Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,4,Mod(51,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.51");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.d (of order \(5\), 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: | \(14.7504775014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 51.5 | ||
Character | \(\chi\) | \(=\) | 250.51 |
Dual form | 250.4.d.d.201.5 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | − | 1.17557i | 0.572061 | − | 0.415627i | ||||
\(3\) | 0.0763140 | − | 0.234870i | 0.0146866 | − | 0.0452008i | −0.943445 | − | 0.331530i | \(-0.892435\pi\) |
0.958131 | + | 0.286329i | \(0.0924351\pi\) | |||||||
\(4\) | 1.23607 | − | 3.80423i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.152628 | − | 0.469741i | −0.0103850 | − | 0.0319618i | ||||
\(7\) | 19.9138 | 1.07524 | 0.537622 | − | 0.843186i | \(-0.319323\pi\) | ||||
0.537622 | + | 0.843186i | \(0.319323\pi\) | |||||||
\(8\) | −2.47214 | − | 7.60845i | −0.109254 | − | 0.336249i | ||||
\(9\) | 21.7941 | + | 15.8344i | 0.807190 | + | 0.586458i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.78841 | − | 1.29936i | 0.0490206 | − | 0.0356155i | −0.563005 | − | 0.826453i | \(-0.690355\pi\) |
0.612026 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(12\) | −0.799170 | − | 0.580631i | −0.0192250 | − | 0.0139678i | ||||
\(13\) | −9.95462 | − | 7.23245i | −0.212378 | − | 0.154302i | 0.476511 | − | 0.879169i | \(-0.341901\pi\) |
−0.688889 | + | 0.724867i | \(0.741901\pi\) | |||||||
\(14\) | 32.2212 | − | 23.4101i | 0.615105 | − | 0.446900i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.9443 | − | 9.40456i | −0.202254 | − | 0.146946i | ||||
\(17\) | 23.0023 | + | 70.7939i | 0.328170 | + | 1.01000i | 0.969989 | + | 0.243147i | \(0.0781797\pi\) |
−0.641820 | + | 0.766856i | \(0.721820\pi\) | |||||||
\(18\) | 53.8780 | 0.705510 | ||||||||
\(19\) | −15.5949 | − | 47.9960i | −0.188300 | − | 0.579529i | 0.811689 | − | 0.584089i | \(-0.198548\pi\) |
−0.999990 | + | 0.00456072i | \(0.998548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.51970 | − | 4.67716i | 0.0157917 | − | 0.0486019i | ||||
\(22\) | 1.36622 | − | 4.20481i | 0.0132400 | − | 0.0407485i | ||||
\(23\) | 161.248 | − | 117.154i | 1.46185 | − | 1.06210i | 0.478974 | − | 0.877829i | \(-0.341009\pi\) |
0.982876 | − | 0.184268i | \(-0.0589914\pi\) | |||||||
\(24\) | −1.97566 | −0.0168033 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −24.6092 | −0.185625 | ||||||||
\(27\) | 10.7766 | − | 7.82967i | 0.0768133 | − | 0.0558082i | ||||
\(28\) | 24.6148 | − | 75.7565i | 0.166134 | − | 0.511309i | ||||
\(29\) | 74.5475 | − | 229.434i | 0.477349 | − | 1.46913i | −0.365414 | − | 0.930845i | \(-0.619072\pi\) |
0.842763 | − | 0.538285i | \(-0.180928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15.8456 | − | 48.7679i | −0.0918052 | − | 0.282547i | 0.894603 | − | 0.446862i | \(-0.147459\pi\) |
−0.986408 | + | 0.164315i | \(0.947459\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −0.168700 | − | 0.519204i | −0.000889903 | − | 0.00273884i | ||||
\(34\) | 120.442 | + | 87.5061i | 0.607517 | + | 0.441387i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 87.1765 | − | 63.3374i | 0.403595 | − | 0.293229i | ||||
\(37\) | 225.001 | + | 163.473i | 0.999729 | + | 0.726345i | 0.962030 | − | 0.272944i | \(-0.0879973\pi\) |
0.0376986 | + | 0.999289i | \(0.487997\pi\) | |||||||
\(38\) | −81.6557 | − | 59.3264i | −0.348587 | − | 0.253263i | ||||
\(39\) | −2.45836 | + | 1.78611i | −0.0100937 | + | 0.00733348i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −214.861 | − | 156.106i | −0.818431 | − | 0.594625i | 0.0978313 | − | 0.995203i | \(-0.468809\pi\) |
−0.916263 | + | 0.400578i | \(0.868809\pi\) | |||||||
\(42\) | −3.03940 | − | 9.35431i | −0.0111664 | − | 0.0343667i | ||||
\(43\) | 103.714 | 0.367818 | 0.183909 | − | 0.982943i | \(-0.441125\pi\) | ||||
0.183909 | + | 0.982943i | \(0.441125\pi\) | |||||||
\(44\) | −2.73245 | − | 8.40961i | −0.00936210 | − | 0.0288136i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 123.183 | − | 379.117i | 0.394832 | − | 1.21517i | ||||
\(47\) | −127.174 | + | 391.402i | −0.394686 | + | 1.21472i | 0.534520 | + | 0.845156i | \(0.320493\pi\) |
−0.929206 | + | 0.369563i | \(0.879507\pi\) | |||||||
\(48\) | −3.19668 | + | 2.32252i | −0.00961252 | + | 0.00698391i | ||||
\(49\) | 53.5589 | 0.156148 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.3828 | 0.0504726 | ||||||||
\(52\) | −39.8185 | + | 28.9298i | −0.106189 | + | 0.0771508i | ||||
\(53\) | −132.965 | + | 409.226i | −0.344608 | + | 1.06059i | 0.617186 | + | 0.786818i | \(0.288273\pi\) |
−0.961793 | + | 0.273776i | \(0.911727\pi\) | |||||||
\(54\) | 8.23260 | − | 25.3373i | 0.0207466 | − | 0.0638514i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −49.2296 | − | 151.513i | −0.117475 | − | 0.361550i | ||||
\(57\) | −12.4629 | −0.0289607 | ||||||||
\(58\) | −149.095 | − | 458.867i | −0.337537 | − | 1.03883i | ||||
\(59\) | −445.750 | − | 323.856i | −0.983589 | − | 0.714619i | −0.0250809 | − | 0.999685i | \(-0.507984\pi\) |
−0.958508 | + | 0.285066i | \(0.907984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 413.338 | − | 300.308i | 0.867583 | − | 0.630336i | −0.0623543 | − | 0.998054i | \(-0.519861\pi\) |
0.929937 | + | 0.367718i | \(0.119861\pi\) | |||||||
\(62\) | −82.9688 | − | 60.2804i | −0.169952 | − | 0.123478i | ||||
\(63\) | 434.003 | + | 315.322i | 0.867925 | + | 0.630585i | ||||
\(64\) | −51.7771 | + | 37.6183i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.883322 | − | 0.641771i | −0.00164742 | − | 0.00119692i | ||||
\(67\) | 23.5632 | + | 72.5200i | 0.0429657 | + | 0.132235i | 0.970238 | − | 0.242152i | \(-0.0778532\pi\) |
−0.927273 | + | 0.374387i | \(0.877853\pi\) | |||||||
\(68\) | 297.748 | 0.530990 | ||||||||
\(69\) | −15.2104 | − | 46.8129i | −0.0265380 | − | 0.0816754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −264.409 | + | 813.766i | −0.441965 | + | 1.36023i | 0.443812 | + | 0.896120i | \(0.353626\pi\) |
−0.885778 | + | 0.464110i | \(0.846374\pi\) | |||||||
\(72\) | 66.5969 | − | 204.964i | 0.109007 | − | 0.335490i | ||||
\(73\) | −417.952 | + | 303.660i | −0.670104 | + | 0.486859i | −0.870060 | − | 0.492946i | \(-0.835920\pi\) |
0.199956 | + | 0.979805i | \(0.435920\pi\) | |||||||
\(74\) | 556.233 | 0.873795 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −201.864 | −0.304676 | ||||||||
\(77\) | 35.6140 | − | 25.8751i | 0.0527090 | − | 0.0382954i | ||||
\(78\) | −1.87802 | + | 5.77996i | −0.00272621 | + | 0.00839041i | ||||
\(79\) | 42.1044 | − | 129.584i | 0.0599634 | − | 0.184549i | −0.916588 | − | 0.399833i | \(-0.869068\pi\) |
0.976551 | + | 0.215285i | \(0.0690680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 223.748 | + | 688.626i | 0.306925 | + | 0.944617i | ||||
\(82\) | −531.166 | −0.715335 | ||||||||
\(83\) | −283.533 | − | 872.626i | −0.374962 | − | 1.15401i | −0.943504 | − | 0.331360i | \(-0.892493\pi\) |
0.568543 | − | 0.822654i | \(-0.307507\pi\) | |||||||
\(84\) | −15.9145 | − | 11.5626i | −0.0206716 | − | 0.0150188i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 167.812 | − | 121.923i | 0.210415 | − | 0.152875i | ||||
\(87\) | −48.1981 | − | 35.0180i | −0.0593952 | − | 0.0431531i | ||||
\(88\) | −14.3073 | − | 10.3949i | −0.0173314 | − | 0.0125920i | ||||
\(89\) | −1053.94 | + | 765.734i | −1.25526 | + | 0.911997i | −0.998515 | − | 0.0544837i | \(-0.982649\pi\) |
−0.256741 | + | 0.966480i | \(0.582649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −198.234 | − | 144.026i | −0.228358 | − | 0.165912i | ||||
\(92\) | −246.365 | − | 758.234i | −0.279189 | − | 0.859254i | ||||
\(93\) | −12.6634 | −0.0141197 | ||||||||
\(94\) | 254.348 | + | 782.803i | 0.279085 | + | 0.858936i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.44205 | + | 7.51585i | −0.00259625 | + | 0.00799045i | ||||
\(97\) | 137.189 | − | 422.225i | 0.143603 | − | 0.441963i | −0.853226 | − | 0.521541i | \(-0.825357\pi\) |
0.996829 | + | 0.0795779i | \(0.0253572\pi\) | |||||||
\(98\) | 86.6601 | − | 62.9623i | 0.0893265 | − | 0.0648995i | ||||
\(99\) | 59.5513 | 0.0604559 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −493.360 | −0.486051 | −0.243025 | − | 0.970020i | \(-0.578140\pi\) | ||||
−0.243025 | + | 0.970020i | \(0.578140\pi\) | |||||||
\(102\) | 29.7440 | − | 21.6103i | 0.0288734 | − | 0.0209778i | ||||
\(103\) | −531.904 | + | 1637.03i | −0.508835 | + | 1.56603i | 0.285391 | + | 0.958411i | \(0.407877\pi\) |
−0.794226 | + | 0.607623i | \(0.792123\pi\) | |||||||
\(104\) | −30.4186 | + | 93.6188i | −0.0286807 | + | 0.0882700i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 265.931 | + | 818.451i | 0.243675 | + | 0.749953i | ||||
\(107\) | 1241.00 | 1.12124 | 0.560618 | − | 0.828074i | \(-0.310563\pi\) | ||||
0.560618 | + | 0.828074i | \(0.310563\pi\) | |||||||
\(108\) | −16.4652 | − | 50.6747i | −0.0146700 | − | 0.0451498i | ||||
\(109\) | −142.969 | − | 103.873i | −0.125632 | − | 0.0912772i | 0.523195 | − | 0.852213i | \(-0.324740\pi\) |
−0.648827 | + | 0.760936i | \(0.724740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 55.5657 | − | 40.3708i | 0.0475140 | − | 0.0345210i | ||||
\(112\) | −257.769 | − | 187.280i | −0.217473 | − | 0.158003i | ||||
\(113\) | 155.126 | + | 112.705i | 0.129141 | + | 0.0938268i | 0.650481 | − | 0.759523i | \(-0.274567\pi\) |
−0.521339 | + | 0.853349i | \(0.674567\pi\) | |||||||
\(114\) | −20.1655 | + | 14.6511i | −0.0165673 | + | 0.0120368i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −780.672 | − | 567.191i | −0.624858 | − | 0.453986i | ||||
\(117\) | −102.431 | − | 315.250i | −0.0809379 | − | 0.249101i | ||||
\(118\) | −1101.96 | −0.859688 | ||||||||
\(119\) | 458.064 | + | 1409.77i | 0.352862 | + | 1.08600i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −409.792 | + | 1261.21i | −0.307882 | + | 0.947565i | ||||
\(122\) | 315.762 | − | 971.817i | 0.234326 | − | 0.721182i | ||||
\(123\) | −53.0615 | + | 38.5515i | −0.0388975 | + | 0.0282607i | ||||
\(124\) | −205.110 | −0.148544 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1072.92 | 0.758595 | ||||||||
\(127\) | 248.648 | − | 180.653i | 0.173732 | − | 0.126224i | −0.497521 | − | 0.867452i | \(-0.665756\pi\) |
0.671253 | + | 0.741228i | \(0.265756\pi\) | |||||||
\(128\) | −39.5542 | + | 121.735i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 7.91481 | − | 24.3593i | 0.00540201 | − | 0.0166257i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 868.243 | + | 2672.18i | 0.579074 | + | 1.78221i | 0.621867 | + | 0.783123i | \(0.286374\pi\) |
−0.0427928 | + | 0.999084i | \(0.513626\pi\) | |||||||
\(132\) | −2.18369 | −0.00143989 | ||||||||
\(133\) | −310.553 | − | 955.783i | −0.202469 | − | 0.623134i | ||||
\(134\) | 123.378 | + | 89.6397i | 0.0795394 | + | 0.0577887i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 481.767 | − | 350.024i | 0.303759 | − | 0.220694i | ||||
\(137\) | −1586.38 | − | 1152.57i | −0.989293 | − | 0.718764i | −0.0295271 | − | 0.999564i | \(-0.509400\pi\) |
−0.959766 | + | 0.280800i | \(0.909400\pi\) | |||||||
\(138\) | −79.6428 | − | 57.8639i | −0.0491279 | − | 0.0356935i | ||||
\(139\) | 1277.07 | − | 927.849i | 0.779281 | − | 0.566181i | −0.125482 | − | 0.992096i | \(-0.540048\pi\) |
0.904763 | + | 0.425915i | \(0.140048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 82.2234 | + | 59.7388i | 0.0491097 | + | 0.0356803i | ||||
\(142\) | 528.817 | + | 1627.53i | 0.312517 | + | 0.961828i | ||||
\(143\) | −27.2005 | −0.0159064 | ||||||||
\(144\) | −133.194 | − | 409.928i | −0.0770797 | − | 0.237227i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −319.287 | + | 982.665i | −0.180989 | + | 0.557027i | ||||
\(147\) | 4.08729 | − | 12.5794i | 0.00229329 | − | 0.00705803i | ||||
\(148\) | 900.005 | − | 653.892i | 0.499864 | − | 0.363173i | ||||
\(149\) | −1448.55 | −0.796443 | −0.398221 | − | 0.917289i | \(-0.630372\pi\) | ||||
−0.398221 | + | 0.917289i | \(0.630372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1804.96 | −0.972754 | −0.486377 | − | 0.873749i | \(-0.661682\pi\) | ||||
−0.486377 | + | 0.873749i | \(0.661682\pi\) | |||||||
\(152\) | −326.623 | + | 237.305i | −0.174294 | + | 0.126632i | ||||
\(153\) | −619.660 | + | 1907.12i | −0.327428 | + | 1.00772i | ||||
\(154\) | 27.2067 | − | 83.7336i | 0.0142362 | − | 0.0438146i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.75605 | + | 11.5599i | 0.00192772 | + | 0.00593291i | ||||
\(157\) | −1998.98 | −1.01615 | −0.508076 | − | 0.861312i | \(-0.669643\pi\) | ||||
−0.508076 | + | 0.861312i | \(0.669643\pi\) | |||||||
\(158\) | −84.2087 | − | 259.168i | −0.0424006 | − | 0.130495i | ||||
\(159\) | 85.9678 | + | 62.4593i | 0.0428786 | + | 0.0311531i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3211.06 | − | 2332.97i | 1.57185 | − | 1.14201i | ||||
\(162\) | 1171.56 | + | 851.188i | 0.568188 | + | 0.412813i | ||||
\(163\) | 397.428 | + | 288.748i | 0.190975 | + | 0.138752i | 0.679164 | − | 0.733986i | \(-0.262342\pi\) |
−0.488189 | + | 0.872738i | \(0.662342\pi\) | |||||||
\(164\) | −859.445 | + | 624.423i | −0.409216 | + | 0.297313i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1484.60 | − | 1078.63i | −0.694140 | − | 0.504323i | ||||
\(167\) | −105.206 | − | 323.790i | −0.0487489 | − | 0.150034i | 0.923719 | − | 0.383071i | \(-0.125134\pi\) |
−0.972468 | + | 0.233037i | \(0.925134\pi\) | |||||||
\(168\) | −39.3428 | −0.0180676 | ||||||||
\(169\) | −632.124 | − | 1945.48i | −0.287722 | − | 0.885516i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 420.110 | − | 1292.97i | 0.187875 | − | 0.578220i | ||||
\(172\) | 128.197 | − | 394.550i | 0.0568311 | − | 0.174908i | ||||
\(173\) | 1762.17 | − | 1280.29i | 0.774423 | − | 0.562651i | −0.128877 | − | 0.991661i | \(-0.541137\pi\) |
0.903300 | + | 0.429009i | \(0.141137\pi\) | |||||||
\(174\) | −119.152 | −0.0519133 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −35.3696 | −0.0151482 | ||||||||
\(177\) | −110.081 | + | 79.9787i | −0.0467470 | + | 0.0339637i | ||||
\(178\) | −805.141 | + | 2477.97i | −0.339033 | + | 1.04344i | ||||
\(179\) | −1063.04 | + | 3271.69i | −0.443884 | + | 1.36613i | 0.439820 | + | 0.898086i | \(0.355042\pi\) |
−0.883703 | + | 0.468047i | \(0.844958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −624.898 | − | 1923.24i | −0.256621 | − | 0.789797i | −0.993506 | − | 0.113779i | \(-0.963704\pi\) |
0.736886 | − | 0.676018i | \(-0.236296\pi\) | |||||||
\(182\) | −490.062 | −0.199592 | ||||||||
\(183\) | −38.9899 | − | 119.999i | −0.0157498 | − | 0.0484730i | ||||
\(184\) | −1289.99 | − | 937.229i | −0.516842 | − | 0.375508i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.4898 | + | 14.8867i | −0.00807732 | + | 0.00586852i | ||||
\(187\) | 133.124 | + | 96.7204i | 0.0520588 | + | 0.0378230i | ||||
\(188\) | 1331.78 | + | 967.598i | 0.516651 | + | 0.375369i | ||||
\(189\) | 214.603 | − | 155.918i | 0.0825930 | − | 0.0600074i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3904.88 | − | 2837.06i | −1.47930 | − | 1.07478i | −0.977780 | − | 0.209633i | \(-0.932773\pi\) |
−0.501523 | − | 0.865144i | \(-0.667227\pi\) | |||||||
\(192\) | 4.88409 | + | 15.0317i | 0.00183583 | + | 0.00565010i | ||||
\(193\) | −3075.17 | −1.14692 | −0.573460 | − | 0.819233i | \(-0.694399\pi\) | ||||
−0.573460 | + | 0.819233i | \(0.694399\pi\) | |||||||
\(194\) | −274.378 | − | 844.450i | −0.101542 | − | 0.312515i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 66.2025 | − | 203.750i | 0.0241263 | − | 0.0742530i | ||||
\(197\) | −1308.56 | + | 4027.34i | −0.473255 | + | 1.45653i | 0.375042 | + | 0.927008i | \(0.377628\pi\) |
−0.848297 | + | 0.529521i | \(0.822372\pi\) | |||||||
\(198\) | 96.3561 | − | 70.0068i | 0.0345845 | − | 0.0251271i | ||||
\(199\) | 4126.17 | 1.46983 | 0.734915 | − | 0.678159i | \(-0.237222\pi\) | ||||
0.734915 | + | 0.678159i | \(0.237222\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.8310 | 0.00660814 | ||||||||
\(202\) | −798.273 | + | 579.979i | −0.278051 | + | 0.202016i | ||||
\(203\) | 1484.52 | − | 4568.89i | 0.513267 | − | 1.57967i | ||||
\(204\) | 22.7224 | − | 69.9322i | 0.00779845 | − | 0.0240012i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1063.81 | + | 3274.06i | 0.359801 | + | 1.10735i | ||||
\(207\) | 5369.31 | 1.80287 | ||||||||
\(208\) | 60.8372 | + | 187.238i | 0.0202803 | + | 0.0624163i | ||||
\(209\) | −90.2540 | − | 65.5734i | −0.0298708 | − | 0.0217024i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4109.67 | − | 2985.85i | 1.34086 | − | 0.974192i | 0.341449 | − | 0.939900i | \(-0.389082\pi\) |
0.999412 | − | 0.0342918i | \(-0.0109176\pi\) | |||||||
\(212\) | 1392.43 | + | 1011.66i | 0.451098 | + | 0.327742i | ||||
\(213\) | 170.951 | + | 124.203i | 0.0549925 | + | 0.0399544i | ||||
\(214\) | 2007.99 | − | 1458.89i | 0.641416 | − | 0.466016i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −86.2129 | − | 62.6373i | −0.0271576 | − | 0.0197312i | ||||
\(217\) | −315.547 | − | 971.153i | −0.0987129 | − | 0.303807i | ||||
\(218\) | −353.438 | −0.109807 | ||||||||
\(219\) | 39.4251 | + | 121.338i | 0.0121649 | + | 0.0374396i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 283.034 | − | 871.089i | 0.0861490 | − | 0.265139i | ||||
\(222\) | 42.4484 | − | 130.643i | 0.0128331 | − | 0.0394962i | ||||
\(223\) | 3992.51 | − | 2900.73i | 1.19892 | − | 0.871064i | 0.204740 | − | 0.978816i | \(-0.434365\pi\) |
0.994178 | + | 0.107752i | \(0.0343653\pi\) | |||||||
\(224\) | −637.241 | −0.190078 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 383.492 | 0.112874 | ||||||||
\(227\) | −564.855 | + | 410.391i | −0.165158 | + | 0.119994i | −0.667294 | − | 0.744794i | \(-0.732548\pi\) |
0.502136 | + | 0.864788i | \(0.332548\pi\) | |||||||
\(228\) | −15.4050 | + | 47.4119i | −0.00447467 | + | 0.0137716i | ||||
\(229\) | 1916.69 | − | 5898.95i | 0.553092 | − | 1.70224i | −0.147836 | − | 0.989012i | \(-0.547231\pi\) |
0.700929 | − | 0.713231i | \(-0.252769\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.35945 | − | 10.3393i | −0.000956863 | − | 0.00294492i | ||||
\(232\) | −1929.93 | −0.546146 | ||||||||
\(233\) | −844.535 | − | 2599.21i | −0.237456 | − | 0.730815i | −0.996786 | − | 0.0801094i | \(-0.974473\pi\) |
0.759330 | − | 0.650706i | \(-0.225527\pi\) | |||||||
\(234\) | −536.335 | − | 389.670i | −0.149835 | − | 0.108861i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1783.00 | + | 1295.43i | −0.491794 | + | 0.357310i | ||||
\(237\) | −27.2223 | − | 19.7781i | −0.00746108 | − | 0.00542079i | ||||
\(238\) | 2398.45 | + | 1742.58i | 0.653229 | + | 0.474599i | ||||
\(239\) | 1197.49 | − | 870.027i | 0.324097 | − | 0.235470i | −0.413825 | − | 0.910357i | \(-0.635807\pi\) |
0.737922 | + | 0.674886i | \(0.235807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −209.377 | − | 152.121i | −0.0559633 | − | 0.0406597i | 0.559452 | − | 0.828863i | \(-0.311012\pi\) |
−0.615415 | + | 0.788203i | \(0.711012\pi\) | |||||||
\(242\) | 819.583 | + | 2522.42i | 0.217706 | + | 0.670029i | ||||
\(243\) | 538.470 | 0.142152 | ||||||||
\(244\) | −631.525 | − | 1943.63i | −0.165694 | − | 0.509952i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −40.5354 | + | 124.755i | −0.0105059 | + | 0.0323337i | ||||
\(247\) | −191.888 | + | 590.571i | −0.0494314 | + | 0.152134i | ||||
\(248\) | −331.875 | + | 241.122i | −0.0849762 | + | 0.0617388i | ||||
\(249\) | −226.591 | −0.0576693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3432.35 | −0.863139 | −0.431570 | − | 0.902080i | \(-0.642040\pi\) | ||||
−0.431570 | + | 0.902080i | \(0.642040\pi\) | |||||||
\(252\) | 1736.01 | − | 1261.29i | 0.433963 | − | 0.315292i | ||||
\(253\) | 136.154 | − | 419.038i | 0.0338336 | − | 0.104129i | ||||
\(254\) | 189.950 | − | 584.607i | 0.0469234 | − | 0.144415i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 79.1084 | + | 243.470i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −3106.91 | −0.754100 | −0.377050 | − | 0.926193i | \(-0.623061\pi\) | ||||
−0.377050 | + | 0.926193i | \(0.623061\pi\) | |||||||
\(258\) | −15.8296 | − | 48.7185i | −0.00381980 | − | 0.0117561i | ||||
\(259\) | 4480.62 | + | 3255.36i | 1.07495 | + | 0.780998i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5257.63 | − | 3819.89i | 1.24689 | − | 0.905921i | ||||
\(262\) | 4546.18 | + | 3302.99i | 1.07200 | + | 0.778853i | ||||
\(263\) | 4010.07 | + | 2913.49i | 0.940195 | + | 0.683092i | 0.948468 | − | 0.316874i | \(-0.102633\pi\) |
−0.00827224 | + | 0.999966i | \(0.502633\pi\) | |||||||
\(264\) | −3.53329 | + | 2.56708i | −0.000823708 | + | 0.000598459i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1626.07 | − | 1181.41i | −0.374816 | − | 0.272320i | ||||
\(267\) | 99.4177 | + | 305.976i | 0.0227875 | + | 0.0701327i | ||||
\(268\) | 305.008 | 0.0695200 | ||||||||
\(269\) | 740.660 | + | 2279.52i | 0.167877 | + | 0.516671i | 0.999237 | − | 0.0390628i | \(-0.0124373\pi\) |
−0.831360 | + | 0.555734i | \(0.812437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2005.70 | + | 6172.92i | −0.449586 | + | 1.38368i | 0.427789 | + | 0.903879i | \(0.359293\pi\) |
−0.877375 | + | 0.479805i | \(0.840707\pi\) | |||||||
\(272\) | 368.037 | − | 1132.70i | 0.0820424 | − | 0.252501i | ||||
\(273\) | −48.9553 | + | 35.5681i | −0.0108532 | + | 0.00788528i | ||||
\(274\) | −3921.74 | −0.864674 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −196.888 | −0.0429393 | ||||||||
\(277\) | 3077.41 | − | 2235.87i | 0.667521 | − | 0.484983i | −0.201673 | − | 0.979453i | \(-0.564638\pi\) |
0.869195 | + | 0.494470i | \(0.164638\pi\) | |||||||
\(278\) | 975.598 | − | 3002.58i | 0.210477 | − | 0.647780i | ||||
\(279\) | 426.866 | − | 1313.76i | 0.0915978 | − | 0.281909i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 78.9690 | + | 243.042i | 0.0167647 | + | 0.0515966i | 0.959089 | − | 0.283105i | \(-0.0913645\pi\) |
−0.942324 | + | 0.334702i | \(0.891364\pi\) | |||||||
\(282\) | 203.268 | 0.0429234 | ||||||||
\(283\) | −633.484 | − | 1949.66i | −0.133063 | − | 0.409525i | 0.862221 | − | 0.506532i | \(-0.169073\pi\) |
−0.995284 | + | 0.0970075i | \(0.969073\pi\) | |||||||
\(284\) | 2768.92 | + | 2011.74i | 0.578540 | + | 0.420334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −44.0113 | + | 31.9761i | −0.00909945 | + | 0.00661114i | ||||
\(287\) | −4278.70 | − | 3108.66i | −0.880013 | − | 0.639367i | ||||
\(288\) | −697.412 | − | 506.699i | −0.142692 | − | 0.103672i | ||||
\(289\) | −507.968 | + | 369.060i | −0.103393 | + | 0.0751191i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −88.6986 | − | 64.4433i | −0.0178681 | − | 0.0129819i | ||||
\(292\) | 638.574 | + | 1965.33i | 0.127979 | + | 0.393878i | ||||
\(293\) | −6743.02 | −1.34448 | −0.672238 | − | 0.740335i | \(-0.734667\pi\) | ||||
−0.672238 | + | 0.740335i | \(0.734667\pi\) | |||||||
\(294\) | −8.17459 | − | 25.1588i | −0.00162160 | − | 0.00499078i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 687.542 | − | 2116.04i | 0.135009 | − | 0.415514i | ||||
\(297\) | 9.09948 | − | 28.0053i | 0.00177780 | − | 0.00547150i | ||||
\(298\) | −2343.81 | + | 1702.87i | −0.455614 | + | 0.331023i | ||||
\(299\) | −2452.47 | −0.474348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2065.33 | 0.395494 | ||||||||
\(302\) | −2920.49 | + | 2121.86i | −0.556475 | + | 0.404303i | ||||
\(303\) | −37.6503 | + | 115.876i | −0.00713845 | + | 0.0219699i | ||||
\(304\) | −249.518 | + | 767.937i | −0.0470751 | + | 0.144882i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1239.32 | + | 3814.24i | 0.231527 | + | 0.712566i | ||||
\(307\) | 4999.71 | 0.929474 | 0.464737 | − | 0.885449i | \(-0.346149\pi\) | ||||
0.464737 | + | 0.885449i | \(0.346149\pi\) | |||||||
\(308\) | −54.4134 | − | 167.467i | −0.0100665 | − | 0.0309816i | ||||
\(309\) | 343.898 | + | 249.857i | 0.0633129 | + | 0.0459995i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5557.45 | + | 4037.73i | −1.01329 | + | 0.736201i | −0.964897 | − | 0.262627i | \(-0.915411\pi\) |
−0.0483961 | + | 0.998828i | \(0.515411\pi\) | |||||||
\(312\) | 19.6669 | + | 14.2889i | 0.00356865 | + | 0.00259278i | ||||
\(313\) | −363.202 | − | 263.882i | −0.0655892 | − | 0.0476533i | 0.554508 | − | 0.832179i | \(-0.312907\pi\) |
−0.620097 | + | 0.784525i | \(0.712907\pi\) | |||||||
\(314\) | −3234.42 | + | 2349.94i | −0.581301 | + | 0.422340i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −440.923 | − | 320.349i | −0.0784932 | − | 0.0570286i | ||||
\(317\) | −2069.60 | − | 6369.56i | −0.366688 | − | 1.12855i | −0.948917 | − | 0.315525i | \(-0.897819\pi\) |
0.582229 | − | 0.813025i | \(-0.302181\pi\) | |||||||
\(318\) | 212.524 | 0.0374772 | ||||||||
\(319\) | −164.795 | − | 507.186i | −0.0289239 | − | 0.0890186i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 94.7059 | − | 291.475i | 0.0164672 | − | 0.0506808i | ||||
\(322\) | 2453.03 | − | 7549.66i | 0.424541 | − | 1.30660i | ||||
\(323\) | 3039.11 | − | 2208.04i | 0.523531 | − | 0.380368i | ||||
\(324\) | 2896.25 | 0.496614 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 982.496 | 0.166918 | ||||||||
\(327\) | −35.3071 | + | 25.6521i | −0.00597091 | + | 0.00433812i | ||||
\(328\) | −656.558 | + | 2020.68i | −0.110525 | + | 0.340162i | ||||
\(329\) | −2532.52 | + | 7794.29i | −0.424384 | + | 1.30612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −130.339 | − | 401.141i | −0.0216437 | − | 0.0666125i | 0.939651 | − | 0.342134i | \(-0.111150\pi\) |
−0.961295 | + | 0.275521i | \(0.911150\pi\) | |||||||
\(332\) | −3670.13 | −0.606701 | ||||||||
\(333\) | 2315.21 | + | 7125.50i | 0.381000 | + | 1.17260i | ||||
\(334\) | −550.865 | − | 400.227i | −0.0902454 | − | 0.0655672i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −63.6580 | + | 46.2503i | −0.0103358 | + | 0.00750940i | ||||
\(337\) | −3694.07 | − | 2683.90i | −0.597118 | − | 0.433832i | 0.247737 | − | 0.968827i | \(-0.420313\pi\) |
−0.844855 | + | 0.534996i | \(0.820313\pi\) | |||||||
\(338\) | −3309.85 | − | 2404.74i | −0.532639 | − | 0.386985i | ||||
\(339\) | 38.3094 | − | 27.8334i | 0.00613770 | − | 0.00445930i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −91.7054 | − | 66.6279i | −0.0145634 | − | 0.0105809i | ||||
\(342\) | −840.220 | − | 2585.93i | −0.132848 | − | 0.408863i | ||||
\(343\) | −5763.87 | −0.907346 | ||||||||
\(344\) | −256.394 | − | 789.101i | −0.0401856 | − | 0.123679i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1346.18 | − | 4143.11i | 0.209165 | − | 0.643742i | ||||
\(347\) | −1897.93 | + | 5841.24i | −0.293621 | + | 0.903672i | 0.690060 | + | 0.723752i | \(0.257584\pi\) |
−0.983681 | + | 0.179920i | \(0.942416\pi\) | |||||||
\(348\) | −192.793 | + | 140.072i | −0.0296976 | + | 0.0215766i | ||||
\(349\) | −7456.55 | −1.14367 | −0.571834 | − | 0.820369i | \(-0.693768\pi\) | ||||
−0.571834 | + | 0.820369i | \(0.693768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −163.905 | −0.0249248 | ||||||||
\(352\) | −57.2292 | + | 41.5794i | −0.00866569 | + | 0.00629600i | ||||
\(353\) | −2041.06 | + | 6281.74i | −0.307747 | + | 0.947149i | 0.670890 | + | 0.741557i | \(0.265912\pi\) |
−0.978638 | + | 0.205592i | \(0.934088\pi\) | |||||||
\(354\) | −84.0946 | + | 258.816i | −0.0126259 | + | 0.0388586i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1610.28 | + | 4955.94i | 0.239732 | + | 0.737821i | ||||
\(357\) | 366.071 | 0.0542704 | ||||||||
\(358\) | 2126.08 | + | 6543.39i | 0.313873 | + | 0.966002i | ||||
\(359\) | −861.031 | − | 625.575i | −0.126583 | − | 0.0919683i | 0.522692 | − | 0.852522i | \(-0.324928\pi\) |
−0.649275 | + | 0.760553i | \(0.724928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3488.63 | − | 2534.64i | 0.508620 | − | 0.369534i | ||||
\(362\) | −3272.01 | − | 2377.25i | −0.475063 | − | 0.345154i | ||||
\(363\) | 264.948 | + | 192.496i | 0.0383089 | + | 0.0278331i | ||||
\(364\) | −792.937 | + | 576.102i | −0.114179 | + | 0.0829559i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −204.154 | − | 148.326i | −0.0291565 | − | 0.0211835i | ||||
\(367\) | 498.684 | + | 1534.79i | 0.0709295 | + | 0.218298i | 0.980237 | − | 0.197826i | \(-0.0633881\pi\) |
−0.909308 | + | 0.416124i | \(0.863388\pi\) | |||||||
\(368\) | −3189.02 | −0.451737 | ||||||||
\(369\) | −2210.88 | − | 6804.38i | −0.311907 | − | 0.959951i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2647.85 | + | 8149.23i | −0.370537 | + | 1.14040i | ||||
\(372\) | −15.6528 | + | 48.1743i | −0.00218161 | + | 0.00671430i | ||||
\(373\) | −6039.40 | + | 4387.88i | −0.838360 | + | 0.609105i | −0.921912 | − | 0.387399i | \(-0.873374\pi\) |
0.0835517 | + | 0.996503i | \(0.473374\pi\) | |||||||
\(374\) | 329.101 | 0.0455011 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3292.35 | 0.451569 | ||||||||
\(377\) | −2401.46 | + | 1744.76i | −0.328068 | + | 0.238355i | ||||
\(378\) | 163.942 | − | 504.562i | 0.0223076 | − | 0.0686558i | ||||
\(379\) | −2315.82 | + | 7127.35i | −0.313867 | + | 0.965982i | 0.662352 | + | 0.749193i | \(0.269558\pi\) |
−0.976218 | + | 0.216789i | \(0.930442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.4548 | − | 72.1864i | −0.00315387 | − | 0.00970662i | ||||
\(382\) | −9653.39 | −1.29296 | ||||||||
\(383\) | 1357.19 | + | 4177.01i | 0.181069 | + | 0.557272i | 0.999859 | − | 0.0168213i | \(-0.00535463\pi\) |
−0.818790 | + | 0.574093i | \(0.805355\pi\) | |||||||
\(384\) | 25.5734 | + | 18.5802i | 0.00339854 | + | 0.00246918i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4975.73 | + | 3615.08i | −0.656109 | + | 0.476691i | ||||
\(387\) | 2260.35 | + | 1642.24i | 0.296899 | + | 0.215710i | ||||
\(388\) | −1436.66 | − | 1043.80i | −0.187978 | − | 0.136574i | ||||
\(389\) | −4663.78 | + | 3388.43i | −0.607874 | + | 0.441646i | −0.848665 | − | 0.528931i | \(-0.822593\pi\) |
0.240791 | + | 0.970577i | \(0.422593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12002.8 | + | 8720.58i | 1.55246 | + | 1.12792i | ||||
\(392\) | −132.405 | − | 407.500i | −0.0170598 | − | 0.0525048i | ||||
\(393\) | 693.874 | 0.0890618 | ||||||||
\(394\) | 2617.13 | + | 8054.68i | 0.334642 | + | 1.02992i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 73.6095 | − | 226.547i | 0.00934095 | − | 0.0287485i | ||||
\(397\) | −493.669 | + | 1519.36i | −0.0624094 | + | 0.192076i | −0.977400 | − | 0.211399i | \(-0.932198\pi\) |
0.914990 | + | 0.403476i | \(0.132198\pi\) | |||||||
\(398\) | 6676.28 | − | 4850.60i | 0.840833 | − | 0.610901i | ||||
\(399\) | −248.184 | −0.0311398 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4722.70 | −0.588130 | −0.294065 | − | 0.955785i | \(-0.595008\pi\) | ||||
−0.294065 | + | 0.955785i | \(0.595008\pi\) | |||||||
\(402\) | 30.4692 | − | 22.1372i | 0.00378026 | − | 0.00274652i | ||||
\(403\) | −194.974 | + | 600.068i | −0.0241001 | + | 0.0741725i | ||||
\(404\) | −609.826 | + | 1876.85i | −0.0750990 | + | 0.231131i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2969.05 | − | 9137.79i | −0.362934 | − | 1.11700i | ||||
\(407\) | 614.804 | 0.0748764 | ||||||||
\(408\) | −45.4447 | − | 139.864i | −0.00551434 | − | 0.0169714i | ||||
\(409\) | −4715.79 | − | 3426.22i | −0.570124 | − | 0.414219i | 0.265026 | − | 0.964241i | \(-0.414619\pi\) |
−0.835150 | + | 0.550022i | \(0.814619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −391.767 | + | 284.635i | −0.0470181 | + | 0.0341606i | ||||
\(412\) | 5570.17 | + | 4046.96i | 0.666074 | + | 0.483931i | ||||
\(413\) | −8876.57 | − | 6449.21i | −1.05760 | − | 0.768389i | ||||
\(414\) | 8687.73 | − | 6312.01i | 1.03135 | − | 0.749319i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 318.548 | + | 231.438i | 0.0375435 | + | 0.0272769i | ||||
\(417\) | −120.466 | − | 370.755i | −0.0141468 | − | 0.0435394i | ||||
\(418\) | −223.120 | −0.0261080 | ||||||||
\(419\) | 351.782 | + | 1082.68i | 0.0410160 | + | 0.126234i | 0.969468 | − | 0.245219i | \(-0.0788597\pi\) |
−0.928452 | + | 0.371453i | \(0.878860\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −317.103 | + | 975.942i | −0.0367094 | + | 0.112980i | −0.967732 | − | 0.251982i | \(-0.918918\pi\) |
0.931023 | + | 0.364961i | \(0.118918\pi\) | |||||||
\(422\) | 3139.51 | − | 9662.42i | 0.362154 | − | 1.11460i | ||||
\(423\) | −8969.24 | + | 6516.53i | −1.03097 | + | 0.749042i | ||||
\(424\) | 3442.28 | 0.394274 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 422.615 | 0.0480652 | ||||||||
\(427\) | 8231.13 | − | 5980.27i | 0.932863 | − | 0.677765i | ||||
\(428\) | 1533.96 | − | 4721.06i | 0.173241 | − | 0.533180i | ||||
\(429\) | −2.07578 | + | 6.38859i | −0.000233612 | + | 0.000718983i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1729.47 | − | 5322.77i | −0.193285 | − | 0.594870i | −0.999992 | − | 0.00391889i | \(-0.998753\pi\) |
0.806707 | − | 0.590951i | \(-0.201247\pi\) | |||||||
\(432\) | −213.130 | −0.0237366 | ||||||||
\(433\) | −271.516 | − | 835.639i | −0.0301344 | − | 0.0927443i | 0.934858 | − | 0.355022i | \(-0.115526\pi\) |
−0.964993 | + | 0.262277i | \(0.915526\pi\) | |||||||
\(434\) | −1652.22 | − | 1200.41i | −0.182740 | − | 0.132769i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −571.875 | + | 415.491i | −0.0628161 | + | 0.0456386i | ||||
\(437\) | −8137.55 | − | 5912.28i | −0.890782 | − | 0.647191i | ||||
\(438\) | 206.433 | + | 149.982i | 0.0225199 | + | 0.0163617i | ||||
\(439\) | 5667.04 | − | 4117.35i | 0.616112 | − | 0.447632i | −0.235449 | − | 0.971887i | \(-0.575656\pi\) |
0.851561 | + | 0.524255i | \(0.175656\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1167.27 | + | 848.071i | 0.126041 | + | 0.0915744i | ||||
\(442\) | −566.068 | − | 1742.18i | −0.0609166 | − | 0.187482i | ||||
\(443\) | 17736.5 | 1.90223 | 0.951114 | − | 0.308839i | \(-0.0999405\pi\) | ||||
0.951114 | + | 0.308839i | \(0.0999405\pi\) | |||||||
\(444\) | −84.8968 | − | 261.285i | −0.00907437 | − | 0.0279281i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3050.01 | − | 9386.97i | 0.323816 | − | 0.996605i | ||||
\(447\) | −110.545 | + | 340.222i | −0.0116971 | + | 0.0359999i | ||||
\(448\) | −1031.08 | + | 749.122i | −0.108736 | + | 0.0790015i | ||||
\(449\) | 4292.26 | 0.451146 | 0.225573 | − | 0.974226i | \(-0.427575\pi\) | ||||
0.225573 | + | 0.974226i | \(0.427575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −587.097 | −0.0612979 | ||||||||
\(452\) | 620.502 | − | 450.821i | 0.0645707 | − | 0.0469134i | ||||
\(453\) | −137.744 | + | 423.932i | −0.0142865 | + | 0.0439692i | ||||
\(454\) | −431.511 | + | 1328.05i | −0.0446075 | + | 0.137288i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.8101 | + | 94.8237i | 0.00316407 | + | 0.00973800i | ||||
\(457\) | 17409.6 | 1.78203 | 0.891015 | − | 0.453973i | \(-0.149994\pi\) | ||||
0.891015 | + | 0.453973i | \(0.149994\pi\) | |||||||
\(458\) | −3833.37 | − | 11797.9i | −0.391095 | − | 1.20367i | ||||
\(459\) | 802.180 | + | 582.818i | 0.0815742 | + | 0.0592671i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11842.5 | + | 8604.09i | −1.19644 | + | 0.869267i | −0.993930 | − | 0.110012i | \(-0.964911\pi\) |
−0.202513 | + | 0.979279i | \(0.564911\pi\) | |||||||
\(462\) | −17.5903 | − | 12.7801i | −0.00177137 | − | 0.00128698i | ||||
\(463\) | 6102.97 | + | 4434.07i | 0.612590 | + | 0.445072i | 0.850325 | − | 0.526258i | \(-0.176405\pi\) |
−0.237736 | + | 0.971330i | \(0.576405\pi\) | |||||||
\(464\) | −3122.69 | + | 2268.77i | −0.312429 | + | 0.226993i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4422.04 | − | 3212.80i | −0.439586 | − | 0.319378i | ||||
\(467\) | 1090.40 | + | 3355.89i | 0.108046 | + | 0.332532i | 0.990433 | − | 0.137992i | \(-0.0440649\pi\) |
−0.882387 | + | 0.470524i | \(0.844065\pi\) | |||||||
\(468\) | −1325.89 | −0.130960 | ||||||||
\(469\) | 469.232 | + | 1444.15i | 0.0461986 | + | 0.142185i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −152.550 | + | 469.501i | −0.0149239 | + | 0.0459309i | ||||
\(472\) | −1362.09 | + | 4192.09i | −0.132829 | + | 0.408806i | ||||
\(473\) | 185.483 | − | 134.761i | 0.0180307 | − | 0.0131001i | ||||
\(474\) | −67.2971 | −0.00652122 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5929.30 | 0.570943 | ||||||||
\(477\) | −9377.69 | + | 6813.29i | −0.900157 | + | 0.654002i | ||||
\(478\) | 914.801 | − | 2815.47i | 0.0875356 | − | 0.269407i | ||||
\(479\) | 2295.73 | − | 7065.53i | 0.218987 | − | 0.673971i | −0.779860 | − | 0.625954i | \(-0.784710\pi\) |
0.998847 | − | 0.0480172i | \(-0.0152902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1057.49 | − | 3254.62i | −0.100244 | − | 0.308520i | ||||
\(482\) | −517.608 | −0.0489137 | ||||||||
\(483\) | −302.897 | − | 932.221i | −0.0285348 | − | 0.0878210i | ||||
\(484\) | 4291.39 | + | 3117.88i | 0.403023 | + | 0.292814i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 871.262 | − | 633.009i | 0.0813195 | − | 0.0590820i | ||||
\(487\) | 11340.5 | + | 8239.35i | 1.05521 | + | 0.766654i | 0.973196 | − | 0.229977i | \(-0.0738651\pi\) |
0.0820130 | + | 0.996631i | \(0.473865\pi\) | |||||||
\(488\) | −3306.71 | − | 2402.46i | −0.306737 | − | 0.222857i | ||||
\(489\) | 98.1477 | − | 71.3085i | 0.00907647 | − | 0.00659444i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2914.25 | + | 2117.33i | 0.267858 | + | 0.194610i | 0.713604 | − | 0.700549i | \(-0.247062\pi\) |
−0.445746 | + | 0.895159i | \(0.647062\pi\) | |||||||
\(492\) | 81.0708 | + | 249.510i | 0.00742877 | + | 0.0228634i | ||||
\(493\) | 17957.3 | 1.64048 | ||||||||
\(494\) | 383.776 | + | 1181.14i | 0.0349533 | + | 0.107575i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −253.530 | + | 780.286i | −0.0229513 | + | 0.0706368i | ||||
\(497\) | −5265.38 | + | 16205.2i | −0.475220 | + | 1.46258i | ||||
\(498\) | −366.633 | + | 266.374i | −0.0329904 | + | 0.0239689i | ||||
\(499\) | 4905.02 | 0.440037 | 0.220019 | − | 0.975496i | \(-0.429388\pi\) | ||||
0.220019 | + | 0.975496i | \(0.429388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −84.0774 | −0.00749760 | ||||||||
\(502\) | −5553.66 | + | 4034.97i | −0.493769 | + | 0.358744i | ||||
\(503\) | 5019.49 | − | 15448.4i | 0.444946 | − | 1.36940i | −0.437597 | − | 0.899171i | \(-0.644170\pi\) |
0.882543 | − | 0.470232i | \(-0.155830\pi\) | |||||||
\(504\) | 1326.20 | − | 4081.61i | 0.117209 | − | 0.360733i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −272.307 | − | 838.076i | −0.0239240 | − | 0.0736304i | ||||
\(507\) | −505.175 | −0.0442517 | ||||||||
\(508\) | −379.901 | − | 1169.21i | −0.0331798 | − | 0.102117i | ||||
\(509\) | −11603.2 | − | 8430.21i | −1.01042 | − | 0.734111i | −0.0461207 | − | 0.998936i | \(-0.514686\pi\) |
−0.964297 | + | 0.264825i | \(0.914686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8323.01 | + | 6047.02i | −0.720525 | + | 0.523492i | ||||
\(512\) | 414.217 | + | 300.946i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −543.853 | − | 395.132i | −0.0468064 | − | 0.0340068i | ||||
\(514\) | −5027.08 | + | 3652.39i | −0.431391 | + | 0.313424i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −82.8849 | − | 60.2194i | −0.00707133 | − | 0.00513762i | ||||
\(517\) | 281.131 | + | 865.232i | 0.0239151 | + | 0.0736032i | ||||
\(518\) | 11076.7 | 0.939542 | ||||||||
\(519\) | −166.224 | − | 511.585i | −0.0140586 | − | 0.0432680i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3425.75 | − | 10543.4i | 0.288071 | − | 0.886591i | −0.697390 | − | 0.716692i | \(-0.745656\pi\) |
0.985461 | − | 0.169900i | \(-0.0543444\pi\) | |||||||
\(522\) | 4016.47 | − | 12361.4i | 0.336774 | − | 1.03649i | ||||
\(523\) | −13.3330 | + | 9.68700i | −0.00111475 | + | 0.000809910i | −0.588342 | − | 0.808612i | \(-0.700219\pi\) |
0.587228 | + | 0.809422i | \(0.300219\pi\) | |||||||
\(524\) | 11238.8 | 0.936962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9913.43 | 0.821761 | ||||||||
\(527\) | 3087.98 | − | 2243.55i | 0.255246 | − | 0.185447i | ||||
\(528\) | −2.69919 | + | 8.30726i | −0.000222476 | + | 0.000684710i | ||||
\(529\) | 8516.18 | − | 26210.1i | 0.699941 | − | 2.15420i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4586.67 | − | 14116.3i | −0.374849 | − | 1.15367i | ||||
\(532\) | −4019.88 | −0.327601 | ||||||||
\(533\) | 1009.83 | + | 3107.95i | 0.0820652 | + | 0.252571i | ||||
\(534\) | 520.558 | + | 378.207i | 0.0421849 | + | 0.0306491i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 493.514 | − | 358.559i | 0.0397697 | − | 0.0288944i | ||||
\(537\) | 687.299 | + | 499.352i | 0.0552312 | + | 0.0401278i | ||||
\(538\) | 3878.15 | + | 2817.64i | 0.310778 | + | 0.225794i | ||||
\(539\) | 95.7854 | − | 69.5921i | 0.00765448 | − | 0.00556131i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19911.1 | + | 14466.2i | 1.58233 | + | 1.14963i | 0.913957 | + | 0.405811i | \(0.133011\pi\) |
0.668378 | + | 0.743822i | \(0.266989\pi\) | |||||||
\(542\) | 4011.41 | + | 12345.8i | 0.317905 | + | 0.978413i | ||||
\(543\) | −499.400 | −0.0394683 | ||||||||
\(544\) | −736.075 | − | 2265.40i | −0.0580128 | − | 0.178545i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −37.3986 | + | 115.101i | −0.00293134 | + | 0.00902173i | ||||
\(547\) | 1642.96 | − | 5056.52i | 0.128424 | − | 0.395249i | −0.866085 | − | 0.499897i | \(-0.833371\pi\) |
0.994509 | + | 0.104647i | \(0.0333714\pi\) | |||||||
\(548\) | −6345.50 | + | 4610.28i | −0.494647 | + | 0.359382i | ||||
\(549\) | 13763.5 | 1.06997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12174.5 | −0.941288 | ||||||||
\(552\) | −318.571 | + | 231.455i | −0.0245639 | + | 0.0178467i | ||||
\(553\) | 838.458 | − | 2580.51i | 0.0644753 | − | 0.198435i | ||||
\(554\) | 2350.93 | − | 7235.42i | 0.180291 | − | 0.554880i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1951.20 | − | 6005.17i | −0.148829 | − | 0.458050i | ||||
\(557\) | 9362.34 | 0.712199 | 0.356100 | − | 0.934448i | \(-0.384106\pi\) | ||||
0.356100 | + | 0.934448i | \(0.384106\pi\) | |||||||
\(558\) | −853.732 | − | 2627.52i | −0.0647694 | − | 0.199340i | ||||
\(559\) | −1032.43 | − | 750.105i | −0.0781166 | − | 0.0567550i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.8760 | − | 23.8858i | 0.00247420 | − | 0.00179761i | ||||
\(562\) | 413.487 | + | 300.416i | 0.0310354 | + | 0.0225485i | ||||
\(563\) | −9823.74 | − | 7137.36i | −0.735384 | − | 0.534288i | 0.155878 | − | 0.987776i | \(-0.450179\pi\) |
−0.891262 | + | 0.453488i | \(0.850179\pi\) | |||||||
\(564\) | 328.894 | − | 238.955i | 0.0245548 | − | 0.0178401i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3316.97 | − | 2409.92i | −0.246330 | − | 0.178969i | ||||
\(567\) | 4455.67 | + | 13713.1i | 0.330019 | + | 1.01569i | ||||
\(568\) | 6845.16 | 0.505663 | ||||||||
\(569\) | 2883.62 | + | 8874.88i | 0.212456 | + | 0.653874i | 0.999324 | + | 0.0367524i | \(0.0117013\pi\) |
−0.786868 | + | 0.617121i | \(0.788299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5676.39 | − | 17470.1i | 0.416024 | − | 1.28039i | −0.495308 | − | 0.868717i | \(-0.664945\pi\) |
0.911332 | − | 0.411672i | \(-0.135055\pi\) | |||||||
\(572\) | −33.6217 | + | 103.477i | −0.00245768 | + | 0.00756396i | ||||
\(573\) | −964.337 | + | 700.632i | −0.0703068 | + | 0.0510809i | ||||
\(574\) | −10577.5 | −0.769160 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1724.10 | −0.124718 | ||||||||
\(577\) | 233.016 | − | 169.296i | 0.0168121 | − | 0.0122147i | −0.579347 | − | 0.815081i | \(-0.696693\pi\) |
0.596160 | + | 0.802866i | \(0.296693\pi\) | |||||||
\(578\) | −388.053 | + | 1194.30i | −0.0279254 | + | 0.0859455i | ||||
\(579\) | −234.678 | + | 722.266i | −0.0168444 | + | 0.0518417i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5646.22 | − | 17377.3i | −0.403175 | − | 1.24085i | ||||
\(582\) | −219.275 | −0.0156173 | ||||||||
\(583\) | 293.933 | + | 904.633i | 0.0208807 | + | 0.0642643i | ||||
\(584\) | 3343.62 | + | 2429.28i | 0.236918 | + | 0.172131i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10910.4 | + | 7926.90i | −0.769123 | + | 0.558801i | ||||
\(587\) | −12259.0 | − | 8906.66i | −0.861979 | − | 0.626264i | 0.0664436 | − | 0.997790i | \(-0.478835\pi\) |
−0.928423 | + | 0.371526i | \(0.878835\pi\) | |||||||
\(588\) | −42.8027 | − | 31.0980i | −0.00300196 | − | 0.00218105i | ||||
\(589\) | −2093.55 | + | 1521.06i | −0.146457 | + | 0.106407i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 846.041 | + | 614.685i | 0.0588858 | + | 0.0427830i | ||||
\(592\) | −1375.08 | − | 4232.08i | −0.0954656 | − | 0.293813i | ||||
\(593\) | 8594.02 | 0.595133 | 0.297567 | − | 0.954701i | \(-0.403825\pi\) | ||||
0.297567 | + | 0.954701i | \(0.403825\pi\) | |||||||
\(594\) | −18.1990 | − | 56.0107i | −0.00125709 | − | 0.00386893i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1790.51 | + | 5510.62i | −0.123057 | + | 0.378731i | ||||
\(597\) | 314.884 | − | 969.114i | 0.0215869 | − | 0.0664375i | ||||
\(598\) | −3968.18 | + | 2883.05i | −0.271356 | + | 0.197152i | ||||
\(599\) | −12431.0 | −0.847942 | −0.423971 | − | 0.905676i | \(-0.639364\pi\) | ||||
−0.423971 | + | 0.905676i | \(0.639364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16440.3 | 1.11583 | 0.557913 | − | 0.829899i | \(-0.311602\pi\) | ||||
0.557913 | + | 0.829899i | \(0.311602\pi\) | |||||||
\(602\) | 3341.78 | − | 2427.94i | 0.226247 | − | 0.164378i | ||||
\(603\) | −634.769 | + | 1953.62i | −0.0428686 | + | 0.131936i | ||||
\(604\) | −2231.06 | + | 6866.49i | −0.150299 | + | 0.462572i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 75.3005 | + | 231.751i | 0.00504765 | + | 0.0155351i | ||||
\(607\) | −10367.1 | −0.693228 | −0.346614 | − | 0.938008i | \(-0.612669\pi\) | ||||
−0.346614 | + | 0.938008i | \(0.612669\pi\) | |||||||
\(608\) | 499.035 | + | 1535.87i | 0.0332871 | + | 0.102447i | ||||
\(609\) | −959.807 | − | 697.341i | −0.0638643 | − | 0.0464001i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4096.76 | − | 2976.47i | 0.271256 | − | 0.197079i | ||||
\(612\) | 6489.16 | + | 4714.65i | 0.428609 | + | 0.311403i | ||||
\(613\) | −11720.9 | − | 8515.76i | −0.772274 | − | 0.561090i | 0.130376 | − | 0.991465i | \(-0.458382\pi\) |
−0.902650 | + | 0.430375i | \(0.858382\pi\) | |||||||
\(614\) | 8089.70 | − | 5877.51i | 0.531716 | − | 0.386314i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −284.912 | − | 207.001i | −0.0186355 | − | 0.0135395i | ||||
\(617\) | 797.436 | + | 2454.25i | 0.0520317 | + | 0.160137i | 0.973696 | − | 0.227851i | \(-0.0731700\pi\) |
−0.921664 | + | 0.387988i | \(0.873170\pi\) | |||||||
\(618\) | 850.163 | 0.0553375 | ||||||||
\(619\) | 1815.76 | + | 5588.34i | 0.117903 | + | 0.362867i | 0.992541 | − | 0.121908i | \(-0.0389014\pi\) |
−0.874639 | + | 0.484775i | \(0.838901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 820.435 | − | 2525.04i | 0.0530160 | − | 0.163166i | ||||
\(622\) | −4245.52 | + | 13066.4i | −0.273681 | + | 0.842304i | ||||
\(623\) | −20988.0 | + | 15248.7i | −1.34971 | + | 0.980618i | ||||
\(624\) | 48.6193 | 0.00311912 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −897.886 | −0.0573270 | ||||||||
\(627\) | −22.2889 | + | 16.1938i | −0.00141967 | + | 0.00103145i | ||||
\(628\) | −2470.87 | + | 7604.57i | −0.157004 | + | 0.483209i | ||||
\(629\) | −6397.33 | + | 19689.0i | −0.405530 | + | 1.24809i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1241.27 | − | 3820.25i | −0.0783111 | − | 0.241017i | 0.904235 | − | 0.427035i | \(-0.140442\pi\) |
−0.982546 | + | 0.186018i | \(0.940442\pi\) | |||||||
\(632\) | −1090.02 | −0.0686055 | ||||||||
\(633\) | −387.662 | − | 1193.10i | −0.0243415 | − | 0.0749156i | ||||
\(634\) | −10836.5 | − | 7873.21i | −0.678824 | − | 0.493194i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 343.871 | − | 249.837i | 0.0214393 | − | 0.0155766i | ||||
\(637\) | −533.158 | − | 387.362i | −0.0331625 | − | 0.0240940i | ||||
\(638\) | −862.876 | − | 626.916i | −0.0535448 | − | 0.0389026i | ||||
\(639\) | −18648.0 | + | 13548.6i | −1.15447 | + | 0.838769i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3281.65 | − | 2384.26i | −0.202211 | − | 0.146915i | 0.482071 | − | 0.876132i | \(-0.339885\pi\) |
−0.684283 | + | 0.729217i | \(0.739885\pi\) | |||||||
\(642\) | −189.412 | − | 582.950i | −0.0116441 | − | 0.0358367i | ||||
\(643\) | 3520.39 | 0.215911 | 0.107955 | − | 0.994156i | \(-0.465570\pi\) | ||||
0.107955 | + | 0.994156i | \(0.465570\pi\) | |||||||
\(644\) | −4906.06 | − | 15099.3i | −0.300196 | − | 0.923907i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2321.67 | − | 7145.37i | 0.141401 | − | 0.435187i | ||||
\(647\) | −6582.66 | + | 20259.4i | −0.399986 | + | 1.23103i | 0.525023 | + | 0.851088i | \(0.324057\pi\) |
−0.925010 | + | 0.379944i | \(0.875943\pi\) | |||||||
\(648\) | 4686.24 | − | 3404.75i | 0.284094 | − | 0.206406i | ||||
\(649\) | −1217.99 | −0.0736676 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −252.176 | −0.0151821 | ||||||||
\(652\) | 1589.71 | − | 1154.99i | 0.0954876 | − | 0.0693758i | ||||
\(653\) | −2749.81 | + | 8463.06i | −0.164791 | + | 0.507175i | −0.999021 | − | 0.0442423i | \(-0.985913\pi\) |
0.834230 | + | 0.551417i | \(0.185913\pi\) | |||||||
\(654\) | −26.9723 | + | 83.0121i | −0.00161269 | + | 0.00496335i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1313.12 | + | 4041.35i | 0.0781533 | + | 0.240531i | ||||
\(657\) | −13917.2 | −0.826424 | ||||||||
\(658\) | 5065.04 | + | 15588.6i | 0.300085 | + | 0.923565i | ||||
\(659\) | 17979.8 | + | 13063.1i | 1.06281 | + | 0.772177i | 0.974606 | − | 0.223926i | \(-0.0718873\pi\) |
0.0882040 | + | 0.996102i | \(0.471887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22654.3 | + | 16459.3i | −1.33306 | + | 0.968522i | −0.333387 | + | 0.942790i | \(0.608192\pi\) |
−0.999669 | + | 0.0257322i | \(0.991808\pi\) | |||||||
\(662\) | −682.463 | − | 495.838i | −0.0400675 | − | 0.0291107i | ||||
\(663\) | −182.994 | − | 132.953i | −0.0107193 | − | 0.00778801i | ||||
\(664\) | −5938.40 | + | 4314.50i | −0.347070 | + | 0.252161i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12122.6 | + | 8807.60i | 0.705318 | + | 0.512444i | ||||
\(667\) | −14858.3 | − | 45729.3i | −0.862545 | − | 2.65464i | ||||
\(668\) | −1361.81 | −0.0788774 | ||||||||
\(669\) | −376.611 | − | 1159.09i | −0.0217648 | − | 0.0669850i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 349.012 | − | 1074.15i | 0.0200797 | − | 0.0617989i | ||||
\(672\) | −48.6304 | + | 149.669i | −0.00279161 | + | 0.00859168i | ||||
\(673\) | 17047.7 | − | 12385.9i | 0.976436 | − | 0.709422i | 0.0195266 | − | 0.999809i | \(-0.493784\pi\) |
0.956909 | + | 0.290387i | \(0.0937841\pi\) | |||||||
\(674\) | −9132.24 | −0.521900 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8182.39 | −0.465543 | ||||||||
\(677\) | 10063.0 | − | 7311.23i | 0.571277 | − | 0.415057i | −0.264292 | − | 0.964443i | \(-0.585138\pi\) |
0.835569 | + | 0.549386i | \(0.185138\pi\) | |||||||
\(678\) | 29.2658 | − | 90.0707i | 0.00165774 | − | 0.00510199i | ||||
\(679\) | 2731.96 | − | 8408.10i | 0.154408 | − | 0.475218i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.2824 | + | 163.986i | 0.00299822 | + | 0.00922756i | ||||
\(682\) | −226.708 | −0.0127289 | ||||||||
\(683\) | 1807.44 | + | 5562.74i | 0.101259 | + | 0.311643i | 0.988834 | − | 0.149020i | \(-0.0476118\pi\) |
−0.887575 | + | 0.460663i | \(0.847612\pi\) | |||||||
\(684\) | −4399.45 | − | 3196.39i | −0.245932 | − | 0.178680i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9326.13 | + | 6775.83i | −0.519058 | + | 0.377117i | ||||
\(687\) | −1239.22 | − | 900.345i | −0.0688197 | − | 0.0500004i | ||||
\(688\) | −1342.50 | − | 975.382i | −0.0743929 | − | 0.0540496i | ||||
\(689\) | 4283.33 | − | 3112.02i | 0.236839 | − | 0.172073i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5923.87 | + | 4303.94i | 0.326128 | + | 0.236946i | 0.738786 | − | 0.673940i | \(-0.235399\pi\) |
−0.412658 | + | 0.910886i | \(0.635399\pi\) | |||||||
\(692\) | −2692.35 | − | 8286.21i | −0.147902 | − | 0.455194i | ||||
\(693\) | 1185.89 | 0.0650048 | ||||||||
\(694\) | 3795.87 | + | 11682.5i | 0.207621 | + | 0.638993i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −147.280 | + | 453.282i | −0.00802105 | + | 0.0246862i | ||||
\(697\) | 6109.03 | − | 18801.7i | 0.331989 | − | 1.02176i | ||||
\(698\) | −12065.0 | + | 8765.70i | −0.654248 | + | 0.475339i | ||||
\(699\) | −674.927 | −0.0365209 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15238.8 | 0.821060 | 0.410530 | − | 0.911847i | \(-0.365344\pi\) | ||||
0.410530 | + | 0.911847i | \(0.365344\pi\) | |||||||
\(702\) | −265.204 | + | 192.682i | −0.0142585 | + | 0.0103594i | ||||
\(703\) | 4337.19 | − | 13348.5i | 0.232689 | − | 0.716143i | ||||
\(704\) | −43.7192 | + | 134.554i | −0.00234052 | + | 0.00720339i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4082.13 | + | 12563.5i | 0.217610 | + | 0.669735i | ||||
\(707\) | −9824.66 | −0.522623 | ||||||||
\(708\) | 168.189 | + | 517.633i | 0.00892787 | + | 0.0274772i | ||||
\(709\) | 9001.43 | + | 6539.92i | 0.476807 | + | 0.346420i | 0.800088 | − | 0.599883i | \(-0.204786\pi\) |
−0.323281 | + | 0.946303i | \(0.604786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2969.51 | − | 2157.47i | 0.156632 | − | 0.113800i | ||||
\(712\) | 8431.54 | + | 6125.88i | 0.443800 | + | 0.322439i | ||||
\(713\) | −8268.41 | − | 6007.35i | −0.434298 | − | 0.315536i | ||||
\(714\) | 592.315 | − | 430.342i | 0.0310460 | − | 0.0225562i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11132.3 | + | 8088.07i | 0.581051 | + | 0.422158i | ||||
\(717\) | −112.958 | − | 347.650i | −0.00588355 | − | 0.0181077i | ||||
\(718\) | −2128.59 | −0.110638 | ||||||||
\(719\) | −8073.67 | − | 24848.2i | −0.418772 | − | 1.28885i | −0.908833 | − | 0.417160i | \(-0.863026\pi\) |
0.490061 | − | 0.871688i | \(-0.336974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10592.2 | + | 32599.5i | −0.547122 | + | 1.68387i | ||||
\(722\) | 2665.07 | − | 8202.26i | 0.137374 | − | 0.422793i | ||||
\(723\) | −51.7071 | + | 37.5674i | −0.00265976 | + | 0.00193243i | ||||
\(724\) | −8088.85 | −0.415221 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 654.986 | 0.0334832 | ||||||||
\(727\) | −3162.84 | + | 2297.94i | −0.161352 | + | 0.117229i | −0.665532 | − | 0.746370i | \(-0.731795\pi\) |
0.504179 | + | 0.863599i | \(0.331795\pi\) | |||||||
\(728\) | −605.750 | + | 1864.31i | −0.0308387 | + | 0.0949118i | ||||
\(729\) | −6000.10 | + | 18466.4i | −0.304837 | + | 0.938191i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2385.66 | + | 7342.30i | 0.120707 | + | 0.371498i | ||||
\(732\) | −504.696 | −0.0254837 | ||||||||
\(733\) | 1440.84 | + | 4434.46i | 0.0726040 | + | 0.223452i | 0.980773 | − | 0.195151i | \(-0.0625197\pi\) |
−0.908169 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(734\) | 2611.15 | + | 1897.11i | 0.131307 | + | 0.0953999i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5159.94 | + | 3748.92i | −0.258421 | + | 0.187754i | ||||
\(737\) | 136.370 | + | 99.0787i | 0.00681582 | + | 0.00495198i | ||||
\(738\) | −11576.3 | − | 8410.67i | −0.577411 | − | 0.419514i | ||||
\(739\) | 14248.6 | − | 10352.2i | 0.709261 | − | 0.515308i | −0.173674 | − | 0.984803i | \(-0.555564\pi\) |
0.882935 | + | 0.469495i | \(0.155564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 124.064 | + | 90.1377i | 0.00615061 | + | 0.00446868i | ||||
\(742\) | 5295.69 | + | 16298.5i | 0.262009 | + | 0.806382i | ||||
\(743\) | −26680.2 | −1.31737 | −0.658683 | − | 0.752421i | \(-0.728886\pi\) | ||||
−0.658683 | + | 0.752421i | \(0.728886\pi\) | |||||||
\(744\) | 31.3056 | + | 96.3486i | 0.00154263 | + | 0.00474773i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4613.69 | + | 14199.5i | −0.226433 | + | 0.696890i | ||||
\(747\) | 7638.11 | − | 23507.7i | 0.374115 | − | 1.15141i | ||||
\(748\) | 532.497 | − | 386.881i | 0.0260294 | − | 0.0189115i | ||||
\(749\) | 24713.1 | 1.20560 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8017.53 | 0.389566 | 0.194783 | − | 0.980846i | \(-0.437600\pi\) | ||||
0.194783 | + | 0.980846i | \(0.437600\pi\) | |||||||
\(752\) | 5327.14 | − | 3870.39i | 0.258325 | − | 0.187684i | ||||
\(753\) | −261.936 | + | 806.157i | −0.0126766 | + | 0.0390146i | ||||
\(754\) | −1834.55 | + | 5646.17i | −0.0886081 | + | 0.272708i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −327.885 | − | 1009.12i | −0.0157739 | − | 0.0485470i | ||||
\(757\) | 4716.28 | 0.226441 | 0.113221 | − | 0.993570i | \(-0.463883\pi\) | ||||
0.113221 | + | 0.993570i | \(0.463883\pi\) | |||||||
\(758\) | 4631.63 | + | 14254.7i | 0.221937 | + | 0.683052i | ||||
\(759\) | −88.0291 | − | 63.9569i | −0.00420982 | − | 0.00305861i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4294.37 | − | 3120.04i | 0.204561 | − | 0.148622i | −0.480789 | − | 0.876837i | \(-0.659650\pi\) |
0.685349 | + | 0.728214i | \(0.259650\pi\) | |||||||
\(762\) | −122.811 | − | 89.2273i | −0.00583854 | − | 0.00424195i | ||||
\(763\) | −2847.05 | − | 2068.50i | −0.135085 | − | 0.0981452i | ||||
\(764\) | −15619.5 | + | 11348.2i | −0.739652 | + | 0.537388i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7106.35 | + | 5163.07i | 0.335200 | + | 0.243537i | ||||
\(767\) | 2095.00 | + | 6447.73i | 0.0986257 | + | 0.303539i | ||||
\(768\) | 63.2210 | 0.00297043 | ||||||||
\(769\) | 12806.7 | + | 39415.0i | 0.600548 | + | 1.84830i | 0.524902 | + | 0.851163i | \(0.324102\pi\) |
0.0756466 | + | 0.997135i | \(0.475898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −237.100 | + | 729.720i | −0.0110752 | + | 0.0340859i | ||||
\(772\) | −3801.12 | + | 11698.6i | −0.177209 | + | 0.545393i | ||||
\(773\) | 6750.04 | − | 4904.19i | 0.314078 | − | 0.228191i | −0.419566 | − | 0.907725i | \(-0.637818\pi\) |
0.733644 | + | 0.679534i | \(0.237818\pi\) | |||||||
\(774\) | 5587.89 | 0.259499 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3551.63 | −0.164299 | ||||||||
\(777\) | 1106.52 | − | 803.936i | 0.0510892 | − | 0.0371184i | ||||
\(778\) | −3562.81 | + | 10965.2i | −0.164181 | + | 0.505297i | ||||
\(779\) | −4141.73 | + | 12746.9i | −0.190492 | + | 0.586273i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 584.501 | + | 1798.91i | 0.0267799 | + | 0.0824201i | ||||
\(782\) | 29672.7 | 1.35690 | ||||||||
\(783\) | −993.020 | − | 3056.20i | −0.0453227 | − | 0.139489i | ||||
\(784\) | −693.281 | − | 503.698i | −0.0315817 | − | 0.0229454i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1122.71 | − | 815.697i | 0.0509488 | − | 0.0370165i | ||||
\(787\) | −6549.52 | − | 4758.50i | −0.296652 | − | 0.215530i | 0.429496 | − | 0.903069i | \(-0.358691\pi\) |
−0.726148 | + | 0.687539i | \(0.758691\pi\) | |||||||
\(788\) | 13703.4 | + | 9956.14i | 0.619499 | + | 0.450092i | ||||
\(789\) | 990.315 | − | 719.506i | 0.0446846 | − | 0.0324653i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3089.14 | + | 2244.39i | 0.138859 | + | 0.100887i | ||||
\(792\) | −147.219 | − | 453.093i | −0.00660505 | − | 0.0203282i | ||||
\(793\) | −6286.59 | −0.281517 | ||||||||
\(794\) | 987.338 | + | 3038.71i | 0.0441301 | + | 0.135819i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5100.22 | − | 15696.9i | 0.227101 | − | 0.698946i | ||||
\(797\) | 6192.35 | − | 19058.1i | 0.275212 | − | 0.847016i | −0.713951 | − | 0.700196i | \(-0.753096\pi\) |
0.989163 | − | 0.146821i | \(-0.0469040\pi\) | |||||||
\(798\) | −401.571 | + | 291.758i | −0.0178139 | + | 0.0129425i | ||||
\(799\) | −30634.1 | −1.35639 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35094.7 | −1.54808 | ||||||||
\(802\) | −7641.48 | + | 5551.86i | −0.336447 | + | 0.244443i | ||||
\(803\) | −352.908 | + | 1086.14i | −0.0155091 | + | 0.0477322i | ||||
\(804\) | 23.2764 | − | 71.6374i | 0.00102101 | − | 0.00314236i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 389.948 | + | 1200.14i | 0.0170414 | + | 0.0524479i | ||||
\(807\) | 591.913 | 0.0258195 | ||||||||
\(808\) | 1219.65 | + | 3753.71i | 0.0531030 | + | 0.163434i | ||||
\(809\) | −3586.40 | − | 2605.67i | −0.155860 | − | 0.113239i | 0.507122 | − | 0.861874i | \(-0.330709\pi\) |
−0.662982 | + | 0.748635i | \(0.730709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4379.53 | − | 3181.92i | 0.189625 | − | 0.137771i | −0.488922 | − | 0.872327i | \(-0.662610\pi\) |
0.678548 | + | 0.734557i | \(0.262610\pi\) | |||||||
\(812\) | −15546.1 | − | 11294.9i | −0.671875 | − | 0.488146i | ||||
\(813\) | 1296.77 | + | 942.161i | 0.0559407 | + | 0.0406433i | ||||
\(814\) | 994.774 | − | 722.746i | 0.0428339 | − | 0.0311207i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −237.952 | − | 172.882i | −0.0102083 | − | 0.00741677i | ||||
\(817\) | −1617.40 | − | 4977.85i | −0.0692603 | − | 0.213161i | ||||
\(818\) | −11658.1 | −0.498307 | ||||||||
\(819\) | −2039.79 | − | 6277.82i | −0.0870280 | − | 0.267845i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6717.03 | − | 20672.9i | 0.285537 | − | 0.878793i | −0.700700 | − | 0.713456i | \(-0.747129\pi\) |
0.986237 | − | 0.165337i | \(-0.0528711\pi\) | |||||||
\(822\) | −299.283 | + | 921.099i | −0.0126991 | + | 0.0390840i | ||||
\(823\) | −20823.2 | + | 15129.0i | −0.881959 | + | 0.640780i | −0.933769 | − | 0.357877i | \(-0.883501\pi\) |
0.0518104 | + | 0.998657i | \(0.483501\pi\) | |||||||
\(824\) | 13770.2 | 0.582170 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21944.1 | −0.924374 | ||||||||
\(827\) | −2545.13 | + | 1849.15i | −0.107017 | + | 0.0777523i | −0.640007 | − | 0.768369i | \(-0.721068\pi\) |
0.532990 | + | 0.846122i | \(0.321068\pi\) | |||||||
\(828\) | 6636.84 | − | 20426.1i | 0.278558 | − | 0.857313i | ||||
\(829\) | 3738.37 | − | 11505.5i | 0.156621 | − | 0.482031i | −0.841700 | − | 0.539945i | \(-0.818445\pi\) |
0.998322 | + | 0.0579142i | \(0.0184450\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −290.289 | − | 893.419i | −0.0121180 | − | 0.0372953i | ||||
\(832\) | 787.493 | 0.0328142 | ||||||||
\(833\) | 1231.98 | + | 3791.64i | 0.0512432 | + | 0.157710i | ||||
\(834\) | −630.766 | − | 458.278i | −0.0261890 | − | 0.0190274i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −361.016 | + | 262.293i | −0.0149354 | + | 0.0108512i | ||||
\(837\) | −552.599 | − | 401.486i | −0.0228203 | − | 0.0165799i | ||||
\(838\) | 1841.96 | + | 1338.26i | 0.0759300 | + | 0.0551664i | ||||
\(839\) | 1198.70 | − | 870.909i | 0.0493252 | − | 0.0358369i | −0.562849 | − | 0.826559i | \(-0.690295\pi\) |
0.612175 | + | 0.790723i | \(0.290295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27351.4 | − | 19871.9i | −1.12146 | − | 0.814791i | ||||
\(842\) | 634.205 | + | 1951.88i | 0.0259574 | + | 0.0798888i | ||||
\(843\) | 63.1097 | 0.00257842 | ||||||||
\(844\) | −6279.02 | − | 19324.8i | −0.256082 | − | 0.788138i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6851.89 | + | 21087.9i | −0.278455 | + | 0.856996i | ||||
\(847\) | −8160.50 | + | 25115.4i | −0.331049 | + | 1.01886i | ||||
\(848\) | 5569.73 | − | 4046.65i | 0.225549 | − | 0.163871i | ||||
\(849\) | −506.262 | −0.0204651 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55432.5 | 2.23290 | ||||||||
\(852\) | 683.806 | − | 496.814i | 0.0274962 | − | 0.0199772i | ||||
\(853\) | 5268.61 | − | 16215.1i | 0.211481 | − | 0.650873i | −0.787903 | − | 0.615799i | \(-0.788833\pi\) |
0.999385 | − | 0.0350740i | \(-0.0111667\pi\) | |||||||
\(854\) | 6288.03 | − | 19352.6i | 0.251958 | − | 0.775446i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3067.93 | − | 9442.12i | −0.122500 | − | 0.377015i | ||||
\(857\) | 5794.04 | 0.230946 | 0.115473 | − | 0.993311i | \(-0.463162\pi\) | ||||
0.115473 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(858\) | 4.15155 | + | 12.7772i | 0.000165188 | + | 0.000508398i | ||||
\(859\) | 16171.8 | + | 11749.5i | 0.642346 | + | 0.466692i | 0.860655 | − | 0.509188i | \(-0.170054\pi\) |
−0.218310 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1056.66 | + | 767.706i | −0.0418243 | + | 0.0303872i | ||||
\(862\) | −9055.64 | − | 6579.31i | −0.357815 | − | 0.259968i | ||||
\(863\) | 39553.6 | + | 28737.4i | 1.56016 | + | 1.13353i | 0.935875 | + | 0.352331i | \(0.114611\pi\) |
0.624288 | + | 0.781194i | \(0.285389\pi\) | |||||||
\(864\) | −344.852 | + | 250.549i | −0.0135788 | + | 0.00986558i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1421.67 | − | 1032.91i | −0.0557858 | − | 0.0405307i | ||||
\(867\) | 47.9162 | + | 147.471i | 0.00187696 | + | 0.00577667i | ||||
\(868\) | −4084.52 | −0.159721 | ||||||||
\(869\) | −93.0758 | − | 286.458i | −0.00363335 | − | 0.0111823i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 289.935 | − | 892.329i | 0.0112791 | − | 0.0347134i | ||||
\(872\) | −436.873 | + | 1344.56i | −0.0169661 | + | 0.0522161i | ||||
\(873\) | 9675.58 | − | 7029.72i | 0.375107 | − | 0.272531i | ||||
\(874\) | −20117.1 | −0.778572 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 510.330 | 0.0196832 | ||||||||
\(877\) | −5126.68 | + | 3724.75i | −0.197395 | + | 0.143416i | −0.682092 | − | 0.731266i | \(-0.738930\pi\) |
0.484697 | + | 0.874682i | \(0.338930\pi\) | |||||||
\(878\) | 4329.24 | − | 13324.0i | 0.166406 | − | 0.512146i | ||||
\(879\) | −514.587 | + | 1583.74i | −0.0197458 | + | 0.0607714i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6049.04 | + | 18617.0i | 0.231325 | + | 0.711945i | 0.997588 | + | 0.0694177i | \(0.0221141\pi\) |
−0.766263 | + | 0.642527i | \(0.777886\pi\) | |||||||
\(882\) | 2885.65 | 0.110164 | ||||||||
\(883\) | −14467.5 | − | 44526.5i | −0.551384 | − | 1.69698i | −0.705307 | − | 0.708902i | \(-0.749191\pi\) |
0.153924 | − | 0.988083i | \(-0.450809\pi\) | |||||||
\(884\) | −2963.97 | − | 2153.45i | −0.112771 | − | 0.0819326i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28698.3 | − | 20850.5i | 1.08819 | − | 0.790617i | ||||
\(887\) | 2613.54 | + | 1898.84i | 0.0989334 | + | 0.0718793i | 0.636152 | − | 0.771564i | \(-0.280525\pi\) |
−0.537219 | + | 0.843443i | \(0.680525\pi\) | |||||||
\(888\) | −444.525 | − | 322.966i | −0.0167987 | − | 0.0122050i | ||||
\(889\) | 4951.53 | − | 3597.49i | 0.186804 | − | 0.135721i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1294.92 | + | 940.817i | 0.0486886 | + | 0.0353744i | ||||
\(892\) | −6100.02 | − | 18773.9i | −0.228973 | − | 0.704706i | ||||
\(893\) | 20769.0 | 0.778284 | ||||||||
\(894\) | 221.089 | + | 680.443i | 0.00827107 | + | 0.0254557i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −787.673 | + | 2424.21i | −0.0293687 | + | 0.0903875i | ||||
\(897\) | −187.158 | + | 576.013i | −0.00696658 | + | 0.0214409i | ||||
\(898\) | 6945.03 | − | 5045.86i | 0.258083 | − | 0.187508i | ||||
\(899\) | −12370.2 | −0.458922 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32029.2 | −1.18429 | ||||||||
\(902\) | −949.944 | + | 690.174i | −0.0350661 | + | 0.0254770i | ||||
\(903\) | 157.614 | − | 485.085i | 0.00580848 | − | 0.0178767i | ||||
\(904\) | 474.022 | − | 1458.89i | 0.0174400 | − | 0.0536747i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 275.488 | + | 847.864i | 0.0101021 | + | 0.0310909i | ||||
\(907\) | −24727.7 | −0.905258 | −0.452629 | − | 0.891699i | \(-0.649514\pi\) | ||||
−0.452629 | + | 0.891699i | \(0.649514\pi\) | |||||||
\(908\) | 863.022 | + | 2656.11i | 0.0315423 | + | 0.0970772i | ||||
\(909\) | −10752.3 | − | 7812.04i | −0.392335 | − | 0.285048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10203.7 | − | 7413.45i | 0.371092 | − | 0.269614i | −0.386572 | − | 0.922259i | \(-0.626341\pi\) |
0.757664 | + | 0.652645i | \(0.226341\pi\) | |||||||
\(912\) | 161.324 | + | 117.209i | 0.00585742 | + | 0.00425566i | ||||
\(913\) | −1640.93 | − | 1192.20i | −0.0594817 | − | 0.0432160i | ||||
\(914\) | 28169.4 | − | 20466.2i | 1.01943 | − | 0.740660i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20071.8 | − | 14583.0i | −0.724007 | − | 0.526022i | ||||
\(917\) | 17290.0 | + | 53213.1i | 0.622646 | + | 1.91631i | ||||
\(918\) | 1983.10 | 0.0712985 | ||||||||
\(919\) | −9253.51 | − | 28479.4i | −0.332149 | − | 1.02225i | −0.968109 | − | 0.250528i | \(-0.919396\pi\) |
0.635960 | − | 0.771722i | \(-0.280604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 381.548 | − | 1174.28i | 0.0136508 | − | 0.0420130i | ||||
\(922\) | −9046.87 | + | 27843.4i | −0.323148 | + | 0.994548i | ||||
\(923\) | 8517.61 | − | 6188.41i | 0.303749 | − | 0.220687i | ||||
\(924\) | −43.4856 | −0.00154824 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15087.4 | 0.535423 | ||||||||
\(927\) | −37513.7 | + | 27255.3i | −1.32914 | + | 0.965676i | ||||
\(928\) | −2385.52 | + | 7341.88i | −0.0843842 | + | 0.259708i | ||||
\(929\) | 3387.87 | − | 10426.8i | 0.119647 | − | 0.368237i | −0.873240 | − | 0.487290i | \(-0.837986\pi\) |
0.992888 | + | 0.119052i | \(0.0379856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −835.244 | − | 2570.62i | −0.0294028 | − | 0.0904925i | ||||
\(932\) | −10931.9 | −0.384212 | ||||||||
\(933\) | 524.230 | + | 1613.42i | 0.0183950 | + | 0.0566140i | ||||
\(934\) | 5709.39 | + | 4148.11i | 0.200018 | + | 0.145322i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2145.34 | + | 1558.68i | −0.0749174 | + | 0.0544306i | ||||
\(937\) | 39386.2 | + | 28615.8i | 1.37320 | + | 0.997691i | 0.997479 | + | 0.0709603i | \(0.0226064\pi\) |
0.375725 | + | 0.926731i | \(0.377394\pi\) | |||||||
\(938\) | 2456.93 | + | 1785.07i | 0.0855242 | + | 0.0621370i | ||||
\(939\) | −89.6954 | + | 65.1675i | −0.00311725 | + | 0.00226482i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10133.1 | − | 7362.13i | −0.351041 | − | 0.255046i | 0.398265 | − | 0.917271i | \(-0.369613\pi\) |
−0.749306 | + | 0.662224i | \(0.769613\pi\) | |||||||
\(942\) | 305.100 | + | 939.001i | 0.0105528 | + | 0.0324780i | ||||
\(943\) | −52934.3 | −1.82797 | ||||||||
\(944\) | 2724.18 | + | 8384.17i | 0.0939244 | + | 0.289069i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 141.696 | − | 436.096i | 0.00486992 | − | 0.0149881i | ||||
\(947\) | 10330.1 | − | 31792.8i | 0.354470 | − | 1.09095i | −0.601846 | − | 0.798612i | \(-0.705568\pi\) |
0.956316 | − | 0.292335i | \(-0.0944322\pi\) | |||||||
\(948\) | −108.889 | + | 79.1125i | −0.00373054 | + | 0.00271040i | ||||
\(949\) | 6356.76 | 0.217439 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1653.96 | −0.0563968 | ||||||||
\(952\) | 9593.81 | − | 6970.31i | 0.326615 | − | 0.237299i | ||||
\(953\) | −10938.2 | + | 33664.4i | −0.371799 | + | 1.14428i | 0.573815 | + | 0.818985i | \(0.305463\pi\) |
−0.945613 | + | 0.325293i | \(0.894537\pi\) | |||||||
\(954\) | −7163.92 | + | 22048.3i | −0.243124 | + | 0.748259i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1829.60 | − | 5630.94i | −0.0618970 | − | 0.190499i | ||||
\(957\) | −131.699 | −0.00444851 | ||||||||
\(958\) | −4591.46 | − | 14131.1i | −0.154847 | − | 0.476570i | ||||
\(959\) | −31590.7 | − | 22952.0i | −1.06373 | − | 0.772846i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21974.2 | − | 15965.2i | 0.737612 | − | 0.535907i | ||||
\(962\) | −5537.09 | − | 4022.93i | −0.185575 | − | 0.134828i | ||||
\(963\) | 27046.6 | + | 19650.5i | 0.905051 | + | 0.657558i | ||||
\(964\) | −837.507 | + | 608.485i | −0.0279816 | + | 0.0203298i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1585.99 | − | 1152.29i | −0.0528244 | − | 0.0383792i | ||||
\(967\) | 6943.26 | + | 21369.2i | 0.230900 | + | 0.710637i | 0.997639 | + | 0.0686780i | \(0.0218781\pi\) |
−0.766739 | + | 0.641959i | \(0.778122\pi\) | |||||||
\(968\) | 10608.9 | 0.352255 | ||||||||
\(969\) | −286.677 | − | 882.301i | −0.00950401 | − | 0.0292503i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17654.3 | − | 54334.4i | 0.583475 | − | 1.79575i | −0.0218342 | − | 0.999762i | \(-0.506951\pi\) |
0.605309 | − | 0.795990i | \(-0.293049\pi\) | |||||||
\(972\) | 665.585 | − | 2048.46i | 0.0219636 | − | 0.0675971i | ||||
\(973\) | 25431.4 | − | 18477.0i | 0.837917 | − | 0.608782i | ||||
\(974\) | 28035.2 | 0.922287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8174.63 | −0.268098 | ||||||||
\(977\) | 26432.7 | − | 19204.5i | 0.865566 | − | 0.628870i | −0.0638277 | − | 0.997961i | \(-0.520331\pi\) |
0.929393 | + | 0.369091i | \(0.120331\pi\) | |||||||
\(978\) | 74.9782 | − | 230.759i | 0.00245147 | − | 0.00754485i | ||||
\(979\) | −889.921 | + | 2738.90i | −0.0290521 | + | 0.0894132i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1471.12 | − | 4527.63i | −0.0478788 | − | 0.147356i | ||||
\(982\) | 7204.42 | 0.234116 | ||||||||
\(983\) | 15775.3 | + | 48551.3i | 0.511854 | + | 1.57533i | 0.788933 | + | 0.614479i | \(0.210634\pi\) |
−0.277079 | + | 0.960847i | \(0.589366\pi\) | |||||||
\(984\) | 424.492 | + | 308.412i | 0.0137524 | + | 0.00999167i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29055.5 | − | 21110.0i | 0.938453 | − | 0.681826i | ||||
\(987\) | 1637.38 | + | 1189.63i | 0.0528048 | + | 0.0383650i | ||||
\(988\) | 2009.48 | + | 1459.97i | 0.0647065 | + | 0.0470121i | ||||
\(989\) | 16723.6 | − | 12150.4i | 0.537696 | − | 0.390659i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44985.3 | − | 32683.7i | −1.44198 | − | 1.04766i | −0.987624 | − | 0.156843i | \(-0.949868\pi\) |
−0.454359 | − | 0.890819i | \(-0.650132\pi\) | |||||||
\(992\) | 507.060 | + | 1560.57i | 0.0162290 | + | 0.0499478i | ||||
\(993\) | −104.163 | −0.00332881 | ||||||||
\(994\) | 10530.8 | + | 32410.3i | 0.336032 | + | 1.03420i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −280.082 | + | 862.005i | −0.00891039 | + | 0.0274234i | ||||
\(997\) | −3094.69 | + | 9524.47i | −0.0983047 | + | 0.302551i | −0.988101 | − | 0.153808i | \(-0.950846\pi\) |
0.889796 | + | 0.456358i | \(0.150846\pi\) | |||||||
\(998\) | 7936.48 | − | 5766.19i | 0.251728 | − | 0.182891i | ||||
\(999\) | 3704.69 | 0.117329 |
(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 | 250.4.d.d.51.5 | 32 | ||
5.2 | odd | 4 | 250.4.e.b.199.6 | 32 | |||
5.3 | odd | 4 | 50.4.e.a.39.3 | yes | 32 | ||
5.4 | even | 2 | 250.4.d.c.51.4 | 32 | |||
25.4 | even | 10 | 1250.4.a.n.1.8 | 16 | |||
25.9 | even | 10 | 250.4.d.c.201.4 | 32 | |||
25.12 | odd | 20 | 50.4.e.a.9.3 | ✓ | 32 | ||
25.13 | odd | 20 | 250.4.e.b.49.6 | 32 | |||
25.16 | even | 5 | inner | 250.4.d.d.201.5 | 32 | ||
25.21 | even | 5 | 1250.4.a.m.1.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.4.e.a.9.3 | ✓ | 32 | 25.12 | odd | 20 | ||
50.4.e.a.39.3 | yes | 32 | 5.3 | odd | 4 | ||
250.4.d.c.51.4 | 32 | 5.4 | even | 2 | |||
250.4.d.c.201.4 | 32 | 25.9 | even | 10 | |||
250.4.d.d.51.5 | 32 | 1.1 | even | 1 | trivial | ||
250.4.d.d.201.5 | 32 | 25.16 | even | 5 | inner | ||
250.4.e.b.49.6 | 32 | 25.13 | odd | 20 | |||
250.4.e.b.199.6 | 32 | 5.2 | odd | 4 | |||
1250.4.a.m.1.9 | 16 | 25.21 | even | 5 | |||
1250.4.a.n.1.8 | 16 | 25.4 | even | 10 |