Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.21 | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.7.d.a.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.5562i | 1.94453i | 0.233881 | + | 0.972265i | \(0.424857\pi\) | ||||
−0.233881 | + | 0.972265i | \(0.575143\pi\) | |||||||
\(3\) | 25.2642 | − | 14.5863i | 0.935711 | − | 0.540233i | 0.0470980 | − | 0.998890i | \(-0.485003\pi\) |
0.888613 | + | 0.458657i | \(0.151669\pi\) | |||||||
\(4\) | −177.997 | −2.78120 | ||||||||
\(5\) | −105.706 | + | 61.0294i | −0.845648 | + | 0.488235i | −0.859180 | − | 0.511673i | \(-0.829026\pi\) |
0.0135319 | + | 0.999908i | \(0.495693\pi\) | |||||||
\(6\) | 226.908 | + | 393.016i | 1.05050 | + | 1.81952i | ||||
\(7\) | −10.5188 | − | 6.07303i | −0.0306670 | − | 0.0177056i | 0.484588 | − | 0.874742i | \(-0.338969\pi\) |
−0.515255 | + | 0.857037i | \(0.672303\pi\) | |||||||
\(8\) | − | 1773.36i | − | 3.46359i | ||||||
\(9\) | 61.0201 | − | 105.690i | 0.0837038 | − | 0.144979i | ||||
\(10\) | −949.388 | − | 1644.39i | −0.949388 | − | 1.64439i | ||||
\(11\) | −1760.62 | −1.32278 | −0.661391 | − | 0.750041i | \(-0.730034\pi\) | ||||
−0.661391 | + | 0.750041i | \(0.730034\pi\) | |||||||
\(12\) | −4496.94 | + | 2596.31i | −2.60240 | + | 1.50250i | ||||
\(13\) | 1474.55 | − | 2554.00i | 0.671166 | − | 1.16249i | −0.306407 | − | 0.951900i | \(-0.599127\pi\) |
0.977574 | − | 0.210594i | \(-0.0675397\pi\) | |||||||
\(14\) | 94.4735 | − | 163.633i | 0.0344291 | − | 0.0596330i | ||||
\(15\) | −1780.39 | + | 3083.72i | −0.527522 | + | 0.913694i | ||||
\(16\) | 16195.0 | 3.95386 | ||||||||
\(17\) | 397.814 | − | 689.033i | 0.0809716 | − | 0.140247i | −0.822696 | − | 0.568482i | \(-0.807531\pi\) |
0.903668 | + | 0.428235i | \(0.140864\pi\) | |||||||
\(18\) | 1644.14 | + | 949.243i | 0.281916 | + | 0.162765i | ||||
\(19\) | −10625.8 | + | 6134.79i | −1.54917 | + | 0.894415i | −0.550967 | + | 0.834527i | \(0.685741\pi\) |
−0.998205 | + | 0.0598881i | \(0.980926\pi\) | |||||||
\(20\) | 18815.3 | − | 10863.0i | 2.35192 | − | 1.35788i | ||||
\(21\) | −354.332 | −0.0382606 | ||||||||
\(22\) | − | 27388.7i | − | 2.57219i | ||||||
\(23\) | 2845.62 | + | 4928.76i | 0.233880 | + | 0.405093i | 0.958947 | − | 0.283586i | \(-0.0915243\pi\) |
−0.725066 | + | 0.688679i | \(0.758191\pi\) | |||||||
\(24\) | −25866.8 | − | 44802.5i | −1.87115 | − | 3.24092i | ||||
\(25\) | −363.323 | + | 629.295i | −0.0232527 | + | 0.0402749i | ||||
\(26\) | 39730.6 | + | 22938.5i | 2.26051 | + | 1.30510i | ||||
\(27\) | 17706.6i | 0.899588i | ||||||||
\(28\) | 1872.31 | + | 1080.98i | 0.0852911 | + | 0.0492428i | ||||
\(29\) | 531.069 | + | 306.613i | 0.0217749 | + | 0.0125718i | 0.510848 | − | 0.859671i | \(-0.329332\pi\) |
−0.489073 | + | 0.872243i | \(0.662665\pi\) | |||||||
\(30\) | −47971.1 | − | 27696.1i | −1.77671 | − | 1.02578i | ||||
\(31\) | −3715.65 | − | 6435.70i | −0.124724 | − | 0.216028i | 0.796901 | − | 0.604110i | \(-0.206471\pi\) |
−0.921625 | + | 0.388082i | \(0.873138\pi\) | |||||||
\(32\) | 138439.i | 4.22482i | ||||||||
\(33\) | −44480.7 | + | 25681.0i | −1.23774 | + | 0.714611i | ||||
\(34\) | 10718.8 | + | 6188.48i | 0.272714 | + | 0.157452i | ||||
\(35\) | 1482.53 | 0.0345780 | ||||||||
\(36\) | −10861.4 | + | 18812.4i | −0.232797 | + | 0.403216i | ||||
\(37\) | −86748.7 | + | 50084.4i | −1.71261 | + | 0.988774i | −0.781595 | + | 0.623786i | \(0.785594\pi\) |
−0.931012 | + | 0.364988i | \(0.881073\pi\) | |||||||
\(38\) | −95434.3 | − | 165297.i | −1.73922 | − | 3.01241i | ||||
\(39\) | − | 86033.0i | − | 1.45035i | ||||||
\(40\) | 108227. | + | 187455.i | 1.69105 | + | 2.92898i | ||||
\(41\) | 28578.3 | 0.414653 | 0.207326 | − | 0.978272i | \(-0.433524\pi\) | ||||
0.207326 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(42\) | − | 5512.07i | − | 0.0743990i | ||||||
\(43\) | −79399.3 | − | 4136.63i | −0.998646 | − | 0.0520286i | ||||
\(44\) | 313385. | 3.67892 | ||||||||
\(45\) | 14896.1i | 0.163469i | ||||||||
\(46\) | −76673.0 | + | 44267.2i | −0.787715 | + | 0.454787i | ||||
\(47\) | 6537.35 | 0.0629663 | 0.0314832 | − | 0.999504i | \(-0.489977\pi\) | ||||
0.0314832 | + | 0.999504i | \(0.489977\pi\) | |||||||
\(48\) | 409155. | − | 236226.i | 3.69968 | − | 2.13601i | ||||
\(49\) | −58750.7 | − | 101759.i | −0.499373 | − | 0.864939i | ||||
\(50\) | −9789.46 | − | 5651.95i | −0.0783157 | − | 0.0452156i | ||||
\(51\) | − | 23210.5i | − | 0.174974i | ||||||
\(52\) | −262465. | + | 454603.i | −1.86665 | + | 3.23313i | ||||
\(53\) | 1950.05 | + | 3377.58i | 0.0130984 | + | 0.0226871i | 0.872500 | − | 0.488614i | \(-0.162497\pi\) |
−0.859402 | + | 0.511301i | \(0.829164\pi\) | |||||||
\(54\) | −275448. | −1.74928 | ||||||||
\(55\) | 186108. | − | 107450.i | 1.11861 | − | 0.645829i | ||||
\(56\) | −10769.7 | + | 18653.6i | −0.0613251 | + | 0.106218i | ||||
\(57\) | −178968. | + | 309981.i | −0.966385 | + | 1.67383i | ||||
\(58\) | −4769.74 | + | 8261.44i | −0.0244462 | + | 0.0423420i | ||||
\(59\) | 351135. | 1.70969 | 0.854846 | − | 0.518881i | \(-0.173651\pi\) | ||||
0.854846 | + | 0.518881i | \(0.173651\pi\) | |||||||
\(60\) | 316903. | − | 548892.i | 1.46714 | − | 2.54117i | ||||
\(61\) | 205715. | + | 118769.i | 0.906308 | + | 0.523257i | 0.879242 | − | 0.476376i | \(-0.158050\pi\) |
0.0270668 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(62\) | 100115. | − | 57801.6i | 0.420074 | − | 0.242530i | ||||
\(63\) | −1283.71 | + | 741.153i | −0.00513389 | + | 0.00296405i | ||||
\(64\) | −1.11711e6 | −4.26142 | ||||||||
\(65\) | 359964.i | 1.31075i | ||||||||
\(66\) | −399499. | − | 691953.i | −1.38958 | − | 2.40683i | ||||
\(67\) | 20297.7 | + | 35156.6i | 0.0674872 | + | 0.116891i | 0.897795 | − | 0.440414i | \(-0.145168\pi\) |
−0.830307 | + | 0.557306i | \(0.811835\pi\) | |||||||
\(68\) | −70809.5 | + | 122646.i | −0.225198 | + | 0.390055i | ||||
\(69\) | 143785. | + | 83014.2i | 0.437689 | + | 0.252700i | ||||
\(70\) | 23062.6i | 0.0672380i | ||||||||
\(71\) | −264709. | − | 152830.i | −0.739595 | − | 0.427005i | 0.0823273 | − | 0.996605i | \(-0.473765\pi\) |
−0.821922 | + | 0.569600i | \(0.807098\pi\) | |||||||
\(72\) | −187426. | − | 108211.i | −0.502149 | − | 0.289916i | ||||
\(73\) | −137304. | − | 79272.5i | −0.352951 | − | 0.203777i | 0.313033 | − | 0.949742i | \(-0.398655\pi\) |
−0.665984 | + | 0.745966i | \(0.731988\pi\) | |||||||
\(74\) | −779125. | − | 1.34948e6i | −1.92270 | − | 3.33022i | ||||
\(75\) | 21198.2i | 0.0502475i | ||||||||
\(76\) | 1.89135e6 | − | 1.09197e6i | 4.30855 | − | 2.48755i | ||||
\(77\) | 18519.6 | + | 10692.3i | 0.0405658 | + | 0.0234207i | ||||
\(78\) | 1.33835e6 | 2.82024 | ||||||||
\(79\) | −105586. | + | 182880.i | −0.214153 | + | 0.370925i | −0.953010 | − | 0.302938i | \(-0.902033\pi\) |
0.738857 | + | 0.673862i | \(0.235366\pi\) | |||||||
\(80\) | −1.71191e6 | + | 988373.i | −3.34358 | + | 1.93042i | ||||
\(81\) | 302757. | + | 524391.i | 0.569691 | + | 0.986734i | ||||
\(82\) | 444571.i | 0.806305i | ||||||||
\(83\) | 475073. | + | 822851.i | 0.830857 | + | 1.43909i | 0.897360 | + | 0.441300i | \(0.145482\pi\) |
−0.0665030 | + | 0.997786i | \(0.521184\pi\) | |||||||
\(84\) | 63069.9 | 0.106410 | ||||||||
\(85\) | 97113.3i | 0.158133i | ||||||||
\(86\) | 64350.5 | − | 1.23516e6i | 0.101171 | − | 1.94190i | ||||
\(87\) | 17889.4 | 0.0271667 | ||||||||
\(88\) | 3.12222e6i | 4.58158i | ||||||||
\(89\) | 558925. | − | 322696.i | 0.792836 | − | 0.457744i | −0.0481237 | − | 0.998841i | \(-0.515324\pi\) |
0.840960 | + | 0.541097i | \(0.181991\pi\) | |||||||
\(90\) | −231727. | −0.317870 | ||||||||
\(91\) | −31021.0 | + | 17910.0i | −0.0411653 | + | 0.0237668i | ||||
\(92\) | −506511. | − | 877303.i | −0.650468 | − | 1.12664i | ||||
\(93\) | −187746. | − | 108395.i | −0.233411 | − | 0.134760i | ||||
\(94\) | 101697.i | 0.122440i | ||||||||
\(95\) | 748805. | − | 1.29697e6i | 0.873370 | − | 1.51272i | ||||
\(96\) | 2.01931e6 | + | 3.49755e6i | 2.28239 | + | 3.95321i | ||||
\(97\) | −1.20150e6 | −1.31646 | −0.658231 | − | 0.752816i | \(-0.728695\pi\) | ||||
−0.658231 | + | 0.752816i | \(0.728695\pi\) | |||||||
\(98\) | 1.58299e6 | − | 913941.i | 1.68190 | − | 0.971046i | ||||
\(99\) | −107433. | + | 186080.i | −0.110722 | + | 0.191776i | ||||
\(100\) | 64670.4 | − | 112012.i | 0.0646704 | − | 0.112012i | ||||
\(101\) | −573418. | + | 993189.i | −0.556554 | + | 0.963979i | 0.441227 | + | 0.897395i | \(0.354543\pi\) |
−0.997781 | + | 0.0665838i | \(0.978790\pi\) | |||||||
\(102\) | 361068. | 0.340243 | ||||||||
\(103\) | 360754. | − | 624845.i | 0.330141 | − | 0.571822i | −0.652398 | − | 0.757877i | \(-0.726237\pi\) |
0.982539 | + | 0.186055i | \(0.0595703\pi\) | |||||||
\(104\) | −4.52916e6 | − | 2.61491e6i | −4.02641 | − | 2.32465i | ||||
\(105\) | 37455.0 | − | 21624.7i | 0.0323550 | − | 0.0186802i | ||||
\(106\) | −52542.5 | + | 30335.4i | −0.0441157 | + | 0.0254702i | ||||
\(107\) | 474981. | 0.387726 | 0.193863 | − | 0.981029i | \(-0.437898\pi\) | ||||
0.193863 | + | 0.981029i | \(0.437898\pi\) | |||||||
\(108\) | − | 3.15171e6i | − | 2.50193i | ||||||
\(109\) | 301620. | + | 522420.i | 0.232906 | + | 0.403404i | 0.958662 | − | 0.284547i | \(-0.0918433\pi\) |
−0.725756 | + | 0.687952i | \(0.758510\pi\) | |||||||
\(110\) | 1.67151e6 | + | 2.89515e6i | 1.25583 | + | 2.17517i | ||||
\(111\) | −1.46109e6 | + | 2.53068e6i | −1.06834 | + | 1.85041i | ||||
\(112\) | −170352. | − | 98352.8i | −0.121253 | − | 0.0700056i | ||||
\(113\) | − | 2.23771e6i | − | 1.55084i | −0.631444 | − | 0.775421i | \(-0.717538\pi\) | ||
0.631444 | − | 0.775421i | \(-0.282462\pi\) | |||||||
\(114\) | −4.82214e6 | − | 2.78407e6i | −3.25481 | − | 1.87917i | ||||
\(115\) | −601599. | − | 347333.i | −0.395561 | − | 0.228377i | ||||
\(116\) | −94528.5 | − | 54576.1i | −0.0605604 | − | 0.0349646i | ||||
\(117\) | −179955. | − | 311690.i | −0.112358 | − | 0.194610i | ||||
\(118\) | 5.46234e6i | 3.32455i | ||||||||
\(119\) | −8369.03 | + | 4831.86i | −0.00496632 | + | 0.00286730i | ||||
\(120\) | 5.46854e6 | + | 3.15727e6i | 3.16467 | + | 1.82712i | ||||
\(121\) | 1.32823e6 | 0.749752 | ||||||||
\(122\) | −1.84761e6 | + | 3.20015e6i | −1.01749 | + | 1.76234i | ||||
\(123\) | 722008. | − | 416851.i | 0.387995 | − | 0.224009i | ||||
\(124\) | 661374. | + | 1.14553e6i | 0.346882 | + | 0.600818i | ||||
\(125\) | − | 1.99586e6i | − | 1.02188i | ||||||
\(126\) | −11529.6 | − | 19969.8i | −0.00576369 | − | 0.00998301i | ||||
\(127\) | 1.34717e6 | 0.657676 | 0.328838 | − | 0.944386i | \(-0.393343\pi\) | ||||
0.328838 | + | 0.944386i | \(0.393343\pi\) | |||||||
\(128\) | − | 8.51788e6i | − | 4.06164i | ||||||
\(129\) | −2.06630e6 | + | 1.05363e6i | −0.962552 | + | 0.490818i | ||||
\(130\) | −5.59969e6 | −2.54879 | ||||||||
\(131\) | − | 427630.i | − | 0.190219i | −0.995467 | − | 0.0951096i | \(-0.969680\pi\) | ||
0.995467 | − | 0.0951096i | \(-0.0303201\pi\) | |||||||
\(132\) | 7.91742e6 | − | 4.57113e6i | 3.44241 | − | 1.98747i | ||||
\(133\) | 149027. | 0.0633447 | ||||||||
\(134\) | −546904. | + | 315755.i | −0.227299 | + | 0.131231i | ||||
\(135\) | −1.08062e6 | − | 1.87169e6i | −0.439211 | − | 0.760735i | ||||
\(136\) | −1.22190e6 | − | 705467.i | −0.485758 | − | 0.280453i | ||||
\(137\) | − | 656896.i | − | 0.255467i | −0.991809 | − | 0.127734i | \(-0.959230\pi\) | ||
0.991809 | − | 0.127734i | \(-0.0407702\pi\) | |||||||
\(138\) | −1.29139e6 | + | 2.23675e6i | −0.491383 | + | 0.851100i | ||||
\(139\) | 38542.8 | + | 66758.1i | 0.0143516 | + | 0.0248576i | 0.873112 | − | 0.487520i | \(-0.162098\pi\) |
−0.858760 | + | 0.512377i | \(0.828765\pi\) | |||||||
\(140\) | −263886. | −0.0961683 | ||||||||
\(141\) | 165161. | − | 95355.8i | 0.0589183 | − | 0.0340165i | ||||
\(142\) | 2.37746e6 | − | 4.11788e6i | 0.830324 | − | 1.43816i | ||||
\(143\) | −2.59613e6 | + | 4.49663e6i | −0.887807 | + | 1.53773i | ||||
\(144\) | 988222. | − | 1.71165e6i | 0.330953 | − | 0.573228i | ||||
\(145\) | −74849.6 | −0.0245519 | ||||||||
\(146\) | 1.23318e6 | − | 2.13594e6i | 0.396250 | − | 0.686325i | ||||
\(147\) | −2.96858e6 | − | 1.71391e6i | −0.934538 | − | 0.539556i | ||||
\(148\) | 1.54410e7 | − | 8.91485e6i | 4.76310 | − | 2.74998i | ||||
\(149\) | −2.10889e6 | + | 1.21757e6i | −0.637523 | + | 0.368074i | −0.783660 | − | 0.621190i | \(-0.786649\pi\) |
0.146137 | + | 0.989264i | \(0.453316\pi\) | |||||||
\(150\) | −329764. | −0.0977078 | ||||||||
\(151\) | − | 3.18318e6i | − | 0.924549i | −0.886737 | − | 0.462274i | \(-0.847034\pi\) | ||
0.886737 | − | 0.462274i | \(-0.152966\pi\) | |||||||
\(152\) | 1.08792e7 | + | 1.88433e7i | 3.09789 | + | 5.36570i | ||||
\(153\) | −48549.2 | − | 84089.7i | −0.0135553 | − | 0.0234784i | ||||
\(154\) | −166332. | + | 288096.i | −0.0455422 | + | 0.0788814i | ||||
\(155\) | 785534. | + | 453528.i | 0.210945 | + | 0.121789i | ||||
\(156\) | 1.53136e7i | 4.03370i | ||||||||
\(157\) | −1.06974e6 | − | 617617.i | −0.276427 | − | 0.159595i | 0.355378 | − | 0.934723i | \(-0.384352\pi\) |
−0.631805 | + | 0.775128i | \(0.717686\pi\) | |||||||
\(158\) | −2.84493e6 | − | 1.64252e6i | −0.721274 | − | 0.416428i | ||||
\(159\) | 98532.8 | + | 56887.9i | 0.0245126 | + | 0.0141524i | ||||
\(160\) | −8.44884e6 | − | 1.46338e7i | −2.06270 | − | 3.57271i | ||||
\(161\) | − | 69126.1i | − | 0.0165640i | ||||||
\(162\) | −8.15755e6 | + | 4.70976e6i | −1.91873 | + | 1.10778i | ||||
\(163\) | −5.08360e6 | − | 2.93502e6i | −1.17384 | − | 0.677716i | −0.219257 | − | 0.975667i | \(-0.570363\pi\) |
−0.954581 | + | 0.297951i | \(0.903697\pi\) | |||||||
\(164\) | −5.08684e6 | −1.15323 | ||||||||
\(165\) | 3.13459e6 | − | 5.42927e6i | 0.697796 | − | 1.20862i | ||||
\(166\) | −1.28005e7 | + | 7.39035e6i | −2.79835 | + | 1.61563i | ||||
\(167\) | 1.05874e6 | + | 1.83379e6i | 0.227321 | + | 0.393732i | 0.957013 | − | 0.290044i | \(-0.0936699\pi\) |
−0.729692 | + | 0.683776i | \(0.760337\pi\) | |||||||
\(168\) | 628358.i | 0.132519i | ||||||||
\(169\) | −1.93520e6 | − | 3.35187e6i | −0.400928 | − | 0.694428i | ||||
\(170\) | −1.51072e6 | −0.307494 | ||||||||
\(171\) | 1.49738e6i | 0.299464i | ||||||||
\(172\) | 1.41328e7 | + | 736307.i | 2.77743 | + | 0.144702i | ||||
\(173\) | −728137. | −0.140629 | −0.0703145 | − | 0.997525i | \(-0.522400\pi\) | ||||
−0.0703145 | + | 0.997525i | \(0.522400\pi\) | |||||||
\(174\) | 278292.i | 0.0528266i | ||||||||
\(175\) | 7643.44 | − | 4412.94i | 0.00142618 | − | 0.000823406i | ||||
\(176\) | −2.85133e7 | −5.23010 | ||||||||
\(177\) | 8.87115e6 | − | 5.12176e6i | 1.59978 | − | 0.923633i | ||||
\(178\) | 5.01993e6 | + | 8.69477e6i | 0.890098 | + | 1.54169i | ||||
\(179\) | 8.22427e6 | + | 4.74828e6i | 1.43396 | + | 0.827899i | 0.997420 | − | 0.0717836i | \(-0.0228691\pi\) |
0.436544 | + | 0.899683i | \(0.356202\pi\) | |||||||
\(180\) | − | 2.65145e6i | − | 0.454638i | ||||||
\(181\) | −766289. | + | 1.32725e6i | −0.129228 | + | 0.223830i | −0.923378 | − | 0.383893i | \(-0.874583\pi\) |
0.794150 | + | 0.607722i | \(0.207917\pi\) | |||||||
\(182\) | −278612. | − | 482570.i | −0.0462153 | − | 0.0800473i | ||||
\(183\) | 6.92963e6 | 1.13072 | ||||||||
\(184\) | 8.74047e6 | − | 5.04631e6i | 1.40308 | − | 0.810067i | ||||
\(185\) | 6.11324e6 | − | 1.05884e7i | 0.965509 | − | 1.67231i | ||||
\(186\) | 1.68622e6 | − | 2.92062e6i | 0.262045 | − | 0.453875i | ||||
\(187\) | −700399. | + | 1.21313e6i | −0.107108 | + | 0.185516i | ||||
\(188\) | −1.16363e6 | −0.175122 | ||||||||
\(189\) | 107533. | − | 186252.i | 0.0159278 | − | 0.0275877i | ||||
\(190\) | 2.01760e7 | + | 1.16486e7i | 2.94153 | + | 1.69829i | ||||
\(191\) | −7.74700e6 | + | 4.47273e6i | −1.11182 | + | 0.641908i | −0.939300 | − | 0.343098i | \(-0.888524\pi\) |
−0.172518 | + | 0.985006i | \(0.555190\pi\) | |||||||
\(192\) | −2.82228e7 | + | 1.62944e7i | −3.98746 | + | 2.30216i | ||||
\(193\) | −2.20411e6 | −0.306592 | −0.153296 | − | 0.988180i | \(-0.548989\pi\) | ||||
−0.153296 | + | 0.988180i | \(0.548989\pi\) | |||||||
\(194\) | − | 1.86908e7i | − | 2.55990i | ||||||
\(195\) | 5.25054e6 | + | 9.09421e6i | 0.708110 | + | 1.22648i | ||||
\(196\) | 1.04574e7 | + | 1.81128e7i | 1.38886 | + | 2.40557i | ||||
\(197\) | −2.76894e6 | + | 4.79594e6i | −0.362172 | + | 0.627300i | −0.988318 | − | 0.152406i | \(-0.951298\pi\) |
0.626146 | + | 0.779706i | \(0.284631\pi\) | |||||||
\(198\) | −2.89470e6 | − | 1.67126e6i | −0.372914 | − | 0.215302i | ||||
\(199\) | 9.47238e6i | 1.20199i | 0.799254 | + | 0.600993i | \(0.205228\pi\) | ||||
−0.799254 | + | 0.600993i | \(0.794772\pi\) | |||||||
\(200\) | 1.11597e6 | + | 644303.i | 0.139496 | + | 0.0805379i | ||||
\(201\) | 1.02561e6 | + | 592135.i | 0.126297 | + | 0.0729177i | ||||
\(202\) | −1.54503e7 | − | 8.92023e6i | −1.87449 | − | 1.08224i | ||||
\(203\) | −3724.14 | − | 6450.39i | −0.000445182 | − | 0.000771077i | ||||
\(204\) | 4.13139e6i | 0.486638i | ||||||||
\(205\) | −3.02090e6 | + | 1.74412e6i | −0.350650 | + | 0.202448i | ||||
\(206\) | 9.72024e6 | + | 5.61198e6i | 1.11192 | + | 0.641970i | ||||
\(207\) | 694560. | 0.0783067 | ||||||||
\(208\) | 2.38804e7 | − | 4.13621e7i | 2.65370 | − | 4.59634i | ||||
\(209\) | 1.87080e7 | − | 1.08011e7i | 2.04922 | − | 1.18312i | ||||
\(210\) | 336398. | + | 582659.i | 0.0363242 | + | 0.0629154i | ||||
\(211\) | − | 9.22808e6i | − | 0.982345i | −0.871062 | − | 0.491173i | \(-0.836568\pi\) | ||
0.871062 | − | 0.491173i | \(-0.163432\pi\) | |||||||
\(212\) | −347102. | − | 601198.i | −0.0364292 | − | 0.0630972i | ||||
\(213\) | −8.91689e6 | −0.922729 | ||||||||
\(214\) | 7.38892e6i | 0.753945i | ||||||||
\(215\) | 8.64544e6 | − | 4.40843e6i | 0.869905 | − | 0.443576i | ||||
\(216\) | 3.14002e7 | 3.11581 | ||||||||
\(217\) | 90261.0i | 0.00883326i | ||||||||
\(218\) | −8.12690e6 | + | 4.69207e6i | −0.784432 | + | 0.452892i | ||||
\(219\) | −4.62517e6 | −0.440347 | ||||||||
\(220\) | −3.31267e7 | + | 1.91257e7i | −3.11107 | + | 1.79618i | ||||
\(221\) | −1.17319e6 | − | 2.03203e6i | −0.108691 | − | 0.188258i | ||||
\(222\) | −3.93679e7 | − | 2.27291e7i | −3.59819 | − | 2.07741i | ||||
\(223\) | 8.27051e6i | 0.745792i | 0.927873 | + | 0.372896i | \(0.121635\pi\) | ||||
−0.927873 | + | 0.372896i | \(0.878365\pi\) | |||||||
\(224\) | 840742. | − | 1.45621e6i | 0.0748030 | − | 0.129563i | ||||
\(225\) | 44340.0 | + | 76799.2i | 0.00389268 | + | 0.00674232i | ||||
\(226\) | 3.48103e7 | 3.01566 | ||||||||
\(227\) | −6.16525e6 | + | 3.55951e6i | −0.527076 | + | 0.304307i | −0.739825 | − | 0.672799i | \(-0.765092\pi\) |
0.212749 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(228\) | 3.18557e7 | − | 5.51756e7i | 2.68771 | − | 4.65525i | ||||
\(229\) | −670000. | + | 1.16047e6i | −0.0557915 | + | 0.0966337i | −0.892572 | − | 0.450904i | \(-0.851102\pi\) |
0.836781 | + | 0.547538i | \(0.184435\pi\) | |||||||
\(230\) | 5.40320e6 | − | 9.35862e6i | 0.444087 | − | 0.769180i | ||||
\(231\) | 623845. | 0.0506105 | ||||||||
\(232\) | 543735. | − | 941777.i | 0.0435435 | − | 0.0754196i | ||||
\(233\) | −1.61785e7 | − | 9.34066e6i | −1.27900 | − | 0.738430i | −0.302335 | − | 0.953202i | \(-0.597766\pi\) |
−0.976664 | + | 0.214771i | \(0.931099\pi\) | |||||||
\(234\) | 4.84873e6 | − | 2.79942e6i | 0.378426 | − | 0.218484i | ||||
\(235\) | −691038. | + | 398971.i | −0.0532474 | + | 0.0307424i | ||||
\(236\) | −6.25009e7 | −4.75499 | ||||||||
\(237\) | 6.16044e6i | 0.462771i | ||||||||
\(238\) | −75165.6 | − | 130191.i | −0.00557556 | − | 0.00965715i | ||||
\(239\) | −6.38276e6 | − | 1.10553e7i | −0.467536 | − | 0.809796i | 0.531776 | − | 0.846885i | \(-0.321525\pi\) |
−0.999312 | + | 0.0370893i | \(0.988191\pi\) | |||||||
\(240\) | −2.88334e7 | + | 4.99409e7i | −2.08575 | + | 3.61262i | ||||
\(241\) | −1.66134e7 | − | 9.59173e6i | −1.18688 | − | 0.685245i | −0.229283 | − | 0.973360i | \(-0.573638\pi\) |
−0.957596 | + | 0.288115i | \(0.906972\pi\) | |||||||
\(242\) | 2.06623e7i | 1.45792i | ||||||||
\(243\) | 4.11909e6 | + | 2.37816e6i | 0.287067 | + | 0.165738i | ||||
\(244\) | −3.66165e7 | − | 2.11406e7i | −2.52062 | − | 1.45528i | ||||
\(245\) | 1.24206e7 | + | 7.17105e6i | 0.844588 | + | 0.487623i | ||||
\(246\) | 6.48464e6 | + | 1.12317e7i | 0.435593 | + | 0.754469i | ||||
\(247\) | 3.61843e7i | 2.40120i | ||||||||
\(248\) | −1.14128e7 | + | 6.58919e6i | −0.748234 | + | 0.431993i | ||||
\(249\) | 2.40047e7 | + | 1.38591e7i | 1.55488 | + | 0.897713i | ||||
\(250\) | 3.10481e7 | 1.98708 | ||||||||
\(251\) | −527749. | + | 914088.i | −0.0333738 | + | 0.0578052i | −0.882230 | − | 0.470819i | \(-0.843959\pi\) |
0.848856 | + | 0.528624i | \(0.177292\pi\) | |||||||
\(252\) | 228497. | − | 131923.i | 0.0142784 | − | 0.00824362i | ||||
\(253\) | −5.01007e6 | − | 8.67769e6i | −0.309373 | − | 0.535849i | ||||
\(254\) | 2.09570e7i | 1.27887i | ||||||||
\(255\) | 1.41652e6 | + | 2.45349e6i | 0.0854286 | + | 0.147967i | ||||
\(256\) | 6.10114e7 | 3.63657 | ||||||||
\(257\) | − | 1.66532e7i | − | 0.981067i | −0.871422 | − | 0.490533i | \(-0.836802\pi\) | ||
0.871422 | − | 0.490533i | \(-0.163198\pi\) | |||||||
\(258\) | −1.63906e7 | − | 3.21438e7i | −0.954410 | − | 1.87171i | ||||
\(259\) | 1.21665e6 | 0.0700274 | ||||||||
\(260\) | − | 6.40724e7i | − | 3.64545i | ||||||
\(261\) | 64811.7 | − | 37419.1i | 0.00364529 | − | 0.00210461i | ||||
\(262\) | 6.65231e6 | 0.369887 | ||||||||
\(263\) | −1.98228e7 | + | 1.14447e7i | −1.08968 | + | 0.629126i | −0.933491 | − | 0.358602i | \(-0.883254\pi\) |
−0.156187 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(264\) | 4.55416e7 | + | 7.88804e7i | 2.47512 | + | 4.28704i | ||||
\(265\) | −412263. | − | 238020.i | −0.0221532 | − | 0.0127902i | ||||
\(266\) | 2.31830e6i | 0.123176i | ||||||||
\(267\) | 9.41387e6 | − | 1.63053e7i | 0.494577 | − | 0.856633i | ||||
\(268\) | −3.61292e6 | − | 6.25775e6i | −0.187695 | − | 0.325098i | ||||
\(269\) | 2.07318e7 | 1.06507 | 0.532537 | − | 0.846406i | \(-0.321239\pi\) | ||||
0.532537 | + | 0.846406i | \(0.321239\pi\) | |||||||
\(270\) | 2.91165e7 | − | 1.68104e7i | 1.47927 | − | 0.854058i | ||||
\(271\) | −1.50629e7 | + | 2.60897e7i | −0.756833 | + | 1.31087i | 0.187625 | + | 0.982241i | \(0.439921\pi\) |
−0.944458 | + | 0.328632i | \(0.893412\pi\) | |||||||
\(272\) | 6.44260e6 | − | 1.11589e7i | 0.320151 | − | 0.554517i | ||||
\(273\) | −522481. | + | 904963.i | −0.0256793 | + | 0.0444778i | ||||
\(274\) | 1.02188e7 | 0.496764 | ||||||||
\(275\) | 639675. | − | 1.10795e6i | 0.0307582 | − | 0.0532748i | ||||
\(276\) | −2.55932e7 | − | 1.47762e7i | −1.21730 | − | 0.702808i | ||||
\(277\) | −2.43482e7 | + | 1.40574e7i | −1.14559 | + | 0.661404i | −0.947808 | − | 0.318843i | \(-0.896706\pi\) |
−0.197778 | + | 0.980247i | \(0.563372\pi\) | |||||||
\(278\) | −1.03851e6 | + | 599581.i | −0.0483364 | + | 0.0279070i | ||||
\(279\) | −906918. | −0.0417595 | ||||||||
\(280\) | − | 2.62906e6i | − | 0.119764i | ||||||
\(281\) | −2.66888e6 | − | 4.62263e6i | −0.120284 | − | 0.208339i | 0.799595 | − | 0.600539i | \(-0.205047\pi\) |
−0.919880 | + | 0.392200i | \(0.871714\pi\) | |||||||
\(282\) | 1.48338e6 | + | 2.56929e6i | 0.0661461 | + | 0.114568i | ||||
\(283\) | 8.12759e6 | − | 1.40774e7i | 0.358593 | − | 0.621102i | −0.629133 | − | 0.777298i | \(-0.716590\pi\) |
0.987726 | + | 0.156196i | \(0.0499231\pi\) | |||||||
\(284\) | 4.71173e7 | + | 2.72032e7i | 2.05696 | + | 1.18759i | ||||
\(285\) | − | 4.36892e7i | − | 1.88729i | ||||||
\(286\) | −6.99507e7 | − | 4.03860e7i | −2.99016 | − | 1.72637i | ||||
\(287\) | −300609. | − | 173557.i | −0.0127162 | − | 0.00734168i | ||||
\(288\) | 1.46316e7 | + | 8.44754e6i | 0.612511 | + | 0.353633i | ||||
\(289\) | 1.17523e7 | + | 2.03555e7i | 0.486887 | + | 0.843313i | ||||
\(290\) | − | 1.16438e6i | − | 0.0477420i | ||||||
\(291\) | −3.03549e7 | + | 1.75254e7i | −1.23183 | + | 0.711197i | ||||
\(292\) | 2.44397e7 | + | 1.41103e7i | 0.981628 | + | 0.566743i | ||||
\(293\) | −1.13466e7 | −0.451088 | −0.225544 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225544 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(294\) | 2.66620e7 | − | 4.61800e7i | 1.04918 | − | 1.81724i | ||||
\(295\) | −3.71171e7 | + | 2.14296e7i | −1.44580 | + | 0.834732i | ||||
\(296\) | 8.88176e7 | + | 1.53837e8i | 3.42471 | + | 5.93178i | ||||
\(297\) | − | 3.11746e7i | − | 1.18996i | ||||||
\(298\) | −1.89408e7 | − | 3.28064e7i | −0.715731 | − | 1.23968i | ||||
\(299\) | 1.67841e7 | 0.627890 | ||||||||
\(300\) | − | 3.77320e6i | − | 0.139748i | ||||||
\(301\) | 810063. | + | 525706.i | 0.0297043 | + | 0.0192772i | ||||
\(302\) | 4.95183e7 | 1.79781 | ||||||||
\(303\) | 3.34562e7i | 1.20268i | ||||||||
\(304\) | −1.72085e8 | + | 9.93532e7i | −6.12522 | + | 3.53640i | ||||
\(305\) | −2.89937e7 | −1.02189 | ||||||||
\(306\) | 1.30812e6 | − | 755243.i | 0.0456545 | − | 0.0263586i | ||||
\(307\) | 1.14394e7 | + | 1.98137e7i | 0.395356 | + | 0.684777i | 0.993147 | − | 0.116875i | \(-0.0372877\pi\) |
−0.597790 | + | 0.801653i | \(0.703954\pi\) | |||||||
\(308\) | −3.29643e6 | − | 1.90319e6i | −0.112821 | − | 0.0651375i | ||||
\(309\) | − | 2.10483e7i | − | 0.713413i | ||||||
\(310\) | −7.05519e6 | + | 1.22200e7i | −0.236823 | + | 0.410189i | ||||
\(311\) | 2.55685e6 | + | 4.42860e6i | 0.0850012 | + | 0.147226i | 0.905392 | − | 0.424577i | \(-0.139577\pi\) |
−0.820391 | + | 0.571804i | \(0.806244\pi\) | |||||||
\(312\) | −1.52568e8 | −5.02341 | ||||||||
\(313\) | −2.07838e7 | + | 1.19995e7i | −0.677784 | + | 0.391319i | −0.799020 | − | 0.601305i | \(-0.794648\pi\) |
0.121236 | + | 0.992624i | \(0.461314\pi\) | |||||||
\(314\) | 9.60779e6 | − | 1.66412e7i | 0.310338 | − | 0.537521i | ||||
\(315\) | 90464.2 | − | 156689.i | 0.00289431 | − | 0.00501309i | ||||
\(316\) | 1.87940e7 | − | 3.25521e7i | 0.595603 | − | 1.03162i | ||||
\(317\) | 1.89769e7 | 0.595727 | 0.297864 | − | 0.954608i | \(-0.403726\pi\) | ||||
0.297864 | + | 0.954608i | \(0.403726\pi\) | |||||||
\(318\) | −884962. | + | 1.53280e6i | −0.0275197 | + | 0.0476655i | ||||
\(319\) | −935012. | − | 539830.i | −0.0288035 | − | 0.0166297i | ||||
\(320\) | 1.18085e8 | − | 6.81763e7i | 3.60366 | − | 2.08057i | ||||
\(321\) | 1.20000e7 | − | 6.92821e6i | 0.362799 | − | 0.209462i | ||||
\(322\) | 1.07534e6 | 0.0322092 | ||||||||
\(323\) | 9.76201e6i | 0.289689i | ||||||||
\(324\) | −5.38898e7 | − | 9.33398e7i | −1.58442 | − | 2.74430i | ||||
\(325\) | 1.07148e6 | + | 1.85586e6i | 0.0312129 | + | 0.0540622i | ||||
\(326\) | 4.56578e7 | − | 7.90817e7i | 1.31784 | − | 2.28256i | ||||
\(327\) | 1.52404e7 | + | 8.79903e6i | 0.435865 | + | 0.251647i | ||||
\(328\) | − | 5.06796e7i | − | 1.43619i | ||||||
\(329\) | −68765.0 | − | 39701.5i | −0.00193099 | − | 0.00111486i | ||||
\(330\) | 8.44590e7 | + | 4.87624e7i | 2.35020 | + | 1.35689i | ||||
\(331\) | 4.30140e7 | + | 2.48342e7i | 1.18611 | + | 0.684803i | 0.957421 | − | 0.288696i | \(-0.0932216\pi\) |
0.228693 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(332\) | −8.45614e7 | − | 1.46465e8i | −2.31078 | − | 4.00238i | ||||
\(333\) | 1.22246e7i | 0.331057i | ||||||||
\(334\) | −2.85269e7 | + | 1.64700e7i | −0.765624 | + | 0.442033i | ||||
\(335\) | −4.29117e6 | − | 2.47751e6i | −0.114141 | − | 0.0658993i | ||||
\(336\) | −5.73841e6 | −0.151277 | ||||||||
\(337\) | −1.30149e7 | + | 2.25425e7i | −0.340057 | + | 0.588995i | −0.984443 | − | 0.175705i | \(-0.943780\pi\) |
0.644386 | + | 0.764700i | \(0.277113\pi\) | |||||||
\(338\) | 5.21425e7 | − | 3.01045e7i | 1.35034 | − | 0.779617i | ||||
\(339\) | −3.26398e7 | − | 5.65339e7i | −0.837817 | − | 1.45114i | ||||
\(340\) | − | 1.72858e7i | − | 0.439799i | ||||||
\(341\) | 6.54186e6 | + | 1.13308e7i | 0.164983 | + | 0.285758i | ||||
\(342\) | −2.32936e7 | −0.582316 | ||||||||
\(343\) | 2.85615e6i | 0.0707780i | ||||||||
\(344\) | −7.33574e6 | + | 1.40804e8i | −0.180206 | + | 3.45890i | ||||
\(345\) | −2.02652e7 | −0.493508 | ||||||||
\(346\) | − | 1.13271e7i | − | 0.273457i | ||||||
\(347\) | 4.54465e7 | − | 2.62386e7i | 1.08771 | − | 0.627988i | 0.154742 | − | 0.987955i | \(-0.450545\pi\) |
0.932965 | + | 0.359967i | \(0.117212\pi\) | |||||||
\(348\) | −3.18425e6 | −0.0755561 | ||||||||
\(349\) | −1.27427e7 | + | 7.35698e6i | −0.299767 | + | 0.173071i | −0.642338 | − | 0.766421i | \(-0.722036\pi\) |
0.342571 | + | 0.939492i | \(0.388702\pi\) | |||||||
\(350\) | 68648.8 | + | 118903.i | 0.00160114 | + | 0.00277325i | ||||
\(351\) | 4.52226e7 | + | 2.61093e7i | 1.04577 | + | 0.603773i | ||||
\(352\) | − | 2.43738e8i | − | 5.58851i | ||||||
\(353\) | 1.60938e7 | − | 2.78753e7i | 0.365877 | − | 0.633718i | −0.623039 | − | 0.782191i | \(-0.714102\pi\) |
0.988917 | + | 0.148473i | \(0.0474357\pi\) | |||||||
\(354\) | 7.96753e7 | + | 1.38002e8i | 1.79603 | + | 3.11082i | ||||
\(355\) | 3.73085e7 | 0.833916 | ||||||||
\(356\) | −9.94868e7 | + | 5.74387e7i | −2.20504 | + | 1.27308i | ||||
\(357\) | −140958. | + | 244146.i | −0.00309803 | + | 0.00536594i | ||||
\(358\) | −7.38655e7 | + | 1.27939e8i | −1.60988 | + | 2.78839i | ||||
\(359\) | −8.92817e6 | + | 1.54640e7i | −0.192965 | + | 0.334225i | −0.946232 | − | 0.323490i | \(-0.895144\pi\) |
0.753266 | + | 0.657716i | \(0.228477\pi\) | |||||||
\(360\) | 2.64161e7 | 0.566189 | ||||||||
\(361\) | 5.17484e7 | − | 8.96309e7i | 1.09996 | − | 1.90518i | ||||
\(362\) | −2.06470e7 | − | 1.19206e7i | −0.435243 | − | 0.251288i | ||||
\(363\) | 3.35567e7 | − | 1.93740e7i | 0.701551 | − | 0.405041i | ||||
\(364\) | 5.52164e6 | − | 3.18792e6i | 0.114489 | − | 0.0661002i | ||||
\(365\) | 1.93518e7 | 0.397964 | ||||||||
\(366\) | 1.07799e8i | 2.19873i | ||||||||
\(367\) | −7.58524e6 | − | 1.31380e7i | −0.153451 | − | 0.265786i | 0.779043 | − | 0.626971i | \(-0.215706\pi\) |
−0.932494 | + | 0.361185i | \(0.882372\pi\) | |||||||
\(368\) | 4.60849e7 | + | 7.98215e7i | 0.924731 | + | 1.60168i | ||||
\(369\) | 1.74385e6 | − | 3.02043e6i | 0.0347080 | − | 0.0601160i | ||||
\(370\) | 1.64716e8 | + | 9.50991e7i | 3.25186 | + | 1.87746i | ||||
\(371\) | − | 47370.7i | − | 0.000927659i | ||||||
\(372\) | 3.34182e7 | + | 1.92940e7i | 0.649163 | + | 0.374795i | ||||
\(373\) | 4.79103e7 | + | 2.76610e7i | 0.923214 | + | 0.533018i | 0.884659 | − | 0.466239i | \(-0.154391\pi\) |
0.0385548 | + | 0.999256i | \(0.487725\pi\) | |||||||
\(374\) | −1.88717e7 | − | 1.08956e7i | −0.360742 | − | 0.208274i | ||||
\(375\) | −2.91122e7 | − | 5.04239e7i | −0.552054 | − | 0.956186i | ||||
\(376\) | − | 1.15931e7i | − | 0.218090i | ||||||
\(377\) | 1.56618e6 | − | 904233.i | 0.0292292 | − | 0.0168755i | ||||
\(378\) | 2.89738e6 | + | 1.67280e6i | 0.0536451 | + | 0.0309720i | ||||
\(379\) | −2.33796e7 | −0.429457 | −0.214728 | − | 0.976674i | \(-0.568887\pi\) | ||||
−0.214728 | + | 0.976674i | \(0.568887\pi\) | |||||||
\(380\) | −1.33285e8 | + | 2.30856e8i | −2.42901 | + | 4.20718i | ||||
\(381\) | 3.40353e7 | − | 1.96503e7i | 0.615395 | − | 0.355299i | ||||
\(382\) | −6.95789e7 | − | 1.20514e8i | −1.24821 | − | 2.16196i | ||||
\(383\) | 3.22634e7i | 0.574268i | 0.957890 | + | 0.287134i | \(0.0927024\pi\) | ||||
−0.957890 | + | 0.287134i | \(0.907298\pi\) | |||||||
\(384\) | −1.24244e8 | − | 2.15197e8i | −2.19423 | − | 3.80052i | ||||
\(385\) | −2.61018e6 | −0.0457392 | ||||||||
\(386\) | − | 3.42876e7i | − | 0.596177i | ||||||
\(387\) | −5.28215e6 | + | 8.13928e6i | −0.0911335 | + | 0.140428i | ||||
\(388\) | 2.13863e8 | 3.66134 | ||||||||
\(389\) | − | 1.03052e8i | − | 1.75069i | −0.483499 | − | 0.875345i | \(-0.660634\pi\) | ||
0.483499 | − | 0.875345i | \(-0.339366\pi\) | |||||||
\(390\) | −1.41472e8 | + | 8.16787e7i | −2.38493 | + | 1.37694i | ||||
\(391\) | 4.52811e6 | 0.0757507 | ||||||||
\(392\) | −1.80456e8 | + | 1.04186e8i | −2.99580 | + | 1.72963i | ||||
\(393\) | −6.23754e6 | − | 1.08037e7i | −0.102763 | − | 0.177990i | ||||
\(394\) | −7.46069e7 | − | 4.30743e7i | −1.21980 | − | 0.704254i | ||||
\(395\) | − | 2.57754e7i | − | 0.418229i | ||||||
\(396\) | 1.91228e7 | − | 3.31216e7i | 0.307939 | − | 0.533367i | ||||
\(397\) | 3.44680e7 | + | 5.97003e7i | 0.550864 | + | 0.954124i | 0.998213 | + | 0.0597642i | \(0.0190349\pi\) |
−0.447349 | + | 0.894360i | \(0.647632\pi\) | |||||||
\(398\) | −1.47355e8 | −2.33730 | ||||||||
\(399\) | 3.76505e6 | − | 2.17375e6i | 0.0592723 | − | 0.0342209i | ||||
\(400\) | −5.88403e6 | + | 1.01914e7i | −0.0919380 | + | 0.159241i | ||||
\(401\) | −4.92073e7 | + | 8.52295e7i | −0.763126 | + | 1.32177i | 0.178106 | + | 0.984011i | \(0.443003\pi\) |
−0.941232 | + | 0.337762i | \(0.890330\pi\) | |||||||
\(402\) | −9.21140e6 | + | 1.59546e7i | −0.141791 | + | 0.245589i | ||||
\(403\) | −2.19157e7 | −0.334842 | ||||||||
\(404\) | 1.02066e8 | − | 1.76784e8i | 1.54789 | − | 2.68102i | ||||
\(405\) | −6.40065e7 | − | 3.69542e7i | −0.963517 | − | 0.556287i | ||||
\(406\) | 100344. | − | 57933.6i | 0.00149938 | − | 0.000865669i | ||||
\(407\) | 1.52732e8 | − | 8.81797e7i | 2.26541 | − | 1.30793i | ||||
\(408\) | −4.11606e7 | −0.606040 | ||||||||
\(409\) | − | 3.88645e7i | − | 0.568045i | −0.958818 | − | 0.284023i | \(-0.908331\pi\) | ||
0.958818 | − | 0.284023i | \(-0.0916691\pi\) | |||||||
\(410\) | −2.71319e7 | − | 4.69938e7i | −0.393666 | − | 0.681850i | ||||
\(411\) | −9.58168e6 | − | 1.65960e7i | −0.138012 | − | 0.239043i | ||||
\(412\) | −6.42131e7 | + | 1.11220e8i | −0.918188 | + | 1.59035i | ||||
\(413\) | −3.69351e6 | − | 2.13245e6i | −0.0524312 | − | 0.0302712i | ||||
\(414\) | 1.08047e7i | 0.152270i | ||||||||
\(415\) | −1.00436e8 | − | 5.79869e7i | −1.40523 | − | 0.811307i | ||||
\(416\) | 3.53573e8 | + | 2.04135e8i | 4.91132 | + | 2.83555i | ||||
\(417\) | 1.94751e6 | + | 1.12439e6i | 0.0268578 | + | 0.0155064i | ||||
\(418\) | 1.68024e8 | + | 2.91026e8i | 2.30060 | + | 3.98476i | ||||
\(419\) | 4.04998e7i | 0.550568i | 0.961363 | + | 0.275284i | \(0.0887719\pi\) | ||||
−0.961363 | + | 0.275284i | \(0.911228\pi\) | |||||||
\(420\) | −6.66687e6 | + | 3.84912e6i | −0.0899858 | + | 0.0519533i | ||||
\(421\) | −6.63420e7 | − | 3.83026e7i | −0.889083 | − | 0.513312i | −0.0154406 | − | 0.999881i | \(-0.504915\pi\) |
−0.873642 | + | 0.486568i | \(0.838248\pi\) | |||||||
\(422\) | 1.43554e8 | 1.91020 | ||||||||
\(423\) | 398910. | − | 690932.i | 0.00527052 | − | 0.00912881i | ||||
\(424\) | 5.98967e6 | − | 3.45814e6i | 0.0785787 | − | 0.0453675i | ||||
\(425\) | 289070. | + | 500684.i | 0.00376562 | + | 0.00652224i | ||||
\(426\) | − | 1.38713e8i | − | 1.79428i | ||||||
\(427\) | −1.44258e6 | − | 2.49862e6i | −0.0185292 | − | 0.0320935i | ||||
\(428\) | −8.45450e7 | −1.07834 | ||||||||
\(429\) | 1.51472e8i | 1.91849i | ||||||||
\(430\) | 6.85785e7 | + | 1.34491e8i | 0.862547 | + | 1.69156i | ||||
\(431\) | −1.20184e8 | −1.50112 | −0.750561 | − | 0.660801i | \(-0.770217\pi\) | ||||
−0.750561 | + | 0.660801i | \(0.770217\pi\) | |||||||
\(432\) | 2.86759e8i | 3.55685i | ||||||||
\(433\) | −1.69668e7 | + | 9.79579e6i | −0.208995 | + | 0.120663i | −0.600844 | − | 0.799366i | \(-0.705169\pi\) |
0.391849 | + | 0.920030i | \(0.371836\pi\) | |||||||
\(434\) | −1.40412e6 | −0.0171765 | ||||||||
\(435\) | −1.89102e6 | + | 1.09178e6i | −0.0229735 | + | 0.0132638i | ||||
\(436\) | −5.36873e7 | − | 9.29891e7i | −0.647757 | − | 1.12195i | ||||
\(437\) | −6.04739e7 | − | 3.49146e7i | −0.724642 | − | 0.418372i | ||||
\(438\) | − | 7.19503e7i | − | 0.856269i | ||||||
\(439\) | 3.95058e7 | − | 6.84261e7i | 0.466947 | − | 0.808775i | −0.532340 | − | 0.846530i | \(-0.678687\pi\) |
0.999287 | + | 0.0377550i | \(0.0120206\pi\) | |||||||
\(440\) | −1.90547e8 | − | 3.30037e8i | −2.23689 | − | 3.87440i | ||||
\(441\) | −1.43399e7 | −0.167198 | ||||||||
\(442\) | 3.16108e7 | − | 1.82505e7i | 0.366073 | − | 0.211353i | ||||
\(443\) | −5.06750e6 | + | 8.77717e6i | −0.0582885 | + | 0.100959i | −0.893697 | − | 0.448671i | \(-0.851898\pi\) |
0.835409 | + | 0.549629i | \(0.185231\pi\) | |||||||
\(444\) | 2.60069e8 | − | 4.50453e8i | 2.97126 | − | 5.14637i | ||||
\(445\) | −3.93878e7 | + | 6.82217e7i | −0.446974 | + | 0.774181i | ||||
\(446\) | −1.28658e8 | −1.45022 | ||||||||
\(447\) | −3.55197e7 | + | 6.15219e7i | −0.397691 | + | 0.688822i | ||||
\(448\) | 1.17506e7 | + | 6.78421e6i | 0.130685 | + | 0.0754510i | ||||
\(449\) | −3.64621e7 | + | 2.10514e7i | −0.402812 | + | 0.232564i | −0.687697 | − | 0.725998i | \(-0.741378\pi\) |
0.284885 | + | 0.958562i | \(0.408045\pi\) | |||||||
\(450\) | −1.19471e6 | + | 689764.i | −0.0131106 | + | 0.00756943i | ||||
\(451\) | −5.03156e7 | −0.548495 | ||||||||
\(452\) | 3.98304e8i | 4.31320i | ||||||||
\(453\) | −4.64307e7 | − | 8.04204e7i | −0.499472 | − | 0.865111i | ||||
\(454\) | −5.53726e7 | − | 9.59081e7i | −0.591735 | − | 1.02492i | ||||
\(455\) | 2.18607e6 | − | 3.78639e6i | 0.0232076 | − | 0.0401967i | ||||
\(456\) | 5.49708e8 | + | 3.17374e8i | 5.79746 | + | 3.34717i | ||||
\(457\) | − | 4.50543e7i | − | 0.472050i | −0.971747 | − | 0.236025i | \(-0.924155\pi\) | ||
0.971747 | − | 0.236025i | \(-0.0758447\pi\) | |||||||
\(458\) | −1.80526e7 | − | 1.04227e7i | −0.187907 | − | 0.108488i | ||||
\(459\) | 1.22004e7 | + | 7.04392e6i | 0.126164 | + | 0.0728411i | ||||
\(460\) | 1.07083e8 | + | 6.18242e7i | 1.10013 | + | 0.635162i | ||||
\(461\) | 3.70341e6 | + | 6.41449e6i | 0.0378006 | + | 0.0654726i | 0.884307 | − | 0.466906i | \(-0.154631\pi\) |
−0.846506 | + | 0.532379i | \(0.821298\pi\) | |||||||
\(462\) | 9.70468e6i | 0.0984136i | ||||||||
\(463\) | −8.70010e7 | + | 5.02301e7i | −0.876559 | + | 0.506082i | −0.869522 | − | 0.493893i | \(-0.835573\pi\) |
−0.00703690 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(464\) | 8.60068e6 | + | 4.96560e6i | 0.0860952 | + | 0.0497071i | ||||
\(465\) | 2.64612e7 | 0.263179 | ||||||||
\(466\) | 1.45305e8 | − | 2.51677e8i | 1.43590 | − | 2.48705i | ||||
\(467\) | 5.14874e7 | − | 2.97262e7i | 0.505534 | − | 0.291870i | −0.225462 | − | 0.974252i | \(-0.572389\pi\) |
0.730996 | + | 0.682382i | \(0.239056\pi\) | |||||||
\(468\) | 3.20313e7 | + | 5.54799e7i | 0.312491 | + | 0.541250i | ||||
\(469\) | − | 493073.i | − | 0.00477961i | ||||||
\(470\) | −6.20649e6 | − | 1.07499e7i | −0.0597795 | − | 0.103541i | ||||
\(471\) | −3.60350e7 | −0.344875 | ||||||||
\(472\) | − | 6.22689e8i | − | 5.92168i | ||||||
\(473\) | 1.39792e8 | + | 7.28305e6i | 1.32099 | + | 0.0688224i | ||||
\(474\) | −9.58332e7 | −0.899873 | ||||||||
\(475\) | − | 8.91565e6i | − | 0.0831902i | ||||||
\(476\) | 1.48966e6 | − | 860056.i | 0.0138123 | − | 0.00797454i | ||||
\(477\) | 475968. | 0.00438553 | ||||||||
\(478\) | 1.71978e8 | − | 9.92918e7i | 1.57467 | − | 0.909137i | ||||
\(479\) | 7.91280e7 | + | 1.37054e8i | 0.719985 | + | 1.24705i | 0.961005 | + | 0.276531i | \(0.0891848\pi\) |
−0.241020 | + | 0.970520i | \(0.577482\pi\) | |||||||
\(480\) | −4.26906e8 | − | 2.46474e8i | −3.86019 | − | 2.22868i | ||||
\(481\) | 2.95408e8i | 2.65453i | ||||||||
\(482\) | 1.49211e8 | − | 2.58442e8i | 1.33248 | − | 2.30792i | ||||
\(483\) | −1.00829e6 | − | 1.74642e6i | −0.00894841 | − | 0.0154991i | ||||
\(484\) | −2.36421e8 | −2.08521 | ||||||||
\(485\) | 1.27006e8 | − | 7.33268e7i | 1.11326 | − | 0.642743i | ||||
\(486\) | −3.69952e7 | + | 6.40776e7i | −0.322283 | + | 0.558210i | ||||
\(487\) | 8.07550e6 | − | 1.39872e7i | 0.0699169 | − | 0.121100i | −0.828948 | − | 0.559326i | \(-0.811060\pi\) |
0.898865 | + | 0.438227i | \(0.144393\pi\) | |||||||
\(488\) | 2.10621e8 | − | 3.64806e8i | 1.81235 | − | 3.13908i | ||||
\(489\) | −1.71244e8 | −1.46450 | ||||||||
\(490\) | −1.11555e8 | + | 1.93218e8i | −0.948198 | + | 1.64233i | ||||
\(491\) | 7.24957e7 | + | 4.18554e7i | 0.612446 | + | 0.353596i | 0.773922 | − | 0.633281i | \(-0.218292\pi\) |
−0.161476 | + | 0.986877i | \(0.551626\pi\) | |||||||
\(492\) | −1.28515e8 | + | 7.41981e7i | −1.07909 | + | 0.623014i | ||||
\(493\) | 422533. | − | 243949.i | 0.00352630 | − | 0.00203591i | ||||
\(494\) | −5.62892e8 | −4.66922 | ||||||||
\(495\) | − | 2.62264e7i | − | 0.216233i | ||||||
\(496\) | −6.01751e7 | − | 1.04226e8i | −0.493142 | − | 0.854147i | ||||
\(497\) | 1.85628e6 | + | 3.21517e6i | 0.0151208 | + | 0.0261900i | ||||
\(498\) | −2.15596e8 | + | 3.73423e8i | −1.74563 | + | 3.02352i | ||||
\(499\) | 1.17207e7 | + | 6.76696e6i | 0.0943307 | + | 0.0544618i | 0.546423 | − | 0.837509i | \(-0.315989\pi\) |
−0.452093 | + | 0.891971i | \(0.649322\pi\) | |||||||
\(500\) | 3.55257e8i | 2.84206i | ||||||||
\(501\) | 5.34965e7 | + | 3.08862e7i | 0.425414 | + | 0.245613i | ||||
\(502\) | −1.42198e7 | − | 8.20979e6i | −0.112404 | − | 0.0648964i | ||||
\(503\) | 1.50905e8 | + | 8.71250e7i | 1.18577 | + | 0.684603i | 0.957342 | − | 0.288959i | \(-0.0933090\pi\) |
0.228425 | + | 0.973561i | \(0.426642\pi\) | |||||||
\(504\) | 1.31433e6 | + | 2.27649e6i | 0.0102663 | + | 0.0177817i | ||||
\(505\) | − | 1.39981e8i | − | 1.08692i | ||||||
\(506\) | 1.34992e8 | − | 7.79378e7i | 1.04198 | − | 0.601585i | ||||
\(507\) | −9.77828e7 | − | 5.64549e7i | −0.750306 | − | 0.433190i | ||||
\(508\) | −2.39792e8 | −1.82913 | ||||||||
\(509\) | −6.33384e7 | + | 1.09705e8i | −0.480302 | + | 0.831907i | −0.999745 | − | 0.0225983i | \(-0.992806\pi\) |
0.519443 | + | 0.854505i | \(0.326139\pi\) | |||||||
\(510\) | −3.81671e7 | + | 2.20358e7i | −0.287726 | + | 0.166118i | ||||
\(511\) | 962848. | + | 1.66770e6i | 0.00721598 | + | 0.0124984i | ||||
\(512\) | 4.03965e8i | 3.00977i | ||||||||
\(513\) | −1.08626e8 | − | 1.88146e8i | −0.804605 | − | 1.39362i | ||||
\(514\) | 2.59061e8 | 1.90771 | ||||||||
\(515\) | 8.80665e7i | 0.644747i | ||||||||
\(516\) | 3.67794e8 | − | 1.87543e8i | 2.67705 | − | 1.36506i | ||||
\(517\) | −1.15098e7 | −0.0832907 | ||||||||
\(518\) | 1.89266e7i | 0.136170i | ||||||||
\(519\) | −1.83958e7 | + | 1.06208e7i | −0.131588 | + | 0.0759725i | ||||
\(520\) | 6.38346e8 | 4.53990 | ||||||||
\(521\) | 5.81545e7 | − | 3.35755e7i | 0.411216 | − | 0.237416i | −0.280096 | − | 0.959972i | \(-0.590366\pi\) |
0.691312 | + | 0.722556i | \(0.257033\pi\) | |||||||
\(522\) | 582100. | + | 1.00823e6i | 0.00409248 | + | 0.00708838i | ||||
\(523\) | −1.98082e8 | − | 1.14363e8i | −1.38465 | − | 0.799430i | −0.391947 | − | 0.919988i | \(-0.628198\pi\) |
−0.992706 | + | 0.120558i | \(0.961532\pi\) | |||||||
\(524\) | 7.61167e7i | 0.529037i | ||||||||
\(525\) | 128737. | − | 222979.i | 0.000889663 | − | 0.00154094i | ||||
\(526\) | −1.78037e8 | − | 3.08368e8i | −1.22335 | − | 2.11891i | ||||
\(527\) | −5.91255e6 | −0.0403964 | ||||||||
\(528\) | −7.20367e8 | + | 4.15904e8i | −4.89386 | + | 2.82547i | ||||
\(529\) | 5.78228e7 | − | 1.00152e8i | 0.390600 | − | 0.676539i | ||||
\(530\) | 3.70270e6 | − | 6.41327e6i | 0.0248709 | − | 0.0430776i | ||||
\(531\) | 2.14263e7 | − | 3.71114e7i | 0.143108 | − | 0.247870i | ||||
\(532\) | −2.65263e7 | −0.176174 | ||||||||
\(533\) | 4.21402e7 | − | 7.29889e7i | 0.278301 | − | 0.482031i | ||||
\(534\) | 2.53649e8 | + | 1.46444e8i | 1.66575 | + | 0.961721i | ||||
\(535\) | −5.02083e7 | + | 2.89878e7i | −0.327880 | + | 0.189301i | ||||
\(536\) | 6.23453e7 | − | 3.59951e7i | 0.404864 | − | 0.233748i | ||||
\(537\) | 2.77040e8 | 1.78904 | ||||||||
\(538\) | 3.22509e8i | 2.07107i | ||||||||
\(539\) | 1.03438e8 | + | 1.79160e8i | 0.660562 | + | 1.14413i | ||||
\(540\) | 1.92347e8 | + | 3.33155e8i | 1.22153 | + | 2.11576i | ||||
\(541\) | 7.65467e7 | − | 1.32583e8i | 0.483431 | − | 0.837327i | −0.516388 | − | 0.856355i | \(-0.672724\pi\) |
0.999819 | + | 0.0190276i | \(0.00605703\pi\) | |||||||
\(542\) | −4.05857e8 | − | 2.34322e8i | −2.54903 | − | 1.47168i | ||||
\(543\) | 4.47093e7i | 0.279253i | ||||||||
\(544\) | 9.53889e7 | + | 5.50728e7i | 0.592518 | + | 0.342090i | ||||
\(545\) | −6.37660e7 | − | 3.68153e7i | −0.393913 | − | 0.227426i | ||||
\(546\) | −1.40778e7 | − | 8.12784e6i | −0.0864884 | − | 0.0499341i | ||||
\(547\) | −2.49314e6 | − | 4.31825e6i | −0.0152330 | − | 0.0263843i | 0.858308 | − | 0.513134i | \(-0.171516\pi\) |
−0.873541 | + | 0.486750i | \(0.838182\pi\) | |||||||
\(548\) | 1.16925e8i | 0.710505i | ||||||||
\(549\) | 2.51055e7 | − | 1.44946e7i | 0.151723 | − | 0.0875972i | ||||
\(550\) | 1.72355e7 | + | 9.95094e6i | 0.103595 | + | 0.0598103i | ||||
\(551\) | −7.52403e6 | −0.0449775 | ||||||||
\(552\) | 1.47214e8 | − | 2.54982e8i | 0.875250 | − | 1.51598i | ||||
\(553\) | 2.22127e6 | − | 1.28245e6i | 0.0131349 | − | 0.00758344i | ||||
\(554\) | −2.18681e8 | − | 3.78766e8i | −1.28612 | − | 2.22763i | ||||
\(555\) | − | 3.56678e8i | − | 2.08640i | ||||||
\(556\) | −6.86049e6 | − | 1.18827e7i | −0.0399145 | − | 0.0691340i | ||||
\(557\) | 2.57034e6 | 0.0148739 | 0.00743695 | − | 0.999972i | \(-0.497633\pi\) | ||||
0.00743695 | + | 0.999972i | \(0.497633\pi\) | |||||||
\(558\) | − | 1.41082e7i | − | 0.0812026i | ||||||
\(559\) | −1.27643e8 | + | 1.96686e8i | −0.730740 | + | 1.12600i | ||||
\(560\) | 2.40097e7 | 0.136717 | ||||||||
\(561\) | 4.08649e7i | 0.231453i | ||||||||
\(562\) | 7.19107e7 | − | 4.15177e7i | 0.405121 | − | 0.233897i | ||||
\(563\) | 2.94593e6 | 0.0165081 | 0.00825405 | − | 0.999966i | \(-0.497373\pi\) | ||||
0.00825405 | + | 0.999966i | \(0.497373\pi\) | |||||||
\(564\) | −2.93981e7 | + | 1.69730e7i | −0.163863 | + | 0.0946066i | ||||
\(565\) | 1.36566e8 | + | 2.36539e8i | 0.757176 | + | 1.31147i | ||||
\(566\) | 2.18991e8 | + | 1.26435e8i | 1.20775 | + | 0.697296i | ||||
\(567\) | − | 7.35461e6i | − | 0.0403469i | ||||||
\(568\) | −2.71022e8 | + | 4.69424e8i | −1.47897 | + | 2.56166i | ||||
\(569\) | 1.23198e8 | + | 2.13385e8i | 0.668754 | + | 1.15832i | 0.978253 | + | 0.207416i | \(0.0665055\pi\) |
−0.309498 | + | 0.950900i | \(0.600161\pi\) | |||||||
\(570\) | 6.79640e8 | 3.66990 | ||||||||
\(571\) | 1.76447e8 | − | 1.01872e8i | 0.947776 | − | 0.547199i | 0.0553865 | − | 0.998465i | \(-0.482361\pi\) |
0.892389 | + | 0.451266i | \(0.149028\pi\) | |||||||
\(572\) | 4.62103e8 | − | 8.00385e8i | 2.46917 | − | 4.27672i | ||||
\(573\) | −1.30481e8 | + | 2.26000e8i | −0.693560 | + | 1.20128i | ||||
\(574\) | 2.69989e6 | − | 4.67634e6i | 0.0142761 | − | 0.0247270i | ||||
\(575\) | −4.13552e6 | −0.0217534 | ||||||||
\(576\) | −6.81658e7 | + | 1.18067e8i | −0.356697 | + | 0.617817i | ||||
\(577\) | 1.56805e8 | + | 9.05314e7i | 0.816268 | + | 0.471272i | 0.849128 | − | 0.528188i | \(-0.177128\pi\) |
−0.0328601 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(578\) | −3.16656e8 | + | 1.82821e8i | −1.63985 | + | 0.946767i | ||||
\(579\) | −5.56850e7 | + | 3.21498e7i | −0.286882 | + | 0.165631i | ||||
\(580\) | 1.33230e7 | 0.0682838 | ||||||||
\(581\) | − | 1.15405e7i | − | 0.0588433i | ||||||
\(582\) | −2.72630e8 | − | 4.72209e8i | −1.38294 | − | 2.39533i | ||||
\(583\) | −3.43330e6 | − | 5.94664e6i | −0.0173263 | − | 0.0300100i | ||||
\(584\) | −1.40579e8 | + | 2.43490e8i | −0.705799 | + | 1.22248i | ||||
\(585\) | 3.80446e7 | + | 2.19650e7i | 0.190031 | + | 0.109715i | ||||
\(586\) | − | 1.76510e8i | − | 0.877154i | ||||||
\(587\) | 7.40697e7 | + | 4.27642e7i | 0.366207 | + | 0.211430i | 0.671800 | − | 0.740733i | \(-0.265521\pi\) |
−0.305593 | + | 0.952162i | \(0.598855\pi\) | |||||||
\(588\) | 5.28398e8 | + | 3.05071e8i | 2.59914 | + | 1.50061i | ||||
\(589\) | 7.89634e7 | + | 4.55895e7i | 0.386438 | + | 0.223110i | ||||
\(590\) | −3.33363e8 | − | 5.77402e8i | −1.62316 | − | 2.81140i | ||||
\(591\) | 1.61554e8i | 0.782629i | ||||||||
\(592\) | −1.40490e9 | + | 8.11118e8i | −6.77142 | + | 3.90948i | ||||
\(593\) | −1.31976e8 | − | 7.61962e7i | −0.632892 | − | 0.365401i | 0.148979 | − | 0.988840i | \(-0.452401\pi\) |
−0.781871 | + | 0.623440i | \(0.785735\pi\) | |||||||
\(594\) | 4.84960e8 | 2.31391 | ||||||||
\(595\) | 589771. | − | 1.02151e6i | 0.00279984 | − | 0.00484946i | ||||
\(596\) | 3.75376e8 | − | 2.16723e8i | 1.77308 | − | 1.02369i | ||||
\(597\) | 1.38167e8 | + | 2.39312e8i | 0.649353 | + | 1.12471i | ||||
\(598\) | 2.61097e8i | 1.22095i | ||||||||
\(599\) | 3.18579e7 | + | 5.51795e7i | 0.148230 | + | 0.256742i | 0.930573 | − | 0.366105i | \(-0.119309\pi\) |
−0.782343 | + | 0.622848i | \(0.785976\pi\) | |||||||
\(600\) | 3.75920e7 | 0.174037 | ||||||||
\(601\) | − | 2.16657e8i | − | 0.998044i | −0.866589 | − | 0.499022i | \(-0.833693\pi\) | ||
0.866589 | − | 0.499022i | \(-0.166307\pi\) | |||||||
\(602\) | −8.17802e6 | + | 1.26015e7i | −0.0374851 | + | 0.0577609i | ||||
\(603\) | 4.95426e6 | 0.0225957 | ||||||||
\(604\) | 5.66595e8i | 2.57135i | ||||||||
\(605\) | −1.40402e8 | + | 8.10612e7i | −0.634026 | + | 0.366055i | ||||
\(606\) | −5.20452e8 | −2.33864 | ||||||||
\(607\) | 6.59918e7 | − | 3.81004e7i | 0.295069 | − | 0.170358i | −0.345156 | − | 0.938545i | \(-0.612174\pi\) |
0.640226 | + | 0.768187i | \(0.278841\pi\) | |||||||
\(608\) | −8.49293e8 | − | 1.47102e9i | −3.77874 | − | 6.54497i | ||||
\(609\) | −188175. | − | 108643.i | −0.000833123 | − | 0.000481004i | ||||
\(610\) | − | 4.51033e8i | − | 1.98710i | ||||||
\(611\) | 9.63967e6 | − | 1.66964e7i | 0.0422609 | − | 0.0731980i | ||||
\(612\) | 8.64160e6 | + | 1.49677e7i | 0.0376999 | + | 0.0652981i | ||||
\(613\) | 1.74252e8 | 0.756478 | 0.378239 | − | 0.925708i | \(-0.376530\pi\) | ||||
0.378239 | + | 0.925708i | \(0.376530\pi\) | |||||||
\(614\) | −3.08226e8 | + | 1.77954e8i | −1.33157 | + | 0.768783i | ||||
\(615\) | −5.08804e7 | + | 8.81274e7i | −0.218738 | + | 0.378866i | ||||
\(616\) | 1.89613e7 | − | 3.28419e7i | 0.0811197 | − | 0.140503i | ||||
\(617\) | −1.14669e8 | + | 1.98612e8i | −0.488191 | + | 0.845571i | −0.999908 | − | 0.0135828i | \(-0.995676\pi\) |
0.511717 | + | 0.859154i | \(0.329010\pi\) | |||||||
\(618\) | 3.27432e8 | 1.38725 | ||||||||
\(619\) | 1.20075e8 | − | 2.07976e8i | 0.506268 | − | 0.876882i | −0.493705 | − | 0.869629i | \(-0.664358\pi\) |
0.999974 | − | 0.00725313i | \(-0.00230876\pi\) | |||||||
\(620\) | −1.39822e8 | − | 8.07265e7i | −0.586681 | − | 0.338720i | ||||
\(621\) | −8.72716e7 | + | 5.03863e7i | −0.364417 | + | 0.210396i | ||||
\(622\) | −6.88924e7 | + | 3.97750e7i | −0.286286 | + | 0.165287i | ||||
\(623\) | −7.83895e6 | −0.0324186 | ||||||||
\(624\) | − | 1.39331e9i | − | 5.73447i | ||||||
\(625\) | 1.16129e8 | + | 2.01142e8i | 0.475666 | + | 0.823878i | ||||
\(626\) | −1.86667e8 | − | 3.23317e8i | −0.760931 | − | 1.31797i | ||||
\(627\) | 3.15095e8 | − | 5.45760e8i | 1.27832 | − | 2.21411i | ||||
\(628\) | 1.90411e8 | + | 1.09934e8i | 0.768799 | + | 0.443866i | ||||
\(629\) | 7.96970e7i | 0.320251i | ||||||||
\(630\) | 2.43749e6 | + | 1.40728e6i | 0.00974811 | + | 0.00562808i | ||||
\(631\) | −3.39232e8 | − | 1.95856e8i | −1.35023 | − | 0.779557i | −0.361951 | − | 0.932197i | \(-0.617889\pi\) |
−0.988282 | + | 0.152640i | \(0.951222\pi\) | |||||||
\(632\) | 3.24313e8 | + | 1.87242e8i | 1.28473 | + | 0.741741i | ||||
\(633\) | −1.34604e8 | − | 2.33140e8i | −0.530696 | − | 0.919192i | ||||
\(634\) | 2.95209e8i | 1.15841i | ||||||||
\(635\) | −1.42404e8 | + | 8.22172e7i | −0.556163 | + | 0.321101i | ||||
\(636\) | −1.75385e7 | − | 1.01259e7i | −0.0681744 | − | 0.0393605i | ||||
\(637\) | −3.46524e8 | −1.34065 | ||||||||
\(638\) | 8.39772e6 | − | 1.45453e7i | 0.0323370 | − | 0.0560093i | ||||
\(639\) | −3.23051e7 | + | 1.86514e7i | −0.123814 | + | 0.0714839i | ||||
\(640\) | 5.19841e8 | + | 9.00391e8i | 1.98304 | + | 3.43472i | ||||
\(641\) | 3.16004e8i | 1.19983i | 0.800066 | + | 0.599913i | \(0.204798\pi\) | ||||
−0.800066 | + | 0.599913i | \(0.795202\pi\) | |||||||
\(642\) | 1.07777e8 | + | 1.86675e8i | 0.407306 | + | 0.705475i | ||||
\(643\) | −2.06061e8 | −0.775108 | −0.387554 | − | 0.921847i | \(-0.626680\pi\) | ||||
−0.387554 | + | 0.921847i | \(0.626680\pi\) | |||||||
\(644\) | 1.23042e7i | 0.0460677i | ||||||||
\(645\) | 1.54118e8 | − | 2.37480e8i | 0.574345 | − | 0.885011i | ||||
\(646\) | −1.51860e8 | −0.563309 | ||||||||
\(647\) | − | 1.14893e8i | − | 0.424211i | −0.977247 | − | 0.212106i | \(-0.931968\pi\) | ||
0.977247 | − | 0.212106i | \(-0.0680321\pi\) | |||||||
\(648\) | 9.29934e8 | − | 5.36898e8i | 3.41765 | − | 1.97318i | ||||
\(649\) | −6.18216e8 | −2.26155 | ||||||||
\(650\) | −2.88701e7 | + | 1.66682e7i | −0.105126 | + | 0.0606943i | ||||
\(651\) | 1.31657e6 | + | 2.28037e6i | 0.00477202 | + | 0.00826538i | ||||
\(652\) | 9.04864e8 | + | 5.22423e8i | 3.26468 | + | 1.88486i | ||||
\(653\) | − | 1.08184e8i | − | 0.388528i | −0.980949 | − | 0.194264i | \(-0.937768\pi\) | ||
0.980949 | − | 0.194264i | \(-0.0622319\pi\) | |||||||
\(654\) | −1.36880e8 | + | 2.37083e8i | −0.489335 | + | 0.847553i | ||||
\(655\) | 2.60980e7 | + | 4.52031e7i | 0.0928717 | + | 0.160858i | ||||
\(656\) | 4.62826e8 | 1.63948 | ||||||||
\(657\) | −1.67566e7 | + | 9.67443e6i | −0.0590867 | + | 0.0341137i | ||||
\(658\) | 617606. | − | 1.06973e6i | 0.00216787 | − | 0.00375487i | ||||
\(659\) | −7.14166e7 | + | 1.23697e8i | −0.249542 | + | 0.432219i | −0.963399 | − | 0.268073i | \(-0.913613\pi\) |
0.713857 | + | 0.700291i | \(0.246947\pi\) | |||||||
\(660\) | −5.57946e8 | + | 9.66391e8i | −1.94071 | + | 3.36141i | ||||
\(661\) | 1.97261e8 | 0.683025 | 0.341513 | − | 0.939877i | \(-0.389061\pi\) | ||||
0.341513 | + | 0.939877i | \(0.389061\pi\) | |||||||
\(662\) | −3.86326e8 | + | 6.69137e8i | −1.33162 | + | 2.30643i | ||||
\(663\) | −5.92796e7 | − | 3.42251e7i | −0.203406 | − | 0.117437i | ||||
\(664\) | 1.45921e9 | − | 8.42476e8i | 4.98441 | − | 2.87775i | ||||
\(665\) | −1.57531e7 | + | 9.09503e6i | −0.0535673 | + | 0.0309271i | ||||
\(666\) | −1.90169e8 | −0.643750 | ||||||||
\(667\) | 3.49002e6i | 0.0117612i | ||||||||
\(668\) | −1.88452e8 | − | 3.26409e8i | −0.632226 | − | 1.09505i | ||||
\(669\) | 1.20636e8 | + | 2.08948e8i | 0.402902 | + | 0.697846i | ||||
\(670\) | 3.85407e7 | − | 6.67545e7i | 0.128143 | − | 0.221950i | ||||
\(671\) | −3.62186e8 | − | 2.09108e8i | −1.19885 | − | 0.692155i | ||||
\(672\) | − | 4.90533e7i | − | 0.161644i | ||||||
\(673\) | −1.61435e8 | − | 9.32043e7i | −0.529604 | − | 0.305767i | 0.211251 | − | 0.977432i | \(-0.432246\pi\) |
−0.740855 | + | 0.671665i | \(0.765580\pi\) | |||||||
\(674\) | −3.50676e8 | − | 2.02463e8i | −1.14532 | − | 0.661251i | ||||
\(675\) | −1.11427e7 | − | 6.43322e6i | −0.0362308 | − | 0.0209178i | ||||
\(676\) | 3.44460e8 | + | 5.96622e8i | 1.11506 | + | 1.93134i | ||||
\(677\) | − | 3.12709e8i | − | 1.00780i | −0.863762 | − | 0.503900i | \(-0.831898\pi\) | ||
0.863762 | − | 0.503900i | \(-0.168102\pi\) | |||||||
\(678\) | 8.79454e8 | − | 5.07753e8i | 2.82179 | − | 1.62916i | ||||
\(679\) | 1.26383e7 | + | 7.29674e6i | 0.0403720 | + | 0.0233088i | ||||
\(680\) | 1.72217e8 | 0.547708 | ||||||||
\(681\) | −1.03840e8 | + | 1.79856e8i | −0.328794 | + | 0.569488i | ||||
\(682\) | −1.76265e8 | + | 1.01767e8i | −0.555666 | + | 0.320814i | ||||
\(683\) | 2.43889e8 | + | 4.22429e8i | 0.765474 | + | 1.32584i | 0.939996 | + | 0.341187i | \(0.110829\pi\) |
−0.174521 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(684\) | − | 2.66529e8i | − | 0.832868i | ||||||
\(685\) | 4.00900e7 | + | 6.94379e7i | 0.124728 | + | 0.216035i | ||||
\(686\) | −4.44310e7 | −0.137630 | ||||||||
\(687\) | 3.90913e7i | 0.120562i | ||||||||
\(688\) | −1.28587e9 | − | 6.69929e7i | −3.94851 | − | 0.205714i | ||||
\(689\) | 1.15018e7 | 0.0351648 | ||||||||
\(690\) | − | 3.15251e8i | − | 0.959641i | ||||||
\(691\) | 4.30022e8 | − | 2.48273e8i | 1.30333 | − | 0.752481i | 0.322360 | − | 0.946617i | \(-0.395524\pi\) |
0.980975 | + | 0.194136i | \(0.0621904\pi\) | |||||||
\(692\) | 1.29606e8 | 0.391117 | ||||||||
\(693\) | 2.26014e6 | − | 1.30489e6i | 0.00679102 | − | 0.00392080i | ||||
\(694\) | 4.08173e8 | + | 7.06977e8i | 1.22114 | + | 2.11508i | ||||
\(695\) | −8.14841e6 | − | 4.70449e6i | −0.0242727 | − | 0.0140139i | ||||
\(696\) | − | 3.17243e7i | − | 0.0940946i | ||||||
\(697\) | 1.13688e7 | − | 1.96914e7i | 0.0335751 | − | 0.0581538i | ||||
\(698\) | −1.14447e8 | − | 1.98228e8i | −0.336541 | − | 0.582906i | ||||
\(699\) | −5.44982e8 | −1.59570 | ||||||||
\(700\) | −1.36051e6 | + | 785489.i | −0.00396649 | + | 0.00229006i | ||||
\(701\) | −6.44281e7 | + | 1.11593e8i | −0.187034 | + | 0.323953i | −0.944260 | − | 0.329200i | \(-0.893221\pi\) |
0.757226 | + | 0.653153i | \(0.226554\pi\) | |||||||
\(702\) | −4.06163e8 | + | 7.03494e8i | −1.17406 | + | 2.03352i | ||||
\(703\) | 6.14515e8 | − | 1.06437e9i | 1.76875 | − | 3.06356i | ||||
\(704\) | 1.96680e9 | 5.63693 | ||||||||
\(705\) | −1.16390e7 | + | 2.01594e7i | −0.0332161 | + | 0.0575320i | ||||
\(706\) | 4.33635e8 | + | 2.50360e8i | 1.23228 | + | 0.711459i | ||||
\(707\) | 1.20633e7 | − | 6.96476e6i | 0.0341357 | − | 0.0197082i | ||||
\(708\) | −1.57903e9 | + | 9.11656e8i | −4.44930 | + | 2.56881i | ||||
\(709\) | −2.23174e8 | −0.626190 | −0.313095 | − | 0.949722i | \(-0.601366\pi\) | ||||
−0.313095 | + | 0.949722i | \(0.601366\pi\) | |||||||
\(710\) | 5.80379e8i | 1.62157i | ||||||||
\(711\) | 1.28857e7 | + | 2.23187e7i | 0.0358509 | + | 0.0620956i | ||||
\(712\) | −5.72255e8 | − | 9.91175e8i | −1.58544 | − | 2.74606i | ||||
\(713\) | 2.11467e7 | − | 3.66271e7i | 0.0583410 | − | 0.101050i | ||||
\(714\) | −3.79800e6 | − | 2.19278e6i | −0.0104342 | − | 0.00602420i | ||||
\(715\) | − | 6.33761e8i | − | 1.73383i | ||||||
\(716\) | −1.46389e9 | − | 8.45179e8i | −3.98814 | − | 2.30255i | ||||
\(717\) | −3.22511e8 | − | 1.86202e8i | −0.874957 | − | 0.505157i | ||||
\(718\) | −2.40562e8 | − | 1.38889e8i | −0.649912 | − | 0.375227i | ||||
\(719\) | −8.48392e7 | − | 1.46946e8i | −0.228249 | − | 0.395340i | 0.729040 | − | 0.684471i | \(-0.239967\pi\) |
−0.957289 | + | 0.289132i | \(0.906634\pi\) | |||||||
\(720\) | 2.41242e8i | 0.646333i | ||||||||
\(721\) | −7.58940e6 | + | 4.38174e6i | −0.0202489 | + | 0.0116907i | ||||
\(722\) | 1.39432e9 | + | 8.05011e8i | 3.70468 | + | 2.13890i | ||||
\(723\) | −5.59631e8 | −1.48077 | ||||||||
\(724\) | 1.36397e8 | − | 2.36246e8i | 0.359409 | − | 0.622514i | ||||
\(725\) | −385900. | + | 222799.i | −0.00101265 | + | 0.000584655i | ||||
\(726\) | 3.01386e8 | + | 5.22016e8i | 0.787614 | + | 1.36419i | ||||
\(727\) | − | 3.79985e8i | − | 0.988925i | −0.869199 | − | 0.494463i | \(-0.835365\pi\) | ||
0.869199 | − | 0.494463i | \(-0.164635\pi\) | |||||||
\(728\) | 3.17609e7 | + | 5.50114e7i | 0.0823186 | + | 0.142580i | ||||
\(729\) | −3.02666e8 | −0.781233 | ||||||||
\(730\) | 3.01042e8i | 0.773852i | ||||||||
\(731\) | −3.44364e7 | + | 5.30632e7i | −0.0881588 | + | 0.135844i | ||||
\(732\) | −1.23345e9 | −3.14477 | ||||||||
\(733\) | 7.46515e8i | 1.89551i | 0.318997 | + | 0.947756i | \(0.396654\pi\) | ||||
−0.318997 | + | 0.947756i | \(0.603346\pi\) | |||||||
\(734\) | 2.04378e8 | − | 1.17998e8i | 0.516828 | − | 0.298391i | ||||
\(735\) | 4.18396e8 | 1.05372 | ||||||||
\(736\) | −6.82332e8 | + | 3.93944e8i | −1.71144 | + | 0.988102i | ||||
\(737\) | −3.57365e7 | − | 6.18975e7i | −0.0892709 | − | 0.154622i | ||||
\(738\) | 4.69866e7 | + | 2.71277e7i | 0.116897 | + | 0.0674908i | ||||
\(739\) | 4.67169e8i | 1.15755i | 0.815487 | + | 0.578776i | \(0.196469\pi\) | ||||
−0.815487 | + | 0.578776i | \(0.803531\pi\) | |||||||
\(740\) | −1.08814e9 | + | 1.88471e9i | −2.68527 | + | 4.65103i | ||||
\(741\) | 5.27795e8 | + | 9.14167e8i | 1.29721 | + | 2.24683i | ||||
\(742\) | 736911. | 0.00180386 | ||||||||
\(743\) | 6.71638e8 | − | 3.87770e8i | 1.63745 | − | 0.945384i | 0.655748 | − | 0.754980i | \(-0.272354\pi\) |
0.981706 | − | 0.190404i | \(-0.0609798\pi\) | |||||||
\(744\) | −1.92224e8 | + | 3.32941e8i | −0.466754 | + | 0.808442i | ||||
\(745\) | 1.48615e8 | − | 2.57409e8i | 0.359413 | − | 0.622522i | ||||
\(746\) | −4.30301e8 | + | 7.45304e8i | −1.03647 | + | 1.79522i | ||||
\(747\) | 1.15956e8 | 0.278183 | ||||||||
\(748\) | 1.24669e8 | − | 2.15933e8i | 0.297888 | − | 0.515957i | ||||
\(749\) | −4.99622e6 | − | 2.88457e6i | −0.0118904 | − | 0.00686492i | ||||
\(750\) | 7.84406e8 | − | 4.52877e8i | 1.85933 | − | 1.07349i | ||||
\(751\) | 4.01930e8 | − | 2.32055e8i | 0.948923 | − | 0.547861i | 0.0561766 | − | 0.998421i | \(-0.482109\pi\) |
0.892746 | + | 0.450560i | \(0.148776\pi\) | |||||||
\(752\) | 1.05873e8 | 0.248960 | ||||||||
\(753\) | 3.07916e7i | 0.0721186i | ||||||||
\(754\) | 1.40665e7 | + | 2.43638e7i | 0.0328149 | + | 0.0568371i | ||||
\(755\) | 1.94267e8 | + | 3.36481e8i | 0.451397 | + | 0.781843i | ||||
\(756\) | −1.91404e7 | + | 3.31522e7i | −0.0442983 | + | 0.0767268i | ||||
\(757\) | −2.51000e8 | − | 1.44915e8i | −0.578610 | − | 0.334061i | 0.181971 | − | 0.983304i | \(-0.441752\pi\) |
−0.760581 | + | 0.649243i | \(0.775086\pi\) | |||||||
\(758\) | − | 3.63699e8i | − | 0.835092i | ||||||
\(759\) | −2.53151e8 | − | 1.46157e8i | −0.578967 | − | 0.334267i | ||||
\(760\) | −2.29999e9 | − | 1.32790e9i | −5.23945 | − | 3.02500i | ||||
\(761\) | 1.65630e8 | + | 9.56263e7i | 0.375823 | + | 0.216982i | 0.676000 | − | 0.736902i | \(-0.263712\pi\) |
−0.300176 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(762\) | 3.05684e8 | + | 5.29461e8i | 0.690889 | + | 1.19665i | ||||
\(763\) | − | 7.32697e6i | − | 0.0164950i | ||||||
\(764\) | 1.37894e9 | − | 7.96132e8i | 3.09219 | − | 1.78527i | ||||
\(765\) | 1.02639e7 | + | 5.92586e6i | 0.0229260 | + | 0.0132363i | ||||
\(766\) | −5.01898e8 | −1.11668 | ||||||||
\(767\) | 5.17767e8 | − | 8.96799e8i | 1.14749 | − | 1.98751i | ||||
\(768\) | 1.54141e9 | − | 8.89931e8i | 3.40278 | − | 1.96459i | ||||
\(769\) | −3.45013e8 | − | 5.97579e8i | −0.758675 | − | 1.31406i | −0.943526 | − | 0.331298i | \(-0.892514\pi\) |
0.184851 | − | 0.982767i | \(-0.440820\pi\) | |||||||
\(770\) | − | 4.06046e7i | − | 0.0889412i | ||||||
\(771\) | −2.42909e8 | − | 4.20730e8i | −0.530005 | − | 0.917995i | ||||
\(772\) | 3.92324e8 | 0.852693 | ||||||||
\(773\) | 4.11780e8i | 0.891511i | 0.895155 | + | 0.445755i | \(0.147065\pi\) | ||||
−0.895155 | + | 0.445755i | \(0.852935\pi\) | |||||||
\(774\) | −1.26617e8 | − | 8.21704e7i | −0.273066 | − | 0.177212i | ||||
\(775\) | 5.39993e6 | 0.0116007 | ||||||||
\(776\) | 2.13069e9i | 4.55969i | ||||||||
\(777\) | 3.07378e7 | − | 1.77465e7i | 0.0655255 | − | 0.0378311i | ||||
\(778\) | 1.60311e9 | 3.40427 | ||||||||
\(779\) | −3.03666e8 | + | 1.75322e8i | −0.642369 | + | 0.370872i | ||||
\(780\) | −9.34579e8 | − | 1.61874e9i | −1.96939 | − | 3.41109i | ||||
\(781\) | 4.66053e8 | + | 2.69076e8i | 0.978322 | + | 0.564835i | ||||
\(782\) | 7.04403e7i | 0.147299i | ||||||||
\(783\) | −5.42907e6 | + | 9.40342e6i | −0.0113094 | + | 0.0195885i | ||||
\(784\) | −9.51470e8 | − | 1.64799e9i | −1.97445 | − | 3.41985i | ||||
\(785\) | 1.50771e8 | 0.311680 | ||||||||
\(786\) | 1.68065e8 | − | 9.70326e7i | 0.346107 | − | 0.199825i | ||||
\(787\) | −4.42621e8 | + | 7.66641e8i | −0.908045 | + | 1.57278i | −0.0912687 | + | 0.995826i | \(0.529092\pi\) |
−0.816777 | + | 0.576954i | \(0.804241\pi\) | |||||||
\(788\) | 4.92862e8 | − | 8.53662e8i | 1.00727 | − | 1.74465i | ||||
\(789\) | −3.33872e8 | + | 5.78283e8i | −0.679749 | + | 1.17736i | ||||
\(790\) | 4.00968e8 | 0.813259 | ||||||||
\(791\) | −1.35896e7 | + | 2.35380e7i | −0.0274586 | + | 0.0475597i | ||||
\(792\) | 3.29987e8 | + | 1.90518e8i | 0.664234 | + | 0.383496i | ||||
\(793\) | 6.06674e8 | − | 3.50264e8i | 1.21657 | − | 0.702385i | ||||
\(794\) | −9.28712e8 | + | 5.36192e8i | −1.85532 | + | 1.07117i | ||||
\(795\) | −1.38873e7 | −0.0276387 | ||||||||
\(796\) | − | 1.68605e9i | − | 3.34296i | ||||||
\(797\) | −1.92614e8 | − | 3.33618e8i | −0.380464 | − | 0.658983i | 0.610665 | − | 0.791889i | \(-0.290902\pi\) |
−0.991129 | + | 0.132907i | \(0.957569\pi\) | |||||||
\(798\) | 3.38154e7 | + | 5.85700e7i | 0.0665436 | + | 0.115257i | ||||
\(799\) | 2.60065e6 | − | 4.50445e6i | 0.00509848 | − | 0.00883084i | ||||
\(800\) | −8.71188e7 | − | 5.02980e7i | −0.170154 | − | 0.0982384i | ||||
\(801\) | − | 7.87636e7i | − | 0.153260i | ||||||
\(802\) | −1.32585e9 | − | 7.65480e8i | −2.57023 | − | 1.48392i | ||||
\(803\) | 2.41741e8 | + | 1.39569e8i | 0.466878 | + | 0.269552i | ||||
\(804\) | −1.82555e8 | − | 1.05398e8i | −0.351257 | − | 0.202798i | ||||
\(805\) | 4.21873e6 | + | 7.30705e6i | 0.00808712 | + | 0.0140073i | ||||
\(806\) | − | 3.40926e8i | − | 0.651111i | ||||||
\(807\) | 5.23772e8 | − | 3.02400e8i | 0.996603 | − | 0.575389i | ||||
\(808\) | 1.76128e9 | + | 1.01688e9i | 3.33883 | + | 1.92768i | ||||
\(809\) | 6.46910e8 | 1.22179 | 0.610897 | − | 0.791710i | \(-0.290809\pi\) | ||||
0.610897 | + | 0.791710i | \(0.290809\pi\) | |||||||
\(810\) | 5.74868e8 | − | 9.95701e8i | 1.08172 | − | 1.87359i | ||||
\(811\) | −1.45804e8 | + | 8.41799e7i | −0.273342 | + | 0.157814i | −0.630405 | − | 0.776266i | \(-0.717111\pi\) |
0.357063 | + | 0.934080i | \(0.383778\pi\) | |||||||
\(812\) | 662884. | + | 1.14815e6i | 0.00123814 | + | 0.00214452i | ||||
\(813\) | 8.78846e8i | 1.63546i | ||||||||
\(814\) | 1.37174e9 | + | 2.37593e9i | 2.54331 | + | 4.40515i | ||||
\(815\) | 7.16489e8 | 1.32354 | ||||||||
\(816\) | − | 3.75895e8i | − | 0.691824i | ||||||
\(817\) | 8.69056e8 | − | 4.43143e8i | 1.59361 | − | 0.812602i | ||||
\(818\) | 6.04585e8 | 1.10458 | ||||||||
\(819\) | 4.37147e6i | 0.00795749i | ||||||||
\(820\) | 5.37710e8 | − | 3.10447e8i | 0.975228 | − | 0.563048i | ||||
\(821\) | −7.16002e8 | −1.29385 | −0.646927 | − | 0.762552i | \(-0.723946\pi\) | ||||
−0.646927 | + | 0.762552i | \(0.723946\pi\) | |||||||
\(822\) | 2.58171e8 | − | 1.49055e8i | 0.464827 | − | 0.268368i | ||||
\(823\) | −1.35506e8 | − | 2.34703e8i | −0.243085 | − | 0.421035i | 0.718507 | − | 0.695520i | \(-0.244826\pi\) |
−0.961591 | + | 0.274485i | \(0.911493\pi\) | |||||||
\(824\) | −1.10807e9 | − | 6.39747e8i | −1.98056 | − | 1.14348i | ||||
\(825\) | − | 3.73220e7i | − | 0.0664665i | ||||||
\(826\) | 3.31729e7 | − | 5.74572e7i | 0.0588632 | − | 0.101954i | ||||
\(827\) | 1.76667e8 | + | 3.05996e8i | 0.312348 | + | 0.541003i | 0.978870 | − | 0.204482i | \(-0.0655511\pi\) |
−0.666522 | + | 0.745485i | \(0.732218\pi\) | |||||||
\(828\) | −1.23629e8 | −0.217786 | ||||||||
\(829\) | −8.33078e8 | + | 4.80978e8i | −1.46225 | + | 0.844231i | −0.999115 | − | 0.0420567i | \(-0.986609\pi\) |
−0.463135 | + | 0.886288i | \(0.653276\pi\) | |||||||
\(830\) | 9.02058e8 | − | 1.56241e9i | 1.57761 | − | 2.73250i | ||||
\(831\) | −4.10092e8 | + | 7.10300e8i | −0.714625 | + | 1.23777i | ||||
\(832\) | −1.64723e9 | + | 2.85309e9i | −2.86012 | + | 4.95387i | ||||
\(833\) | −9.34873e7 | −0.161740 | ||||||||
\(834\) | −1.74913e7 | + | 3.02959e7i | −0.0301526 | + | 0.0522259i | ||||
\(835\) | −2.23831e8 | − | 1.29229e8i | −0.384468 | − | 0.221973i | ||||
\(836\) | −3.32996e9 | + | 1.92255e9i | −5.69928 | + | 3.29048i | ||||
\(837\) | 1.13954e8 | − | 6.57915e7i | 0.194336 | − | 0.112200i | ||||
\(838\) | −6.30025e8 | −1.07060 | ||||||||
\(839\) | − | 1.58102e8i | − | 0.267703i | −0.991001 | − | 0.133851i | \(-0.957266\pi\) | ||
0.991001 | − | 0.133851i | \(-0.0427344\pi\) | |||||||
\(840\) | −3.83483e7 | − | 6.64212e7i | −0.0647006 | − | 0.112065i | ||||
\(841\) | −2.97224e8 | − | 5.14806e8i | −0.499684 | − | 0.865478i | ||||
\(842\) | 5.95844e8 | − | 1.03203e9i | 0.998151 | − | 1.72885i | ||||
\(843\) | −1.34854e8 | − | 7.78580e7i | −0.225103 | − | 0.129963i | ||||
\(844\) | 1.64257e9i | 2.73210i | ||||||||
\(845\) | 4.09126e8 | + | 2.36209e8i | 0.678089 | + | 0.391495i | ||||
\(846\) | 1.07483e7 | + | 6.20554e6i | 0.0177512 | + | 0.0102487i | ||||
\(847\) | −1.39714e7 | − | 8.06638e6i | −0.0229927 | − | 0.0132748i | ||||
\(848\) | 3.15811e7 | + | 5.47000e7i | 0.0517892 | + | 0.0897015i | ||||
\(849\) | − | 4.74206e8i | − | 0.774896i | ||||||
\(850\) | −7.78876e6 | + | 4.49684e6i | −0.0126827 | + | 0.00732235i | ||||
\(851\) | −4.93708e8 | − | 2.85042e8i | −0.801090 | − | 0.462510i | ||||
\(852\) | 1.58718e9 | 2.56629 | ||||||||
\(853\) | 4.16389e7 | − | 7.21206e7i | 0.0670891 | − | 0.116202i | −0.830530 | − | 0.556974i | \(-0.811962\pi\) |
0.897619 | + | 0.440773i | \(0.145296\pi\) | |||||||
\(854\) | 3.88692e7 | − | 2.24411e7i | 0.0624068 | − | 0.0360306i | ||||
\(855\) | −9.13843e7 | − | 1.58282e8i | −0.146209 | − | 0.253241i | ||||
\(856\) | − | 8.42312e8i | − | 1.34292i | ||||||
\(857\) | −9.48265e6 | − | 1.64244e7i | −0.0150656 | − | 0.0260944i | 0.858394 | − | 0.512990i | \(-0.171462\pi\) |
−0.873460 | + | 0.486896i | \(0.838129\pi\) | |||||||
\(858\) | −2.35633e9 | −3.73056 | ||||||||
\(859\) | 9.86301e8i | 1.55607i | 0.628219 | + | 0.778037i | \(0.283784\pi\) | ||||
−0.628219 | + | 0.778037i | \(0.716216\pi\) | |||||||
\(860\) | −1.53886e9 | + | 7.84685e8i | −2.41938 | + | 1.23367i | ||||
\(861\) | −1.01262e7 | −0.0158649 | ||||||||
\(862\) | − | 1.86962e9i | − | 2.91898i | ||||||
\(863\) | −9.53090e8 | + | 5.50267e8i | −1.48286 | + | 0.856132i | −0.999811 | − | 0.0194583i | \(-0.993806\pi\) |
−0.483054 | + | 0.875591i | \(0.660472\pi\) | |||||||
\(864\) | −2.45128e9 | −3.80059 | ||||||||
\(865\) | 7.69685e7 | − | 4.44378e7i | 0.118923 | − | 0.0686600i | ||||
\(866\) | −1.52386e8 | − | 2.63940e8i | −0.234634 | − | 0.406398i | ||||
\(867\) | 5.93824e8 | + | 3.42844e8i | 0.911172 | + | 0.526065i | ||||
\(868\) | − | 1.60662e7i | − | 0.0245670i | ||||||
\(869\) | 1.85897e8 | − | 3.21983e8i | 0.283278 | − | 0.490652i | ||||
\(870\) | −1.69840e7 | − | 2.94171e7i | −0.0257918 | − | 0.0446727i | ||||
\(871\) | 1.19720e8 | 0.181181 | ||||||||
\(872\) | 9.26440e8 | − | 5.34880e8i | 1.39723 | − | 0.806691i | ||||
\(873\) | −7.33156e7 | + | 1.26986e8i | −0.110193 | + | 0.190860i | ||||
\(874\) | 5.43140e8 | − | 9.40746e8i | 0.813537 | − | 1.40909i | ||||
\(875\) | −1.21209e7 | + | 2.09941e7i | −0.0180930 | + | 0.0313381i | ||||
\(876\) | 8.23265e8 | 1.22469 | ||||||||
\(877\) | 4.62691e8 | − | 8.01404e8i | 0.685950 | − | 1.18810i | −0.287187 | − | 0.957874i | \(-0.592720\pi\) |
0.973137 | − | 0.230226i | \(-0.0739464\pi\) | |||||||
\(878\) | 1.06445e9 | + | 6.14562e8i | 1.57269 | + | 0.907992i | ||||
\(879\) | −2.86662e8 | + | 1.65504e8i | −0.422088 | + | 0.243693i | ||||
\(880\) | 3.01403e9 | − | 1.74015e9i | 4.42283 | − | 2.55352i | ||||
\(881\) | 1.00866e9 | 1.47508 | 0.737541 | − | 0.675303i | \(-0.235987\pi\) | ||||
0.737541 | + | 0.675303i | \(0.235987\pi\) | |||||||
\(882\) | − | 2.23075e8i | − | 0.325121i | ||||||
\(883\) | 6.69193e8 | + | 1.15908e9i | 0.972007 | + | 1.68356i | 0.689479 | + | 0.724306i | \(0.257840\pi\) |
0.282528 | + | 0.959259i | \(0.408827\pi\) | |||||||
\(884\) | 2.08825e8 | + | 3.61695e8i | 0.302291 | + | 0.523583i | ||||
\(885\) | −6.25156e8 | + | 1.08280e9i | −0.901900 | + | 1.56214i | ||||
\(886\) | −1.36540e8 | − | 7.88313e7i | −0.196317 | − | 0.113344i | ||||
\(887\) | 7.97642e8i | 1.14298i | 0.820610 | + | 0.571488i | \(0.193634\pi\) | ||||
−0.820610 | + | 0.571488i | \(0.806366\pi\) | |||||||
\(888\) | 4.48781e9 | + | 2.59104e9i | 6.40908 | + | 3.70029i | ||||
\(889\) | −1.41706e7 | − | 8.18142e6i | −0.0201690 | − | 0.0116446i | ||||
\(890\) | −1.06127e9 | − | 6.12727e8i | −1.50542 | − | 0.869154i | ||||
\(891\) | −5.33041e8 | − | 9.23255e8i | −0.753577 | − | 1.30523i | ||||
\(892\) | − | 1.47212e9i | − | 2.07420i | ||||||
\(893\) | −6.94644e7 | + | 4.01053e7i | −0.0975457 | + | 0.0563180i | ||||
\(894\) | −9.57049e8 | − | 5.52553e8i | −1.33943 | − | 0.773323i | ||||
\(895\) | −1.15914e9 | −1.61684 | ||||||||
\(896\) | −5.17293e7 | + | 8.95978e7i | −0.0719138 | + | 0.124558i | ||||
\(897\) | 4.24036e8 | − | 2.44817e8i | 0.587524 | − | 0.339207i | ||||
\(898\) | −3.27480e8 | − | 5.67213e8i | −0.452227 | − | 0.783280i | ||||
\(899\) | − | 4.55707e6i | − | 0.00627201i | ||||||
\(900\) | −7.89238e6 | − | 1.36700e7i | −0.0108263 | − | 0.0187517i | ||||
\(901\) | 3.10302e6 | 0.00424239 | ||||||||
\(902\) | − | 7.82721e8i | − | 1.06657i | ||||||
\(903\) | 2.81337e7 | + | 1.46574e6i | 0.0382088 | + | 0.00199065i | ||||
\(904\) | −3.96826e9 | −5.37149 | ||||||||
\(905\) | − | 1.87065e8i | − | 0.252375i | ||||||
\(906\) | 1.25104e9 | − | 7.22288e8i | 1.68223 | − | 0.971238i | ||||
\(907\) | 8.64861e8 | 1.15911 | 0.579555 | − | 0.814933i | \(-0.303226\pi\) | ||||
0.579555 | + | 0.814933i | \(0.303226\pi\) | |||||||
\(908\) | 1.09739e9 | − | 6.33581e8i | 1.46590 | − | 0.846339i | ||||
\(909\) | 6.99800e7 | + | 1.21209e8i | 0.0931713 | + | 0.161377i | ||||
\(910\) | 5.89020e7 | + | 3.40071e7i | 0.0781638 | + | 0.0451279i | ||||
\(911\) | 9.87812e8i | 1.30653i | 0.757130 | + | 0.653265i | \(0.226601\pi\) | ||||
−0.757130 | + | 0.653265i | \(0.773399\pi\) | |||||||
\(912\) | −2.89839e9 | + | 5.02016e9i | −3.82096 | + | 6.61809i | ||||
\(913\) | −8.36424e8 | − | 1.44873e9i | −1.09904 | − | 1.90360i | ||||
\(914\) | 7.00876e8 | 0.917916 | ||||||||
\(915\) | −7.32503e8 | + | 4.22911e8i | −0.956195 | + | 0.552059i | ||||
\(916\) | 1.19258e8 | − | 2.06560e8i | 0.155167 | − | 0.268758i | ||||
\(917\) | −2.59701e6 | + | 4.49815e6i | −0.00336795 | + | 0.00583345i | ||||
\(918\) | −1.09577e8 | + | 1.89793e8i | −0.141642 | + | 0.245331i | ||||
\(919\) | 7.07776e8 | 0.911904 | 0.455952 | − | 0.890004i | \(-0.349299\pi\) | ||||
0.455952 | + | 0.890004i | \(0.349299\pi\) | |||||||
\(920\) | −6.15947e8 | + | 1.06685e9i | −0.791006 | + | 1.37006i | ||||
\(921\) | 5.78016e8 | + | 3.33717e8i | 0.739879 | + | 0.427169i | ||||
\(922\) | −9.97854e7 | + | 5.76111e7i | −0.127313 | + | 0.0735044i | ||||
\(923\) | −7.80655e8 | + | 4.50711e8i | −0.992782 | + | 0.573183i | ||||
\(924\) | −1.11042e8 | −0.140758 | ||||||||
\(925\) | − | 7.27873e7i | − | 0.0919667i | ||||||
\(926\) | −7.81391e8 | − | 1.35341e9i | −0.984091 | − | 1.70450i | ||||
\(927\) | −4.40265e7 | − | 7.62562e7i | −0.0552682 | − | 0.0957273i | ||||
\(928\) | −4.24471e7 | + | 7.35206e7i | −0.0531134 | + | 0.0919951i | ||||
\(929\) | −9.55525e8 | − | 5.51673e8i | −1.19178 | − | 0.688073i | −0.233068 | − | 0.972460i | \(-0.574876\pi\) |
−0.958709 | + | 0.284387i | \(0.908210\pi\) | |||||||
\(930\) | 4.11637e8i | 0.511759i | ||||||||
\(931\) | 1.24854e9 | + | 7.20847e8i | 1.54723 | + | 0.893293i | ||||
\(932\) | 2.87972e9 | + | 1.66261e9i | 3.55715 | + | 2.05372i | ||||
\(933\) | 1.29194e8 | + | 7.45901e7i | 0.159073 | + | 0.0918409i | ||||
\(934\) | 4.62429e8 | + | 8.00950e8i | 0.567550 | + | 0.983025i | ||||
\(935\) | − | 1.70980e8i | − | 0.209175i | ||||||
\(936\) | −5.52739e8 | + | 3.19124e8i | −0.674051 | + | 0.389164i | ||||
\(937\) | −4.35833e8 | − | 2.51628e8i | −0.529787 | − | 0.305873i | 0.211142 | − | 0.977455i | \(-0.432282\pi\) |
−0.740930 | + | 0.671582i | \(0.765615\pi\) | |||||||
\(938\) | 7.67036e6 | 0.00929410 | ||||||||
\(939\) | −3.50057e8 | + | 6.06316e8i | −0.422807 | + | 0.732323i | ||||
\(940\) | 1.23002e8 | − | 7.10155e7i | 0.148091 | − | 0.0855007i | ||||
\(941\) | −8.22526e7 | − | 1.42466e8i | −0.0987144 | − | 0.170978i | 0.812438 | − | 0.583047i | \(-0.198140\pi\) |
−0.911153 | + | 0.412069i | \(0.864806\pi\) | |||||||
\(942\) | − | 5.60569e8i | − | 0.670619i | ||||||
\(943\) | 8.13230e7 | + | 1.40856e8i | 0.0969791 | + | 0.167973i | ||||
\(944\) | 5.68664e9 | 6.75989 | ||||||||
\(945\) | 2.62506e7i | 0.0311060i | ||||||||
\(946\) | −1.13297e8 | + | 2.17464e9i | −0.133827 | + | 2.56871i | ||||
\(947\) | −6.33053e8 | −0.745401 | −0.372700 | − | 0.927952i | \(-0.621568\pi\) | ||||
−0.372700 | + | 0.927952i | \(0.621568\pi\) | |||||||
\(948\) | − | 1.09654e9i | − | 1.28706i | ||||||
\(949\) | −4.04924e8 | + | 2.33783e8i | −0.473778 | + | 0.273536i | ||||
\(950\) | 1.38694e8 | 0.161766 | ||||||||
\(951\) | 4.79436e8 | − | 2.76803e8i | 0.557429 | − | 0.321832i | ||||
\(952\) | 8.56863e6 | + | 1.48413e7i | 0.00993118 | + | 0.0172013i | ||||
\(953\) | −6.64437e8 | − | 3.83613e8i | −0.767671 | − | 0.443215i | 0.0643720 | − | 0.997926i | \(-0.479496\pi\) |
−0.832043 | + | 0.554711i | \(0.812829\pi\) | |||||||
\(954\) | 7.40427e6i | 0.00852781i | ||||||||
\(955\) | 5.45937e8 | − | 9.45590e8i | 0.626805 | − | 1.08566i | ||||
\(956\) | 1.13611e9 | + | 1.96780e9i | 1.30031 | + | 2.25220i | ||||
\(957\) | −3.14965e7 | −0.0359357 | ||||||||
\(958\) | −2.13204e9 | + | 1.23093e9i | −2.42493 | + | 1.40003i | ||||
\(959\) | −3.98935e6 | + | 6.90975e6i | −0.00452320 | + | 0.00783442i | ||||
\(960\) | 1.98888e9 | − | 3.44484e9i | 2.24799 | − | 3.89363i | ||||
\(961\) | 4.16140e8 | − | 7.20775e8i | 0.468888 | − | 0.812138i | ||||
\(962\) | −4.59544e9 | −5.16181 | ||||||||
\(963\) | 2.89834e7 | − | 5.02007e7i | 0.0324541 | − | 0.0562122i | ||||
\(964\) | 2.95712e9 | + | 1.70730e9i | 3.30095 | + | 1.90580i | ||||
\(965\) | 2.32987e8 | − | 1.34515e8i | 0.259269 | − | 0.149689i | ||||
\(966\) | 2.71677e7 | − | 1.56853e7i | 0.0301385 | − | 0.0174005i | ||||
\(967\) | −9.31483e8 | −1.03014 | −0.515069 | − | 0.857149i | \(-0.672234\pi\) | ||||
−0.515069 | + | 0.857149i | \(0.672234\pi\) | |||||||
\(968\) | − | 2.35543e9i | − | 2.59684i | ||||||
\(969\) | 1.42392e8 | + | 2.46630e8i | 0.156500 | + | 0.271065i | ||||
\(970\) | 1.14069e9 | + | 1.97573e9i | 1.24983 | + | 2.16478i | ||||
\(971\) | 2.93148e8 | − | 5.07747e8i | 0.320206 | − | 0.554612i | −0.660325 | − | 0.750980i | \(-0.729581\pi\) |
0.980530 | + | 0.196368i | \(0.0629147\pi\) | |||||||
\(972\) | −7.33185e8 | − | 4.23305e8i | −0.798390 | − | 0.460950i | ||||
\(973\) | − | 936286.i | − | 0.00101641i | ||||||
\(974\) | 2.17588e8 | + | 1.25624e8i | 0.235482 | + | 0.135956i | ||||
\(975\) | 5.41401e7 | + | 3.12578e7i | 0.0584124 | + | 0.0337244i | ||||
\(976\) | 3.33156e9 | + | 1.92348e9i | 3.58342 | + | 2.06889i | ||||
\(977\) | −5.35234e8 | − | 9.27053e8i | −0.573932 | − | 0.994079i | −0.996157 | − | 0.0875876i | \(-0.972084\pi\) |
0.422225 | − | 0.906491i | \(-0.361249\pi\) | |||||||
\(978\) | − | 2.66391e9i | − | 2.84776i | ||||||
\(979\) | −9.84056e8 | + | 5.68145e8i | −1.04875 | + | 0.605496i | ||||
\(980\) | −2.21083e9 | − | 1.27642e9i | −2.34897 | − | 1.35618i | ||||
\(981\) | 7.36194e7 | 0.0779804 | ||||||||
\(982\) | −6.51113e8 | + | 1.12776e9i | −0.687578 | + | 1.19092i | ||||
\(983\) | −1.08560e9 | + | 6.26769e8i | −1.14290 | + | 0.659853i | −0.947147 | − | 0.320801i | \(-0.896048\pi\) |
−0.195752 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(984\) | −7.39227e8 | − | 1.28038e9i | −0.775877 | − | 1.34386i | ||||
\(985\) | − | 6.75947e8i | − | 0.707300i | ||||||
\(986\) | 3.79494e6 | + | 6.57302e6i | 0.00395889 | + | 0.00685701i | ||||
\(987\) | −2.31639e6 | −0.00240913 | ||||||||
\(988\) | − | 6.44068e9i | − | 6.67823i | ||||||
\(989\) | −2.05552e8 | − | 4.03112e8i | −0.212487 | − | 0.416712i | ||||
\(990\) | 4.07984e8 | 0.420472 | ||||||||
\(991\) | 1.44253e9i | 1.48219i | 0.671400 | + | 0.741095i | \(0.265693\pi\) | ||||
−0.671400 | + | 0.741095i | \(0.734307\pi\) | |||||||
\(992\) | 8.90950e8 | − | 5.14390e8i | 0.912680 | − | 0.526936i | ||||
\(993\) | 1.44895e9 | 1.47981 | ||||||||
\(994\) | −5.00160e7 | + | 2.88767e7i | −0.0509272 | + | 0.0294028i | ||||
\(995\) | −5.78093e8 | − | 1.00129e9i | −0.586852 | − | 1.01646i | ||||
\(996\) | −4.27275e9 | − | 2.46688e9i | −4.32444 | − | 2.49672i | ||||
\(997\) | − | 6.09032e8i | − | 0.614547i | −0.951621 | − | 0.307273i | \(-0.900583\pi\) | ||
0.951621 | − | 0.307273i | \(-0.0994166\pi\) | |||||||
\(998\) | −1.05269e8 | + | 1.82330e8i | −0.105903 | + | 0.183429i | ||||
\(999\) | −8.86824e8 | − | 1.53602e9i | −0.889490 | − | 1.54064i |
(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 | 43.7.d.a.7.21 | ✓ | 42 | |
43.37 | odd | 6 | inner | 43.7.d.a.37.1 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.21 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.7.d.a.37.1 | yes | 42 | 43.37 | odd | 6 | inner |