Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\), degree \(1\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.11 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.7.b.a.39.12 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.52919 | − | 4.62273i | −0.816149 | − | 0.577841i | ||||
\(3\) | 11.8519i | 0.438959i | 0.975617 | + | 0.219480i | \(0.0704359\pi\) | ||||
−0.975617 | + | 0.219480i | \(0.929564\pi\) | |||||||
\(4\) | 21.2607 | + | 60.3654i | 0.332199 | + | 0.943209i | ||||
\(5\) | 179.762 | 1.43810 | 0.719048 | − | 0.694960i | \(-0.244578\pi\) | ||||
0.719048 | + | 0.694960i | \(0.244578\pi\) | |||||||
\(6\) | 54.7881 | − | 77.3834i | 0.253649 | − | 0.358256i | ||||
\(7\) | 39.4677i | 0.115066i | 0.998344 | + | 0.0575330i | \(0.0183234\pi\) | ||||
−0.998344 | + | 0.0575330i | \(0.981677\pi\) | |||||||
\(8\) | 140.237 | − | 492.420i | 0.273901 | − | 0.961758i | ||||
\(9\) | 588.532 | 0.807315 | ||||||||
\(10\) | −1173.70 | − | 830.991i | −1.17370 | − | 0.830991i | ||||
\(11\) | 536.570i | 0.403133i | 0.979475 | + | 0.201566i | \(0.0646032\pi\) | ||||
−0.979475 | + | 0.201566i | \(0.935397\pi\) | |||||||
\(12\) | −715.445 | + | 251.980i | −0.414030 | + | 0.145822i | ||||
\(13\) | −1508.07 | −0.686421 | −0.343211 | − | 0.939258i | \(-0.611515\pi\) | ||||
−0.343211 | + | 0.939258i | \(0.611515\pi\) | |||||||
\(14\) | 182.448 | − | 257.692i | 0.0664899 | − | 0.0939111i | ||||
\(15\) | 2130.52i | 0.631266i | ||||||||
\(16\) | −3191.96 | + | 2566.83i | −0.779288 | + | 0.626667i | ||||
\(17\) | 2145.25 | 0.436648 | 0.218324 | − | 0.975876i | \(-0.429941\pi\) | ||||
0.218324 | + | 0.975876i | \(0.429941\pi\) | |||||||
\(18\) | −3842.64 | − | 2720.63i | −0.658889 | − | 0.466500i | ||||
\(19\) | 1573.56i | 0.229416i | ||||||||
\(20\) | 3821.87 | + | 10851.4i | 0.477734 | + | 1.35643i | ||||
\(21\) | −467.767 | −0.0505093 | ||||||||
\(22\) | 2480.42 | − | 3503.37i | 0.232947 | − | 0.329016i | ||||
\(23\) | − | 261.443i | − | 0.0214879i | −0.999942 | − | 0.0107439i | \(-0.996580\pi\) | ||
0.999942 | − | 0.0107439i | \(-0.00341997\pi\) | |||||||
\(24\) | 5836.11 | + | 1662.08i | 0.422173 | + | 0.120231i | ||||
\(25\) | 16689.4 | 1.06812 | ||||||||
\(26\) | 9846.47 | + | 6971.39i | 0.560222 | + | 0.396643i | ||||
\(27\) | 15615.3i | 0.793338i | ||||||||
\(28\) | −2382.48 | + | 839.112i | −0.108531 | + | 0.0382248i | ||||
\(29\) | 40536.1 | 1.66207 | 0.831033 | − | 0.556223i | \(-0.187750\pi\) | ||||
0.831033 | + | 0.556223i | \(0.187750\pi\) | |||||||
\(30\) | 9848.83 | − | 13910.6i | 0.364771 | − | 0.515207i | ||||
\(31\) | − | 26418.9i | − | 0.886807i | −0.896322 | − | 0.443404i | \(-0.853771\pi\) | ||
0.896322 | − | 0.443404i | \(-0.146229\pi\) | |||||||
\(32\) | 32706.7 | − | 2003.73i | 0.998129 | − | 0.0611489i | ||||
\(33\) | −6359.37 | −0.176959 | ||||||||
\(34\) | −14006.8 | − | 9916.92i | −0.356370 | − | 0.252313i | ||||
\(35\) | 7094.79i | 0.165476i | ||||||||
\(36\) | 12512.6 | + | 35527.0i | 0.268189 | + | 0.761467i | ||||
\(37\) | 17559.3 | 0.346659 | 0.173330 | − | 0.984864i | \(-0.444547\pi\) | ||||
0.173330 | + | 0.984864i | \(0.444547\pi\) | |||||||
\(38\) | 7274.15 | − | 10274.1i | 0.132566 | − | 0.187237i | ||||
\(39\) | − | 17873.5i | − | 0.301311i | ||||||
\(40\) | 25209.4 | − | 88518.4i | 0.393896 | − | 1.38310i | ||||
\(41\) | 30619.5 | 0.444270 | 0.222135 | − | 0.975016i | \(-0.428697\pi\) | ||||
0.222135 | + | 0.975016i | \(0.428697\pi\) | |||||||
\(42\) | 3054.14 | + | 2162.36i | 0.0412231 | + | 0.0291864i | ||||
\(43\) | 131724.i | 1.65676i | 0.560167 | + | 0.828380i | \(0.310737\pi\) | ||||
−0.560167 | + | 0.828380i | \(0.689263\pi\) | |||||||
\(44\) | −32390.2 | + | 11407.9i | −0.380239 | + | 0.133920i | ||||
\(45\) | 105796. | 1.16100 | ||||||||
\(46\) | −1208.58 | + | 1707.01i | −0.0124166 | + | 0.0175373i | ||||
\(47\) | 198201.i | 1.90902i | 0.298172 | + | 0.954512i | \(0.403623\pi\) | ||||
−0.298172 | + | 0.954512i | \(0.596377\pi\) | |||||||
\(48\) | −30421.8 | − | 37830.8i | −0.275081 | − | 0.342075i | ||||
\(49\) | 116091. | 0.986760 | ||||||||
\(50\) | −108968. | − | 77150.5i | −0.871746 | − | 0.617204i | ||||
\(51\) | 25425.3i | 0.191671i | ||||||||
\(52\) | −32062.6 | − | 91035.1i | −0.228029 | − | 0.647439i | ||||
\(53\) | −128125. | −0.860607 | −0.430304 | − | 0.902684i | \(-0.641593\pi\) | ||||
−0.430304 | + | 0.902684i | \(0.641593\pi\) | |||||||
\(54\) | 72185.1 | − | 101955.i | 0.458423 | − | 0.647482i | ||||
\(55\) | 96454.9i | 0.579744i | ||||||||
\(56\) | 19434.7 | + | 5534.84i | 0.110666 | + | 0.0315167i | ||||
\(57\) | −18649.7 | −0.100704 | ||||||||
\(58\) | −264668. | − | 187388.i | −1.35649 | − | 0.960410i | ||||
\(59\) | − | 18873.2i | − | 0.0918947i | −0.998944 | − | 0.0459474i | \(-0.985369\pi\) | ||
0.998944 | − | 0.0459474i | \(-0.0146306\pi\) | |||||||
\(60\) | −128610. | + | 45296.5i | −0.595416 | + | 0.209706i | ||||
\(61\) | −166795. | −0.734841 | −0.367421 | − | 0.930055i | \(-0.619759\pi\) | ||||
−0.367421 | + | 0.930055i | \(0.619759\pi\) | |||||||
\(62\) | −122127. | + | 172494.i | −0.512434 | + | 0.723767i | ||||
\(63\) | 23228.0i | 0.0928945i | ||||||||
\(64\) | −222811. | − | 138111.i | −0.849956 | − | 0.526853i | ||||
\(65\) | −271093. | −0.987140 | ||||||||
\(66\) | 41521.6 | + | 29397.7i | 0.144425 | + | 0.102254i | ||||
\(67\) | − | 267170.i | − | 0.888307i | −0.895951 | − | 0.444154i | \(-0.853504\pi\) | ||
0.895951 | − | 0.444154i | \(-0.146496\pi\) | |||||||
\(68\) | 45609.6 | + | 129499.i | 0.145054 | + | 0.411850i | ||||
\(69\) | 3098.60 | 0.00943231 | ||||||||
\(70\) | 32797.3 | − | 46323.2i | 0.0956189 | − | 0.135053i | ||||
\(71\) | 104773.i | 0.292736i | 0.989230 | + | 0.146368i | \(0.0467583\pi\) | ||||
−0.989230 | + | 0.146368i | \(0.953242\pi\) | |||||||
\(72\) | 82534.3 | − | 289805.i | 0.221124 | − | 0.776441i | ||||
\(73\) | 263046. | 0.676180 | 0.338090 | − | 0.941114i | \(-0.390219\pi\) | ||||
0.338090 | + | 0.941114i | \(0.390219\pi\) | |||||||
\(74\) | −114648. | − | 81172.0i | −0.282926 | − | 0.200314i | ||||
\(75\) | 197801.i | 0.468862i | ||||||||
\(76\) | −94988.7 | + | 33455.1i | −0.216387 | + | 0.0762117i | ||||
\(77\) | −21177.1 | −0.0463869 | ||||||||
\(78\) | −82624.2 | + | 116699.i | −0.174110 | + | 0.245915i | ||||
\(79\) | 48638.0i | 0.0986495i | 0.998783 | + | 0.0493247i | \(0.0157069\pi\) | ||||
−0.998783 | + | 0.0493247i | \(0.984293\pi\) | |||||||
\(80\) | −573794. | + | 461418.i | −1.12069 | + | 0.901207i | ||||
\(81\) | 243970. | 0.459072 | ||||||||
\(82\) | −199921. | − | 141546.i | −0.362591 | − | 0.256718i | ||||
\(83\) | − | 317734.i | − | 0.555686i | −0.960626 | − | 0.277843i | \(-0.910380\pi\) | ||
0.960626 | − | 0.277843i | \(-0.0896195\pi\) | |||||||
\(84\) | −9945.07 | − | 28236.9i | −0.0167791 | − | 0.0476408i | ||||
\(85\) | 385635. | 0.627942 | ||||||||
\(86\) | 608924. | − | 860051.i | 0.957344 | − | 1.35216i | ||||
\(87\) | 480430.i | 0.729579i | ||||||||
\(88\) | 264218. | + | 75247.1i | 0.387716 | + | 0.110419i | ||||
\(89\) | 30232.1 | 0.0428843 | 0.0214421 | − | 0.999770i | \(-0.493174\pi\) | ||||
0.0214421 | + | 0.999770i | \(0.493174\pi\) | |||||||
\(90\) | −690761. | − | 489065.i | −0.947546 | − | 0.670872i | ||||
\(91\) | − | 59519.9i | − | 0.0789838i | ||||||
\(92\) | 15782.1 | − | 5558.47i | 0.0202676 | − | 0.00713826i | ||||
\(93\) | 313114. | 0.389272 | ||||||||
\(94\) | 916228. | − | 1.29409e6i | 1.10311 | − | 1.55805i | ||||
\(95\) | 282867.i | 0.329922i | ||||||||
\(96\) | 23748.0 | + | 387636.i | 0.0268419 | + | 0.438138i | ||||
\(97\) | 666671. | 0.730460 | 0.365230 | − | 0.930917i | \(-0.380990\pi\) | ||||
0.365230 | + | 0.930917i | \(0.380990\pi\) | |||||||
\(98\) | −757983. | − | 536659.i | −0.805343 | − | 0.570190i | ||||
\(99\) | 315789.i | 0.325455i | ||||||||
\(100\) | 354829. | + | 1.00746e6i | 0.354829 | + | 1.00746i | ||||
\(101\) | 57446.0 | 0.0557565 | 0.0278782 | − | 0.999611i | \(-0.491125\pi\) | ||||
0.0278782 | + | 0.999611i | \(0.491125\pi\) | |||||||
\(102\) | 117534. | − | 166007.i | 0.110755 | − | 0.156432i | ||||
\(103\) | 1.33511e6i | 1.22182i | 0.791701 | + | 0.610909i | \(0.209196\pi\) | ||||
−0.791701 | + | 0.610909i | \(0.790804\pi\) | |||||||
\(104\) | −211488. | + | 742603.i | −0.188012 | + | 0.660171i | ||||
\(105\) | −84086.7 | −0.0726372 | ||||||||
\(106\) | 836550. | + | 592285.i | 0.702384 | + | 0.497294i | ||||
\(107\) | − | 1.95799e6i | − | 1.59830i | −0.601130 | − | 0.799151i | \(-0.705283\pi\) | ||
0.601130 | − | 0.799151i | \(-0.294717\pi\) | |||||||
\(108\) | −942622. | + | 331992.i | −0.748283 | + | 0.263546i | ||||
\(109\) | −160354. | −0.123823 | −0.0619114 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619114 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(110\) | 445885. | − | 629773.i | 0.335000 | − | 0.473157i | ||||
\(111\) | 208111.i | 0.152169i | ||||||||
\(112\) | −101307. | − | 125979.i | −0.0721080 | − | 0.0896695i | ||||
\(113\) | −1.35711e6 | −0.940547 | −0.470274 | − | 0.882521i | \(-0.655845\pi\) | ||||
−0.470274 | + | 0.882521i | \(0.655845\pi\) | |||||||
\(114\) | 121768. | + | 86212.5i | 0.0821896 | + | 0.0581910i | ||||
\(115\) | − | 46997.5i | − | 0.0309016i | ||||||
\(116\) | 861828. | + | 2.44698e6i | 0.552137 | + | 1.56768i | ||||
\(117\) | −887547. | −0.554158 | ||||||||
\(118\) | −87245.9 | + | 123227.i | −0.0531005 | + | 0.0749998i | ||||
\(119\) | 84668.0i | 0.0502434i | ||||||||
\(120\) | 1.04911e6 | + | 298779.i | 0.607125 | + | 0.172904i | ||||
\(121\) | 1.48365e6 | 0.837484 | ||||||||
\(122\) | 1.08904e6 | + | 771048.i | 0.599740 | + | 0.424622i | ||||
\(123\) | 362900.i | 0.195017i | ||||||||
\(124\) | 1.59479e6 | − | 561685.i | 0.836445 | − | 0.294597i | ||||
\(125\) | 191337. | 0.0979645 | ||||||||
\(126\) | 107377. | − | 151660.i | 0.0536783 | − | 0.0758158i | ||||
\(127\) | − | 1.61576e6i | − | 0.788799i | −0.918939 | − | 0.394400i | \(-0.870953\pi\) | ||
0.918939 | − | 0.394400i | \(-0.129047\pi\) | |||||||
\(128\) | 816324. | + | 1.93175e6i | 0.389254 | + | 0.921131i | ||||
\(129\) | −1.56118e6 | −0.727250 | ||||||||
\(130\) | 1.77002e6 | + | 1.25319e6i | 0.805654 | + | 0.570410i | ||||
\(131\) | − | 3.34081e6i | − | 1.48606i | −0.669256 | − | 0.743032i | \(-0.733387\pi\) | ||
0.669256 | − | 0.743032i | \(-0.266613\pi\) | |||||||
\(132\) | −135205. | − | 383886.i | −0.0587856 | − | 0.166909i | ||||
\(133\) | −62104.8 | −0.0263980 | ||||||||
\(134\) | −1.23505e6 | + | 1.74440e6i | −0.513301 | + | 0.724991i | ||||
\(135\) | 2.80703e6i | 1.14090i | ||||||||
\(136\) | 300845. | − | 1.05636e6i | 0.119598 | − | 0.419950i | ||||
\(137\) | −4.68940e6 | −1.82371 | −0.911856 | − | 0.410511i | \(-0.865350\pi\) | ||||
−0.911856 | + | 0.410511i | \(0.865350\pi\) | |||||||
\(138\) | −20231.3 | − | 14324.0i | −0.00769817 | − | 0.00545037i | ||||
\(139\) | − | 1.72450e6i | − | 0.642125i | −0.947058 | − | 0.321063i | \(-0.895960\pi\) | ||
0.947058 | − | 0.321063i | \(-0.104040\pi\) | |||||||
\(140\) | −428280. | + | 150840.i | −0.156079 | + | 0.0549710i | ||||
\(141\) | −2.34905e6 | −0.837984 | ||||||||
\(142\) | 484339. | − | 684085.i | 0.169155 | − | 0.238916i | ||||
\(143\) | − | 809184.i | − | 0.276719i | ||||||
\(144\) | −1.87857e6 | + | 1.51066e6i | −0.629130 | + | 0.505917i | ||||
\(145\) | 7.28686e6 | 2.39021 | ||||||||
\(146\) | −1.71748e6 | − | 1.21599e6i | −0.551864 | − | 0.390725i | ||||
\(147\) | 1.37590e6i | 0.433147i | ||||||||
\(148\) | 373324. | + | 1.05998e6i | 0.115160 | + | 0.326972i | ||||
\(149\) | −2.31907e6 | −0.701060 | −0.350530 | − | 0.936551i | \(-0.613999\pi\) | ||||
−0.350530 | + | 0.936551i | \(0.613999\pi\) | |||||||
\(150\) | 914380. | − | 1.29148e6i | 0.270928 | − | 0.382661i | ||||
\(151\) | − | 4.41731e6i | − | 1.28300i | −0.767122 | − | 0.641501i | \(-0.778312\pi\) | ||
0.767122 | − | 0.641501i | \(-0.221688\pi\) | |||||||
\(152\) | 774854. | + | 220672.i | 0.220642 | + | 0.0628372i | ||||
\(153\) | 1.26255e6 | 0.352512 | ||||||||
\(154\) | 138270. | + | 97896.2i | 0.0378586 | + | 0.0268043i | ||||
\(155\) | − | 4.74911e6i | − | 1.27531i | ||||||
\(156\) | 1.07894e6 | − | 380003.i | 0.284199 | − | 0.100095i | ||||
\(157\) | 4.01544e6 | 1.03761 | 0.518804 | − | 0.854893i | \(-0.326377\pi\) | ||||
0.518804 | + | 0.854893i | \(0.326377\pi\) | |||||||
\(158\) | 224840. | − | 317567.i | 0.0570037 | − | 0.0805127i | ||||
\(159\) | − | 1.51852e6i | − | 0.377771i | ||||||
\(160\) | 5.87942e6 | − | 360194.i | 1.43541 | − | 0.0879381i | ||||
\(161\) | 10318.5 | 0.00247253 | ||||||||
\(162\) | −1.59293e6 | − | 1.12781e6i | −0.374671 | − | 0.265271i | ||||
\(163\) | 4.61245e6i | 1.06505i | 0.846415 | + | 0.532524i | \(0.178756\pi\) | ||||
−0.846415 | + | 0.532524i | \(0.821244\pi\) | |||||||
\(164\) | 650994. | + | 1.84836e6i | 0.147586 | + | 0.419040i | ||||
\(165\) | −1.14317e6 | −0.254484 | ||||||||
\(166\) | −1.46880e6 | + | 2.07455e6i | −0.321098 | + | 0.453523i | ||||
\(167\) | − | 1.92901e6i | − | 0.414175i | −0.978322 | − | 0.207088i | \(-0.933601\pi\) | ||
0.978322 | − | 0.207088i | \(-0.0663985\pi\) | |||||||
\(168\) | −65598.4 | + | 230338.i | −0.0138346 | + | 0.0485777i | ||||
\(169\) | −2.55254e6 | −0.528826 | ||||||||
\(170\) | −2.51788e6 | − | 1.78269e6i | −0.512494 | − | 0.362851i | ||||
\(171\) | 926093.i | 0.185211i | ||||||||
\(172\) | −7.95157e6 | + | 2.80055e6i | −1.56267 | + | 0.550374i | ||||
\(173\) | −4.01149e6 | −0.774761 | −0.387381 | − | 0.921920i | \(-0.626620\pi\) | ||||
−0.387381 | + | 0.921920i | \(0.626620\pi\) | |||||||
\(174\) | 2.22090e6 | − | 3.13682e6i | 0.421581 | − | 0.595445i | ||||
\(175\) | 658691.i | 0.122904i | ||||||||
\(176\) | −1.37728e6 | − | 1.71271e6i | −0.252630 | − | 0.314156i | ||||
\(177\) | 223684. | 0.0403380 | ||||||||
\(178\) | −197391. | − | 139755.i | −0.0350000 | − | 0.0247803i | ||||
\(179\) | 8.33008e6i | 1.45241i | 0.687477 | + | 0.726206i | \(0.258718\pi\) | ||||
−0.687477 | + | 0.726206i | \(0.741282\pi\) | |||||||
\(180\) | 2.24930e6 | + | 6.38640e6i | 0.385682 | + | 1.09506i | ||||
\(181\) | −7.40325e6 | −1.24849 | −0.624247 | − | 0.781227i | \(-0.714594\pi\) | ||||
−0.624247 | + | 0.781227i | \(0.714594\pi\) | |||||||
\(182\) | −275144. | + | 388617.i | −0.0456401 | + | 0.0644626i | ||||
\(183\) | − | 1.97684e6i | − | 0.322565i | ||||||
\(184\) | −128740. | − | 36664.1i | −0.0206661 | − | 0.00588556i | ||||
\(185\) | 3.15650e6 | 0.498529 | ||||||||
\(186\) | −2.04438e6 | − | 1.44744e6i | −0.317704 | − | 0.224938i | ||||
\(187\) | 1.15108e6i | 0.176027i | ||||||||
\(188\) | −1.19645e7 | + | 4.21389e6i | −1.80061 | + | 0.634176i | ||||
\(189\) | −616298. | −0.0912862 | ||||||||
\(190\) | 1.30762e6 | − | 1.84689e6i | 0.190642 | − | 0.269266i | ||||
\(191\) | − | 1.18467e7i | − | 1.70019i | −0.526626 | − | 0.850097i | \(-0.676543\pi\) | ||
0.526626 | − | 0.850097i | \(-0.323457\pi\) | |||||||
\(192\) | 1.63688e6 | − | 2.64073e6i | 0.231267 | − | 0.373096i | ||||
\(193\) | −1.00117e7 | −1.39264 | −0.696318 | − | 0.717733i | \(-0.745180\pi\) | ||||
−0.696318 | + | 0.717733i | \(0.745180\pi\) | |||||||
\(194\) | −4.35283e6 | − | 3.08184e6i | −0.596164 | − | 0.422090i | ||||
\(195\) | − | 3.21297e6i | − | 0.433314i | ||||||
\(196\) | 2.46819e6 | + | 7.00790e6i | 0.327801 | + | 0.930721i | ||||
\(197\) | −3.12661e6 | −0.408954 | −0.204477 | − | 0.978871i | \(-0.565549\pi\) | ||||
−0.204477 | + | 0.978871i | \(0.565549\pi\) | |||||||
\(198\) | 1.45981e6 | − | 2.06185e6i | 0.188061 | − | 0.265620i | ||||
\(199\) | 546538.i | 0.0693523i | 0.999399 | + | 0.0346762i | \(0.0110400\pi\) | ||||
−0.999399 | + | 0.0346762i | \(0.988960\pi\) | |||||||
\(200\) | 2.34048e6 | − | 8.21819e6i | 0.292560 | − | 1.02727i | ||||
\(201\) | 3.16647e6 | 0.389931 | ||||||||
\(202\) | −375076. | − | 265557.i | −0.0455056 | − | 0.0322184i | ||||
\(203\) | 1.59987e6i | 0.191247i | ||||||||
\(204\) | −1.53481e6 | + | 540561.i | −0.180786 | + | 0.0636728i | ||||
\(205\) | 5.50423e6 | 0.638903 | ||||||||
\(206\) | 6.17187e6 | − | 8.71722e6i | 0.706017 | − | 0.997186i | ||||
\(207\) | − | 153868.i | − | 0.0173475i | ||||||
\(208\) | 4.81370e6 | − | 3.87095e6i | 0.534920 | − | 0.430157i | ||||
\(209\) | −844326. | −0.0924850 | ||||||||
\(210\) | 549018. | + | 388710.i | 0.0592828 | + | 0.0419728i | ||||
\(211\) | − | 3.19130e6i | − | 0.339719i | −0.985468 | − | 0.169859i | \(-0.945669\pi\) | ||
0.985468 | − | 0.169859i | \(-0.0543314\pi\) | |||||||
\(212\) | −2.72402e6 | − | 7.73429e6i | −0.285893 | − | 0.811733i | ||||
\(213\) | −1.24176e6 | −0.128499 | ||||||||
\(214\) | −9.05125e6 | + | 1.27841e7i | −0.923565 | + | 1.30445i | ||||
\(215\) | 2.36790e7i | 2.38258i | ||||||||
\(216\) | 7.68927e6 | + | 2.18984e6i | 0.762999 | + | 0.217296i | ||||
\(217\) | 1.04269e6 | 0.102041 | ||||||||
\(218\) | 1.04698e6 | + | 741273.i | 0.101058 | + | 0.0715499i | ||||
\(219\) | 3.11759e6i | 0.296815i | ||||||||
\(220\) | −5.82254e6 | + | 2.05070e6i | −0.546820 | + | 0.192590i | ||||
\(221\) | −3.23519e6 | −0.299725 | ||||||||
\(222\) | 962042. | − | 1.35880e6i | 0.0879296 | − | 0.124193i | ||||
\(223\) | − | 1.82721e7i | − | 1.64768i | −0.566821 | − | 0.823841i | \(-0.691827\pi\) | ||
0.566821 | − | 0.823841i | \(-0.308173\pi\) | |||||||
\(224\) | 79082.5 | + | 1.29086e6i | 0.00703617 | + | 0.114851i | ||||
\(225\) | 9.82225e6 | 0.862310 | ||||||||
\(226\) | 8.86085e6 | + | 6.27357e6i | 0.767627 | + | 0.543487i | ||||
\(227\) | 1.50032e7i | 1.28265i | 0.767271 | + | 0.641323i | \(0.221614\pi\) | ||||
−0.767271 | + | 0.641323i | \(0.778386\pi\) | |||||||
\(228\) | −396507. | − | 1.12580e6i | −0.0334538 | − | 0.0949851i | ||||
\(229\) | 1.07397e7 | 0.894308 | 0.447154 | − | 0.894457i | \(-0.352438\pi\) | ||||
0.447154 | + | 0.894457i | \(0.352438\pi\) | |||||||
\(230\) | −217257. | + | 306856.i | −0.0178562 | + | 0.0252204i | ||||
\(231\) | − | 250989.i | − | 0.0203620i | ||||||
\(232\) | 5.68468e6 | − | 1.99608e7i | 0.455242 | − | 1.59850i | ||||
\(233\) | 2.09886e7 | 1.65926 | 0.829631 | − | 0.558312i | \(-0.188551\pi\) | ||||
0.829631 | + | 0.558312i | \(0.188551\pi\) | |||||||
\(234\) | 5.79497e6 | + | 4.10289e6i | 0.452276 | + | 0.320215i | ||||
\(235\) | 3.56290e7i | 2.74536i | ||||||||
\(236\) | 1.13929e6 | − | 401259.i | 0.0866759 | − | 0.0305273i | ||||
\(237\) | −576453. | −0.0433031 | ||||||||
\(238\) | 391398. | − | 552814.i | 0.0290327 | − | 0.0410061i | ||||
\(239\) | 1.23002e6i | 0.0900990i | 0.998985 | + | 0.0450495i | \(0.0143446\pi\) | ||||
−0.998985 | + | 0.0450495i | \(0.985655\pi\) | |||||||
\(240\) | −5.46868e6 | − | 6.80054e6i | −0.395593 | − | 0.491937i | ||||
\(241\) | 1.95724e7 | 1.39828 | 0.699139 | − | 0.714985i | \(-0.253567\pi\) | ||||
0.699139 | + | 0.714985i | \(0.253567\pi\) | |||||||
\(242\) | −9.68706e6 | − | 6.85853e6i | −0.683512 | − | 0.483933i | ||||
\(243\) | 1.42750e7i | 0.994851i | ||||||||
\(244\) | −3.54619e6 | − | 1.00686e7i | −0.244114 | − | 0.693109i | ||||
\(245\) | 2.08688e7 | 1.41906 | ||||||||
\(246\) | 1.67759e6 | − | 2.36944e6i | 0.112689 | − | 0.159163i | ||||
\(247\) | − | 2.37304e6i | − | 0.157476i | ||||||
\(248\) | −1.30092e7 | − | 3.70491e6i | −0.852894 | − | 0.242898i | ||||
\(249\) | 3.76575e6 | 0.243924 | ||||||||
\(250\) | −1.24928e6 | − | 884499.i | −0.0799537 | − | 0.0566079i | ||||
\(251\) | 1.20797e6i | 0.0763897i | 0.999270 | + | 0.0381949i | \(0.0121608\pi\) | ||||
−0.999270 | + | 0.0381949i | \(0.987839\pi\) | |||||||
\(252\) | −1.40217e6 | + | 493844.i | −0.0876190 | + | 0.0308595i | ||||
\(253\) | 140282. | 0.00866247 | ||||||||
\(254\) | −7.46924e6 | + | 1.05496e7i | −0.455801 | + | 0.643778i | ||||
\(255\) | 4.57051e6i | 0.275641i | ||||||||
\(256\) | 3.60002e6 | − | 1.63864e7i | 0.214578 | − | 0.976707i | ||||
\(257\) | −2.44754e7 | −1.44189 | −0.720943 | − | 0.692994i | \(-0.756291\pi\) | ||||
−0.720943 | + | 0.692994i | \(0.756291\pi\) | |||||||
\(258\) | 1.01932e7 | + | 7.21691e6i | 0.593544 | + | 0.420235i | ||||
\(259\) | 693025.i | 0.0398887i | ||||||||
\(260\) | −5.76365e6 | − | 1.63647e7i | −0.327927 | − | 0.931080i | ||||
\(261\) | 2.38568e7 | 1.34181 | ||||||||
\(262\) | −1.54437e7 | + | 2.18128e7i | −0.858709 | + | 1.21285i | ||||
\(263\) | − | 8.19021e6i | − | 0.450223i | −0.974333 | − | 0.225111i | \(-0.927725\pi\) | ||
0.974333 | − | 0.225111i | \(-0.0722746\pi\) | |||||||
\(264\) | −891822. | + | 3.13148e6i | −0.0484692 | + | 0.170192i | ||||
\(265\) | −2.30319e7 | −1.23764 | ||||||||
\(266\) | 405494. | + | 287094.i | 0.0215447 | + | 0.0152538i | ||||
\(267\) | 358308.i | 0.0188244i | ||||||||
\(268\) | 1.61278e7 | − | 5.68023e6i | 0.837860 | − | 0.295095i | ||||
\(269\) | 4.43886e6 | 0.228042 | 0.114021 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114021 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(270\) | 1.29761e7 | − | 1.83277e7i | 0.659257 | − | 0.931141i | ||||
\(271\) | − | 3.52126e7i | − | 1.76925i | −0.466301 | − | 0.884626i | \(-0.654414\pi\) | ||
0.466301 | − | 0.884626i | \(-0.345586\pi\) | |||||||
\(272\) | −6.84756e6 | + | 5.50649e6i | −0.340274 | + | 0.273633i | ||||
\(273\) | 705424. | 0.0346707 | ||||||||
\(274\) | 3.06180e7 | + | 2.16779e7i | 1.48842 | + | 1.05382i | ||||
\(275\) | 8.95502e6i | 0.430595i | ||||||||
\(276\) | 65878.5 | + | 187048.i | 0.00313340 | + | 0.00889664i | ||||
\(277\) | 1.56422e7 | 0.735965 | 0.367983 | − | 0.929833i | \(-0.380049\pi\) | ||||
0.367983 | + | 0.929833i | \(0.380049\pi\) | |||||||
\(278\) | −7.97191e6 | + | 1.12596e7i | −0.371046 | + | 0.524070i | ||||
\(279\) | − | 1.55484e7i | − | 0.715932i | ||||||
\(280\) | 3.49361e6 | + | 994954.i | 0.159148 | + | 0.0453241i | ||||
\(281\) | 2.32657e7 | 1.04857 | 0.524285 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524285 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(282\) | 1.53374e7 | + | 1.08590e7i | 0.683920 | + | 0.484222i | ||||
\(283\) | − | 1.17289e7i | − | 0.517486i | −0.965946 | − | 0.258743i | \(-0.916692\pi\) | ||
0.965946 | − | 0.258743i | \(-0.0833083\pi\) | |||||||
\(284\) | −6.32468e6 | + | 2.22756e6i | −0.276111 | + | 0.0972465i | ||||
\(285\) | −3.35251e6 | −0.144822 | ||||||||
\(286\) | −3.74064e6 | + | 5.28332e6i | −0.159900 | + | 0.225844i | ||||
\(287\) | 1.20848e6i | 0.0511204i | ||||||||
\(288\) | 1.92489e7 | − | 1.17926e6i | 0.805804 | − | 0.0493664i | ||||
\(289\) | −1.95355e7 | −0.809339 | ||||||||
\(290\) | −4.75773e7 | − | 3.36852e7i | −1.95077 | − | 1.38116i | ||||
\(291\) | 7.90132e6i | 0.320642i | ||||||||
\(292\) | 5.59254e6 | + | 1.58788e7i | 0.224626 | + | 0.637779i | ||||
\(293\) | −4.52757e7 | −1.79996 | −0.899979 | − | 0.435934i | \(-0.856418\pi\) | ||||
−0.899979 | + | 0.435934i | \(0.856418\pi\) | |||||||
\(294\) | 6.36043e6 | − | 8.98353e6i | 0.250290 | − | 0.353513i | ||||
\(295\) | − | 3.39269e6i | − | 0.132153i | ||||||
\(296\) | 2.46247e6 | − | 8.64656e6i | 0.0949503 | − | 0.333402i | ||||
\(297\) | −8.37868e6 | −0.319820 | ||||||||
\(298\) | 1.51417e7 | + | 1.07204e7i | 0.572170 | + | 0.405102i | ||||
\(299\) | 394274.i | 0.0147497i | ||||||||
\(300\) | −1.19403e7 | + | 4.20540e6i | −0.442235 | + | 0.155755i | ||||
\(301\) | −5.19884e6 | −0.190637 | ||||||||
\(302\) | −2.04200e7 | + | 2.88415e7i | −0.741372 | + | 1.04712i | ||||
\(303\) | 680844.i | 0.0244748i | ||||||||
\(304\) | −4.03906e6 | − | 5.02275e6i | −0.143767 | − | 0.178781i | ||||
\(305\) | −2.99834e7 | −1.05677 | ||||||||
\(306\) | −8.24344e6 | − | 5.83643e6i | −0.287703 | − | 0.203696i | ||||
\(307\) | − | 3.91648e7i | − | 1.35357i | −0.736181 | − | 0.676785i | \(-0.763373\pi\) | ||
0.736181 | − | 0.676785i | \(-0.236627\pi\) | |||||||
\(308\) | −450242. | − | 1.27837e6i | −0.0154097 | − | 0.0437525i | ||||
\(309\) | −1.58236e7 | −0.536329 | ||||||||
\(310\) | −2.19539e7 | + | 3.10079e7i | −0.736929 | + | 1.04085i | ||||
\(311\) | 3.14497e7i | 1.04553i | 0.852478 | + | 0.522763i | \(0.175099\pi\) | ||||
−0.852478 | + | 0.522763i | \(0.824901\pi\) | |||||||
\(312\) | −8.80125e6 | − | 2.50653e6i | −0.289788 | − | 0.0825295i | ||||
\(313\) | −2.43745e7 | −0.794883 | −0.397441 | − | 0.917628i | \(-0.630102\pi\) | ||||
−0.397441 | + | 0.917628i | \(0.630102\pi\) | |||||||
\(314\) | −2.62176e7 | − | 1.85623e7i | −0.846844 | − | 0.599573i | ||||
\(315\) | 4.17551e6i | 0.133591i | ||||||||
\(316\) | −2.93605e6 | + | 1.03408e6i | −0.0930471 | + | 0.0327713i | ||||
\(317\) | −3.40937e7 | −1.07028 | −0.535139 | − | 0.844764i | \(-0.679741\pi\) | ||||
−0.535139 | + | 0.844764i | \(0.679741\pi\) | |||||||
\(318\) | −7.01971e6 | + | 9.91471e6i | −0.218292 | + | 0.308318i | ||||
\(319\) | 2.17505e7i | 0.670033i | ||||||||
\(320\) | −4.00529e7 | − | 2.48272e7i | −1.22232 | − | 0.757666i | ||||
\(321\) | 2.32059e7 | 0.701589 | ||||||||
\(322\) | −67371.8 | − | 47699.8i | −0.00201795 | − | 0.00142873i | ||||
\(323\) | 3.37569e6i | 0.100174i | ||||||||
\(324\) | 5.18698e6 | + | 1.47273e7i | 0.152503 | + | 0.433001i | ||||
\(325\) | −2.51687e7 | −0.733181 | ||||||||
\(326\) | 2.13221e7 | − | 3.01156e7i | 0.615429 | − | 0.869238i | ||||
\(327\) | − | 1.90050e6i | − | 0.0543531i | ||||||
\(328\) | 4.29401e6 | − | 1.50777e7i | 0.121686 | − | 0.427280i | ||||
\(329\) | −7.82251e6 | −0.219664 | ||||||||
\(330\) | 7.46400e6 | + | 5.28458e6i | 0.207697 | + | 0.147051i | ||||
\(331\) | 1.75934e7i | 0.485139i | 0.970134 | + | 0.242569i | \(0.0779902\pi\) | ||||
−0.970134 | + | 0.242569i | \(0.922010\pi\) | |||||||
\(332\) | 1.91801e7 | − | 6.75526e6i | 0.524128 | − | 0.184598i | ||||
\(333\) | 1.03342e7 | 0.279863 | ||||||||
\(334\) | −8.91727e6 | + | 1.25949e7i | −0.239328 | + | 0.338029i | ||||
\(335\) | − | 4.80270e7i | − | 1.27747i | ||||||
\(336\) | 1.49309e6 | − | 1.20068e6i | 0.0393613 | − | 0.0316525i | ||||
\(337\) | 1.32250e7 | 0.345546 | 0.172773 | − | 0.984962i | \(-0.444727\pi\) | ||||
0.172773 | + | 0.984962i | \(0.444727\pi\) | |||||||
\(338\) | 1.66660e7 | + | 1.17997e7i | 0.431601 | + | 0.305577i | ||||
\(339\) | − | 1.60844e7i | − | 0.412862i | ||||||
\(340\) | 8.19888e6 | + | 2.32790e7i | 0.208602 | + | 0.592281i | ||||
\(341\) | 1.41756e7 | 0.357501 | ||||||||
\(342\) | 4.28108e6 | − | 6.04664e6i | 0.107022 | − | 0.151160i | ||||
\(343\) | 9.22518e6i | 0.228609i | ||||||||
\(344\) | 6.48635e7 | + | 1.84726e7i | 1.59340 | + | 0.453788i | ||||
\(345\) | 557010. | 0.0135646 | ||||||||
\(346\) | 2.61918e7 | + | 1.85440e7i | 0.632321 | + | 0.447689i | ||||
\(347\) | − | 5.96821e7i | − | 1.42842i | −0.699932 | − | 0.714209i | \(-0.746786\pi\) | ||
0.699932 | − | 0.714209i | \(-0.253214\pi\) | |||||||
\(348\) | −2.90013e7 | + | 1.02143e7i | −0.688146 | + | 0.242366i | ||||
\(349\) | −4.24552e6 | −0.0998745 | −0.0499372 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499372 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(350\) | 3.04495e6 | − | 4.30072e6i | 0.0710193 | − | 0.100308i | ||||
\(351\) | − | 2.35489e7i | − | 0.544564i | ||||||
\(352\) | 1.07514e6 | + | 1.75494e7i | 0.0246511 | + | 0.402378i | ||||
\(353\) | 1.08089e7 | 0.245729 | 0.122864 | − | 0.992423i | \(-0.460792\pi\) | ||||
0.122864 | + | 0.992423i | \(0.460792\pi\) | |||||||
\(354\) | −1.46047e6 | − | 1.03403e6i | −0.0329219 | − | 0.0233090i | ||||
\(355\) | 1.88343e7i | 0.420982i | ||||||||
\(356\) | 642757. | + | 1.82497e6i | 0.0142461 | + | 0.0404488i | ||||
\(357\) | −1.00348e6 | −0.0220548 | ||||||||
\(358\) | 3.85077e7 | − | 5.43887e7i | 0.839264 | − | 1.18539i | ||||
\(359\) | − | 2.56464e7i | − | 0.554299i | −0.960827 | − | 0.277149i | \(-0.910610\pi\) | ||
0.960827 | − | 0.277149i | \(-0.0893897\pi\) | |||||||
\(360\) | 1.48365e7 | − | 5.20960e7i | 0.317998 | − | 1.11660i | ||||
\(361\) | −2.47610e6 | −0.0526316 | ||||||||
\(362\) | 4.83372e7 | + | 3.42232e7i | 1.01896 | + | 0.721432i | ||||
\(363\) | 1.75841e7i | 0.367621i | ||||||||
\(364\) | 3.59294e6 | − | 1.26544e6i | 0.0744983 | − | 0.0262383i | ||||
\(365\) | 4.72856e7 | 0.972412 | ||||||||
\(366\) | −9.13839e6 | + | 1.29072e7i | −0.186392 | + | 0.263261i | ||||
\(367\) | 1.00057e7i | 0.202418i | 0.994865 | + | 0.101209i | \(0.0322711\pi\) | ||||
−0.994865 | + | 0.101209i | \(0.967729\pi\) | |||||||
\(368\) | 671079. | + | 834516.i | 0.0134657 | + | 0.0167452i | ||||
\(369\) | 1.80206e7 | 0.358666 | ||||||||
\(370\) | −2.06094e7 | − | 1.45916e7i | −0.406874 | − | 0.288071i | ||||
\(371\) | − | 5.05678e6i | − | 0.0990266i | ||||||
\(372\) | 6.65703e6 | + | 1.89012e7i | 0.129316 | + | 0.367165i | ||||
\(373\) | −1.42935e7 | −0.275430 | −0.137715 | − | 0.990472i | \(-0.543976\pi\) | ||||
−0.137715 | + | 0.990472i | \(0.543976\pi\) | |||||||
\(374\) | 5.32112e6 | − | 7.51561e6i | 0.101716 | − | 0.143664i | ||||
\(375\) | 2.26771e6i | 0.0430024i | ||||||||
\(376\) | 9.75980e7 | + | 2.77951e7i | 1.83602 | + | 0.522884i | ||||
\(377\) | −6.11312e7 | −1.14088 | ||||||||
\(378\) | 4.02393e6 | + | 2.84898e6i | 0.0745032 | + | 0.0527489i | ||||
\(379\) | − | 7.62386e7i | − | 1.40042i | −0.713938 | − | 0.700209i | \(-0.753090\pi\) | ||
0.713938 | − | 0.700209i | \(-0.246910\pi\) | |||||||
\(380\) | −1.70754e7 | + | 6.01396e6i | −0.311185 | + | 0.109600i | ||||
\(381\) | 1.91499e7 | 0.346251 | ||||||||
\(382\) | −5.47642e7 | + | 7.73496e7i | −0.982442 | + | 1.38761i | ||||
\(383\) | − | 1.02902e8i | − | 1.83158i | −0.401654 | − | 0.915791i | \(-0.631565\pi\) | ||
0.401654 | − | 0.915791i | \(-0.368435\pi\) | |||||||
\(384\) | −2.28949e7 | + | 9.67499e6i | −0.404339 | + | 0.170866i | ||||
\(385\) | −3.80685e6 | −0.0667088 | ||||||||
\(386\) | 6.53686e7 | + | 4.62816e7i | 1.13660 | + | 0.804723i | ||||
\(387\) | 7.75238e7i | 1.33753i | ||||||||
\(388\) | 1.41739e7 | + | 4.02439e7i | 0.242658 | + | 0.688977i | ||||
\(389\) | 3.71426e7 | 0.630991 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(390\) | −1.48527e7 | + | 2.09781e7i | −0.250387 | + | 0.353649i | ||||
\(391\) | − | 560861.i | − | 0.00938264i | ||||||
\(392\) | 1.62803e7 | − | 5.71657e7i | 0.270275 | − | 0.949024i | ||||
\(393\) | 3.95949e7 | 0.652322 | ||||||||
\(394\) | 2.04142e7 | + | 1.44535e7i | 0.333768 | + | 0.236311i | ||||
\(395\) | 8.74327e6i | 0.141867i | ||||||||
\(396\) | −1.90627e7 | + | 6.71390e6i | −0.306972 | + | 0.108116i | ||||
\(397\) | −7.61528e7 | −1.21707 | −0.608533 | − | 0.793528i | \(-0.708242\pi\) | ||||
−0.608533 | + | 0.793528i | \(0.708242\pi\) | |||||||
\(398\) | 2.52650e6 | − | 3.56845e6i | 0.0400746 | − | 0.0566019i | ||||
\(399\) | − | 736060.i | − | 0.0115876i | ||||||
\(400\) | −5.32719e7 | + | 4.28388e7i | −0.832373 | + | 0.669356i | ||||
\(401\) | −5.07560e7 | −0.787144 | −0.393572 | − | 0.919294i | \(-0.628761\pi\) | ||||
−0.393572 | + | 0.919294i | \(0.628761\pi\) | |||||||
\(402\) | −2.06745e7 | − | 1.46377e7i | −0.318242 | − | 0.225318i | ||||
\(403\) | 3.98415e7i | 0.608723i | ||||||||
\(404\) | 1.22134e6 | + | 3.46775e6i | 0.0185223 | + | 0.0525900i | ||||
\(405\) | 4.38565e7 | 0.660190 | ||||||||
\(406\) | 7.39575e6 | − | 1.04458e7i | 0.110511 | − | 0.156086i | ||||
\(407\) | 9.42180e6i | 0.139750i | ||||||||
\(408\) | 1.25199e7 | + | 3.56558e6i | 0.184341 | + | 0.0524988i | ||||
\(409\) | −3.37620e7 | −0.493467 | −0.246733 | − | 0.969083i | \(-0.579357\pi\) | ||||
−0.246733 | + | 0.969083i | \(0.579357\pi\) | |||||||
\(410\) | −3.59382e7 | − | 2.54446e7i | −0.521440 | − | 0.369185i | ||||
\(411\) | − | 5.55784e7i | − | 0.800535i | ||||||
\(412\) | −8.05947e7 | + | 2.83855e7i | −1.15243 | + | 0.405887i | ||||
\(413\) | 744883. | 0.0105740 | ||||||||
\(414\) | −711289. | + | 1.00463e6i | −0.0100241 | + | 0.0141581i | ||||
\(415\) | − | 5.71165e7i | − | 0.799130i | ||||||
\(416\) | −4.93239e7 | + | 3.02176e6i | −0.685137 | + | 0.0419739i | ||||
\(417\) | 2.04386e7 | 0.281867 | ||||||||
\(418\) | 5.51277e6 | + | 3.90309e6i | 0.0754816 | + | 0.0534416i | ||||
\(419\) | 1.08092e8i | 1.46943i | 0.678373 | + | 0.734717i | \(0.262685\pi\) | ||||
−0.678373 | + | 0.734717i | \(0.737315\pi\) | |||||||
\(420\) | −1.78775e6 | − | 5.07593e6i | −0.0241300 | − | 0.0685121i | ||||
\(421\) | 6.92888e7 | 0.928574 | 0.464287 | − | 0.885685i | \(-0.346311\pi\) | ||||
0.464287 | + | 0.885685i | \(0.346311\pi\) | |||||||
\(422\) | −1.47525e7 | + | 2.08366e7i | −0.196304 | + | 0.277261i | ||||
\(423\) | 1.16648e8i | 1.54118i | ||||||||
\(424\) | −1.79679e7 | + | 6.30911e7i | −0.235721 | + | 0.827696i | ||||
\(425\) | 3.58029e7 | 0.466393 | ||||||||
\(426\) | 8.10771e6 | + | 5.74034e6i | 0.104874 | + | 0.0742521i | ||||
\(427\) | − | 6.58301e6i | − | 0.0845553i | ||||||
\(428\) | 1.18195e8 | − | 4.16283e7i | 1.50753 | − | 0.530954i | ||||
\(429\) | 9.59036e6 | 0.121468 | ||||||||
\(430\) | 1.09461e8 | − | 1.54605e8i | 1.37675 | − | 1.94454i | ||||
\(431\) | 6.55929e7i | 0.819266i | 0.912250 | + | 0.409633i | \(0.134343\pi\) | ||||
−0.912250 | + | 0.409633i | \(0.865657\pi\) | |||||||
\(432\) | −4.00817e7 | − | 4.98433e7i | −0.497158 | − | 0.618238i | ||||
\(433\) | 2.87571e7 | 0.354227 | 0.177114 | − | 0.984190i | \(-0.443324\pi\) | ||||
0.177114 | + | 0.984190i | \(0.443324\pi\) | |||||||
\(434\) | −6.80793e6 | − | 4.82008e6i | −0.0832810 | − | 0.0589637i | ||||
\(435\) | 8.63631e7i | 1.04921i | ||||||||
\(436\) | −3.40925e6 | − | 9.67983e6i | −0.0411338 | − | 0.116791i | ||||
\(437\) | 411397. | 0.00492966 | ||||||||
\(438\) | 1.44118e7 | − | 2.03553e7i | 0.171512 | − | 0.242246i | ||||
\(439\) | − | 7.76307e7i | − | 0.917571i | −0.888547 | − | 0.458786i | \(-0.848285\pi\) | ||
0.888547 | − | 0.458786i | \(-0.151715\pi\) | |||||||
\(440\) | 4.74963e7 | + | 1.35266e7i | 0.557573 | + | 0.158792i | ||||
\(441\) | 6.83235e7 | 0.796626 | ||||||||
\(442\) | 2.11232e7 | + | 1.49554e7i | 0.244620 | + | 0.173193i | ||||
\(443\) | 5.26161e7i | 0.605212i | 0.953116 | + | 0.302606i | \(0.0978567\pi\) | ||||
−0.953116 | + | 0.302606i | \(0.902143\pi\) | |||||||
\(444\) | −1.25627e7 | + | 4.42460e6i | −0.143527 | + | 0.0505505i | ||||
\(445\) | 5.43458e6 | 0.0616717 | ||||||||
\(446\) | −8.44669e7 | + | 1.19302e8i | −0.952098 | + | 1.34475i | ||||
\(447\) | − | 2.74854e7i | − | 0.307737i | ||||||
\(448\) | 5.45093e6 | − | 8.79382e6i | 0.0606229 | − | 0.0978011i | ||||
\(449\) | 5.92286e7 | 0.654323 | 0.327161 | − | 0.944968i | \(-0.393908\pi\) | ||||
0.327161 | + | 0.944968i | \(0.393908\pi\) | |||||||
\(450\) | −6.41314e7 | − | 4.54056e7i | −0.703773 | − | 0.498278i | ||||
\(451\) | 1.64295e7i | 0.179100i | ||||||||
\(452\) | −2.88532e7 | − | 8.19227e7i | −0.312449 | − | 0.887133i | ||||
\(453\) | 5.23536e7 | 0.563186 | ||||||||
\(454\) | 6.93558e7 | − | 9.79589e7i | 0.741166 | − | 1.04683i | ||||
\(455\) | − | 1.06994e7i | − | 0.113586i | ||||||
\(456\) | −2.61539e6 | + | 9.18349e6i | −0.0275830 | + | 0.0968530i | ||||
\(457\) | −1.52328e8 | −1.59600 | −0.797999 | − | 0.602659i | \(-0.794108\pi\) | ||||
−0.797999 | + | 0.602659i | \(0.794108\pi\) | |||||||
\(458\) | −7.01218e7 | − | 4.96469e7i | −0.729888 | − | 0.516768i | ||||
\(459\) | 3.34987e7i | 0.346409i | ||||||||
\(460\) | 2.83703e6 | − | 999203.i | 0.0291467 | − | 0.0102655i | ||||
\(461\) | −1.17190e7 | −0.119616 | −0.0598078 | − | 0.998210i | \(-0.519049\pi\) | ||||
−0.0598078 | + | 0.998210i | \(0.519049\pi\) | |||||||
\(462\) | −1.16026e6 | + | 1.63876e6i | −0.0117660 | + | 0.0166184i | ||||
\(463\) | − | 6.00475e7i | − | 0.604995i | −0.953150 | − | 0.302497i | \(-0.902180\pi\) | ||
0.953150 | − | 0.302497i | \(-0.0978204\pi\) | |||||||
\(464\) | −1.29390e8 | + | 1.04049e8i | −1.29523 | + | 1.04156i | ||||
\(465\) | 5.62860e7 | 0.559811 | ||||||||
\(466\) | −1.37038e8 | − | 9.70245e7i | −1.35421 | − | 0.958790i | ||||
\(467\) | 9.87028e7i | 0.969123i | 0.874757 | + | 0.484562i | \(0.161021\pi\) | ||||
−0.874757 | + | 0.484562i | \(0.838979\pi\) | |||||||
\(468\) | −1.88699e7 | − | 5.35771e7i | −0.184091 | − | 0.522687i | ||||
\(469\) | 1.05446e7 | 0.102214 | ||||||||
\(470\) | 1.64703e8 | − | 2.32628e8i | 1.58638 | − | 2.24062i | ||||
\(471\) | 4.75905e7i | 0.455468i | ||||||||
\(472\) | −9.29356e6 | − | 2.64673e6i | −0.0883805 | − | 0.0251701i | ||||
\(473\) | −7.06791e7 | −0.667894 | ||||||||
\(474\) | 3.76377e6 | + | 2.66479e6i | 0.0353418 | + | 0.0250223i | ||||
\(475\) | 2.62618e7i | 0.245044i | ||||||||
\(476\) | −5.11102e6 | + | 1.80011e6i | −0.0473900 | + | 0.0166908i | ||||
\(477\) | −7.54055e7 | −0.694781 | ||||||||
\(478\) | 5.68607e6 | − | 8.03107e6i | 0.0520629 | − | 0.0735343i | ||||
\(479\) | 2.40198e7i | 0.218556i | 0.994011 | + | 0.109278i | \(0.0348539\pi\) | ||||
−0.994011 | + | 0.109278i | \(0.965146\pi\) | |||||||
\(480\) | 4.26899e6 | + | 6.96823e7i | 0.0386012 | + | 0.630084i | ||||
\(481\) | −2.64807e7 | −0.237954 | ||||||||
\(482\) | −1.27792e8 | − | 9.04781e7i | −1.14120 | − | 0.807983i | ||||
\(483\) | 122294.i | 0.00108534i | ||||||||
\(484\) | 3.15436e7 | + | 8.95614e7i | 0.278211 | + | 0.789923i | ||||
\(485\) | 1.19842e8 | 1.05047 | ||||||||
\(486\) | 6.59896e7 | − | 9.32044e7i | 0.574866 | − | 0.811947i | ||||
\(487\) | − | 1.88299e8i | − | 1.63028i | −0.579266 | − | 0.815139i | \(-0.696661\pi\) | ||
0.579266 | − | 0.815139i | \(-0.303339\pi\) | |||||||
\(488\) | −2.33909e7 | + | 8.21332e7i | −0.201274 | + | 0.706739i | ||||
\(489\) | −5.46663e7 | −0.467513 | ||||||||
\(490\) | −1.36256e8 | − | 9.64709e7i | −1.15816 | − | 0.819989i | ||||
\(491\) | − | 1.38868e8i | − | 1.17316i | −0.809890 | − | 0.586582i | \(-0.800473\pi\) | ||
0.809890 | − | 0.586582i | \(-0.199527\pi\) | |||||||
\(492\) | −2.19066e7 | + | 7.71552e6i | −0.183941 | + | 0.0647843i | ||||
\(493\) | 8.69602e7 | 0.725738 | ||||||||
\(494\) | −1.09699e7 | + | 1.54940e7i | −0.0909961 | + | 0.128524i | ||||
\(495\) | 5.67668e7i | 0.468036i | ||||||||
\(496\) | 6.78126e7 | + | 8.43280e7i | 0.555732 | + | 0.691078i | ||||
\(497\) | −4.13516e6 | −0.0336839 | ||||||||
\(498\) | −2.45873e7 | − | 1.74081e7i | −0.199078 | − | 0.140949i | ||||
\(499\) | 2.11975e8i | 1.70602i | 0.521896 | + | 0.853009i | \(0.325225\pi\) | ||||
−0.521896 | + | 0.853009i | \(0.674775\pi\) | |||||||
\(500\) | 4.06797e6 | + | 1.15501e7i | 0.0325437 | + | 0.0924010i | ||||
\(501\) | 2.28624e7 | 0.181806 | ||||||||
\(502\) | 5.58412e6 | − | 7.88707e6i | 0.0441411 | − | 0.0623454i | ||||
\(503\) | − | 5.05810e7i | − | 0.397451i | −0.980055 | − | 0.198726i | \(-0.936320\pi\) | ||
0.980055 | − | 0.198726i | \(-0.0636802\pi\) | |||||||
\(504\) | 1.14379e7 | + | 3.25743e6i | 0.0893420 | + | 0.0254439i | ||||
\(505\) | 1.03266e7 | 0.0801832 | ||||||||
\(506\) | −915931. | − | 648488.i | −0.00706987 | − | 0.00500553i | ||||
\(507\) | − | 3.02524e7i | − | 0.232133i | ||||||
\(508\) | 9.75362e7 | − | 3.43523e7i | 0.744003 | − | 0.262038i | ||||
\(509\) | −2.28416e8 | −1.73210 | −0.866050 | − | 0.499957i | \(-0.833349\pi\) | ||||
−0.866050 | + | 0.499957i | \(0.833349\pi\) | |||||||
\(510\) | 2.11282e7 | − | 2.98417e7i | 0.159277 | − | 0.224964i | ||||
\(511\) | 1.03818e7i | 0.0778054i | ||||||||
\(512\) | −9.92552e7 | + | 9.03482e7i | −0.739509 | + | 0.673146i | ||||
\(513\) | −2.45716e7 | −0.182004 | ||||||||
\(514\) | 1.59805e8 | + | 1.13143e8i | 1.17679 | + | 0.833182i | ||||
\(515\) | 2.40003e8i | 1.75709i | ||||||||
\(516\) | −3.31918e7 | − | 9.42412e7i | −0.241592 | − | 0.685949i | ||||
\(517\) | −1.06348e8 | −0.769590 | ||||||||
\(518\) | 3.20367e6 | − | 4.52490e6i | 0.0230493 | − | 0.0325551i | ||||
\(519\) | − | 4.75438e7i | − | 0.340089i | ||||||
\(520\) | −3.80174e7 | + | 1.33492e8i | −0.270379 | + | 0.949390i | ||||
\(521\) | 1.65550e8 | 1.17062 | 0.585310 | − | 0.810809i | \(-0.300973\pi\) | ||||
0.585310 | + | 0.810809i | \(0.300973\pi\) | |||||||
\(522\) | −1.55766e8 | − | 1.10284e8i | −1.09512 | − | 0.775353i | ||||
\(523\) | 1.35143e8i | 0.944686i | 0.881415 | + | 0.472343i | \(0.156592\pi\) | ||||
−0.881415 | + | 0.472343i | \(0.843408\pi\) | |||||||
\(524\) | 2.01669e8 | − | 7.10281e7i | 1.40167 | − | 0.493669i | ||||
\(525\) | −7.80674e6 | −0.0539500 | ||||||||
\(526\) | −3.78611e7 | + | 5.34754e7i | −0.260157 | + | 0.367449i | ||||
\(527\) | − | 5.66751e7i | − | 0.387223i | ||||||
\(528\) | 2.02989e7 | − | 1.63234e7i | 0.137902 | − | 0.110894i | ||||
\(529\) | 1.47968e8 | 0.999538 | ||||||||
\(530\) | 1.50380e8 | + | 1.06470e8i | 1.01010 | + | 0.715157i | ||||
\(531\) | − | 1.11075e7i | − | 0.0741880i | ||||||
\(532\) | −1.32039e6 | − | 3.74898e6i | −0.00876938 | − | 0.0248988i | ||||
\(533\) | −4.61764e7 | −0.304957 | ||||||||
\(534\) | 1.65636e6 | − | 2.33946e6i | 0.0108775 | − | 0.0153636i | ||||
\(535\) | − | 3.51972e8i | − | 2.29851i | ||||||
\(536\) | −1.31560e8 | − | 3.74672e7i | −0.854337 | − | 0.243308i | ||||
\(537\) | −9.87272e7 | −0.637550 | ||||||||
\(538\) | −2.89822e7 | − | 2.05197e7i | −0.186116 | − | 0.131772i | ||||
\(539\) | 6.22911e7i | 0.397795i | ||||||||
\(540\) | −1.69448e8 | + | 5.96796e7i | −1.07610 | + | 0.379005i | ||||
\(541\) | 1.34292e8 | 0.848121 | 0.424060 | − | 0.905634i | \(-0.360604\pi\) | ||||
0.424060 | + | 0.905634i | \(0.360604\pi\) | |||||||
\(542\) | −1.62778e8 | + | 2.29910e8i | −1.02235 | + | 1.44397i | ||||
\(543\) | − | 8.77426e7i | − | 0.548038i | ||||||
\(544\) | 7.01641e7 | − | 4.29850e6i | 0.435831 | − | 0.0267006i | ||||
\(545\) | −2.88256e7 | −0.178069 | ||||||||
\(546\) | −4.60585e6 | − | 3.26098e6i | −0.0282964 | − | 0.0200341i | ||||
\(547\) | − | 6.77658e7i | − | 0.414046i | −0.978336 | − | 0.207023i | \(-0.933623\pi\) | ||
0.978336 | − | 0.207023i | \(-0.0663775\pi\) | |||||||
\(548\) | −9.97002e7 | − | 2.83078e8i | −0.605835 | − | 1.72014i | ||||
\(549\) | −9.81643e7 | −0.593248 | ||||||||
\(550\) | 4.13966e7 | − | 5.84691e7i | 0.248815 | − | 0.351429i | ||||
\(551\) | 6.37861e7i | 0.381304i | ||||||||
\(552\) | 434539. | − | 1.52581e6i | 0.00258352 | − | 0.00907159i | ||||
\(553\) | −1.91963e6 | −0.0113512 | ||||||||
\(554\) | −1.02131e8 | − | 7.23094e7i | −0.600657 | − | 0.425271i | ||||
\(555\) | 3.74105e7i | 0.218834i | ||||||||
\(556\) | 1.04100e8 | − | 3.66642e7i | 0.605658 | − | 0.213313i | ||||
\(557\) | 4.33122e7 | 0.250637 | 0.125318 | − | 0.992117i | \(-0.460005\pi\) | ||||
0.125318 | + | 0.992117i | \(0.460005\pi\) | |||||||
\(558\) | −7.18759e7 | + | 1.01518e8i | −0.413695 | + | 0.584308i | ||||
\(559\) | − | 1.98649e8i | − | 1.13724i | ||||||
\(560\) | −1.82111e7 | − | 2.26463e7i | −0.103698 | − | 0.128953i | ||||
\(561\) | −1.36425e7 | −0.0772687 | ||||||||
\(562\) | −1.51906e8 | − | 1.07551e8i | −0.855790 | − | 0.605907i | ||||
\(563\) | 2.30319e8i | 1.29064i | 0.763913 | + | 0.645319i | \(0.223276\pi\) | ||||
−0.763913 | + | 0.645319i | \(0.776724\pi\) | |||||||
\(564\) | −4.99426e7 | − | 1.41802e8i | −0.278377 | − | 0.790394i | ||||
\(565\) | −2.43957e8 | −1.35260 | ||||||||
\(566\) | −5.42196e7 | + | 7.65804e7i | −0.299025 | + | 0.422346i | ||||
\(567\) | 9.62891e6i | 0.0528236i | ||||||||
\(568\) | 5.15925e7 | + | 1.46931e7i | 0.281541 | + | 0.0801807i | ||||
\(569\) | 3.28302e8 | 1.78212 | 0.891059 | − | 0.453887i | \(-0.149963\pi\) | ||||
0.891059 | + | 0.453887i | \(0.149963\pi\) | |||||||
\(570\) | 2.18892e7 | + | 1.54977e7i | 0.118197 | + | 0.0836843i | ||||
\(571\) | 3.59864e8i | 1.93299i | 0.256683 | + | 0.966496i | \(0.417370\pi\) | ||||
−0.256683 | + | 0.966496i | \(0.582630\pi\) | |||||||
\(572\) | 4.88467e7 | − | 1.72038e7i | 0.261004 | − | 0.0919258i | ||||
\(573\) | 1.40406e8 | 0.746316 | ||||||||
\(574\) | 5.58648e6 | − | 7.89041e6i | 0.0295395 | − | 0.0417219i | ||||
\(575\) | − | 4.36333e6i | − | 0.0229517i | ||||||
\(576\) | −1.31131e8 | − | 8.12830e7i | −0.686182 | − | 0.425336i | ||||
\(577\) | 9.65385e6 | 0.0502543 | 0.0251271 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251271 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(578\) | 1.27551e8 | + | 9.03072e7i | 0.660541 | + | 0.467669i | ||||
\(579\) | − | 1.18658e8i | − | 0.611311i | ||||||
\(580\) | 1.54924e8 | + | 4.39874e8i | 0.794026 | + | 2.25447i | ||||
\(581\) | 1.25402e7 | 0.0639406 | ||||||||
\(582\) | 3.65257e7 | − | 5.15892e7i | 0.185280 | − | 0.261692i | ||||
\(583\) | − | 6.87478e7i | − | 0.346939i | ||||||
\(584\) | 3.68888e7 | − | 1.29529e8i | 0.185207 | − | 0.650321i | ||||
\(585\) | −1.59547e8 | −0.796933 | ||||||||
\(586\) | 2.95614e8 | + | 2.09297e8i | 1.46903 | + | 1.04009i | ||||
\(587\) | 2.03874e8i | 1.00797i | 0.863712 | + | 0.503986i | \(0.168134\pi\) | ||||
−0.863712 | + | 0.503986i | \(0.831866\pi\) | |||||||
\(588\) | −8.30569e7 | + | 2.92527e7i | −0.408549 | + | 0.143891i | ||||
\(589\) | 4.15717e7 | 0.203448 | ||||||||
\(590\) | −1.56835e7 | + | 2.21515e7i | −0.0763637 | + | 0.107857i | ||||
\(591\) | − | 3.70562e7i | − | 0.179514i | ||||||
\(592\) | −5.60487e7 | + | 4.50717e7i | −0.270147 | + | 0.217240i | ||||
\(593\) | 1.07600e8 | 0.515997 | 0.257998 | − | 0.966145i | \(-0.416937\pi\) | ||||
0.257998 | + | 0.966145i | \(0.416937\pi\) | |||||||
\(594\) | 5.47060e7 | + | 3.87324e7i | 0.261021 | + | 0.184805i | ||||
\(595\) | 1.52201e7i | 0.0722548i | ||||||||
\(596\) | −4.93052e7 | − | 1.39992e8i | −0.232892 | − | 0.661247i | ||||
\(597\) | −6.47751e6 | −0.0304429 | ||||||||
\(598\) | 1.82262e6 | − | 2.57429e6i | 0.00852301 | − | 0.0120380i | ||||
\(599\) | 3.19378e8i | 1.48602i | 0.669280 | + | 0.743010i | \(0.266603\pi\) | ||||
−0.669280 | + | 0.743010i | \(0.733397\pi\) | |||||||
\(600\) | 9.74012e7 | + | 2.77391e7i | 0.450931 | + | 0.128422i | ||||
\(601\) | −2.26861e8 | −1.04505 | −0.522524 | − | 0.852625i | \(-0.675009\pi\) | ||||
−0.522524 | + | 0.852625i | \(0.675009\pi\) | |||||||
\(602\) | 3.39442e7 | + | 2.40328e7i | 0.155588 | + | 0.110158i | ||||
\(603\) | − | 1.57238e8i | − | 0.717144i | ||||||
\(604\) | 2.66653e8 | − | 9.39154e7i | 1.21014 | − | 0.426212i | ||||
\(605\) | 2.66705e8 | 1.20438 | ||||||||
\(606\) | 3.14736e6 | − | 4.44536e6i | 0.0141426 | − | 0.0199751i | ||||
\(607\) | − | 2.08398e8i | − | 0.931810i | −0.884835 | − | 0.465905i | \(-0.845729\pi\) | ||
0.884835 | − | 0.465905i | \(-0.154271\pi\) | |||||||
\(608\) | 3.15299e6 | + | 5.14660e7i | 0.0140285 | + | 0.228986i | ||||
\(609\) | −1.89614e7 | −0.0839498 | ||||||||
\(610\) | 1.95768e8 | + | 1.38605e8i | 0.862484 | + | 0.610647i | ||||
\(611\) | − | 2.98900e8i | − | 1.31040i | ||||||
\(612\) | 2.68428e7 | + | 7.62143e7i | 0.117104 | + | 0.332493i | ||||
\(613\) | 1.66040e8 | 0.720828 | 0.360414 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360414 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(614\) | −1.81048e8 | + | 2.55714e8i | −0.782148 | + | 1.10471i | ||||
\(615\) | 6.52356e7i | 0.280453i | ||||||||
\(616\) | −2.96983e6 | + | 1.04281e7i | −0.0127054 | + | 0.0446130i | ||||
\(617\) | 1.10651e8 | 0.471084 | 0.235542 | − | 0.971864i | \(-0.424314\pi\) | ||||
0.235542 | + | 0.971864i | \(0.424314\pi\) | |||||||
\(618\) | 1.03316e8 | + | 7.31484e7i | 0.437724 | + | 0.309913i | ||||
\(619\) | − | 4.44270e8i | − | 1.87316i | −0.350452 | − | 0.936581i | \(-0.613972\pi\) | ||
0.350452 | − | 0.936581i | \(-0.386028\pi\) | |||||||
\(620\) | 2.86682e8 | − | 1.00970e8i | 1.20289 | − | 0.423658i | ||||
\(621\) | 4.08250e6 | 0.0170471 | ||||||||
\(622\) | 1.45383e8 | − | 2.05341e8i | 0.604148 | − | 0.853305i | ||||
\(623\) | 1.19319e6i | 0.00493452i | ||||||||
\(624\) | 4.58781e7 | + | 5.70514e7i | 0.188822 | + | 0.234808i | ||||
\(625\) | −2.26377e8 | −0.927239 | ||||||||
\(626\) | 1.59146e8 | + | 1.12677e8i | 0.648743 | + | 0.459316i | ||||
\(627\) | − | 1.00069e7i | − | 0.0405971i | ||||||
\(628\) | 8.53711e7 | + | 2.42393e8i | 0.344693 | + | 0.978682i | ||||
\(629\) | 3.76692e7 | 0.151368 | ||||||||
\(630\) | 1.93023e7 | − | 2.72627e7i | 0.0771945 | − | 0.109030i | ||||
\(631\) | − | 4.95484e8i | − | 1.97216i | −0.166280 | − | 0.986078i | \(-0.553176\pi\) | ||
0.166280 | − | 0.986078i | \(-0.446824\pi\) | |||||||
\(632\) | 2.39503e7 | + | 6.82087e6i | 0.0948769 | + | 0.0270202i | ||||
\(633\) | 3.78229e7 | 0.149123 | ||||||||
\(634\) | 2.22604e8 | + | 1.57606e8i | 0.873506 | + | 0.618450i | ||||
\(635\) | − | 2.90453e8i | − | 1.13437i | ||||||
\(636\) | 9.16660e7 | − | 3.22849e7i | 0.356318 | − | 0.125495i | ||||
\(637\) | −1.75074e8 | −0.677333 | ||||||||
\(638\) | 1.00546e8 | − | 1.42013e8i | 0.387173 | − | 0.546847i | ||||
\(639\) | 6.16625e7i | 0.236330i | ||||||||
\(640\) | 1.46744e8 | + | 3.47255e8i | 0.559784 | + | 1.32467i | ||||
\(641\) | 7.93560e7 | 0.301305 | 0.150652 | − | 0.988587i | \(-0.451863\pi\) | ||||
0.150652 | + | 0.988587i | \(0.451863\pi\) | |||||||
\(642\) | −1.51516e8 | − | 1.07275e8i | −0.572602 | − | 0.405407i | ||||
\(643\) | 2.02965e8i | 0.763465i | 0.924273 | + | 0.381732i | \(0.124672\pi\) | ||||
−0.924273 | + | 0.381732i | \(0.875328\pi\) | |||||||
\(644\) | 219380. | + | 622883.i | 0.000821371 | + | 0.00233211i | ||||
\(645\) | −2.80641e8 | −1.04586 | ||||||||
\(646\) | 1.56049e7 | − | 2.20405e7i | 0.0578846 | − | 0.0817569i | ||||
\(647\) | 3.38684e8i | 1.25050i | 0.780427 | + | 0.625248i | \(0.215002\pi\) | ||||
−0.780427 | + | 0.625248i | \(0.784998\pi\) | |||||||
\(648\) | 3.42137e7 | − | 1.20136e8i | 0.125740 | − | 0.441516i | ||||
\(649\) | 1.01268e7 | 0.0370458 | ||||||||
\(650\) | 1.64332e8 | + | 1.16348e8i | 0.598385 | + | 0.423662i | ||||
\(651\) | 1.23579e7i | 0.0447920i | ||||||||
\(652\) | −2.78433e8 | + | 9.80642e7i | −1.00456 | + | 0.353808i | ||||
\(653\) | −5.27856e8 | −1.89573 | −0.947864 | − | 0.318676i | \(-0.896762\pi\) | ||||
−0.947864 | + | 0.318676i | \(0.896762\pi\) | |||||||
\(654\) | −8.78550e6 | + | 1.24087e7i | −0.0314075 | + | 0.0443603i | ||||
\(655\) | − | 6.00551e8i | − | 2.13710i | ||||||
\(656\) | −9.77364e7 | + | 7.85950e7i | −0.346214 | + | 0.278409i | ||||
\(657\) | 1.54811e8 | 0.545890 | ||||||||
\(658\) | 5.10747e7 | + | 3.61614e7i | 0.179278 | + | 0.126931i | ||||
\(659\) | 1.03582e8i | 0.361933i | 0.983489 | + | 0.180967i | \(0.0579226\pi\) | ||||
−0.983489 | + | 0.180967i | \(0.942077\pi\) | |||||||
\(660\) | −2.43047e7 | − | 6.90081e7i | −0.0845393 | − | 0.240032i | ||||
\(661\) | 2.81482e7 | 0.0974646 | 0.0487323 | − | 0.998812i | \(-0.484482\pi\) | ||||
0.0487323 | + | 0.998812i | \(0.484482\pi\) | |||||||
\(662\) | 8.13296e7 | − | 1.14871e8i | 0.280333 | − | 0.395946i | ||||
\(663\) | − | 3.83431e7i | − | 0.131567i | ||||||
\(664\) | −1.56459e8 | − | 4.45582e7i | −0.534436 | − | 0.152203i | ||||
\(665\) | −1.11641e7 | −0.0379628 | ||||||||
\(666\) | −6.74742e7 | − | 4.77724e7i | −0.228410 | − | 0.161716i | ||||
\(667\) | − | 1.05979e7i | − | 0.0357143i | ||||||
\(668\) | 1.16445e8 | − | 4.10121e7i | 0.390654 | − | 0.137589i | ||||
\(669\) | 2.16559e8 | 0.723265 | ||||||||
\(670\) | −2.22016e8 | + | 3.13578e8i | −0.738176 | + | 1.04261i | ||||
\(671\) | − | 8.94972e7i | − | 0.296239i | ||||||
\(672\) | −1.52991e7 | + | 937277.i | −0.0504148 | + | 0.00308859i | ||||
\(673\) | −1.18540e8 | −0.388883 | −0.194441 | − | 0.980914i | \(-0.562289\pi\) | ||||
−0.194441 | + | 0.980914i | \(0.562289\pi\) | |||||||
\(674\) | −8.63485e7 | − | 6.11356e7i | −0.282017 | − | 0.199671i | ||||
\(675\) | 2.60609e8i | 0.847380i | ||||||||
\(676\) | −5.42689e7 | − | 1.54085e8i | −0.175675 | − | 0.498793i | ||||
\(677\) | 7.24887e6 | 0.0233617 | 0.0116809 | − | 0.999932i | \(-0.496282\pi\) | ||||
0.0116809 | + | 0.999932i | \(0.496282\pi\) | |||||||
\(678\) | −7.43537e7 | + | 1.05018e8i | −0.238569 | + | 0.336957i | ||||
\(679\) | 2.63119e7i | 0.0840511i | ||||||||
\(680\) | 5.40804e7 | − | 1.89894e8i | 0.171994 | − | 0.603928i | ||||
\(681\) | −1.77817e8 | −0.563029 | ||||||||
\(682\) | −9.25550e7 | − | 6.55298e7i | −0.291774 | − | 0.206579i | ||||
\(683\) | 3.89119e8i | 1.22130i | 0.791903 | + | 0.610648i | \(0.209091\pi\) | ||||
−0.791903 | + | 0.610648i | \(0.790909\pi\) | |||||||
\(684\) | −5.59039e7 | + | 1.96894e7i | −0.174692 | + | 0.0615268i | ||||
\(685\) | −8.42977e8 | −2.62267 | ||||||||
\(686\) | 4.26455e7 | − | 6.02330e7i | 0.132099 | − | 0.186579i | ||||
\(687\) | 1.27286e8i | 0.392565i | ||||||||
\(688\) | −3.38112e8 | − | 4.20458e8i | −1.03824 | − | 1.29109i | ||||
\(689\) | 1.93221e8 | 0.590739 | ||||||||
\(690\) | −3.63683e6 | − | 2.57491e6i | −0.0110707 | − | 0.00783816i | ||||
\(691\) | 1.28087e8i | 0.388214i | 0.980980 | + | 0.194107i | \(0.0621810\pi\) | ||||
−0.980980 | + | 0.194107i | \(0.937819\pi\) | |||||||
\(692\) | −8.52873e7 | − | 2.42155e8i | −0.257375 | − | 0.730762i | ||||
\(693\) | −1.24634e7 | −0.0374488 | ||||||||
\(694\) | −2.75894e8 | + | 3.89676e8i | −0.825399 | + | 1.16580i | ||||
\(695\) | − | 3.10000e8i | − | 0.923438i | ||||||
\(696\) | 2.36573e8 | + | 6.73743e7i | 0.701678 | + | 0.199833i | ||||
\(697\) | 6.56866e7 | 0.193990 | ||||||||
\(698\) | 2.77198e7 | + | 1.96259e7i | 0.0815125 | + | 0.0577116i | ||||
\(699\) | 2.48754e8i | 0.728348i | ||||||||
\(700\) | −3.97621e7 | + | 1.40043e7i | −0.115925 | + | 0.0408287i | ||||
\(701\) | 5.13901e8 | 1.49185 | 0.745926 | − | 0.666029i | \(-0.232007\pi\) | ||||
0.745926 | + | 0.666029i | \(0.232007\pi\) | |||||||
\(702\) | −1.08860e8 | + | 1.53755e8i | −0.314671 | + | 0.444445i | ||||
\(703\) | 2.76307e7i | 0.0795291i | ||||||||
\(704\) | 7.41064e7 | − | 1.19554e8i | 0.212392 | − | 0.342645i | ||||
\(705\) | −4.22271e8 | −1.20510 | ||||||||
\(706\) | −7.05732e7 | − | 4.99665e7i | −0.200551 | − | 0.141992i | ||||
\(707\) | 2.26726e6i | 0.00641568i | ||||||||
\(708\) | 4.75568e6 | + | 1.35028e7i | 0.0134003 | + | 0.0380472i | ||||
\(709\) | 1.30532e7 | 0.0366250 | 0.0183125 | − | 0.999832i | \(-0.494171\pi\) | ||||
0.0183125 | + | 0.999832i | \(0.494171\pi\) | |||||||
\(710\) | 8.70657e7 | − | 1.22973e8i | 0.243261 | − | 0.343584i | ||||
\(711\) | 2.86251e7i | 0.0796412i | ||||||||
\(712\) | 4.23967e6 | − | 1.48869e7i | 0.0117461 | − | 0.0412443i | ||||
\(713\) | −6.90703e6 | −0.0190556 | ||||||||
\(714\) | 6.55190e6 | + | 4.63880e6i | 0.0180000 | + | 0.0127442i | ||||
\(715\) | − | 1.45460e8i | − | 0.397949i | ||||||
\(716\) | −5.02848e8 | + | 1.77104e8i | −1.36993 | + | 0.482490i | ||||
\(717\) | −1.45781e7 | −0.0395498 | ||||||||
\(718\) | −1.18557e8 | + | 1.67451e8i | −0.320297 | + | 0.452390i | ||||
\(719\) | − | 3.77365e8i | − | 1.01525i | −0.861577 | − | 0.507627i | \(-0.830523\pi\) | ||
0.861577 | − | 0.507627i | \(-0.169477\pi\) | |||||||
\(720\) | −3.37696e8 | + | 2.71559e8i | −0.904750 | + | 0.727558i | ||||
\(721\) | −5.26938e7 | −0.140590 | ||||||||
\(722\) | 1.61669e7 | + | 1.14463e7i | 0.0429552 | + | 0.0304127i | ||||
\(723\) | 2.31971e8i | 0.613787i | ||||||||
\(724\) | −1.57399e8 | − | 4.46900e8i | −0.414749 | − | 1.17759i | ||||
\(725\) | 6.76523e8 | 1.77529 | ||||||||
\(726\) | 8.12866e7 | − | 1.14810e8i | 0.212427 | − | 0.300034i | ||||
\(727\) | − | 3.44700e8i | − | 0.897094i | −0.893759 | − | 0.448547i | \(-0.851942\pi\) | ||
0.893759 | − | 0.448547i | \(-0.148058\pi\) | |||||||
\(728\) | −2.93088e7 | − | 8.34692e6i | −0.0759633 | − | 0.0216338i | ||||
\(729\) | 8.66763e6 | 0.0223727 | ||||||||
\(730\) | −3.08737e8 | − | 2.18589e8i | −0.793633 | − | 0.561900i | ||||
\(731\) | 2.82581e8i | 0.723421i | ||||||||
\(732\) | 1.19333e8 | − | 4.20290e7i | 0.304247 | − | 0.107156i | ||||
\(733\) | −5.51510e8 | −1.40036 | −0.700182 | − | 0.713964i | \(-0.746898\pi\) | ||||
−0.700182 | + | 0.713964i | \(0.746898\pi\) | |||||||
\(734\) | 4.62536e7 | − | 6.53291e7i | 0.116965 | − | 0.165203i | ||||
\(735\) | 2.47335e8i | 0.622908i | ||||||||
\(736\) | −523861. | − | 8.55093e6i | −0.00131396 | − | 0.0214477i | ||||
\(737\) | 1.43355e8 | 0.358106 | ||||||||
\(738\) | −1.17660e8 | − | 8.33043e7i | −0.292725 | − | 0.207252i | ||||
\(739\) | − | 3.56434e8i | − | 0.883173i | −0.897219 | − | 0.441587i | \(-0.854416\pi\) | ||
0.897219 | − | 0.441587i | \(-0.145584\pi\) | |||||||
\(740\) | 6.71095e7 | + | 1.90543e8i | 0.165611 | + | 0.470217i | ||||
\(741\) | 2.81250e7 | 0.0691255 | ||||||||
\(742\) | −2.33761e7 | + | 3.30167e7i | −0.0572217 | + | 0.0808205i | ||||
\(743\) | 5.02630e8i | 1.22541i | 0.790311 | + | 0.612706i | \(0.209919\pi\) | ||||
−0.790311 | + | 0.612706i | \(0.790081\pi\) | |||||||
\(744\) | 4.39103e7 | − | 1.54184e8i | 0.106622 | − | 0.374386i | ||||
\(745\) | −4.16881e8 | −1.00819 | ||||||||
\(746\) | 9.33248e7 | + | 6.60748e7i | 0.224792 | + | 0.159155i | ||||
\(747\) | − | 1.86997e8i | − | 0.448614i | ||||||
\(748\) | −6.94852e7 | + | 2.44728e7i | −0.166030 | + | 0.0584761i | ||||
\(749\) | 7.72772e7 | 0.183910 | ||||||||
\(750\) | 1.04830e7 | − | 1.48063e7i | 0.0248486 | − | 0.0350964i | ||||
\(751\) | 6.61475e8i | 1.56169i | 0.624727 | + | 0.780843i | \(0.285210\pi\) | ||||
−0.624727 | + | 0.780843i | \(0.714790\pi\) | |||||||
\(752\) | −5.08747e8 | − | 6.32649e8i | −1.19632 | − | 1.48768i | ||||
\(753\) | −1.43167e7 | −0.0335320 | ||||||||
\(754\) | 3.99138e8 | + | 2.82593e8i | 0.931126 | + | 0.659246i | ||||
\(755\) | − | 7.94065e8i | − | 1.84508i | ||||||
\(756\) | −1.31029e7 | − | 3.72031e7i | −0.0303252 | − | 0.0861020i | ||||
\(757\) | −5.73592e8 | −1.32226 | −0.661128 | − | 0.750273i | \(-0.729922\pi\) | ||||
−0.661128 | + | 0.750273i | \(0.729922\pi\) | |||||||
\(758\) | −3.52431e8 | + | 4.97777e8i | −0.809219 | + | 1.14295i | ||||
\(759\) | 1.66261e6i | 0.00380247i | ||||||||
\(760\) | 1.39289e8 | + | 3.96685e7i | 0.317305 | + | 0.0903660i | ||||
\(761\) | 2.81973e7 | 0.0639814 | 0.0319907 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319907 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(762\) | −1.25033e8 | − | 8.85246e7i | −0.282592 | − | 0.200078i | ||||
\(763\) | − | 6.32880e6i | − | 0.0142478i | ||||||
\(764\) | 7.15133e8 | − | 2.51870e8i | 1.60364 | − | 0.564803i | ||||
\(765\) | 2.26959e8 | 0.506947 | ||||||||
\(766\) | −4.75687e8 | + | 6.71866e8i | −1.05836 | + | 1.49484i | ||||
\(767\) | 2.84621e7i | 0.0630785i | ||||||||
\(768\) | 1.94210e8 | + | 4.26671e7i | 0.428735 | + | 0.0941911i | ||||
\(769\) | 4.90996e8 | 1.07969 | 0.539844 | − | 0.841765i | \(-0.318483\pi\) | ||||
0.539844 | + | 0.841765i | \(0.318483\pi\) | |||||||
\(770\) | 2.48556e7 | + | 1.75980e7i | 0.0544444 | + | 0.0385471i | ||||
\(771\) | − | 2.90080e8i | − | 0.632930i | ||||||
\(772\) | −2.12857e8 | − | 6.04363e8i | −0.462633 | − | 1.31355i | ||||
\(773\) | 8.28311e8 | 1.79331 | 0.896654 | − | 0.442731i | \(-0.145990\pi\) | ||||
0.896654 | + | 0.442731i | \(0.145990\pi\) | |||||||
\(774\) | 3.58372e8 | − | 5.06168e8i | 0.772878 | − | 1.09162i | ||||
\(775\) | − | 4.40915e8i | − | 0.947217i | ||||||
\(776\) | 9.34922e7 | − | 3.28282e8i | 0.200074 | − | 0.702526i | ||||
\(777\) | −8.21367e6 | −0.0175095 | ||||||||
\(778\) | −2.42511e8 | − | 1.71700e8i | −0.514983 | − | 0.364613i | ||||
\(779\) | 4.81818e7i | 0.101923i | ||||||||
\(780\) | 1.93952e8 | − | 6.83102e7i | 0.408706 | − | 0.143947i | ||||
\(781\) | −5.62182e7 | −0.118011 | ||||||||
\(782\) | −2.59271e6 | + | 3.66197e6i | −0.00542168 | + | 0.00765764i | ||||
\(783\) | 6.32982e8i | 1.31858i | ||||||||
\(784\) | −3.70559e8 | + | 2.97986e8i | −0.768970 | + | 0.618369i | ||||
\(785\) | 7.21823e8 | 1.49218 | ||||||||
\(786\) | −2.58523e8 | − | 1.83037e8i | −0.532392 | − | 0.376938i | ||||
\(787\) | 5.08364e8i | 1.04292i | 0.853276 | + | 0.521459i | \(0.174612\pi\) | ||||
−0.853276 | + | 0.521459i | \(0.825388\pi\) | |||||||
\(788\) | −6.64740e7 | − | 1.88739e8i | −0.135854 | − | 0.385729i | ||||
\(789\) | 9.70695e7 | 0.197630 | ||||||||
\(790\) | 4.04178e7 | − | 5.70865e7i | 0.0819768 | − | 0.115785i | ||||
\(791\) | − | 5.35621e7i | − | 0.108225i | ||||||
\(792\) | 1.55501e8 | + | 4.42854e7i | 0.313009 | + | 0.0891425i | ||||
\(793\) | 2.51538e8 | 0.504411 | ||||||||
\(794\) | 4.97216e8 | + | 3.52034e8i | 0.993308 | + | 0.703271i | ||||
\(795\) | − | 2.72972e8i | − | 0.543272i | ||||||
\(796\) | −3.29920e7 | + | 1.16198e7i | −0.0654138 | + | 0.0230388i | ||||
\(797\) | −1.24758e8 | −0.246431 | −0.123215 | − | 0.992380i | \(-0.539321\pi\) | ||||
−0.123215 | + | 0.992380i | \(0.539321\pi\) | |||||||
\(798\) | −3.40261e6 | + | 4.80588e6i | −0.00669581 | + | 0.00945723i | ||||
\(799\) | 4.25190e8i | 0.833572i | ||||||||
\(800\) | 5.45855e8 | − | 3.34410e7i | 1.06612 | − | 0.0653145i | ||||
\(801\) | 1.77926e7 | 0.0346211 | ||||||||
\(802\) | 3.31396e8 | + | 2.34631e8i | 0.642427 | + | 0.454844i | ||||
\(803\) | 1.41142e8i | 0.272590i | ||||||||
\(804\) | 6.73215e7 | + | 1.91145e8i | 0.129535 | + | 0.367786i | ||||
\(805\) | 1.85488e6 | 0.00355573 | ||||||||
\(806\) | 1.84176e8 | − | 2.60133e8i | 0.351745 | − | 0.496809i | ||||
\(807\) | 5.26090e7i | 0.100101i | ||||||||
\(808\) | 8.05607e6 | − | 2.82875e7i | 0.0152718 | − | 0.0536242i | ||||
\(809\) | 7.72600e7 | 0.145918 | 0.0729591 | − | 0.997335i | \(-0.476756\pi\) | ||||
0.0729591 | + | 0.997335i | \(0.476756\pi\) | |||||||
\(810\) | −2.86347e8 | − | 2.02737e8i | −0.538813 | − | 0.381485i | ||||
\(811\) | 5.47814e8i | 1.02700i | 0.858090 | + | 0.513500i | \(0.171651\pi\) | ||||
−0.858090 | + | 0.513500i | \(0.828349\pi\) | |||||||
\(812\) | −9.65765e7 | + | 3.40143e7i | −0.180386 | + | 0.0635322i | ||||
\(813\) | 4.17336e8 | 0.776629 | ||||||||
\(814\) | 4.35544e7 | − | 6.15168e7i | 0.0807531 | − | 0.114057i | ||||
\(815\) | 8.29144e8i | 1.53164i | ||||||||
\(816\) | −6.52623e7 | − | 8.11566e7i | −0.120114 | − | 0.149367i | ||||
\(817\) | −2.07276e8 | −0.380087 | ||||||||
\(818\) | 2.20438e8 | + | 1.56072e8i | 0.402743 | + | 0.285145i | ||||
\(819\) | − | 3.50294e7i | − | 0.0637648i | ||||||
\(820\) | 1.17024e8 | + | 3.32265e8i | 0.212243 | + | 0.602620i | ||||
\(821\) | −7.87142e8 | −1.42241 | −0.711203 | − | 0.702987i | \(-0.751849\pi\) | ||||
−0.711203 | + | 0.702987i | \(0.751849\pi\) | |||||||
\(822\) | −2.56924e8 | + | 3.62882e8i | −0.462582 | + | 0.653356i | ||||
\(823\) | − | 3.81472e7i | − | 0.0684326i | −0.999414 | − | 0.0342163i | \(-0.989106\pi\) | ||
0.999414 | − | 0.0342163i | \(-0.0108935\pi\) | |||||||
\(824\) | 6.57437e8 | + | 1.87233e8i | 1.17509 | + | 0.334658i | ||||
\(825\) | −1.06134e8 | −0.189013 | ||||||||
\(826\) | −4.86348e6 | − | 3.44339e6i | −0.00862993 | − | 0.00611007i | ||||
\(827\) | − | 3.67173e8i | − | 0.649164i | −0.945858 | − | 0.324582i | \(-0.894776\pi\) | ||
0.945858 | − | 0.324582i | \(-0.105224\pi\) | |||||||
\(828\) | 9.28829e6 | − | 3.27134e6i | 0.0163623 | − | 0.00576282i | ||||
\(829\) | 6.07250e8 | 1.06587 | 0.532935 | − | 0.846156i | \(-0.321089\pi\) | ||||
0.532935 | + | 0.846156i | \(0.321089\pi\) | |||||||
\(830\) | −2.64034e8 | + | 3.72925e8i | −0.461770 | + | 0.652210i | ||||
\(831\) | 1.85389e8i | 0.323059i | ||||||||
\(832\) | 3.36014e8 | + | 2.08281e8i | 0.583428 | + | 0.361643i | ||||
\(833\) | 2.49045e8 | 0.430867 | ||||||||
\(834\) | −1.33448e8 | − | 9.44823e7i | −0.230045 | − | 0.162874i | ||||
\(835\) | − | 3.46762e8i | − | 0.595624i | ||||||
\(836\) | −1.79510e7 | − | 5.09681e7i | −0.0307234 | − | 0.0872327i | ||||
\(837\) | 4.12538e8 | 0.703537 | ||||||||
\(838\) | 4.99679e8 | − | 7.05752e8i | 0.849100 | − | 1.19928i | ||||
\(839\) | 2.91590e8i | 0.493728i | 0.969050 | + | 0.246864i | \(0.0794000\pi\) | ||||
−0.969050 | + | 0.246864i | \(0.920600\pi\) | |||||||
\(840\) | −1.17921e7 | + | 4.14060e7i | −0.0198954 | + | 0.0698594i | ||||
\(841\) | 1.04835e9 | 1.76246 | ||||||||
\(842\) | −4.52400e8 | − | 3.20303e8i | −0.757855 | − | 0.536568i | ||||
\(843\) | 2.75743e8i | 0.460280i | ||||||||
\(844\) | 1.92644e8 | − | 6.78493e7i | 0.320426 | − | 0.112854i | ||||
\(845\) | −4.58850e8 | −0.760502 | ||||||||
\(846\) | 5.39230e8 | − | 7.61614e8i | 0.890559 | − | 1.25784i | ||||
\(847\) | 5.85563e7i | 0.0963660i | ||||||||
\(848\) | 4.08969e8 | − | 3.28874e8i | 0.670660 | − | 0.539314i | ||||
\(849\) | 1.39010e8 | 0.227155 | ||||||||
\(850\) | −2.33764e8 | − | 1.65507e8i | −0.380646 | − | 0.269501i | ||||
\(851\) | − | 4.59076e6i | − | 0.00744897i | ||||||
\(852\) | −2.64008e7 | − | 7.49595e7i | −0.0426873 | − | 0.121202i | ||||
\(853\) | 1.01563e9 | 1.63640 | 0.818198 | − | 0.574937i | \(-0.194973\pi\) | ||||
0.818198 | + | 0.574937i | \(0.194973\pi\) | |||||||
\(854\) | −3.04315e7 | + | 4.29817e7i | −0.0488595 | + | 0.0690097i | ||||
\(855\) | 1.66476e8i | 0.266351i | ||||||||
\(856\) | −9.64153e8 | − | 2.74583e8i | −1.53718 | − | 0.437777i | ||||
\(857\) | −6.83024e8 | −1.08516 | −0.542580 | − | 0.840004i | \(-0.682552\pi\) | ||||
−0.542580 | + | 0.840004i | \(0.682552\pi\) | |||||||
\(858\) | −6.26173e7 | − | 4.43337e7i | −0.0991363 | − | 0.0701894i | ||||
\(859\) | 5.32877e8i | 0.840713i | 0.907359 | + | 0.420356i | \(0.138095\pi\) | ||||
−0.907359 | + | 0.420356i | \(0.861905\pi\) | |||||||
\(860\) | −1.42939e9 | + | 5.03432e8i | −2.24727 | + | 0.791491i | ||||
\(861\) | −1.43228e7 | −0.0224398 | ||||||||
\(862\) | 3.03218e8 | − | 4.28269e8i | 0.473406 | − | 0.668643i | ||||
\(863\) | 7.75563e8i | 1.20666i | 0.797492 | + | 0.603330i | \(0.206160\pi\) | ||||
−0.797492 | + | 0.603330i | \(0.793840\pi\) | |||||||
\(864\) | 3.12887e7 | + | 5.10723e8i | 0.0485117 | + | 0.791853i | ||||
\(865\) | −7.21114e8 | −1.11418 | ||||||||
\(866\) | −1.87761e8 | − | 1.32936e8i | −0.289102 | − | 0.204687i | ||||
\(867\) | − | 2.31532e8i | − | 0.355267i | ||||||
\(868\) | 2.21684e7 | + | 6.29424e7i | 0.0338981 | + | 0.0962464i | ||||
\(869\) | −2.60977e7 | −0.0397688 | ||||||||
\(870\) | 3.99233e8 | − | 5.63881e8i | 0.606274 | − | 0.856308i | ||||
\(871\) | 4.02910e8i | 0.609753i | ||||||||
\(872\) | −2.24876e7 | + | 7.89615e7i | −0.0339152 | + | 0.119087i | ||||
\(873\) | 3.92358e8 | 0.589711 | ||||||||
\(874\) | −2.68609e6 | − | 1.90178e6i | −0.00402334 | − | 0.00284856i | ||||
\(875\) | 7.55162e6i | 0.0112724i | ||||||||
\(876\) | −1.88195e8 | + | 6.62823e7i | −0.279959 | + | 0.0986018i | ||||
\(877\) | 4.34542e8 | 0.644218 | 0.322109 | − | 0.946703i | \(-0.395608\pi\) | ||||
0.322109 | + | 0.946703i | \(0.395608\pi\) | |||||||
\(878\) | −3.58866e8 | + | 5.06866e8i | −0.530211 | + | 0.748875i | ||||
\(879\) | − | 5.36603e8i | − | 0.790108i | ||||||
\(880\) | −2.47583e8 | − | 3.07880e8i | −0.363306 | − | 0.451787i | ||||
\(881\) | −7.44134e8 | −1.08824 | −0.544118 | − | 0.839009i | \(-0.683136\pi\) | ||||
−0.544118 | + | 0.839009i | \(0.683136\pi\) | |||||||
\(882\) | −4.46097e8 | − | 3.15841e8i | −0.650165 | − | 0.460323i | ||||
\(883\) | − | 4.95209e8i | − | 0.719295i | −0.933088 | − | 0.359647i | \(-0.882897\pi\) | ||
0.933088 | − | 0.359647i | \(-0.117103\pi\) | |||||||
\(884\) | −6.87824e7 | − | 1.95293e8i | −0.0995682 | − | 0.282703i | ||||
\(885\) | 4.02099e7 | 0.0580100 | ||||||||
\(886\) | 2.43230e8 | − | 3.43541e8i | 0.349717 | − | 0.493944i | ||||
\(887\) | − | 1.36360e9i | − | 1.95397i | −0.213311 | − | 0.976984i | \(-0.568425\pi\) | ||
0.213311 | − | 0.976984i | \(-0.431575\pi\) | |||||||
\(888\) | 1.02478e8 | + | 2.91850e7i | 0.146350 | + | 0.0416793i | ||||
\(889\) | 6.37704e7 | 0.0907640 | ||||||||
\(890\) | −3.54834e7 | − | 2.51226e7i | −0.0503333 | − | 0.0356365i | ||||
\(891\) | 1.30907e8i | 0.185067i | ||||||||
\(892\) | 1.10300e9 | − | 3.88478e8i | 1.55411 | − | 0.547358i | ||||
\(893\) | −3.11881e8 | −0.437960 | ||||||||
\(894\) | −1.27058e8 | + | 1.79458e8i | −0.177823 | + | 0.251159i | ||||
\(895\) | 1.49743e9i | 2.08871i | ||||||||
\(896\) | −7.62417e7 | + | 3.22184e7i | −0.105991 | + | 0.0447899i | ||||
\(897\) | −4.67290e6 | −0.00647454 | ||||||||
\(898\) | −3.86715e8 | − | 2.73798e8i | −0.534025 | − | 0.378095i | ||||
\(899\) | − | 1.07092e9i | − | 1.47393i | ||||||
\(900\) | 2.08828e8 | + | 5.92924e8i | 0.286459 | + | 0.813339i | ||||
\(901\) | −2.74860e8 | −0.375782 | ||||||||
\(902\) | 7.59492e7 | − | 1.07272e8i | 0.103491 | − | 0.146172i | ||||
\(903\) | − | 6.16161e7i | − | 0.0836818i | ||||||
\(904\) | −1.90318e8 | + | 6.68270e8i | −0.257617 | + | 0.904579i | ||||
\(905\) | −1.33082e9 | −1.79546 | ||||||||
\(906\) | −3.41827e8 | − | 2.42016e8i | −0.459644 | − | 0.325432i | ||||
\(907\) | 8.48842e8i | 1.13764i | 0.822462 | + | 0.568820i | \(0.192600\pi\) | ||||
−0.822462 | + | 0.568820i | \(0.807400\pi\) | |||||||
\(908\) | −9.05675e8 | + | 3.18980e8i | −1.20980 | + | 0.426094i | ||||
\(909\) | 3.38088e7 | 0.0450130 | ||||||||
\(910\) | −4.94605e7 | + | 6.98586e7i | −0.0656349 | + | 0.0927034i | ||||
\(911\) | − | 5.90719e8i | − | 0.781315i | −0.920536 | − | 0.390657i | \(-0.872248\pi\) | ||
0.920536 | − | 0.390657i | \(-0.127752\pi\) | |||||||
\(912\) | 5.95291e7 | − | 4.78706e7i | 0.0784775 | − | 0.0631079i | ||||
\(913\) | 1.70487e8 | 0.224015 | ||||||||
\(914\) | 9.94581e8 | + | 7.04173e8i | 1.30257 | + | 0.922233i | ||||
\(915\) | − | 3.55360e8i | − | 0.463880i | ||||||
\(916\) | 2.28335e8 | + | 6.48308e8i | 0.297088 | + | 0.843519i | ||||
\(917\) | 1.31854e8 | 0.170996 | ||||||||
\(918\) | 1.54855e8 | − | 2.18719e8i | 0.200170 | − | 0.282722i | ||||
\(919\) | − | 4.57837e8i | − | 0.589881i | −0.955516 | − | 0.294940i | \(-0.904700\pi\) | ||
0.955516 | − | 0.294940i | \(-0.0952998\pi\) | |||||||
\(920\) | −2.31425e7 | − | 6.59081e6i | −0.0297199 | − | 0.00846400i | ||||
\(921\) | 4.64177e8 | 0.594162 | ||||||||
\(922\) | 7.65157e7 | + | 5.41738e7i | 0.0976242 | + | 0.0691189i | ||||
\(923\) | − | 1.58005e8i | − | 0.200940i | ||||||
\(924\) | 1.51511e7 | − | 5.33622e6i | 0.0192056 | − | 0.00676422i | ||||
\(925\) | 2.93054e8 | 0.370274 | ||||||||
\(926\) | −2.77583e8 | + | 3.92062e8i | −0.349591 | + | 0.493766i | ||||
\(927\) | 7.85758e8i | 0.986392i | ||||||||
\(928\) | 1.32580e9 | − | 8.12234e7i | 1.65896 | − | 0.101634i | ||||
\(929\) | 3.31295e7 | 0.0413207 | 0.0206604 | − | 0.999787i | \(-0.493423\pi\) | ||||
0.0206604 | + | 0.999787i | \(0.493423\pi\) | |||||||
\(930\) | −3.67502e8 | − | 2.60195e8i | −0.456889 | − | 0.323482i | ||||
\(931\) | 1.82677e8i | 0.226378i | ||||||||
\(932\) | 4.46232e8 | + | 1.26698e9i | 0.551205 | + | 1.56503i | ||||
\(933\) | −3.72738e8 | −0.458943 | ||||||||
\(934\) | 4.56276e8 | − | 6.44450e8i | 0.559999 | − | 0.790949i | ||||
\(935\) | 2.06920e8i | 0.253144i | ||||||||
\(936\) | −1.24467e8 | + | 4.37046e8i | −0.151785 | + | 0.532966i | ||||
\(937\) | −2.76382e8 | −0.335962 | −0.167981 | − | 0.985790i | \(-0.553725\pi\) | ||||
−0.167981 | + | 0.985790i | \(0.553725\pi\) | |||||||
\(938\) | −6.88476e7 | − | 4.87447e7i | −0.0834219 | − | 0.0590635i | ||||
\(939\) | − | 2.88884e8i | − | 0.348921i | ||||||
\(940\) | −2.15076e9 | + | 7.57498e8i | −2.58945 | + | 0.912006i | ||||
\(941\) | −4.58833e8 | −0.550663 | −0.275331 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275331 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(942\) | 2.19998e8 | − | 3.10728e8i | 0.263188 | − | 0.371730i | ||||
\(943\) | − | 8.00527e6i | − | 0.00954643i | ||||||
\(944\) | 4.84443e7 | + | 6.02427e7i | 0.0575873 | + | 0.0716124i | ||||
\(945\) | −1.10787e8 | −0.131278 | ||||||||
\(946\) | 4.61477e8 | + | 3.26730e8i | 0.545101 | + | 0.385937i | ||||
\(947\) | − | 1.75733e8i | − | 0.206921i | −0.994634 | − | 0.103460i | \(-0.967009\pi\) | ||
0.994634 | − | 0.103460i | \(-0.0329915\pi\) | |||||||
\(948\) | −1.22558e7 | − | 3.47978e7i | −0.0143852 | − | 0.0408439i | ||||
\(949\) | −3.96691e8 | −0.464144 | ||||||||
\(950\) | 1.21401e8 | − | 1.71468e8i | 0.141596 | − | 0.199992i | ||||
\(951\) | − | 4.04075e8i | − | 0.469808i | ||||||
\(952\) | 4.16922e7 | + | 1.18736e7i | 0.0483219 | + | 0.0137617i | ||||
\(953\) | −1.55427e7 | −0.0179576 | −0.00897879 | − | 0.999960i | \(-0.502858\pi\) | ||||
−0.00897879 | + | 0.999960i | \(0.502858\pi\) | |||||||
\(954\) | 4.92337e8 | + | 3.48579e8i | 0.567045 | + | 0.401473i | ||||
\(955\) | − | 2.12959e9i | − | 2.44504i | ||||||
\(956\) | −7.42509e7 | + | 2.61512e7i | −0.0849823 | + | 0.0299308i | ||||
\(957\) | −2.57784e8 | −0.294117 | ||||||||
\(958\) | 1.11037e8 | − | 1.56830e8i | 0.126291 | − | 0.178374i | ||||
\(959\) | − | 1.85080e8i | − | 0.209847i | ||||||
\(960\) | 2.94249e8 | − | 4.74704e8i | 0.332584 | − | 0.536548i | ||||
\(961\) | 1.89547e8 | 0.213573 | ||||||||
\(962\) | 1.72897e8 | + | 1.22413e8i | 0.194206 | + | 0.137500i | ||||
\(963\) | − | 1.15234e9i | − | 1.29033i | ||||||
\(964\) | 4.16124e8 | + | 1.18150e9i | 0.464507 | + | 1.31887i | ||||
\(965\) | −1.79973e9 | −2.00275 | ||||||||
\(966\) | 565334. | − | 798484.i | 0.000627153 | − | 0.000885798i | ||||
\(967\) | − | 1.66888e9i | − | 1.84564i | −0.385236 | − | 0.922818i | \(-0.625880\pi\) | ||
0.385236 | − | 0.922818i | \(-0.374120\pi\) | |||||||
\(968\) | 2.08064e8 | − | 7.30581e8i | 0.229388 | − | 0.805457i | ||||
\(969\) | −4.00083e7 | −0.0439723 | ||||||||
\(970\) | −7.82473e8 | − | 5.53998e8i | −0.857342 | − | 0.607006i | ||||
\(971\) | 1.09973e9i | 1.20124i | 0.799535 | + | 0.600620i | \(0.205079\pi\) | ||||
−0.799535 | + | 0.600620i | \(0.794921\pi\) | |||||||
\(972\) | −8.61718e8 | + | 3.03498e8i | −0.938353 | + | 0.330489i | ||||
\(973\) | 6.80621e7 | 0.0738868 | ||||||||
\(974\) | −8.70456e8 | + | 1.22944e9i | −0.942042 | + | 1.33055i | ||||
\(975\) | − | 2.98297e8i | − | 0.321837i | ||||||
\(976\) | 5.32403e8 | − | 4.28134e8i | 0.572653 | − | 0.460500i | ||||
\(977\) | −3.80732e8 | −0.408259 | −0.204129 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204129 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(978\) | 3.56927e8 | + | 2.52708e8i | 0.381560 | + | 0.270148i | ||||
\(979\) | 1.62216e7i | 0.0172881i | ||||||||
\(980\) | 4.43686e8 | + | 1.25975e9i | 0.471409 | + | 1.33847i | ||||
\(981\) | −9.43736e7 | −0.0999639 | ||||||||
\(982\) | −6.41951e8 | + | 9.06698e8i | −0.677902 | + | 0.957477i | ||||
\(983\) | 5.81394e7i | 0.0612083i | 0.999532 | + | 0.0306041i | \(0.00974312\pi\) | ||||
−0.999532 | + | 0.0306041i | \(0.990257\pi\) | |||||||
\(984\) | 1.78699e8 | + | 5.08921e7i | 0.187559 | + | 0.0534153i | ||||
\(985\) | −5.62045e8 | −0.588115 | ||||||||
\(986\) | −5.67780e8 | − | 4.01993e8i | −0.592310 | − | 0.419361i | ||||
\(987\) | − | 9.27117e7i | − | 0.0964235i | ||||||
\(988\) | 1.43249e8 | − | 5.04526e7i | 0.148533 | − | 0.0523133i | ||||
\(989\) | 3.44383e7 | 0.0356002 | ||||||||
\(990\) | 2.62418e8 | − | 3.70642e8i | 0.270450 | − | 0.381987i | ||||
\(991\) | − | 5.54527e8i | − | 0.569773i | −0.958561 | − | 0.284887i | \(-0.908044\pi\) | ||
0.958561 | − | 0.284887i | \(-0.0919559\pi\) | |||||||
\(992\) | −5.29362e7 | − | 8.64074e8i | −0.0542273 | − | 0.885148i | ||||
\(993\) | −2.08515e8 | −0.212956 | ||||||||
\(994\) | 2.69992e7 | + | 1.91157e7i | 0.0274911 | + | 0.0194640i | ||||
\(995\) | 9.82468e7i | 0.0997354i | ||||||||
\(996\) | 8.00627e7 | + | 2.27321e8i | 0.0810312 | + | 0.230071i | ||||
\(997\) | 1.07984e9 | 1.08961 | 0.544807 | − | 0.838561i | \(-0.316603\pi\) | ||||
0.544807 | + | 0.838561i | \(0.316603\pi\) | |||||||
\(998\) | 9.79905e8 | − | 1.38403e9i | 0.985808 | − | 1.39237i | ||||
\(999\) | 2.74193e8i | 0.275018i |
(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 | 76.7.b.a.39.11 | ✓ | 54 | |
4.3 | odd | 2 | inner | 76.7.b.a.39.12 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.b.a.39.11 | ✓ | 54 | 1.1 | even | 1 | trivial | |
76.7.b.a.39.12 | yes | 54 | 4.3 | odd | 2 | inner |