Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,3,Mod(6,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.6");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.d (of order \(4\), 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: | \(1.00817697813\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} - 2054 x^{3} + 3042 x^{2} + 312 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 6.3 | ||
Root | \(-0.0496173 + 0.0496173i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.6 |
Dual form | 37.3.d.a.31.3 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04962 | + | 1.04962i | −0.524809 | + | 0.524809i | −0.919020 | − | 0.394211i | \(-0.871018\pi\) |
0.394211 | + | 0.919020i | \(0.371018\pi\) | |||||||
\(3\) | − | 0.377912i | − | 0.125971i | −0.998014 | − | 0.0629853i | \(-0.979938\pi\) | ||
0.998014 | − | 0.0629853i | \(-0.0200621\pi\) | |||||||
\(4\) | 1.79661i | 0.449152i | ||||||||
\(5\) | 5.26886 | + | 5.26886i | 1.05377 | + | 1.05377i | 0.998470 | + | 0.0553026i | \(0.0176123\pi\) |
0.0553026 | + | 0.998470i | \(0.482388\pi\) | |||||||
\(6\) | 0.396663 | + | 0.396663i | 0.0661105 | + | 0.0661105i | ||||
\(7\) | −5.54265 | −0.791807 | −0.395903 | − | 0.918292i | \(-0.629568\pi\) | ||||
−0.395903 | + | 0.918292i | \(0.629568\pi\) | |||||||
\(8\) | −6.08422 | − | 6.08422i | −0.760527 | − | 0.760527i | ||||
\(9\) | 8.85718 | 0.984131 | ||||||||
\(10\) | −11.0606 | −1.10606 | ||||||||
\(11\) | − | 18.1924i | − | 1.65385i | −0.562310 | − | 0.826927i | \(-0.690087\pi\) | ||
0.562310 | − | 0.826927i | \(-0.309913\pi\) | |||||||
\(12\) | 0.678959 | 0.0565799 | ||||||||
\(13\) | 7.75987 | + | 7.75987i | 0.596913 | + | 0.596913i | 0.939490 | − | 0.342577i | \(-0.111300\pi\) |
−0.342577 | + | 0.939490i | \(0.611300\pi\) | |||||||
\(14\) | 5.81766 | − | 5.81766i | 0.415547 | − | 0.415547i | ||||
\(15\) | 1.99117 | − | 1.99117i | 0.132744 | − | 0.132744i | ||||
\(16\) | 5.58578 | 0.349111 | ||||||||
\(17\) | −18.1161 | − | 18.1161i | −1.06565 | − | 1.06565i | −0.997688 | − | 0.0679669i | \(-0.978349\pi\) |
−0.0679669 | − | 0.997688i | \(-0.521651\pi\) | |||||||
\(18\) | −9.29665 | + | 9.29665i | −0.516481 | + | 0.516481i | ||||
\(19\) | 2.37917 | + | 2.37917i | 0.125219 | + | 0.125219i | 0.766939 | − | 0.641720i | \(-0.221779\pi\) |
−0.641720 | + | 0.766939i | \(0.721779\pi\) | |||||||
\(20\) | −9.46607 | + | 9.46607i | −0.473304 | + | 0.473304i | ||||
\(21\) | 2.09463i | 0.0997444i | ||||||||
\(22\) | 19.0950 | + | 19.0950i | 0.867957 | + | 0.867957i | ||||
\(23\) | 16.3967 | + | 16.3967i | 0.712901 | + | 0.712901i | 0.967141 | − | 0.254240i | \(-0.0818254\pi\) |
−0.254240 | + | 0.967141i | \(0.581825\pi\) | |||||||
\(24\) | −2.29930 | + | 2.29930i | −0.0958041 | + | 0.0958041i | ||||
\(25\) | 30.5218i | 1.22087i | ||||||||
\(26\) | −16.2898 | −0.626530 | ||||||||
\(27\) | − | 6.74844i | − | 0.249942i | ||||||
\(28\) | − | 9.95796i | − | 0.355641i | ||||||
\(29\) | 20.1686 | − | 20.1686i | 0.695469 | − | 0.695469i | −0.267960 | − | 0.963430i | \(-0.586350\pi\) |
0.963430 | + | 0.267960i | \(0.0863497\pi\) | |||||||
\(30\) | 4.17992i | 0.139331i | ||||||||
\(31\) | −10.4372 | + | 10.4372i | −0.336684 | + | 0.336684i | −0.855118 | − | 0.518434i | \(-0.826515\pi\) |
0.518434 | + | 0.855118i | \(0.326515\pi\) | |||||||
\(32\) | 18.4739 | − | 18.4739i | 0.577311 | − | 0.577311i | ||||
\(33\) | −6.87512 | −0.208337 | ||||||||
\(34\) | 38.0300 | 1.11853 | ||||||||
\(35\) | −29.2034 | − | 29.2034i | −0.834384 | − | 0.834384i | ||||
\(36\) | 15.9129i | 0.442024i | ||||||||
\(37\) | −32.1547 | + | 18.3051i | −0.869045 | + | 0.494732i | ||||
\(38\) | −4.99444 | −0.131433 | ||||||||
\(39\) | 2.93255 | − | 2.93255i | 0.0751935 | − | 0.0751935i | ||||
\(40\) | − | 64.1138i | − | 1.60285i | ||||||
\(41\) | 2.51067i | 0.0612359i | 0.999531 | + | 0.0306180i | \(0.00974753\pi\) | ||||
−0.999531 | + | 0.0306180i | \(0.990252\pi\) | |||||||
\(42\) | −2.19856 | − | 2.19856i | −0.0523467 | − | 0.0523467i | ||||
\(43\) | −19.0228 | − | 19.0228i | −0.442391 | − | 0.442391i | 0.450424 | − | 0.892815i | \(-0.351273\pi\) |
−0.892815 | + | 0.450424i | \(0.851273\pi\) | |||||||
\(44\) | 32.6846 | 0.742831 | ||||||||
\(45\) | 46.6673 | + | 46.6673i | 1.03705 | + | 1.03705i | ||||
\(46\) | −34.4206 | −0.748273 | ||||||||
\(47\) | −33.0588 | −0.703378 | −0.351689 | − | 0.936117i | \(-0.614393\pi\) | ||||
−0.351689 | + | 0.936117i | \(0.614393\pi\) | |||||||
\(48\) | − | 2.11093i | − | 0.0439777i | ||||||
\(49\) | −18.2791 | −0.373042 | ||||||||
\(50\) | −32.0362 | − | 32.0362i | −0.640724 | − | 0.640724i | ||||
\(51\) | −6.84630 | + | 6.84630i | −0.134241 | + | 0.134241i | ||||
\(52\) | −13.9414 | + | 13.9414i | −0.268104 | + | 0.268104i | ||||
\(53\) | −39.9577 | −0.753918 | −0.376959 | − | 0.926230i | \(-0.623030\pi\) | ||||
−0.376959 | + | 0.926230i | \(0.623030\pi\) | |||||||
\(54\) | 7.08328 | + | 7.08328i | 0.131172 | + | 0.131172i | ||||
\(55\) | 95.8532 | − | 95.8532i | 1.74278 | − | 1.74278i | ||||
\(56\) | 33.7227 | + | 33.7227i | 0.602191 | + | 0.602191i | ||||
\(57\) | 0.899117 | − | 0.899117i | 0.0157740 | − | 0.0157740i | ||||
\(58\) | 42.3387i | 0.729977i | ||||||||
\(59\) | 46.2148 | + | 46.2148i | 0.783303 | + | 0.783303i | 0.980387 | − | 0.197084i | \(-0.0631472\pi\) |
−0.197084 | + | 0.980387i | \(0.563147\pi\) | |||||||
\(60\) | 3.57734 | + | 3.57734i | 0.0596224 | + | 0.0596224i | ||||
\(61\) | 3.22864 | − | 3.22864i | 0.0529286 | − | 0.0529286i | −0.680147 | − | 0.733076i | \(-0.738084\pi\) |
0.733076 | + | 0.680147i | \(0.238084\pi\) | |||||||
\(62\) | − | 21.9101i | − | 0.353389i | ||||||
\(63\) | −49.0922 | −0.779242 | ||||||||
\(64\) | 61.1243i | 0.955066i | ||||||||
\(65\) | 81.7713i | 1.25802i | ||||||||
\(66\) | 7.21625 | − | 7.21625i | 0.109337 | − | 0.109337i | ||||
\(67\) | − | 44.2028i | − | 0.659743i | −0.944026 | − | 0.329872i | \(-0.892995\pi\) | ||
0.944026 | − | 0.329872i | \(-0.107005\pi\) | |||||||
\(68\) | 32.5476 | − | 32.5476i | 0.478641 | − | 0.478641i | ||||
\(69\) | 6.19652 | − | 6.19652i | 0.0898046 | − | 0.0898046i | ||||
\(70\) | 61.3049 | 0.875784 | ||||||||
\(71\) | −92.4046 | −1.30147 | −0.650736 | − | 0.759304i | \(-0.725540\pi\) | ||||
−0.650736 | + | 0.759304i | \(0.725540\pi\) | |||||||
\(72\) | −53.8890 | − | 53.8890i | −0.748459 | − | 0.748459i | ||||
\(73\) | 87.3712i | 1.19687i | 0.801173 | + | 0.598433i | \(0.204210\pi\) | ||||
−0.801173 | + | 0.598433i | \(0.795790\pi\) | |||||||
\(74\) | 14.5368 | − | 52.9635i | 0.196443 | − | 0.715722i | ||||
\(75\) | 11.5346 | 0.153794 | ||||||||
\(76\) | −4.27443 | + | 4.27443i | −0.0562425 | + | 0.0562425i | ||||
\(77\) | 100.834i | 1.30953i | ||||||||
\(78\) | 6.15610i | 0.0789244i | ||||||||
\(79\) | 39.7257 | + | 39.7257i | 0.502857 | + | 0.502857i | 0.912325 | − | 0.409467i | \(-0.134285\pi\) |
−0.409467 | + | 0.912325i | \(0.634285\pi\) | |||||||
\(80\) | 29.4307 | + | 29.4307i | 0.367883 | + | 0.367883i | ||||
\(81\) | 77.1643 | 0.952646 | ||||||||
\(82\) | −2.63525 | − | 2.63525i | −0.0321372 | − | 0.0321372i | ||||
\(83\) | −112.357 | −1.35370 | −0.676849 | − | 0.736122i | \(-0.736655\pi\) | ||||
−0.676849 | + | 0.736122i | \(0.736655\pi\) | |||||||
\(84\) | −3.76323 | −0.0448004 | ||||||||
\(85\) | − | 190.903i | − | 2.24591i | ||||||
\(86\) | 39.9334 | 0.464342 | ||||||||
\(87\) | −7.62196 | − | 7.62196i | −0.0876087 | − | 0.0876087i | ||||
\(88\) | −110.686 | + | 110.686i | −1.25780 | + | 1.25780i | ||||
\(89\) | 113.101 | − | 113.101i | 1.27080 | − | 1.27080i | 0.325124 | − | 0.945671i | \(-0.394594\pi\) |
0.945671 | − | 0.325124i | \(-0.105406\pi\) | |||||||
\(90\) | −97.9655 | −1.08851 | ||||||||
\(91\) | −43.0102 | − | 43.0102i | −0.472639 | − | 0.472639i | ||||
\(92\) | −29.4585 | + | 29.4585i | −0.320201 | + | 0.320201i | ||||
\(93\) | 3.94434 | + | 3.94434i | 0.0424123 | + | 0.0424123i | ||||
\(94\) | 34.6991 | − | 34.6991i | 0.369139 | − | 0.369139i | ||||
\(95\) | 25.0710i | 0.263906i | ||||||||
\(96\) | −6.98153 | − | 6.98153i | −0.0727242 | − | 0.0727242i | ||||
\(97\) | −6.42063 | − | 6.42063i | −0.0661921 | − | 0.0661921i | 0.673236 | − | 0.739428i | \(-0.264904\pi\) |
−0.739428 | + | 0.673236i | \(0.764904\pi\) | |||||||
\(98\) | 19.1860 | − | 19.1860i | 0.195776 | − | 0.195776i | ||||
\(99\) | − | 161.133i | − | 1.62761i | ||||||
\(100\) | −54.8357 | −0.548357 | ||||||||
\(101\) | 72.9137i | 0.721918i | 0.932582 | + | 0.360959i | \(0.117551\pi\) | ||||
−0.932582 | + | 0.360959i | \(0.882449\pi\) | |||||||
\(102\) | − | 14.3720i | − | 0.140902i | ||||||
\(103\) | 59.4600 | − | 59.4600i | 0.577282 | − | 0.577282i | −0.356872 | − | 0.934153i | \(-0.616157\pi\) |
0.934153 | + | 0.356872i | \(0.116157\pi\) | |||||||
\(104\) | − | 94.4255i | − | 0.907937i | ||||||
\(105\) | −11.0363 | + | 11.0363i | −0.105108 | + | 0.105108i | ||||
\(106\) | 41.9402 | − | 41.9402i | 0.395663 | − | 0.395663i | ||||
\(107\) | 64.2881 | 0.600824 | 0.300412 | − | 0.953810i | \(-0.402876\pi\) | ||||
0.300412 | + | 0.953810i | \(0.402876\pi\) | |||||||
\(108\) | 12.1243 | 0.112262 | ||||||||
\(109\) | −25.6002 | − | 25.6002i | −0.234864 | − | 0.234864i | 0.579855 | − | 0.814720i | \(-0.303109\pi\) |
−0.814720 | + | 0.579855i | \(0.803109\pi\) | |||||||
\(110\) | 201.218i | 1.82926i | ||||||||
\(111\) | 6.91772 | + | 12.1516i | 0.0623218 | + | 0.109474i | ||||
\(112\) | −30.9600 | −0.276428 | ||||||||
\(113\) | 55.8577 | − | 55.8577i | 0.494316 | − | 0.494316i | −0.415347 | − | 0.909663i | \(-0.636340\pi\) |
0.909663 | + | 0.415347i | \(0.136340\pi\) | |||||||
\(114\) | 1.88746i | 0.0165566i | ||||||||
\(115\) | 172.784i | 1.50247i | ||||||||
\(116\) | 36.2351 | + | 36.2351i | 0.312371 | + | 0.312371i | ||||
\(117\) | 68.7306 | + | 68.7306i | 0.587441 | + | 0.587441i | ||||
\(118\) | −97.0158 | −0.822168 | ||||||||
\(119\) | 100.411 | + | 100.411i | 0.843792 | + | 0.843792i | ||||
\(120\) | −24.2294 | −0.201911 | ||||||||
\(121\) | −209.963 | −1.73523 | ||||||||
\(122\) | 6.77768i | 0.0555547i | ||||||||
\(123\) | 0.948814 | 0.00771393 | ||||||||
\(124\) | −18.7515 | − | 18.7515i | −0.151222 | − | 0.151222i | ||||
\(125\) | −29.0936 | + | 29.0936i | −0.232749 | + | 0.232749i | ||||
\(126\) | 51.5281 | − | 51.5281i | 0.408953 | − | 0.408953i | ||||
\(127\) | 132.802 | 1.04568 | 0.522841 | − | 0.852430i | \(-0.324872\pi\) | ||||
0.522841 | + | 0.852430i | \(0.324872\pi\) | |||||||
\(128\) | 9.73872 | + | 9.73872i | 0.0760838 | + | 0.0760838i | ||||
\(129\) | −7.18896 | + | 7.18896i | −0.0557283 | + | 0.0557283i | ||||
\(130\) | −85.8286 | − | 85.8286i | −0.660220 | − | 0.660220i | ||||
\(131\) | −90.8033 | + | 90.8033i | −0.693155 | + | 0.693155i | −0.962925 | − | 0.269770i | \(-0.913052\pi\) |
0.269770 | + | 0.962925i | \(0.413052\pi\) | |||||||
\(132\) | − | 12.3519i | − | 0.0935749i | ||||||
\(133\) | −13.1869 | − | 13.1869i | −0.0991496 | − | 0.0991496i | ||||
\(134\) | 46.3960 | + | 46.3960i | 0.346239 | + | 0.346239i | ||||
\(135\) | 35.5566 | − | 35.5566i | 0.263382 | − | 0.263382i | ||||
\(136\) | 220.445i | 1.62092i | ||||||||
\(137\) | 15.1210 | 0.110372 | 0.0551860 | − | 0.998476i | \(-0.482425\pi\) | ||||
0.0551860 | + | 0.998476i | \(0.482425\pi\) | |||||||
\(138\) | 13.0079i | 0.0942605i | ||||||||
\(139\) | 218.618i | 1.57279i | 0.617724 | + | 0.786395i | \(0.288055\pi\) | ||||
−0.617724 | + | 0.786395i | \(0.711945\pi\) | |||||||
\(140\) | 52.4671 | − | 52.4671i | 0.374765 | − | 0.374765i | ||||
\(141\) | 12.4933i | 0.0886050i | ||||||||
\(142\) | 96.9894 | − | 96.9894i | 0.683024 | − | 0.683024i | ||||
\(143\) | 141.170 | − | 141.170i | 0.987206 | − | 0.987206i | ||||
\(144\) | 49.4742 | 0.343571 | ||||||||
\(145\) | 212.531 | 1.46573 | ||||||||
\(146\) | −91.7063 | − | 91.7063i | −0.628126 | − | 0.628126i | ||||
\(147\) | 6.90788i | 0.0469924i | ||||||||
\(148\) | −32.8871 | − | 57.7693i | −0.222210 | − | 0.390333i | ||||
\(149\) | −224.519 | −1.50684 | −0.753421 | − | 0.657539i | \(-0.771598\pi\) | ||||
−0.753421 | + | 0.657539i | \(0.771598\pi\) | |||||||
\(150\) | −12.1069 | + | 12.1069i | −0.0807124 | + | 0.0807124i | ||||
\(151\) | − | 220.465i | − | 1.46004i | −0.683428 | − | 0.730018i | \(-0.739512\pi\) | ||
0.683428 | − | 0.730018i | \(-0.260488\pi\) | |||||||
\(152\) | − | 28.9508i | − | 0.190466i | ||||||
\(153\) | −160.458 | − | 160.458i | −1.04874 | − | 1.04874i | ||||
\(154\) | −105.837 | − | 105.837i | −0.687254 | − | 0.687254i | ||||
\(155\) | −109.984 | −0.709576 | ||||||||
\(156\) | 5.26863 | + | 5.26863i | 0.0337733 | + | 0.0337733i | ||||
\(157\) | 82.7157 | 0.526851 | 0.263426 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263426 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(158\) | −83.3936 | −0.527808 | ||||||||
\(159\) | 15.1005i | 0.0949716i | ||||||||
\(160\) | 194.673 | 1.21671 | ||||||||
\(161\) | −90.8812 | − | 90.8812i | −0.564480 | − | 0.564480i | ||||
\(162\) | −80.9930 | + | 80.9930i | −0.499957 | + | 0.499957i | ||||
\(163\) | −139.231 | + | 139.231i | −0.854180 | + | 0.854180i | −0.990645 | − | 0.136465i | \(-0.956426\pi\) |
0.136465 | + | 0.990645i | \(0.456426\pi\) | |||||||
\(164\) | −4.51069 | −0.0275042 | ||||||||
\(165\) | −36.2241 | − | 36.2241i | −0.219540 | − | 0.219540i | ||||
\(166\) | 117.932 | − | 117.932i | 0.710433 | − | 0.710433i | ||||
\(167\) | 75.9417 | + | 75.9417i | 0.454741 | + | 0.454741i | 0.896924 | − | 0.442184i | \(-0.145796\pi\) |
−0.442184 | + | 0.896924i | \(0.645796\pi\) | |||||||
\(168\) | 12.7442 | − | 12.7442i | 0.0758583 | − | 0.0758583i | ||||
\(169\) | − | 48.5690i | − | 0.287390i | ||||||
\(170\) | 200.375 | + | 200.375i | 1.17868 | + | 1.17868i | ||||
\(171\) | 21.0727 | + | 21.0727i | 0.123232 | + | 0.123232i | ||||
\(172\) | 34.1766 | − | 34.1766i | 0.198701 | − | 0.198701i | ||||
\(173\) | − | 79.1788i | − | 0.457681i | −0.973464 | − | 0.228841i | \(-0.926507\pi\) | ||
0.973464 | − | 0.228841i | \(-0.0734935\pi\) | |||||||
\(174\) | 16.0003 | 0.0919557 | ||||||||
\(175\) | − | 169.171i | − | 0.966694i | ||||||
\(176\) | − | 101.619i | − | 0.577378i | ||||||
\(177\) | 17.4651 | − | 17.4651i | 0.0986731 | − | 0.0986731i | ||||
\(178\) | 237.425i | 1.33385i | ||||||||
\(179\) | −122.752 | + | 122.752i | −0.685767 | + | 0.685767i | −0.961293 | − | 0.275527i | \(-0.911148\pi\) |
0.275527 | + | 0.961293i | \(0.411148\pi\) | |||||||
\(180\) | −83.8427 | + | 83.8427i | −0.465793 | + | 0.465793i | ||||
\(181\) | 136.182 | 0.752387 | 0.376193 | − | 0.926541i | \(-0.377233\pi\) | ||||
0.376193 | + | 0.926541i | \(0.377233\pi\) | |||||||
\(182\) | 90.2885 | 0.496091 | ||||||||
\(183\) | −1.22014 | − | 1.22014i | −0.00666745 | − | 0.00666745i | ||||
\(184\) | − | 199.523i | − | 1.08436i | ||||||
\(185\) | −265.866 | − | 72.9715i | −1.43711 | − | 0.394441i | ||||
\(186\) | −8.28010 | −0.0445167 | ||||||||
\(187\) | −329.576 | + | 329.576i | −1.76244 | + | 1.76244i | ||||
\(188\) | − | 59.3936i | − | 0.315924i | ||||||
\(189\) | 37.4042i | 0.197906i | ||||||||
\(190\) | −26.3150 | − | 26.3150i | −0.138500 | − | 0.138500i | ||||
\(191\) | 124.156 | + | 124.156i | 0.650033 | + | 0.650033i | 0.953001 | − | 0.302968i | \(-0.0979774\pi\) |
−0.302968 | + | 0.953001i | \(0.597977\pi\) | |||||||
\(192\) | 23.0996 | 0.120310 | ||||||||
\(193\) | 66.0477 | + | 66.0477i | 0.342216 | + | 0.342216i | 0.857200 | − | 0.514984i | \(-0.172202\pi\) |
−0.514984 | + | 0.857200i | \(0.672202\pi\) | |||||||
\(194\) | 13.4784 | 0.0694763 | ||||||||
\(195\) | 30.9024 | 0.158474 | ||||||||
\(196\) | − | 32.8403i | − | 0.167553i | ||||||
\(197\) | 59.3236 | 0.301135 | 0.150568 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150568 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(198\) | 169.128 | + | 169.128i | 0.854183 | + | 0.854183i | ||||
\(199\) | 24.4969 | − | 24.4969i | 0.123100 | − | 0.123100i | −0.642873 | − | 0.765973i | \(-0.722258\pi\) |
0.765973 | + | 0.642873i | \(0.222258\pi\) | |||||||
\(200\) | 185.701 | − | 185.701i | 0.928506 | − | 0.928506i | ||||
\(201\) | −16.7048 | −0.0831083 | ||||||||
\(202\) | −76.5315 | − | 76.5315i | −0.378869 | − | 0.378869i | ||||
\(203\) | −111.787 | + | 111.787i | −0.550677 | + | 0.550677i | ||||
\(204\) | −12.3001 | − | 12.3001i | −0.0602947 | − | 0.0602947i | ||||
\(205\) | −13.2284 | + | 13.2284i | −0.0645287 | + | 0.0645287i | ||||
\(206\) | 124.821i | 0.605925i | ||||||||
\(207\) | 145.229 | + | 145.229i | 0.701588 | + | 0.701588i | ||||
\(208\) | 43.3449 | + | 43.3449i | 0.208389 | + | 0.208389i | ||||
\(209\) | 43.2828 | − | 43.2828i | 0.207095 | − | 0.207095i | ||||
\(210\) | − | 23.1678i | − | 0.110323i | ||||||
\(211\) | 33.2939 | 0.157791 | 0.0788955 | − | 0.996883i | \(-0.474861\pi\) | ||||
0.0788955 | + | 0.996883i | \(0.474861\pi\) | |||||||
\(212\) | − | 71.7882i | − | 0.338624i | ||||||
\(213\) | 34.9208i | 0.163947i | ||||||||
\(214\) | −67.4779 | + | 67.4779i | −0.315317 | + | 0.315317i | ||||
\(215\) | − | 200.457i | − | 0.932360i | ||||||
\(216\) | −41.0590 | + | 41.0590i | −0.190088 | + | 0.190088i | ||||
\(217\) | 57.8497 | − | 57.8497i | 0.266588 | − | 0.266588i | ||||
\(218\) | 53.7409 | 0.246518 | ||||||||
\(219\) | 33.0186 | 0.150770 | ||||||||
\(220\) | 172.210 | + | 172.210i | 0.782775 | + | 0.782775i | ||||
\(221\) | − | 281.157i | − | 1.27221i | ||||||
\(222\) | −20.0155 | − | 5.49362i | −0.0901600 | − | 0.0247460i | ||||
\(223\) | 356.943 | 1.60064 | 0.800320 | − | 0.599574i | \(-0.204663\pi\) | ||||
0.800320 | + | 0.599574i | \(0.204663\pi\) | |||||||
\(224\) | −102.395 | + | 102.395i | −0.457119 | + | 0.457119i | ||||
\(225\) | 270.337i | 1.20150i | ||||||||
\(226\) | 117.258i | 0.518843i | ||||||||
\(227\) | −126.548 | − | 126.548i | −0.557479 | − | 0.557479i | 0.371110 | − | 0.928589i | \(-0.378977\pi\) |
−0.928589 | + | 0.371110i | \(0.878977\pi\) | |||||||
\(228\) | 1.61536 | + | 1.61536i | 0.00708491 | + | 0.00708491i | ||||
\(229\) | −235.918 | −1.03021 | −0.515104 | − | 0.857128i | \(-0.672247\pi\) | ||||
−0.515104 | + | 0.857128i | \(0.672247\pi\) | |||||||
\(230\) | −181.357 | − | 181.357i | −0.788510 | − | 0.788510i | ||||
\(231\) | 38.1064 | 0.164963 | ||||||||
\(232\) | −245.421 | −1.05785 | ||||||||
\(233\) | − | 33.5791i | − | 0.144116i | −0.997400 | − | 0.0720582i | \(-0.977043\pi\) | ||
0.997400 | − | 0.0720582i | \(-0.0229567\pi\) | |||||||
\(234\) | −144.282 | −0.616588 | ||||||||
\(235\) | −174.182 | − | 174.182i | −0.741200 | − | 0.741200i | ||||
\(236\) | −83.0299 | + | 83.0299i | −0.351822 | + | 0.351822i | ||||
\(237\) | 15.0128 | − | 15.0128i | 0.0633453 | − | 0.0633453i | ||||
\(238\) | −210.787 | −0.885659 | ||||||||
\(239\) | −5.37141 | − | 5.37141i | −0.0224745 | − | 0.0224745i | 0.695780 | − | 0.718255i | \(-0.255059\pi\) |
−0.718255 | + | 0.695780i | \(0.755059\pi\) | |||||||
\(240\) | 11.1222 | − | 11.1222i | 0.0463425 | − | 0.0463425i | ||||
\(241\) | 264.741 | + | 264.741i | 1.09851 | + | 1.09851i | 0.994585 | + | 0.103924i | \(0.0331400\pi\) |
0.103924 | + | 0.994585i | \(0.466860\pi\) | |||||||
\(242\) | 220.381 | − | 220.381i | 0.910664 | − | 0.910664i | ||||
\(243\) | − | 89.8973i | − | 0.369948i | ||||||
\(244\) | 5.80060 | + | 5.80060i | 0.0237730 | + | 0.0237730i | ||||
\(245\) | −96.3099 | − | 96.3099i | −0.393102 | − | 0.393102i | ||||
\(246\) | −0.995891 | + | 0.995891i | −0.00404834 | + | 0.00404834i | ||||
\(247\) | 36.9241i | 0.149490i | ||||||||
\(248\) | 127.004 | 0.512115 | ||||||||
\(249\) | 42.4610i | 0.170526i | ||||||||
\(250\) | − | 61.0742i | − | 0.244297i | ||||||
\(251\) | −60.1852 | + | 60.1852i | −0.239782 | + | 0.239782i | −0.816760 | − | 0.576978i | \(-0.804232\pi\) |
0.576978 | + | 0.816760i | \(0.304232\pi\) | |||||||
\(252\) | − | 88.1994i | − | 0.349998i | ||||||
\(253\) | 298.296 | − | 298.296i | 1.17903 | − | 1.17903i | ||||
\(254\) | −139.391 | + | 139.391i | −0.548783 | + | 0.548783i | ||||
\(255\) | −72.1444 | −0.282919 | ||||||||
\(256\) | −264.941 | −1.03493 | ||||||||
\(257\) | 103.677 | + | 103.677i | 0.403412 | + | 0.403412i | 0.879434 | − | 0.476021i | \(-0.157922\pi\) |
−0.476021 | + | 0.879434i | \(0.657922\pi\) | |||||||
\(258\) | − | 15.0913i | − | 0.0584934i | ||||||
\(259\) | 178.222 | − | 101.459i | 0.688116 | − | 0.391732i | ||||
\(260\) | −146.911 | −0.565042 | ||||||||
\(261\) | 178.637 | − | 178.637i | 0.684433 | − | 0.684433i | ||||
\(262\) | − | 190.617i | − | 0.727547i | ||||||
\(263\) | 232.453i | 0.883851i | 0.897052 | + | 0.441926i | \(0.145704\pi\) | ||||
−0.897052 | + | 0.441926i | \(0.854296\pi\) | |||||||
\(264\) | 41.8297 | + | 41.8297i | 0.158446 | + | 0.158446i | ||||
\(265\) | −210.531 | − | 210.531i | −0.794458 | − | 0.794458i | ||||
\(266\) | 27.6824 | 0.104069 | ||||||||
\(267\) | −42.7421 | − | 42.7421i | −0.160083 | − | 0.160083i | ||||
\(268\) | 79.4150 | 0.296325 | ||||||||
\(269\) | 183.875 | 0.683550 | 0.341775 | − | 0.939782i | \(-0.388972\pi\) | ||||
0.341775 | + | 0.939782i | \(0.388972\pi\) | |||||||
\(270\) | 74.6417i | 0.276451i | ||||||||
\(271\) | 10.9050 | 0.0402398 | 0.0201199 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201199 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(272\) | −101.193 | − | 101.193i | −0.372032 | − | 0.372032i | ||||
\(273\) | −16.2541 | + | 16.2541i | −0.0595387 | + | 0.0595387i | ||||
\(274\) | −15.8712 | + | 15.8712i | −0.0579242 | + | 0.0579242i | ||||
\(275\) | 555.264 | 2.01914 | ||||||||
\(276\) | 11.1327 | + | 11.1327i | 0.0403359 | + | 0.0403359i | ||||
\(277\) | −210.314 | + | 210.314i | −0.759256 | + | 0.759256i | −0.976187 | − | 0.216931i | \(-0.930395\pi\) |
0.216931 | + | 0.976187i | \(0.430395\pi\) | |||||||
\(278\) | −229.465 | − | 229.465i | −0.825414 | − | 0.825414i | ||||
\(279\) | −92.4442 | + | 92.4442i | −0.331341 | + | 0.331341i | ||||
\(280\) | 355.360i | 1.26914i | ||||||||
\(281\) | −353.860 | − | 353.860i | −1.25929 | − | 1.25929i | −0.951433 | − | 0.307856i | \(-0.900389\pi\) |
−0.307856 | − | 0.951433i | \(-0.599611\pi\) | |||||||
\(282\) | −13.1132 | − | 13.1132i | −0.0465007 | − | 0.0465007i | ||||
\(283\) | 305.613 | − | 305.613i | 1.07991 | − | 1.07991i | 0.0833885 | − | 0.996517i | \(-0.473426\pi\) |
0.996517 | − | 0.0833885i | \(-0.0265742\pi\) | |||||||
\(284\) | − | 166.015i | − | 0.584559i | ||||||
\(285\) | 9.47464 | 0.0332444 | ||||||||
\(286\) | 296.350i | 1.03619i | ||||||||
\(287\) | − | 13.9158i | − | 0.0484870i | ||||||
\(288\) | 163.627 | − | 163.627i | 0.568150 | − | 0.568150i | ||||
\(289\) | 367.388i | 1.27124i | ||||||||
\(290\) | −223.076 | + | 223.076i | −0.769229 | + | 0.769229i | ||||
\(291\) | −2.42643 | + | 2.42643i | −0.00833826 | + | 0.00833826i | ||||
\(292\) | −156.972 | −0.537574 | ||||||||
\(293\) | −81.8505 | −0.279353 | −0.139677 | − | 0.990197i | \(-0.544606\pi\) | ||||
−0.139677 | + | 0.990197i | \(0.544606\pi\) | |||||||
\(294\) | −7.25063 | − | 7.25063i | −0.0246620 | − | 0.0246620i | ||||
\(295\) | 486.999i | 1.65084i | ||||||||
\(296\) | 307.008 | + | 84.2639i | 1.03719 | + | 0.284675i | ||||
\(297\) | −122.770 | −0.413368 | ||||||||
\(298\) | 235.659 | − | 235.659i | 0.790804 | − | 0.790804i | ||||
\(299\) | 254.473i | 0.851079i | ||||||||
\(300\) | 20.7231i | 0.0690769i | ||||||||
\(301\) | 105.437 | + | 105.437i | 0.350288 | + | 0.350288i | ||||
\(302\) | 231.404 | + | 231.404i | 0.766239 | + | 0.766239i | ||||
\(303\) | 27.5550 | 0.0909405 | ||||||||
\(304\) | 13.2895 | + | 13.2895i | 0.0437155 | + | 0.0437155i | ||||
\(305\) | 34.0225 | 0.111549 | ||||||||
\(306\) | 336.839 | 1.10078 | ||||||||
\(307\) | 441.470i | 1.43801i | 0.695003 | + | 0.719007i | \(0.255403\pi\) | ||||
−0.695003 | + | 0.719007i | \(0.744597\pi\) | |||||||
\(308\) | −181.159 | −0.588179 | ||||||||
\(309\) | −22.4706 | − | 22.4706i | −0.0727205 | − | 0.0727205i | ||||
\(310\) | 115.441 | − | 115.441i | 0.372392 | − | 0.372392i | ||||
\(311\) | −26.4826 | + | 26.4826i | −0.0851531 | + | 0.0851531i | −0.748400 | − | 0.663247i | \(-0.769178\pi\) |
0.663247 | + | 0.748400i | \(0.269178\pi\) | |||||||
\(312\) | −35.6845 | −0.114373 | ||||||||
\(313\) | 301.149 | + | 301.149i | 0.962137 | + | 0.962137i | 0.999309 | − | 0.0371719i | \(-0.0118349\pi\) |
−0.0371719 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(314\) | −86.8198 | + | 86.8198i | −0.276496 | + | 0.276496i | ||||
\(315\) | −258.660 | − | 258.660i | −0.821143 | − | 0.821143i | ||||
\(316\) | −71.3715 | + | 71.3715i | −0.225859 | + | 0.225859i | ||||
\(317\) | − | 374.514i | − | 1.18143i | −0.806880 | − | 0.590716i | \(-0.798845\pi\) | ||
0.806880 | − | 0.590716i | \(-0.201155\pi\) | |||||||
\(318\) | −15.8497 | − | 15.8497i | −0.0498419 | − | 0.0498419i | ||||
\(319\) | −366.915 | − | 366.915i | −1.15020 | − | 1.15020i | ||||
\(320\) | −322.055 | + | 322.055i | −1.00642 | + | 1.00642i | ||||
\(321\) | − | 24.2953i | − | 0.0756861i | ||||||
\(322\) | 190.781 | 0.592488 | ||||||||
\(323\) | − | 86.2027i | − | 0.266881i | ||||||
\(324\) | 138.634i | 0.427883i | ||||||||
\(325\) | −236.845 | + | 236.845i | −0.728754 | + | 0.728754i | ||||
\(326\) | − | 292.279i | − | 0.896562i | ||||||
\(327\) | −9.67463 | + | 9.67463i | −0.0295860 | + | 0.0295860i | ||||
\(328\) | 15.2755 | − | 15.2755i | 0.0465716 | − | 0.0465716i | ||||
\(329\) | 183.233 | 0.556939 | ||||||||
\(330\) | 76.0428 | 0.230433 | ||||||||
\(331\) | −284.416 | − | 284.416i | −0.859261 | − | 0.859261i | 0.131990 | − | 0.991251i | \(-0.457863\pi\) |
−0.991251 | + | 0.131990i | \(0.957863\pi\) | |||||||
\(332\) | − | 201.861i | − | 0.608016i | ||||||
\(333\) | −284.800 | + | 162.132i | −0.855255 | + | 0.486882i | ||||
\(334\) | −159.419 | −0.477304 | ||||||||
\(335\) | 232.898 | − | 232.898i | 0.695219 | − | 0.695219i | ||||
\(336\) | 11.7001i | 0.0348219i | ||||||||
\(337\) | − | 408.598i | − | 1.21246i | −0.795290 | − | 0.606229i | \(-0.792681\pi\) | ||
0.795290 | − | 0.606229i | \(-0.207319\pi\) | |||||||
\(338\) | 50.9788 | + | 50.9788i | 0.150825 | + | 0.150825i | ||||
\(339\) | −21.1093 | − | 21.1093i | −0.0622693 | − | 0.0622693i | ||||
\(340\) | 342.977 | 1.00876 | ||||||||
\(341\) | 189.878 | + | 189.878i | 0.556826 | + | 0.556826i | ||||
\(342\) | −44.2366 | −0.129347 | ||||||||
\(343\) | 372.904 | 1.08718 | ||||||||
\(344\) | 231.478i | 0.672902i | ||||||||
\(345\) | 65.2972 | 0.189267 | ||||||||
\(346\) | 83.1075 | + | 83.1075i | 0.240195 | + | 0.240195i | ||||
\(347\) | 169.743 | − | 169.743i | 0.489173 | − | 0.489173i | −0.418872 | − | 0.908045i | \(-0.637574\pi\) |
0.908045 | + | 0.418872i | \(0.137574\pi\) | |||||||
\(348\) | 13.6937 | − | 13.6937i | 0.0393496 | − | 0.0393496i | ||||
\(349\) | −70.7682 | −0.202774 | −0.101387 | − | 0.994847i | \(-0.532328\pi\) | ||||
−0.101387 | + | 0.994847i | \(0.532328\pi\) | |||||||
\(350\) | 177.565 | + | 177.565i | 0.507330 | + | 0.507330i | ||||
\(351\) | 52.3670 | − | 52.3670i | 0.149194 | − | 0.149194i | ||||
\(352\) | −336.085 | − | 336.085i | −0.954788 | − | 0.954788i | ||||
\(353\) | 35.6639 | − | 35.6639i | 0.101031 | − | 0.101031i | −0.654785 | − | 0.755816i | \(-0.727241\pi\) |
0.755816 | + | 0.654785i | \(0.227241\pi\) | |||||||
\(354\) | 36.6634i | 0.103569i | ||||||||
\(355\) | −486.867 | − | 486.867i | −1.37146 | − | 1.37146i | ||||
\(356\) | 203.198 | + | 203.198i | 0.570780 | + | 0.570780i | ||||
\(357\) | 37.9466 | − | 37.9466i | 0.106293 | − | 0.106293i | ||||
\(358\) | − | 257.686i | − | 0.719793i | ||||||
\(359\) | −623.797 | −1.73760 | −0.868798 | − | 0.495168i | \(-0.835107\pi\) | ||||
−0.868798 | + | 0.495168i | \(0.835107\pi\) | |||||||
\(360\) | − | 567.868i | − | 1.57741i | ||||||
\(361\) | − | 349.679i | − | 0.968640i | ||||||
\(362\) | −142.939 | + | 142.939i | −0.394859 | + | 0.394859i | ||||
\(363\) | 79.3475i | 0.218588i | ||||||||
\(364\) | 77.2724 | − | 77.2724i | 0.212287 | − | 0.212287i | ||||
\(365\) | −460.347 | + | 460.347i | −1.26122 | + | 1.26122i | ||||
\(366\) | 2.56137 | 0.00699827 | ||||||||
\(367\) | −189.927 | −0.517512 | −0.258756 | − | 0.965943i | \(-0.583313\pi\) | ||||
−0.258756 | + | 0.965943i | \(0.583313\pi\) | |||||||
\(368\) | 91.5884 | + | 91.5884i | 0.248882 | + | 0.248882i | ||||
\(369\) | 22.2375i | 0.0602642i | ||||||||
\(370\) | 355.649 | − | 202.465i | 0.961214 | − | 0.547202i | ||||
\(371\) | 221.471 | 0.596957 | ||||||||
\(372\) | −7.08643 | + | 7.08643i | −0.0190496 | + | 0.0190496i | ||||
\(373\) | 149.878i | 0.401817i | 0.979610 | + | 0.200909i | \(0.0643894\pi\) | ||||
−0.979610 | + | 0.200909i | \(0.935611\pi\) | |||||||
\(374\) | − | 691.857i | − | 1.84988i | ||||||
\(375\) | 10.9948 | + | 10.9948i | 0.0293195 | + | 0.0293195i | ||||
\(376\) | 201.137 | + | 201.137i | 0.534938 | + | 0.534938i | ||||
\(377\) | 313.011 | 0.830269 | ||||||||
\(378\) | −39.2601 | − | 39.2601i | −0.103863 | − | 0.103863i | ||||
\(379\) | −226.618 | −0.597937 | −0.298968 | − | 0.954263i | \(-0.596643\pi\) | ||||
−0.298968 | + | 0.954263i | \(0.596643\pi\) | |||||||
\(380\) | −45.0428 | −0.118534 | ||||||||
\(381\) | − | 50.1873i | − | 0.131725i | ||||||
\(382\) | −260.633 | −0.682286 | ||||||||
\(383\) | 427.831 | + | 427.831i | 1.11705 | + | 1.11705i | 0.992172 | + | 0.124879i | \(0.0398543\pi\) |
0.124879 | + | 0.992172i | \(0.460146\pi\) | |||||||
\(384\) | 3.68038 | − | 3.68038i | 0.00958432 | − | 0.00958432i | ||||
\(385\) | −531.280 | + | 531.280i | −1.37995 | + | 1.37995i | ||||
\(386\) | −138.650 | −0.359196 | ||||||||
\(387\) | −168.489 | − | 168.489i | −0.435371 | − | 0.435371i | ||||
\(388\) | 11.5353 | − | 11.5353i | 0.0297303 | − | 0.0297303i | ||||
\(389\) | 539.254 | + | 539.254i | 1.38626 | + | 1.38626i | 0.833033 | + | 0.553223i | \(0.186602\pi\) |
0.553223 | + | 0.833033i | \(0.313398\pi\) | |||||||
\(390\) | −32.4357 | + | 32.4357i | −0.0831683 | + | 0.0831683i | ||||
\(391\) | − | 594.090i | − | 1.51941i | ||||||
\(392\) | 111.214 | + | 111.214i | 0.283709 | + | 0.283709i | ||||
\(393\) | 34.3157 | + | 34.3157i | 0.0873172 | + | 0.0873172i | ||||
\(394\) | −62.2671 | + | 62.2671i | −0.158038 | + | 0.158038i | ||||
\(395\) | 418.619i | 1.05979i | ||||||||
\(396\) | 289.493 | 0.731043 | ||||||||
\(397\) | 249.597i | 0.628707i | 0.949306 | + | 0.314354i | \(0.101788\pi\) | ||||
−0.949306 | + | 0.314354i | \(0.898212\pi\) | |||||||
\(398\) | 51.4248i | 0.129208i | ||||||||
\(399\) | −4.98349 | + | 4.98349i | −0.0124899 | + | 0.0124899i | ||||
\(400\) | 170.488i | 0.426220i | ||||||||
\(401\) | −252.449 | + | 252.449i | −0.629550 | + | 0.629550i | −0.947955 | − | 0.318405i | \(-0.896853\pi\) |
0.318405 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(402\) | 17.5336 | − | 17.5336i | 0.0436159 | − | 0.0436159i | ||||
\(403\) | −161.983 | −0.401942 | ||||||||
\(404\) | −130.997 | −0.324251 | ||||||||
\(405\) | 406.568 | + | 406.568i | 1.00387 | + | 1.00387i | ||||
\(406\) | − | 234.668i | − | 0.578000i | ||||||
\(407\) | 333.013 | + | 584.970i | 0.818215 | + | 1.43727i | ||||
\(408\) | 83.3088 | 0.204188 | ||||||||
\(409\) | 27.2406 | − | 27.2406i | 0.0666030 | − | 0.0666030i | −0.673021 | − | 0.739624i | \(-0.735004\pi\) |
0.739624 | + | 0.673021i | \(0.235004\pi\) | |||||||
\(410\) | − | 27.7695i | − | 0.0677305i | ||||||
\(411\) | − | 5.71439i | − | 0.0139036i | ||||||
\(412\) | 106.826 | + | 106.826i | 0.259287 | + | 0.259287i | ||||
\(413\) | −256.153 | − | 256.153i | −0.620224 | − | 0.620224i | ||||
\(414\) | −304.869 | −0.736399 | ||||||||
\(415\) | −591.993 | − | 591.993i | −1.42649 | − | 1.42649i | ||||
\(416\) | 286.711 | 0.689209 | ||||||||
\(417\) | 82.6183 | 0.198125 | ||||||||
\(418\) | 90.8607i | 0.217370i | ||||||||
\(419\) | 221.675 | 0.529058 | 0.264529 | − | 0.964378i | \(-0.414783\pi\) | ||||
0.264529 | + | 0.964378i | \(0.414783\pi\) | |||||||
\(420\) | −19.8279 | − | 19.8279i | −0.0472094 | − | 0.0472094i | ||||
\(421\) | 138.621 | − | 138.621i | 0.329266 | − | 0.329266i | −0.523041 | − | 0.852307i | \(-0.675203\pi\) |
0.852307 | + | 0.523041i | \(0.175203\pi\) | |||||||
\(422\) | −34.9458 | + | 34.9458i | −0.0828101 | + | 0.0828101i | ||||
\(423\) | −292.808 | −0.692217 | ||||||||
\(424\) | 243.111 | + | 243.111i | 0.573375 | + | 0.573375i | ||||
\(425\) | 552.937 | − | 552.937i | 1.30103 | − | 1.30103i | ||||
\(426\) | −36.6535 | − | 36.6535i | −0.0860410 | − | 0.0860410i | ||||
\(427\) | −17.8952 | + | 17.8952i | −0.0419092 | + | 0.0419092i | ||||
\(428\) | 115.500i | 0.269861i | ||||||||
\(429\) | −53.3500 | − | 53.3500i | −0.124359 | − | 0.124359i | ||||
\(430\) | 210.403 | + | 210.403i | 0.489310 | + | 0.489310i | ||||
\(431\) | −525.402 | + | 525.402i | −1.21903 | + | 1.21903i | −0.251058 | + | 0.967972i | \(0.580779\pi\) |
−0.967972 | + | 0.251058i | \(0.919221\pi\) | |||||||
\(432\) | − | 37.6953i | − | 0.0872576i | ||||||
\(433\) | 229.718 | 0.530527 | 0.265263 | − | 0.964176i | \(-0.414541\pi\) | ||||
0.265263 | + | 0.964176i | \(0.414541\pi\) | |||||||
\(434\) | 121.440i | 0.279816i | ||||||||
\(435\) | − | 80.3181i | − | 0.184639i | ||||||
\(436\) | 45.9935 | − | 45.9935i | 0.105490 | − | 0.105490i | ||||
\(437\) | 78.0212i | 0.178538i | ||||||||
\(438\) | −34.6569 | + | 34.6569i | −0.0791254 | + | 0.0791254i | ||||
\(439\) | 420.037 | − | 420.037i | 0.956803 | − | 0.956803i | −0.0423019 | − | 0.999105i | \(-0.513469\pi\) |
0.999105 | + | 0.0423019i | \(0.0134691\pi\) | |||||||
\(440\) | −1166.38 | −2.65087 | ||||||||
\(441\) | −161.901 | −0.367123 | ||||||||
\(442\) | 295.108 | + | 295.108i | 0.667665 | + | 0.667665i | ||||
\(443\) | − | 637.682i | − | 1.43946i | −0.694252 | − | 0.719732i | \(-0.744265\pi\) | ||
0.694252 | − | 0.719732i | \(-0.255735\pi\) | |||||||
\(444\) | −21.8317 | + | 12.4284i | −0.0491705 | + | 0.0279919i | ||||
\(445\) | 1191.82 | 2.67826 | ||||||||
\(446\) | −374.653 | + | 374.653i | −0.840029 | + | 0.840029i | ||||
\(447\) | 84.8486i | 0.189818i | ||||||||
\(448\) | − | 338.790i | − | 0.756228i | ||||||
\(449\) | 208.249 | + | 208.249i | 0.463807 | + | 0.463807i | 0.899901 | − | 0.436094i | \(-0.143639\pi\) |
−0.436094 | + | 0.899901i | \(0.643639\pi\) | |||||||
\(450\) | −283.750 | − | 283.750i | −0.630557 | − | 0.630557i | ||||
\(451\) | 45.6752 | 0.101275 | ||||||||
\(452\) | 100.354 | + | 100.354i | 0.222023 | + | 0.222023i | ||||
\(453\) | −83.3165 | −0.183922 | ||||||||
\(454\) | 265.653 | 0.585139 | ||||||||
\(455\) | − | 453.229i | − | 0.996109i | ||||||
\(456\) | −10.9408 | −0.0239931 | ||||||||
\(457\) | 167.982 | + | 167.982i | 0.367576 | + | 0.367576i | 0.866592 | − | 0.499017i | \(-0.166305\pi\) |
−0.499017 | + | 0.866592i | \(0.666305\pi\) | |||||||
\(458\) | 247.623 | − | 247.623i | 0.540662 | − | 0.540662i | ||||
\(459\) | −122.256 | + | 122.256i | −0.266352 | + | 0.266352i | ||||
\(460\) | −310.425 | −0.674837 | ||||||||
\(461\) | −579.698 | − | 579.698i | −1.25748 | − | 1.25748i | −0.952293 | − | 0.305186i | \(-0.901281\pi\) |
−0.305186 | − | 0.952293i | \(-0.598719\pi\) | |||||||
\(462\) | −39.9971 | + | 39.9971i | −0.0865738 | + | 0.0865738i | ||||
\(463\) | 235.818 | + | 235.818i | 0.509325 | + | 0.509325i | 0.914319 | − | 0.404994i | \(-0.132726\pi\) |
−0.404994 | + | 0.914319i | \(0.632726\pi\) | |||||||
\(464\) | 112.657 | − | 112.657i | 0.242796 | − | 0.242796i | ||||
\(465\) | 41.5644i | 0.0893858i | ||||||||
\(466\) | 35.2452 | + | 35.2452i | 0.0756335 | + | 0.0756335i | ||||
\(467\) | −172.057 | − | 172.057i | −0.368430 | − | 0.368430i | 0.498474 | − | 0.866905i | \(-0.333894\pi\) |
−0.866905 | + | 0.498474i | \(0.833894\pi\) | |||||||
\(468\) | −123.482 | + | 123.482i | −0.263850 | + | 0.263850i | ||||
\(469\) | 245.000i | 0.522389i | ||||||||
\(470\) | 365.649 | 0.777977 | ||||||||
\(471\) | − | 31.2592i | − | 0.0663678i | ||||||
\(472\) | − | 562.363i | − | 1.19145i | ||||||
\(473\) | −346.071 | + | 346.071i | −0.731651 | + | 0.731651i | ||||
\(474\) | 31.5155i | 0.0664883i | ||||||||
\(475\) | −72.6165 | + | 72.6165i | −0.152877 | + | 0.152877i | ||||
\(476\) | −180.400 | + | 180.400i | −0.378991 | + | 0.378991i | ||||
\(477\) | −353.912 | −0.741954 | ||||||||
\(478\) | 11.2759 | 0.0235897 | ||||||||
\(479\) | 56.2384 | + | 56.2384i | 0.117408 | + | 0.117408i | 0.763370 | − | 0.645962i | \(-0.223543\pi\) |
−0.645962 | + | 0.763370i | \(0.723543\pi\) | |||||||
\(480\) | − | 73.5694i | − | 0.153270i | ||||||
\(481\) | −391.561 | − | 107.471i | −0.814056 | − | 0.223432i | ||||
\(482\) | −555.753 | −1.15301 | ||||||||
\(483\) | −34.3451 | + | 34.3451i | −0.0711079 | + | 0.0711079i | ||||
\(484\) | − | 377.221i | − | 0.779382i | ||||||
\(485\) | − | 67.6588i | − | 0.139503i | ||||||
\(486\) | 94.3578 | + | 94.3578i | 0.194152 | + | 0.194152i | ||||
\(487\) | −152.415 | − | 152.415i | −0.312967 | − | 0.312967i | 0.533091 | − | 0.846058i | \(-0.321030\pi\) |
−0.846058 | + | 0.533091i | \(0.821030\pi\) | |||||||
\(488\) | −39.2875 | −0.0805072 | ||||||||
\(489\) | 52.6172 | + | 52.6172i | 0.107602 | + | 0.107602i | ||||
\(490\) | 202.177 | 0.412606 | ||||||||
\(491\) | 487.992 | 0.993874 | 0.496937 | − | 0.867786i | \(-0.334458\pi\) | ||||
0.496937 | + | 0.867786i | \(0.334458\pi\) | |||||||
\(492\) | 1.70465i | 0.00346473i | ||||||||
\(493\) | −730.754 | −1.48226 | ||||||||
\(494\) | −38.7561 | − | 38.7561i | −0.0784537 | − | 0.0784537i | ||||
\(495\) | 848.989 | − | 848.989i | 1.71513 | − | 1.71513i | ||||
\(496\) | −58.2998 | + | 58.2998i | −0.117540 | + | 0.117540i | ||||
\(497\) | 512.166 | 1.03051 | ||||||||
\(498\) | −44.5678 | − | 44.5678i | −0.0894937 | − | 0.0894937i | ||||
\(499\) | −588.787 | + | 588.787i | −1.17993 | + | 1.17993i | −0.200174 | + | 0.979760i | \(0.564151\pi\) |
−0.979760 | + | 0.200174i | \(0.935849\pi\) | |||||||
\(500\) | −52.2697 | − | 52.2697i | −0.104539 | − | 0.104539i | ||||
\(501\) | 28.6993 | − | 28.6993i | 0.0572840 | − | 0.0572840i | ||||
\(502\) | − | 126.343i | − | 0.251679i | ||||||
\(503\) | −90.4426 | − | 90.4426i | −0.179806 | − | 0.179806i | 0.611465 | − | 0.791271i | \(-0.290580\pi\) |
−0.791271 | + | 0.611465i | \(0.790580\pi\) | |||||||
\(504\) | 298.688 | + | 298.688i | 0.592635 | + | 0.592635i | ||||
\(505\) | −384.172 | + | 384.172i | −0.760737 | + | 0.760737i | ||||
\(506\) | 626.192i | 1.23753i | ||||||||
\(507\) | −18.3548 | −0.0362027 | ||||||||
\(508\) | 238.592i | 0.469670i | ||||||||
\(509\) | − | 925.458i | − | 1.81819i | −0.416590 | − | 0.909094i | \(-0.636775\pi\) | ||
0.416590 | − | 0.909094i | \(-0.363225\pi\) | |||||||
\(510\) | 75.7240 | − | 75.7240i | 0.148478 | − | 0.148478i | ||||
\(511\) | − | 484.268i | − | 0.947686i | ||||||
\(512\) | 239.132 | − | 239.132i | 0.467054 | − | 0.467054i | ||||
\(513\) | 16.0557 | − | 16.0557i | 0.0312976 | − | 0.0312976i | ||||
\(514\) | −217.642 | −0.423428 | ||||||||
\(515\) | 626.573 | 1.21665 | ||||||||
\(516\) | −12.9157 | − | 12.9157i | −0.0250305 | − | 0.0250305i | ||||
\(517\) | 601.418i | 1.16328i | ||||||||
\(518\) | −80.5721 | + | 293.558i | −0.155545 | + | 0.566714i | ||||
\(519\) | −29.9226 | −0.0576544 | ||||||||
\(520\) | 497.515 | − | 497.515i | 0.956759 | − | 0.956759i | ||||
\(521\) | − | 87.8448i | − | 0.168608i | −0.996440 | − | 0.0843040i | \(-0.973133\pi\) | ||
0.996440 | − | 0.0843040i | \(-0.0268667\pi\) | |||||||
\(522\) | 375.001i | 0.718393i | ||||||||
\(523\) | 17.6675 | + | 17.6675i | 0.0337811 | + | 0.0337811i | 0.723796 | − | 0.690014i | \(-0.242396\pi\) |
−0.690014 | + | 0.723796i | \(0.742396\pi\) | |||||||
\(524\) | −163.138 | − | 163.138i | −0.311332 | − | 0.311332i | ||||
\(525\) | −63.9319 | −0.121775 | ||||||||
\(526\) | −243.987 | − | 243.987i | −0.463853 | − | 0.463853i | ||||
\(527\) | 378.163 | 0.717577 | ||||||||
\(528\) | −38.4029 | −0.0727327 | ||||||||
\(529\) | 8.70501i | 0.0164556i | ||||||||
\(530\) | 441.955 | 0.833877 | ||||||||
\(531\) | 409.333 | + | 409.333i | 0.770873 | + | 0.770873i | ||||
\(532\) | 23.6917 | − | 23.6917i | 0.0445332 | − | 0.0445332i | ||||
\(533\) | −19.4825 | + | 19.4825i | −0.0365525 | + | 0.0365525i | ||||
\(534\) | 89.7258 | 0.168026 | ||||||||
\(535\) | 338.725 | + | 338.725i | 0.633131 | + | 0.633131i | ||||
\(536\) | −268.939 | + | 268.939i | −0.501753 | + | 0.501753i | ||||
\(537\) | 46.3895 | + | 46.3895i | 0.0863865 | + | 0.0863865i | ||||
\(538\) | −192.998 | + | 192.998i | −0.358733 | + | 0.358733i | ||||
\(539\) | 332.540i | 0.616957i | ||||||||
\(540\) | 63.8813 | + | 63.8813i | 0.118299 | + | 0.118299i | ||||
\(541\) | 89.2845 | + | 89.2845i | 0.165036 | + | 0.165036i | 0.784793 | − | 0.619757i | \(-0.212769\pi\) |
−0.619757 | + | 0.784793i | \(0.712769\pi\) | |||||||
\(542\) | −11.4461 | + | 11.4461i | −0.0211182 | + | 0.0211182i | ||||
\(543\) | − | 51.4648i | − | 0.0947786i | ||||||
\(544\) | −669.353 | −1.23043 | ||||||||
\(545\) | − | 269.768i | − | 0.494987i | ||||||
\(546\) | − | 34.1211i | − | 0.0624929i | ||||||
\(547\) | −75.5441 | + | 75.5441i | −0.138106 | + | 0.138106i | −0.772780 | − | 0.634674i | \(-0.781134\pi\) |
0.634674 | + | 0.772780i | \(0.281134\pi\) | |||||||
\(548\) | 27.1664i | 0.0495738i | ||||||||
\(549\) | 28.5967 | − | 28.5967i | 0.0520887 | − | 0.0520887i | ||||
\(550\) | −582.815 | + | 582.815i | −1.05966 | + | 1.05966i | ||||
\(551\) | 95.9691 | 0.174173 | ||||||||
\(552\) | −75.4019 | −0.136598 | ||||||||
\(553\) | −220.186 | − | 220.186i | −0.398166 | − | 0.398166i | ||||
\(554\) | − | 441.498i | − | 0.796928i | ||||||
\(555\) | −27.5768 | + | 100.474i | −0.0496880 | + | 0.181034i | ||||
\(556\) | −392.770 | −0.706422 | ||||||||
\(557\) | −154.792 | + | 154.792i | −0.277902 | + | 0.277902i | −0.832271 | − | 0.554369i | \(-0.812960\pi\) |
0.554369 | + | 0.832271i | \(0.312960\pi\) | |||||||
\(558\) | − | 194.062i | − | 0.347781i | ||||||
\(559\) | − | 295.229i | − | 0.528138i | ||||||
\(560\) | −163.124 | − | 163.124i | −0.291292 | − | 0.291292i | ||||
\(561\) | 124.551 | + | 124.551i | 0.222015 | + | 0.222015i | ||||
\(562\) | 742.835 | 1.32177 | ||||||||
\(563\) | −65.2182 | − | 65.2182i | −0.115840 | − | 0.115840i | 0.646810 | − | 0.762651i | \(-0.276103\pi\) |
−0.762651 | + | 0.646810i | \(0.776103\pi\) | |||||||
\(564\) | −22.4456 | −0.0397971 | ||||||||
\(565\) | 588.613 | 1.04179 | ||||||||
\(566\) | 641.554i | 1.13349i | ||||||||
\(567\) | −427.695 | −0.754311 | ||||||||
\(568\) | 562.210 | + | 562.210i | 0.989806 | + | 0.989806i | ||||
\(569\) | 511.812 | − | 511.812i | 0.899494 | − | 0.899494i | −0.0958970 | − | 0.995391i | \(-0.530572\pi\) |
0.995391 | + | 0.0958970i | \(0.0305719\pi\) | |||||||
\(570\) | −9.94475 | + | 9.94475i | −0.0174469 | + | 0.0174469i | ||||
\(571\) | 124.918 | 0.218771 | 0.109386 | − | 0.993999i | \(-0.465112\pi\) | ||||
0.109386 | + | 0.993999i | \(0.465112\pi\) | |||||||
\(572\) | 253.628 | + | 253.628i | 0.443405 | + | 0.443405i | ||||
\(573\) | 46.9202 | − | 46.9202i | 0.0818851 | − | 0.0818851i | ||||
\(574\) | 14.6062 | + | 14.6062i | 0.0254464 | + | 0.0254464i | ||||
\(575\) | −500.457 | + | 500.457i | −0.870361 | + | 0.870361i | ||||
\(576\) | 541.389i | 0.939911i | ||||||||
\(577\) | −86.4511 | − | 86.4511i | −0.149829 | − | 0.149829i | 0.628213 | − | 0.778041i | \(-0.283787\pi\) |
−0.778041 | + | 0.628213i | \(0.783787\pi\) | |||||||
\(578\) | −385.617 | − | 385.617i | −0.667157 | − | 0.667157i | ||||
\(579\) | 24.9602 | − | 24.9602i | 0.0431092 | − | 0.0431092i | ||||
\(580\) | 381.835i | 0.658336i | ||||||||
\(581\) | 622.755 | 1.07187 | ||||||||
\(582\) | − | 5.09365i | − | 0.00875198i | ||||||
\(583\) | 726.925i | 1.24687i | ||||||||
\(584\) | 531.586 | − | 531.586i | 0.910249 | − | 0.910249i | ||||
\(585\) | 724.263i | 1.23806i | ||||||||
\(586\) | 85.9117 | − | 85.9117i | 0.146607 | − | 0.146607i | ||||
\(587\) | 500.633 | − | 500.633i | 0.852867 | − | 0.852867i | −0.137619 | − | 0.990485i | \(-0.543945\pi\) |
0.990485 | + | 0.137619i | \(0.0439449\pi\) | |||||||
\(588\) | −12.4107 | −0.0211067 | ||||||||
\(589\) | −49.6637 | −0.0843187 | ||||||||
\(590\) | −511.163 | − | 511.163i | −0.866378 | − | 0.866378i | ||||
\(591\) | − | 22.4191i | − | 0.0379342i | ||||||
\(592\) | −179.609 | + | 102.248i | −0.303393 | + | 0.172716i | ||||
\(593\) | −719.626 | −1.21354 | −0.606768 | − | 0.794879i | \(-0.707534\pi\) | ||||
−0.606768 | + | 0.794879i | \(0.707534\pi\) | |||||||
\(594\) | 128.862 | − | 128.862i | 0.216939 | − | 0.216939i | ||||
\(595\) | 1058.11i | 1.77833i | ||||||||
\(596\) | − | 403.373i | − | 0.676801i | ||||||
\(597\) | −9.25768 | − | 9.25768i | −0.0155070 | − | 0.0155070i | ||||
\(598\) | −267.099 | − | 267.099i | −0.446654 | − | 0.446654i | ||||
\(599\) | −259.577 | −0.433351 | −0.216676 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216676 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(600\) | −70.1787 | − | 70.1787i | −0.116965 | − | 0.116965i | ||||
\(601\) | −292.942 | −0.487424 | −0.243712 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243712 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(602\) | −221.337 | −0.367669 | ||||||||
\(603\) | − | 391.512i | − | 0.649274i | ||||||
\(604\) | 396.090 | 0.655777 | ||||||||
\(605\) | −1106.27 | − | 1106.27i | −1.82854 | − | 1.82854i | ||||
\(606\) | −28.9222 | + | 28.9222i | −0.0477263 | + | 0.0477263i | ||||
\(607\) | −315.803 | + | 315.803i | −0.520268 | + | 0.520268i | −0.917652 | − | 0.397384i | \(-0.869918\pi\) |
0.397384 | + | 0.917652i | \(0.369918\pi\) | |||||||
\(608\) | 87.9053 | 0.144581 | ||||||||
\(609\) | 42.2458 | + | 42.2458i | 0.0693692 | + | 0.0693692i | ||||
\(610\) | −35.7106 | + | 35.7106i | −0.0585420 | + | 0.0585420i | ||||
\(611\) | −256.532 | − | 256.532i | −0.419855 | − | 0.419855i | ||||
\(612\) | 288.280 | − | 288.280i | 0.471045 | − | 0.471045i | ||||
\(613\) | − | 405.498i | − | 0.661498i | −0.943719 | − | 0.330749i | \(-0.892699\pi\) | ||
0.943719 | − | 0.330749i | \(-0.107301\pi\) | |||||||
\(614\) | −463.375 | − | 463.375i | −0.754682 | − | 0.754682i | ||||
\(615\) | 4.99917 | + | 4.99917i | 0.00812873 | + | 0.00812873i | ||||
\(616\) | 613.496 | − | 613.496i | 0.995935 | − | 0.995935i | ||||
\(617\) | − | 327.089i | − | 0.530128i | −0.964231 | − | 0.265064i | \(-0.914607\pi\) | ||
0.964231 | − | 0.265064i | \(-0.0853931\pi\) | |||||||
\(618\) | 47.1712 | 0.0763287 | ||||||||
\(619\) | − | 525.496i | − | 0.848943i | −0.905441 | − | 0.424472i | \(-0.860460\pi\) | ||
0.905441 | − | 0.424472i | \(-0.139540\pi\) | |||||||
\(620\) | − | 197.599i | − | 0.318707i | ||||||
\(621\) | 110.652 | − | 110.652i | 0.178184 | − | 0.178184i | ||||
\(622\) | − | 55.5932i | − | 0.0893782i | ||||||
\(623\) | −626.878 | + | 626.878i | −1.00622 | + | 1.00622i | ||||
\(624\) | 16.3805 | − | 16.3805i | 0.0262509 | − | 0.0262509i | ||||
\(625\) | 456.465 | 0.730344 | ||||||||
\(626\) | −632.182 | −1.00988 | ||||||||
\(627\) | −16.3571 | − | 16.3571i | −0.0260878 | − | 0.0260878i | ||||
\(628\) | 148.608i | 0.236636i | ||||||||
\(629\) | 914.136 | + | 250.901i | 1.45332 | + | 0.398888i | ||||
\(630\) | 542.988 | 0.861886 | ||||||||
\(631\) | 517.188 | − | 517.188i | 0.819632 | − | 0.819632i | −0.166422 | − | 0.986055i | \(-0.553221\pi\) |
0.986055 | + | 0.166422i | \(0.0532215\pi\) | |||||||
\(632\) | − | 483.400i | − | 0.764874i | ||||||
\(633\) | − | 12.5822i | − | 0.0198770i | ||||||
\(634\) | 393.096 | + | 393.096i | 0.620026 | + | 0.620026i | ||||
\(635\) | 699.713 | + | 699.713i | 1.10191 | + | 1.10191i | ||||
\(636\) | −27.1296 | −0.0426566 | ||||||||
\(637\) | −141.843 | − | 141.843i | −0.222674 | − | 0.222674i | ||||
\(638\) | 770.241 | 1.20727 | ||||||||
\(639\) | −818.444 | −1.28082 | ||||||||
\(640\) | 102.624i | 0.160350i | ||||||||
\(641\) | −1064.31 | −1.66039 | −0.830196 | − | 0.557472i | \(-0.811772\pi\) | ||||
−0.830196 | + | 0.557472i | \(0.811772\pi\) | |||||||
\(642\) | 25.5007 | + | 25.5007i | 0.0397207 | + | 0.0397207i | ||||
\(643\) | −607.938 | + | 607.938i | −0.945470 | + | 0.945470i | −0.998588 | − | 0.0531178i | \(-0.983084\pi\) |
0.0531178 | + | 0.998588i | \(0.483084\pi\) | |||||||
\(644\) | 163.278 | − | 163.278i | 0.253537 | − | 0.253537i | ||||
\(645\) | −75.7552 | −0.117450 | ||||||||
\(646\) | 90.4798 | + | 90.4798i | 0.140062 | + | 0.140062i | ||||
\(647\) | 506.664 | − | 506.664i | 0.783097 | − | 0.783097i | −0.197255 | − | 0.980352i | \(-0.563203\pi\) |
0.980352 | + | 0.197255i | \(0.0632028\pi\) | |||||||
\(648\) | −469.485 | − | 469.485i | −0.724513 | − | 0.724513i | ||||
\(649\) | 840.758 | − | 840.758i | 1.29547 | − | 1.29547i | ||||
\(650\) | − | 497.193i | − | 0.764913i | ||||||
\(651\) | −21.8621 | − | 21.8621i | −0.0335823 | − | 0.0335823i | ||||
\(652\) | −250.144 | − | 250.144i | −0.383657 | − | 0.383657i | ||||
\(653\) | 124.218 | − | 124.218i | 0.190226 | − | 0.190226i | −0.605568 | − | 0.795794i | \(-0.707054\pi\) |
0.795794 | + | 0.605568i | \(0.207054\pi\) | |||||||
\(654\) | − | 20.3093i | − | 0.0310540i | ||||||
\(655\) | −956.860 | −1.46085 | ||||||||
\(656\) | 14.0241i | 0.0213781i | ||||||||
\(657\) | 773.863i | 1.17787i | ||||||||
\(658\) | −192.325 | + | 192.325i | −0.292287 | + | 0.292287i | ||||
\(659\) | 454.252i | 0.689305i | 0.938730 | + | 0.344653i | \(0.112003\pi\) | ||||
−0.938730 | + | 0.344653i | \(0.887997\pi\) | |||||||
\(660\) | 65.0804 | − | 65.0804i | 0.0986067 | − | 0.0986067i | ||||
\(661\) | −389.416 | + | 389.416i | −0.589132 | + | 0.589132i | −0.937396 | − | 0.348265i | \(-0.886771\pi\) |
0.348265 | + | 0.937396i | \(0.386771\pi\) | |||||||
\(662\) | 597.055 | 0.901896 | ||||||||
\(663\) | −106.253 | −0.160261 | ||||||||
\(664\) | 683.604 | + | 683.604i | 1.02952 | + | 1.02952i | ||||
\(665\) | − | 138.960i | − | 0.208962i | ||||||
\(666\) | 128.755 | − | 469.107i | 0.193325 | − | 0.704365i | ||||
\(667\) | 661.398 | 0.991602 | ||||||||
\(668\) | −136.437 | + | 136.437i | −0.204247 | + | 0.204247i | ||||
\(669\) | − | 134.893i | − | 0.201634i | ||||||
\(670\) | 488.908i | 0.729714i | ||||||||
\(671\) | −58.7367 | − | 58.7367i | −0.0875361 | − | 0.0875361i | ||||
\(672\) | 38.6961 | + | 38.6961i | 0.0575835 | + | 0.0575835i | ||||
\(673\) | −25.6563 | −0.0381222 | −0.0190611 | − | 0.999818i | \(-0.506068\pi\) | ||||
−0.0190611 | + | 0.999818i | \(0.506068\pi\) | |||||||
\(674\) | 428.872 | + | 428.872i | 0.636309 | + | 0.636309i | ||||
\(675\) | 205.975 | 0.305148 | ||||||||
\(676\) | 87.2593 | 0.129082 | ||||||||
\(677\) | 37.6324i | 0.0555870i | 0.999614 | + | 0.0277935i | \(0.00884809\pi\) | ||||
−0.999614 | + | 0.0277935i | \(0.991152\pi\) | |||||||
\(678\) | 44.3134 | 0.0653590 | ||||||||
\(679\) | 35.5873 | + | 35.5873i | 0.0524113 | + | 0.0524113i | ||||
\(680\) | −1161.49 | + | 1161.49i | −1.70808 | + | 1.70808i | ||||
\(681\) | −47.8239 | + | 47.8239i | −0.0702260 | + | 0.0702260i | ||||
\(682\) | −398.598 | −0.584454 | ||||||||
\(683\) | −136.128 | − | 136.128i | −0.199308 | − | 0.199308i | 0.600395 | − | 0.799703i | \(-0.295010\pi\) |
−0.799703 | + | 0.600395i | \(0.795010\pi\) | |||||||
\(684\) | −37.8594 | + | 37.8594i | −0.0553500 | + | 0.0553500i | ||||
\(685\) | 79.6702 | + | 79.6702i | 0.116307 | + | 0.116307i | ||||
\(686\) | −391.407 | + | 391.407i | −0.570564 | + | 0.570564i | ||||
\(687\) | 89.1561i | 0.129776i | ||||||||
\(688\) | −106.257 | − | 106.257i | −0.154444 | − | 0.154444i | ||||
\(689\) | −310.066 | − | 310.066i | −0.450023 | − | 0.450023i | ||||
\(690\) | −68.5371 | + | 68.5371i | −0.0993291 | + | 0.0993291i | ||||
\(691\) | − | 1141.32i | − | 1.65170i | −0.563890 | − | 0.825850i | \(-0.690696\pi\) | ||
0.563890 | − | 0.825850i | \(-0.309304\pi\) | |||||||
\(692\) | 142.253 | 0.205568 | ||||||||
\(693\) | 893.105i | 1.28875i | ||||||||
\(694\) | 356.331i | 0.513445i | ||||||||
\(695\) | −1151.87 | + | 1151.87i | −1.65736 | + | 1.65736i | ||||
\(696\) | 92.7474i | 0.133258i | ||||||||
\(697\) | 45.4837 | − | 45.4837i | 0.0652564 | − | 0.0652564i | ||||
\(698\) | 74.2795 | − | 74.2795i | 0.106418 | − | 0.106418i | ||||
\(699\) | −12.6899 | −0.0181544 | ||||||||
\(700\) | 303.935 | 0.434192 | ||||||||
\(701\) | 30.7153 | + | 30.7153i | 0.0438163 | + | 0.0438163i | 0.728675 | − | 0.684859i | \(-0.240136\pi\) |
−0.684859 | + | 0.728675i | \(0.740136\pi\) | |||||||
\(702\) | 109.931i | 0.156596i | ||||||||
\(703\) | −120.052 | − | 32.9505i | −0.170771 | − | 0.0468713i | ||||
\(704\) | 1112.00 | 1.57954 | ||||||||
\(705\) | −65.8255 | + | 65.8255i | −0.0933695 | + | 0.0933695i | ||||
\(706\) | 74.8669i | 0.106044i | ||||||||
\(707\) | − | 404.135i | − | 0.571619i | ||||||
\(708\) | 31.3780 | + | 31.3780i | 0.0443192 | + | 0.0443192i | ||||
\(709\) | 180.362 | + | 180.362i | 0.254390 | + | 0.254390i | 0.822768 | − | 0.568378i | \(-0.192429\pi\) |
−0.568378 | + | 0.822768i | \(0.692429\pi\) | |||||||
\(710\) | 1022.05 | 1.43950 | ||||||||
\(711\) | 351.858 | + | 351.858i | 0.494878 | + | 0.494878i | ||||
\(712\) | −1376.26 | −1.93295 | ||||||||
\(713\) | −342.272 | −0.480044 | ||||||||
\(714\) | 79.6589i | 0.111567i | ||||||||
\(715\) | 1487.62 | 2.08058 | ||||||||
\(716\) | −220.538 | − | 220.538i | −0.308013 | − | 0.308013i | ||||
\(717\) | −2.02992 | + | 2.02992i | −0.00283113 | + | 0.00283113i | ||||
\(718\) | 654.748 | − | 654.748i | 0.911905 | − | 0.911905i | ||||
\(719\) | −171.807 | −0.238952 | −0.119476 | − | 0.992837i | \(-0.538122\pi\) | ||||
−0.119476 | + | 0.992837i | \(0.538122\pi\) | |||||||
\(720\) | 260.673 | + | 260.673i | 0.362046 | + | 0.362046i | ||||
\(721\) | −329.566 | + | 329.566i | −0.457095 | + | 0.457095i | ||||
\(722\) | 367.029 | + | 367.029i | 0.508351 | + | 0.508351i | ||||
\(723\) | 100.049 | − | 100.049i | 0.138380 | − | 0.138380i | ||||
\(724\) | 244.665i | 0.337936i | ||||||||
\(725\) | 615.582 | + | 615.582i | 0.849079 | + | 0.849079i | ||||
\(726\) | −83.2845 | − | 83.2845i | −0.114717 | − | 0.114717i | ||||
\(727\) | 304.684 | − | 304.684i | 0.419098 | − | 0.419098i | −0.465795 | − | 0.884893i | \(-0.654232\pi\) |
0.884893 | + | 0.465795i | \(0.154232\pi\) | |||||||
\(728\) | 523.367i | 0.718910i | ||||||||
\(729\) | 660.506 | 0.906043 | ||||||||
\(730\) | − | 966.376i | − | 1.32380i | ||||||
\(731\) | 689.240i | 0.942873i | ||||||||
\(732\) | 2.19212 | − | 2.19212i | 0.00299469 | − | 0.00299469i | ||||
\(733\) | − | 641.352i | − | 0.874968i | −0.899226 | − | 0.437484i | \(-0.855870\pi\) | ||
0.899226 | − | 0.437484i | \(-0.144130\pi\) | |||||||
\(734\) | 199.351 | − | 199.351i | 0.271595 | − | 0.271595i | ||||
\(735\) | −36.3967 | + | 36.3967i | −0.0495193 | + | 0.0495193i | ||||
\(736\) | 605.824 | 0.823131 | ||||||||
\(737\) | −804.154 | −1.09112 | ||||||||
\(738\) | −23.3409 | − | 23.3409i | −0.0316272 | − | 0.0316272i | ||||
\(739\) | − | 6.01293i | − | 0.00813658i | −0.999992 | − | 0.00406829i | \(-0.998705\pi\) | ||
0.999992 | − | 0.00406829i | \(-0.00129498\pi\) | |||||||
\(740\) | 131.101 | − | 477.656i | 0.177164 | − | 0.645481i | ||||
\(741\) | 13.9541 | 0.0188314 | ||||||||
\(742\) | −232.460 | + | 232.460i | −0.313288 | + | 0.313288i | ||||
\(743\) | 529.715i | 0.712941i | 0.934307 | + | 0.356471i | \(0.116020\pi\) | ||||
−0.934307 | + | 0.356471i | \(0.883980\pi\) | |||||||
\(744\) | − | 47.9965i | − | 0.0645114i | ||||||
\(745\) | −1182.96 | − | 1182.96i | −1.58787 | − | 1.58787i | ||||
\(746\) | −157.314 | − | 157.314i | −0.210877 | − | 0.210877i | ||||
\(747\) | −995.166 | −1.33222 | ||||||||
\(748\) | −592.118 | − | 592.118i | −0.791601 | − | 0.791601i | ||||
\(749\) | −356.326 | −0.475736 | ||||||||
\(750\) | −23.0807 | −0.0307742 | ||||||||
\(751\) | 696.245i | 0.927091i | 0.886073 | + | 0.463545i | \(0.153423\pi\) | ||||
−0.886073 | + | 0.463545i | \(0.846577\pi\) | |||||||
\(752\) | −184.659 | −0.245557 | ||||||||
\(753\) | 22.7447 | + | 22.7447i | 0.0302054 | + | 0.0302054i | ||||
\(754\) | −328.542 | + | 328.542i | −0.435732 | + | 0.435732i | ||||
\(755\) | 1161.60 | − | 1161.60i | 1.53854 | − | 1.53854i | ||||
\(756\) | −67.2007 | −0.0888898 | ||||||||
\(757\) | −503.637 | − | 503.637i | −0.665306 | − | 0.665306i | 0.291320 | − | 0.956626i | \(-0.405906\pi\) |
−0.956626 | + | 0.291320i | \(0.905906\pi\) | |||||||
\(758\) | 237.862 | − | 237.862i | 0.313802 | − | 0.313802i | ||||
\(759\) | −112.729 | − | 112.729i | −0.148524 | − | 0.148524i | ||||
\(760\) | 152.538 | − | 152.538i | 0.200707 | − | 0.200707i | ||||
\(761\) | − | 246.317i | − | 0.323676i | −0.986817 | − | 0.161838i | \(-0.948258\pi\) | ||
0.986817 | − | 0.161838i | \(-0.0517422\pi\) | |||||||
\(762\) | 52.6774 | + | 52.6774i | 0.0691305 | + | 0.0691305i | ||||
\(763\) | 141.893 | + | 141.893i | 0.185967 | + | 0.185967i | ||||
\(764\) | −223.060 | + | 223.060i | −0.291964 | + | 0.291964i | ||||
\(765\) | − | 1690.86i | − | 2.21027i | ||||||
\(766\) | −898.117 | −1.17248 | ||||||||
\(767\) | 717.242i | 0.935127i | ||||||||
\(768\) | 100.124i | 0.130370i | ||||||||
\(769\) | 810.146 | − | 810.146i | 1.05351 | − | 1.05351i | 0.0550210 | − | 0.998485i | \(-0.482477\pi\) |
0.998485 | − | 0.0550210i | \(-0.0175226\pi\) | |||||||
\(770\) | − | 1115.28i | − | 1.44842i | ||||||
\(771\) | 39.1808 | − | 39.1808i | 0.0508181 | − | 0.0508181i | ||||
\(772\) | −118.662 | + | 118.662i | −0.153707 | + | 0.153707i | ||||
\(773\) | 294.190 | 0.380582 | 0.190291 | − | 0.981728i | \(-0.439057\pi\) | ||||
0.190291 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(774\) | 353.697 | 0.456973 | ||||||||
\(775\) | −318.562 | − | 318.562i | −0.411048 | − | 0.411048i | ||||
\(776\) | 78.1290i | 0.100682i | ||||||||
\(777\) | −38.3424 | − | 67.3522i | −0.0493468 | − | 0.0866824i | ||||
\(778\) | −1132.02 | −1.45504 | ||||||||
\(779\) | −5.97332 | + | 5.97332i | −0.00766793 | + | 0.00766793i | ||||
\(780\) | 55.5194i | 0.0711787i | ||||||||
\(781\) | 1681.06i | 2.15245i | ||||||||
\(782\) | 623.567 | + | 623.567i | 0.797401 | + | 0.797401i | ||||
\(783\) | −136.107 | − | 136.107i | −0.173827 | − | 0.173827i | ||||
\(784\) | −102.103 | −0.130233 | ||||||||
\(785\) | 435.817 | + | 435.817i | 0.555181 | + | 0.555181i | ||||
\(786\) | −72.0366 | −0.0916496 | ||||||||
\(787\) | 887.447 | 1.12763 | 0.563816 | − | 0.825900i | \(-0.309333\pi\) | ||||
0.563816 | + | 0.825900i | \(0.309333\pi\) | |||||||
\(788\) | 106.581i | 0.135255i | ||||||||
\(789\) | 87.8467 | 0.111339 | ||||||||
\(790\) | −439.389 | − | 439.389i | −0.556189 | − | 0.556189i | ||||
\(791\) | −309.600 | + | 309.600i | −0.391403 | + | 0.391403i | ||||
\(792\) | −980.370 | + | 980.370i | −1.23784 | + | 1.23784i | ||||
\(793\) | 50.1077 | 0.0631875 | ||||||||
\(794\) | −261.981 | − | 261.981i | −0.329951 | − | 0.329951i | ||||
\(795\) | −79.5623 | + | 79.5623i | −0.100078 | + | 0.100078i | ||||
\(796\) | 44.0113 | + | 44.0113i | 0.0552906 | + | 0.0552906i | ||||
\(797\) | −522.357 | + | 522.357i | −0.655404 | + | 0.655404i | −0.954289 | − | 0.298885i | \(-0.903385\pi\) |
0.298885 | + | 0.954289i | \(0.403385\pi\) | |||||||
\(798\) | − | 10.4615i | − | 0.0131097i | ||||||
\(799\) | 598.897 | + | 598.897i | 0.749558 | + | 0.749558i | ||||
\(800\) | 563.858 | + | 563.858i | 0.704823 | + | 0.704823i | ||||
\(801\) | 1001.75 | − | 1001.75i | 1.25063 | − | 1.25063i | ||||
\(802\) | − | 529.951i | − | 0.660786i | ||||||
\(803\) | 1589.49 | 1.97944 | ||||||||
\(804\) | − | 30.0119i | − | 0.0373282i | ||||||
\(805\) | − | 957.681i | − | 1.18967i | ||||||
\(806\) | 170.020 | − | 170.020i | 0.210943 | − | 0.210943i | ||||
\(807\) | − | 69.4885i | − | 0.0861072i | ||||||
\(808\) | 443.623 | − | 443.623i | 0.549038 | − | 0.549038i | ||||
\(809\) | 180.910 | − | 180.910i | 0.223622 | − | 0.223622i | −0.586400 | − | 0.810022i | \(-0.699455\pi\) |
0.810022 | + | 0.586400i | \(0.199455\pi\) | |||||||
\(810\) | −853.482 | −1.05368 | ||||||||
\(811\) | 914.793 | 1.12798 | 0.563991 | − | 0.825781i | \(-0.309265\pi\) | ||||
0.563991 | + | 0.825781i | \(0.309265\pi\) | |||||||
\(812\) | −200.838 | − | 200.838i | −0.247338 | − | 0.247338i | ||||
\(813\) | − | 4.12112i | − | 0.00506903i | ||||||
\(814\) | −963.532 | − | 264.458i | −1.18370 | − | 0.324888i | ||||
\(815\) | −1467.18 | −1.80022 | ||||||||
\(816\) | −38.2419 | + | 38.2419i | −0.0468651 | + | 0.0468651i | ||||
\(817\) | − | 90.5171i | − | 0.110792i | ||||||
\(818\) | 57.1845i | 0.0699077i | ||||||||
\(819\) | −380.949 | − | 380.949i | −0.465139 | − | 0.465139i | ||||
\(820\) | −23.7662 | − | 23.7662i | −0.0289832 | − | 0.0289832i | ||||
\(821\) | −1307.60 | −1.59270 | −0.796348 | − | 0.604839i | \(-0.793237\pi\) | ||||
−0.796348 | + | 0.604839i | \(0.793237\pi\) | |||||||
\(822\) | 5.99792 | + | 5.99792i | 0.00729675 | + | 0.00729675i | ||||
\(823\) | 71.3330 | 0.0866743 | 0.0433372 | − | 0.999061i | \(-0.486201\pi\) | ||||
0.0433372 | + | 0.999061i | \(0.486201\pi\) | |||||||
\(824\) | −723.535 | −0.878077 | ||||||||
\(825\) | − | 209.841i | − | 0.254353i | ||||||
\(826\) | 537.724 | 0.650998 | ||||||||
\(827\) | −423.902 | − | 423.902i | −0.512578 | − | 0.512578i | 0.402737 | − | 0.915316i | \(-0.368059\pi\) |
−0.915316 | + | 0.402737i | \(0.868059\pi\) | |||||||
\(828\) | −260.919 | + | 260.919i | −0.315120 | + | 0.315120i | ||||
\(829\) | 139.431 | − | 139.431i | 0.168191 | − | 0.168191i | −0.617993 | − | 0.786184i | \(-0.712054\pi\) |
0.786184 | + | 0.617993i | \(0.212054\pi\) | |||||||
\(830\) | 1242.73 | 1.49727 | ||||||||
\(831\) | 79.4802 | + | 79.4802i | 0.0956440 | + | 0.0956440i | ||||
\(832\) | −474.316 | + | 474.316i | −0.570091 | + | 0.570091i | ||||
\(833\) | 331.146 | + | 331.146i | 0.397534 | + | 0.397534i | ||||
\(834\) | −86.7176 | + | 86.7176i | −0.103978 | + | 0.103978i | ||||
\(835\) | 800.252i | 0.958386i | ||||||||
\(836\) | 77.7621 | + | 77.7621i | 0.0930169 | + | 0.0930169i | ||||
\(837\) | 70.4348 | + | 70.4348i | 0.0841515 | + | 0.0841515i | ||||
\(838\) | −232.674 | + | 232.674i | −0.277654 | + | 0.277654i | ||||
\(839\) | 946.465i | 1.12809i | 0.825745 | + | 0.564043i | \(0.190755\pi\) | ||||
−0.825745 | + | 0.564043i | \(0.809245\pi\) | |||||||
\(840\) | 134.295 | 0.159875 | ||||||||
\(841\) | 27.4541i | 0.0326446i | ||||||||
\(842\) | 290.998i | 0.345604i | ||||||||
\(843\) | −133.728 | + | 133.728i | −0.158633 | + | 0.158633i | ||||
\(844\) | 59.8160i | 0.0708721i | ||||||||
\(845\) | 255.903 | − | 255.903i | 0.302844 | − | 0.302844i | ||||
\(846\) | 307.336 | − | 307.336i | 0.363281 | − | 0.363281i | ||||
\(847\) | 1163.75 | 1.37397 | ||||||||
\(848\) | −223.194 | −0.263201 | ||||||||
\(849\) | −115.495 | − | 115.495i | −0.136036 | − | 0.136036i | ||||
\(850\) | 1160.74i | 1.36558i | ||||||||
\(851\) | −827.375 | − | 227.088i | −0.972238 | − | 0.266848i | ||||
\(852\) | −62.7389 | −0.0736372 | ||||||||
\(853\) | −718.017 | + | 718.017i | −0.841755 | + | 0.841755i | −0.989087 | − | 0.147332i | \(-0.952931\pi\) |
0.147332 | + | 0.989087i | \(0.452931\pi\) | |||||||
\(854\) | − | 37.5663i | − | 0.0439886i | ||||||
\(855\) | 222.059i | 0.259718i | ||||||||
\(856\) | −391.143 | − | 391.143i | −0.456943 | − | 0.456943i | ||||
\(857\) | 241.022 | + | 241.022i | 0.281239 | + | 0.281239i | 0.833603 | − | 0.552364i | \(-0.186274\pi\) |
−0.552364 | + | 0.833603i | \(0.686274\pi\) | |||||||
\(858\) | 111.994 | 0.130529 | ||||||||
\(859\) | 944.215 | + | 944.215i | 1.09920 | + | 1.09920i | 0.994504 | + | 0.104698i | \(0.0333877\pi\) |
0.104698 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(860\) | 360.143 | 0.418771 | ||||||||
\(861\) | −5.25894 | −0.00610794 | ||||||||
\(862\) | − | 1102.94i | − | 1.27952i | ||||||
\(863\) | 1108.91 | 1.28495 | 0.642473 | − | 0.766309i | \(-0.277909\pi\) | ||||
0.642473 | + | 0.766309i | \(0.277909\pi\) | |||||||
\(864\) | −124.670 | − | 124.670i | −0.144294 | − | 0.144294i | ||||
\(865\) | 417.182 | − | 417.182i | 0.482292 | − | 0.482292i | ||||
\(866\) | −241.116 | + | 241.116i | −0.278425 | + | 0.278425i | ||||
\(867\) | 138.840 | 0.160139 | ||||||||
\(868\) | 103.933 | + | 103.933i | 0.119739 | + | 0.119739i | ||||
\(869\) | 722.706 | − | 722.706i | 0.831652 | − | 0.831652i | ||||
\(870\) | 84.3033 | + | 84.3033i | 0.0969003 | + | 0.0969003i | ||||
\(871\) | 343.008 | − | 343.008i | 0.393809 | − | 0.393809i | ||||
\(872\) | 311.515i | 0.357242i | ||||||||
\(873\) | −56.8687 | − | 56.8687i | −0.0651417 | − | 0.0651417i | ||||
\(874\) | −81.8924 | − | 81.8924i | −0.0936984 | − | 0.0936984i | ||||
\(875\) | 161.255 | − | 161.255i | 0.184292 | − | 0.184292i | ||||
\(876\) | 59.3215i | 0.0677186i | ||||||||
\(877\) | −696.297 | −0.793954 | −0.396977 | − | 0.917829i | \(-0.629941\pi\) | ||||
−0.396977 | + | 0.917829i | \(0.629941\pi\) | |||||||
\(878\) | 881.755i | 1.00428i | ||||||||
\(879\) | 30.9323i | 0.0351903i | ||||||||
\(880\) | 535.414 | − | 535.414i | 0.608425 | − | 0.608425i | ||||
\(881\) | 310.219i | 0.352121i | 0.984379 | + | 0.176061i | \(0.0563355\pi\) | ||||
−0.984379 | + | 0.176061i | \(0.943664\pi\) | |||||||
\(882\) | 169.934 | − | 169.934i | 0.192669 | − | 0.192669i | ||||
\(883\) | 534.700 | − | 534.700i | 0.605549 | − | 0.605549i | −0.336231 | − | 0.941780i | \(-0.609152\pi\) |
0.941780 | + | 0.336231i | \(0.109152\pi\) | |||||||
\(884\) | 505.129 | 0.571413 | ||||||||
\(885\) | 184.043 | 0.207958 | ||||||||
\(886\) | 669.322 | + | 669.322i | 0.755443 | + | 0.755443i | ||||
\(887\) | − | 474.335i | − | 0.534764i | −0.963591 | − | 0.267382i | \(-0.913841\pi\) | ||
0.963591 | − | 0.267382i | \(-0.0861585\pi\) | |||||||
\(888\) | 31.8443 | − | 116.022i | 0.0358607 | − | 0.130656i | ||||
\(889\) | −736.072 | −0.827977 | ||||||||
\(890\) | −1250.96 | + | 1250.96i | −1.40557 | + | 1.40557i | ||||
\(891\) | − | 1403.80i | − | 1.57554i | ||||||
\(892\) | 641.285i | 0.718930i | ||||||||
\(893\) | −78.6524 | − | 78.6524i | −0.0880766 | − | 0.0880766i | ||||
\(894\) | −89.0585 | − | 89.0585i | −0.0996181 | − | 0.0996181i | ||||
\(895\) | −1293.53 | −1.44528 | ||||||||
\(896\) | −53.9783 | − | 53.9783i | −0.0602436 | − | 0.0602436i | ||||
\(897\) | 96.1683 | 0.107211 | ||||||||
\(898\) | −437.164 | −0.486820 | ||||||||
\(899\) | 421.008i | 0.468307i | ||||||||
\(900\) | −485.690 | −0.539655 | ||||||||
\(901\) | 723.878 | + | 723.878i | 0.803416 | + | 0.803416i | ||||
\(902\) | −47.9414 | + | 47.9414i | −0.0531501 | + | 0.0531501i | ||||
\(903\) | 39.8458 | − | 39.8458i | 0.0441261 | − | 0.0441261i | ||||
\(904\) | −679.701 | −0.751882 | ||||||||
\(905\) | 717.524 | + | 717.524i | 0.792844 | + | 0.792844i | ||||
\(906\) | 87.4504 | − | 87.4504i | 0.0965236 | − | 0.0965236i | ||||
\(907\) | −729.638 | − | 729.638i | −0.804452 | − | 0.804452i | 0.179336 | − | 0.983788i | \(-0.442605\pi\) |
−0.983788 | + | 0.179336i | \(0.942605\pi\) | |||||||
\(908\) | 227.356 | − | 227.356i | 0.250393 | − | 0.250393i | ||||
\(909\) | 645.810i | 0.710462i | ||||||||
\(910\) | 475.717 | + | 475.717i | 0.522766 | + | 0.522766i | ||||
\(911\) | 199.232 | + | 199.232i | 0.218696 | + | 0.218696i | 0.807949 | − | 0.589253i | \(-0.200578\pi\) |
−0.589253 | + | 0.807949i | \(0.700578\pi\) | |||||||
\(912\) | 5.02226 | − | 5.02226i | 0.00550687 | − | 0.00550687i | ||||
\(913\) | 2044.04i | 2.23882i | ||||||||
\(914\) | −352.634 | −0.385814 | ||||||||
\(915\) | − | 12.8575i | − | 0.0140519i | ||||||
\(916\) | − | 423.851i | − | 0.462720i | ||||||
\(917\) | 503.291 | − | 503.291i | 0.548845 | − | 0.548845i | ||||
\(918\) | − | 256.643i | − | 0.279568i | ||||||
\(919\) | −77.9734 | + | 77.9734i | −0.0848459 | + | 0.0848459i | −0.748256 | − | 0.663410i | \(-0.769109\pi\) |
0.663410 | + | 0.748256i | \(0.269109\pi\) | |||||||
\(920\) | 1051.26 | − | 1051.26i | 1.14267 | − | 1.14267i | ||||
\(921\) | 166.837 | 0.181148 | ||||||||
\(922\) | 1216.92 | 1.31987 | ||||||||
\(923\) | −717.047 | − | 717.047i | −0.776866 | − | 0.776866i | ||||
\(924\) | 68.4622i | 0.0740932i | ||||||||
\(925\) | −558.704 | − | 981.419i | −0.604005 | − | 1.06099i | ||||
\(926\) | −495.037 | −0.534597 | ||||||||
\(927\) | 526.648 | − | 526.648i | 0.568121 | − | 0.568121i | ||||
\(928\) | − | 745.188i | − | 0.803004i | ||||||
\(929\) | 1756.58i | 1.89083i | 0.325870 | + | 0.945415i | \(0.394343\pi\) | ||||
−0.325870 | + | 0.945415i | \(0.605657\pi\) | |||||||
\(930\) | −43.6267 | − | 43.6267i | −0.0469104 | − | 0.0469104i | ||||
\(931\) | −43.4890 | − | 43.4890i | −0.0467122 | − | 0.0467122i | ||||
\(932\) | 60.3285 | 0.0647301 | ||||||||
\(933\) | 10.0081 | + | 10.0081i | 0.0107268 | + | 0.0107268i | ||||
\(934\) | 361.188 | 0.386711 | ||||||||
\(935\) | −3472.98 | −3.71441 | ||||||||
\(936\) | − | 836.343i | − | 0.893529i | ||||||
\(937\) | −1070.63 | −1.14261 | −0.571306 | − | 0.820737i | \(-0.693563\pi\) | ||||
−0.571306 | + | 0.820737i | \(0.693563\pi\) | |||||||
\(938\) | −257.157 | − | 257.157i | −0.274154 | − | 0.274154i | ||||
\(939\) | 113.808 | − | 113.808i | 0.121201 | − | 0.121201i | ||||
\(940\) | 312.937 | − | 312.937i | 0.332911 | − | 0.332911i | ||||
\(941\) | 1074.54 | 1.14191 | 0.570957 | − | 0.820980i | \(-0.306572\pi\) | ||||
0.570957 | + | 0.820980i | \(0.306572\pi\) | |||||||
\(942\) | 32.8102 | + | 32.8102i | 0.0348304 | + | 0.0348304i | ||||
\(943\) | −41.1668 | + | 41.1668i | −0.0436552 | + | 0.0436552i | ||||
\(944\) | 258.146 | + | 258.146i | 0.273459 | + | 0.273459i | ||||
\(945\) | −197.078 | + | 197.078i | −0.208548 | + | 0.208548i | ||||
\(946\) | − | 726.484i | − | 0.767953i | ||||||
\(947\) | −129.643 | − | 129.643i | −0.136899 | − | 0.136899i | 0.635336 | − | 0.772236i | \(-0.280861\pi\) |
−0.772236 | + | 0.635336i | \(0.780861\pi\) | |||||||
\(948\) | 26.9722 | + | 26.9722i | 0.0284516 | + | 0.0284516i | ||||
\(949\) | −677.989 | + | 677.989i | −0.714425 | + | 0.714425i | ||||
\(950\) | − | 152.439i | − | 0.160462i | ||||||
\(951\) | −141.533 | −0.148826 | ||||||||
\(952\) | − | 1221.85i | − | 1.28345i | ||||||
\(953\) | − | 502.255i | − | 0.527025i | −0.964656 | − | 0.263512i | \(-0.915119\pi\) | ||
0.964656 | − | 0.263512i | \(-0.0848810\pi\) | |||||||
\(954\) | 371.472 | − | 371.472i | 0.389384 | − | 0.389384i | ||||
\(955\) | 1308.32i | 1.36997i | ||||||||
\(956\) | 9.65032 | − | 9.65032i | 0.0100945 | − | 0.0100945i | ||||
\(957\) | −138.662 | + | 138.662i | −0.144892 | + | 0.144892i | ||||
\(958\) | −118.058 | −0.123233 | ||||||||
\(959\) | −83.8101 | −0.0873932 | ||||||||
\(960\) | 121.709 | + | 121.709i | 0.126780 | + | 0.126780i | ||||
\(961\) | 743.130i | 0.773288i | ||||||||
\(962\) | 523.793 | − | 298.186i | 0.544483 | − | 0.309965i | ||||
\(963\) | 569.412 | 0.591289 | ||||||||
\(964\) | −475.635 | + | 475.635i | −0.493398 | + | 0.493398i | ||||
\(965\) | 695.992i | 0.721236i | ||||||||
\(966\) | − | 72.0984i | − | 0.0746361i | ||||||
\(967\) | −85.0575 | − | 85.0575i | −0.0879602 | − | 0.0879602i | 0.661758 | − | 0.749718i | \(-0.269811\pi\) |
−0.749718 | + | 0.661758i | \(0.769811\pi\) | |||||||
\(968\) | 1277.46 | + | 1277.46i | 1.31969 | + | 1.31969i | ||||
\(969\) | −32.5770 | −0.0336192 | ||||||||
\(970\) | 71.0159 | + | 71.0159i | 0.0732122 | + | 0.0732122i | ||||
\(971\) | −496.661 | −0.511494 | −0.255747 | − | 0.966744i | \(-0.582321\pi\) | ||||
−0.255747 | + | 0.966744i | \(0.582321\pi\) | |||||||
\(972\) | 161.510 | 0.166163 | ||||||||
\(973\) | − | 1211.72i | − | 1.24535i | ||||||
\(974\) | 319.955 | 0.328496 | ||||||||
\(975\) | 89.5066 | + | 89.5066i | 0.0918016 | + | 0.0918016i | ||||
\(976\) | 18.0345 | − | 18.0345i | 0.0184779 | − | 0.0184779i | ||||
\(977\) | 1186.94 | − | 1186.94i | 1.21488 | − | 1.21488i | 0.245479 | − | 0.969402i | \(-0.421055\pi\) |
0.969402 | − | 0.245479i | \(-0.0789451\pi\) | |||||||
\(978\) | −110.456 | −0.112941 | ||||||||
\(979\) | −2057.57 | − | 2057.57i | −2.10171 | − | 2.10171i | ||||
\(980\) | 173.031 | − | 173.031i | 0.176562 | − | 0.176562i | ||||
\(981\) | −226.746 | − | 226.746i | −0.231137 | − | 0.231137i | ||||
\(982\) | −512.205 | + | 512.205i | −0.521594 | + | 0.521594i | ||||
\(983\) | − | 1471.76i | − | 1.49721i | −0.663017 | − | 0.748605i | \(-0.730724\pi\) | ||
0.663017 | − | 0.748605i | \(-0.269276\pi\) | |||||||
\(984\) | −5.77279 | − | 5.77279i | −0.00586666 | − | 0.00586666i | ||||
\(985\) | 312.568 | + | 312.568i | 0.317328 | + | 0.317328i | ||||
\(986\) | 767.012 | − | 767.012i | 0.777903 | − | 0.777903i | ||||
\(987\) | − | 69.2460i | − | 0.0701580i | ||||||
\(988\) | −66.3381 | −0.0671438 | ||||||||
\(989\) | − | 623.824i | − | 0.630763i | ||||||
\(990\) | 1782.23i | 1.80023i | ||||||||
\(991\) | 672.226 | − | 672.226i | 0.678331 | − | 0.678331i | −0.281291 | − | 0.959622i | \(-0.590763\pi\) |
0.959622 | + | 0.281291i | \(0.0907628\pi\) | |||||||
\(992\) | 385.633i | 0.388743i | ||||||||
\(993\) | −107.484 | + | 107.484i | −0.108242 | + | 0.108242i | ||||
\(994\) | −537.578 | + | 537.578i | −0.540823 | + | 0.540823i | ||||
\(995\) | 258.142 | 0.259439 | ||||||||
\(996\) | −76.2858 | −0.0765922 | ||||||||
\(997\) | −584.483 | − | 584.483i | −0.586242 | − | 0.586242i | 0.350370 | − | 0.936611i | \(-0.386056\pi\) |
−0.936611 | + | 0.350370i | \(0.886056\pi\) | |||||||
\(998\) | − | 1236.00i | − | 1.23848i | ||||||
\(999\) | 123.531 | + | 216.994i | 0.123655 | + | 0.217211i |
(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 | 37.3.d.a.6.3 | ✓ | 12 | |
3.2 | odd | 2 | 333.3.i.a.154.4 | 12 | |||
4.3 | odd | 2 | 592.3.k.e.561.4 | 12 | |||
37.31 | odd | 4 | inner | 37.3.d.a.31.3 | yes | 12 | |
111.68 | even | 4 | 333.3.i.a.253.4 | 12 | |||
148.31 | even | 4 | 592.3.k.e.401.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.3.d.a.6.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
37.3.d.a.31.3 | yes | 12 | 37.31 | odd | 4 | inner | |
333.3.i.a.154.4 | 12 | 3.2 | odd | 2 | |||
333.3.i.a.253.4 | 12 | 111.68 | even | 4 | |||
592.3.k.e.401.3 | 12 | 148.31 | even | 4 | |||
592.3.k.e.561.4 | 12 | 4.3 | odd | 2 |