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 | 39.20 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.7.b.a.39.19 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.60097 | + | 6.54454i | −0.575122 | + | 0.818068i | ||||
\(3\) | − | 21.0346i | − | 0.779060i | −0.921014 | − | 0.389530i | \(-0.872637\pi\) | ||
0.921014 | − | 0.389530i | \(-0.127363\pi\) | |||||||
\(4\) | −21.6621 | − | 60.2225i | −0.338470 | − | 0.940977i | ||||
\(5\) | −46.6232 | −0.372986 | −0.186493 | − | 0.982456i | \(-0.559712\pi\) | ||||
−0.186493 | + | 0.982456i | \(0.559712\pi\) | |||||||
\(6\) | 137.662 | + | 96.7797i | 0.637324 | + | 0.448054i | ||||
\(7\) | − | 184.040i | − | 0.536561i | −0.963341 | − | 0.268280i | \(-0.913545\pi\) | ||
0.963341 | − | 0.268280i | \(-0.0864554\pi\) | |||||||
\(8\) | 493.796 | + | 135.314i | 0.964445 | + | 0.264284i | ||||
\(9\) | 286.545 | 0.393066 | ||||||||
\(10\) | 214.512 | − | 305.128i | 0.214512 | − | 0.305128i | ||||
\(11\) | − | 790.519i | − | 0.593929i | −0.954889 | − | 0.296964i | \(-0.904026\pi\) | ||
0.954889 | − | 0.296964i | \(-0.0959743\pi\) | |||||||
\(12\) | −1266.76 | + | 455.654i | −0.733077 | + | 0.263689i | ||||
\(13\) | 775.625 | 0.353038 | 0.176519 | − | 0.984297i | \(-0.443516\pi\) | ||||
0.176519 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(14\) | 1204.46 | + | 846.765i | 0.438943 | + | 0.308588i | ||||
\(15\) | 980.702i | 0.290578i | ||||||||
\(16\) | −3157.51 | + | 2609.09i | −0.770876 | + | 0.636986i | ||||
\(17\) | −6841.14 | −1.39246 | −0.696228 | − | 0.717820i | \(-0.745140\pi\) | ||||
−0.696228 | + | 0.717820i | \(0.745140\pi\) | |||||||
\(18\) | −1318.39 | + | 1875.31i | −0.226061 | + | 0.321554i | ||||
\(19\) | 1573.56i | 0.229416i | ||||||||
\(20\) | 1009.96 | + | 2807.77i | 0.126245 | + | 0.350971i | ||||
\(21\) | −3871.22 | −0.418013 | ||||||||
\(22\) | 5173.59 | + | 3637.16i | 0.485874 | + | 0.341581i | ||||
\(23\) | 8630.01i | 0.709297i | 0.935000 | + | 0.354648i | \(0.115399\pi\) | ||||
−0.935000 | + | 0.354648i | \(0.884601\pi\) | |||||||
\(24\) | 2846.27 | − | 10386.8i | 0.205893 | − | 0.751360i | ||||
\(25\) | −13451.3 | −0.860882 | ||||||||
\(26\) | −3568.63 | + | 5076.11i | −0.203040 | + | 0.288809i | ||||
\(27\) | − | 21361.6i | − | 1.08528i | ||||||
\(28\) | −11083.4 | + | 3986.70i | −0.504891 | + | 0.181610i | ||||
\(29\) | −25149.9 | −1.03120 | −0.515600 | − | 0.856830i | \(-0.672431\pi\) | ||||
−0.515600 | + | 0.856830i | \(0.672431\pi\) | |||||||
\(30\) | −6418.25 | − | 4512.18i | −0.237713 | − | 0.167118i | ||||
\(31\) | − | 18917.2i | − | 0.634999i | −0.948258 | − | 0.317499i | \(-0.897157\pi\) | ||
0.948258 | − | 0.317499i | \(-0.102843\pi\) | |||||||
\(32\) | −2547.73 | − | 32668.8i | −0.0777504 | − | 0.996973i | ||||
\(33\) | −16628.3 | −0.462706 | ||||||||
\(34\) | 31475.9 | − | 44772.1i | 0.800832 | − | 1.13912i | ||||
\(35\) | 8580.56i | 0.200130i | ||||||||
\(36\) | −6207.16 | − | 17256.5i | −0.133041 | − | 0.369866i | ||||
\(37\) | −17259.5 | −0.340740 | −0.170370 | − | 0.985380i | \(-0.554496\pi\) | ||||
−0.170370 | + | 0.985380i | \(0.554496\pi\) | |||||||
\(38\) | −10298.2 | − | 7239.92i | −0.187678 | − | 0.131942i | ||||
\(39\) | − | 16315.0i | − | 0.275038i | ||||||
\(40\) | −23022.4 | − | 6308.76i | −0.359724 | − | 0.0985743i | ||||
\(41\) | −100532. | −1.45866 | −0.729330 | − | 0.684162i | \(-0.760168\pi\) | ||||
−0.729330 | + | 0.684162i | \(0.760168\pi\) | |||||||
\(42\) | 17811.4 | − | 25335.4i | 0.240408 | − | 0.341963i | ||||
\(43\) | − | 29182.4i | − | 0.367041i | −0.983016 | − | 0.183521i | \(-0.941251\pi\) | ||
0.983016 | − | 0.183521i | \(-0.0587494\pi\) | |||||||
\(44\) | −47607.1 | + | 17124.3i | −0.558874 | + | 0.201027i | ||||
\(45\) | −13359.6 | −0.146608 | ||||||||
\(46\) | −56479.5 | − | 39706.5i | −0.580253 | − | 0.407932i | ||||
\(47\) | 156598.i | 1.50832i | 0.656691 | + | 0.754160i | \(0.271955\pi\) | ||||
−0.656691 | + | 0.754160i | \(0.728045\pi\) | |||||||
\(48\) | 54881.3 | + | 66416.9i | 0.496250 | + | 0.600558i | ||||
\(49\) | 83778.1 | 0.712102 | ||||||||
\(50\) | 61888.9 | − | 88032.5i | 0.495112 | − | 0.704260i | ||||
\(51\) | 143901.i | 1.08481i | ||||||||
\(52\) | −16801.7 | − | 46710.1i | −0.119493 | − | 0.332201i | ||||
\(53\) | −8209.91 | −0.0551456 | −0.0275728 | − | 0.999620i | \(-0.508778\pi\) | ||||
−0.0275728 | + | 0.999620i | \(0.508778\pi\) | |||||||
\(54\) | 139802. | + | 98284.1i | 0.887834 | + | 0.624169i | ||||
\(55\) | 36856.6i | 0.221527i | ||||||||
\(56\) | 24903.2 | − | 90878.3i | 0.141805 | − | 0.517483i | ||||
\(57\) | 33099.3 | 0.178729 | ||||||||
\(58\) | 115714. | − | 164595.i | 0.593065 | − | 0.843591i | ||||
\(59\) | 296739.i | 1.44484i | 0.691456 | + | 0.722418i | \(0.256970\pi\) | ||||
−0.691456 | + | 0.722418i | \(0.743030\pi\) | |||||||
\(60\) | 59060.3 | − | 21244.1i | 0.273428 | − | 0.0983521i | ||||
\(61\) | −233354. | −1.02808 | −0.514038 | − | 0.857767i | \(-0.671851\pi\) | ||||
−0.514038 | + | 0.857767i | \(0.671851\pi\) | |||||||
\(62\) | 123805. | + | 87037.7i | 0.519472 | + | 0.365201i | ||||
\(63\) | − | 52735.8i | − | 0.210904i | ||||||
\(64\) | 225524. | + | 133635.i | 0.860307 | + | 0.509775i | ||||
\(65\) | −36162.2 | −0.131678 | ||||||||
\(66\) | 76506.2 | − | 108824.i | 0.266112 | − | 0.378525i | ||||
\(67\) | 188870.i | 0.627969i | 0.949428 | + | 0.313985i | \(0.101664\pi\) | ||||
−0.949428 | + | 0.313985i | \(0.898336\pi\) | |||||||
\(68\) | 148193. | + | 411991.i | 0.471305 | + | 1.31027i | ||||
\(69\) | 181529. | 0.552585 | ||||||||
\(70\) | −56155.8 | − | 39478.9i | −0.163720 | − | 0.115099i | ||||
\(71\) | − | 153617.i | − | 0.429205i | −0.976702 | − | 0.214602i | \(-0.931154\pi\) | ||
0.976702 | − | 0.214602i | \(-0.0688455\pi\) | |||||||
\(72\) | 141495. | + | 38773.4i | 0.379090 | + | 0.103881i | ||||
\(73\) | −306135. | −0.786946 | −0.393473 | − | 0.919336i | \(-0.628726\pi\) | ||||
−0.393473 | + | 0.919336i | \(0.628726\pi\) | |||||||
\(74\) | 79410.6 | − | 112956.i | 0.195967 | − | 0.278749i | ||||
\(75\) | 282942.i | 0.670678i | ||||||||
\(76\) | 94763.9 | − | 34086.7i | 0.215875 | − | 0.0776504i | ||||
\(77\) | −145487. | −0.318679 | ||||||||
\(78\) | 106774. | + | 75064.8i | 0.225000 | + | 0.158180i | ||||
\(79\) | − | 447677.i | − | 0.907994i | −0.891003 | − | 0.453997i | \(-0.849998\pi\) | ||
0.891003 | − | 0.453997i | \(-0.150002\pi\) | |||||||
\(80\) | 147213. | − | 121644.i | 0.287526 | − | 0.237587i | ||||
\(81\) | −240442. | −0.452434 | ||||||||
\(82\) | 462546. | − | 657938.i | 0.838907 | − | 1.19328i | ||||
\(83\) | − | 356959.i | − | 0.624287i | −0.950035 | − | 0.312143i | \(-0.898953\pi\) | ||
0.950035 | − | 0.312143i | \(-0.101047\pi\) | |||||||
\(84\) | 83858.7 | + | 233135.i | 0.141485 | + | 0.393341i | ||||
\(85\) | 318956. | 0.519367 | ||||||||
\(86\) | 190985. | + | 134267.i | 0.300265 | + | 0.211093i | ||||
\(87\) | 529019.i | 0.803366i | ||||||||
\(88\) | 106968. | − | 390355.i | 0.156966 | − | 0.572812i | ||||
\(89\) | 167074. | 0.236995 | 0.118497 | − | 0.992954i | \(-0.462192\pi\) | ||||
0.118497 | + | 0.992954i | \(0.462192\pi\) | |||||||
\(90\) | 61467.4 | − | 87432.8i | 0.0843174 | − | 0.119935i | ||||
\(91\) | − | 142746.i | − | 0.189427i | ||||||
\(92\) | 519721. | − | 186944.i | 0.667432 | − | 0.240076i | ||||
\(93\) | −397917. | −0.494702 | ||||||||
\(94\) | −1.02486e6 | − | 720504.i | −1.23391 | − | 0.867467i | ||||
\(95\) | − | 73364.6i | − | 0.0855688i | ||||||
\(96\) | −687176. | + | 53590.4i | −0.776702 | + | 0.0605722i | ||||
\(97\) | 61902.8 | 0.0678258 | 0.0339129 | − | 0.999425i | \(-0.489203\pi\) | ||||
0.0339129 | + | 0.999425i | \(0.489203\pi\) | |||||||
\(98\) | −385461. | + | 548290.i | −0.409545 | + | 0.582548i | ||||
\(99\) | − | 226519.i | − | 0.233453i | ||||||
\(100\) | 291383. | + | 810070.i | 0.291383 | + | 0.810070i | ||||
\(101\) | −217585. | −0.211185 | −0.105593 | − | 0.994409i | \(-0.533674\pi\) | ||||
−0.105593 | + | 0.994409i | \(0.533674\pi\) | |||||||
\(102\) | −941765. | − | 662083.i | −0.887446 | − | 0.623896i | ||||
\(103\) | − | 479972.i | − | 0.439242i | −0.975585 | − | 0.219621i | \(-0.929518\pi\) | ||
0.975585 | − | 0.219621i | \(-0.0704822\pi\) | |||||||
\(104\) | 383000. | + | 104953.i | 0.340486 | + | 0.0933025i | ||||
\(105\) | 180489. | 0.155913 | ||||||||
\(106\) | 37773.6 | − | 53730.1i | 0.0317154 | − | 0.0451128i | ||||
\(107\) | 242954.i | 0.198323i | 0.995071 | + | 0.0991614i | \(0.0316160\pi\) | ||||
−0.995071 | + | 0.0991614i | \(0.968384\pi\) | |||||||
\(108\) | −1.28645e6 | + | 462737.i | −1.02123 | + | 0.367336i | ||||
\(109\) | −615978. | −0.475648 | −0.237824 | − | 0.971308i | \(-0.576434\pi\) | ||||
−0.237824 | + | 0.971308i | \(0.576434\pi\) | |||||||
\(110\) | −241209. | − | 169576.i | −0.181224 | − | 0.127405i | ||||
\(111\) | 363048.i | 0.265457i | ||||||||
\(112\) | 480179. | + | 581109.i | 0.341782 | + | 0.413622i | ||||
\(113\) | 16570.1 | 0.0114839 | 0.00574197 | − | 0.999984i | \(-0.498172\pi\) | ||||
0.00574197 | + | 0.999984i | \(0.498172\pi\) | |||||||
\(114\) | −152289. | + | 216620.i | −0.102791 | + | 0.146212i | ||||
\(115\) | − | 402359.i | − | 0.264558i | ||||||
\(116\) | 544800. | + | 1.51459e6i | 0.349031 | + | 0.970335i | ||||
\(117\) | 222251. | 0.138767 | ||||||||
\(118\) | −1.94202e6 | − | 1.36529e6i | −1.18197 | − | 0.830957i | ||||
\(119\) | 1.25905e6i | 0.747138i | ||||||||
\(120\) | −132702. | + | 484266.i | −0.0767953 | + | 0.280247i | ||||
\(121\) | 1.14664e6 | 0.647248 | ||||||||
\(122\) | 1.07365e6 | − | 1.52719e6i | 0.591269 | − | 0.841036i | ||||
\(123\) | 2.11466e6i | 1.13638i | ||||||||
\(124\) | −1.13924e6 | + | 409787.i | −0.597519 | + | 0.214928i | ||||
\(125\) | 1.35563e6 | 0.694082 | ||||||||
\(126\) | 345132. | + | 242636.i | 0.172534 | + | 0.121295i | ||||
\(127\) | − | 2.17917e6i | − | 1.06385i | −0.846792 | − | 0.531924i | \(-0.821469\pi\) | ||
0.846792 | − | 0.531924i | \(-0.178531\pi\) | |||||||
\(128\) | −1.91221e6 | + | 861106.i | −0.911812 | + | 0.410607i | ||||
\(129\) | −613840. | −0.285947 | ||||||||
\(130\) | 166381. | − | 236665.i | 0.0757310 | − | 0.107722i | ||||
\(131\) | − | 1.94960e6i | − | 0.867226i | −0.901099 | − | 0.433613i | \(-0.857239\pi\) | ||
0.901099 | − | 0.433613i | \(-0.142761\pi\) | |||||||
\(132\) | 360203. | + | 1.00140e6i | 0.156612 | + | 0.435396i | ||||
\(133\) | 289599. | 0.123095 | ||||||||
\(134\) | −1.23607e6 | − | 868985.i | −0.513721 | − | 0.361159i | ||||
\(135\) | 995947.i | 0.404795i | ||||||||
\(136\) | −3.37813e6 | − | 925699.i | −1.34295 | − | 0.368005i | ||||
\(137\) | −3.69369e6 | −1.43648 | −0.718238 | − | 0.695797i | \(-0.755051\pi\) | ||||
−0.718238 | + | 0.695797i | \(0.755051\pi\) | |||||||
\(138\) | −835210. | + | 1.18802e6i | −0.317803 | + | 0.452052i | ||||
\(139\) | − | 1.27664e6i | − | 0.475360i | −0.971344 | − | 0.237680i | \(-0.923613\pi\) | ||
0.971344 | − | 0.237680i | \(-0.0763869\pi\) | |||||||
\(140\) | 516743. | − | 185873.i | 0.188317 | − | 0.0677379i | ||||
\(141\) | 3.29398e6 | 1.17507 | ||||||||
\(142\) | 1.00535e6 | + | 706788.i | 0.351119 | + | 0.246845i | ||||
\(143\) | − | 613147.i | − | 0.209680i | ||||||
\(144\) | −904767. | + | 747622.i | −0.303005 | + | 0.250377i | ||||
\(145\) | 1.17257e6 | 0.384623 | ||||||||
\(146\) | 1.40852e6 | − | 2.00352e6i | 0.452590 | − | 0.643775i | ||||
\(147\) | − | 1.76224e6i | − | 0.554770i | ||||||
\(148\) | 373878. | + | 1.03941e6i | 0.115331 | + | 0.320629i | ||||
\(149\) | 3.94418e6 | 1.19233 | 0.596166 | − | 0.802861i | \(-0.296690\pi\) | ||||
0.596166 | + | 0.802861i | \(0.296690\pi\) | |||||||
\(150\) | −1.85173e6 | − | 1.30181e6i | −0.548660 | − | 0.385722i | ||||
\(151\) | − | 4.79389e6i | − | 1.39238i | −0.717858 | − | 0.696190i | \(-0.754877\pi\) | ||
0.717858 | − | 0.696190i | \(-0.245123\pi\) | |||||||
\(152\) | −212924. | + | 777018.i | −0.0606310 | + | 0.221259i | ||||
\(153\) | −1.96029e6 | −0.547327 | ||||||||
\(154\) | 669384. | − | 952149.i | 0.183279 | − | 0.260701i | ||||
\(155\) | 881983.i | 0.236846i | ||||||||
\(156\) | −982529. | + | 353417.i | −0.258804 | + | 0.0930922i | ||||
\(157\) | 4.30231e6 | 1.11174 | 0.555870 | − | 0.831270i | \(-0.312385\pi\) | ||||
0.555870 | + | 0.831270i | \(0.312385\pi\) | |||||||
\(158\) | 2.92984e6 | + | 2.05975e6i | 0.742801 | + | 0.522207i | ||||
\(159\) | 172692.i | 0.0429617i | ||||||||
\(160\) | 118783. | + | 1.52313e6i | 0.0289998 | + | 0.371857i | ||||
\(161\) | 1.58827e6 | 0.380581 | ||||||||
\(162\) | 1.10627e6 | − | 1.57358e6i | 0.260204 | − | 0.370122i | ||||
\(163\) | − | 5.38798e6i | − | 1.24412i | −0.782969 | − | 0.622061i | \(-0.786296\pi\) | ||
0.782969 | − | 0.622061i | \(-0.213704\pi\) | |||||||
\(164\) | 2.17774e6 | + | 6.05431e6i | 0.493713 | + | 1.37257i | ||||
\(165\) | 775264. | 0.172583 | ||||||||
\(166\) | 2.33613e6 | + | 1.64236e6i | 0.510709 | + | 0.359041i | ||||
\(167\) | − | 3.29435e6i | − | 0.707327i | −0.935373 | − | 0.353664i | \(-0.884936\pi\) | ||
0.935373 | − | 0.353664i | \(-0.115064\pi\) | |||||||
\(168\) | −1.91159e6 | − | 523829.i | −0.403150 | − | 0.110474i | ||||
\(169\) | −4.22521e6 | −0.875364 | ||||||||
\(170\) | −1.46751e6 | + | 2.08742e6i | −0.298699 | + | 0.424877i | ||||
\(171\) | 450896.i | 0.0901754i | ||||||||
\(172\) | −1.75744e6 | + | 632151.i | −0.345378 | + | 0.124233i | ||||
\(173\) | 5.24468e6 | 1.01293 | 0.506467 | − | 0.862260i | \(-0.330951\pi\) | ||||
0.506467 | + | 0.862260i | \(0.330951\pi\) | |||||||
\(174\) | −3.46219e6 | − | 2.43400e6i | −0.657208 | − | 0.462033i | ||||
\(175\) | 2.47558e6i | 0.461915i | ||||||||
\(176\) | 2.06254e6 | + | 2.49607e6i | 0.378324 | + | 0.457845i | ||||
\(177\) | 6.24179e6 | 1.12561 | ||||||||
\(178\) | −768703. | + | 1.09342e6i | −0.136301 | + | 0.193878i | ||||
\(179\) | 8.28153e6i | 1.44395i | 0.691920 | + | 0.721974i | \(0.256765\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(180\) | 289398. | + | 804552.i | 0.0496224 | + | 0.137955i | ||||
\(181\) | −7.95450e6 | −1.34146 | −0.670729 | − | 0.741702i | \(-0.734019\pi\) | ||||
−0.670729 | + | 0.741702i | \(0.734019\pi\) | |||||||
\(182\) | 934210. | + | 656772.i | 0.154964 | + | 0.108943i | ||||
\(183\) | 4.90851e6i | 0.800933i | ||||||||
\(184\) | −1.16776e6 | + | 4.26146e6i | −0.187456 | + | 0.684078i | ||||
\(185\) | 804695. | 0.127091 | ||||||||
\(186\) | 1.83081e6 | − | 2.60419e6i | 0.284514 | − | 0.404700i | ||||
\(187\) | 5.40805e6i | 0.827020i | ||||||||
\(188\) | 9.43074e6 | − | 3.39225e6i | 1.41929 | − | 0.510521i | ||||
\(189\) | −3.93140e6 | −0.582320 | ||||||||
\(190\) | 480138. | + | 337548.i | 0.0700011 | + | 0.0492125i | ||||
\(191\) | − | 4.53876e6i | − | 0.651383i | −0.945476 | − | 0.325692i | \(-0.894403\pi\) | ||
0.945476 | − | 0.325692i | \(-0.105597\pi\) | |||||||
\(192\) | 2.81095e6 | − | 4.74382e6i | 0.397146 | − | 0.670231i | ||||
\(193\) | −9.49200e6 | −1.32034 | −0.660170 | − | 0.751116i | \(-0.729516\pi\) | ||||
−0.660170 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(194\) | −284813. | + | 405125.i | −0.0390081 | + | 0.0554861i | ||||
\(195\) | 760657.i | 0.102585i | ||||||||
\(196\) | −1.81481e6 | − | 5.04533e6i | −0.241026 | − | 0.670072i | ||||
\(197\) | 1.43544e7 | 1.87752 | 0.938761 | − | 0.344569i | \(-0.111975\pi\) | ||||
0.938761 | + | 0.344569i | \(0.111975\pi\) | |||||||
\(198\) | 1.48247e6 | + | 1.04221e6i | 0.190980 | + | 0.134264i | ||||
\(199\) | − | 2.03059e6i | − | 0.257670i | −0.991666 | − | 0.128835i | \(-0.958876\pi\) | ||
0.991666 | − | 0.128835i | \(-0.0411237\pi\) | |||||||
\(200\) | −6.64218e6 | − | 1.82014e6i | −0.830273 | − | 0.227518i | ||||
\(201\) | 3.97281e6 | 0.489226 | ||||||||
\(202\) | 1.00110e6 | − | 1.42399e6i | 0.121457 | − | 0.172764i | ||||
\(203\) | 4.62860e6i | 0.553301i | ||||||||
\(204\) | 8.66607e6 | − | 3.11719e6i | 1.02078 | − | 0.367175i | ||||
\(205\) | 4.68714e6 | 0.544060 | ||||||||
\(206\) | 3.14120e6 | + | 2.20834e6i | 0.359330 | + | 0.252618i | ||||
\(207\) | 2.47289e6i | 0.278800i | ||||||||
\(208\) | −2.44904e6 | + | 2.02368e6i | −0.272149 | + | 0.224880i | ||||
\(209\) | 1.24393e6 | 0.136257 | ||||||||
\(210\) | −830424. | + | 1.18122e6i | −0.0896689 | + | 0.127547i | ||||
\(211\) | − | 4.59589e6i | − | 0.489241i | −0.969619 | − | 0.244620i | \(-0.921337\pi\) | ||
0.969619 | − | 0.244620i | \(-0.0786633\pi\) | |||||||
\(212\) | 177844. | + | 494422.i | 0.0186651 | + | 0.0518907i | ||||
\(213\) | −3.23128e6 | −0.334376 | ||||||||
\(214\) | −1.59002e6 | − | 1.11782e6i | −0.162241 | − | 0.114060i | ||||
\(215\) | 1.36058e6i | 0.136901i | ||||||||
\(216\) | 2.89052e6 | − | 1.05483e7i | 0.286823 | − | 1.04669i | ||||
\(217\) | −3.48154e6 | −0.340715 | ||||||||
\(218\) | 2.83410e6 | − | 4.03129e6i | 0.273555 | − | 0.389112i | ||||
\(219\) | 6.43944e6i | 0.613078i | ||||||||
\(220\) | 2.21960e6 | − | 798391.i | 0.208452 | − | 0.0749804i | ||||
\(221\) | −5.30616e6 | −0.491591 | ||||||||
\(222\) | −2.37598e6 | − | 1.67037e6i | −0.217162 | − | 0.152670i | ||||
\(223\) | 4.53610e6i | 0.409042i | 0.978862 | + | 0.204521i | \(0.0655636\pi\) | ||||
−0.978862 | + | 0.204521i | \(0.934436\pi\) | |||||||
\(224\) | −6.01238e6 | + | 468884.i | −0.534937 | + | 0.0417178i | ||||
\(225\) | −3.85439e6 | −0.338383 | ||||||||
\(226\) | −76238.8 | + | 108444.i | −0.00660466 | + | 0.00939464i | ||||
\(227\) | 1.42284e7i | 1.21641i | 0.793780 | + | 0.608204i | \(0.208110\pi\) | ||||
−0.793780 | + | 0.608204i | \(0.791890\pi\) | |||||||
\(228\) | −717000. | − | 1.99332e6i | −0.0604943 | − | 0.168180i | ||||
\(229\) | −2.05799e7 | −1.71371 | −0.856856 | − | 0.515556i | \(-0.827585\pi\) | ||||
−0.856856 | + | 0.515556i | \(0.827585\pi\) | |||||||
\(230\) | 2.63326e6 | + | 1.85124e6i | 0.216426 | + | 0.152153i | ||||
\(231\) | 3.06027e6i | 0.248270i | ||||||||
\(232\) | −1.24189e7 | − | 3.40313e6i | −0.994535 | − | 0.272530i | ||||
\(233\) | −1.57338e7 | −1.24384 | −0.621922 | − | 0.783079i | \(-0.713648\pi\) | ||||
−0.621922 | + | 0.783079i | \(0.713648\pi\) | |||||||
\(234\) | −1.02257e6 | + | 1.45453e6i | −0.0798080 | + | 0.113521i | ||||
\(235\) | − | 7.30111e6i | − | 0.562582i | ||||||
\(236\) | 1.78704e7 | − | 6.42799e6i | 1.35956 | − | 0.489034i | ||||
\(237\) | −9.41671e6 | −0.707382 | ||||||||
\(238\) | −8.23988e6 | − | 5.79284e6i | −0.611209 | − | 0.429695i | ||||
\(239\) | 1.15354e6i | 0.0844967i | 0.999107 | + | 0.0422484i | \(0.0134521\pi\) | ||||
−0.999107 | + | 0.0422484i | \(0.986548\pi\) | |||||||
\(240\) | −2.55874e6 | − | 3.09657e6i | −0.185094 | − | 0.224000i | ||||
\(241\) | 980922. | 0.0700782 | 0.0350391 | − | 0.999386i | \(-0.488844\pi\) | ||||
0.0350391 | + | 0.999386i | \(0.488844\pi\) | |||||||
\(242\) | −5.27566e6 | + | 7.50424e6i | −0.372246 | + | 0.529493i | ||||
\(243\) | − | 1.05150e7i | − | 0.732809i | ||||||
\(244\) | 5.05493e6 | + | 1.40531e7i | 0.347973 | + | 0.967396i | ||||
\(245\) | −3.90601e6 | −0.265604 | ||||||||
\(246\) | −1.38395e7 | − | 9.72949e6i | −0.929639 | − | 0.653559i | ||||
\(247\) | 1.22049e6i | 0.0809926i | ||||||||
\(248\) | 2.55976e6 | − | 9.34126e6i | 0.167820 | − | 0.612421i | ||||
\(249\) | −7.50850e6 | −0.486357 | ||||||||
\(250\) | −6.23722e6 | + | 8.87198e6i | −0.399182 | + | 0.567807i | ||||
\(251\) | − | 1.37549e7i | − | 0.869831i | −0.900471 | − | 0.434915i | \(-0.856778\pi\) | ||
0.900471 | − | 0.434915i | \(-0.143222\pi\) | |||||||
\(252\) | −3.17588e6 | + | 1.14237e6i | −0.198455 | + | 0.0713846i | ||||
\(253\) | 6.82219e6 | 0.421272 | ||||||||
\(254\) | 1.42616e7 | + | 1.00263e7i | 0.870299 | + | 0.611841i | ||||
\(255\) | − | 6.70912e6i | − | 0.404618i | ||||||
\(256\) | 3.16248e6 | − | 1.64765e7i | 0.188498 | − | 0.982073i | ||||
\(257\) | −1.62126e7 | −0.955109 | −0.477554 | − | 0.878602i | \(-0.658477\pi\) | ||||
−0.477554 | + | 0.878602i | \(0.658477\pi\) | |||||||
\(258\) | 2.82426e6 | − | 4.01730e6i | 0.164454 | − | 0.233924i | ||||
\(259\) | 3.17645e6i | 0.182828i | ||||||||
\(260\) | 783348. | + | 2.17778e6i | 0.0445692 | + | 0.123906i | ||||
\(261\) | −7.20658e6 | −0.405329 | ||||||||
\(262\) | 1.27593e7 | + | 8.97007e6i | 0.709449 | + | 0.498760i | ||||
\(263\) | 4.62826e6i | 0.254420i | 0.991876 | + | 0.127210i | \(0.0406022\pi\) | ||||
−0.991876 | + | 0.127210i | \(0.959398\pi\) | |||||||
\(264\) | −8.21097e6 | − | 2.25003e6i | −0.446255 | − | 0.122286i | ||||
\(265\) | 382773. | 0.0205685 | ||||||||
\(266\) | −1.33244e6 | + | 1.89529e6i | −0.0707949 | + | 0.100700i | ||||
\(267\) | − | 3.51434e6i | − | 0.184633i | ||||||
\(268\) | 1.13742e7 | − | 4.09132e6i | 0.590905 | − | 0.212549i | ||||
\(269\) | −1.96403e7 | −1.00900 | −0.504501 | − | 0.863411i | \(-0.668323\pi\) | ||||
−0.504501 | + | 0.863411i | \(0.668323\pi\) | |||||||
\(270\) | −6.51802e6 | − | 4.58232e6i | −0.331150 | − | 0.232806i | ||||
\(271\) | − | 2.71295e7i | − | 1.36312i | −0.731762 | − | 0.681560i | \(-0.761302\pi\) | ||
0.731762 | − | 0.681560i | \(-0.238698\pi\) | |||||||
\(272\) | 2.16009e7 | − | 1.78492e7i | 1.07341 | − | 0.886975i | ||||
\(273\) | −3.00262e6 | −0.147575 | ||||||||
\(274\) | 1.69946e7 | − | 2.41735e7i | 0.826149 | − | 1.17514i | ||||
\(275\) | 1.06335e7i | 0.511303i | ||||||||
\(276\) | −3.93230e6 | − | 1.09321e7i | −0.187034 | − | 0.519970i | ||||
\(277\) | 9.32068e6 | 0.438539 | 0.219269 | − | 0.975664i | \(-0.429633\pi\) | ||||
0.219269 | + | 0.975664i | \(0.429633\pi\) | |||||||
\(278\) | 8.35500e6 | + | 5.87377e6i | 0.388877 | + | 0.273390i | ||||
\(279\) | − | 5.42064e6i | − | 0.249596i | ||||||
\(280\) | −1.16107e6 | + | 4.23704e6i | −0.0528911 | + | 0.193014i | ||||
\(281\) | 2.95862e7 | 1.33343 | 0.666714 | − | 0.745313i | \(-0.267700\pi\) | ||||
0.666714 | + | 0.745313i | \(0.267700\pi\) | |||||||
\(282\) | −1.51555e7 | + | 2.15576e7i | −0.675809 | + | 0.961288i | ||||
\(283\) | 2.39922e7i | 1.05855i | 0.848450 | + | 0.529275i | \(0.177536\pi\) | ||||
−0.848450 | + | 0.529275i | \(0.822464\pi\) | |||||||
\(284\) | −9.25121e6 | + | 3.32767e6i | −0.403872 | + | 0.145273i | ||||
\(285\) | −1.54320e6 | −0.0666632 | ||||||||
\(286\) | 4.01277e6 | + | 2.82107e6i | 0.171532 | + | 0.120591i | ||||
\(287\) | 1.85020e7i | 0.782660i | ||||||||
\(288\) | −730038. | − | 9.36108e6i | −0.0305610 | − | 0.391876i | ||||
\(289\) | 2.26636e7 | 0.938936 | ||||||||
\(290\) | −5.39497e6 | + | 7.67394e6i | −0.221205 | + | 0.314648i | ||||
\(291\) | − | 1.30210e6i | − | 0.0528404i | ||||||
\(292\) | 6.63154e6 | + | 1.84362e7i | 0.266358 | + | 0.740498i | ||||
\(293\) | 2.48324e7 | 0.987222 | 0.493611 | − | 0.869683i | \(-0.335677\pi\) | ||||
0.493611 | + | 0.869683i | \(0.335677\pi\) | |||||||
\(294\) | 1.15331e7 | + | 8.10802e6i | 0.453840 | + | 0.319060i | ||||
\(295\) | − | 1.38349e7i | − | 0.538904i | ||||||
\(296\) | −8.52268e6 | − | 2.33545e6i | −0.328625 | − | 0.0900524i | ||||
\(297\) | −1.68868e7 | −0.644580 | ||||||||
\(298\) | −1.81470e7 | + | 2.58128e7i | −0.685736 | + | 0.975409i | ||||
\(299\) | 6.69366e6i | 0.250409i | ||||||||
\(300\) | 1.70395e7 | − | 6.12913e6i | 0.631093 | − | 0.227005i | ||||
\(301\) | −5.37073e6 | −0.196940 | ||||||||
\(302\) | 3.13738e7 | + | 2.20566e7i | 1.13906 | + | 0.800787i | ||||
\(303\) | 4.57681e6i | 0.164526i | ||||||||
\(304\) | −4.10557e6 | − | 4.96853e6i | −0.146135 | − | 0.176851i | ||||
\(305\) | 1.08797e7 | 0.383458 | ||||||||
\(306\) | 9.01926e6 | − | 1.28292e7i | 0.314780 | − | 0.447751i | ||||
\(307\) | 5.04876e7i | 1.74490i | 0.488707 | + | 0.872448i | \(0.337469\pi\) | ||||
−0.488707 | + | 0.872448i | \(0.662531\pi\) | |||||||
\(308\) | 3.15157e6 | + | 8.76163e6i | 0.107863 | + | 0.299870i | ||||
\(309\) | −1.00960e7 | −0.342196 | ||||||||
\(310\) | −5.77218e6 | − | 4.05798e6i | −0.193756 | − | 0.136215i | ||||
\(311\) | − | 3.95162e7i | − | 1.31369i | −0.754024 | − | 0.656847i | \(-0.771890\pi\) | ||
0.754024 | − | 0.656847i | \(-0.228110\pi\) | |||||||
\(312\) | 2.20764e6 | − | 8.05627e6i | 0.0726883 | − | 0.265259i | ||||
\(313\) | 3.76092e7 | 1.22648 | 0.613241 | − | 0.789896i | \(-0.289865\pi\) | ||||
0.613241 | + | 0.789896i | \(0.289865\pi\) | |||||||
\(314\) | −1.97948e7 | + | 2.81567e7i | −0.639385 | + | 0.909478i | ||||
\(315\) | 2.45871e6i | 0.0786641i | ||||||||
\(316\) | −2.69602e7 | + | 9.69762e6i | −0.854402 | + | 0.307329i | ||||
\(317\) | 2.67605e7 | 0.840072 | 0.420036 | − | 0.907507i | \(-0.362017\pi\) | ||||
0.420036 | + | 0.907507i | \(0.362017\pi\) | |||||||
\(318\) | −1.13019e6 | − | 794553.i | −0.0351456 | − | 0.0247082i | ||||
\(319\) | 1.98815e7i | 0.612459i | ||||||||
\(320\) | −1.05147e7 | − | 6.23048e6i | −0.320882 | − | 0.190139i | ||||
\(321\) | 5.11044e6 | 0.154505 | ||||||||
\(322\) | −7.30759e6 | + | 1.03945e7i | −0.218880 | + | 0.311341i | ||||
\(323\) | − | 1.07650e7i | − | 0.319451i | ||||||
\(324\) | 5.20848e6 | + | 1.44800e7i | 0.153135 | + | 0.425730i | ||||
\(325\) | −1.04331e7 | −0.303924 | ||||||||
\(326\) | 3.52618e7 | + | 2.47899e7i | 1.01778 | + | 0.715521i | ||||
\(327\) | 1.29569e7i | 0.370558i | ||||||||
\(328\) | −4.96424e7 | − | 1.36034e7i | −1.40680 | − | 0.385501i | ||||
\(329\) | 2.88204e7 | 0.809305 | ||||||||
\(330\) | −3.56697e6 | + | 5.07375e6i | −0.0992561 | + | 0.141185i | ||||
\(331\) | 3.90986e6i | 0.107815i | 0.998546 | + | 0.0539073i | \(0.0171675\pi\) | ||||
−0.998546 | + | 0.0539073i | \(0.982832\pi\) | |||||||
\(332\) | −2.14970e7 | + | 7.73248e6i | −0.587439 | + | 0.211303i | ||||
\(333\) | −4.94563e6 | −0.133933 | ||||||||
\(334\) | 2.15600e7 | + | 1.51572e7i | 0.578642 | + | 0.406799i | ||||
\(335\) | − | 8.80572e6i | − | 0.234224i | ||||||
\(336\) | 1.22234e7 | − | 1.01004e7i | 0.322236 | − | 0.266268i | ||||
\(337\) | 1.97548e7 | 0.516158 | 0.258079 | − | 0.966124i | \(-0.416910\pi\) | ||||
0.258079 | + | 0.966124i | \(0.416910\pi\) | |||||||
\(338\) | 1.94401e7 | − | 2.76521e7i | 0.503441 | − | 0.716107i | ||||
\(339\) | − | 348547.i | − | 0.00894668i | ||||||
\(340\) | −6.90926e6 | − | 1.92083e7i | −0.175790 | − | 0.488712i | ||||
\(341\) | −1.49545e7 | −0.377144 | ||||||||
\(342\) | −2.95091e6 | − | 2.07456e6i | −0.0737696 | − | 0.0518618i | ||||
\(343\) | − | 3.70707e7i | − | 0.918647i | ||||||
\(344\) | 3.94877e6 | − | 1.44101e7i | 0.0970033 | − | 0.353991i | ||||
\(345\) | −8.46347e6 | −0.206106 | ||||||||
\(346\) | −2.41306e7 | + | 3.43241e7i | −0.582560 | + | 0.828648i | ||||
\(347\) | 6.53911e6i | 0.156506i | 0.996934 | + | 0.0782528i | \(0.0249341\pi\) | ||||
−0.996934 | + | 0.0782528i | \(0.975066\pi\) | |||||||
\(348\) | 3.18589e7 | − | 1.14597e7i | 0.755949 | − | 0.271916i | ||||
\(349\) | 8.10847e7 | 1.90749 | 0.953746 | − | 0.300613i | \(-0.0971912\pi\) | ||||
0.953746 | + | 0.300613i | \(0.0971912\pi\) | |||||||
\(350\) | −1.62015e7 | − | 1.13901e7i | −0.377878 | − | 0.265657i | ||||
\(351\) | − | 1.65686e7i | − | 0.383146i | ||||||
\(352\) | −2.58253e7 | + | 2.01403e6i | −0.592131 | + | 0.0461782i | ||||
\(353\) | 6.22241e7 | 1.41460 | 0.707302 | − | 0.706912i | \(-0.249912\pi\) | ||||
0.707302 | + | 0.706912i | \(0.249912\pi\) | |||||||
\(354\) | −2.87183e7 | + | 4.08497e7i | −0.647365 | + | 0.920829i | ||||
\(355\) | 7.16212e6i | 0.160087i | ||||||||
\(356\) | −3.61917e6 | − | 1.00616e7i | −0.0802157 | − | 0.223007i | ||||
\(357\) | 2.64835e7 | 0.582065 | ||||||||
\(358\) | −5.41989e7 | − | 3.81031e7i | −1.18125 | − | 0.830446i | ||||
\(359\) | − | 4.53790e7i | − | 0.980779i | −0.871503 | − | 0.490390i | \(-0.836854\pi\) | ||
0.871503 | − | 0.490390i | \(-0.163146\pi\) | |||||||
\(360\) | −6.59694e6 | − | 1.80774e6i | −0.141395 | − | 0.0387462i | ||||
\(361\) | −2.47610e6 | −0.0526316 | ||||||||
\(362\) | 3.65985e7 | − | 5.20586e7i | 0.771502 | − | 1.09740i | ||||
\(363\) | − | 2.41191e7i | − | 0.504245i | ||||||
\(364\) | −8.59655e6 | + | 3.09219e6i | −0.178246 | + | 0.0641153i | ||||
\(365\) | 1.42730e7 | 0.293520 | ||||||||
\(366\) | −3.21239e7 | − | 2.25839e7i | −0.655217 | − | 0.460634i | ||||
\(367\) | − | 8.51540e7i | − | 1.72269i | −0.508021 | − | 0.861345i | \(-0.669623\pi\) | ||
0.508021 | − | 0.861345i | \(-0.330377\pi\) | |||||||
\(368\) | −2.25165e7 | − | 2.72493e7i | −0.451812 | − | 0.546780i | ||||
\(369\) | −2.88070e7 | −0.573349 | ||||||||
\(370\) | −3.70238e6 | + | 5.26636e6i | −0.0730930 | + | 0.103969i | ||||
\(371\) | 1.51095e6i | 0.0295890i | ||||||||
\(372\) | 8.61972e6 | + | 2.39636e7i | 0.167442 | + | 0.465503i | ||||
\(373\) | −4.61806e7 | −0.889883 | −0.444941 | − | 0.895560i | \(-0.646776\pi\) | ||||
−0.444941 | + | 0.895560i | \(0.646776\pi\) | |||||||
\(374\) | −3.53932e7 | − | 2.48823e7i | −0.676559 | − | 0.475637i | ||||
\(375\) | − | 2.85152e7i | − | 0.540732i | ||||||
\(376\) | −2.11899e7 | + | 7.73275e7i | −0.398625 | + | 1.45469i | ||||
\(377\) | −1.95069e7 | −0.364053 | ||||||||
\(378\) | 1.80882e7 | − | 2.57292e7i | 0.334905 | − | 0.476377i | ||||
\(379\) | − | 4.25418e6i | − | 0.0781445i | −0.999236 | − | 0.0390723i | \(-0.987560\pi\) | ||
0.999236 | − | 0.0390723i | \(-0.0124403\pi\) | |||||||
\(380\) | −4.41820e6 | + | 1.58923e6i | −0.0805183 | + | 0.0289625i | ||||
\(381\) | −4.58379e7 | −0.828801 | ||||||||
\(382\) | 2.97041e7 | + | 2.08827e7i | 0.532876 | + | 0.374625i | ||||
\(383\) | 8.21742e7i | 1.46265i | 0.682031 | + | 0.731323i | \(0.261097\pi\) | ||||
−0.682031 | + | 0.731323i | \(0.738903\pi\) | |||||||
\(384\) | 1.81130e7 | + | 4.02226e7i | 0.319888 | + | 0.710356i | ||||
\(385\) | 6.78310e6 | 0.118863 | ||||||||
\(386\) | 4.36724e7 | − | 6.21208e7i | 0.759356 | − | 1.08013i | ||||
\(387\) | − | 8.36206e6i | − | 0.144271i | ||||||
\(388\) | −1.34094e6 | − | 3.72794e6i | −0.0229570 | − | 0.0638225i | ||||
\(389\) | −3.26067e7 | −0.553934 | −0.276967 | − | 0.960879i | \(-0.589329\pi\) | ||||
−0.276967 | + | 0.960879i | \(0.589329\pi\) | |||||||
\(390\) | −4.97815e6 | − | 3.49976e6i | −0.0839217 | − | 0.0589990i | ||||
\(391\) | − | 5.90391e7i | − | 0.987665i | ||||||
\(392\) | 4.13693e7 | + | 1.13363e7i | 0.686784 | + | 0.188198i | ||||
\(393\) | −4.10091e7 | −0.675621 | ||||||||
\(394\) | −6.60440e7 | + | 9.39427e7i | −1.07980 | + | 1.53594i | ||||
\(395\) | 2.08721e7i | 0.338669i | ||||||||
\(396\) | −1.36416e7 | + | 4.90688e6i | −0.219674 | + | 0.0790170i | ||||
\(397\) | −1.56492e7 | −0.250104 | −0.125052 | − | 0.992150i | \(-0.539910\pi\) | ||||
−0.125052 | + | 0.992150i | \(0.539910\pi\) | |||||||
\(398\) | 1.32893e7 | + | 9.34270e6i | 0.210791 | + | 0.148191i | ||||
\(399\) | − | 6.09160e6i | − | 0.0958988i | ||||||
\(400\) | 4.24725e7 | − | 3.50956e7i | 0.663633 | − | 0.548369i | ||||
\(401\) | −1.19804e8 | −1.85797 | −0.928987 | − | 0.370112i | \(-0.879319\pi\) | ||||
−0.928987 | + | 0.370112i | \(0.879319\pi\) | |||||||
\(402\) | −1.82788e7 | + | 2.60002e7i | −0.281364 | + | 0.400220i | ||||
\(403\) | − | 1.46727e7i | − | 0.224179i | ||||||
\(404\) | 4.71334e6 | + | 1.31035e7i | 0.0714800 | + | 0.198721i | ||||
\(405\) | 1.12102e7 | 0.168751 | ||||||||
\(406\) | −3.02921e7 | − | 2.12961e7i | −0.452638 | − | 0.318216i | ||||
\(407\) | 1.36440e7i | 0.202376i | ||||||||
\(408\) | −1.94717e7 | + | 7.10576e7i | −0.286698 | + | 1.04624i | ||||
\(409\) | 4.27283e7 | 0.624519 | 0.312259 | − | 0.949997i | \(-0.398914\pi\) | ||||
0.312259 | + | 0.949997i | \(0.398914\pi\) | |||||||
\(410\) | −2.15654e7 | + | 3.06752e7i | −0.312900 | + | 0.445078i | ||||
\(411\) | 7.76953e7i | 1.11910i | ||||||||
\(412\) | −2.89051e7 | + | 1.03972e7i | −0.413317 | + | 0.148671i | ||||
\(413\) | 5.46120e7 | 0.775243 | ||||||||
\(414\) | −1.61839e7 | − | 1.13777e7i | −0.228078 | − | 0.160344i | ||||
\(415\) | 1.66426e7i | 0.232850i | ||||||||
\(416\) | −1.97608e6 | − | 2.53388e7i | −0.0274489 | − | 0.351970i | ||||
\(417\) | −2.68535e7 | −0.370334 | ||||||||
\(418\) | −5.72330e6 | + | 8.14097e6i | −0.0783641 | + | 0.111467i | ||||
\(419\) | − | 1.83025e7i | − | 0.248810i | −0.992232 | − | 0.124405i | \(-0.960298\pi\) | ||
0.992232 | − | 0.124405i | \(-0.0397022\pi\) | |||||||
\(420\) | −3.90977e6 | − | 1.08695e7i | −0.0527719 | − | 0.146710i | ||||
\(421\) | −8.97845e7 | −1.20325 | −0.601624 | − | 0.798779i | \(-0.705479\pi\) | ||||
−0.601624 | + | 0.798779i | \(0.705479\pi\) | |||||||
\(422\) | 3.00780e7 | + | 2.11456e7i | 0.400232 | + | 0.281373i | ||||
\(423\) | 4.48724e7i | 0.592868i | ||||||||
\(424\) | −4.05402e6 | − | 1.11091e6i | −0.0531849 | − | 0.0145741i | ||||
\(425\) | 9.20221e7 | 1.19874 | ||||||||
\(426\) | 1.48670e7 | − | 2.11472e7i | 0.192307 | − | 0.273542i | ||||
\(427\) | 4.29465e7i | 0.551625i | ||||||||
\(428\) | 1.46313e7 | − | 5.26289e6i | 0.186617 | − | 0.0671264i | ||||
\(429\) | −1.28973e7 | −0.163353 | ||||||||
\(430\) | −8.90435e6 | − | 6.25997e6i | −0.111995 | − | 0.0787348i | ||||
\(431\) | − | 1.07911e8i | − | 1.34783i | −0.738808 | − | 0.673916i | \(-0.764611\pi\) | ||
0.738808 | − | 0.673916i | \(-0.235389\pi\) | |||||||
\(432\) | 5.57344e7 | + | 6.74494e7i | 0.691309 | + | 0.836617i | ||||
\(433\) | 1.35906e7 | 0.167407 | 0.0837036 | − | 0.996491i | \(-0.473325\pi\) | ||||
0.0837036 | + | 0.996491i | \(0.473325\pi\) | |||||||
\(434\) | 1.60185e7 | − | 2.27851e7i | 0.195953 | − | 0.278728i | ||||
\(435\) | − | 2.46646e7i | − | 0.299644i | ||||||
\(436\) | 1.33434e7 | + | 3.70957e7i | 0.160993 | + | 0.447574i | ||||
\(437\) | −1.35799e7 | −0.162724 | ||||||||
\(438\) | −4.21432e7 | − | 2.96277e7i | −0.501539 | − | 0.352594i | ||||
\(439\) | − | 2.82075e6i | − | 0.0333404i | −0.999861 | − | 0.0166702i | \(-0.994693\pi\) | ||
0.999861 | − | 0.0166702i | \(-0.00530654\pi\) | |||||||
\(440\) | −4.98720e6 | + | 1.81996e7i | −0.0585462 | + | 0.213651i | ||||
\(441\) | 2.40062e7 | 0.279903 | ||||||||
\(442\) | 2.44135e7 | − | 3.47264e7i | 0.282724 | − | 0.402155i | ||||
\(443\) | 1.48199e8i | 1.70464i | 0.523020 | + | 0.852320i | \(0.324805\pi\) | ||||
−0.523020 | + | 0.852320i | \(0.675195\pi\) | |||||||
\(444\) | 2.18636e7 | − | 7.86437e6i | 0.249789 | − | 0.0898494i | ||||
\(445\) | −7.78953e6 | −0.0883957 | ||||||||
\(446\) | −2.96867e7 | − | 2.08705e7i | −0.334624 | − | 0.235249i | ||||
\(447\) | − | 8.29642e7i | − | 0.928899i | ||||||
\(448\) | 2.45942e7 | − | 4.15056e7i | 0.273526 | − | 0.461607i | ||||
\(449\) | −8.77824e7 | −0.969770 | −0.484885 | − | 0.874578i | \(-0.661138\pi\) | ||||
−0.484885 | + | 0.874578i | \(0.661138\pi\) | |||||||
\(450\) | 1.77340e7 | − | 2.52252e7i | 0.194611 | − | 0.276820i | ||||
\(451\) | 7.94728e7i | 0.866341i | ||||||||
\(452\) | −358944. | − | 997896.i | −0.00388697 | − | 0.0108061i | ||||
\(453\) | −1.00838e8 | −1.08475 | ||||||||
\(454\) | −9.31186e7 | − | 6.54646e7i | −0.995105 | − | 0.699583i | ||||
\(455\) | 6.65530e6i | 0.0706534i | ||||||||
\(456\) | 1.63443e7 | + | 4.47878e6i | 0.172374 | + | 0.0472352i | ||||
\(457\) | 1.42771e8 | 1.49586 | 0.747932 | − | 0.663775i | \(-0.231047\pi\) | ||||
0.747932 | + | 0.663775i | \(0.231047\pi\) | |||||||
\(458\) | 9.46878e7 | − | 1.34686e8i | 0.985593 | − | 1.40193i | ||||
\(459\) | 1.46138e8i | 1.51121i | ||||||||
\(460\) | −2.42311e7 | + | 8.71595e6i | −0.248943 | + | 0.0895449i | ||||
\(461\) | 1.10553e7 | 0.112841 | 0.0564204 | − | 0.998407i | \(-0.482031\pi\) | ||||
0.0564204 | + | 0.998407i | \(0.482031\pi\) | |||||||
\(462\) | −2.00281e7 | − | 1.40802e7i | −0.203102 | − | 0.142785i | ||||
\(463\) | − | 1.64073e8i | − | 1.65309i | −0.562874 | − | 0.826543i | \(-0.690304\pi\) | ||
0.562874 | − | 0.826543i | \(-0.309696\pi\) | |||||||
\(464\) | 7.94111e7 | − | 6.56185e7i | 0.794927 | − | 0.656859i | ||||
\(465\) | 1.85522e7 | 0.184517 | ||||||||
\(466\) | 7.23908e7 | − | 1.02971e8i | 0.715361 | − | 1.01755i | ||||
\(467\) | 1.37689e8i | 1.35191i | 0.736943 | + | 0.675955i | \(0.236269\pi\) | ||||
−0.736943 | + | 0.675955i | \(0.763731\pi\) | |||||||
\(468\) | −4.81443e6 | − | 1.33845e7i | −0.0469686 | − | 0.130577i | ||||
\(469\) | 3.47597e7 | 0.336944 | ||||||||
\(470\) | 4.77825e7 | + | 3.35922e7i | 0.460230 | + | 0.323553i | ||||
\(471\) | − | 9.04975e7i | − | 0.866111i | ||||||
\(472\) | −4.01528e7 | + | 1.46529e8i | −0.381848 | + | 1.39347i | ||||
\(473\) | −2.30692e7 | −0.217997 | ||||||||
\(474\) | 4.33260e7 | − | 6.16281e7i | 0.406831 | − | 0.578687i | ||||
\(475\) | − | 2.11664e7i | − | 0.197500i | ||||||
\(476\) | 7.58229e7 | − | 2.72736e7i | 0.703039 | − | 0.252884i | ||||
\(477\) | −2.35251e6 | −0.0216758 | ||||||||
\(478\) | −7.54941e6 | − | 5.30742e6i | −0.0691241 | − | 0.0485959i | ||||
\(479\) | 1.79988e7i | 0.163771i | 0.996642 | + | 0.0818853i | \(0.0260941\pi\) | ||||
−0.996642 | + | 0.0818853i | \(0.973906\pi\) | |||||||
\(480\) | 3.20384e7 | − | 2.49856e6i | 0.289699 | − | 0.0225926i | ||||
\(481\) | −1.33869e7 | −0.120294 | ||||||||
\(482\) | −4.51319e6 | + | 6.41969e6i | −0.0403035 | + | 0.0573288i | ||||
\(483\) | − | 3.34087e7i | − | 0.296495i | ||||||
\(484\) | −2.48386e7 | − | 6.90536e7i | −0.219074 | − | 0.609046i | ||||
\(485\) | −2.88611e6 | −0.0252981 | ||||||||
\(486\) | 6.88159e7 | + | 4.83792e7i | 0.599487 | + | 0.421454i | ||||
\(487\) | 5.51546e7i | 0.477523i | 0.971078 | + | 0.238762i | \(0.0767415\pi\) | ||||
−0.971078 | + | 0.238762i | \(0.923259\pi\) | |||||||
\(488\) | −1.15229e8 | − | 3.15759e7i | −0.991522 | − | 0.271704i | ||||
\(489\) | −1.13334e8 | −0.969245 | ||||||||
\(490\) | 1.79714e7 | − | 2.55630e7i | 0.152755 | − | 0.217282i | ||||
\(491\) | 5.60530e7i | 0.473538i | 0.971566 | + | 0.236769i | \(0.0760884\pi\) | ||||
−0.971566 | + | 0.236769i | \(0.923912\pi\) | |||||||
\(492\) | 1.27350e8 | − | 4.58080e7i | 1.06931 | − | 0.384632i | ||||
\(493\) | 1.72054e8 | 1.43590 | ||||||||
\(494\) | −7.98758e6 | − | 5.61546e6i | −0.0662574 | − | 0.0465806i | ||||
\(495\) | 1.05611e7i | 0.0870747i | ||||||||
\(496\) | 4.93569e7 | + | 5.97313e7i | 0.404485 | + | 0.489505i | ||||
\(497\) | −2.82717e7 | −0.230294 | ||||||||
\(498\) | 3.45464e7 | − | 4.91397e7i | 0.279714 | − | 0.397873i | ||||
\(499\) | 3.33630e7i | 0.268512i | 0.990947 | + | 0.134256i | \(0.0428645\pi\) | ||||
−0.990947 | + | 0.134256i | \(0.957136\pi\) | |||||||
\(500\) | −2.93658e7 | − | 8.16395e7i | −0.234926 | − | 0.653116i | ||||
\(501\) | −6.92954e7 | −0.551050 | ||||||||
\(502\) | 9.00192e7 | + | 6.32857e7i | 0.711581 | + | 0.500258i | ||||
\(503\) | 6.56486e7i | 0.515848i | 0.966165 | + | 0.257924i | \(0.0830384\pi\) | ||||
−0.966165 | + | 0.257924i | \(0.916962\pi\) | |||||||
\(504\) | 7.13588e6 | − | 2.60407e7i | 0.0557385 | − | 0.203405i | ||||
\(505\) | 1.01445e7 | 0.0787692 | ||||||||
\(506\) | −3.13887e7 | + | 4.46482e7i | −0.242283 | + | 0.344629i | ||||
\(507\) | 8.88758e7i | 0.681961i | ||||||||
\(508\) | −1.31235e8 | + | 4.72053e7i | −1.00106 | + | 0.360081i | ||||
\(509\) | −2.39636e8 | −1.81718 | −0.908592 | − | 0.417686i | \(-0.862841\pi\) | ||||
−0.908592 | + | 0.417686i | \(0.862841\pi\) | |||||||
\(510\) | 4.39081e7 | + | 3.08685e7i | 0.331005 | + | 0.232704i | ||||
\(511\) | 5.63413e7i | 0.422244i | ||||||||
\(512\) | 9.32804e7 | + | 9.65047e7i | 0.694993 | + | 0.719016i | ||||
\(513\) | 3.36138e7 | 0.248981 | ||||||||
\(514\) | 7.45936e7 | − | 1.06104e8i | 0.549304 | − | 0.781344i | ||||
\(515\) | 2.23778e7i | 0.163831i | ||||||||
\(516\) | 1.32971e7 | + | 3.69670e7i | 0.0967847 | + | 0.269070i | ||||
\(517\) | 1.23794e8 | 0.895834 | ||||||||
\(518\) | −2.07884e7 | − | 1.46148e7i | −0.149566 | − | 0.105148i | ||||
\(519\) | − | 1.10320e8i | − | 0.789136i | ||||||
\(520\) | −1.78567e7 | − | 4.89323e6i | −0.126996 | − | 0.0348005i | ||||
\(521\) | −1.41796e8 | −1.00265 | −0.501326 | − | 0.865259i | \(-0.667154\pi\) | ||||
−0.501326 | + | 0.865259i | \(0.667154\pi\) | |||||||
\(522\) | 3.31573e7 | − | 4.71638e7i | 0.233114 | − | 0.331587i | ||||
\(523\) | − | 1.25526e8i | − | 0.877466i | −0.898618 | − | 0.438733i | \(-0.855427\pi\) | ||
0.898618 | − | 0.438733i | \(-0.144573\pi\) | |||||||
\(524\) | −1.17410e8 | + | 4.22325e7i | −0.816039 | + | 0.293530i | ||||
\(525\) | 5.20728e7 | 0.359860 | ||||||||
\(526\) | −3.02899e7 | − | 2.12945e7i | −0.208133 | − | 0.146322i | ||||
\(527\) | 1.29416e8i | 0.884208i | ||||||||
\(528\) | 5.25039e7 | − | 4.33847e7i | 0.356689 | − | 0.294737i | ||||
\(529\) | 7.35587e7 | 0.496898 | ||||||||
\(530\) | −1.76113e6 | + | 2.50507e6i | −0.0118294 | + | 0.0168265i | ||||
\(531\) | 8.50291e7i | 0.567916i | ||||||||
\(532\) | −6.27332e6 | − | 1.74404e7i | −0.0416642 | − | 0.115830i | ||||
\(533\) | −7.79754e7 | −0.514963 | ||||||||
\(534\) | 2.29997e7 | + | 1.61694e7i | 0.151042 | + | 0.106186i | ||||
\(535\) | − | 1.13273e7i | − | 0.0739716i | ||||||
\(536\) | −2.55567e7 | + | 9.32631e7i | −0.165962 | + | 0.605642i | ||||
\(537\) | 1.74199e8 | 1.12492 | ||||||||
\(538\) | 9.03646e7 | − | 1.28537e8i | 0.580298 | − | 0.825432i | ||||
\(539\) | − | 6.62283e7i | − | 0.422938i | ||||||
\(540\) | 5.99784e7 | − | 2.15743e7i | 0.380902 | − | 0.137011i | ||||
\(541\) | 1.61470e6 | 0.0101976 | 0.00509882 | − | 0.999987i | \(-0.498377\pi\) | ||||
0.00509882 | + | 0.999987i | \(0.498377\pi\) | |||||||
\(542\) | 1.77550e8 | + | 1.24822e8i | 1.11513 | + | 0.783960i | ||||
\(543\) | 1.67320e8i | 1.04508i | ||||||||
\(544\) | 1.74293e7 | + | 2.23492e8i | 0.108264 | + | 1.38824i | ||||
\(545\) | 2.87189e7 | 0.177410 | ||||||||
\(546\) | 1.38149e7 | − | 1.96507e7i | 0.0848734 | − | 0.120726i | ||||
\(547\) | − | 2.46031e8i | − | 1.50324i | −0.659599 | − | 0.751618i | \(-0.729274\pi\) | ||
0.659599 | − | 0.751618i | \(-0.270726\pi\) | |||||||
\(548\) | 8.00131e7 | + | 2.22443e8i | 0.486205 | + | 1.35169i | ||||
\(549\) | −6.68663e7 | −0.404101 | ||||||||
\(550\) | −6.95914e7 | − | 4.89244e7i | −0.418280 | − | 0.294061i | ||||
\(551\) | − | 3.95750e7i | − | 0.236573i | ||||||
\(552\) | 8.96383e7 | + | 2.45634e7i | 0.532937 | + | 0.146040i | ||||
\(553\) | −8.23906e7 | −0.487194 | ||||||||
\(554\) | −4.28842e7 | + | 6.09996e7i | −0.252213 | + | 0.358755i | ||||
\(555\) | − | 1.69264e7i | − | 0.0990118i | ||||||
\(556\) | −7.68822e7 | + | 2.76546e7i | −0.447303 | + | 0.160895i | ||||
\(557\) | 1.91348e8 | 1.10728 | 0.553642 | − | 0.832755i | \(-0.313238\pi\) | ||||
0.553642 | + | 0.832755i | \(0.313238\pi\) | |||||||
\(558\) | 3.54756e7 | + | 2.49402e7i | 0.204187 | + | 0.143548i | ||||
\(559\) | − | 2.26346e7i | − | 0.129580i | ||||||
\(560\) | −2.23875e7 | − | 2.70932e7i | −0.127480 | − | 0.154275i | ||||
\(561\) | 1.13756e8 | 0.644298 | ||||||||
\(562\) | −1.36125e8 | + | 1.93628e8i | −0.766884 | + | 1.09084i | ||||
\(563\) | 2.18743e8i | 1.22577i | 0.790172 | + | 0.612885i | \(0.209991\pi\) | ||||
−0.790172 | + | 0.612885i | \(0.790009\pi\) | |||||||
\(564\) | −7.13546e7 | − | 1.98372e8i | −0.397727 | − | 1.10571i | ||||
\(565\) | −772553. | −0.00428335 | ||||||||
\(566\) | −1.57018e8 | − | 1.10388e8i | −0.865966 | − | 0.608795i | ||||
\(567\) | 4.42510e7i | 0.242758i | ||||||||
\(568\) | 2.07865e7 | − | 7.58555e7i | 0.113432 | − | 0.413944i | ||||
\(569\) | −5.50261e7 | −0.298698 | −0.149349 | − | 0.988785i | \(-0.547718\pi\) | ||||
−0.149349 | + | 0.988785i | \(0.547718\pi\) | |||||||
\(570\) | 7.10020e6 | − | 1.00995e7i | 0.0383395 | − | 0.0545351i | ||||
\(571\) | − | 2.81053e8i | − | 1.50966i | −0.655920 | − | 0.754831i | \(-0.727719\pi\) | ||
0.655920 | − | 0.754831i | \(-0.272281\pi\) | |||||||
\(572\) | −3.69253e7 | + | 1.32821e7i | −0.197304 | + | 0.0709704i | ||||
\(573\) | −9.54710e7 | −0.507467 | ||||||||
\(574\) | −1.21087e8 | − | 8.51272e7i | −0.640269 | − | 0.450125i | ||||
\(575\) | − | 1.16085e8i | − | 0.610621i | ||||||
\(576\) | 6.46229e7 | + | 3.82923e7i | 0.338157 | + | 0.200375i | ||||
\(577\) | −1.88729e8 | −0.982453 | −0.491226 | − | 0.871032i | \(-0.663451\pi\) | ||||
−0.491226 | + | 0.871032i | \(0.663451\pi\) | |||||||
\(578\) | −1.04275e8 | + | 1.48323e8i | −0.540002 | + | 0.768113i | ||||
\(579\) | 1.99661e8i | 1.02862i | ||||||||
\(580\) | −2.54003e7 | − | 7.06152e7i | −0.130183 | − | 0.361921i | ||||
\(581\) | −6.56949e7 | −0.334968 | ||||||||
\(582\) | 8.52166e6 | + | 5.99093e6i | 0.0432270 | + | 0.0303896i | ||||
\(583\) | 6.49009e6i | 0.0327526i | ||||||||
\(584\) | −1.51168e8 | − | 4.14243e7i | −0.758966 | − | 0.207978i | ||||
\(585\) | −1.03621e7 | −0.0517582 | ||||||||
\(586\) | −1.14253e8 | + | 1.62516e8i | −0.567773 | + | 0.807615i | ||||
\(587\) | 3.09526e7i | 0.153032i | 0.997068 | + | 0.0765161i | \(0.0243797\pi\) | ||||
−0.997068 | + | 0.0765161i | \(0.975620\pi\) | |||||||
\(588\) | −1.06127e8 | + | 3.81739e7i | −0.522026 | + | 0.187773i | ||||
\(589\) | 2.97675e7 | 0.145679 | ||||||||
\(590\) | 9.05433e7 | + | 6.36542e7i | 0.440860 | + | 0.309935i | ||||
\(591\) | − | 3.01938e8i | − | 1.46270i | ||||||
\(592\) | 5.44971e7 | − | 4.50317e7i | 0.262669 | − | 0.217047i | ||||
\(593\) | −3.20132e8 | −1.53520 | −0.767601 | − | 0.640928i | \(-0.778550\pi\) | ||||
−0.767601 | + | 0.640928i | \(0.778550\pi\) | |||||||
\(594\) | 7.76955e7 | − | 1.10516e8i | 0.370712 | − | 0.527310i | ||||
\(595\) | − | 5.87008e7i | − | 0.278672i | ||||||
\(596\) | −8.54392e7 | − | 2.37528e8i | −0.403569 | − | 1.12196i | ||||
\(597\) | −4.27127e7 | −0.200740 | ||||||||
\(598\) | −4.38069e7 | − | 3.07973e7i | −0.204852 | − | 0.144016i | ||||
\(599\) | − | 3.38491e8i | − | 1.57495i | −0.616347 | − | 0.787475i | \(-0.711388\pi\) | ||
0.616347 | − | 0.787475i | \(-0.288612\pi\) | |||||||
\(600\) | −3.82860e7 | + | 1.39716e8i | −0.177250 | + | 0.646832i | ||||
\(601\) | 1.12162e8 | 0.516682 | 0.258341 | − | 0.966054i | \(-0.416824\pi\) | ||||
0.258341 | + | 0.966054i | \(0.416824\pi\) | |||||||
\(602\) | 2.47106e7 | − | 3.51490e7i | 0.113264 | − | 0.161110i | ||||
\(603\) | 5.41197e7i | 0.246833i | ||||||||
\(604\) | −2.88700e8 | + | 1.03846e8i | −1.31020 | + | 0.471279i | ||||
\(605\) | −5.34601e7 | −0.241414 | ||||||||
\(606\) | −2.99531e7 | − | 2.10578e7i | −0.134594 | − | 0.0946225i | ||||
\(607\) | 5.34945e7i | 0.239190i | 0.992823 | + | 0.119595i | \(0.0381596\pi\) | ||||
−0.992823 | + | 0.119595i | \(0.961840\pi\) | |||||||
\(608\) | 5.14064e7 | − | 4.00901e6i | 0.228721 | − | 0.0178372i | ||||
\(609\) | 9.73609e7 | 0.431055 | ||||||||
\(610\) | −5.00572e7 | + | 7.12027e7i | −0.220535 | + | 0.313694i | ||||
\(611\) | 1.21462e8i | 0.532494i | ||||||||
\(612\) | 4.24641e7 | + | 1.18054e8i | 0.185254 | + | 0.515022i | ||||
\(613\) | 4.29793e8 | 1.86585 | 0.932927 | − | 0.360065i | \(-0.117246\pi\) | ||||
0.932927 | + | 0.360065i | \(0.117246\pi\) | |||||||
\(614\) | −3.30418e8 | − | 2.32292e8i | −1.42744 | − | 1.00353i | ||||
\(615\) | − | 9.85922e7i | − | 0.423855i | ||||||
\(616\) | −7.18411e7 | − | 1.96864e7i | −0.307348 | − | 0.0842219i | ||||
\(617\) | −422369. | −0.00179820 | −0.000899098 | − | 1.00000i | \(-0.500286\pi\) | ||||
−0.000899098 | 1.00000i | \(0.500286\pi\) | ||||||||
\(618\) | 4.64516e7 | − | 6.60739e7i | 0.196804 | − | 0.279940i | ||||
\(619\) | − | 5.53231e7i | − | 0.233257i | −0.993176 | − | 0.116628i | \(-0.962791\pi\) | ||
0.993176 | − | 0.116628i | \(-0.0372087\pi\) | |||||||
\(620\) | 5.31153e7 | − | 1.91056e7i | 0.222866 | − | 0.0801652i | ||||
\(621\) | 1.84351e8 | 0.769787 | ||||||||
\(622\) | 2.58615e8 | + | 1.81813e8i | 1.07469 | + | 0.755533i | ||||
\(623\) | − | 3.07483e7i | − | 0.127162i | ||||||
\(624\) | 4.25673e7 | + | 5.15147e7i | 0.175195 | + | 0.212020i | ||||
\(625\) | 1.46972e8 | 0.601999 | ||||||||
\(626\) | −1.73039e8 | + | 2.46135e8i | −0.705377 | + | 1.00335i | ||||
\(627\) | − | 2.61656e7i | − | 0.106152i | ||||||
\(628\) | −9.31971e7 | − | 2.59096e8i | −0.376291 | − | 1.04612i | ||||
\(629\) | 1.18075e8 | 0.474466 | ||||||||
\(630\) | −1.60912e7 | − | 1.13125e7i | −0.0643526 | − | 0.0452414i | ||||
\(631\) | − | 3.51832e8i | − | 1.40039i | −0.713954 | − | 0.700193i | \(-0.753097\pi\) | ||
0.713954 | − | 0.700193i | \(-0.246903\pi\) | |||||||
\(632\) | 6.05768e7 | − | 2.21061e8i | 0.239969 | − | 0.875711i | ||||
\(633\) | −9.66728e7 | −0.381148 | ||||||||
\(634\) | −1.23124e8 | + | 1.75135e8i | −0.483144 | + | 0.687236i | ||||
\(635\) | 1.01600e8i | 0.396800i | ||||||||
\(636\) | 1.04000e7 | − | 3.74088e6i | 0.0404260 | − | 0.0145413i | ||||
\(637\) | 6.49804e7 | 0.251399 | ||||||||
\(638\) | −1.30115e8 | − | 9.14743e7i | −0.501033 | − | 0.352239i | ||||
\(639\) | − | 4.40182e7i | − | 0.168706i | ||||||
\(640\) | 8.91534e7 | − | 4.01475e7i | 0.340093 | − | 0.153151i | ||||
\(641\) | −4.66445e8 | −1.77103 | −0.885515 | − | 0.464611i | \(-0.846194\pi\) | ||||
−0.885515 | + | 0.464611i | \(0.846194\pi\) | |||||||
\(642\) | −2.35130e7 | + | 3.34455e7i | −0.0888593 | + | 0.126396i | ||||
\(643\) | 5.04498e8i | 1.89770i | 0.315732 | + | 0.948849i | \(0.397750\pi\) | ||||
−0.315732 | + | 0.948849i | \(0.602250\pi\) | |||||||
\(644\) | −3.44053e7 | − | 9.56497e7i | −0.128815 | − | 0.358118i | ||||
\(645\) | 2.86192e7 | 0.106654 | ||||||||
\(646\) | 7.04518e7 | + | 4.95293e7i | 0.261333 | + | 0.183723i | ||||
\(647\) | − | 4.91604e8i | − | 1.81511i | −0.419933 | − | 0.907555i | \(-0.637946\pi\) | ||
0.419933 | − | 0.907555i | \(-0.362054\pi\) | |||||||
\(648\) | −1.18729e8 | − | 3.25351e7i | −0.436347 | − | 0.119571i | ||||
\(649\) | 2.34578e8 | 0.858130 | ||||||||
\(650\) | 4.80026e7 | − | 6.82802e7i | 0.174793 | − | 0.248631i | ||||
\(651\) | 7.32328e7i | 0.265438i | ||||||||
\(652\) | −3.24478e8 | + | 1.16715e8i | −1.17069 | + | 0.421098i | ||||
\(653\) | 1.28322e8 | 0.460851 | 0.230425 | − | 0.973090i | \(-0.425988\pi\) | ||||
0.230425 | + | 0.973090i | \(0.425988\pi\) | |||||||
\(654\) | −8.47967e7 | − | 5.96141e7i | −0.303142 | − | 0.213116i | ||||
\(655\) | 9.08967e7i | 0.323463i | ||||||||
\(656\) | 3.17431e8 | − | 2.62298e8i | 1.12445 | − | 0.929146i | ||||
\(657\) | −8.77215e7 | −0.309321 | ||||||||
\(658\) | −1.32602e8 | + | 1.88616e8i | −0.465449 | + | 0.662066i | ||||
\(659\) | − | 2.71006e8i | − | 0.946941i | −0.880810 | − | 0.473471i | \(-0.843001\pi\) | ||
0.880810 | − | 0.473471i | \(-0.156999\pi\) | |||||||
\(660\) | −1.67938e7 | − | 4.66883e7i | −0.0584142 | − | 0.162397i | ||||
\(661\) | 1.40824e8 | 0.487609 | 0.243804 | − | 0.969824i | \(-0.421605\pi\) | ||||
0.243804 | + | 0.969824i | \(0.421605\pi\) | |||||||
\(662\) | −2.55882e7 | − | 1.79892e7i | −0.0881996 | − | 0.0620064i | ||||
\(663\) | 1.11613e8i | 0.382979i | ||||||||
\(664\) | 4.83014e7 | − | 1.76265e8i | 0.164989 | − | 0.602090i | ||||
\(665\) | −1.35020e7 | −0.0459129 | ||||||||
\(666\) | 2.27547e7 | − | 3.23669e7i | 0.0770280 | − | 0.109567i | ||||
\(667\) | − | 2.17044e8i | − | 0.731427i | ||||||
\(668\) | −1.98394e8 | + | 7.13625e7i | −0.665579 | + | 0.239409i | ||||
\(669\) | 9.54151e7 | 0.318668 | ||||||||
\(670\) | 5.76294e7 | + | 4.05149e7i | 0.191611 | + | 0.134707i | ||||
\(671\) | 1.84471e8i | 0.610604i | ||||||||
\(672\) | 9.86280e6 | + | 1.26468e8i | 0.0325007 | + | 0.416748i | ||||
\(673\) | 5.04359e7 | 0.165461 | 0.0827303 | − | 0.996572i | \(-0.473636\pi\) | ||||
0.0827303 | + | 0.996572i | \(0.473636\pi\) | |||||||
\(674\) | −9.08913e7 | + | 1.29286e8i | −0.296854 | + | 0.422253i | ||||
\(675\) | 2.87341e8i | 0.934299i | ||||||||
\(676\) | 9.15270e7 | + | 2.54453e8i | 0.296285 | + | 0.823697i | ||||
\(677\) | −2.71022e8 | −0.873452 | −0.436726 | − | 0.899594i | \(-0.643862\pi\) | ||||
−0.436726 | + | 0.899594i | \(0.643862\pi\) | |||||||
\(678\) | 2.28108e6 | + | 1.60365e6i | 0.00731899 | + | 0.00514543i | ||||
\(679\) | − | 1.13926e7i | − | 0.0363927i | ||||||
\(680\) | 1.57499e8 | + | 4.31591e7i | 0.500900 | + | 0.137260i | ||||
\(681\) | 2.99290e8 | 0.947655 | ||||||||
\(682\) | 6.88050e7 | − | 9.78701e7i | 0.216904 | − | 0.308530i | ||||
\(683\) | 1.66132e7i | 0.0521425i | 0.999660 | + | 0.0260713i | \(0.00829968\pi\) | ||||
−0.999660 | + | 0.0260713i | \(0.991700\pi\) | |||||||
\(684\) | 2.71541e7 | − | 9.76736e6i | 0.0848530 | − | 0.0305217i | ||||
\(685\) | 1.72212e8 | 0.535785 | ||||||||
\(686\) | 2.42611e8 | + | 1.70561e8i | 0.751516 | + | 0.528334i | ||||
\(687\) | 4.32891e8i | 1.33508i | ||||||||
\(688\) | 7.61395e7 | + | 9.21435e7i | 0.233800 | + | 0.282943i | ||||
\(689\) | −6.36781e6 | −0.0194685 | ||||||||
\(690\) | 3.89402e7 | − | 5.53896e7i | 0.118536 | − | 0.168609i | ||||
\(691\) | − | 6.71702e7i | − | 0.203583i | −0.994806 | − | 0.101792i | \(-0.967542\pi\) | ||
0.994806 | − | 0.101792i | \(-0.0324575\pi\) | |||||||
\(692\) | −1.13611e8 | − | 3.15848e8i | −0.342848 | − | 0.953147i | ||||
\(693\) | −4.16887e7 | −0.125262 | ||||||||
\(694\) | −4.27955e7 | − | 3.00863e7i | −0.128032 | − | 0.0900098i | ||||
\(695\) | 5.95209e7i | 0.177303i | ||||||||
\(696\) | −7.15835e7 | + | 2.61227e8i | −0.212317 | + | 0.774802i | ||||
\(697\) | 6.87756e8 | 2.03112 | ||||||||
\(698\) | −3.73069e8 | + | 5.30663e8i | −1.09704 | + | 1.56046i | ||||
\(699\) | 3.30954e8i | 0.969029i | ||||||||
\(700\) | 1.49086e8 | − | 5.36262e7i | 0.434652 | − | 0.156345i | ||||
\(701\) | 1.39571e8 | 0.405173 | 0.202586 | − | 0.979264i | \(-0.435065\pi\) | ||||
0.202586 | + | 0.979264i | \(0.435065\pi\) | |||||||
\(702\) | 1.08434e8 | + | 7.62316e7i | 0.313439 | + | 0.220356i | ||||
\(703\) | − | 2.71589e7i | − | 0.0781712i | ||||||
\(704\) | 1.05641e8 | − | 1.78281e8i | 0.302770 | − | 0.510962i | ||||
\(705\) | −1.53576e8 | −0.438285 | ||||||||
\(706\) | −2.86292e8 | + | 4.07229e8i | −0.813569 | + | 1.15724i | ||||
\(707\) | 4.00443e7i | 0.113314i | ||||||||
\(708\) | −1.35210e8 | − | 3.75897e8i | −0.380987 | − | 1.05918i | ||||
\(709\) | 7.51108e7 | 0.210748 | 0.105374 | − | 0.994433i | \(-0.466396\pi\) | ||||
0.105374 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(710\) | −4.68728e7 | − | 3.29527e7i | −0.130962 | − | 0.0920696i | ||||
\(711\) | − | 1.28279e8i | − | 0.356901i | ||||||
\(712\) | 8.25004e7 | + | 2.26074e7i | 0.228568 | + | 0.0626340i | ||||
\(713\) | 1.63256e8 | 0.450403 | ||||||||
\(714\) | −1.21850e8 | + | 1.73323e8i | −0.334758 | + | 0.476169i | ||||
\(715\) | 2.85869e7i | 0.0782076i | ||||||||
\(716\) | 4.98735e8 | − | 1.79395e8i | 1.35872 | − | 0.488734i | ||||
\(717\) | 2.42643e7 | 0.0658280 | ||||||||
\(718\) | 2.96985e8 | + | 2.08787e8i | 0.802344 | + | 0.564067i | ||||
\(719\) | − | 3.96575e8i | − | 1.06694i | −0.845820 | − | 0.533468i | \(-0.820888\pi\) | ||
0.845820 | − | 0.533468i | \(-0.179112\pi\) | |||||||
\(720\) | 4.21832e7 | − | 3.48566e7i | 0.113016 | − | 0.0933871i | ||||
\(721\) | −8.83342e7 | −0.235680 | ||||||||
\(722\) | 1.13925e7 | − | 1.62049e7i | 0.0302696 | − | 0.0430562i | ||||
\(723\) | − | 2.06333e7i | − | 0.0545952i | ||||||
\(724\) | 1.72311e8 | + | 4.79040e8i | 0.454044 | + | 1.26228i | ||||
\(725\) | 3.38299e8 | 0.887741 | ||||||||
\(726\) | 1.57849e8 | + | 1.10971e8i | 0.412507 | + | 0.290002i | ||||
\(727\) | 5.28973e8i | 1.37667i | 0.725392 | + | 0.688336i | \(0.241658\pi\) | ||||
−0.725392 | + | 0.688336i | \(0.758342\pi\) | |||||||
\(728\) | 1.93155e7 | − | 7.04875e7i | 0.0500625 | − | 0.182691i | ||||
\(729\) | −3.96461e8 | −1.02334 | ||||||||
\(730\) | −6.56698e7 | + | 9.34104e7i | −0.168809 | + | 0.240119i | ||||
\(731\) | 1.99641e8i | 0.511089i | ||||||||
\(732\) | 2.95603e8 | − | 1.06329e8i | 0.753659 | − | 0.271092i | ||||
\(733\) | −5.41561e8 | −1.37510 | −0.687551 | − | 0.726136i | \(-0.741314\pi\) | ||||
−0.687551 | + | 0.726136i | \(0.741314\pi\) | |||||||
\(734\) | 5.57294e8 | + | 3.91791e8i | 1.40928 | + | 0.990756i | ||||
\(735\) | 8.21614e7i | 0.206922i | ||||||||
\(736\) | 2.81932e8 | − | 2.19869e7i | 0.707150 | − | 0.0551481i | ||||
\(737\) | 1.49305e8 | 0.372969 | ||||||||
\(738\) | 1.32540e8 | − | 1.88529e8i | 0.329745 | − | 0.469039i | ||||
\(739\) | − | 6.74728e8i | − | 1.67184i | −0.548848 | − | 0.835922i | \(-0.684934\pi\) | ||
0.548848 | − | 0.835922i | \(-0.315066\pi\) | |||||||
\(740\) | −1.74314e7 | − | 4.84608e7i | −0.0430167 | − | 0.119590i | ||||
\(741\) | 2.56726e7 | 0.0630981 | ||||||||
\(742\) | −9.88851e6 | − | 6.95186e6i | −0.0242058 | − | 0.0170173i | ||||
\(743\) | − | 5.91590e8i | − | 1.44230i | −0.692781 | − | 0.721148i | \(-0.743615\pi\) | ||
0.692781 | − | 0.721148i | \(-0.256385\pi\) | |||||||
\(744\) | −1.96490e8 | − | 5.38436e7i | −0.477113 | − | 0.130742i | ||||
\(745\) | −1.83890e8 | −0.444723 | ||||||||
\(746\) | 2.12476e8 | − | 3.02231e8i | 0.511791 | − | 0.727985i | ||||
\(747\) | − | 1.02285e8i | − | 0.245386i | ||||||
\(748\) | 3.25687e8 | − | 1.17150e8i | 0.778207 | − | 0.279922i | ||||
\(749\) | 4.47133e7 | 0.106412 | ||||||||
\(750\) | 1.86619e8 | + | 1.31197e8i | 0.442355 | + | 0.310987i | ||||
\(751\) | − | 2.10445e8i | − | 0.496842i | −0.968652 | − | 0.248421i | \(-0.920088\pi\) | ||
0.968652 | − | 0.248421i | \(-0.0799116\pi\) | |||||||
\(752\) | −4.08579e8 | − | 4.94460e8i | −0.960778 | − | 1.16273i | ||||
\(753\) | −2.89328e8 | −0.677650 | ||||||||
\(754\) | 8.97508e7 | − | 1.27664e8i | 0.209375 | − | 0.297820i | ||||
\(755\) | 2.23507e8i | 0.519338i | ||||||||
\(756\) | 8.51623e7 | + | 2.36759e8i | 0.197098 | + | 0.547949i | ||||
\(757\) | −2.20837e8 | −0.509078 | −0.254539 | − | 0.967063i | \(-0.581924\pi\) | ||||
−0.254539 | + | 0.967063i | \(0.581924\pi\) | |||||||
\(758\) | 2.78417e7 | + | 1.95734e7i | 0.0639275 | + | 0.0449426i | ||||
\(759\) | − | 1.43502e8i | − | 0.328196i | ||||||
\(760\) | 9.92722e6 | − | 3.62271e7i | 0.0226145 | − | 0.0825264i | ||||
\(761\) | −2.53245e8 | −0.574627 | −0.287314 | − | 0.957837i | \(-0.592762\pi\) | ||||
−0.287314 | + | 0.957837i | \(0.592762\pi\) | |||||||
\(762\) | 2.10899e8 | − | 2.99988e8i | 0.476661 | − | 0.678015i | ||||
\(763\) | 1.13365e8i | 0.255214i | ||||||||
\(764\) | −2.73335e8 | + | 9.83190e7i | −0.612937 | + | 0.220474i | ||||
\(765\) | 9.13952e7 | 0.204145 | ||||||||
\(766\) | −5.37793e8 | − | 3.78081e8i | −1.19654 | − | 0.841199i | ||||
\(767\) | 2.30158e8i | 0.510083i | ||||||||
\(768\) | −3.46576e8 | − | 6.65215e7i | −0.765094 | − | 0.146852i | ||||
\(769\) | 9.07521e7 | 0.199562 | 0.0997809 | − | 0.995009i | \(-0.468186\pi\) | ||||
0.0997809 | + | 0.995009i | \(0.468186\pi\) | |||||||
\(770\) | −3.12088e7 | + | 4.43923e7i | −0.0683605 | + | 0.0972378i | ||||
\(771\) | 3.41025e8i | 0.744087i | ||||||||
\(772\) | 2.05617e8 | + | 5.71632e8i | 0.446896 | + | 1.24241i | ||||
\(773\) | −3.93346e8 | −0.851602 | −0.425801 | − | 0.904817i | \(-0.640008\pi\) | ||||
−0.425801 | + | 0.904817i | \(0.640008\pi\) | |||||||
\(774\) | 5.47258e7 | + | 3.84736e7i | 0.118024 | + | 0.0829736i | ||||
\(775\) | 2.54461e8i | 0.546659i | ||||||||
\(776\) | 3.05673e7 | + | 8.37629e6i | 0.0654142 | + | 0.0179253i | ||||
\(777\) | 6.68154e7 | 0.142434 | ||||||||
\(778\) | 1.50023e8 | − | 2.13396e8i | 0.318580 | − | 0.453156i | ||||
\(779\) | − | 1.58194e8i | − | 0.334640i | ||||||
\(780\) | 4.58087e7 | − | 1.64774e7i | 0.0965304 | − | 0.0347221i | ||||
\(781\) | −1.21437e8 | −0.254917 | ||||||||
\(782\) | 3.86384e8 | + | 2.71637e8i | 0.807977 | + | 0.568028i | ||||
\(783\) | 5.37243e8i | 1.11914i | ||||||||
\(784\) | −2.64530e8 | + | 2.18585e8i | −0.548942 | + | 0.453599i | ||||
\(785\) | −2.00588e8 | −0.414663 | ||||||||
\(786\) | 1.88682e8 | − | 2.68386e8i | 0.388564 | − | 0.552704i | ||||
\(787\) | 4.00467e7i | 0.0821565i | 0.999156 | + | 0.0410783i | \(0.0130793\pi\) | ||||
−0.999156 | + | 0.0410783i | \(0.986921\pi\) | |||||||
\(788\) | −3.10946e8 | − | 8.64456e8i | −0.635486 | − | 1.76671i | ||||
\(789\) | 9.73537e7 | 0.198208 | ||||||||
\(790\) | −1.36599e8 | − | 9.60321e7i | −0.277054 | − | 0.194776i | ||||
\(791\) | − | 3.04957e6i | − | 0.00616183i | ||||||
\(792\) | 3.06511e7 | − | 1.11854e8i | 0.0616980 | − | 0.225153i | ||||
\(793\) | −1.80995e8 | −0.362950 | ||||||||
\(794\) | 7.20016e7 | − | 1.02417e8i | 0.143840 | − | 0.204602i | ||||
\(795\) | − | 8.05147e6i | − | 0.0160241i | ||||||
\(796\) | −1.22287e8 | + | 4.39869e7i | −0.242461 | + | 0.0872136i | ||||
\(797\) | 5.42316e7 | 0.107122 | 0.0535608 | − | 0.998565i | \(-0.482943\pi\) | ||||
0.0535608 | + | 0.998565i | \(0.482943\pi\) | |||||||
\(798\) | 3.98668e7 | + | 2.80273e7i | 0.0784517 | + | 0.0551534i | ||||
\(799\) | − | 1.07131e9i | − | 2.10027i | ||||||
\(800\) | 3.42702e7 | + | 4.39437e8i | 0.0669339 | + | 0.858276i | ||||
\(801\) | 4.78742e7 | 0.0931545 | ||||||||
\(802\) | 5.51217e8 | − | 7.84065e8i | 1.06856 | − | 1.51995i | ||||
\(803\) | 2.42006e8i | 0.467390i | ||||||||
\(804\) | −8.60593e7 | − | 2.39252e8i | −0.165588 | − | 0.460350i | ||||
\(805\) | −7.40503e7 | −0.141951 | ||||||||
\(806\) | 9.60261e7 | + | 6.75087e7i | 0.183394 | + | 0.128930i | ||||
\(807\) | 4.13127e8i | 0.786072i | ||||||||
\(808\) | −1.07442e8 | − | 2.94422e7i | −0.203677 | − | 0.0558130i | ||||
\(809\) | −7.90659e8 | −1.49329 | −0.746644 | − | 0.665223i | \(-0.768336\pi\) | ||||
−0.746644 | + | 0.665223i | \(0.768336\pi\) | |||||||
\(810\) | −5.15777e7 | + | 7.33655e7i | −0.0970525 | + | 0.138050i | ||||
\(811\) | 1.04890e9i | 1.96640i | 0.182525 | + | 0.983201i | \(0.441573\pi\) | ||||
−0.182525 | + | 0.983201i | \(0.558427\pi\) | |||||||
\(812\) | 2.78746e8 | − | 1.00265e8i | 0.520644 | − | 0.187276i | ||||
\(813\) | −5.70659e8 | −1.06195 | ||||||||
\(814\) | −8.92937e7 | − | 6.27756e7i | −0.165557 | − | 0.116391i | ||||
\(815\) | 2.51205e8i | 0.464040i | ||||||||
\(816\) | −3.75451e8 | − | 4.54368e8i | −0.691007 | − | 0.836251i | ||||
\(817\) | 4.59203e7 | 0.0842051 | ||||||||
\(818\) | −1.96592e8 | + | 2.79637e8i | −0.359174 | + | 0.510899i | ||||
\(819\) | − | 4.09032e7i | − | 0.0744571i | ||||||
\(820\) | −1.01533e8 | − | 2.82271e8i | −0.184148 | − | 0.511948i | ||||
\(821\) | −5.47461e8 | −0.989290 | −0.494645 | − | 0.869095i | \(-0.664702\pi\) | ||||
−0.494645 | + | 0.869095i | \(0.664702\pi\) | |||||||
\(822\) | −5.08481e8 | − | 3.57474e8i | −0.915501 | − | 0.643619i | ||||
\(823\) | 5.77332e8i | 1.03568i | 0.855477 | + | 0.517841i | \(0.173264\pi\) | ||||
−0.855477 | + | 0.517841i | \(0.826736\pi\) | |||||||
\(824\) | 6.49468e7 | − | 2.37008e8i | 0.116085 | − | 0.423625i | ||||
\(825\) | 2.23671e8 | 0.398335 | ||||||||
\(826\) | −2.51268e8 | + | 3.57410e8i | −0.445859 | + | 0.634201i | ||||
\(827\) | − | 7.17000e8i | − | 1.26766i | −0.773473 | − | 0.633830i | \(-0.781482\pi\) | ||
0.773473 | − | 0.633830i | \(-0.218518\pi\) | |||||||
\(828\) | 1.48923e8 | − | 5.35679e7i | 0.262345 | − | 0.0943656i | ||||
\(829\) | −3.64346e8 | −0.639514 | −0.319757 | − | 0.947500i | \(-0.603601\pi\) | ||||
−0.319757 | + | 0.947500i | \(0.603601\pi\) | |||||||
\(830\) | −1.08918e8 | − | 7.65720e7i | −0.190487 | − | 0.133917i | ||||
\(831\) | − | 1.96057e8i | − | 0.341648i | ||||||
\(832\) | 1.74922e8 | + | 1.03650e8i | 0.303722 | + | 0.179970i | ||||
\(833\) | −5.73138e8 | −0.991572 | ||||||||
\(834\) | 1.23552e8 | − | 1.75744e8i | 0.212987 | − | 0.302958i | ||||
\(835\) | 1.53593e8i | 0.263823i | ||||||||
\(836\) | −2.69462e7 | − | 7.49127e7i | −0.0461188 | − | 0.128214i | ||||
\(837\) | −4.04103e8 | −0.689153 | ||||||||
\(838\) | 1.19781e8 | + | 8.42093e7i | 0.203544 | + | 0.143096i | ||||
\(839\) | 6.25953e8i | 1.05988i | 0.848036 | + | 0.529939i | \(0.177785\pi\) | ||||
−0.848036 | + | 0.529939i | \(0.822215\pi\) | |||||||
\(840\) | 8.91246e7 | + | 2.44226e7i | 0.150369 | + | 0.0412054i | ||||
\(841\) | 3.76955e7 | 0.0633726 | ||||||||
\(842\) | 4.13096e8 | − | 5.87599e8i | 0.692014 | − | 0.984339i | ||||
\(843\) | − | 6.22334e8i | − | 1.03882i | ||||||
\(844\) | −2.76776e8 | + | 9.95567e7i | −0.460364 | + | 0.165593i | ||||
\(845\) | 1.96993e8 | 0.326498 | ||||||||
\(846\) | −2.93669e8 | − | 2.06457e8i | −0.485007 | − | 0.340971i | ||||
\(847\) | − | 2.11028e8i | − | 0.347288i | ||||||
\(848\) | 2.59228e7 | − | 2.14204e7i | 0.0425104 | − | 0.0351270i | ||||
\(849\) | 5.04667e8 | 0.824674 | ||||||||
\(850\) | −4.23391e8 | + | 6.02242e8i | −0.689421 | + | 0.980651i | ||||
\(851\) | − | 1.48950e8i | − | 0.241686i | ||||||
\(852\) | 6.99962e7 | + | 1.94596e8i | 0.113176 | + | 0.314640i | ||||
\(853\) | 4.97529e8 | 0.801625 | 0.400812 | − | 0.916160i | \(-0.368728\pi\) | ||||
0.400812 | + | 0.916160i | \(0.368728\pi\) | |||||||
\(854\) | −2.81065e8 | − | 1.97596e8i | −0.451267 | − | 0.317252i | ||||
\(855\) | − | 2.10222e7i | − | 0.0336342i | ||||||
\(856\) | −3.28750e7 | + | 1.19970e8i | −0.0524136 | + | 0.191271i | ||||
\(857\) | 7.64394e8 | 1.21444 | 0.607218 | − | 0.794535i | \(-0.292285\pi\) | ||||
0.607218 | + | 0.794535i | \(0.292285\pi\) | |||||||
\(858\) | 5.93402e7 | − | 8.44070e7i | 0.0939479 | − | 0.133634i | ||||
\(859\) | 3.81161e7i | 0.0601352i | 0.999548 | + | 0.0300676i | \(0.00957226\pi\) | ||||
−0.999548 | + | 0.0300676i | \(0.990428\pi\) | |||||||
\(860\) | 8.19373e7 | − | 2.94729e7i | 0.128821 | − | 0.0463370i | ||||
\(861\) | 3.89183e8 | 0.609739 | ||||||||
\(862\) | 7.06231e8 | + | 4.96497e8i | 1.10262 | + | 0.775167i | ||||
\(863\) | 5.14459e7i | 0.0800421i | 0.999199 | + | 0.0400210i | \(0.0127425\pi\) | ||||
−0.999199 | + | 0.0400210i | \(0.987258\pi\) | |||||||
\(864\) | −6.97858e8 | + | 5.44235e7i | −1.08200 | + | 0.0843811i | ||||
\(865\) | −2.44524e8 | −0.377810 | ||||||||
\(866\) | −6.25299e7 | + | 8.89442e7i | −0.0962795 | + | 0.136951i | ||||
\(867\) | − | 4.76721e8i | − | 0.731487i | ||||||
\(868\) | 7.54174e7 | + | 2.09667e8i | 0.115322 | + | 0.320605i | ||||
\(869\) | −3.53897e8 | −0.539284 | ||||||||
\(870\) | 1.61418e8 | + | 1.13481e8i | 0.245129 | + | 0.172332i | ||||
\(871\) | 1.46492e8i | 0.221697i | ||||||||
\(872\) | −3.04167e8 | − | 8.33502e7i | −0.458736 | − | 0.125706i | ||||
\(873\) | 1.77379e7 | 0.0266600 | ||||||||
\(874\) | 6.24806e7 | − | 8.88740e7i | 0.0935860 | − | 0.133119i | ||||
\(875\) | − | 2.49491e8i | − | 0.372417i | ||||||
\(876\) | 3.87799e8 | − | 1.39492e8i | 0.576892 | − | 0.207509i | ||||
\(877\) | 8.20835e8 | 1.21691 | 0.608453 | − | 0.793590i | \(-0.291790\pi\) | ||||
0.608453 | + | 0.793590i | \(0.291790\pi\) | |||||||
\(878\) | 1.84605e7 | + | 1.29782e7i | 0.0272747 | + | 0.0191748i | ||||
\(879\) | − | 5.22339e8i | − | 0.769105i | ||||||
\(880\) | −9.61622e7 | − | 1.16375e8i | −0.141110 | − | 0.170770i | ||||
\(881\) | −6.47450e8 | −0.946844 | −0.473422 | − | 0.880836i | \(-0.656981\pi\) | ||||
−0.473422 | + | 0.880836i | \(0.656981\pi\) | |||||||
\(882\) | −1.10452e8 | + | 1.57110e8i | −0.160978 | + | 0.228980i | ||||
\(883\) | 1.73373e8i | 0.251826i | 0.992041 | + | 0.125913i | \(0.0401860\pi\) | ||||
−0.992041 | + | 0.125913i | \(0.959814\pi\) | |||||||
\(884\) | 1.14943e8 | + | 3.19550e8i | 0.166389 | + | 0.462576i | ||||
\(885\) | −2.91013e8 | −0.419838 | ||||||||
\(886\) | −9.69892e8 | − | 6.81858e8i | −1.39451 | − | 0.980376i | ||||
\(887\) | 5.63804e8i | 0.807900i | 0.914781 | + | 0.403950i | \(0.132363\pi\) | ||||
−0.914781 | + | 0.403950i | \(0.867637\pi\) | |||||||
\(888\) | −4.91253e7 | + | 1.79271e8i | −0.0701562 | + | 0.256019i | ||||
\(889\) | −4.01055e8 | −0.570819 | ||||||||
\(890\) | 3.58394e7 | − | 5.09789e7i | 0.0508383 | − | 0.0723137i | ||||
\(891\) | 1.90074e8i | 0.268714i | ||||||||
\(892\) | 2.73175e8 | − | 9.82614e7i | 0.384899 | − | 0.138449i | ||||
\(893\) | −2.46417e8 | −0.346032 | ||||||||
\(894\) | 5.42963e8 | + | 3.81716e8i | 0.759902 | + | 0.534230i | ||||
\(895\) | − | 3.86112e8i | − | 0.538572i | ||||||
\(896\) | 1.58478e8 | + | 3.51924e8i | 0.220316 | + | 0.489243i | ||||
\(897\) | 1.40799e8 | 0.195084 | ||||||||
\(898\) | 4.03885e8 | − | 5.74496e8i | 0.557735 | − | 0.793337i | ||||
\(899\) | 4.75767e8i | 0.654810i | ||||||||
\(900\) | 8.34943e7 | + | 2.32121e8i | 0.114533 | + | 0.318411i | ||||
\(901\) | 5.61651e7 | 0.0767879 | ||||||||
\(902\) | −5.20113e8 | − | 3.65652e8i | −0.708725 | − | 0.498251i | ||||
\(903\) | 1.12971e8i | 0.153428i | ||||||||
\(904\) | 8.18227e6 | + | 2.24217e6i | 0.0110756 | + | 0.00303503i | ||||
\(905\) | 3.70865e8 | 0.500345 | ||||||||
\(906\) | 4.63952e8 | − | 6.59937e8i | 0.623861 | − | 0.887397i | ||||
\(907\) | − | 7.10297e7i | − | 0.0951959i | −0.998867 | − | 0.0475980i | \(-0.984843\pi\) | ||
0.998867 | − | 0.0475980i | \(-0.0151566\pi\) | |||||||
\(908\) | 8.56872e8 | − | 3.08218e8i | 1.14461 | − | 0.411718i | ||||
\(909\) | −6.23477e7 | −0.0830097 | ||||||||
\(910\) | −4.35559e7 | − | 3.06208e7i | −0.0577993 | − | 0.0406343i | ||||
\(911\) | 1.31086e9i | 1.73382i | 0.498469 | + | 0.866908i | \(0.333896\pi\) | ||||
−0.498469 | + | 0.866908i | \(0.666104\pi\) | |||||||
\(912\) | −1.04511e8 | + | 8.63591e7i | −0.137778 | + | 0.113848i | ||||
\(913\) | −2.82183e8 | −0.370782 | ||||||||
\(914\) | −6.56887e8 | + | 9.34373e8i | −0.860304 | + | 1.22372i | ||||
\(915\) | − | 2.28850e8i | − | 0.298737i | ||||||
\(916\) | 4.45805e8 | + | 1.23938e9i | 0.580041 | + | 1.61256i | ||||
\(917\) | −3.58805e8 | −0.465319 | ||||||||
\(918\) | −9.56404e8 | − | 6.72375e8i | −1.23627 | − | 0.869128i | ||||
\(919\) | 2.11036e8i | 0.271901i | 0.990716 | + | 0.135950i | \(0.0434088\pi\) | ||||
−0.990716 | + | 0.135950i | \(0.956591\pi\) | |||||||
\(920\) | 5.44447e7 | − | 1.98683e8i | 0.0699185 | − | 0.255151i | ||||
\(921\) | 1.06199e9 | 1.35938 | ||||||||
\(922\) | −5.08649e7 | + | 7.23516e7i | −0.0648971 | + | 0.0923114i | ||||
\(923\) | − | 1.19149e8i | − | 0.151526i | ||||||
\(924\) | 1.84297e8 | − | 6.62920e7i | 0.233616 | − | 0.0840321i | ||||
\(925\) | 2.32163e8 | 0.293337 | ||||||||
\(926\) | 1.07379e9 | + | 7.54898e8i | 1.35234 | + | 0.950725i | ||||
\(927\) | − | 1.37534e8i | − | 0.172651i | ||||||
\(928\) | 6.40751e7 | + | 8.21618e8i | 0.0801762 | + | 1.02808i | ||||
\(929\) | 1.07162e9 | 1.33657 | 0.668285 | − | 0.743905i | \(-0.267029\pi\) | ||||
0.668285 | + | 0.743905i | \(0.267029\pi\) | |||||||
\(930\) | −8.53581e7 | + | 1.21416e8i | −0.106120 | + | 0.150947i | ||||
\(931\) | 1.31830e8i | 0.163368i | ||||||||
\(932\) | 3.40827e8 | + | 9.47529e8i | 0.421004 | + | 1.17043i | ||||
\(933\) | −8.31208e8 | −1.02345 | ||||||||
\(934\) | −9.01110e8 | − | 6.33502e8i | −1.10595 | − | 0.777512i | ||||
\(935\) | − | 2.52141e8i | − | 0.308467i | ||||||
\(936\) | 1.09747e8 | + | 3.00736e7i | 0.133833 | + | 0.0366740i | ||||
\(937\) | 1.02180e9 | 1.24208 | 0.621039 | − | 0.783779i | \(-0.286711\pi\) | ||||
0.621039 | + | 0.783779i | \(0.286711\pi\) | |||||||
\(938\) | −1.59928e8 | + | 2.27486e8i | −0.193784 | + | 0.275643i | ||||
\(939\) | − | 7.91096e8i | − | 0.955504i | ||||||
\(940\) | −4.39692e8 | + | 1.58157e8i | −0.529376 | + | 0.190417i | ||||
\(941\) | −2.94539e8 | −0.353488 | −0.176744 | − | 0.984257i | \(-0.556556\pi\) | ||||
−0.176744 | + | 0.984257i | \(0.556556\pi\) | |||||||
\(942\) | 5.92265e8 | + | 4.16376e8i | 0.708538 | + | 0.498119i | ||||
\(943\) | − | 8.67595e8i | − | 1.03462i | ||||||
\(944\) | −7.74220e8 | − | 9.36956e8i | −0.920340 | − | 1.11379i | ||||
\(945\) | 1.83294e8 | 0.217197 | ||||||||
\(946\) | 1.06141e8 | − | 1.50978e8i | 0.125374 | − | 0.178336i | ||||
\(947\) | − | 8.16992e7i | − | 0.0961984i | −0.998843 | − | 0.0480992i | \(-0.984684\pi\) | ||
0.998843 | − | 0.0480992i | \(-0.0153164\pi\) | |||||||
\(948\) | 2.03986e8 | + | 5.67098e8i | 0.239428 | + | 0.665630i | ||||
\(949\) | −2.37446e8 | −0.277822 | ||||||||
\(950\) | 1.38525e8 | + | 9.73861e7i | 0.161568 | + | 0.113586i | ||||
\(951\) | − | 5.62897e8i | − | 0.654467i | ||||||
\(952\) | −1.70366e8 | + | 6.21711e8i | −0.197457 | + | 0.720573i | ||||
\(953\) | 2.06256e8 | 0.238302 | 0.119151 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119151 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(954\) | 1.08238e7 | − | 1.53961e7i | 0.0124662 | − | 0.0177323i | ||||
\(955\) | 2.11611e8i | 0.242957i | ||||||||
\(956\) | 6.94693e7 | − | 2.49882e7i | 0.0795095 | − | 0.0285996i | ||||
\(957\) | 4.18200e8 | 0.477143 | ||||||||
\(958\) | −1.17794e8 | − | 8.28118e7i | −0.133975 | − | 0.0941880i | ||||
\(959\) | 6.79788e8i | 0.770757i | ||||||||
\(960\) | −1.31056e8 | + | 2.21172e8i | −0.148130 | + | 0.249987i | ||||
\(961\) | 5.29641e8 | 0.596777 | ||||||||
\(962\) | 6.15929e7 | − | 8.76113e7i | 0.0691839 | − | 0.0984090i | ||||
\(963\) | 6.96172e7i | 0.0779539i | ||||||||
\(964\) | −2.12488e7 | − | 5.90736e7i | −0.0237194 | − | 0.0659420i | ||||
\(965\) | 4.42548e8 | 0.492468 | ||||||||
\(966\) | 2.18645e8 | + | 1.53712e8i | 0.242553 | + | 0.170521i | ||||
\(967\) | 9.87671e7i | 0.109228i | 0.998508 | + | 0.0546139i | \(0.0173928\pi\) | ||||
−0.998508 | + | 0.0546139i | \(0.982607\pi\) | |||||||
\(968\) | 5.66206e8 | + | 1.55156e8i | 0.624235 | + | 0.171058i | ||||
\(969\) | −2.26437e8 | −0.248872 | ||||||||
\(970\) | 1.32789e7 | − | 1.88883e7i | 0.0145495 | − | 0.0206955i | ||||
\(971\) | − | 8.01547e8i | − | 0.875531i | −0.899089 | − | 0.437765i | \(-0.855770\pi\) | ||
0.899089 | − | 0.437765i | \(-0.144230\pi\) | |||||||
\(972\) | −6.33240e8 | + | 2.27777e8i | −0.689556 | + | 0.248034i | ||||
\(973\) | −2.34952e8 | −0.255060 | ||||||||
\(974\) | −3.60962e8 | − | 2.53765e8i | −0.390647 | − | 0.274634i | ||||
\(975\) | 2.19457e8i | 0.236775i | ||||||||
\(976\) | 7.36816e8 | − | 6.08842e8i | 0.792519 | − | 0.654870i | ||||
\(977\) | 1.72774e9 | 1.85265 | 0.926326 | − | 0.376723i | \(-0.122949\pi\) | ||||
0.926326 | + | 0.376723i | \(0.122949\pi\) | |||||||
\(978\) | 5.21447e8 | − | 7.41719e8i | 0.557434 | − | 0.792908i | ||||
\(979\) | − | 1.32075e8i | − | 0.140758i | ||||||
\(980\) | 8.46123e7 | + | 2.35230e8i | 0.0898991 | + | 0.249927i | ||||
\(981\) | −1.76505e8 | −0.186961 | ||||||||
\(982\) | −3.66841e8 | − | 2.57898e8i | −0.387386 | − | 0.272342i | ||||
\(983\) | − | 1.11905e9i | − | 1.17812i | −0.808090 | − | 0.589059i | \(-0.799499\pi\) | ||
0.808090 | − | 0.589059i | \(-0.200501\pi\) | |||||||
\(984\) | −2.86142e8 | + | 1.04421e9i | −0.300328 | + | 1.09598i | ||||
\(985\) | −6.69246e8 | −0.700289 | ||||||||
\(986\) | −7.91617e8 | + | 1.12602e9i | −0.825818 | + | 1.17466i | ||||
\(987\) | − | 6.06226e8i | − | 0.630497i | ||||||
\(988\) | 7.35013e7 | − | 2.64385e7i | 0.0762121 | − | 0.0274136i | ||||
\(989\) | 2.51844e8 | 0.260341 | ||||||||
\(990\) | −6.91173e7 | − | 4.85911e7i | −0.0712330 | − | 0.0500785i | ||||
\(991\) | 5.35058e8i | 0.549769i | 0.961477 | + | 0.274885i | \(0.0886396\pi\) | ||||
−0.961477 | + | 0.274885i | \(0.911360\pi\) | |||||||
\(992\) | −6.18004e8 | + | 4.81960e7i | −0.633077 | + | 0.0493714i | ||||
\(993\) | 8.22424e7 | 0.0839940 | ||||||||
\(994\) | 1.30078e8 | − | 1.85026e8i | 0.132447 | − | 0.188396i | ||||
\(995\) | 9.46728e7i | 0.0961072i | ||||||||
\(996\) | 1.62650e8 | + | 4.52181e8i | 0.164617 | + | 0.457650i | ||||
\(997\) | 3.06306e8 | 0.309079 | 0.154539 | − | 0.987987i | \(-0.450611\pi\) | ||||
0.154539 | + | 0.987987i | \(0.450611\pi\) | |||||||
\(998\) | −2.18346e8 | − | 1.53502e8i | −0.219661 | − | 0.154427i | ||||
\(999\) | 3.68691e8i | 0.369799i |
(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.39.20 | yes | 54 | |
4.3 | odd | 2 | inner | 76.7.b.a.39.19 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.b.a.39.19 | ✓ | 54 | 4.3 | odd | 2 | inner | |
76.7.b.a.39.20 | yes | 54 | 1.1 | even | 1 | trivial |