Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
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: | yes |
Analytic conductor: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.38595\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.38595 | −0.193833 | −0.0969167 | − | 0.995292i | \(-0.530898\pi\) | ||||
−0.0969167 | + | 0.995292i | \(0.530898\pi\) | |||||||
\(3\) | 117.920 | 0.840505 | 0.420253 | − | 0.907407i | \(-0.361941\pi\) | ||||
0.420253 | + | 0.907407i | \(0.361941\pi\) | |||||||
\(4\) | −492.763 | −0.962429 | ||||||||
\(5\) | −1237.15 | −0.885229 | −0.442614 | − | 0.896712i | \(-0.645949\pi\) | ||||
−0.442614 | + | 0.896712i | \(0.645949\pi\) | |||||||
\(6\) | −517.190 | −0.162918 | ||||||||
\(7\) | 12549.3 | 1.97550 | 0.987750 | − | 0.156046i | \(-0.0498748\pi\) | ||||
0.987750 | + | 0.156046i | \(0.0498748\pi\) | |||||||
\(8\) | 4406.84 | 0.380384 | ||||||||
\(9\) | −5777.96 | −0.293551 | ||||||||
\(10\) | 5426.06 | 0.171587 | ||||||||
\(11\) | 27918.0 | 0.574933 | 0.287467 | − | 0.957791i | \(-0.407187\pi\) | ||||
0.287467 | + | 0.957791i | \(0.407187\pi\) | |||||||
\(12\) | −58106.5 | −0.808926 | ||||||||
\(13\) | −139652. | −1.35613 | −0.678067 | − | 0.735000i | \(-0.737182\pi\) | ||||
−0.678067 | + | 0.735000i | \(0.737182\pi\) | |||||||
\(14\) | −55040.4 | −0.382918 | ||||||||
\(15\) | −145884. | −0.744040 | ||||||||
\(16\) | 232967. | 0.888697 | ||||||||
\(17\) | −408645. | −1.18666 | −0.593330 | − | 0.804959i | \(-0.702187\pi\) | ||||
−0.593330 | + | 0.804959i | \(0.702187\pi\) | |||||||
\(18\) | 25341.8 | 0.0568999 | ||||||||
\(19\) | −157490. | −0.277244 | −0.138622 | − | 0.990345i | \(-0.544267\pi\) | ||||
−0.138622 | + | 0.990345i | \(0.544267\pi\) | |||||||
\(20\) | 609620. | 0.851970 | ||||||||
\(21\) | 1.47980e6 | 1.66042 | ||||||||
\(22\) | −122447. | −0.111441 | ||||||||
\(23\) | −730739. | −0.544487 | −0.272243 | − | 0.962228i | \(-0.587766\pi\) | ||||
−0.272243 | + | 0.962228i | \(0.587766\pi\) | |||||||
\(24\) | 519653. | 0.319715 | ||||||||
\(25\) | −422597. | −0.216370 | ||||||||
\(26\) | 612508. | 0.262864 | ||||||||
\(27\) | −3.00235e6 | −1.08724 | ||||||||
\(28\) | −6.18382e6 | −1.90128 | ||||||||
\(29\) | −6.14391e6 | −1.61307 | −0.806537 | − | 0.591184i | \(-0.798661\pi\) | ||||
−0.806537 | + | 0.591184i | \(0.798661\pi\) | |||||||
\(30\) | 639839. | 0.144220 | ||||||||
\(31\) | 6.18625e6 | 1.20309 | 0.601547 | − | 0.798837i | \(-0.294551\pi\) | ||||
0.601547 | + | 0.798837i | \(0.294551\pi\) | |||||||
\(32\) | −3.27808e6 | −0.552644 | ||||||||
\(33\) | 3.29208e6 | 0.483234 | ||||||||
\(34\) | 1.79230e6 | 0.230015 | ||||||||
\(35\) | −1.55253e7 | −1.74877 | ||||||||
\(36\) | 2.84717e6 | 0.282521 | ||||||||
\(37\) | −2.16507e7 | −1.89917 | −0.949587 | − | 0.313503i | \(-0.898497\pi\) | ||||
−0.949587 | + | 0.313503i | \(0.898497\pi\) | |||||||
\(38\) | 690744. | 0.0537392 | ||||||||
\(39\) | −1.64677e7 | −1.13984 | ||||||||
\(40\) | −5.45190e6 | −0.336727 | ||||||||
\(41\) | 2.42738e7 | 1.34156 | 0.670780 | − | 0.741657i | \(-0.265960\pi\) | ||||
0.670780 | + | 0.741657i | \(0.265960\pi\) | |||||||
\(42\) | −6.49035e6 | −0.321845 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | −1.37570e7 | −0.553332 | ||||||||
\(45\) | 7.14817e6 | 0.259859 | ||||||||
\(46\) | 3.20499e6 | 0.105540 | ||||||||
\(47\) | −3.21569e7 | −0.961243 | −0.480622 | − | 0.876928i | \(-0.659589\pi\) | ||||
−0.480622 | + | 0.876928i | \(0.659589\pi\) | |||||||
\(48\) | 2.74713e7 | 0.746955 | ||||||||
\(49\) | 1.17130e8 | 2.90260 | ||||||||
\(50\) | 1.85349e6 | 0.0419397 | ||||||||
\(51\) | −4.81873e7 | −0.997395 | ||||||||
\(52\) | 6.88155e7 | 1.30518 | ||||||||
\(53\) | −6.96541e7 | −1.21257 | −0.606283 | − | 0.795249i | \(-0.707340\pi\) | ||||
−0.606283 | + | 0.795249i | \(0.707340\pi\) | |||||||
\(54\) | 1.31681e7 | 0.210743 | ||||||||
\(55\) | −3.45386e7 | −0.508947 | ||||||||
\(56\) | 5.53026e7 | 0.751449 | ||||||||
\(57\) | −1.85712e7 | −0.233025 | ||||||||
\(58\) | 2.69469e7 | 0.312668 | ||||||||
\(59\) | −1.12041e8 | −1.20377 | −0.601886 | − | 0.798582i | \(-0.705584\pi\) | ||||
−0.601886 | + | 0.798582i | \(0.705584\pi\) | |||||||
\(60\) | 7.18862e7 | 0.716085 | ||||||||
\(61\) | 8.03385e7 | 0.742915 | 0.371458 | − | 0.928450i | \(-0.378858\pi\) | ||||
0.371458 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(62\) | −2.71326e7 | −0.233200 | ||||||||
\(63\) | −7.25091e7 | −0.579909 | ||||||||
\(64\) | −1.04901e8 | −0.781577 | ||||||||
\(65\) | 1.72770e8 | 1.20049 | ||||||||
\(66\) | −1.44389e7 | −0.0936670 | ||||||||
\(67\) | −5.78429e7 | −0.350682 | −0.175341 | − | 0.984508i | \(-0.556103\pi\) | ||||
−0.175341 | + | 0.984508i | \(0.556103\pi\) | |||||||
\(68\) | 2.01366e8 | 1.14208 | ||||||||
\(69\) | −8.61685e7 | −0.457644 | ||||||||
\(70\) | 6.80930e7 | 0.338970 | ||||||||
\(71\) | 3.11039e8 | 1.45262 | 0.726311 | − | 0.687366i | \(-0.241233\pi\) | ||||
0.726311 | + | 0.687366i | \(0.241233\pi\) | |||||||
\(72\) | −2.54625e7 | −0.111662 | ||||||||
\(73\) | −3.23803e7 | −0.133453 | −0.0667265 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667265 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(74\) | 9.49590e7 | 0.368124 | ||||||||
\(75\) | −4.98325e7 | −0.181860 | ||||||||
\(76\) | 7.76054e7 | 0.266828 | ||||||||
\(77\) | 3.50350e8 | 1.13578 | ||||||||
\(78\) | 7.22267e7 | 0.220939 | ||||||||
\(79\) | 2.36871e8 | 0.684210 | 0.342105 | − | 0.939662i | \(-0.388860\pi\) | ||||
0.342105 | + | 0.939662i | \(0.388860\pi\) | |||||||
\(80\) | −2.88214e8 | −0.786701 | ||||||||
\(81\) | −2.40308e8 | −0.620277 | ||||||||
\(82\) | −1.06464e8 | −0.260039 | ||||||||
\(83\) | 4.61987e8 | 1.06851 | 0.534255 | − | 0.845324i | \(-0.320592\pi\) | ||||
0.534255 | + | 0.845324i | \(0.320592\pi\) | |||||||
\(84\) | −7.29193e8 | −1.59803 | ||||||||
\(85\) | 5.05554e8 | 1.05047 | ||||||||
\(86\) | 1.49947e7 | 0.0295593 | ||||||||
\(87\) | −7.24488e8 | −1.35580 | ||||||||
\(88\) | 1.23030e8 | 0.218696 | ||||||||
\(89\) | 6.16826e8 | 1.04210 | 0.521048 | − | 0.853527i | \(-0.325541\pi\) | ||||
0.521048 | + | 0.853527i | \(0.325541\pi\) | |||||||
\(90\) | −3.13515e7 | −0.0503695 | ||||||||
\(91\) | −1.75253e9 | −2.67904 | ||||||||
\(92\) | 3.60082e8 | 0.524029 | ||||||||
\(93\) | 7.29481e8 | 1.01121 | ||||||||
\(94\) | 1.41038e8 | 0.186321 | ||||||||
\(95\) | 1.94838e8 | 0.245425 | ||||||||
\(96\) | −3.86551e8 | −0.464500 | ||||||||
\(97\) | −1.00137e9 | −1.14848 | −0.574240 | − | 0.818687i | \(-0.694702\pi\) | ||||
−0.574240 | + | 0.818687i | \(0.694702\pi\) | |||||||
\(98\) | −5.13728e8 | −0.562621 | ||||||||
\(99\) | −1.61309e8 | −0.168772 | ||||||||
\(100\) | 2.08240e8 | 0.208240 | ||||||||
\(101\) | −3.05585e8 | −0.292203 | −0.146102 | − | 0.989270i | \(-0.546673\pi\) | ||||
−0.146102 | + | 0.989270i | \(0.546673\pi\) | |||||||
\(102\) | 2.11347e8 | 0.193328 | ||||||||
\(103\) | −3.81600e8 | −0.334073 | −0.167036 | − | 0.985951i | \(-0.553420\pi\) | ||||
−0.167036 | + | 0.985951i | \(0.553420\pi\) | |||||||
\(104\) | −6.15425e8 | −0.515852 | ||||||||
\(105\) | −1.83073e9 | −1.46985 | ||||||||
\(106\) | 3.05499e8 | 0.235036 | ||||||||
\(107\) | −1.99829e9 | −1.47378 | −0.736888 | − | 0.676015i | \(-0.763705\pi\) | ||||
−0.736888 | + | 0.676015i | \(0.763705\pi\) | |||||||
\(108\) | 1.47945e9 | 1.04639 | ||||||||
\(109\) | 5.64232e8 | 0.382859 | 0.191429 | − | 0.981506i | \(-0.438688\pi\) | ||||
0.191429 | + | 0.981506i | \(0.438688\pi\) | |||||||
\(110\) | 1.51485e8 | 0.0986510 | ||||||||
\(111\) | −2.55305e9 | −1.59627 | ||||||||
\(112\) | 2.92356e9 | 1.75562 | ||||||||
\(113\) | 9.01181e8 | 0.519947 | 0.259973 | − | 0.965616i | \(-0.416286\pi\) | ||||
0.259973 | + | 0.965616i | \(0.416286\pi\) | |||||||
\(114\) | 8.14523e7 | 0.0451681 | ||||||||
\(115\) | 9.04030e8 | 0.481995 | ||||||||
\(116\) | 3.02750e9 | 1.55247 | ||||||||
\(117\) | 8.06904e8 | 0.398094 | ||||||||
\(118\) | 4.91407e8 | 0.233331 | ||||||||
\(119\) | −5.12820e9 | −2.34425 | ||||||||
\(120\) | −6.42887e8 | −0.283021 | ||||||||
\(121\) | −1.57853e9 | −0.669452 | ||||||||
\(122\) | −3.52361e8 | −0.144002 | ||||||||
\(123\) | 2.86235e9 | 1.12759 | ||||||||
\(124\) | −3.04836e9 | −1.15789 | ||||||||
\(125\) | 2.93911e9 | 1.07677 | ||||||||
\(126\) | 3.18021e8 | 0.112406 | ||||||||
\(127\) | 3.22590e9 | 1.10036 | 0.550179 | − | 0.835047i | \(-0.314559\pi\) | ||||
0.550179 | + | 0.835047i | \(0.314559\pi\) | |||||||
\(128\) | 2.13847e9 | 0.704139 | ||||||||
\(129\) | −4.03144e8 | −0.128176 | ||||||||
\(130\) | −7.57761e8 | −0.232695 | ||||||||
\(131\) | −3.22175e9 | −0.955808 | −0.477904 | − | 0.878412i | \(-0.658603\pi\) | ||||
−0.477904 | + | 0.878412i | \(0.658603\pi\) | |||||||
\(132\) | −1.62222e9 | −0.465079 | ||||||||
\(133\) | −1.97639e9 | −0.547696 | ||||||||
\(134\) | 2.53696e8 | 0.0679739 | ||||||||
\(135\) | 3.71434e9 | 0.962453 | ||||||||
\(136\) | −1.80084e9 | −0.451387 | ||||||||
\(137\) | −4.02495e9 | −0.976153 | −0.488077 | − | 0.872801i | \(-0.662301\pi\) | ||||
−0.488077 | + | 0.872801i | \(0.662301\pi\) | |||||||
\(138\) | 3.77931e8 | 0.0887067 | ||||||||
\(139\) | 2.36428e9 | 0.537196 | 0.268598 | − | 0.963252i | \(-0.413440\pi\) | ||||
0.268598 | + | 0.963252i | \(0.413440\pi\) | |||||||
\(140\) | 7.65028e9 | 1.68307 | ||||||||
\(141\) | −3.79193e9 | −0.807930 | ||||||||
\(142\) | −1.36420e9 | −0.281567 | ||||||||
\(143\) | −3.89881e9 | −0.779686 | ||||||||
\(144\) | −1.34607e9 | −0.260878 | ||||||||
\(145\) | 7.60091e9 | 1.42794 | ||||||||
\(146\) | 1.42018e8 | 0.0258676 | ||||||||
\(147\) | 1.38120e10 | 2.43965 | ||||||||
\(148\) | 1.06687e10 | 1.82782 | ||||||||
\(149\) | 3.40025e9 | 0.565161 | 0.282581 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282581 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(150\) | 2.18563e8 | 0.0352505 | ||||||||
\(151\) | −2.71186e9 | −0.424494 | −0.212247 | − | 0.977216i | \(-0.568078\pi\) | ||||
−0.212247 | + | 0.977216i | \(0.568078\pi\) | |||||||
\(152\) | −6.94035e8 | −0.105459 | ||||||||
\(153\) | 2.36114e9 | 0.348345 | ||||||||
\(154\) | −1.53662e9 | −0.220152 | ||||||||
\(155\) | −7.65329e9 | −1.06501 | ||||||||
\(156\) | 8.11470e9 | 1.09701 | ||||||||
\(157\) | 2.25484e9 | 0.296188 | 0.148094 | − | 0.988973i | \(-0.452686\pi\) | ||||
0.148094 | + | 0.988973i | \(0.452686\pi\) | |||||||
\(158\) | −1.03890e9 | −0.132623 | ||||||||
\(159\) | −8.21359e9 | −1.01917 | ||||||||
\(160\) | 4.05547e9 | 0.489216 | ||||||||
\(161\) | −9.17024e9 | −1.07563 | ||||||||
\(162\) | 1.05398e9 | 0.120231 | ||||||||
\(163\) | 2.12327e9 | 0.235592 | 0.117796 | − | 0.993038i | \(-0.462417\pi\) | ||||
0.117796 | + | 0.993038i | \(0.462417\pi\) | |||||||
\(164\) | −1.19612e10 | −1.29116 | ||||||||
\(165\) | −4.07278e9 | −0.427773 | ||||||||
\(166\) | −2.02625e9 | −0.207113 | ||||||||
\(167\) | −7.94637e9 | −0.790578 | −0.395289 | − | 0.918557i | \(-0.629355\pi\) | ||||
−0.395289 | + | 0.918557i | \(0.629355\pi\) | |||||||
\(168\) | 6.52127e9 | 0.631597 | ||||||||
\(169\) | 8.89824e9 | 0.839100 | ||||||||
\(170\) | −2.21733e9 | −0.203616 | ||||||||
\(171\) | 9.09972e8 | 0.0813852 | ||||||||
\(172\) | 1.68466e9 | 0.146769 | ||||||||
\(173\) | −1.13404e10 | −0.962548 | −0.481274 | − | 0.876570i | \(-0.659826\pi\) | ||||
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(174\) | 3.17757e9 | 0.262799 | ||||||||
\(175\) | −5.30328e9 | −0.427438 | ||||||||
\(176\) | 6.50396e9 | 0.510941 | ||||||||
\(177\) | −1.32119e10 | −1.01178 | ||||||||
\(178\) | −2.70537e9 | −0.201993 | ||||||||
\(179\) | −1.54500e10 | −1.12484 | −0.562420 | − | 0.826852i | \(-0.690130\pi\) | ||||
−0.562420 | + | 0.826852i | \(0.690130\pi\) | |||||||
\(180\) | −3.52236e9 | −0.250096 | ||||||||
\(181\) | 1.12851e10 | 0.781540 | 0.390770 | − | 0.920488i | \(-0.372209\pi\) | ||||
0.390770 | + | 0.920488i | \(0.372209\pi\) | |||||||
\(182\) | 7.68652e9 | 0.519288 | ||||||||
\(183\) | 9.47348e9 | 0.624424 | ||||||||
\(184\) | −3.22025e9 | −0.207114 | ||||||||
\(185\) | 2.67851e10 | 1.68120 | ||||||||
\(186\) | −3.19947e9 | −0.196006 | ||||||||
\(187\) | −1.14086e10 | −0.682250 | ||||||||
\(188\) | 1.58457e10 | 0.925128 | ||||||||
\(189\) | −3.76772e10 | −2.14783 | ||||||||
\(190\) | −8.54551e8 | −0.0475715 | ||||||||
\(191\) | 1.87758e10 | 1.02082 | 0.510409 | − | 0.859932i | \(-0.329494\pi\) | ||||
0.510409 | + | 0.859932i | \(0.329494\pi\) | |||||||
\(192\) | −1.23699e10 | −0.656919 | ||||||||
\(193\) | 2.54039e9 | 0.131793 | 0.0658966 | − | 0.997826i | \(-0.479009\pi\) | ||||
0.0658966 | + | 0.997826i | \(0.479009\pi\) | |||||||
\(194\) | 4.39197e9 | 0.222614 | ||||||||
\(195\) | 2.03730e10 | 1.00902 | ||||||||
\(196\) | −5.77175e10 | −2.79354 | ||||||||
\(197\) | −2.66438e10 | −1.26037 | −0.630186 | − | 0.776444i | \(-0.717021\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(198\) | 7.07493e8 | 0.0327137 | ||||||||
\(199\) | 2.48904e10 | 1.12511 | 0.562553 | − | 0.826761i | \(-0.309819\pi\) | ||||
0.562553 | + | 0.826761i | \(0.309819\pi\) | |||||||
\(200\) | −1.86232e9 | −0.0823036 | ||||||||
\(201\) | −6.82081e9 | −0.294750 | ||||||||
\(202\) | 1.34028e9 | 0.0566388 | ||||||||
\(203\) | −7.71016e10 | −3.18663 | ||||||||
\(204\) | 2.37450e10 | 0.959921 | ||||||||
\(205\) | −3.00302e10 | −1.18759 | ||||||||
\(206\) | 1.67368e9 | 0.0647545 | ||||||||
\(207\) | 4.22218e9 | 0.159834 | ||||||||
\(208\) | −3.25343e10 | −1.20519 | ||||||||
\(209\) | −4.39681e9 | −0.159397 | ||||||||
\(210\) | 8.02950e9 | 0.284906 | ||||||||
\(211\) | 2.83390e10 | 0.984267 | 0.492134 | − | 0.870520i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870520i | \(0.336217\pi\) | |||||||
\(212\) | 3.43230e10 | 1.16701 | ||||||||
\(213\) | 3.66777e10 | 1.22094 | ||||||||
\(214\) | 8.76440e9 | 0.285667 | ||||||||
\(215\) | 4.22955e9 | 0.134996 | ||||||||
\(216\) | −1.32309e10 | −0.413568 | ||||||||
\(217\) | 7.76329e10 | 2.37671 | ||||||||
\(218\) | −2.47470e9 | −0.0742109 | ||||||||
\(219\) | −3.81827e9 | −0.112168 | ||||||||
\(220\) | 1.70194e10 | 0.489826 | ||||||||
\(221\) | 5.70682e10 | 1.60927 | ||||||||
\(222\) | 1.11975e10 | 0.309410 | ||||||||
\(223\) | −8.66457e9 | −0.234626 | −0.117313 | − | 0.993095i | \(-0.537428\pi\) | ||||
−0.117313 | + | 0.993095i | \(0.537428\pi\) | |||||||
\(224\) | −4.11375e10 | −1.09175 | ||||||||
\(225\) | 2.44175e9 | 0.0635154 | ||||||||
\(226\) | −3.95254e9 | −0.100783 | ||||||||
\(227\) | −1.92752e10 | −0.481817 | −0.240908 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240908 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(228\) | 9.15120e9 | 0.224270 | ||||||||
\(229\) | −2.30675e9 | −0.0554294 | −0.0277147 | − | 0.999616i | \(-0.508823\pi\) | ||||
−0.0277147 | + | 0.999616i | \(0.508823\pi\) | |||||||
\(230\) | −3.96503e9 | −0.0934268 | ||||||||
\(231\) | 4.13132e10 | 0.954629 | ||||||||
\(232\) | −2.70753e10 | −0.613588 | ||||||||
\(233\) | −2.20050e10 | −0.489125 | −0.244562 | − | 0.969634i | \(-0.578644\pi\) | ||||
−0.244562 | + | 0.969634i | \(0.578644\pi\) | |||||||
\(234\) | −3.53904e9 | −0.0771639 | ||||||||
\(235\) | 3.97827e10 | 0.850920 | ||||||||
\(236\) | 5.52098e10 | 1.15854 | ||||||||
\(237\) | 2.79317e10 | 0.575083 | ||||||||
\(238\) | 2.24920e10 | 0.454394 | ||||||||
\(239\) | −3.65120e10 | −0.723845 | −0.361922 | − | 0.932208i | \(-0.617879\pi\) | ||||
−0.361922 | + | 0.932208i | \(0.617879\pi\) | |||||||
\(240\) | −3.39860e10 | −0.661226 | ||||||||
\(241\) | 8.05560e10 | 1.53823 | 0.769115 | − | 0.639110i | \(-0.220697\pi\) | ||||
0.769115 | + | 0.639110i | \(0.220697\pi\) | |||||||
\(242\) | 6.92337e9 | 0.129762 | ||||||||
\(243\) | 3.07581e10 | 0.565890 | ||||||||
\(244\) | −3.95879e10 | −0.715003 | ||||||||
\(245\) | −1.44907e11 | −2.56946 | ||||||||
\(246\) | −1.25541e10 | −0.218564 | ||||||||
\(247\) | 2.19939e10 | 0.375980 | ||||||||
\(248\) | 2.72618e10 | 0.457638 | ||||||||
\(249\) | 5.44773e10 | 0.898088 | ||||||||
\(250\) | −1.28908e10 | −0.208713 | ||||||||
\(251\) | 2.34339e10 | 0.372661 | 0.186330 | − | 0.982487i | \(-0.440341\pi\) | ||||
0.186330 | + | 0.982487i | \(0.440341\pi\) | |||||||
\(252\) | 3.57298e10 | 0.558121 | ||||||||
\(253\) | −2.04008e10 | −0.313043 | ||||||||
\(254\) | −1.41486e10 | −0.213286 | ||||||||
\(255\) | 5.96147e10 | 0.882923 | ||||||||
\(256\) | 4.43303e10 | 0.645091 | ||||||||
\(257\) | −1.48746e10 | −0.212689 | −0.106345 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106345 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(258\) | 1.76817e9 | 0.0248448 | ||||||||
\(259\) | −2.71701e11 | −3.75182 | ||||||||
\(260\) | −8.51348e10 | −1.15539 | ||||||||
\(261\) | 3.54993e10 | 0.473519 | ||||||||
\(262\) | 1.41304e10 | 0.185268 | ||||||||
\(263\) | −1.29482e10 | −0.166882 | −0.0834410 | − | 0.996513i | \(-0.526591\pi\) | ||||
−0.0834410 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(264\) | 1.45077e10 | 0.183815 | ||||||||
\(265\) | 8.61722e10 | 1.07340 | ||||||||
\(266\) | 8.66833e9 | 0.106162 | ||||||||
\(267\) | 7.27359e10 | 0.875887 | ||||||||
\(268\) | 2.85028e10 | 0.337506 | ||||||||
\(269\) | 1.38611e11 | 1.61403 | 0.807016 | − | 0.590529i | \(-0.201081\pi\) | ||||
0.807016 | + | 0.590529i | \(0.201081\pi\) | |||||||
\(270\) | −1.62909e10 | −0.186556 | ||||||||
\(271\) | −3.55761e10 | −0.400679 | −0.200339 | − | 0.979727i | \(-0.564204\pi\) | ||||
−0.200339 | + | 0.979727i | \(0.564204\pi\) | |||||||
\(272\) | −9.52008e10 | −1.05458 | ||||||||
\(273\) | −2.06658e11 | −2.25175 | ||||||||
\(274\) | 1.76532e10 | 0.189211 | ||||||||
\(275\) | −1.17981e10 | −0.124398 | ||||||||
\(276\) | 4.24607e10 | 0.440450 | ||||||||
\(277\) | 1.13489e11 | 1.15823 | 0.579114 | − | 0.815247i | \(-0.303399\pi\) | ||||
0.579114 | + | 0.815247i | \(0.303399\pi\) | |||||||
\(278\) | −1.03696e10 | −0.104126 | ||||||||
\(279\) | −3.57439e10 | −0.353169 | ||||||||
\(280\) | −6.84174e10 | −0.665205 | ||||||||
\(281\) | 2.84629e10 | 0.272334 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(282\) | 1.66312e10 | 0.156604 | ||||||||
\(283\) | 1.03614e11 | 0.960243 | 0.480121 | − | 0.877202i | \(-0.340593\pi\) | ||||
0.480121 | + | 0.877202i | \(0.340593\pi\) | |||||||
\(284\) | −1.53269e11 | −1.39805 | ||||||||
\(285\) | 2.29753e10 | 0.206281 | ||||||||
\(286\) | 1.71000e10 | 0.151129 | ||||||||
\(287\) | 3.04618e11 | 2.65025 | ||||||||
\(288\) | 1.89406e10 | 0.162229 | ||||||||
\(289\) | 4.84032e10 | 0.408163 | ||||||||
\(290\) | −3.33372e10 | −0.276782 | ||||||||
\(291\) | −1.18082e11 | −0.965303 | ||||||||
\(292\) | 1.59558e10 | 0.128439 | ||||||||
\(293\) | −1.91800e11 | −1.52035 | −0.760176 | − | 0.649717i | \(-0.774888\pi\) | ||||
−0.760176 | + | 0.649717i | \(0.774888\pi\) | |||||||
\(294\) | −6.05786e10 | −0.472886 | ||||||||
\(295\) | 1.38611e11 | 1.06561 | ||||||||
\(296\) | −9.54114e10 | −0.722416 | ||||||||
\(297\) | −8.38195e10 | −0.625088 | ||||||||
\(298\) | −1.49133e10 | −0.109547 | ||||||||
\(299\) | 1.02049e11 | 0.738397 | ||||||||
\(300\) | 2.45556e10 | 0.175027 | ||||||||
\(301\) | −4.29034e10 | −0.301261 | ||||||||
\(302\) | 1.18941e10 | 0.0822811 | ||||||||
\(303\) | −3.60344e10 | −0.245599 | ||||||||
\(304\) | −3.66900e10 | −0.246386 | ||||||||
\(305\) | −9.93904e10 | −0.657650 | ||||||||
\(306\) | −1.03558e10 | −0.0675209 | ||||||||
\(307\) | −5.93480e10 | −0.381315 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(308\) | −1.72640e11 | −1.09311 | ||||||||
\(309\) | −4.49982e10 | −0.280790 | ||||||||
\(310\) | 3.35670e10 | 0.206435 | ||||||||
\(311\) | −1.46203e11 | −0.886205 | −0.443102 | − | 0.896471i | \(-0.646122\pi\) | ||||
−0.443102 | + | 0.896471i | \(0.646122\pi\) | |||||||
\(312\) | −7.25707e10 | −0.433577 | ||||||||
\(313\) | −1.38227e11 | −0.814036 | −0.407018 | − | 0.913420i | \(-0.633431\pi\) | ||||
−0.407018 | + | 0.913420i | \(0.633431\pi\) | |||||||
\(314\) | −9.88963e9 | −0.0574112 | ||||||||
\(315\) | 8.97042e10 | 0.513352 | ||||||||
\(316\) | −1.16721e11 | −0.658504 | ||||||||
\(317\) | 5.56681e10 | 0.309628 | 0.154814 | − | 0.987944i | \(-0.450522\pi\) | ||||
0.154814 | + | 0.987944i | \(0.450522\pi\) | |||||||
\(318\) | 3.60244e10 | 0.197549 | ||||||||
\(319\) | −1.71526e11 | −0.927409 | ||||||||
\(320\) | 1.29778e11 | 0.691874 | ||||||||
\(321\) | −2.35638e11 | −1.23872 | ||||||||
\(322\) | 4.02202e10 | 0.208494 | ||||||||
\(323\) | 6.43577e10 | 0.328995 | ||||||||
\(324\) | 1.18415e11 | 0.596973 | ||||||||
\(325\) | 5.90166e10 | 0.293426 | ||||||||
\(326\) | −9.31255e9 | −0.0456656 | ||||||||
\(327\) | 6.65341e10 | 0.321795 | ||||||||
\(328\) | 1.06971e11 | 0.510308 | ||||||||
\(329\) | −4.03545e11 | −1.89894 | ||||||||
\(330\) | 1.78630e10 | 0.0829167 | ||||||||
\(331\) | 2.09845e11 | 0.960888 | 0.480444 | − | 0.877025i | \(-0.340476\pi\) | ||||
0.480444 | + | 0.877025i | \(0.340476\pi\) | |||||||
\(332\) | −2.27650e11 | −1.02836 | ||||||||
\(333\) | 1.25097e11 | 0.557504 | ||||||||
\(334\) | 3.48524e10 | 0.153240 | ||||||||
\(335\) | 7.15600e10 | 0.310434 | ||||||||
\(336\) | 3.44745e11 | 1.47561 | ||||||||
\(337\) | 2.40308e11 | 1.01493 | 0.507463 | − | 0.861673i | \(-0.330583\pi\) | ||||
0.507463 | + | 0.861673i | \(0.330583\pi\) | |||||||
\(338\) | −3.90272e10 | −0.162646 | ||||||||
\(339\) | 1.06267e11 | 0.437018 | ||||||||
\(340\) | −2.49118e11 | −1.01100 | ||||||||
\(341\) | 1.72708e11 | 0.691699 | ||||||||
\(342\) | −3.99109e9 | −0.0157752 | ||||||||
\(343\) | 9.63491e11 | 3.75858 | ||||||||
\(344\) | −1.50661e10 | −0.0580081 | ||||||||
\(345\) | 1.06603e11 | 0.405120 | ||||||||
\(346\) | 4.97386e10 | 0.186574 | ||||||||
\(347\) | 1.62927e10 | 0.0603266 | 0.0301633 | − | 0.999545i | \(-0.490397\pi\) | ||||
0.0301633 | + | 0.999545i | \(0.490397\pi\) | |||||||
\(348\) | 3.57001e11 | 1.30486 | ||||||||
\(349\) | −1.41443e11 | −0.510347 | −0.255174 | − | 0.966895i | \(-0.582133\pi\) | ||||
−0.255174 | + | 0.966895i | \(0.582133\pi\) | |||||||
\(350\) | 2.32599e10 | 0.0828518 | ||||||||
\(351\) | 4.19284e11 | 1.47444 | ||||||||
\(352\) | −9.15176e10 | −0.317733 | ||||||||
\(353\) | 3.15790e10 | 0.108246 | 0.0541230 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541230 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(354\) | 5.79466e10 | 0.196116 | ||||||||
\(355\) | −3.84801e11 | −1.28590 | ||||||||
\(356\) | −3.03949e11 | −1.00294 | ||||||||
\(357\) | −6.04715e11 | −1.97035 | ||||||||
\(358\) | 6.77631e10 | 0.218032 | ||||||||
\(359\) | 9.18482e10 | 0.291840 | 0.145920 | − | 0.989296i | \(-0.453386\pi\) | ||||
0.145920 | + | 0.989296i | \(0.453386\pi\) | |||||||
\(360\) | 3.15009e10 | 0.0988465 | ||||||||
\(361\) | −2.97885e11 | −0.923136 | ||||||||
\(362\) | −4.94958e10 | −0.151489 | ||||||||
\(363\) | −1.86140e11 | −0.562678 | ||||||||
\(364\) | 8.63584e11 | 2.57839 | ||||||||
\(365\) | 4.00591e10 | 0.118136 | ||||||||
\(366\) | −4.15502e10 | −0.121034 | ||||||||
\(367\) | 2.61752e11 | 0.753169 | 0.376584 | − | 0.926382i | \(-0.377098\pi\) | ||||
0.376584 | + | 0.926382i | \(0.377098\pi\) | |||||||
\(368\) | −1.70238e11 | −0.483884 | ||||||||
\(369\) | −1.40253e11 | −0.393816 | ||||||||
\(370\) | −1.17478e11 | −0.325874 | ||||||||
\(371\) | −8.74107e11 | −2.39542 | ||||||||
\(372\) | −3.59461e11 | −0.973215 | ||||||||
\(373\) | 2.92272e11 | 0.781803 | 0.390902 | − | 0.920433i | \(-0.372163\pi\) | ||||
0.390902 | + | 0.920433i | \(0.372163\pi\) | |||||||
\(374\) | 5.00374e10 | 0.132243 | ||||||||
\(375\) | 3.46579e11 | 0.905027 | ||||||||
\(376\) | −1.41710e11 | −0.365642 | ||||||||
\(377\) | 8.58011e11 | 2.18754 | ||||||||
\(378\) | 1.65251e11 | 0.416322 | ||||||||
\(379\) | 4.04776e11 | 1.00772 | 0.503859 | − | 0.863786i | \(-0.331913\pi\) | ||||
0.503859 | + | 0.863786i | \(0.331913\pi\) | |||||||
\(380\) | −9.60092e10 | −0.236204 | ||||||||
\(381\) | 3.80397e11 | 0.924857 | ||||||||
\(382\) | −8.23497e10 | −0.197869 | ||||||||
\(383\) | −6.03567e11 | −1.43328 | −0.716640 | − | 0.697443i | \(-0.754321\pi\) | ||||
−0.716640 | + | 0.697443i | \(0.754321\pi\) | |||||||
\(384\) | 2.52168e11 | 0.591833 | ||||||||
\(385\) | −4.33434e11 | −1.00543 | ||||||||
\(386\) | −1.11420e10 | −0.0255459 | ||||||||
\(387\) | 1.97537e10 | 0.0447660 | ||||||||
\(388\) | 4.93440e11 | 1.10533 | ||||||||
\(389\) | −4.00613e11 | −0.887057 | −0.443529 | − | 0.896260i | \(-0.646274\pi\) | ||||
−0.443529 | + | 0.896260i | \(0.646274\pi\) | |||||||
\(390\) | −8.93549e10 | −0.195581 | ||||||||
\(391\) | 2.98613e11 | 0.646121 | ||||||||
\(392\) | 5.16175e11 | 1.10410 | ||||||||
\(393\) | −3.79907e11 | −0.803362 | ||||||||
\(394\) | 1.16859e11 | 0.244302 | ||||||||
\(395\) | −2.93044e11 | −0.605683 | ||||||||
\(396\) | 7.94872e10 | 0.162431 | ||||||||
\(397\) | −7.65107e11 | −1.54584 | −0.772920 | − | 0.634503i | \(-0.781205\pi\) | ||||
−0.772920 | + | 0.634503i | \(0.781205\pi\) | |||||||
\(398\) | −1.09168e11 | −0.218083 | ||||||||
\(399\) | −2.33055e11 | −0.460341 | ||||||||
\(400\) | −9.84510e10 | −0.192287 | ||||||||
\(401\) | 5.13976e11 | 0.992643 | 0.496322 | − | 0.868139i | \(-0.334684\pi\) | ||||
0.496322 | + | 0.868139i | \(0.334684\pi\) | |||||||
\(402\) | 2.99157e10 | 0.0571324 | ||||||||
\(403\) | −8.63924e11 | −1.63156 | ||||||||
\(404\) | 1.50581e11 | 0.281225 | ||||||||
\(405\) | 2.97296e11 | 0.549088 | ||||||||
\(406\) | 3.38164e11 | 0.617675 | ||||||||
\(407\) | −6.04445e11 | −1.09190 | ||||||||
\(408\) | −2.12354e11 | −0.379393 | ||||||||
\(409\) | 3.29917e11 | 0.582975 | 0.291488 | − | 0.956575i | \(-0.405850\pi\) | ||||
0.291488 | + | 0.956575i | \(0.405850\pi\) | |||||||
\(410\) | 1.31711e11 | 0.230194 | ||||||||
\(411\) | −4.74621e11 | −0.820462 | ||||||||
\(412\) | 1.88039e11 | 0.321521 | ||||||||
\(413\) | −1.40603e12 | −2.37805 | ||||||||
\(414\) | −1.85183e10 | −0.0309812 | ||||||||
\(415\) | −5.71545e11 | −0.945875 | ||||||||
\(416\) | 4.57792e11 | 0.749459 | ||||||||
\(417\) | 2.78795e11 | 0.451516 | ||||||||
\(418\) | 1.92842e10 | 0.0308964 | ||||||||
\(419\) | 1.13273e11 | 0.179541 | 0.0897707 | − | 0.995962i | \(-0.471387\pi\) | ||||
0.0897707 | + | 0.995962i | \(0.471387\pi\) | |||||||
\(420\) | 9.02118e11 | 1.41463 | ||||||||
\(421\) | −5.70807e11 | −0.885564 | −0.442782 | − | 0.896629i | \(-0.646008\pi\) | ||||
−0.442782 | + | 0.896629i | \(0.646008\pi\) | |||||||
\(422\) | −1.24293e11 | −0.190784 | ||||||||
\(423\) | 1.85801e11 | 0.282173 | ||||||||
\(424\) | −3.06955e11 | −0.461241 | ||||||||
\(425\) | 1.72692e11 | 0.256757 | ||||||||
\(426\) | −1.60866e11 | −0.236658 | ||||||||
\(427\) | 1.00819e12 | 1.46763 | ||||||||
\(428\) | 9.84684e11 | 1.41840 | ||||||||
\(429\) | −4.59746e11 | −0.655331 | ||||||||
\(430\) | −1.85506e10 | −0.0261668 | ||||||||
\(431\) | −5.38814e11 | −0.752127 | −0.376064 | − | 0.926594i | \(-0.622723\pi\) | ||||
−0.376064 | + | 0.926594i | \(0.622723\pi\) | |||||||
\(432\) | −6.99447e11 | −0.966224 | ||||||||
\(433\) | −8.64588e11 | −1.18199 | −0.590995 | − | 0.806675i | \(-0.701265\pi\) | ||||
−0.590995 | + | 0.806675i | \(0.701265\pi\) | |||||||
\(434\) | −3.40494e11 | −0.460687 | ||||||||
\(435\) | 8.96297e11 | 1.20019 | ||||||||
\(436\) | −2.78033e11 | −0.368474 | ||||||||
\(437\) | 1.15084e11 | 0.150956 | ||||||||
\(438\) | 1.67468e10 | 0.0217419 | ||||||||
\(439\) | −3.81449e10 | −0.0490170 | −0.0245085 | − | 0.999700i | \(-0.507802\pi\) | ||||
−0.0245085 | + | 0.999700i | \(0.507802\pi\) | |||||||
\(440\) | −1.52206e11 | −0.193596 | ||||||||
\(441\) | −6.76774e11 | −0.852059 | ||||||||
\(442\) | −2.50298e11 | −0.311931 | ||||||||
\(443\) | 4.04411e11 | 0.498891 | 0.249446 | − | 0.968389i | \(-0.419752\pi\) | ||||
0.249446 | + | 0.968389i | \(0.419752\pi\) | |||||||
\(444\) | 1.25805e12 | 1.53629 | ||||||||
\(445\) | −7.63103e11 | −0.922494 | ||||||||
\(446\) | 3.80024e10 | 0.0454783 | ||||||||
\(447\) | 4.00956e11 | 0.475021 | ||||||||
\(448\) | −1.31644e12 | −1.54400 | ||||||||
\(449\) | 5.23002e11 | 0.607288 | 0.303644 | − | 0.952786i | \(-0.401797\pi\) | ||||
0.303644 | + | 0.952786i | \(0.401797\pi\) | |||||||
\(450\) | −1.07094e10 | −0.0123114 | ||||||||
\(451\) | 6.77675e11 | 0.771307 | ||||||||
\(452\) | −4.44069e11 | −0.500412 | ||||||||
\(453\) | −3.19782e11 | −0.356789 | ||||||||
\(454\) | 8.45400e10 | 0.0933923 | ||||||||
\(455\) | 2.16814e12 | 2.37157 | ||||||||
\(456\) | −8.18403e10 | −0.0886392 | ||||||||
\(457\) | −1.62214e12 | −1.73966 | −0.869832 | − | 0.493347i | \(-0.835773\pi\) | ||||
−0.869832 | + | 0.493347i | \(0.835773\pi\) | |||||||
\(458\) | 1.01173e10 | 0.0107441 | ||||||||
\(459\) | 1.22690e12 | 1.29018 | ||||||||
\(460\) | −4.45473e11 | −0.463886 | ||||||||
\(461\) | −5.64486e11 | −0.582102 | −0.291051 | − | 0.956708i | \(-0.594005\pi\) | ||||
−0.291051 | + | 0.956708i | \(0.594005\pi\) | |||||||
\(462\) | −1.81198e11 | −0.185039 | ||||||||
\(463\) | −1.76040e11 | −0.178031 | −0.0890156 | − | 0.996030i | \(-0.528372\pi\) | ||||
−0.0890156 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(464\) | −1.43133e12 | −1.43353 | ||||||||
\(465\) | −9.02473e11 | −0.895150 | ||||||||
\(466\) | 9.65129e10 | 0.0948088 | ||||||||
\(467\) | 1.36802e11 | 0.133097 | 0.0665483 | − | 0.997783i | \(-0.478801\pi\) | ||||
0.0665483 | + | 0.997783i | \(0.478801\pi\) | |||||||
\(468\) | −3.97613e11 | −0.383137 | ||||||||
\(469\) | −7.25885e11 | −0.692772 | ||||||||
\(470\) | −1.74485e11 | −0.164937 | ||||||||
\(471\) | 2.65890e11 | 0.248948 | ||||||||
\(472\) | −4.93748e11 | −0.457896 | ||||||||
\(473\) | −9.54461e10 | −0.0876765 | ||||||||
\(474\) | −1.22507e11 | −0.111470 | ||||||||
\(475\) | 6.65549e10 | 0.0599872 | ||||||||
\(476\) | 2.52699e12 | 2.25617 | ||||||||
\(477\) | 4.02458e11 | 0.355949 | ||||||||
\(478\) | 1.60140e11 | 0.140305 | ||||||||
\(479\) | −4.86473e11 | −0.422230 | −0.211115 | − | 0.977461i | \(-0.567709\pi\) | ||||
−0.211115 | + | 0.977461i | \(0.567709\pi\) | |||||||
\(480\) | 4.78219e11 | 0.411189 | ||||||||
\(481\) | 3.02357e12 | 2.57554 | ||||||||
\(482\) | −3.53315e11 | −0.298160 | ||||||||
\(483\) | −1.08135e12 | −0.904075 | ||||||||
\(484\) | 7.77843e11 | 0.644300 | ||||||||
\(485\) | 1.23884e12 | 1.01667 | ||||||||
\(486\) | −1.34904e11 | −0.109688 | ||||||||
\(487\) | −8.10600e11 | −0.653020 | −0.326510 | − | 0.945194i | \(-0.605873\pi\) | ||||
−0.326510 | + | 0.945194i | \(0.605873\pi\) | |||||||
\(488\) | 3.54039e11 | 0.282593 | ||||||||
\(489\) | 2.50375e11 | 0.198016 | ||||||||
\(490\) | 6.35556e11 | 0.498048 | ||||||||
\(491\) | 1.12030e12 | 0.869893 | 0.434947 | − | 0.900456i | \(-0.356767\pi\) | ||||
0.434947 | + | 0.900456i | \(0.356767\pi\) | |||||||
\(492\) | −1.41046e12 | −1.08522 | ||||||||
\(493\) | 2.51068e12 | 1.91417 | ||||||||
\(494\) | −9.64640e10 | −0.0728776 | ||||||||
\(495\) | 1.99563e11 | 0.149402 | ||||||||
\(496\) | 1.44119e12 | 1.06919 | ||||||||
\(497\) | 3.90331e12 | 2.86966 | ||||||||
\(498\) | −2.38935e11 | −0.174079 | ||||||||
\(499\) | 1.93337e12 | 1.39593 | 0.697963 | − | 0.716134i | \(-0.254090\pi\) | ||||
0.697963 | + | 0.716134i | \(0.254090\pi\) | |||||||
\(500\) | −1.44829e12 | −1.03631 | ||||||||
\(501\) | −9.37033e11 | −0.664485 | ||||||||
\(502\) | −1.02780e11 | −0.0722341 | ||||||||
\(503\) | −9.53953e11 | −0.664463 | −0.332232 | − | 0.943198i | \(-0.607802\pi\) | ||||
−0.332232 | + | 0.943198i | \(0.607802\pi\) | |||||||
\(504\) | −3.19536e11 | −0.220588 | ||||||||
\(505\) | 3.78052e11 | 0.258667 | ||||||||
\(506\) | 8.94768e10 | 0.0606783 | ||||||||
\(507\) | 1.04928e12 | 0.705268 | ||||||||
\(508\) | −1.58961e12 | −1.05902 | ||||||||
\(509\) | −2.27539e12 | −1.50254 | −0.751270 | − | 0.659995i | \(-0.770558\pi\) | ||||
−0.751270 | + | 0.659995i | \(0.770558\pi\) | |||||||
\(510\) | −2.61467e11 | −0.171140 | ||||||||
\(511\) | −4.06349e11 | −0.263636 | ||||||||
\(512\) | −1.28933e12 | −0.829180 | ||||||||
\(513\) | 4.72840e11 | 0.301430 | ||||||||
\(514\) | 6.52392e10 | 0.0412263 | ||||||||
\(515\) | 4.72095e11 | 0.295731 | ||||||||
\(516\) | 1.98655e11 | 0.123360 | ||||||||
\(517\) | −8.97755e11 | −0.552650 | ||||||||
\(518\) | 1.19167e12 | 0.727228 | ||||||||
\(519\) | −1.33726e12 | −0.809027 | ||||||||
\(520\) | 7.61370e11 | 0.456647 | ||||||||
\(521\) | 8.63866e11 | 0.513661 | 0.256830 | − | 0.966456i | \(-0.417322\pi\) | ||||
0.256830 | + | 0.966456i | \(0.417322\pi\) | |||||||
\(522\) | −1.55698e11 | −0.0917837 | ||||||||
\(523\) | −3.96246e11 | −0.231583 | −0.115792 | − | 0.993274i | \(-0.536940\pi\) | ||||
−0.115792 | + | 0.993274i | \(0.536940\pi\) | |||||||
\(524\) | 1.58756e12 | 0.919897 | ||||||||
\(525\) | −6.25361e11 | −0.359264 | ||||||||
\(526\) | 5.67903e10 | 0.0323473 | ||||||||
\(527\) | −2.52798e12 | −1.42767 | ||||||||
\(528\) | 7.66945e11 | 0.429449 | ||||||||
\(529\) | −1.26717e12 | −0.703534 | ||||||||
\(530\) | −3.77947e11 | −0.208061 | ||||||||
\(531\) | 6.47369e11 | 0.353368 | ||||||||
\(532\) | 9.73891e11 | 0.527118 | ||||||||
\(533\) | −3.38989e12 | −1.81933 | ||||||||
\(534\) | −3.19016e11 | −0.169776 | ||||||||
\(535\) | 2.47217e12 | 1.30463 | ||||||||
\(536\) | −2.54904e11 | −0.133394 | ||||||||
\(537\) | −1.82186e12 | −0.945434 | ||||||||
\(538\) | −6.07941e11 | −0.312854 | ||||||||
\(539\) | 3.27004e12 | 1.66880 | ||||||||
\(540\) | −1.83029e12 | −0.926292 | ||||||||
\(541\) | −3.00813e12 | −1.50976 | −0.754881 | − | 0.655862i | \(-0.772305\pi\) | ||||
−0.754881 | + | 0.655862i | \(0.772305\pi\) | |||||||
\(542\) | 1.56035e11 | 0.0776650 | ||||||||
\(543\) | 1.33073e12 | 0.656888 | ||||||||
\(544\) | 1.33957e12 | 0.655800 | ||||||||
\(545\) | −6.98037e11 | −0.338918 | ||||||||
\(546\) | 9.06392e11 | 0.436465 | ||||||||
\(547\) | −1.67014e12 | −0.797645 | −0.398823 | − | 0.917028i | \(-0.630581\pi\) | ||||
−0.398823 | + | 0.917028i | \(0.630581\pi\) | |||||||
\(548\) | 1.98335e12 | 0.939478 | ||||||||
\(549\) | −4.64192e11 | −0.218083 | ||||||||
\(550\) | 5.17457e10 | 0.0241125 | ||||||||
\(551\) | 9.67606e11 | 0.447215 | ||||||||
\(552\) | −3.79731e11 | −0.174081 | ||||||||
\(553\) | 2.97255e12 | 1.35166 | ||||||||
\(554\) | −4.97756e11 | −0.224503 | ||||||||
\(555\) | 3.15849e12 | 1.41306 | ||||||||
\(556\) | −1.16503e12 | −0.517012 | ||||||||
\(557\) | −3.27102e12 | −1.43991 | −0.719954 | − | 0.694022i | \(-0.755837\pi\) | ||||
−0.719954 | + | 0.694022i | \(0.755837\pi\) | |||||||
\(558\) | 1.56771e11 | 0.0684560 | ||||||||
\(559\) | 4.77443e11 | 0.206809 | ||||||||
\(560\) | −3.61687e12 | −1.55413 | ||||||||
\(561\) | −1.34529e12 | −0.573435 | ||||||||
\(562\) | −1.24837e11 | −0.0527874 | ||||||||
\(563\) | −3.16570e12 | −1.32795 | −0.663976 | − | 0.747754i | \(-0.731132\pi\) | ||||
−0.663976 | + | 0.747754i | \(0.731132\pi\) | |||||||
\(564\) | 1.86852e12 | 0.777575 | ||||||||
\(565\) | −1.11489e12 | −0.460272 | ||||||||
\(566\) | −4.54448e11 | −0.186127 | ||||||||
\(567\) | −3.01569e12 | −1.22536 | ||||||||
\(568\) | 1.37070e12 | 0.552555 | ||||||||
\(569\) | −3.41258e12 | −1.36483 | −0.682414 | − | 0.730966i | \(-0.739070\pi\) | ||||
−0.682414 | + | 0.730966i | \(0.739070\pi\) | |||||||
\(570\) | −1.00768e11 | −0.0399841 | ||||||||
\(571\) | 5.10789e11 | 0.201085 | 0.100542 | − | 0.994933i | \(-0.467942\pi\) | ||||
0.100542 | + | 0.994933i | \(0.467942\pi\) | |||||||
\(572\) | 1.92119e12 | 0.750393 | ||||||||
\(573\) | 2.21403e12 | 0.858002 | ||||||||
\(574\) | −1.33604e12 | −0.513707 | ||||||||
\(575\) | 3.08808e11 | 0.117810 | ||||||||
\(576\) | 6.06116e11 | 0.229432 | ||||||||
\(577\) | 3.29567e12 | 1.23781 | 0.618903 | − | 0.785467i | \(-0.287577\pi\) | ||||
0.618903 | + | 0.785467i | \(0.287577\pi\) | |||||||
\(578\) | −2.12294e11 | −0.0791157 | ||||||||
\(579\) | 2.99562e11 | 0.110773 | ||||||||
\(580\) | −3.74545e12 | −1.37429 | ||||||||
\(581\) | 5.79759e12 | 2.11084 | ||||||||
\(582\) | 5.17900e11 | 0.187108 | ||||||||
\(583\) | −1.94460e12 | −0.697144 | ||||||||
\(584\) | −1.42695e11 | −0.0507634 | ||||||||
\(585\) | −9.98258e11 | −0.352404 | ||||||||
\(586\) | 8.41226e11 | 0.294695 | ||||||||
\(587\) | 3.75472e12 | 1.30529 | 0.652644 | − | 0.757665i | \(-0.273660\pi\) | ||||
0.652644 | + | 0.757665i | \(0.273660\pi\) | |||||||
\(588\) | −6.80603e12 | −2.34799 | ||||||||
\(589\) | −9.74274e11 | −0.333551 | ||||||||
\(590\) | −6.07942e11 | −0.206551 | ||||||||
\(591\) | −3.14183e12 | −1.05935 | ||||||||
\(592\) | −5.04390e12 | −1.68779 | ||||||||
\(593\) | −7.28844e11 | −0.242041 | −0.121020 | − | 0.992650i | \(-0.538617\pi\) | ||||
−0.121020 | + | 0.992650i | \(0.538617\pi\) | |||||||
\(594\) | 3.67628e11 | 0.121163 | ||||||||
\(595\) | 6.34432e12 | 2.07520 | ||||||||
\(596\) | −1.67552e12 | −0.543927 | ||||||||
\(597\) | 2.93507e12 | 0.945658 | ||||||||
\(598\) | −4.47583e11 | −0.143126 | ||||||||
\(599\) | 1.79149e12 | 0.568582 | 0.284291 | − | 0.958738i | \(-0.408242\pi\) | ||||
0.284291 | + | 0.958738i | \(0.408242\pi\) | |||||||
\(600\) | −2.19604e11 | −0.0691767 | ||||||||
\(601\) | 3.67032e11 | 0.114754 | 0.0573772 | − | 0.998353i | \(-0.481726\pi\) | ||||
0.0573772 | + | 0.998353i | \(0.481726\pi\) | |||||||
\(602\) | 1.88172e11 | 0.0583944 | ||||||||
\(603\) | 3.34213e11 | 0.102943 | ||||||||
\(604\) | 1.33631e12 | 0.408545 | ||||||||
\(605\) | 1.95287e12 | 0.592618 | ||||||||
\(606\) | 1.58045e11 | 0.0476052 | ||||||||
\(607\) | −3.38377e12 | −1.01170 | −0.505850 | − | 0.862622i | \(-0.668821\pi\) | ||||
−0.505850 | + | 0.862622i | \(0.668821\pi\) | |||||||
\(608\) | 5.16266e11 | 0.153217 | ||||||||
\(609\) | −9.09179e12 | −2.67838 | ||||||||
\(610\) | 4.35921e11 | 0.127475 | ||||||||
\(611\) | 4.49078e12 | 1.30357 | ||||||||
\(612\) | −1.16348e12 | −0.335257 | ||||||||
\(613\) | 3.01980e11 | 0.0863786 | 0.0431893 | − | 0.999067i | \(-0.486248\pi\) | ||||
0.0431893 | + | 0.999067i | \(0.486248\pi\) | |||||||
\(614\) | 2.60298e11 | 0.0739116 | ||||||||
\(615\) | −3.54115e12 | −0.998174 | ||||||||
\(616\) | 1.54394e12 | 0.432033 | ||||||||
\(617\) | 3.65251e12 | 1.01463 | 0.507315 | − | 0.861761i | \(-0.330638\pi\) | ||||
0.507315 | + | 0.861761i | \(0.330638\pi\) | |||||||
\(618\) | 1.97360e11 | 0.0544265 | ||||||||
\(619\) | 1.83928e10 | 0.00503546 | 0.00251773 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251773 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(620\) | 3.77126e12 | 1.02500 | ||||||||
\(621\) | 2.19393e12 | 0.591986 | ||||||||
\(622\) | 6.41239e11 | 0.171776 | ||||||||
\(623\) | 7.74071e12 | 2.05866 | ||||||||
\(624\) | −3.83643e12 | −1.01297 | ||||||||
\(625\) | −2.81072e12 | −0.736815 | ||||||||
\(626\) | 6.06257e11 | 0.157787 | ||||||||
\(627\) | −5.18471e11 | −0.133974 | ||||||||
\(628\) | −1.11110e12 | −0.285060 | ||||||||
\(629\) | 8.84747e12 | 2.25367 | ||||||||
\(630\) | −3.93438e11 | −0.0995049 | ||||||||
\(631\) | −3.45921e12 | −0.868650 | −0.434325 | − | 0.900756i | \(-0.643013\pi\) | ||||
−0.434325 | + | 0.900756i | \(0.643013\pi\) | |||||||
\(632\) | 1.04385e12 | 0.260263 | ||||||||
\(633\) | 3.34172e12 | 0.827282 | ||||||||
\(634\) | −2.44157e11 | −0.0600162 | ||||||||
\(635\) | −3.99091e12 | −0.974069 | ||||||||
\(636\) | 4.04736e12 | 0.980877 | ||||||||
\(637\) | −1.63575e13 | −3.93631 | ||||||||
\(638\) | 7.52304e11 | 0.179763 | ||||||||
\(639\) | −1.79717e12 | −0.426418 | ||||||||
\(640\) | −2.64560e12 | −0.623325 | ||||||||
\(641\) | −1.71702e12 | −0.401710 | −0.200855 | − | 0.979621i | \(-0.564372\pi\) | ||||
−0.200855 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(642\) | 1.03349e12 | 0.240105 | ||||||||
\(643\) | −5.95110e11 | −0.137293 | −0.0686464 | − | 0.997641i | \(-0.521868\pi\) | ||||
−0.0686464 | + | 0.997641i | \(0.521868\pi\) | |||||||
\(644\) | 4.51876e12 | 1.03522 | ||||||||
\(645\) | 4.98747e11 | 0.113465 | ||||||||
\(646\) | −2.82270e11 | −0.0637702 | ||||||||
\(647\) | −2.77664e12 | −0.622946 | −0.311473 | − | 0.950255i | \(-0.600822\pi\) | ||||
−0.311473 | + | 0.950255i | \(0.600822\pi\) | |||||||
\(648\) | −1.05900e12 | −0.235944 | ||||||||
\(649\) | −3.12797e12 | −0.692088 | ||||||||
\(650\) | −2.58844e11 | −0.0568758 | ||||||||
\(651\) | 9.15444e12 | 1.99764 | ||||||||
\(652\) | −1.04627e12 | −0.226740 | ||||||||
\(653\) | 2.92497e12 | 0.629523 | 0.314761 | − | 0.949171i | \(-0.398075\pi\) | ||||
0.314761 | + | 0.949171i | \(0.398075\pi\) | |||||||
\(654\) | −2.91815e11 | −0.0623747 | ||||||||
\(655\) | 3.98577e12 | 0.846109 | ||||||||
\(656\) | 5.65498e12 | 1.19224 | ||||||||
\(657\) | 1.87092e11 | 0.0391752 | ||||||||
\(658\) | 1.76993e12 | 0.368077 | ||||||||
\(659\) | −3.06130e12 | −0.632299 | −0.316149 | − | 0.948709i | \(-0.602390\pi\) | ||||
−0.316149 | + | 0.948709i | \(0.602390\pi\) | |||||||
\(660\) | 2.00692e12 | 0.411701 | ||||||||
\(661\) | 7.09295e12 | 1.44517 | 0.722587 | − | 0.691280i | \(-0.242953\pi\) | ||||
0.722587 | + | 0.691280i | \(0.242953\pi\) | |||||||
\(662\) | −9.20370e11 | −0.186252 | ||||||||
\(663\) | 6.72947e12 | 1.35260 | ||||||||
\(664\) | 2.03590e12 | 0.406444 | ||||||||
\(665\) | 2.44508e12 | 0.484836 | ||||||||
\(666\) | −5.48669e11 | −0.108063 | ||||||||
\(667\) | 4.48960e12 | 0.878297 | ||||||||
\(668\) | 3.91568e12 | 0.760875 | ||||||||
\(669\) | −1.02172e12 | −0.197204 | ||||||||
\(670\) | −3.13859e11 | −0.0601724 | ||||||||
\(671\) | 2.24289e12 | 0.427127 | ||||||||
\(672\) | −4.85092e12 | −0.917620 | ||||||||
\(673\) | 3.65617e12 | 0.687003 | 0.343502 | − | 0.939152i | \(-0.388387\pi\) | ||||
0.343502 | + | 0.939152i | \(0.388387\pi\) | |||||||
\(674\) | −1.05398e12 | −0.196727 | ||||||||
\(675\) | 1.26878e12 | 0.235245 | ||||||||
\(676\) | −4.38473e12 | −0.807574 | ||||||||
\(677\) | −1.69929e12 | −0.310898 | −0.155449 | − | 0.987844i | \(-0.549682\pi\) | ||||
−0.155449 | + | 0.987844i | \(0.549682\pi\) | |||||||
\(678\) | −4.66082e11 | −0.0847088 | ||||||||
\(679\) | −1.25665e13 | −2.26882 | ||||||||
\(680\) | 2.22790e12 | 0.399581 | ||||||||
\(681\) | −2.27292e12 | −0.404970 | ||||||||
\(682\) | −7.57488e11 | −0.134074 | ||||||||
\(683\) | −3.57423e12 | −0.628477 | −0.314239 | − | 0.949344i | \(-0.601749\pi\) | ||||
−0.314239 | + | 0.949344i | \(0.601749\pi\) | |||||||
\(684\) | −4.48401e11 | −0.0783274 | ||||||||
\(685\) | 4.97945e12 | 0.864119 | ||||||||
\(686\) | −4.22582e12 | −0.728539 | ||||||||
\(687\) | −2.72011e11 | −0.0465887 | ||||||||
\(688\) | −7.96467e11 | −0.135525 | ||||||||
\(689\) | 9.72735e12 | 1.64440 | ||||||||
\(690\) | −4.67555e11 | −0.0785257 | ||||||||
\(691\) | 9.20422e11 | 0.153580 | 0.0767902 | − | 0.997047i | \(-0.475533\pi\) | ||||
0.0767902 | + | 0.997047i | \(0.475533\pi\) | |||||||
\(692\) | 5.58815e12 | 0.926384 | ||||||||
\(693\) | −2.02431e12 | −0.333409 | ||||||||
\(694\) | −7.14588e10 | −0.0116933 | ||||||||
\(695\) | −2.92496e12 | −0.475541 | ||||||||
\(696\) | −3.19271e12 | −0.515724 | ||||||||
\(697\) | −9.91937e12 | −1.59198 | ||||||||
\(698\) | 6.20360e11 | 0.0989224 | ||||||||
\(699\) | −2.59482e12 | −0.411112 | ||||||||
\(700\) | 2.61326e12 | 0.411379 | ||||||||
\(701\) | 3.78617e11 | 0.0592200 | 0.0296100 | − | 0.999562i | \(-0.490573\pi\) | ||||
0.0296100 | + | 0.999562i | \(0.490573\pi\) | |||||||
\(702\) | −1.83896e12 | −0.285796 | ||||||||
\(703\) | 3.40978e12 | 0.526535 | ||||||||
\(704\) | −2.92864e12 | −0.449354 | ||||||||
\(705\) | 4.69116e12 | 0.715203 | ||||||||
\(706\) | −1.38504e11 | −0.0209817 | ||||||||
\(707\) | −3.83486e12 | −0.577248 | ||||||||
\(708\) | 6.51032e12 | 0.973762 | ||||||||
\(709\) | −4.49168e12 | −0.667576 | −0.333788 | − | 0.942648i | \(-0.608327\pi\) | ||||
−0.333788 | + | 0.942648i | \(0.608327\pi\) | |||||||
\(710\) | 1.68772e12 | 0.249251 | ||||||||
\(711\) | −1.36863e12 | −0.200850 | ||||||||
\(712\) | 2.71826e12 | 0.396397 | ||||||||
\(713\) | −4.52054e12 | −0.655069 | ||||||||
\(714\) | 2.65225e12 | 0.381920 | ||||||||
\(715\) | 4.82339e12 | 0.690201 | ||||||||
\(716\) | 7.61321e12 | 1.08258 | ||||||||
\(717\) | −4.30549e12 | −0.608395 | ||||||||
\(718\) | −4.02842e11 | −0.0565684 | ||||||||
\(719\) | −8.71449e12 | −1.21608 | −0.608039 | − | 0.793907i | \(-0.708044\pi\) | ||||
−0.608039 | + | 0.793907i | \(0.708044\pi\) | |||||||
\(720\) | 1.66529e12 | 0.230936 | ||||||||
\(721\) | −4.78880e12 | −0.659961 | ||||||||
\(722\) | 1.30651e12 | 0.178935 | ||||||||
\(723\) | 9.49914e12 | 1.29289 | ||||||||
\(724\) | −5.56087e12 | −0.752176 | ||||||||
\(725\) | 2.59640e12 | 0.349020 | ||||||||
\(726\) | 8.16401e11 | 0.109066 | ||||||||
\(727\) | 1.20858e13 | 1.60461 | 0.802306 | − | 0.596913i | \(-0.203606\pi\) | ||||
0.802306 | + | 0.596913i | \(0.203606\pi\) | |||||||
\(728\) | −7.72313e12 | −1.01907 | ||||||||
\(729\) | 8.35698e12 | 1.09591 | ||||||||
\(730\) | −1.75697e11 | −0.0228988 | ||||||||
\(731\) | 1.39708e12 | 0.180964 | ||||||||
\(732\) | −4.66819e12 | −0.600964 | ||||||||
\(733\) | −2.17693e12 | −0.278534 | −0.139267 | − | 0.990255i | \(-0.544475\pi\) | ||||
−0.139267 | + | 0.990255i | \(0.544475\pi\) | |||||||
\(734\) | −1.14803e12 | −0.145989 | ||||||||
\(735\) | −1.70874e13 | −2.15965 | ||||||||
\(736\) | 2.39542e12 | 0.300907 | ||||||||
\(737\) | −1.61486e12 | −0.201619 | ||||||||
\(738\) | 6.15142e11 | 0.0763346 | ||||||||
\(739\) | 1.41514e13 | 1.74542 | 0.872709 | − | 0.488240i | \(-0.162361\pi\) | ||||
0.872709 | + | 0.488240i | \(0.162361\pi\) | |||||||
\(740\) | −1.31987e13 | −1.61804 | ||||||||
\(741\) | 2.59351e12 | 0.316014 | ||||||||
\(742\) | 3.83379e12 | 0.464313 | ||||||||
\(743\) | −1.36261e13 | −1.64030 | −0.820148 | − | 0.572152i | \(-0.806109\pi\) | ||||
−0.820148 | + | 0.572152i | \(0.806109\pi\) | |||||||
\(744\) | 3.21471e12 | 0.384648 | ||||||||
\(745\) | −4.20660e12 | −0.500297 | ||||||||
\(746\) | −1.28189e12 | −0.151540 | ||||||||
\(747\) | −2.66934e12 | −0.313661 | ||||||||
\(748\) | 5.62172e12 | 0.656617 | ||||||||
\(749\) | −2.50770e13 | −2.91144 | ||||||||
\(750\) | −1.52008e12 | −0.175425 | ||||||||
\(751\) | −1.39601e13 | −1.60143 | −0.800715 | − | 0.599046i | \(-0.795547\pi\) | ||||
−0.800715 | + | 0.599046i | \(0.795547\pi\) | |||||||
\(752\) | −7.49148e12 | −0.854254 | ||||||||
\(753\) | 2.76332e12 | 0.313223 | ||||||||
\(754\) | −3.76319e12 | −0.424019 | ||||||||
\(755\) | 3.35497e12 | 0.375774 | ||||||||
\(756\) | 1.85660e13 | 2.06714 | ||||||||
\(757\) | 6.22034e12 | 0.688467 | 0.344233 | − | 0.938884i | \(-0.388139\pi\) | ||||
0.344233 | + | 0.938884i | \(0.388139\pi\) | |||||||
\(758\) | −1.77533e12 | −0.195329 | ||||||||
\(759\) | −2.40565e12 | −0.263115 | ||||||||
\(760\) | 8.58622e11 | 0.0933557 | ||||||||
\(761\) | −7.99871e12 | −0.864548 | −0.432274 | − | 0.901742i | \(-0.642289\pi\) | ||||
−0.432274 | + | 0.901742i | \(0.642289\pi\) | |||||||
\(762\) | −1.66840e12 | −0.179268 | ||||||||
\(763\) | 7.08070e12 | 0.756338 | ||||||||
\(764\) | −9.25202e12 | −0.982464 | ||||||||
\(765\) | −2.92107e12 | −0.308365 | ||||||||
\(766\) | 2.64721e12 | 0.277818 | ||||||||
\(767\) | 1.56468e13 | 1.63248 | ||||||||
\(768\) | 5.22741e12 | 0.542202 | ||||||||
\(769\) | −1.87310e13 | −1.93149 | −0.965745 | − | 0.259493i | \(-0.916444\pi\) | ||||
−0.965745 | + | 0.259493i | \(0.916444\pi\) | |||||||
\(770\) | 1.90102e12 | 0.194885 | ||||||||
\(771\) | −1.75401e12 | −0.178767 | ||||||||
\(772\) | −1.25181e12 | −0.126842 | ||||||||
\(773\) | −7.45839e12 | −0.751342 | −0.375671 | − | 0.926753i | \(-0.622588\pi\) | ||||
−0.375671 | + | 0.926753i | \(0.622588\pi\) | |||||||
\(774\) | −8.66387e10 | −0.00867716 | ||||||||
\(775\) | −2.61429e12 | −0.260313 | ||||||||
\(776\) | −4.41289e12 | −0.436863 | ||||||||
\(777\) | −3.20388e13 | −3.15342 | ||||||||
\(778\) | 1.75707e12 | 0.171941 | ||||||||
\(779\) | −3.82288e12 | −0.371939 | ||||||||
\(780\) | −1.00391e13 | −0.971108 | ||||||||
\(781\) | 8.68360e12 | 0.835161 | ||||||||
\(782\) | −1.30970e12 | −0.125240 | ||||||||
\(783\) | 1.84462e13 | 1.75379 | ||||||||
\(784\) | 2.72875e13 | 2.57953 | ||||||||
\(785\) | −2.78957e12 | −0.262194 | ||||||||
\(786\) | 1.66626e12 | 0.155718 | ||||||||
\(787\) | −1.24079e13 | −1.15295 | −0.576476 | − | 0.817114i | \(-0.695573\pi\) | ||||
−0.576476 | + | 0.817114i | \(0.695573\pi\) | |||||||
\(788\) | 1.31291e13 | 1.21302 | ||||||||
\(789\) | −1.52685e12 | −0.140265 | ||||||||
\(790\) | 1.28527e12 | 0.117402 | ||||||||
\(791\) | 1.13092e13 | 1.02715 | ||||||||
\(792\) | −7.10863e11 | −0.0641982 | ||||||||
\(793\) | −1.12194e13 | −1.00749 | ||||||||
\(794\) | 3.35572e12 | 0.299636 | ||||||||
\(795\) | 1.01614e13 | 0.902197 | ||||||||
\(796\) | −1.22651e13 | −1.08283 | ||||||||
\(797\) | 4.11416e12 | 0.361176 | 0.180588 | − | 0.983559i | \(-0.442200\pi\) | ||||
0.180588 | + | 0.983559i | \(0.442200\pi\) | |||||||
\(798\) | 1.02217e12 | 0.0892295 | ||||||||
\(799\) | 1.31408e13 | 1.14067 | ||||||||
\(800\) | 1.38531e12 | 0.119575 | ||||||||
\(801\) | −3.56399e12 | −0.305908 | ||||||||
\(802\) | −2.25427e12 | −0.192408 | ||||||||
\(803\) | −9.03993e11 | −0.0767265 | ||||||||
\(804\) | 3.36105e12 | 0.283676 | ||||||||
\(805\) | 1.13449e13 | 0.952181 | ||||||||
\(806\) | 3.78913e12 | 0.316251 | ||||||||
\(807\) | 1.63450e13 | 1.35660 | ||||||||
\(808\) | −1.34666e12 | −0.111150 | ||||||||
\(809\) | 1.87181e13 | 1.53636 | 0.768182 | − | 0.640231i | \(-0.221162\pi\) | ||||
0.768182 | + | 0.640231i | \(0.221162\pi\) | |||||||
\(810\) | −1.30393e12 | −0.106432 | ||||||||
\(811\) | −1.17522e13 | −0.953949 | −0.476975 | − | 0.878917i | \(-0.658267\pi\) | ||||
−0.476975 | + | 0.878917i | \(0.658267\pi\) | |||||||
\(812\) | 3.79928e13 | 3.06690 | ||||||||
\(813\) | −4.19512e12 | −0.336773 | ||||||||
\(814\) | 2.65107e12 | 0.211646 | ||||||||
\(815\) | −2.62679e12 | −0.208553 | ||||||||
\(816\) | −1.12260e13 | −0.886382 | ||||||||
\(817\) | 5.38428e11 | 0.0422793 | ||||||||
\(818\) | −1.44700e12 | −0.113000 | ||||||||
\(819\) | 1.01261e13 | 0.786435 | ||||||||
\(820\) | 1.47978e13 | 1.14297 | ||||||||
\(821\) | 2.29795e13 | 1.76521 | 0.882605 | − | 0.470115i | \(-0.155787\pi\) | ||||
0.882605 | + | 0.470115i | \(0.155787\pi\) | |||||||
\(822\) | 2.08166e12 | 0.159033 | ||||||||
\(823\) | 7.89246e12 | 0.599671 | 0.299836 | − | 0.953991i | \(-0.403068\pi\) | ||||
0.299836 | + | 0.953991i | \(0.403068\pi\) | |||||||
\(824\) | −1.68165e12 | −0.127076 | ||||||||
\(825\) | −1.39122e12 | −0.104557 | ||||||||
\(826\) | 6.16680e12 | 0.460946 | ||||||||
\(827\) | −1.43874e13 | −1.06957 | −0.534784 | − | 0.844989i | \(-0.679607\pi\) | ||||
−0.534784 | + | 0.844989i | \(0.679607\pi\) | |||||||
\(828\) | −2.08054e12 | −0.153829 | ||||||||
\(829\) | −1.40139e12 | −0.103053 | −0.0515267 | − | 0.998672i | \(-0.516409\pi\) | ||||
−0.0515267 | + | 0.998672i | \(0.516409\pi\) | |||||||
\(830\) | 2.50677e12 | 0.183342 | ||||||||
\(831\) | 1.33826e13 | 0.973496 | ||||||||
\(832\) | 1.46497e13 | 1.05992 | ||||||||
\(833\) | −4.78648e13 | −3.44440 | ||||||||
\(834\) | −1.22278e12 | −0.0875189 | ||||||||
\(835\) | 9.83081e12 | 0.699842 | ||||||||
\(836\) | 2.16659e12 | 0.153408 | ||||||||
\(837\) | −1.85733e13 | −1.30805 | ||||||||
\(838\) | −4.96811e11 | −0.0348011 | ||||||||
\(839\) | −2.01539e13 | −1.40420 | −0.702101 | − | 0.712078i | \(-0.747754\pi\) | ||||
−0.702101 | + | 0.712078i | \(0.747754\pi\) | |||||||
\(840\) | −8.06775e12 | −0.559108 | ||||||||
\(841\) | 2.32405e13 | 1.60200 | ||||||||
\(842\) | 2.50353e12 | 0.171652 | ||||||||
\(843\) | 3.35634e12 | 0.228898 | ||||||||
\(844\) | −1.39644e13 | −0.947287 | ||||||||
\(845\) | −1.10084e13 | −0.742796 | ||||||||
\(846\) | −8.14914e11 | −0.0546947 | ||||||||
\(847\) | −1.98094e13 | −1.32250 | ||||||||
\(848\) | −1.62271e13 | −1.07760 | ||||||||
\(849\) | 1.22182e13 | 0.807089 | ||||||||
\(850\) | −7.57420e11 | −0.0497682 | ||||||||
\(851\) | 1.58210e13 | 1.03407 | ||||||||
\(852\) | −1.80734e13 | −1.17506 | ||||||||
\(853\) | −1.31259e13 | −0.848907 | −0.424453 | − | 0.905450i | \(-0.639534\pi\) | ||||
−0.424453 | + | 0.905450i | \(0.639534\pi\) | |||||||
\(854\) | −4.42187e12 | −0.284476 | ||||||||
\(855\) | −1.12577e12 | −0.0720445 | ||||||||
\(856\) | −8.80615e12 | −0.560601 | ||||||||
\(857\) | −8.66664e12 | −0.548829 | −0.274414 | − | 0.961612i | \(-0.588484\pi\) | ||||
−0.274414 | + | 0.961612i | \(0.588484\pi\) | |||||||
\(858\) | 2.01643e12 | 0.127025 | ||||||||
\(859\) | 1.00716e13 | 0.631143 | 0.315571 | − | 0.948902i | \(-0.397804\pi\) | ||||
0.315571 | + | 0.948902i | \(0.397804\pi\) | |||||||
\(860\) | −2.08417e12 | −0.129924 | ||||||||
\(861\) | 3.59204e13 | 2.22755 | ||||||||
\(862\) | 2.36321e12 | 0.145787 | ||||||||
\(863\) | −8.56376e12 | −0.525552 | −0.262776 | − | 0.964857i | \(-0.584638\pi\) | ||||
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(864\) | 9.84195e12 | 0.600854 | ||||||||
\(865\) | 1.40298e13 | 0.852075 | ||||||||
\(866\) | 3.79204e12 | 0.229109 | ||||||||
\(867\) | 5.70769e12 | 0.343063 | ||||||||
\(868\) | −3.82546e13 | −2.28742 | ||||||||
\(869\) | 6.61296e12 | 0.393375 | ||||||||
\(870\) | −3.93111e12 | −0.232637 | ||||||||
\(871\) | 8.07788e12 | 0.475571 | ||||||||
\(872\) | 2.48648e12 | 0.145634 | ||||||||
\(873\) | 5.78589e12 | 0.337137 | ||||||||
\(874\) | −5.04754e11 | −0.0292603 | ||||||||
\(875\) | 3.68837e13 | 2.12715 | ||||||||
\(876\) | 1.88151e12 | 0.107954 | ||||||||
\(877\) | −1.86361e12 | −0.106379 | −0.0531896 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531896 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(878\) | 1.67302e11 | 0.00950113 | ||||||||
\(879\) | −2.26170e13 | −1.27786 | ||||||||
\(880\) | −8.04635e12 | −0.452300 | ||||||||
\(881\) | 1.12984e13 | 0.631868 | 0.315934 | − | 0.948781i | \(-0.397682\pi\) | ||||
0.315934 | + | 0.948781i | \(0.397682\pi\) | |||||||
\(882\) | 2.96830e12 | 0.165158 | ||||||||
\(883\) | −1.69207e13 | −0.936690 | −0.468345 | − | 0.883546i | \(-0.655150\pi\) | ||||
−0.468345 | + | 0.883546i | \(0.655150\pi\) | |||||||
\(884\) | −2.81211e13 | −1.54881 | ||||||||
\(885\) | 1.63450e13 | 0.895654 | ||||||||
\(886\) | −1.77373e12 | −0.0967018 | ||||||||
\(887\) | 1.15592e13 | 0.627004 | 0.313502 | − | 0.949588i | \(-0.398498\pi\) | ||||
0.313502 | + | 0.949588i | \(0.398498\pi\) | |||||||
\(888\) | −1.12509e13 | −0.607195 | ||||||||
\(889\) | 4.04827e13 | 2.17376 | ||||||||
\(890\) | 3.34693e12 | 0.178810 | ||||||||
\(891\) | −6.70893e12 | −0.356618 | ||||||||
\(892\) | 4.26959e12 | 0.225810 | ||||||||
\(893\) | 5.06439e12 | 0.266499 | ||||||||
\(894\) | −1.75857e12 | −0.0920750 | ||||||||
\(895\) | 1.91139e13 | 0.995741 | ||||||||
\(896\) | 2.68362e13 | 1.39103 | ||||||||
\(897\) | 1.20336e13 | 0.620627 | ||||||||
\(898\) | −2.29386e12 | −0.117713 | ||||||||
\(899\) | −3.80078e13 | −1.94068 | ||||||||
\(900\) | −1.20320e12 | −0.0611291 | ||||||||
\(901\) | 2.84638e13 | 1.43890 | ||||||||
\(902\) | −2.97225e12 | −0.149505 | ||||||||
\(903\) | −5.05916e12 | −0.253211 | ||||||||
\(904\) | 3.97136e12 | 0.197780 | ||||||||
\(905\) | −1.39613e13 | −0.691842 | ||||||||
\(906\) | 1.40255e12 | 0.0691577 | ||||||||
\(907\) | −8.82407e12 | −0.432948 | −0.216474 | − | 0.976288i | \(-0.569456\pi\) | ||||
−0.216474 | + | 0.976288i | \(0.569456\pi\) | |||||||
\(908\) | 9.49810e12 | 0.463714 | ||||||||
\(909\) | 1.76565e12 | 0.0857765 | ||||||||
\(910\) | −9.50934e12 | −0.459689 | ||||||||
\(911\) | −9.12800e12 | −0.439079 | −0.219540 | − | 0.975604i | \(-0.570456\pi\) | ||||
−0.219540 | + | 0.975604i | \(0.570456\pi\) | |||||||
\(912\) | −4.32647e12 | −0.207089 | ||||||||
\(913\) | 1.28978e13 | 0.614321 | ||||||||
\(914\) | 7.11463e12 | 0.337205 | ||||||||
\(915\) | −1.17201e13 | −0.552759 | ||||||||
\(916\) | 1.13668e12 | 0.0533468 | ||||||||
\(917\) | −4.04306e13 | −1.88820 | ||||||||
\(918\) | −5.38110e12 | −0.250080 | ||||||||
\(919\) | −1.89826e13 | −0.877881 | −0.438940 | − | 0.898516i | \(-0.644646\pi\) | ||||
−0.438940 | + | 0.898516i | \(0.644646\pi\) | |||||||
\(920\) | 3.98392e12 | 0.183343 | ||||||||
\(921\) | −6.99830e12 | −0.320497 | ||||||||
\(922\) | 2.47581e12 | 0.112831 | ||||||||
\(923\) | −4.34373e13 | −1.96995 | ||||||||
\(924\) | −2.03576e13 | −0.918763 | ||||||||
\(925\) | 9.14953e12 | 0.410924 | ||||||||
\(926\) | 7.72101e11 | 0.0345084 | ||||||||
\(927\) | 2.20487e12 | 0.0980673 | ||||||||
\(928\) | 2.01403e13 | 0.891455 | ||||||||
\(929\) | 1.66439e13 | 0.733136 | 0.366568 | − | 0.930391i | \(-0.380533\pi\) | ||||
0.366568 | + | 0.930391i | \(0.380533\pi\) | |||||||
\(930\) | 3.95820e12 | 0.173510 | ||||||||
\(931\) | −1.84469e13 | −0.804729 | ||||||||
\(932\) | 1.08433e13 | 0.470748 | ||||||||
\(933\) | −1.72402e13 | −0.744860 | ||||||||
\(934\) | −6.00008e11 | −0.0257986 | ||||||||
\(935\) | 1.41141e13 | 0.603948 | ||||||||
\(936\) | 3.55590e12 | 0.151429 | ||||||||
\(937\) | 1.20784e13 | 0.511896 | 0.255948 | − | 0.966691i | \(-0.417612\pi\) | ||||
0.255948 | + | 0.966691i | \(0.417612\pi\) | |||||||
\(938\) | 3.18370e12 | 0.134282 | ||||||||
\(939\) | −1.62997e13 | −0.684201 | ||||||||
\(940\) | −1.96035e13 | −0.818950 | ||||||||
\(941\) | −1.09033e13 | −0.453320 | −0.226660 | − | 0.973974i | \(-0.572781\pi\) | ||||
−0.226660 | + | 0.973974i | \(0.572781\pi\) | |||||||
\(942\) | −1.16618e12 | −0.0482544 | ||||||||
\(943\) | −1.77378e13 | −0.730461 | ||||||||
\(944\) | −2.61019e13 | −1.06979 | ||||||||
\(945\) | 4.66122e13 | 1.90133 | ||||||||
\(946\) | 4.18622e11 | 0.0169946 | ||||||||
\(947\) | 2.49583e13 | 1.00842 | 0.504209 | − | 0.863582i | \(-0.331784\pi\) | ||||
0.504209 | + | 0.863582i | \(0.331784\pi\) | |||||||
\(948\) | −1.37637e13 | −0.553476 | ||||||||
\(949\) | 4.52198e12 | 0.180980 | ||||||||
\(950\) | −2.91907e11 | −0.0116275 | ||||||||
\(951\) | 6.56436e12 | 0.260244 | ||||||||
\(952\) | −2.25992e13 | −0.891715 | ||||||||
\(953\) | −1.44768e13 | −0.568530 | −0.284265 | − | 0.958746i | \(-0.591750\pi\) | ||||
−0.284265 | + | 0.958746i | \(0.591750\pi\) | |||||||
\(954\) | −1.76516e12 | −0.0689949 | ||||||||
\(955\) | −2.32284e13 | −0.903657 | ||||||||
\(956\) | 1.79918e13 | 0.696649 | ||||||||
\(957\) | −2.02263e13 | −0.779492 | ||||||||
\(958\) | 2.13365e12 | 0.0818423 | ||||||||
\(959\) | −5.05102e13 | −1.92839 | ||||||||
\(960\) | 1.53034e13 | 0.581524 | ||||||||
\(961\) | 1.18301e13 | 0.447437 | ||||||||
\(962\) | −1.32612e13 | −0.499225 | ||||||||
\(963\) | 1.15460e13 | 0.432628 | ||||||||
\(964\) | −3.96951e13 | −1.48044 | ||||||||
\(965\) | −3.14284e12 | −0.116667 | ||||||||
\(966\) | 4.74275e12 | 0.175240 | ||||||||
\(967\) | −1.31877e12 | −0.0485007 | −0.0242504 | − | 0.999706i | \(-0.507720\pi\) | ||||
−0.0242504 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(968\) | −6.95635e12 | −0.254649 | ||||||||
\(969\) | 7.58903e12 | 0.276522 | ||||||||
\(970\) | −5.43351e12 | −0.197064 | ||||||||
\(971\) | −5.24865e13 | −1.89479 | −0.947394 | − | 0.320069i | \(-0.896294\pi\) | ||||
−0.947394 | + | 0.320069i | \(0.896294\pi\) | |||||||
\(972\) | −1.51565e13 | −0.544628 | ||||||||
\(973\) | 2.96700e13 | 1.06123 | ||||||||
\(974\) | 3.55525e12 | 0.126577 | ||||||||
\(975\) | 6.95922e12 | 0.246626 | ||||||||
\(976\) | 1.87162e13 | 0.660227 | ||||||||
\(977\) | 5.15657e13 | 1.81065 | 0.905327 | − | 0.424714i | \(-0.139625\pi\) | ||||
0.905327 | + | 0.424714i | \(0.139625\pi\) | |||||||
\(978\) | −1.09813e12 | −0.0383822 | ||||||||
\(979\) | 1.72206e13 | 0.599135 | ||||||||
\(980\) | 7.14050e13 | 2.47293 | ||||||||
\(981\) | −3.26011e12 | −0.112388 | ||||||||
\(982\) | −4.91356e12 | −0.168614 | ||||||||
\(983\) | 2.11520e13 | 0.722537 | 0.361269 | − | 0.932462i | \(-0.382344\pi\) | ||||
0.361269 | + | 0.932462i | \(0.382344\pi\) | |||||||
\(984\) | 1.26139e13 | 0.428917 | ||||||||
\(985\) | 3.29623e13 | 1.11572 | ||||||||
\(986\) | −1.10117e13 | −0.371030 | ||||||||
\(987\) | −4.75859e13 | −1.59607 | ||||||||
\(988\) | −1.08378e13 | −0.361854 | ||||||||
\(989\) | 2.49825e12 | 0.0830334 | ||||||||
\(990\) | −8.75272e11 | −0.0289591 | ||||||||
\(991\) | −4.73443e13 | −1.55932 | −0.779661 | − | 0.626201i | \(-0.784609\pi\) | ||||
−0.779661 | + | 0.626201i | \(0.784609\pi\) | |||||||
\(992\) | −2.02791e13 | −0.664883 | ||||||||
\(993\) | 2.47449e13 | 0.807632 | ||||||||
\(994\) | −1.71197e13 | −0.556235 | ||||||||
\(995\) | −3.07931e13 | −0.995977 | ||||||||
\(996\) | −2.68444e13 | −0.864345 | ||||||||
\(997\) | −1.49776e13 | −0.480081 | −0.240041 | − | 0.970763i | \(-0.577161\pi\) | ||||
−0.240041 | + | 0.970763i | \(0.577161\pi\) | |||||||
\(998\) | −8.47966e12 | −0.270577 | ||||||||
\(999\) | 6.50030e13 | 2.06485 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.10.a.a.1.8 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.8 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.8 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.8 | 15 | 3.2 | odd | 2 |