Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.343361479062744140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 323.3 | ||
Root | \(1.13127 - 1.31158i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.323 |
Dual form | 363.3.h.l.245.3 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.465695 | − | 0.640974i | 0.232847 | − | 0.320487i | −0.676565 | − | 0.736383i | \(-0.736532\pi\) |
0.909412 | + | 0.415896i | \(0.136532\pi\) | |||||||
\(3\) | 2.90519 | + | 0.748234i | 0.968398 | + | 0.249411i | ||||
\(4\) | 1.04209 | + | 3.20723i | 0.260523 | + | 0.801808i | ||||
\(5\) | 1.48377 | + | 2.04223i | 0.296754 | + | 0.408446i | 0.931193 | − | 0.364526i | \(-0.118769\pi\) |
−0.634439 | + | 0.772973i | \(0.718769\pi\) | |||||||
\(6\) | 1.83253 | − | 1.51370i | 0.305422 | − | 0.252284i | ||||
\(7\) | 1.46615 | + | 4.51235i | 0.209450 | + | 0.644621i | 0.999501 | + | 0.0315801i | \(0.0100539\pi\) |
−0.790051 | + | 0.613041i | \(0.789946\pi\) | |||||||
\(8\) | 5.55509 | + | 1.80496i | 0.694386 | + | 0.225620i | ||||
\(9\) | 7.88029 | + | 4.34753i | 0.875588 | + | 0.483059i | ||||
\(10\) | 2.00000 | 0.200000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.627719 | + | 10.0974i | 0.0523099 | + | 0.841446i | ||||
\(13\) | −10.9129 | − | 7.92871i | −0.839456 | − | 0.609901i | 0.0827624 | − | 0.996569i | \(-0.473626\pi\) |
−0.922219 | + | 0.386669i | \(0.873626\pi\) | |||||||
\(14\) | 3.57507 | + | 1.16161i | 0.255362 | + | 0.0829723i | ||||
\(15\) | 2.78257 | + | 7.04328i | 0.185504 | + | 0.469552i | ||||
\(16\) | −7.16903 | + | 5.20860i | −0.448064 | + | 0.325538i | ||||
\(17\) | −13.3216 | − | 18.3357i | −0.783626 | − | 1.07857i | −0.994873 | − | 0.101136i | \(-0.967752\pi\) |
0.211246 | − | 0.977433i | \(-0.432248\pi\) | |||||||
\(18\) | 6.45646 | − | 3.02644i | 0.358692 | − | 0.168135i | ||||
\(19\) | −2.54435 | + | 7.83070i | −0.133913 | + | 0.412142i | −0.995419 | − | 0.0956047i | \(-0.969522\pi\) |
0.861506 | + | 0.507747i | \(0.169522\pi\) | |||||||
\(20\) | −5.00368 | + | 6.88698i | −0.250184 | + | 0.344349i | ||||
\(21\) | 0.883156 | + | 14.2063i | 0.0420550 | + | 0.676489i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.2372i | 1.31466i | 0.753603 | + | 0.657329i | \(0.228314\pi\) | ||||
−0.753603 | + | 0.657329i | \(0.771686\pi\) | |||||||
\(24\) | 14.7881 | + | 9.40025i | 0.616169 | + | 0.391677i | ||||
\(25\) | 5.75628 | − | 17.7160i | 0.230251 | − | 0.708641i | ||||
\(26\) | −10.1642 | + | 3.30254i | −0.390930 | + | 0.127021i | ||||
\(27\) | 19.6408 | + | 18.5267i | 0.727437 | + | 0.686175i | ||||
\(28\) | −12.9443 | + | 9.40456i | −0.462295 | + | 0.335877i | ||||
\(29\) | 51.0298 | − | 16.5806i | 1.75965 | − | 0.571744i | 0.762484 | − | 0.647007i | \(-0.223979\pi\) |
0.997164 | + | 0.0752622i | \(0.0239794\pi\) | |||||||
\(30\) | 5.81039 | + | 1.49647i | 0.193680 | + | 0.0498823i | ||||
\(31\) | −20.9223 | − | 15.2010i | −0.674913 | − | 0.490353i | 0.196753 | − | 0.980453i | \(-0.436960\pi\) |
−0.871666 | + | 0.490100i | \(0.836960\pi\) | |||||||
\(32\) | 30.3846i | 0.949520i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.9565 | −0.528132 | ||||||||
\(35\) | −7.03983 | + | 9.68950i | −0.201138 | + | 0.276843i | ||||
\(36\) | −5.73154 | + | 29.8044i | −0.159210 | + | 0.827901i | ||||
\(37\) | −13.1660 | − | 40.5207i | −0.355837 | − | 1.09515i | −0.955523 | − | 0.294918i | \(-0.904708\pi\) |
0.599686 | − | 0.800236i | \(-0.295292\pi\) | |||||||
\(38\) | 3.83438 | + | 5.27758i | 0.100905 | + | 0.138884i | ||||
\(39\) | −25.7716 | − | 31.1999i | −0.660811 | − | 0.799996i | ||||
\(40\) | 4.55632 | + | 14.0229i | 0.113908 | + | 0.350573i | ||||
\(41\) | 29.3705 | + | 9.54305i | 0.716353 | + | 0.232757i | 0.644441 | − | 0.764654i | \(-0.277090\pi\) |
0.0719120 | + | 0.997411i | \(0.477090\pi\) | |||||||
\(42\) | 9.51712 | + | 6.04970i | 0.226598 | + | 0.144040i | ||||
\(43\) | −35.4891 | −0.825328 | −0.412664 | − | 0.910883i | \(-0.635402\pi\) | ||||
−0.412664 | + | 0.910883i | \(0.635402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.81386 | + | 22.5441i | 0.0625302 | + | 0.500980i | ||||
\(46\) | 19.3812 | + | 14.0813i | 0.421331 | + | 0.306115i | ||||
\(47\) | 29.7554 | + | 9.66813i | 0.633094 | + | 0.205705i | 0.607945 | − | 0.793979i | \(-0.291994\pi\) |
0.0251491 | + | 0.999684i | \(0.491994\pi\) | |||||||
\(48\) | −24.7247 | + | 9.76788i | −0.515097 | + | 0.203498i | ||||
\(49\) | 21.4302 | − | 15.5699i | 0.437350 | − | 0.317753i | ||||
\(50\) | −8.67483 | − | 11.9399i | −0.173497 | − | 0.238798i | ||||
\(51\) | −24.9826 | − | 63.2364i | −0.489854 | − | 1.23993i | ||||
\(52\) | 14.0569 | − | 43.2627i | 0.270325 | − | 0.831976i | ||||
\(53\) | −5.82625 | + | 8.01914i | −0.109929 | + | 0.151305i | −0.860437 | − | 0.509557i | \(-0.829809\pi\) |
0.750507 | + | 0.660862i | \(0.229809\pi\) | |||||||
\(54\) | 21.0217 | − | 3.96143i | 0.389292 | − | 0.0733599i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 27.7128i | 0.494872i | ||||||||
\(57\) | −13.2510 | + | 20.8459i | −0.232474 | + | 0.365718i | ||||
\(58\) | 13.1366 | − | 40.4302i | 0.226493 | − | 0.697073i | ||||
\(59\) | 58.5127 | − | 19.0119i | 0.991740 | − | 0.322236i | 0.232180 | − | 0.972673i | \(-0.425414\pi\) |
0.759560 | + | 0.650437i | \(0.225414\pi\) | |||||||
\(60\) | −19.6897 | + | 16.2641i | −0.328162 | + | 0.271068i | ||||
\(61\) | 41.6204 | − | 30.2390i | 0.682301 | − | 0.495721i | −0.191819 | − | 0.981430i | \(-0.561439\pi\) |
0.874120 | + | 0.485709i | \(0.161439\pi\) | |||||||
\(62\) | −19.4868 | + | 6.33165i | −0.314304 | + | 0.102123i | ||||
\(63\) | −8.06388 | + | 41.9327i | −0.127998 | + | 0.665599i | ||||
\(64\) | −9.20037 | − | 6.68446i | −0.143756 | − | 0.104445i | ||||
\(65\) | − | 34.0511i | − | 0.523863i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.3288 | 0.512370 | 0.256185 | − | 0.966628i | \(-0.417534\pi\) | ||||
0.256185 | + | 0.966628i | \(0.417534\pi\) | |||||||
\(68\) | 44.9243 | − | 61.8330i | 0.660652 | − | 0.909309i | ||||
\(69\) | −22.6245 | + | 87.8448i | −0.327891 | + | 1.27311i | ||||
\(70\) | 2.93230 | + | 9.02469i | 0.0418900 | + | 0.128924i | ||||
\(71\) | 8.52360 | + | 11.7317i | 0.120051 | + | 0.165236i | 0.864813 | − | 0.502094i | \(-0.167437\pi\) |
−0.744762 | + | 0.667330i | \(0.767437\pi\) | |||||||
\(72\) | 35.9286 | + | 38.3745i | 0.499008 | + | 0.532979i | ||||
\(73\) | 27.2657 | + | 83.9152i | 0.373503 | + | 1.14952i | 0.944483 | + | 0.328560i | \(0.106563\pi\) |
−0.570980 | + | 0.820964i | \(0.693437\pi\) | |||||||
\(74\) | −32.1040 | − | 10.4312i | −0.433838 | − | 0.140963i | ||||
\(75\) | 29.9788 | − | 47.1614i | 0.399718 | − | 0.628818i | ||||
\(76\) | −27.7663 | −0.365346 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0000 | + | 1.98933i | −0.410256 | + | 0.0255043i | ||||
\(79\) | −75.7882 | − | 55.0633i | −0.959344 | − | 0.697004i | −0.00634552 | − | 0.999980i | \(-0.502020\pi\) |
−0.952998 | + | 0.302976i | \(0.902020\pi\) | |||||||
\(80\) | −21.2744 | − | 6.91246i | −0.265929 | − | 0.0864057i | ||||
\(81\) | 43.1980 | + | 68.5196i | 0.533308 | + | 0.845921i | ||||
\(82\) | 19.7945 | − | 14.3816i | 0.241397 | − | 0.175385i | ||||
\(83\) | 20.0793 | + | 27.6368i | 0.241919 | + | 0.332973i | 0.912661 | − | 0.408718i | \(-0.134024\pi\) |
−0.670742 | + | 0.741691i | \(0.734024\pi\) | |||||||
\(84\) | −44.6424 | + | 17.6367i | −0.531457 | + | 0.209961i | ||||
\(85\) | 17.6795 | − | 54.4118i | 0.207994 | − | 0.640139i | ||||
\(86\) | −16.5271 | + | 22.7476i | −0.192176 | + | 0.264507i | ||||
\(87\) | 160.658 | − | 9.98755i | 1.84664 | − | 0.114799i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 143.482i | − | 1.61216i | −0.591805 | − | 0.806081i | \(-0.701584\pi\) | ||
0.591805 | − | 0.806081i | \(-0.298416\pi\) | |||||||
\(90\) | 15.7606 | + | 8.69506i | 0.175118 | + | 0.0966118i | ||||
\(91\) | 19.7771 | − | 60.8676i | 0.217331 | − | 0.668875i | ||||
\(92\) | −96.9775 | + | 31.5099i | −1.05410 | + | 0.342499i | ||||
\(93\) | −49.4095 | − | 59.8165i | −0.531285 | − | 0.643188i | ||||
\(94\) | 20.0540 | − | 14.5701i | 0.213340 | − | 0.155001i | ||||
\(95\) | −19.7673 | + | 6.42280i | −0.208077 | + | 0.0676084i | ||||
\(96\) | −22.7348 | + | 88.2732i | −0.236821 | + | 0.919513i | ||||
\(97\) | 32.5915 | + | 23.6791i | 0.335995 | + | 0.244114i | 0.742970 | − | 0.669325i | \(-0.233417\pi\) |
−0.406975 | + | 0.913439i | \(0.633417\pi\) | |||||||
\(98\) | − | 20.9870i | − | 0.214153i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 62.8179 | 0.628179 | ||||||||
\(101\) | −54.5204 | + | 75.0409i | −0.539806 | + | 0.742979i | −0.988585 | − | 0.150663i | \(-0.951859\pi\) |
0.448779 | + | 0.893643i | \(0.351859\pi\) | |||||||
\(102\) | −52.1671 | − | 13.4357i | −0.511442 | − | 0.131722i | ||||
\(103\) | −6.04935 | − | 18.6180i | −0.0587316 | − | 0.180757i | 0.917387 | − | 0.397997i | \(-0.130295\pi\) |
−0.976118 | + | 0.217240i | \(0.930295\pi\) | |||||||
\(104\) | −46.3113 | − | 63.7420i | −0.445301 | − | 0.612904i | ||||
\(105\) | −27.7021 | + | 22.8824i | −0.263829 | + | 0.217928i | ||||
\(106\) | 2.42681 | + | 7.46894i | 0.0228944 | + | 0.0704617i | ||||
\(107\) | −80.2959 | − | 26.0897i | −0.750429 | − | 0.243829i | −0.0912630 | − | 0.995827i | \(-0.529090\pi\) |
−0.659166 | + | 0.751998i | \(0.729090\pi\) | |||||||
\(108\) | −38.9519 | + | 82.2991i | −0.360666 | + | 0.762029i | ||||
\(109\) | −167.723 | −1.53874 | −0.769371 | − | 0.638803i | \(-0.779430\pi\) | ||||
−0.769371 | + | 0.638803i | \(0.779430\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.93070 | − | 127.572i | −0.0714478 | − | 1.14929i | ||||
\(112\) | −34.0139 | − | 24.7125i | −0.303696 | − | 0.220648i | ||||
\(113\) | −117.463 | − | 38.1659i | −1.03949 | − | 0.337751i | −0.260955 | − | 0.965351i | \(-0.584037\pi\) |
−0.778536 | + | 0.627600i | \(0.784037\pi\) | |||||||
\(114\) | 7.19076 | + | 18.2014i | 0.0630768 | + | 0.159661i | ||||
\(115\) | −61.7513 | + | 44.8649i | −0.536968 | + | 0.390130i | ||||
\(116\) | 106.356 | + | 146.386i | 0.916858 | + | 1.26195i | ||||
\(117\) | −51.5268 | − | 109.925i | −0.440400 | − | 0.939529i | ||||
\(118\) | 15.0629 | − | 46.3588i | 0.127652 | − | 0.392871i | ||||
\(119\) | 63.2054 | − | 86.9947i | 0.531138 | − | 0.731048i | ||||
\(120\) | 2.74456 | + | 44.1485i | 0.0228714 | + | 0.367904i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 40.7597i | − | 0.334096i | ||||||
\(123\) | 78.1865 | + | 49.7004i | 0.635663 | + | 0.404068i | ||||
\(124\) | 26.9500 | − | 82.9435i | 0.217338 | − | 0.668899i | ||||
\(125\) | 104.741 | − | 34.0324i | 0.837927 | − | 0.272259i | ||||
\(126\) | 23.1225 | + | 24.6966i | 0.183512 | + | 0.196005i | ||||
\(127\) | −104.240 | + | 75.7348i | −0.820788 | + | 0.596337i | −0.916938 | − | 0.399030i | \(-0.869347\pi\) |
0.0961504 | + | 0.995367i | \(0.469347\pi\) | |||||||
\(128\) | −124.159 | + | 40.3417i | −0.969993 | + | 0.315170i | ||||
\(129\) | −103.103 | − | 26.5542i | −0.799246 | − | 0.205846i | ||||
\(130\) | −21.8259 | − | 15.8574i | −0.167891 | − | 0.121980i | ||||
\(131\) | − | 125.997i | − | 0.961811i | −0.876772 | − | 0.480906i | \(-0.840308\pi\) | ||
0.876772 | − | 0.480906i | \(-0.159692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.0652 | −0.293724 | ||||||||
\(134\) | 15.9867 | − | 22.0038i | 0.119304 | − | 0.164208i | ||||
\(135\) | −8.69348 | + | 67.6004i | −0.0643961 | + | 0.500744i | ||||
\(136\) | −40.9078 | − | 125.901i | −0.300793 | − | 0.925744i | ||||
\(137\) | −34.8644 | − | 47.9868i | −0.254485 | − | 0.350268i | 0.662591 | − | 0.748982i | \(-0.269457\pi\) |
−0.917076 | + | 0.398713i | \(0.869457\pi\) | |||||||
\(138\) | 45.7701 | + | 55.4105i | 0.331667 | + | 0.401526i | ||||
\(139\) | 40.4611 | + | 124.526i | 0.291087 | + | 0.895873i | 0.984508 | + | 0.175340i | \(0.0561026\pi\) |
−0.693421 | + | 0.720533i | \(0.743897\pi\) | |||||||
\(140\) | −38.4126 | − | 12.4810i | −0.274376 | − | 0.0891501i | ||||
\(141\) | 79.2113 | + | 50.3518i | 0.561782 | + | 0.357105i | ||||
\(142\) | 11.4891 | 0.0809093 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −79.1386 | + | 9.87774i | −0.549574 | + | 0.0685954i | ||||
\(145\) | 109.578 | + | 79.6129i | 0.755709 | + | 0.549055i | ||||
\(146\) | 66.4849 | + | 21.6023i | 0.455376 | + | 0.147961i | ||||
\(147\) | 73.9087 | − | 29.1988i | 0.502780 | − | 0.198632i | ||||
\(148\) | 116.239 | − | 84.4526i | 0.785399 | − | 0.570626i | ||||
\(149\) | −43.6905 | − | 60.1348i | −0.293225 | − | 0.403589i | 0.636833 | − | 0.771001i | \(-0.280244\pi\) |
−0.930058 | + | 0.367412i | \(0.880244\pi\) | |||||||
\(150\) | −16.2682 | − | 41.1784i | −0.108455 | − | 0.274523i | ||||
\(151\) | 1.92632 | − | 5.92859i | 0.0127571 | − | 0.0392622i | −0.944475 | − | 0.328582i | \(-0.893429\pi\) |
0.957232 | + | 0.289320i | \(0.0934292\pi\) | |||||||
\(152\) | −28.2682 | + | 38.9078i | −0.185975 | + | 0.255972i | ||||
\(153\) | −25.2635 | − | 202.407i | −0.165121 | − | 1.32292i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 65.2829i | − | 0.421180i | ||||||
\(156\) | 73.2087 | − | 115.169i | 0.469287 | − | 0.738261i | ||||
\(157\) | 30.5297 | − | 93.9607i | 0.194457 | − | 0.598476i | −0.805526 | − | 0.592561i | \(-0.798117\pi\) |
0.999983 | − | 0.00591538i | \(-0.00188293\pi\) | |||||||
\(158\) | −70.5883 | + | 22.9355i | −0.446761 | + | 0.145162i | ||||
\(159\) | −22.9266 | + | 18.9378i | −0.144192 | + | 0.119105i | ||||
\(160\) | −62.0525 | + | 45.0838i | −0.387828 | + | 0.281773i | ||||
\(161\) | −136.441 | + | 44.3322i | −0.847457 | + | 0.275355i | ||||
\(162\) | 64.0363 | + | 4.22047i | 0.395286 | + | 0.0260523i | ||||
\(163\) | −168.170 | − | 122.183i | −1.03172 | − | 0.749587i | −0.0630658 | − | 0.998009i | \(-0.520088\pi\) |
−0.968652 | + | 0.248423i | \(0.920088\pi\) | |||||||
\(164\) | 104.143i | 0.635016i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.0652 | 0.163044 | ||||||||
\(167\) | −37.1265 | + | 51.1002i | −0.222314 | + | 0.305989i | −0.905576 | − | 0.424184i | \(-0.860561\pi\) |
0.683262 | + | 0.730174i | \(0.260561\pi\) | |||||||
\(168\) | −20.7357 | + | 80.5111i | −0.123427 | + | 0.479233i | ||||
\(169\) | 4.00378 | + | 12.3224i | 0.0236910 | + | 0.0729134i | ||||
\(170\) | −26.6433 | − | 36.6713i | −0.156725 | − | 0.215714i | ||||
\(171\) | −54.0944 | + | 50.6466i | −0.316342 | + | 0.296179i | ||||
\(172\) | −36.9829 | − | 113.822i | −0.215017 | − | 0.661755i | ||||
\(173\) | 183.895 | + | 59.7512i | 1.06298 | + | 0.345383i | 0.787749 | − | 0.615996i | \(-0.211246\pi\) |
0.275229 | + | 0.961379i | \(0.411246\pi\) | |||||||
\(174\) | 68.4156 | − | 107.628i | 0.393193 | − | 0.618554i | ||||
\(175\) | 88.3804 | 0.505031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 184.216 | − | 11.4521i | 1.04077 | − | 0.0647011i | ||||
\(178\) | −91.9685 | − | 66.8190i | −0.516677 | − | 0.375388i | ||||
\(179\) | 29.4944 | + | 9.58330i | 0.164773 | + | 0.0535380i | 0.390242 | − | 0.920712i | \(-0.372391\pi\) |
−0.225469 | + | 0.974250i | \(0.572391\pi\) | |||||||
\(180\) | −69.3719 | + | 32.5177i | −0.385399 | + | 0.180654i | ||||
\(181\) | −82.6319 | + | 60.0356i | −0.456530 | + | 0.331688i | −0.792168 | − | 0.610303i | \(-0.791048\pi\) |
0.335639 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(182\) | −29.8045 | − | 41.0223i | −0.163761 | − | 0.225397i | ||||
\(183\) | 143.541 | − | 56.7083i | 0.784378 | − | 0.309881i | ||||
\(184\) | −54.5767 | + | 167.970i | −0.296613 | + | 0.912880i | ||||
\(185\) | 63.2174 | − | 87.0113i | 0.341716 | − | 0.470331i | ||||
\(186\) | −61.3505 | + | 3.81396i | −0.329842 | + | 0.0205052i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 105.508i | 0.561211i | ||||||||
\(189\) | −54.8026 | + | 115.789i | −0.289961 | + | 0.612640i | ||||
\(190\) | −5.08870 | + | 15.6614i | −0.0267826 | + | 0.0824284i | ||||
\(191\) | 66.0867 | − | 21.4729i | 0.346003 | − | 0.112423i | −0.130860 | − | 0.991401i | \(-0.541774\pi\) |
0.476863 | + | 0.878978i | \(0.341774\pi\) | |||||||
\(192\) | −21.7273 | − | 26.3037i | −0.113163 | − | 0.136998i | ||||
\(193\) | 219.652 | − | 159.587i | 1.13810 | − | 0.826875i | 0.151243 | − | 0.988497i | \(-0.451673\pi\) |
0.986853 | + | 0.161622i | \(0.0516725\pi\) | |||||||
\(194\) | 30.3554 | − | 9.86305i | 0.156471 | − | 0.0508405i | ||||
\(195\) | 25.4782 | − | 98.9250i | 0.130658 | − | 0.507308i | ||||
\(196\) | 72.2685 | + | 52.5061i | 0.368717 | + | 0.267888i | ||||
\(197\) | 106.612i | 0.541178i | 0.962695 | + | 0.270589i | \(0.0872185\pi\) | ||||
−0.962695 | + | 0.270589i | \(0.912782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −289.272 | −1.45363 | −0.726813 | − | 0.686835i | \(-0.758999\pi\) | ||||
−0.726813 | + | 0.686835i | \(0.758999\pi\) | |||||||
\(200\) | 63.9533 | − | 88.0241i | 0.319766 | − | 0.440121i | ||||
\(201\) | 99.7317 | + | 25.6860i | 0.496178 | + | 0.127791i | ||||
\(202\) | 22.7094 | + | 69.8923i | 0.112423 | + | 0.346002i | ||||
\(203\) | 149.635 | + | 205.955i | 0.737117 | + | 1.01455i | ||||
\(204\) | 176.779 | − | 146.023i | 0.866566 | − | 0.715799i | ||||
\(205\) | 24.0899 | + | 74.1410i | 0.117512 | + | 0.361664i | ||||
\(206\) | −14.7508 | − | 4.79283i | −0.0716058 | − | 0.0232661i | ||||
\(207\) | −131.457 | + | 238.278i | −0.635058 | + | 1.15110i | ||||
\(208\) | 119.533 | 0.574676 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.76631 | + | 28.4125i | 0.00841101 | + | 0.135298i | ||||
\(211\) | −151.458 | − | 110.040i | −0.717809 | − | 0.521519i | 0.167875 | − | 0.985808i | \(-0.446310\pi\) |
−0.885683 | + | 0.464290i | \(0.846310\pi\) | |||||||
\(212\) | −31.7907 | − | 10.3294i | −0.149956 | − | 0.0487237i | ||||
\(213\) | 15.9846 | + | 40.4606i | 0.0750452 | + | 0.189956i | ||||
\(214\) | −54.1162 | + | 39.3177i | −0.252879 | + | 0.183728i | ||||
\(215\) | −52.6576 | − | 72.4770i | −0.244919 | − | 0.337102i | ||||
\(216\) | 75.6663 | + | 138.368i | 0.350307 | + | 0.640594i | ||||
\(217\) | 37.9167 | − | 116.696i | 0.174731 | − | 0.537768i | ||||
\(218\) | −78.1076 | + | 107.506i | −0.358292 | + | 0.493146i | ||||
\(219\) | 16.4239 | + | 264.191i | 0.0749949 | + | 1.20635i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 305.719i | 1.38335i | ||||||||
\(222\) | −85.4633 | − | 54.3260i | −0.384970 | − | 0.244712i | ||||
\(223\) | −70.3727 | + | 216.585i | −0.315573 | + | 0.971233i | 0.659945 | + | 0.751314i | \(0.270579\pi\) |
−0.975518 | + | 0.219919i | \(0.929421\pi\) | |||||||
\(224\) | −137.106 | + | 44.5484i | −0.612080 | + | 0.198877i | ||||
\(225\) | 122.382 | − | 114.582i | 0.543920 | − | 0.509252i | ||||
\(226\) | −79.1650 | + | 57.5167i | −0.350288 | + | 0.254499i | ||||
\(227\) | 405.472 | − | 131.746i | 1.78622 | − | 0.580378i | 0.786895 | − | 0.617087i | \(-0.211688\pi\) |
0.999326 | + | 0.0367091i | \(0.0116875\pi\) | |||||||
\(228\) | −80.6665 | − | 20.7757i | −0.353800 | − | 0.0911215i | ||||
\(229\) | 82.1834 | + | 59.7097i | 0.358879 | + | 0.260741i | 0.752585 | − | 0.658496i | \(-0.228807\pi\) |
−0.393705 | + | 0.919237i | \(0.628807\pi\) | |||||||
\(230\) | 60.4743i | 0.262932i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 313.402 | 1.35087 | ||||||||
\(233\) | −101.807 | + | 140.126i | −0.436942 | + | 0.601399i | −0.969529 | − | 0.244976i | \(-0.921220\pi\) |
0.532587 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(234\) | −94.4547 | − | 18.1641i | −0.403652 | − | 0.0776244i | ||||
\(235\) | 24.4056 | + | 75.1128i | 0.103854 | + | 0.319629i | ||||
\(236\) | 121.951 | + | 167.851i | 0.516742 | + | 0.711235i | ||||
\(237\) | −178.979 | − | 216.677i | −0.755185 | − | 0.914248i | ||||
\(238\) | −26.3269 | − | 81.0260i | −0.110617 | − | 0.340445i | ||||
\(239\) | −153.403 | − | 49.8436i | −0.641852 | − | 0.208550i | −0.0300341 | − | 0.999549i | \(-0.509562\pi\) |
−0.611818 | + | 0.790998i | \(0.709562\pi\) | |||||||
\(240\) | −56.6340 | − | 36.0002i | −0.235975 | − | 0.150001i | ||||
\(241\) | 56.7011 | 0.235274 | 0.117637 | − | 0.993057i | \(-0.462468\pi\) | ||||
0.117637 | + | 0.993057i | \(0.462468\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 74.2296 | + | 231.385i | 0.305472 | + | 0.952201i | ||||
\(244\) | 140.356 | + | 101.974i | 0.575228 | + | 0.417928i | ||||
\(245\) | 63.5948 | + | 20.6632i | 0.259570 | + | 0.0843396i | ||||
\(246\) | 68.2677 | − | 26.9703i | 0.277511 | − | 0.109635i | ||||
\(247\) | 89.8537 | − | 65.2825i | 0.363780 | − | 0.264302i | ||||
\(248\) | −88.7882 | − | 122.206i | −0.358017 | − | 0.492768i | ||||
\(249\) | 37.6554 | + | 95.3141i | 0.151227 | + | 0.382788i | ||||
\(250\) | 26.9634 | − | 82.9849i | 0.107854 | − | 0.331939i | ||||
\(251\) | 39.6707 | − | 54.6021i | 0.158051 | − | 0.217538i | −0.722647 | − | 0.691218i | \(-0.757075\pi\) |
0.880697 | + | 0.473680i | \(0.157075\pi\) | |||||||
\(252\) | −142.891 | + | 17.8351i | −0.567029 | + | 0.0707741i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 102.084i | 0.401907i | ||||||||
\(255\) | 92.0750 | − | 144.848i | 0.361079 | − | 0.568033i | ||||
\(256\) | −17.9053 | + | 55.1069i | −0.0699427 | + | 0.215261i | ||||
\(257\) | −139.493 | + | 45.3242i | −0.542776 | + | 0.176359i | −0.567557 | − | 0.823334i | \(-0.692111\pi\) |
0.0247807 | + | 0.999693i | \(0.492111\pi\) | |||||||
\(258\) | −65.0349 | + | 53.7200i | −0.252073 | + | 0.208217i | ||||
\(259\) | 163.540 | − | 118.819i | 0.631429 | − | 0.458760i | ||||
\(260\) | 109.210 | − | 35.4844i | 0.420037 | − | 0.136478i | ||||
\(261\) | 474.214 | + | 91.1938i | 1.81691 | + | 0.349401i | ||||
\(262\) | −80.7609 | − | 58.6763i | −0.308248 | − | 0.223955i | ||||
\(263\) | 146.192i | 0.555863i | 0.960601 | + | 0.277932i | \(0.0896488\pi\) | ||||
−0.960601 | + | 0.277932i | \(0.910351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.0217 | −0.0944217 | ||||||||
\(266\) | −18.1925 | + | 25.0398i | −0.0683928 | + | 0.0941346i | ||||
\(267\) | 107.359 | − | 416.844i | 0.402092 | − | 1.56121i | ||||
\(268\) | 35.7738 | + | 110.100i | 0.133484 | + | 0.410822i | ||||
\(269\) | −33.5098 | − | 46.1222i | −0.124572 | − | 0.171458i | 0.742176 | − | 0.670205i | \(-0.233794\pi\) |
−0.866748 | + | 0.498747i | \(0.833794\pi\) | |||||||
\(270\) | 39.2816 | + | 37.0534i | 0.145487 | + | 0.137235i | ||||
\(271\) | −39.6717 | − | 122.097i | −0.146390 | − | 0.450542i | 0.850797 | − | 0.525494i | \(-0.176120\pi\) |
−0.997187 | + | 0.0749520i | \(0.976120\pi\) | |||||||
\(272\) | 191.007 | + | 62.0618i | 0.702230 | + | 0.228168i | ||||
\(273\) | 103.000 | − | 162.034i | 0.377288 | − | 0.593532i | ||||
\(274\) | −46.9944 | −0.171513 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −305.315 | + | 18.9804i | −1.10621 | + | 0.0687697i | ||||
\(277\) | 191.152 | + | 138.880i | 0.690080 | + | 0.501373i | 0.876687 | − | 0.481062i | \(-0.159749\pi\) |
−0.186606 | + | 0.982435i | \(0.559749\pi\) | |||||||
\(278\) | 98.6606 | + | 32.0568i | 0.354894 | + | 0.115312i | ||||
\(279\) | −98.7873 | − | 210.748i | −0.354076 | − | 0.755370i | ||||
\(280\) | −56.5960 | + | 41.1194i | −0.202129 | + | 0.146855i | ||||
\(281\) | −119.895 | − | 165.021i | −0.426672 | − | 0.587264i | 0.540513 | − | 0.841335i | \(-0.318230\pi\) |
−0.967185 | + | 0.254072i | \(0.918230\pi\) | |||||||
\(282\) | 69.1624 | − | 27.3238i | 0.245257 | − | 0.0968928i | ||||
\(283\) | −148.085 | + | 455.758i | −0.523267 | + | 1.61045i | 0.244450 | + | 0.969662i | \(0.421393\pi\) |
−0.767717 | + | 0.640789i | \(0.778607\pi\) | |||||||
\(284\) | −28.7440 | + | 39.5627i | −0.101211 | + | 0.139305i | ||||
\(285\) | −62.2337 | + | 3.86886i | −0.218364 | + | 0.0135750i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 146.521i | 0.510528i | ||||||||
\(288\) | −132.098 | + | 239.440i | −0.458674 | + | 0.831388i | ||||
\(289\) | −69.4247 | + | 213.667i | −0.240224 | + | 0.739333i | ||||
\(290\) | 102.060 | − | 33.1612i | 0.351930 | − | 0.114349i | ||||
\(291\) | 76.9670 | + | 93.1784i | 0.264491 | + | 0.320201i | ||||
\(292\) | −240.722 | + | 174.895i | −0.824391 | + | 0.598955i | ||||
\(293\) | 8.89881 | − | 2.89140i | 0.0303714 | − | 0.00986825i | −0.293792 | − | 0.955869i | \(-0.594917\pi\) |
0.324163 | + | 0.946001i | \(0.394917\pi\) | |||||||
\(294\) | 15.7032 | − | 60.9713i | 0.0534122 | − | 0.207385i | ||||
\(295\) | 125.646 | + | 91.2872i | 0.425919 | + | 0.309448i | ||||
\(296\) | − | 248.860i | − | 0.840743i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −58.8913 | −0.197622 | ||||||||
\(299\) | 239.742 | − | 329.976i | 0.801811 | − | 1.10360i | ||||
\(300\) | 182.498 | + | 47.0025i | 0.608327 | + | 0.156675i | ||||
\(301\) | −52.0324 | − | 160.139i | −0.172865 | − | 0.532024i | ||||
\(302\) | −2.90299 | − | 3.99563i | −0.00961257 | − | 0.0132306i | ||||
\(303\) | −214.541 | + | 177.214i | −0.708055 | + | 0.584866i | ||||
\(304\) | −22.5465 | − | 69.3910i | −0.0741662 | − | 0.228260i | ||||
\(305\) | 123.510 | + | 40.1308i | 0.404951 | + | 0.131577i | ||||
\(306\) | −141.502 | − | 78.0664i | −0.462426 | − | 0.255119i | ||||
\(307\) | −72.5271 | −0.236245 | −0.118122 | − | 0.992999i | \(-0.537687\pi\) | ||||
−0.118122 | + | 0.992999i | \(0.537687\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.64391 | − | 58.6152i | −0.0117926 | − | 0.189693i | ||||
\(310\) | −41.8446 | − | 30.4019i | −0.134983 | − | 0.0980707i | ||||
\(311\) | 362.016 | + | 117.626i | 1.16404 | + | 0.378219i | 0.826415 | − | 0.563062i | \(-0.190377\pi\) |
0.337624 | + | 0.941281i | \(0.390377\pi\) | |||||||
\(312\) | −86.8493 | − | 219.835i | −0.278363 | − | 0.704598i | ||||
\(313\) | −42.9593 | + | 31.2118i | −0.137250 | + | 0.0997181i | −0.654292 | − | 0.756242i | \(-0.727033\pi\) |
0.517042 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(314\) | −46.0088 | − | 63.3257i | −0.146525 | − | 0.201674i | ||||
\(315\) | −97.6013 | + | 45.7502i | −0.309845 | + | 0.145239i | ||||
\(316\) | 97.6225 | − | 300.451i | 0.308932 | − | 0.950795i | ||||
\(317\) | −43.0533 | + | 59.2578i | −0.135815 | + | 0.186933i | −0.871507 | − | 0.490383i | \(-0.836857\pi\) |
0.735692 | + | 0.677316i | \(0.236857\pi\) | |||||||
\(318\) | 1.46182 | + | 23.5145i | 0.00459692 | + | 0.0739451i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 28.7075i | − | 0.0897109i | ||||||
\(321\) | −213.754 | − | 135.876i | −0.665899 | − | 0.423289i | ||||
\(322\) | −35.1238 | + | 108.100i | −0.109080 | + | 0.335714i | ||||
\(323\) | 177.476 | − | 57.6655i | 0.549462 | − | 0.178531i | ||||
\(324\) | −174.742 | + | 209.950i | −0.539327 | + | 0.647992i | ||||
\(325\) | −203.283 | + | 147.694i | −0.625486 | + | 0.454442i | ||||
\(326\) | −156.632 | + | 50.8927i | −0.480465 | + | 0.156113i | ||||
\(327\) | −487.267 | − | 125.496i | −1.49011 | − | 0.383780i | ||||
\(328\) | 145.931 | + | 106.025i | 0.444911 | + | 0.323247i | ||||
\(329\) | 148.442i | 0.451191i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −167.351 | −0.505591 | −0.252795 | − | 0.967520i | \(-0.581350\pi\) | ||||
−0.252795 | + | 0.967520i | \(0.581350\pi\) | |||||||
\(332\) | −67.7130 | + | 93.1989i | −0.203955 | + | 0.280720i | ||||
\(333\) | 72.4133 | − | 376.554i | 0.217457 | − | 1.13079i | ||||
\(334\) | 15.4643 | + | 47.5942i | 0.0463003 | + | 0.142498i | ||||
\(335\) | 50.9360 | + | 70.1073i | 0.152048 | + | 0.209276i | ||||
\(336\) | −80.3262 | − | 97.2451i | −0.239066 | − | 0.289420i | ||||
\(337\) | −132.652 | − | 408.262i | −0.393627 | − | 1.21146i | −0.930026 | − | 0.367494i | \(-0.880216\pi\) |
0.536399 | − | 0.843965i | \(-0.319784\pi\) | |||||||
\(338\) | 9.76285 | + | 3.17214i | 0.0288842 | + | 0.00938504i | ||||
\(339\) | −312.694 | − | 198.769i | −0.922402 | − | 0.586339i | ||||
\(340\) | 192.935 | 0.567455 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.27163 | + | 58.2589i | 0.0212621 | + | 0.170348i | ||||
\(343\) | 289.760 | + | 210.523i | 0.844781 | + | 0.613769i | ||||
\(344\) | −197.145 | − | 64.0563i | −0.573096 | − | 0.186210i | ||||
\(345\) | −212.969 | + | 84.1368i | −0.617301 | + | 0.243875i | ||||
\(346\) | 123.938 | − | 90.0462i | 0.358202 | − | 0.260249i | ||||
\(347\) | 302.906 | + | 416.915i | 0.872929 | + | 1.20148i | 0.978329 | + | 0.207054i | \(0.0663876\pi\) |
−0.105400 | + | 0.994430i | \(0.533612\pi\) | |||||||
\(348\) | 199.452 | + | 504.858i | 0.573139 | + | 1.45074i | ||||
\(349\) | −86.5298 | + | 266.311i | −0.247936 | + | 0.763069i | 0.747203 | + | 0.664595i | \(0.231396\pi\) |
−0.995140 | + | 0.0984739i | \(0.968604\pi\) | |||||||
\(350\) | 41.1583 | − | 56.6495i | 0.117595 | − | 0.161856i | ||||
\(351\) | −67.4456 | − | 357.907i | −0.192153 | − | 1.01968i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 373.911i | − | 1.05924i | −0.848236 | − | 0.529619i | \(-0.822335\pi\) | ||
0.848236 | − | 0.529619i | \(-0.177665\pi\) | |||||||
\(354\) | 78.4479 | − | 123.411i | 0.221604 | − | 0.348618i | ||||
\(355\) | −11.3119 | + | 34.8143i | −0.0318644 | + | 0.0980686i | ||||
\(356\) | 460.181 | − | 149.522i | 1.29264 | − | 0.420006i | ||||
\(357\) | 248.716 | − | 205.444i | 0.696684 | − | 0.575474i | ||||
\(358\) | 19.8780 | − | 14.4422i | 0.0555252 | − | 0.0403414i | ||||
\(359\) | −103.534 | + | 33.6402i | −0.288395 | + | 0.0937052i | −0.449642 | − | 0.893209i | \(-0.648448\pi\) |
0.161247 | + | 0.986914i | \(0.448448\pi\) | |||||||
\(360\) | −25.0599 | + | 130.313i | −0.0696109 | + | 0.361982i | ||||
\(361\) | 237.209 | + | 172.342i | 0.657088 | + | 0.477403i | ||||
\(362\) | 80.9231i | 0.223544i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 215.826 | 0.592929 | ||||||||
\(365\) | −130.918 | + | 180.194i | −0.358680 | + | 0.493681i | ||||
\(366\) | 30.4978 | − | 118.415i | 0.0833274 | − | 0.323538i | ||||
\(367\) | 147.699 | + | 454.571i | 0.402450 | + | 1.23861i | 0.923006 | + | 0.384786i | \(0.125725\pi\) |
−0.520556 | + | 0.853828i | \(0.674275\pi\) | |||||||
\(368\) | −157.493 | − | 216.771i | −0.427971 | − | 0.589052i | ||||
\(369\) | 189.959 | + | 202.891i | 0.514795 | + | 0.549840i | ||||
\(370\) | −26.3319 | − | 81.0414i | −0.0711674 | − | 0.219031i | ||||
\(371\) | −44.7273 | − | 14.5328i | −0.120559 | − | 0.0391719i | ||||
\(372\) | 140.356 | − | 220.802i | 0.377301 | − | 0.593554i | ||||
\(373\) | 207.081 | 0.555178 | 0.277589 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277589 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 329.757 | − | 20.4999i | 0.879351 | − | 0.0546663i | ||||
\(376\) | 147.843 | + | 107.415i | 0.393201 | + | 0.285677i | ||||
\(377\) | −688.347 | − | 223.658i | −1.82585 | − | 0.593256i | ||||
\(378\) | 48.6964 | + | 89.0494i | 0.128827 | + | 0.235580i | ||||
\(379\) | −251.286 | + | 182.570i | −0.663022 | + | 0.481714i | −0.867682 | − | 0.497119i | \(-0.834391\pi\) |
0.204660 | + | 0.978833i | \(0.434391\pi\) | |||||||
\(380\) | −41.1988 | − | 56.7053i | −0.108418 | − | 0.149224i | ||||
\(381\) | −359.505 | + | 142.028i | −0.943582 | + | 0.372778i | ||||
\(382\) | 17.0127 | − | 52.3596i | 0.0445358 | − | 0.137067i | ||||
\(383\) | −211.526 | + | 291.140i | −0.552287 | + | 0.760158i | −0.990320 | − | 0.138801i | \(-0.955675\pi\) |
0.438033 | + | 0.898959i | \(0.355675\pi\) | |||||||
\(384\) | −390.891 | + | 24.3004i | −1.01795 | + | 0.0632823i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 215.110i | − | 0.557280i | ||||||
\(387\) | −279.665 | − | 154.290i | −0.722648 | − | 0.398682i | ||||
\(388\) | −41.9810 | + | 129.204i | −0.108198 | + | 0.333000i | ||||
\(389\) | −593.973 | + | 192.994i | −1.52692 | + | 0.496128i | −0.947733 | − | 0.319064i | \(-0.896631\pi\) |
−0.579191 | + | 0.815192i | \(0.696631\pi\) | |||||||
\(390\) | −51.5433 | − | 62.3997i | −0.132162 | − | 0.159999i | ||||
\(391\) | 554.418 | − | 402.809i | 1.41795 | − | 1.03020i | ||||
\(392\) | 147.149 | − | 47.8117i | 0.375381 | − | 0.121969i | ||||
\(393\) | 94.2755 | − | 366.046i | 0.239887 | − | 0.931416i | ||||
\(394\) | 68.3355 | + | 49.6487i | 0.173440 | + | 0.126012i | ||||
\(395\) | − | 236.478i | − | 0.598679i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −78.7284 | −0.198308 | −0.0991541 | − | 0.995072i | \(-0.531614\pi\) | ||||
−0.0991541 | + | 0.995072i | \(0.531614\pi\) | |||||||
\(398\) | −134.712 | + | 185.415i | −0.338473 | + | 0.465868i | ||||
\(399\) | −113.492 | − | 29.2300i | −0.284441 | − | 0.0732581i | ||||
\(400\) | 51.0088 | + | 156.989i | 0.127522 | + | 0.392472i | ||||
\(401\) | −464.411 | − | 639.207i | −1.15813 | − | 1.59403i | −0.717894 | − | 0.696153i | \(-0.754894\pi\) |
−0.440239 | − | 0.897881i | \(-0.645106\pi\) | |||||||
\(402\) | 62.9086 | − | 51.9636i | 0.156489 | − | 0.129263i | ||||
\(403\) | 107.800 | + | 331.774i | 0.267494 | + | 0.823260i | ||||
\(404\) | −297.489 | − | 96.6600i | −0.736359 | − | 0.239257i | ||||
\(405\) | −75.8372 | + | 189.887i | −0.187252 | + | 0.468858i | ||||
\(406\) | 201.696 | 0.496787 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −24.6414 | − | 396.376i | −0.0603955 | − | 0.971510i | ||||
\(409\) | −410.734 | − | 298.416i | −1.00424 | − | 0.729623i | −0.0412471 | − | 0.999149i | \(-0.513133\pi\) |
−0.962993 | + | 0.269526i | \(0.913133\pi\) | |||||||
\(410\) | 58.7410 | + | 19.0861i | 0.143271 | + | 0.0465515i | ||||
\(411\) | −65.3826 | − | 165.498i | −0.159082 | − | 0.402671i | ||||
\(412\) | 53.4082 | − | 38.8033i | 0.129632 | − | 0.0941829i | ||||
\(413\) | 171.577 | + | 236.155i | 0.415440 | + | 0.571804i | ||||
\(414\) | 91.5108 | + | 195.225i | 0.221041 | + | 0.471558i | ||||
\(415\) | −26.6477 | + | 82.0131i | −0.0642113 | + | 0.197622i | ||||
\(416\) | 240.911 | − | 331.585i | 0.579113 | − | 0.797080i | ||||
\(417\) | 24.3723 | + | 392.047i | 0.0584467 | + | 0.940162i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 334.392i | − | 0.798073i | −0.916935 | − | 0.399036i | \(-0.869345\pi\) | ||
0.916935 | − | 0.399036i | \(-0.130655\pi\) | |||||||
\(420\) | −102.257 | − | 65.0014i | −0.243470 | − | 0.154765i | ||||
\(421\) | −136.992 | + | 421.618i | −0.325396 | + | 1.00147i | 0.645865 | + | 0.763452i | \(0.276497\pi\) |
−0.971261 | + | 0.238016i | \(0.923503\pi\) | |||||||
\(422\) | −141.066 | + | 45.8351i | −0.334280 | + | 0.108614i | ||||
\(423\) | 192.449 | + | 205.550i | 0.454962 | + | 0.485935i | ||||
\(424\) | −46.8395 | + | 34.0309i | −0.110471 | + | 0.0802615i | ||||
\(425\) | −401.518 | + | 130.461i | −0.944749 | + | 0.306967i | ||||
\(426\) | 33.3781 | + | 8.59656i | 0.0783524 | + | 0.0201797i | ||||
\(427\) | 197.471 | + | 143.471i | 0.462460 | + | 0.335997i | ||||
\(428\) | − | 284.715i | − | 0.665222i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −70.9783 | −0.165066 | ||||||||
\(431\) | 467.467 | − | 643.414i | 1.08461 | − | 1.49284i | 0.230270 | − | 0.973127i | \(-0.426039\pi\) |
0.854341 | − | 0.519712i | \(-0.173961\pi\) | |||||||
\(432\) | −237.304 | − | 30.5175i | −0.549314 | − | 0.0706423i | ||||
\(433\) | −5.75456 | − | 17.7107i | −0.0132900 | − | 0.0409024i | 0.944192 | − | 0.329397i | \(-0.106845\pi\) |
−0.957482 | + | 0.288494i | \(0.906845\pi\) | |||||||
\(434\) | −57.1412 | − | 78.6481i | −0.131662 | − | 0.181217i | ||||
\(435\) | 258.776 | + | 313.281i | 0.594886 | + | 0.720186i | ||||
\(436\) | −174.783 | − | 537.926i | −0.400878 | − | 1.23377i | ||||
\(437\) | −236.778 | − | 76.9339i | −0.541826 | − | 0.176050i | ||||
\(438\) | 176.988 | + | 112.505i | 0.404082 | + | 0.256861i | ||||
\(439\) | 254.891 | 0.580618 | 0.290309 | − | 0.956933i | \(-0.406242\pi\) | ||||
0.290309 | + | 0.956933i | \(0.406242\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 236.567 | − | 29.5272i | 0.536432 | − | 0.0669551i | ||||
\(442\) | 195.958 | + | 142.372i | 0.443344 | + | 0.322108i | ||||
\(443\) | 58.5394 | + | 19.0206i | 0.132143 | + | 0.0429359i | 0.374342 | − | 0.927291i | \(-0.377869\pi\) |
−0.242199 | + | 0.970227i | \(0.577869\pi\) | |||||||
\(444\) | 400.887 | − | 158.377i | 0.902899 | − | 0.356705i | ||||
\(445\) | 293.025 | − | 212.895i | 0.658482 | − | 0.478415i | ||||
\(446\) | 106.053 | + | 145.970i | 0.237787 | + | 0.327286i | ||||
\(447\) | −81.9344 | − | 207.394i | −0.183298 | − | 0.463969i | ||||
\(448\) | 16.6735 | − | 51.3157i | 0.0372176 | − | 0.114544i | ||||
\(449\) | −80.7809 | + | 111.185i | −0.179913 | + | 0.247629i | −0.889443 | − | 0.457046i | \(-0.848907\pi\) |
0.709530 | + | 0.704675i | \(0.248907\pi\) | |||||||
\(450\) | −16.4512 | − | 131.804i | −0.0365582 | − | 0.292897i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 416.502i | − | 0.921464i | ||||||
\(453\) | 10.0323 | − | 15.7824i | 0.0221463 | − | 0.0348396i | ||||
\(454\) | 104.381 | − | 321.250i | 0.229913 | − | 0.707600i | ||||
\(455\) | 153.650 | − | 49.9240i | 0.337693 | − | 0.109723i | ||||
\(456\) | −111.237 | + | 91.8834i | −0.243940 | + | 0.201499i | ||||
\(457\) | −248.847 | + | 180.798i | −0.544524 | + | 0.395620i | −0.825762 | − | 0.564018i | \(-0.809255\pi\) |
0.281239 | + | 0.959638i | \(0.409255\pi\) | |||||||
\(458\) | 76.5447 | − | 24.8709i | 0.167128 | − | 0.0543032i | ||||
\(459\) | 78.0522 | − | 606.933i | 0.170048 | − | 1.32230i | ||||
\(460\) | −208.243 | − | 151.297i | −0.452702 | − | 0.328907i | ||||
\(461\) | − | 528.162i | − | 1.14569i | −0.819664 | − | 0.572844i | \(-0.805840\pi\) | ||
0.819664 | − | 0.572844i | \(-0.194160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −45.9484 | −0.0992406 | −0.0496203 | − | 0.998768i | \(-0.515801\pi\) | ||||
−0.0496203 | + | 0.998768i | \(0.515801\pi\) | |||||||
\(464\) | −279.472 | + | 384.661i | −0.602311 | + | 0.829010i | ||||
\(465\) | 48.8469 | − | 189.659i | 0.105047 | − | 0.407870i | ||||
\(466\) | 42.4058 | + | 130.512i | 0.0909996 | + | 0.280068i | ||||
\(467\) | 211.054 | + | 290.491i | 0.451936 | + | 0.622036i | 0.972812 | − | 0.231596i | \(-0.0743948\pi\) |
−0.520876 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(468\) | 298.859 | − | 279.810i | 0.638587 | − | 0.597885i | ||||
\(469\) | 50.3312 | + | 154.903i | 0.107316 | + | 0.330284i | ||||
\(470\) | 59.5109 | + | 19.3363i | 0.126619 | + | 0.0411410i | ||||
\(471\) | 158.999 | − | 250.131i | 0.337578 | − | 0.531063i | ||||
\(472\) | 359.359 | 0.761353 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −222.234 | + | 13.8155i | −0.468847 | + | 0.0291467i | ||||
\(475\) | 124.083 | + | 90.1515i | 0.261227 | + | 0.189793i | ||||
\(476\) | 344.878 | + | 112.058i | 0.724534 | + | 0.235415i | ||||
\(477\) | −80.7760 | + | 37.8634i | −0.169342 | + | 0.0793781i | ||||
\(478\) | −103.387 | + | 75.1152i | −0.216291 | + | 0.157145i | ||||
\(479\) | 339.387 | + | 467.127i | 0.708533 | + | 0.975213i | 0.999827 | + | 0.0185790i | \(0.00591421\pi\) |
−0.291294 | + | 0.956634i | \(0.594086\pi\) | |||||||
\(480\) | −214.008 | + | 84.5472i | −0.445849 | + | 0.176140i | ||||
\(481\) | −177.597 | + | 546.589i | −0.369225 | + | 1.13636i | ||||
\(482\) | 26.4054 | − | 36.3439i | 0.0547829 | − | 0.0754023i | ||||
\(483\) | −429.557 | + | 26.7041i | −0.889352 | + | 0.0552880i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 101.694i | 0.209678i | ||||||||
\(486\) | 182.880 | + | 60.1754i | 0.376296 | + | 0.123818i | ||||
\(487\) | −187.542 | + | 577.196i | −0.385097 | + | 1.18521i | 0.551313 | + | 0.834299i | \(0.314127\pi\) |
−0.936410 | + | 0.350908i | \(0.885873\pi\) | |||||||
\(488\) | 285.785 | − | 92.8571i | 0.585625 | − | 0.190281i | ||||
\(489\) | −397.145 | − | 480.795i | −0.812157 | − | 0.983220i | ||||
\(490\) | 42.8603 | − | 31.1398i | 0.0874700 | − | 0.0635507i | ||||
\(491\) | −731.236 | + | 237.593i | −1.48928 | + | 0.483896i | −0.936870 | − | 0.349677i | \(-0.886291\pi\) |
−0.552409 | + | 0.833573i | \(0.686291\pi\) | |||||||
\(492\) | −77.9231 | + | 302.555i | −0.158380 | + | 0.614948i | ||||
\(493\) | −983.817 | − | 714.785i | −1.99557 | − | 1.44987i | ||||
\(494\) | − | 87.9956i | − | 0.178129i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 229.168 | 0.462033 | ||||||||
\(497\) | −40.4408 | + | 55.6619i | −0.0813697 | + | 0.111996i | ||||
\(498\) | 78.6298 | + | 20.2512i | 0.157891 | + | 0.0406650i | ||||
\(499\) | −153.900 | − | 473.657i | −0.308418 | − | 0.949212i | −0.978380 | − | 0.206817i | \(-0.933690\pi\) |
0.669962 | − | 0.742395i | \(-0.266310\pi\) | |||||||
\(500\) | 218.299 | + | 300.463i | 0.436599 | + | 0.600927i | ||||
\(501\) | −146.095 | + | 120.677i | −0.291606 | + | 0.240872i | ||||
\(502\) | −16.5240 | − | 50.8558i | −0.0329164 | − | 0.101306i | ||||
\(503\) | −162.170 | − | 52.6924i | −0.322406 | − | 0.104756i | 0.143342 | − | 0.989673i | \(-0.454215\pi\) |
−0.465749 | + | 0.884917i | \(0.654215\pi\) | |||||||
\(504\) | −120.482 | + | 218.385i | −0.239052 | + | 0.433304i | ||||
\(505\) | −234.147 | −0.463657 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.41173 | + | 38.7946i | 0.00475687 | + | 0.0765180i | ||||
\(508\) | −351.527 | − | 255.399i | −0.691982 | − | 0.502754i | ||||
\(509\) | −392.594 | − | 127.561i | −0.771304 | − | 0.250612i | −0.103181 | − | 0.994663i | \(-0.532902\pi\) |
−0.668123 | + | 0.744051i | \(0.732902\pi\) | |||||||
\(510\) | −49.9651 | − | 126.473i | −0.0979708 | − | 0.247986i | ||||
\(511\) | −338.679 | + | 246.065i | −0.662777 | + | 0.481536i | ||||
\(512\) | −279.955 | − | 385.324i | −0.546786 | − | 0.752587i | ||||
\(513\) | −195.050 | + | 106.663i | −0.380215 | + | 0.207920i | ||||
\(514\) | −35.9097 | + | 110.519i | −0.0698633 | + | 0.215017i | ||||
\(515\) | 29.0464 | − | 39.9790i | 0.0564008 | − | 0.0776291i | ||||
\(516\) | −22.2772 | − | 358.346i | −0.0431728 | − | 0.694469i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 160.158i | − | 0.309186i | ||||||
\(519\) | 489.543 | + | 311.185i | 0.943243 | + | 0.599587i | ||||
\(520\) | 61.4608 | − | 189.157i | 0.118194 | − | 0.363763i | ||||
\(521\) | 105.824 | − | 34.3843i | 0.203117 | − | 0.0659968i | −0.205691 | − | 0.978617i | \(-0.565944\pi\) |
0.408809 | + | 0.912620i | \(0.365944\pi\) | |||||||
\(522\) | 279.292 | − | 261.490i | 0.535042 | − | 0.500939i | ||||
\(523\) | −247.432 | + | 179.770i | −0.473100 | + | 0.343728i | −0.798648 | − | 0.601798i | \(-0.794451\pi\) |
0.325548 | + | 0.945526i | \(0.394451\pi\) | |||||||
\(524\) | 404.102 | − | 131.301i | 0.771188 | − | 0.250574i | ||||
\(525\) | 256.762 | + | 66.1292i | 0.489071 | + | 0.125960i | ||||
\(526\) | 93.7052 | + | 68.0808i | 0.178147 | + | 0.129431i | ||||
\(527\) | 586.126i | 1.11219i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −385.285 | −0.728328 | ||||||||
\(530\) | −11.6525 | + | 16.0383i | −0.0219858 | + | 0.0302609i | ||||
\(531\) | 543.752 | + | 104.566i | 1.02401 | + | 0.196923i | ||||
\(532\) | −40.7096 | − | 125.291i | −0.0765218 | − | 0.235510i | ||||
\(533\) | −244.854 | − | 337.013i | −0.459389 | − | 0.632294i | ||||
\(534\) | −217.190 | − | 262.936i | −0.406723 | − | 0.492390i | ||||
\(535\) | −65.8592 | − | 202.694i | −0.123101 | − | 0.378867i | ||||
\(536\) | 190.699 | + | 61.9620i | 0.355782 | + | 0.115601i | ||||
\(537\) | 78.5162 | + | 49.9100i | 0.146213 | + | 0.0929423i | ||||
\(538\) | −45.1684 | −0.0839562 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −225.870 | + | 42.5639i | −0.418277 | + | 0.0788220i | ||||
\(541\) | 252.246 | + | 183.268i | 0.466259 | + | 0.338757i | 0.795982 | − | 0.605321i | \(-0.206955\pi\) |
−0.329722 | + | 0.944078i | \(0.606955\pi\) | |||||||
\(542\) | −96.7359 | − | 31.4314i | −0.178479 | − | 0.0579915i | ||||
\(543\) | −284.982 | + | 112.587i | −0.524829 | + | 0.207342i | ||||
\(544\) | 557.123 | − | 404.773i | 1.02412 | − | 0.744068i | ||||
\(545\) | −248.862 | − | 342.529i | −0.456627 | − | 0.628493i | ||||
\(546\) | −55.8934 | − | 141.478i | −0.102369 | − | 0.259118i | ||||
\(547\) | 272.857 | − | 839.767i | 0.498824 | − | 1.53522i | −0.312087 | − | 0.950054i | \(-0.601028\pi\) |
0.810911 | − | 0.585170i | \(-0.198972\pi\) | |||||||
\(548\) | 117.573 | − | 161.825i | 0.214549 | − | 0.295301i | ||||
\(549\) | 459.446 | − | 57.3460i | 0.836877 | − | 0.104455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 441.786i | 0.801789i | ||||||||
\(552\) | −284.237 | + | 447.149i | −0.514922 | + | 0.810052i | ||||
\(553\) | 137.348 | − | 422.714i | 0.248369 | − | 0.764401i | ||||
\(554\) | 178.037 | − | 57.8478i | 0.321367 | − | 0.104418i | ||||
\(555\) | 248.764 | − | 205.483i | 0.448223 | − | 0.370240i | ||||
\(556\) | −357.220 | + | 259.536i | −0.642483 | + | 0.466791i | ||||
\(557\) | 308.044 | − | 100.090i | 0.553041 | − | 0.179694i | −0.0191464 | − | 0.999817i | \(-0.506095\pi\) |
0.572188 | + | 0.820123i | \(0.306095\pi\) | |||||||
\(558\) | −181.089 | − | 34.8243i | −0.324532 | − | 0.0624091i | ||||
\(559\) | 387.290 | + | 281.383i | 0.692827 | + | 0.503368i | ||||
\(560\) | − | 106.132i | − | 0.189521i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −161.609 | −0.287560 | ||||||||
\(563\) | 291.084 | − | 400.643i | 0.517024 | − | 0.711622i | −0.468060 | − | 0.883697i | \(-0.655047\pi\) |
0.985084 | + | 0.172074i | \(0.0550470\pi\) | |||||||
\(564\) | −78.9444 | + | 306.520i | −0.139972 | + | 0.543475i | ||||
\(565\) | −96.3436 | − | 296.515i | −0.170520 | − | 0.524805i | ||||
\(566\) | 223.166 | + | 307.162i | 0.394287 | + | 0.542689i | ||||
\(567\) | −245.850 | + | 295.384i | −0.433597 | + | 0.520960i | ||||
\(568\) | 26.1741 | + | 80.5555i | 0.0460811 | + | 0.141823i | ||||
\(569\) | 517.800 | + | 168.244i | 0.910018 | + | 0.295683i | 0.726366 | − | 0.687308i | \(-0.241208\pi\) |
0.183652 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(570\) | −26.5021 | + | 41.6919i | −0.0464948 | + | 0.0731436i | ||||
\(571\) | −779.886 | −1.36582 | −0.682912 | − | 0.730500i | \(-0.739287\pi\) | ||||
−0.682912 | + | 0.730500i | \(0.739287\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 208.061 | − | 12.9345i | 0.363109 | − | 0.0225732i | ||||
\(574\) | 93.9164 | + | 68.2342i | 0.163617 | + | 0.118875i | ||||
\(575\) | 535.682 | + | 174.054i | 0.931620 | + | 0.302702i | ||||
\(576\) | −43.4407 | − | 92.6744i | −0.0754179 | − | 0.160893i | ||||
\(577\) | −918.474 | + | 667.310i | −1.59181 | + | 1.15652i | −0.690507 | + | 0.723326i | \(0.742612\pi\) |
−0.901302 | + | 0.433191i | \(0.857388\pi\) | |||||||
\(578\) | 104.624 | + | 144.003i | 0.181011 | + | 0.249140i | ||||
\(579\) | 757.541 | − | 299.279i | 1.30836 | − | 0.516889i | ||||
\(580\) | −141.147 | + | 434.405i | −0.243357 | + | 0.748975i | ||||
\(581\) | −95.2674 | + | 131.124i | −0.163971 | + | 0.225687i | ||||
\(582\) | 95.5680 | − | 5.94115i | 0.164206 | − | 0.0102082i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 515.370i | 0.882482i | ||||||||
\(585\) | 148.038 | − | 268.333i | 0.253057 | − | 0.458688i | ||||
\(586\) | 2.29082 | − | 7.05041i | 0.00390924 | − | 0.0120314i | ||||
\(587\) | −596.792 | + | 193.909i | −1.01668 | + | 0.330340i | −0.769512 | − | 0.638633i | \(-0.779500\pi\) |
−0.247169 | + | 0.968972i | \(0.579500\pi\) | |||||||
\(588\) | 170.667 | + | 206.614i | 0.290250 | + | 0.351385i | ||||
\(589\) | 172.268 | − | 125.160i | 0.292475 | − | 0.212496i | ||||
\(590\) | 117.025 | − | 38.0238i | 0.198348 | − | 0.0644472i | ||||
\(591\) | −79.7708 | + | 309.729i | −0.134976 | + | 0.524076i | ||||
\(592\) | 305.443 | + | 221.918i | 0.515952 | + | 0.374861i | ||||
\(593\) | 961.677i | 1.62171i | 0.585244 | + | 0.810857i | \(0.300999\pi\) | ||||
−0.585244 | + | 0.810857i | \(0.699001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 271.446 | 0.456211 | ||||||||
\(596\) | 147.337 | − | 202.791i | 0.247209 | − | 0.340254i | ||||
\(597\) | −840.390 | − | 216.443i | −1.40769 | − | 0.362551i | ||||
\(598\) | −99.8595 | − | 307.336i | −0.166989 | − | 0.513940i | ||||
\(599\) | 577.456 | + | 794.800i | 0.964034 | + | 1.32688i | 0.945004 | + | 0.327060i | \(0.106058\pi\) |
0.0190299 | + | 0.999819i | \(0.493942\pi\) | |||||||
\(600\) | 251.659 | − | 207.875i | 0.419432 | − | 0.346458i | ||||
\(601\) | 99.2684 | + | 305.517i | 0.165172 | + | 0.508347i | 0.999049 | − | 0.0436032i | \(-0.0138837\pi\) |
−0.833877 | + | 0.551950i | \(0.813884\pi\) | |||||||
\(602\) | −126.876 | − | 41.2246i | −0.210758 | − | 0.0684794i | ||||
\(603\) | 270.521 | + | 149.245i | 0.448625 | + | 0.247505i | ||||
\(604\) | 21.0217 | 0.0348042 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.6793 | + | 220.043i | 0.0225731 | + | 0.363107i | ||||
\(607\) | −405.771 | − | 294.810i | −0.668485 | − | 0.485683i | 0.201033 | − | 0.979585i | \(-0.435570\pi\) |
−0.869518 | + | 0.493902i | \(0.835570\pi\) | |||||||
\(608\) | −237.933 | − | 77.3091i | −0.391337 | − | 0.127153i | ||||
\(609\) | 280.615 | + | 710.299i | 0.460781 | + | 1.16634i | ||||
\(610\) | 83.2408 | − | 60.4780i | 0.136460 | − | 0.0991442i | ||||
\(611\) | −248.063 | − | 341.430i | −0.405996 | − | 0.558805i | ||||
\(612\) | 622.838 | − | 291.952i | 1.01771 | − | 0.477046i | ||||
\(613\) | 114.259 | − | 351.653i | 0.186393 | − | 0.573659i | −0.813576 | − | 0.581458i | \(-0.802482\pi\) |
0.999970 | + | 0.00779866i | \(0.00248241\pi\) | |||||||
\(614\) | −33.7755 | + | 46.4879i | −0.0550089 | + | 0.0757133i | ||||
\(615\) | 14.5109 | + | 233.419i | 0.0235949 | + | 0.379543i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 560.582i | 0.908560i | 0.890859 | + | 0.454280i | \(0.150103\pi\) | ||||
−0.890859 | + | 0.454280i | \(0.849897\pi\) | |||||||
\(618\) | −39.2678 | − | 24.9611i | −0.0635401 | − | 0.0403902i | ||||
\(619\) | 127.751 | − | 393.176i | 0.206383 | − | 0.635180i | −0.793271 | − | 0.608868i | \(-0.791624\pi\) |
0.999654 | − | 0.0263117i | \(-0.00837625\pi\) | |||||||
\(620\) | 209.377 | − | 68.0308i | 0.337705 | − | 0.109727i | ||||
\(621\) | −560.195 | + | 593.882i | −0.902086 | + | 0.956331i | ||||
\(622\) | 243.984 | − | 177.265i | 0.392258 | − | 0.284992i | ||||
\(623\) | 647.443 | − | 210.367i | 1.03923 | − | 0.337668i | ||||
\(624\) | 347.265 | + | 89.4384i | 0.556515 | + | 0.143331i | ||||
\(625\) | −151.840 | − | 110.318i | −0.242944 | − | 0.176509i | ||||
\(626\) | 42.0710i | 0.0672060i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 333.168 | 0.530523 | ||||||||
\(629\) | −567.582 | + | 781.209i | −0.902356 | + | 1.24199i | ||||
\(630\) | −16.1278 | + | 83.8655i | −0.0255996 | + | 0.133120i | ||||
\(631\) | 338.529 | + | 1041.88i | 0.536496 | + | 1.65116i | 0.740395 | + | 0.672172i | \(0.234639\pi\) |
−0.203899 | + | 0.978992i | \(0.565361\pi\) | |||||||
\(632\) | −321.623 | − | 442.676i | −0.508897 | − | 0.700436i | ||||
\(633\) | −357.678 | − | 433.014i | −0.565052 | − | 0.684067i | ||||
\(634\) | 17.9330 | + | 55.1921i | 0.0282855 | + | 0.0870538i | ||||
\(635\) | −309.336 | − | 100.509i | −0.487144 | − | 0.158283i | ||||
\(636\) | −84.6293 | − | 53.7959i | −0.133065 | − | 0.0845847i | ||||
\(637\) | −357.315 | −0.560934 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.1644 | + | 129.506i | 0.0252964 | + | 0.202670i | ||||
\(640\) | −266.611 | − | 193.704i | −0.416579 | − | 0.302662i | ||||
\(641\) | 939.589 | + | 305.291i | 1.46582 | + | 0.476273i | 0.929841 | − | 0.367961i | \(-0.119944\pi\) |
0.535975 | + | 0.844234i | \(0.319944\pi\) | |||||||
\(642\) | −186.637 | + | 73.7339i | −0.290711 | + | 0.114850i | ||||
\(643\) | 829.799 | − | 602.884i | 1.29051 | − | 0.937611i | 0.290695 | − | 0.956816i | \(-0.406113\pi\) |
0.999816 | + | 0.0192046i | \(0.00611338\pi\) | |||||||
\(644\) | −284.367 | − | 391.398i | −0.441564 | − | 0.607761i | ||||
\(645\) | −98.7508 | − | 249.960i | −0.153102 | − | 0.387535i | ||||
\(646\) | 45.6876 | − | 140.612i | 0.0707239 | − | 0.217666i | ||||
\(647\) | −282.730 | + | 389.145i | −0.436987 | + | 0.601460i | −0.969539 | − | 0.244936i | \(-0.921233\pi\) |
0.532553 | + | 0.846397i | \(0.321233\pi\) | |||||||
\(648\) | 116.293 | + | 458.603i | 0.179465 | + | 0.707720i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 199.079i | 0.306276i | ||||||||
\(651\) | 197.471 | − | 310.653i | 0.303335 | − | 0.477193i | ||||
\(652\) | 216.619 | − | 666.685i | 0.332238 | − | 1.02252i | ||||
\(653\) | −738.203 | + | 239.857i | −1.13048 | + | 0.367315i | −0.813758 | − | 0.581204i | \(-0.802582\pi\) |
−0.316721 | + | 0.948519i | \(0.602582\pi\) | |||||||
\(654\) | −307.357 | + | 253.883i | −0.469965 | + | 0.388200i | ||||
\(655\) | 257.316 | − | 186.951i | 0.392848 | − | 0.285421i | ||||
\(656\) | −260.264 | + | 84.5649i | −0.396744 | + | 0.128910i | ||||
\(657\) | −149.962 | + | 779.815i | −0.228253 | + | 1.18693i | ||||
\(658\) | 95.1473 | + | 69.1285i | 0.144601 | + | 0.105059i | ||||
\(659\) | 52.5987i | 0.0798160i | 0.999203 | + | 0.0399080i | \(0.0127065\pi\) | ||||
−0.999203 | + | 0.0399080i | \(0.987294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −233.530 | −0.353297 | −0.176649 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176649 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(662\) | −77.9342 | + | 107.267i | −0.117725 | + | 0.162035i | ||||
\(663\) | −228.750 | + | 888.174i | −0.345022 | + | 1.33963i | ||||
\(664\) | 61.6590 | + | 189.767i | 0.0928599 | + | 0.285793i | ||||
\(665\) | −57.9638 | − | 79.7803i | −0.0871636 | − | 0.119970i | ||||
\(666\) | −207.639 | − | 221.774i | −0.311770 | − | 0.332994i | ||||
\(667\) | 501.350 | + | 1543.00i | 0.751649 | + | 2.31334i | ||||
\(668\) | −202.579 | − | 65.8220i | −0.303263 | − | 0.0985360i | ||||
\(669\) | −366.503 | + | 576.566i | −0.547837 | + | 0.861832i | ||||
\(670\) | 68.6576 | 0.102474 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −431.652 | + | 26.8344i | −0.642339 | + | 0.0399321i | ||||
\(673\) | 191.341 | + | 139.018i | 0.284311 | + | 0.206564i | 0.720796 | − | 0.693148i | \(-0.243777\pi\) |
−0.436485 | + | 0.899712i | \(0.643777\pi\) | |||||||
\(674\) | −323.460 | − | 105.099i | −0.479911 | − | 0.155933i | ||||
\(675\) | 441.278 | − | 241.311i | 0.653745 | − | 0.357498i | ||||
\(676\) | −35.3484 | + | 25.6821i | −0.0522905 | + | 0.0379912i | ||||
\(677\) | −173.786 | − | 239.196i | −0.256701 | − | 0.353318i | 0.661143 | − | 0.750260i | \(-0.270072\pi\) |
−0.917844 | + | 0.396942i | \(0.870072\pi\) | |||||||
\(678\) | −273.026 | + | 107.863i | −0.402693 | + | 0.159090i | ||||
\(679\) | −59.0643 | + | 181.781i | −0.0869872 | + | 0.267719i | ||||
\(680\) | 196.422 | − | 270.351i | 0.288856 | − | 0.397576i | ||||
\(681\) | 1276.55 | − | 79.3589i | 1.87452 | − | 0.116533i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 905.661i | 1.32600i | 0.748617 | + | 0.663002i | \(0.230718\pi\) | ||||
−0.748617 | + | 0.663002i | \(0.769282\pi\) | |||||||
\(684\) | −218.807 | − | 120.715i | −0.319893 | − | 0.176484i | ||||
\(685\) | 46.2694 | − | 142.403i | 0.0675466 | − | 0.207887i | ||||
\(686\) | 269.879 | − | 87.6891i | 0.393410 | − | 0.127827i | ||||
\(687\) | 194.082 | + | 234.961i | 0.282506 | + | 0.342010i | ||||
\(688\) | 254.423 | − | 184.849i | 0.369800 | − | 0.268676i | ||||
\(689\) | 127.163 | − | 41.3177i | 0.184561 | − | 0.0599677i | ||||
\(690\) | −45.2490 | + | 175.690i | −0.0655782 | + | 0.254622i | ||||
\(691\) | 284.794 | + | 206.915i | 0.412147 | + | 0.299442i | 0.774470 | − | 0.632610i | \(-0.218016\pi\) |
−0.362323 | + | 0.932052i | \(0.618016\pi\) | |||||||
\(692\) | 652.061i | 0.942284i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 408.293 | 0.588319 | ||||||||
\(695\) | −194.277 | + | 267.399i | −0.279535 | + | 0.384747i | ||||
\(696\) | 910.494 | + | 234.498i | 1.30818 | + | 0.336923i | ||||
\(697\) | −216.285 | − | 665.657i | −0.310308 | − | 0.955031i | ||||
\(698\) | 130.402 | + | 179.483i | 0.186822 | + | 0.257139i | ||||
\(699\) | −400.617 | + | 330.917i | −0.573129 | + | 0.473415i | ||||
\(700\) | 92.1005 | + | 283.456i | 0.131572 | + | 0.404937i | ||||
\(701\) | 1189.16 | + | 386.381i | 1.69637 | + | 0.551186i | 0.987973 | − | 0.154624i | \(-0.0494166\pi\) |
0.708401 | + | 0.705810i | \(0.249417\pi\) | |||||||
\(702\) | −260.818 | − | 123.444i | −0.371536 | − | 0.175847i | ||||
\(703\) | 350.804 | 0.499010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7011 | + | 236.478i | 0.0208526 | + | 0.335430i | ||||
\(706\) | −239.667 | − | 174.128i | −0.339472 | − | 0.246641i | ||||
\(707\) | −418.546 | − | 135.994i | −0.592003 | − | 0.192353i | ||||
\(708\) | 228.700 | + | 578.889i | 0.323022 | + | 0.817640i | ||||
\(709\) | 109.162 | − | 79.3109i | 0.153966 | − | 0.111863i | −0.508135 | − | 0.861277i | \(-0.669665\pi\) |
0.662101 | + | 0.749414i | \(0.269665\pi\) | |||||||
\(710\) | 17.0472 | + | 23.4635i | 0.0240101 | + | 0.0330471i | ||||
\(711\) | −357.843 | − | 763.406i | −0.503296 | − | 1.07371i | ||||
\(712\) | 258.980 | − | 797.058i | 0.363736 | − | 1.11946i | ||||
\(713\) | 459.634 | − | 632.631i | 0.644647 | − | 0.887281i | ||||
\(714\) | −15.8584 | − | 255.095i | −0.0222106 | − | 0.357276i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 104.582i | 0.146064i | ||||||||
\(717\) | −408.370 | − | 259.586i | −0.569553 | − | 0.362045i | ||||
\(718\) | −26.6527 | + | 82.0285i | −0.0371207 | + | 0.114246i | ||||
\(719\) | 106.782 | − | 34.6957i | 0.148515 | − | 0.0482554i | −0.233816 | − | 0.972281i | \(-0.575121\pi\) |
0.382331 | + | 0.924025i | \(0.375121\pi\) | |||||||
\(720\) | −137.596 | − | 146.963i | −0.191106 | − | 0.204115i | ||||
\(721\) | 75.1416 | − | 54.5936i | 0.104219 | − | 0.0757192i | ||||
\(722\) | 220.934 | − | 71.7858i | 0.306003 | − | 0.0994263i | ||||
\(723\) | 164.728 | + | 42.4257i | 0.227839 | + | 0.0586801i | ||||
\(724\) | −278.658 | − | 202.457i | −0.384887 | − | 0.279636i | ||||
\(725\) | − | 999.487i | − | 1.37860i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 160.372 | 0.220595 | 0.110297 | − | 0.993899i | \(-0.464820\pi\) | ||||
0.110297 | + | 0.993899i | \(0.464820\pi\) | |||||||
\(728\) | 219.727 | − | 302.428i | 0.301823 | − | 0.415423i | ||||
\(729\) | 42.5213 | + | 727.759i | 0.0583282 | + | 0.998297i | ||||
\(730\) | 54.5314 | + | 167.830i | 0.0747006 | + | 0.229905i | ||||
\(731\) | 472.774 | + | 650.717i | 0.646749 | + | 0.890174i | ||||
\(732\) | 331.459 | + | 401.274i | 0.452814 | + | 0.548189i | ||||
\(733\) | −151.721 | − | 466.948i | −0.206986 | − | 0.637037i | −0.999626 | − | 0.0273472i | \(-0.991294\pi\) |
0.792640 | − | 0.609690i | \(-0.208706\pi\) | |||||||
\(734\) | 360.151 | + | 117.020i | 0.490669 | + | 0.159428i | ||||
\(735\) | 169.294 | + | 107.614i | 0.230332 | + | 0.146414i | ||||
\(736\) | −918.745 | −1.24829 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 218.511 | − | 27.2736i | 0.296085 | − | 0.0369561i | ||||
\(739\) | −192.027 | − | 139.516i | −0.259847 | − | 0.188790i | 0.450232 | − | 0.892911i | \(-0.351341\pi\) |
−0.710080 | + | 0.704121i | \(0.751341\pi\) | |||||||
\(740\) | 344.944 | + | 112.079i | 0.466140 | + | 0.151458i | ||||
\(741\) | 309.889 | − | 122.427i | 0.418204 | − | 0.165218i | ||||
\(742\) | −30.1444 | + | 21.9012i | −0.0406259 | + | 0.0295164i | ||||
\(743\) | −144.127 | − | 198.374i | −0.193980 | − | 0.266991i | 0.700937 | − | 0.713223i | \(-0.252765\pi\) |
−0.894917 | + | 0.446232i | \(0.852765\pi\) | |||||||
\(744\) | −166.508 | − | 421.468i | −0.223801 | − | 0.566489i | ||||
\(745\) | 57.9827 | − | 178.452i | 0.0778291 | − | 0.239533i | ||||
\(746\) | 96.4367 | − | 132.734i | 0.129272 | − | 0.177927i | ||||
\(747\) | 38.0789 | + | 305.081i | 0.0509758 | + | 0.408408i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 400.574i | − | 0.534812i | ||||||
\(750\) | 140.426 | − | 220.912i | 0.187235 | − | 0.294549i | ||||
\(751\) | 228.868 | − | 704.384i | 0.304751 | − | 0.937928i | −0.675019 | − | 0.737801i | \(-0.735864\pi\) |
0.979770 | − | 0.200127i | \(-0.0641356\pi\) | |||||||
\(752\) | −263.675 | + | 85.6732i | −0.350632 | + | 0.113927i | ||||
\(753\) | 156.106 | − | 128.947i | 0.207312 | − | 0.171244i | ||||
\(754\) | −463.918 | + | 337.056i | −0.615276 | + | 0.447024i | ||||
\(755\) | 14.9658 | − | 4.86267i | 0.0198222 | − | 0.00644062i | ||||
\(756\) | −428.471 | − | 55.1018i | −0.566761 | − | 0.0728860i | ||||
\(757\) | −262.702 | − | 190.864i | −0.347030 | − | 0.252132i | 0.400592 | − | 0.916257i | \(-0.368805\pi\) |
−0.747622 | + | 0.664124i | \(0.768805\pi\) | |||||||
\(758\) | 246.089i | 0.324656i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −121.402 | −0.159740 | ||||||||
\(761\) | 398.255 | − | 548.151i | 0.523331 | − | 0.720303i | −0.462765 | − | 0.886481i | \(-0.653143\pi\) |
0.986096 | + | 0.166178i | \(0.0531426\pi\) | |||||||
\(762\) | −76.3831 | + | 296.575i | −0.100240 | + | 0.389206i | ||||
\(763\) | −245.907 | − | 756.824i | −0.322289 | − | 0.991905i | ||||
\(764\) | 137.737 | + | 189.578i | 0.180284 | + | 0.248139i | ||||
\(765\) | 375.876 | − | 351.919i | 0.491341 | − | 0.460024i | ||||
\(766\) | 88.1069 | + | 271.165i | 0.115022 | + | 0.354001i | ||||
\(767\) | −789.285 | − | 256.454i | −1.02905 | − | 0.334360i | ||||
\(768\) | −93.2513 | + | 146.699i | −0.121421 | + | 0.191014i | ||||
\(769\) | −632.440 | −0.822419 | −0.411209 | − | 0.911541i | \(-0.634894\pi\) | ||||
−0.411209 | + | 0.911541i | \(0.634894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −439.168 | + | 27.3016i | −0.569609 | + | 0.0354107i | ||||
\(772\) | 740.730 | + | 538.172i | 0.959494 | + | 0.697114i | ||||
\(773\) | 176.035 | + | 57.1971i | 0.227729 | + | 0.0739937i | 0.420659 | − | 0.907219i | \(-0.361799\pi\) |
−0.192930 | + | 0.981213i | \(0.561799\pi\) | |||||||
\(774\) | −229.134 | + | 107.406i | −0.296039 | + | 0.138767i | ||||
\(775\) | −389.735 | + | 283.159i | −0.502884 | + | 0.365367i | ||||
\(776\) | 138.309 | + | 190.366i | 0.178233 | + | 0.245317i | ||||
\(777\) | 564.020 | − | 222.825i | 0.725894 | − | 0.286776i | ||||
\(778\) | −152.906 | + | 470.597i | −0.196538 | + | 0.604881i | ||||
\(779\) | −149.458 | + | 205.711i | −0.191858 | + | 0.264070i | ||||
\(780\) | 343.826 | − | 21.3745i | 0.440803 | − | 0.0274032i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 542.953i | − | 0.694314i | ||||||
\(783\) | 1309.45 | + | 619.759i | 1.67235 | + | 0.791518i | ||||
\(784\) | −72.5358 | + | 223.242i | −0.0925202 | + | 0.284748i | ||||
\(785\) | 237.189 | − | 77.0673i | 0.302151 | − | 0.0981748i | ||||
\(786\) | −190.722 | − | 230.894i | −0.242649 | − | 0.293758i | ||||
\(787\) | 752.162 | − | 546.477i | 0.955733 | − | 0.694380i | 0.00357686 | − | 0.999994i | \(-0.498861\pi\) |
0.952156 | + | 0.305613i | \(0.0988614\pi\) | |||||||
\(788\) | −341.930 | + | 111.100i | −0.433921 | + | 0.140989i | ||||
\(789\) | −109.386 | + | 424.716i | −0.138639 | + | 0.538296i | ||||
\(790\) | −151.576 | − | 110.127i | −0.191869 | − | 0.139401i | ||||
\(791\) | − | 585.989i | − | 0.740820i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −693.957 | −0.875103 | ||||||||
\(794\) | −36.6634 | + | 50.4628i | −0.0461755 | + | 0.0635552i | ||||
\(795\) | −72.6930 | − | 18.7221i | −0.0914377 | − | 0.0235499i | ||||
\(796\) | −301.448 | − | 927.761i | −0.378703 | − | 1.16553i | ||||
\(797\) | −530.616 | − | 730.331i | −0.665767 | − | 0.916350i | 0.333888 | − | 0.942613i | \(-0.391639\pi\) |
−0.999655 | + | 0.0262628i | \(0.991639\pi\) | |||||||
\(798\) | −71.5883 | + | 59.1332i | −0.0897096 | + | 0.0741017i | ||||
\(799\) | −219.120 | − | 674.381i | −0.274243 | − | 0.844032i | ||||
\(800\) | 538.294 | + | 174.902i | 0.672868 | + | 0.218628i | ||||
\(801\) | 623.795 | − | 1130.68i | 0.778770 | − | 1.41159i | ||||
\(802\) | −625.989 | −0.780535 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.5488 | + | 346.630i | 0.0268020 | + | 0.431132i | ||||
\(805\) | −292.983 | − | 212.864i | −0.363954 | − | 0.264428i | ||||
\(806\) | 262.860 | + | 85.4084i | 0.326129 | + | 0.105966i | ||||
\(807\) | −62.8421 | − | 159.067i | −0.0778712 | − | 0.197109i | ||||
\(808\) | −438.311 | + | 318.452i | −0.542464 | + | 0.394123i | ||||
\(809\) | −180.254 | − | 248.099i | −0.222811 | − | 0.306673i | 0.682947 | − | 0.730468i | \(-0.260698\pi\) |
−0.905758 | + | 0.423794i | \(0.860698\pi\) | |||||||
\(810\) | 86.3959 | + | 137.039i | 0.106662 | + | 0.169184i | ||||
\(811\) | 402.918 | − | 1240.05i | 0.496816 | − | 1.52904i | −0.317291 | − | 0.948328i | \(-0.602773\pi\) |
0.814107 | − | 0.580714i | \(-0.197227\pi\) | |||||||
\(812\) | −504.610 | + | 694.537i | −0.621441 | + | 0.855341i | ||||
\(813\) | −23.8968 | − | 384.399i | −0.0293934 | − | 0.472816i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 524.733i | − | 0.643844i | ||||||
\(816\) | 508.474 | + | 323.219i | 0.623130 | + | 0.396102i | ||||
\(817\) | 90.2967 | − | 277.905i | 0.110522 | − | 0.340153i | ||||
\(818\) | −382.553 | + | 124.299i | −0.467669 | + | 0.151955i | ||||
\(819\) | 420.473 | − | 393.673i | 0.513398 | − | 0.480675i | ||||
\(820\) | −212.683 | + | 154.524i | −0.259370 | + | 0.188443i | ||||
\(821\) | −1296.33 | + | 421.204i | −1.57897 | + | 0.513038i | −0.961791 | − | 0.273786i | \(-0.911724\pi\) |
−0.617178 | + | 0.786824i | \(0.711724\pi\) | |||||||
\(822\) | −136.528 | − | 35.1629i | −0.166092 | − | 0.0427772i | ||||
\(823\) | −217.060 | − | 157.704i | −0.263743 | − | 0.191620i | 0.448053 | − | 0.894007i | \(-0.352118\pi\) |
−0.711796 | + | 0.702387i | \(0.752118\pi\) | |||||||
\(824\) | − | 114.343i | − | 0.138766i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 231.272 | 0.279990 | ||||||||
\(827\) | −374.434 | + | 515.364i | −0.452761 | + | 0.623172i | −0.972988 | − | 0.230856i | \(-0.925847\pi\) |
0.520227 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(828\) | −901.201 | − | 173.306i | −1.08841 | − | 0.209306i | ||||
\(829\) | 8.40302 | + | 25.8618i | 0.0101363 | + | 0.0311964i | 0.955997 | − | 0.293377i | \(-0.0947792\pi\) |
−0.945860 | + | 0.324574i | \(0.894779\pi\) | |||||||
\(830\) | 40.1586 | + | 55.2735i | 0.0483838 | + | 0.0665946i | ||||
\(831\) | 451.419 | + | 546.501i | 0.543224 | + | 0.657642i | ||||
\(832\) | 47.4039 | + | 145.894i | 0.0569758 | + | 0.175353i | ||||
\(833\) | −570.970 | − | 185.519i | −0.685438 | − | 0.222712i | ||||
\(834\) | 262.642 | + | 166.952i | 0.314919 | + | 0.200183i | ||||
\(835\) | −159.446 | −0.190953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −129.307 | − | 686.181i | −0.154489 | − | 0.819810i | ||||
\(838\) | −214.337 | − | 155.725i | −0.255772 | − | 0.185829i | ||||
\(839\) | −964.295 | − | 313.318i | −1.14934 | − | 0.373443i | −0.328444 | − | 0.944523i | \(-0.606524\pi\) |
−0.820894 | + | 0.571081i | \(0.806524\pi\) | |||||||
\(840\) | −195.189 | + | 77.1127i | −0.232368 | + | 0.0918008i | ||||
\(841\) | 1648.74 | − | 1197.88i | 1.96045 | − | 1.42435i | ||||
\(842\) | 206.449 | + | 284.153i | 0.245189 | + | 0.337474i | ||||
\(843\) | −224.843 | − | 569.127i | −0.266718 | − | 0.675121i | ||||
\(844\) | 195.092 | − | 600.432i | 0.231152 | − | 0.711412i | ||||
\(845\) | −19.2244 | + | 26.4602i | −0.0227508 | + | 0.0313138i | ||||
\(846\) | 221.375 | − | 27.6311i | 0.261672 | − | 0.0326608i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 87.8361i | − | 0.103580i | ||||||
\(849\) | −771.228 | + | 1213.26i | −0.908396 | + | 1.42905i | ||||
\(850\) | −103.363 | + | 318.118i | −0.121603 | + | 0.374256i | ||||
\(851\) | 1225.23 | − | 398.101i | 1.43975 | − | 0.467804i | ||||
\(852\) | −113.109 | + | 93.4300i | −0.132757 | + | 0.109660i | ||||
\(853\) | −1043.92 | + | 758.451i | −1.22382 | + | 0.889157i | −0.996411 | − | 0.0846431i | \(-0.973025\pi\) |
−0.227408 | + | 0.973800i | \(0.573025\pi\) | |||||||
\(854\) | 183.922 | − | 59.7599i | 0.215365 | − | 0.0699764i | ||||
\(855\) | −183.696 | − | 35.3256i | −0.214849 | − | 0.0413165i | ||||
\(856\) | −398.960 | − | 289.861i | −0.466074 | − | 0.338623i | ||||
\(857\) | 618.449i | 0.721644i | 0.932635 | + | 0.360822i | \(0.117504\pi\) | ||||
−0.932635 | + | 0.360822i | \(0.882496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1207.23 | 1.40538 | 0.702692 | − | 0.711494i | \(-0.251981\pi\) | ||||
0.702692 | + | 0.711494i | \(0.251981\pi\) | |||||||
\(860\) | 177.576 | − | 244.413i | 0.206484 | − | 0.284201i | ||||
\(861\) | −109.632 | + | 425.673i | −0.127331 | + | 0.494394i | ||||
\(862\) | −194.714 | − | 599.269i | −0.225887 | − | 0.695207i | ||||
\(863\) | −649.669 | − | 894.193i | −0.752803 | − | 1.03614i | −0.997779 | − | 0.0666155i | \(-0.978780\pi\) |
0.244975 | − | 0.969529i | \(-0.421220\pi\) | |||||||
\(864\) | −562.927 | + | 596.778i | −0.651536 | + | 0.690715i | ||||
\(865\) | 150.832 | + | 464.214i | 0.174372 | + | 0.536663i | ||||
\(866\) | −14.0320 | − | 4.55927i | −0.0162032 | − | 0.00526474i | ||||
\(867\) | −361.565 | + | 568.799i | −0.417031 | + | 0.656054i | ||||
\(868\) | 413.783 | 0.476708 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 321.315 | − | 19.9751i | 0.369328 | − | 0.0229599i | ||||
\(871\) | −374.628 | − | 272.183i | −0.430112 | − | 0.312495i | ||||
\(872\) | −931.715 | − | 302.732i | −1.06848 | − | 0.347170i | ||||
\(873\) | 153.885 | + | 328.291i | 0.176271 | + | 0.376049i | ||||
\(874\) | −159.579 | + | 115.941i | −0.182585 | + | 0.132655i | ||||
\(875\) | 307.132 | + | 422.731i | 0.351008 | + | 0.483121i | ||||
\(876\) | −830.206 | + | 327.987i | −0.947724 | + | 0.374414i | ||||
\(877\) | −411.721 | + | 1267.15i | −0.469466 | + | 1.44487i | 0.383813 | + | 0.923411i | \(0.374611\pi\) |
−0.853278 | + | 0.521456i | \(0.825389\pi\) | |||||||
\(878\) | 118.701 | − | 163.379i | 0.135195 | − | 0.186080i | ||||
\(879\) | 28.0162 | − | 1.74167i | 0.0318728 | − | 0.00198143i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1171.98i | − | 1.33029i | −0.746715 | − | 0.665145i | \(-0.768370\pi\) | ||
0.746715 | − | 0.665145i | \(-0.231630\pi\) | |||||||
\(882\) | 91.2416 | − | 165.384i | 0.103449 | − | 0.187510i | ||||
\(883\) | 225.025 | − | 692.555i | 0.254841 | − | 0.784320i | −0.739020 | − | 0.673684i | \(-0.764711\pi\) |
0.993861 | − | 0.110637i | \(-0.0352890\pi\) | |||||||
\(884\) | −980.512 | + | 318.588i | −1.10918 | + | 0.360393i | ||||
\(885\) | 296.722 | + | 359.220i | 0.335279 | + | 0.405898i | ||||
\(886\) | 39.4532 | − | 28.6644i | 0.0445295 | − | 0.0323526i | ||||
\(887\) | 931.819 | − | 302.766i | 1.05053 | − | 0.341337i | 0.267653 | − | 0.963515i | \(-0.413752\pi\) |
0.782876 | + | 0.622178i | \(0.213752\pi\) | |||||||
\(888\) | 186.206 | − | 722.986i | 0.209691 | − | 0.814173i | ||||
\(889\) | −494.573 | − | 359.329i | −0.556325 | − | 0.404194i | ||||
\(890\) | − | 286.965i | − | 0.322433i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −767.973 | −0.860956 | ||||||||
\(893\) | −151.416 | + | 208.407i | −0.169559 | + | 0.233378i | ||||
\(894\) | −171.090 | − | 44.0645i | −0.191376 | − | 0.0492891i | ||||
\(895\) | 24.1915 | + | 74.4537i | 0.0270296 | + | 0.0831885i | ||||
\(896\) | −364.072 | − | 501.102i | −0.406330 | − | 0.559266i | ||||
\(897\) | 943.395 | − | 779.261i | 1.05172 | − | 0.868741i | ||||
\(898\) | 33.6477 | + | 103.557i | 0.0374696 | + | 0.115319i | ||||
\(899\) | −1319.70 | − | 428.797i | −1.46797 | − | 0.476971i | ||||
\(900\) | 495.023 | + | 273.103i | 0.550026 | + | 0.303448i | ||||
\(901\) | 224.652 | 0.249336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.3424 | − | 504.168i | −0.0347092 | − | 0.558325i | ||||
\(904\) | −583.627 | − | 424.030i | −0.645605 | − | 0.469059i | ||||
\(905\) | −245.213 | − | 79.6746i | −0.270954 | − | 0.0880382i | ||||
\(906\) | −5.44409 | − | 13.7802i | −0.00600893 | − | 0.0152099i | ||||
\(907\) | −892.108 | + | 648.154i | −0.983581 | + | 0.714613i | −0.958506 | − | 0.285072i | \(-0.907982\pi\) |
−0.0250750 | + | 0.999686i | \(0.507982\pi\) | |||||||
\(908\) | 845.079 | + | 1163.15i | 0.930703 | + | 1.28100i | ||||
\(909\) | −755.880 | + | 354.315i | −0.831551 | + | 0.389786i | ||||
\(910\) | 39.5542 | − | 121.735i | 0.0434661 | − | 0.133775i | ||||
\(911\) | 272.307 | − | 374.799i | 0.298910 | − | 0.411415i | −0.632973 | − | 0.774174i | \(-0.718165\pi\) |
0.931883 | + | 0.362760i | \(0.118165\pi\) | |||||||
\(912\) | −13.5812 | − | 218.464i | −0.0148917 | − | 0.239544i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 243.701i | 0.266632i | ||||||||
\(915\) | 328.793 | + | 209.002i | 0.359337 | + | 0.228418i | ||||
\(916\) | −105.860 | + | 325.804i | −0.115568 | + | 0.355681i | ||||
\(917\) | 568.543 | − | 184.731i | 0.620004 | − | 0.201451i | ||||
\(918\) | −352.680 | − | 332.675i | −0.384183 | − | 0.362391i | ||||
\(919\) | 158.510 | − | 115.164i | 0.172481 | − | 0.125315i | −0.498196 | − | 0.867065i | \(-0.666004\pi\) |
0.670677 | + | 0.741750i | \(0.266004\pi\) | |||||||
\(920\) | −424.013 | + | 137.770i | −0.460884 | + | 0.149750i | ||||
\(921\) | −210.705 | − | 54.2673i | −0.228779 | − | 0.0589221i | ||||
\(922\) | −338.538 | − | 245.962i | −0.367178 | − | 0.266771i | ||||
\(923\) | − | 195.609i | − | 0.211927i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −793.652 | −0.858002 | ||||||||
\(926\) | −21.3979 | + | 29.4517i | −0.0231079 | + | 0.0318053i | ||||
\(927\) | 33.2717 | − | 173.015i | 0.0358918 | − | 0.186640i | ||||
\(928\) | 503.795 | + | 1550.52i | 0.542882 | + | 1.67082i | ||||
\(929\) | 71.4310 | + | 98.3163i | 0.0768902 | + | 0.105830i | 0.845730 | − | 0.533611i | \(-0.179166\pi\) |
−0.768840 | + | 0.639442i | \(0.779166\pi\) | |||||||
\(930\) | −98.8190 | − | 119.633i | −0.106257 | − | 0.128638i | ||||
\(931\) | 67.3976 | + | 207.428i | 0.0723927 | + | 0.222802i | ||||
\(932\) | −555.509 | − | 180.496i | −0.596039 | − | 0.193665i | ||||
\(933\) | 963.715 | + | 612.600i | 1.03292 | + | 0.656592i | ||||
\(934\) | 284.484 | 0.304586 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −87.8260 | − | 703.645i | −0.0938312 | − | 0.751758i | ||||
\(937\) | 267.314 | + | 194.215i | 0.285288 | + | 0.207274i | 0.721220 | − | 0.692706i | \(-0.243581\pi\) |
−0.435933 | + | 0.899979i | \(0.643581\pi\) | |||||||
\(938\) | 122.728 | + | 39.8767i | 0.130840 | + | 0.0425125i | ||||
\(939\) | −148.159 | + | 58.5326i | −0.157784 | + | 0.0623350i | ||||
\(940\) | −215.471 | + | 156.549i | −0.229225 | + | 0.166541i | ||||
\(941\) | 526.117 | + | 724.138i | 0.559104 | + | 0.769541i | 0.991212 | − | 0.132281i | \(-0.0422301\pi\) |
−0.432108 | + | 0.901822i | \(0.642230\pi\) | |||||||
\(942\) | −86.2820 | − | 218.399i | −0.0915945 | − | 0.231846i | ||||
\(943\) | −288.555 | + | 888.080i | −0.305996 | + | 0.941760i | ||||
\(944\) | −320.453 | + | 441.066i | −0.339463 | + | 0.467231i | ||||
\(945\) | −317.783 | + | 59.8844i | −0.336278 | + | 0.0633697i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1308.11i | − | 1.38132i | −0.723181 | − | 0.690659i | \(-0.757321\pi\) | ||
0.723181 | − | 0.690659i | \(-0.242679\pi\) | |||||||
\(948\) | 508.420 | − | 799.824i | 0.536308 | − | 0.843696i | ||||
\(949\) | 367.791 | − | 1131.94i | 0.387556 | − | 1.19277i | ||||
\(950\) | 115.569 | − | 37.5508i | 0.121652 | − | 0.0395271i | ||||
\(951\) | −169.417 | + | 139.941i | −0.178146 | + | 0.147152i | ||||
\(952\) | 508.133 | − | 369.180i | 0.533753 | − | 0.387794i | ||||
\(953\) | −1.93085 | + | 0.627370i | −0.00202607 | + | 0.000658311i | −0.310030 | − | 0.950727i | \(-0.600339\pi\) |
0.308004 | + | 0.951385i | \(0.400339\pi\) | |||||||
\(954\) | −13.3475 | + | 69.4080i | −0.0139911 | + | 0.0727548i | ||||
\(955\) | 141.910 | + | 103.104i | 0.148597 | + | 0.107962i | ||||
\(956\) | − | 543.939i | − | 0.568974i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 457.467 | 0.477523 | ||||||||
\(959\) | 165.417 | − | 227.676i | 0.172489 | − | 0.237410i | ||||
\(960\) | 21.4799 | − | 83.4008i | 0.0223749 | − | 0.0868758i | ||||
\(961\) | −90.2909 | − | 277.887i | −0.0939552 | − | 0.289164i | ||||
\(962\) | 267.643 | + | 368.379i | 0.278215 | + | 0.382930i | ||||
\(963\) | −519.329 | − | 554.683i | −0.539282 | − | 0.575995i | ||||
\(964\) | 59.0877 | + | 181.853i | 0.0612943 | + | 0.188645i | ||||
\(965\) | 651.827 | + | 211.791i | 0.675468 | + | 0.219473i | ||||
\(966\) | −182.926 | + | 287.771i | −0.189364 | + | 0.297899i | ||||
\(967\) | 520.674 | 0.538442 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 558.750 | − | 34.7356i | 0.576625 | − | 0.0358469i | ||||
\(970\) | 65.1830 | + | 47.3582i | 0.0671989 | + | 0.0488229i | ||||
\(971\) | 1723.37 | + | 559.956i | 1.77484 | + | 0.576680i | 0.998557 | − | 0.0537073i | \(-0.0171038\pi\) |
0.776281 | + | 0.630387i | \(0.217104\pi\) | |||||||
\(972\) | −664.750 | + | 479.196i | −0.683900 | + | 0.493000i | ||||
\(973\) | −502.584 | + | 365.149i | −0.516530 | + | 0.375281i | ||||
\(974\) | 282.630 | + | 389.006i | 0.290174 | + | 0.399391i | ||||
\(975\) | −701.086 | + | 276.975i | −0.719062 | + | 0.284077i | ||||
\(976\) | −140.875 | + | 433.568i | −0.144339 | + | 0.444230i | ||||
\(977\) | 251.212 | − | 345.764i | 0.257126 | − | 0.353904i | −0.660865 | − | 0.750505i | \(-0.729810\pi\) |
0.917991 | + | 0.396601i | \(0.129810\pi\) | |||||||
\(978\) | −493.125 | + | 30.6559i | −0.504218 | + | 0.0313455i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 225.496i | 0.230098i | ||||||||
\(981\) | −1321.70 | − | 729.180i | −1.34730 | − | 0.743303i | ||||
\(982\) | −188.242 | + | 579.349i | −0.191692 | + | 0.589968i | ||||
\(983\) | 954.405 | − | 310.105i | 0.970910 | − | 0.315468i | 0.219727 | − | 0.975561i | \(-0.429483\pi\) |
0.751183 | + | 0.660094i | \(0.229483\pi\) | |||||||
\(984\) | 344.626 | + | 417.213i | 0.350229 | + | 0.423997i | ||||
\(985\) | −217.727 | + | 158.188i | −0.221042 | + | 0.160597i | ||||
\(986\) | −916.317 | + | 297.729i | −0.929327 | + | 0.301957i | ||||
\(987\) | −111.069 | + | 431.252i | −0.112532 | + | 0.436932i | ||||
\(988\) | 303.012 | + | 220.151i | 0.306692 | + | 0.222825i | ||||
\(989\) | − | 1073.09i | − | 1.08503i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 862.380 | 0.870212 | 0.435106 | − | 0.900379i | \(-0.356711\pi\) | ||||
0.435106 | + | 0.900379i | \(0.356711\pi\) | |||||||
\(992\) | 461.875 | − | 635.717i | 0.465600 | − | 0.640844i | ||||
\(993\) | −486.186 | − | 125.217i | −0.489613 | − | 0.126100i | ||||
\(994\) | 16.8448 | + | 51.8429i | 0.0169465 | + | 0.0521559i | ||||
\(995\) | −429.212 | − | 590.760i | −0.431369 | − | 0.593728i | ||||
\(996\) | −266.454 | + | 220.096i | −0.267524 | + | 0.220980i | ||||
\(997\) | 88.1554 | + | 271.314i | 0.0884206 | + | 0.272131i | 0.985483 | − | 0.169773i | \(-0.0543034\pi\) |
−0.897063 | + | 0.441903i | \(0.854303\pi\) | |||||||
\(998\) | −375.272 | − | 121.933i | −0.376024 | − | 0.122178i | ||||
\(999\) | 492.125 | − | 1039.78i | 0.492618 | − | 1.04082i |
(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 | 363.3.h.l.323.3 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.l.323.2 | 16 | ||
11.2 | odd | 10 | 363.3.h.m.269.3 | 16 | |||
11.3 | even | 5 | inner | 363.3.h.l.245.2 | 16 | ||
11.4 | even | 5 | inner | 363.3.h.l.251.3 | 16 | ||
11.5 | even | 5 | 363.3.b.h.122.3 | 4 | |||
11.6 | odd | 10 | 33.3.b.b.23.2 | ✓ | 4 | ||
11.7 | odd | 10 | 363.3.h.m.251.2 | 16 | |||
11.8 | odd | 10 | 363.3.h.m.245.3 | 16 | |||
11.9 | even | 5 | inner | 363.3.h.l.269.2 | 16 | ||
11.10 | odd | 2 | 363.3.h.m.323.2 | 16 | |||
33.2 | even | 10 | 363.3.h.m.269.2 | 16 | |||
33.5 | odd | 10 | 363.3.b.h.122.2 | 4 | |||
33.8 | even | 10 | 363.3.h.m.245.2 | 16 | |||
33.14 | odd | 10 | inner | 363.3.h.l.245.3 | 16 | ||
33.17 | even | 10 | 33.3.b.b.23.3 | yes | 4 | ||
33.20 | odd | 10 | inner | 363.3.h.l.269.3 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.l.251.2 | 16 | ||
33.29 | even | 10 | 363.3.h.m.251.3 | 16 | |||
33.32 | even | 2 | 363.3.h.m.323.3 | 16 | |||
44.39 | even | 10 | 528.3.i.d.353.1 | 4 | |||
132.83 | odd | 10 | 528.3.i.d.353.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.b.23.2 | ✓ | 4 | 11.6 | odd | 10 | ||
33.3.b.b.23.3 | yes | 4 | 33.17 | even | 10 | ||
363.3.b.h.122.2 | 4 | 33.5 | odd | 10 | |||
363.3.b.h.122.3 | 4 | 11.5 | even | 5 | |||
363.3.h.l.245.2 | 16 | 11.3 | even | 5 | inner | ||
363.3.h.l.245.3 | 16 | 33.14 | odd | 10 | inner | ||
363.3.h.l.251.2 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.l.251.3 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.l.269.2 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.l.269.3 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.l.323.2 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.l.323.3 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.m.245.2 | 16 | 33.8 | even | 10 | |||
363.3.h.m.245.3 | 16 | 11.8 | odd | 10 | |||
363.3.h.m.251.2 | 16 | 11.7 | odd | 10 | |||
363.3.h.m.251.3 | 16 | 33.29 | even | 10 | |||
363.3.h.m.269.2 | 16 | 33.2 | even | 10 | |||
363.3.h.m.269.3 | 16 | 11.2 | odd | 10 | |||
363.3.h.m.323.2 | 16 | 11.10 | odd | 2 | |||
363.3.h.m.323.3 | 16 | 33.32 | even | 2 | |||
528.3.i.d.353.1 | 4 | 44.39 | even | 10 | |||
528.3.i.d.353.2 | 4 | 132.83 | odd | 10 |