0.0323279 | − | 0.0559936i | ||||
\(896\) | −13.8810 | + | 24.0425i | −0.463730 | + | 0.803205i | ||||
\(897\) | −5.83120 | + | 23.5068i | −0.194698 | + | 0.784870i | ||||
\(898\) | 41.3560 | + | 71.6307i | 1.38007 | + | 2.39035i | ||||
\(899\) | 23.8636 | 0.795895 | ||||||||
\(900\) | 0.595939 | + | 15.9752i | 0.0198646 | + | 0.532507i | ||||
\(901\) | −8.34295 | −0.277944 | ||||||||
\(902\) | 12.8117 | + | 22.1906i | 0.426584 | + | 0.738865i | ||||
\(903\) | 9.92006 | − | 2.85731i | 0.330119 | − | 0.0950854i | ||||
\(904\) | 57.0001 | − | 98.7271i | 1.89580 | − | 3.28361i | ||||
\(905\) | −3.47697 | + | 6.02228i | −0.115578 | + | 0.200188i | ||||
\(906\) | −2.47933 | + | 0.714131i | −0.0823702 | + | 0.0237254i | ||||
\(907\) | −3.02387 | − | 5.23750i | −0.100406 | − | 0.173908i | 0.811446 | − | 0.584428i | \(-0.198681\pi\) |
−0.911852 | + | 0.410519i | \(0.865348\pi\) | |||||||
\(908\) | 2.85521 | 0.0947536 | ||||||||
\(909\) | −0.630168 | + | 0.395861i | −0.0209013 | + | 0.0131299i | ||||
\(910\) | −5.85045 | −0.193941 | ||||||||
\(911\) | 1.75861 | + | 3.04600i | 0.0582652 | + | 0.100918i | 0.893687 | − | 0.448691i | \(-0.148110\pi\) |
−0.835422 | + | 0.549610i | \(0.814776\pi\) | |||||||
\(912\) | 14.0322 | − | 56.5669i | 0.464654 | − | 1.87312i | ||||
\(913\) | −21.3051 | + | 36.9016i | −0.705097 | + | 1.22126i | ||||
\(914\) | −6.86036 | + | 11.8825i | −0.226920 | + | 0.393038i | ||||
\(915\) | −9.94456 | − | 9.58050i | −0.328757 | − | 0.316722i | ||||
\(916\) | 3.48365 | + | 6.03387i | 0.115103 | + | 0.199365i | ||||
\(917\) | −6.63695 | −0.219171 | ||||||||
\(918\) | 95.2149 | + | 19.8835i | 3.14256 | + | 0.656254i | ||||
\(919\) | −21.2381 | −0.700581 | −0.350290 | − | 0.936641i | \(-0.613917\pi\) | ||||
−0.350290 | + | 0.936641i | \(0.613917\pi\) | |||||||
\(920\) | −29.1539 | − | 50.4960i | −0.961174 | − | 1.66480i | ||||
\(921\) | 31.2314 | + | 30.0880i | 1.02911 | + | 0.991434i | ||||
\(922\) | 7.29786 | − | 12.6403i | 0.240342 | − | 0.416285i | ||||
\(923\) | 16.6578 | − | 28.8521i | 0.548297 | − | 0.949679i | ||||
\(924\) | −9.26144 | + | 37.3348i | −0.304679 | + | 1.22823i | ||||
\(925\) | −1.99387 | − | 3.45348i | −0.0655580 | − | 0.113550i | ||||
\(926\) | 17.0600 | 0.560625 | ||||||||
\(927\) | 10.5357 | + | 5.56981i | 0.346038 | + | 0.182936i | ||||
\(928\) | 86.1580 | 2.82827 | ||||||||
\(929\) | −16.7596 | − | 29.0285i | −0.549866 | − | 0.952395i | −0.998283 | − | 0.0585710i | \(-0.981346\pi\) |
0.448418 | − | 0.893824i | \(-0.351988\pi\) | |||||||
\(930\) | 23.9222 | − | 6.89041i | 0.784441 | − | 0.225945i | ||||
\(931\) | −1.22464 | + | 2.12114i | −0.0401359 | + | 0.0695175i | ||||
\(932\) | 62.9842 | − | 109.092i | 2.06312 | − | 3.57342i | ||||
\(933\) | 13.1426 | − | 3.78550i | 0.430268 | − | 0.123932i | ||||
\(934\) | 5.20736 | + | 9.01941i | 0.170390 | + | 0.295124i | ||||
\(935\) | 28.8184 | 0.942463 | ||||||||
\(936\) | −51.6508 | − | 27.3057i | −1.68826 | − | 0.892516i | ||||
\(937\) | −20.2231 | −0.660661 | −0.330330 | − | 0.943865i | \(-0.607160\pi\) | ||||
−0.330330 | + | 0.943865i | \(0.607160\pi\) | |||||||
\(938\) | −7.83083 | − | 13.5634i | −0.255686 | − | 0.442861i | ||||
\(939\) | −0.346969 | + | 1.39871i | −0.0113229 | + | 0.0456451i | ||||
\(940\) | 7.53584 | − | 13.0525i | 0.245792 | − | 0.425724i | ||||
\(941\) | −12.4190 | + | 21.5104i | −0.404848 | + | 0.701218i | −0.994304 | − | 0.106583i | \(-0.966009\pi\) |
0.589456 | + | 0.807801i | \(0.299342\pi\) | |||||||
\(942\) | −58.4519 | − | 56.3121i | −1.90447 | − | 1.83475i | ||||
\(943\) | 7.34726 | + | 12.7258i | 0.239260 | + | 0.414410i | ||||
\(944\) | −126.264 | −4.10953 | ||||||||
\(945\) | 3.46310 | − | 3.87388i | 0.112655 | − | 0.126017i | ||||
\(946\) | 67.2466 | 2.18637 | ||||||||
\(947\) | −21.9742 | − | 38.0605i | −0.714067 | − | 1.23680i | −0.963318 | − | 0.268361i | \(-0.913518\pi\) |
0.249251 | − | 0.968439i | \(-0.419815\pi\) | |||||||
\(948\) | −75.4413 | − | 72.6795i | −2.45022 | − | 2.36052i | ||||
\(949\) | 6.91789 | − | 11.9821i | 0.224564 | − | 0.388956i | ||||
\(950\) | −3.31531 | + | 5.74228i | −0.107563 | + | 0.186304i | ||||
\(951\) | 7.69221 | − | 31.0089i | 0.249437 | − | 1.00553i | ||||
\(952\) | −31.1563 | − | 53.9643i | −1.00978 | − | 1.74899i | ||||
\(953\) | 14.6532 | 0.474665 | 0.237332 | − | 0.971428i | \(-0.423727\pi\) | ||||
0.237332 | + | 0.971428i | \(0.423727\pi\) | |||||||
\(954\) | −8.29761 | + | 5.21242i | −0.268645 | + | 0.168758i | ||||
\(955\) | 0.636292 | 0.0205899 | ||||||||
\(956\) | 1.22839 | + | 2.12764i | 0.0397290 | + | 0.0688126i | ||||
\(957\) | 31.1782 | − | 8.98037i | 1.00785 | − | 0.290294i | ||||
\(958\) | 27.1771 | − | 47.0721i | 0.878051 | − | 1.52083i | ||||
\(959\) | −10.2885 | + | 17.8201i | −0.332232 | + | 0.575442i | ||||
\(960\) | 40.6382 | − | 11.7052i | 1.31159 | − | 0.377783i | ||||
\(961\) | 1.40599 | + | 2.43525i | 0.0453545 | + | 0.0785563i | ||||
\(962\) | 23.3301 | 0.752192 | ||||||||
\(963\) | 0.499675 | + | 13.3947i | 0.0161018 | + | 0.431637i | ||||
\(964\) | 131.713 | 4.24218 | ||||||||
\(965\) | −3.59304 | − | 6.22333i | −0.115664 | − | 0.200336i | ||||
\(966\) | −7.30466 | + | 29.4466i | −0.235023 | + | 0.947430i | ||||
\(967\) | −20.1998 | + | 34.9871i | −0.649583 | + | 1.12511i | 0.333640 | + | 0.942701i | \(0.391723\pi\) |
−0.983223 | + | 0.182410i | \(0.941610\pi\) | |||||||
\(968\) | −28.6996 | + | 49.7091i | −0.922440 | + | 1.59771i | ||||
\(969\) | 21.1255 | + | 20.3522i | 0.678650 | + | 0.653806i | ||||
\(970\) | 12.0191 | + | 20.8178i | 0.385912 | + | 0.668418i | ||||
\(971\) | 55.6840 | 1.78699 | 0.893493 | − | 0.449077i | \(-0.148247\pi\) | ||||
0.893493 | + | 0.449077i | \(0.148247\pi\) | |||||||
\(972\) | 77.8873 | − | 28.8747i | 2.49824 | − | 0.926155i | ||||
\(973\) | 9.15632 | 0.293538 | ||||||||
\(974\) | 29.8023 | + | 51.6191i | 0.954927 | + | 1.65398i | ||||
\(975\) | 2.69567 | + | 2.59699i | 0.0863306 | + | 0.0831702i | ||||
\(976\) | −54.7638 | + | 94.8537i | −1.75295 | + | 3.03619i | ||||
\(977\) | −14.7158 | + | 25.4886i | −0.470801 | + | 0.815452i | −0.999442 | − | 0.0333938i | \(-0.989368\pi\) |
0.528641 | + | 0.848845i | \(0.322702\pi\) | |||||||
\(978\) | −10.8422 | + | 43.7071i | −0.346694 | + | 1.39760i | ||||
\(979\) | −2.09925 | − | 3.63601i | −0.0670923 | − | 0.116207i | ||||
\(980\) | −5.32877 | −0.170221 | ||||||||
\(981\) | −0.623681 | − | 16.7189i | −0.0199126 | − | 0.533792i | ||||
\(982\) | 26.4804 | 0.845025 | ||||||||
\(983\) | 4.62544 | + | 8.01149i | 0.147529 | + | 0.255527i | 0.930313 | − | 0.366765i | \(-0.119535\pi\) |
−0.782785 | + | 0.622292i | \(0.786202\pi\) | |||||||
\(984\) | −34.0629 | + | 9.81126i | −1.08589 | + | 0.312772i | ||||
\(985\) | −8.14805 | + | 14.1128i | −0.259618 | + | 0.449672i | ||||
\(986\) | −42.0693 | + | 72.8662i | −1.33976 | + | 2.32053i | ||||
\(987\) | −4.70748 | + | 1.35591i | −0.149841 | + | 0.0431592i | ||||
\(988\) | −14.1029 | − | 24.4270i | −0.448673 | − | 0.777125i | ||||
\(989\) | 38.5645 | 1.22628 | ||||||||
\(990\) | 28.6618 | − | 18.0049i | 0.910932 | − | 0.572233i | ||||
\(991\) | −12.0283 | −0.382091 | −0.191046 | − | 0.981581i | \(-0.561188\pi\) | ||||
−0.191046 | + | 0.981581i | \(0.561188\pi\) | |||||||
\(992\) | −50.8855 | − | 88.1363i | −1.61562 | − | 2.79833i | ||||
\(993\) | 3.92688 | − | 15.8301i | 0.124616 | − | 0.502353i | ||||
\(994\) | 20.8669 | − | 36.1426i | 0.661859 | − | 1.14637i | ||||
\(995\) | 5.04080 | − | 8.73093i | 0.159804 | − | 0.276789i | ||||
\(996\) | −67.9580 | − | 65.4701i | −2.15333 | − | 2.07450i | ||||
\(997\) | −9.58480 | − | 16.6014i | −0.303554 | − | 0.525770i | 0.673385 | − | 0.739292i | \(-0.264840\pi\) |
−0.976938 | + | 0.213522i | \(0.931506\pi\) | |||||||
\(998\) | 37.9867 | 1.20245 | ||||||||
\(999\) | −13.8099 | + | 15.4480i | −0.436927 | + | 0.488754i |
(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 | 315.2.i.e.211.1 | yes | 12 | |
3.2 | odd | 2 | 945.2.i.e.631.6 | 12 | |||
9.2 | odd | 6 | 945.2.i.e.316.6 | 12 | |||
9.4 | even | 3 | 2835.2.a.u.1.6 | 6 | |||
9.5 | odd | 6 | 2835.2.a.v.1.1 | 6 | |||
9.7 | even | 3 | inner | 315.2.i.e.106.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.e.106.1 | ✓ | 12 | 9.7 | even | 3 | inner | |
315.2.i.e.211.1 | yes | 12 | 1.1 | even | 1 | trivial | |
945.2.i.e.316.6 | 12 | 9.2 | odd | 6 | |||
945.2.i.e.631.6 | 12 | 3.2 | odd | 2 | |||
2835.2.a.u.1.6 | 6 | 9.4 | even | 3 | |||
2835.2.a.v.1.1 | 6 | 9.5 | odd | 6 |