Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + \cdots + 170905444356096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-33.9466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −35.9466 | −1.58863 | −0.794316 | − | 0.607505i | \(-0.792170\pi\) | ||||
−0.794316 | + | 0.607505i | \(0.792170\pi\) | |||||||
\(3\) | 230.724 | 1.64455 | 0.822274 | − | 0.569092i | \(-0.192705\pi\) | ||||
0.822274 | + | 0.569092i | \(0.192705\pi\) | |||||||
\(4\) | 780.160 | 1.52375 | ||||||||
\(5\) | 434.116 | 0.310628 | 0.155314 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155314 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(6\) | −8293.74 | −2.61258 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −9639.45 | −0.832046 | ||||||||
\(9\) | 33550.4 | 1.70454 | ||||||||
\(10\) | −15605.0 | −0.493474 | ||||||||
\(11\) | −37127.2 | −0.764583 | −0.382292 | − | 0.924042i | \(-0.624865\pi\) | ||||
−0.382292 | + | 0.924042i | \(0.624865\pi\) | |||||||
\(12\) | 180001. | 2.50588 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | −86307.9 | −0.600446 | ||||||||
\(15\) | 100161. | 0.510843 | ||||||||
\(16\) | −52936.3 | −0.201936 | ||||||||
\(17\) | −546796. | −1.58784 | −0.793918 | − | 0.608025i | \(-0.791962\pi\) | ||||
−0.793918 | + | 0.608025i | \(0.791962\pi\) | |||||||
\(18\) | −1.20603e6 | −2.70788 | ||||||||
\(19\) | −902942. | −1.58953 | −0.794765 | − | 0.606917i | \(-0.792406\pi\) | ||||
−0.794765 | + | 0.606917i | \(0.792406\pi\) | |||||||
\(20\) | 338680. | 0.473320 | ||||||||
\(21\) | 553968. | 0.621581 | ||||||||
\(22\) | 1.33460e6 | 1.21464 | ||||||||
\(23\) | −1.65189e6 | −1.23085 | −0.615426 | − | 0.788194i | \(-0.711016\pi\) | ||||
−0.615426 | + | 0.788194i | \(0.711016\pi\) | |||||||
\(24\) | −2.22405e6 | −1.36834 | ||||||||
\(25\) | −1.76467e6 | −0.903510 | ||||||||
\(26\) | −1.02667e6 | −0.440607 | ||||||||
\(27\) | 3.19955e6 | 1.15865 | ||||||||
\(28\) | 1.87316e6 | 0.575923 | ||||||||
\(29\) | −2.15158e6 | −0.564894 | −0.282447 | − | 0.959283i | \(-0.591146\pi\) | ||||
−0.282447 | + | 0.959283i | \(0.591146\pi\) | |||||||
\(30\) | −3.60045e6 | −0.811542 | ||||||||
\(31\) | 2.15325e6 | 0.418762 | 0.209381 | − | 0.977834i | \(-0.432855\pi\) | ||||
0.209381 | + | 0.977834i | \(0.432855\pi\) | |||||||
\(32\) | 6.83828e6 | 1.15285 | ||||||||
\(33\) | −8.56612e6 | −1.25739 | ||||||||
\(34\) | 1.96555e7 | 2.52249 | ||||||||
\(35\) | 1.04231e6 | 0.117407 | ||||||||
\(36\) | 2.61747e7 | 2.59729 | ||||||||
\(37\) | 1.55393e7 | 1.36308 | 0.681542 | − | 0.731779i | \(-0.261310\pi\) | ||||
0.681542 | + | 0.731779i | \(0.261310\pi\) | |||||||
\(38\) | 3.24577e7 | 2.52518 | ||||||||
\(39\) | 6.58970e6 | 0.456116 | ||||||||
\(40\) | −4.18464e6 | −0.258457 | ||||||||
\(41\) | −2.64886e6 | −0.146397 | −0.0731983 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731983 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(42\) | −1.99133e7 | −0.987463 | ||||||||
\(43\) | −3.32538e7 | −1.48331 | −0.741656 | − | 0.670780i | \(-0.765959\pi\) | ||||
−0.741656 | + | 0.670780i | \(0.765959\pi\) | |||||||
\(44\) | −2.89651e7 | −1.16503 | ||||||||
\(45\) | 1.45648e7 | 0.529478 | ||||||||
\(46\) | 5.93799e7 | 1.95537 | ||||||||
\(47\) | −4.58283e6 | −0.136991 | −0.0684956 | − | 0.997651i | \(-0.521820\pi\) | ||||
−0.0684956 | + | 0.997651i | \(0.521820\pi\) | |||||||
\(48\) | −1.22137e7 | −0.332094 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 6.34339e7 | 1.43534 | ||||||||
\(51\) | −1.26159e8 | −2.61127 | ||||||||
\(52\) | 2.22821e7 | 0.422612 | ||||||||
\(53\) | 1.52908e7 | 0.266188 | 0.133094 | − | 0.991103i | \(-0.457509\pi\) | ||||
0.133094 | + | 0.991103i | \(0.457509\pi\) | |||||||
\(54\) | −1.15013e8 | −1.84066 | ||||||||
\(55\) | −1.61175e7 | −0.237501 | ||||||||
\(56\) | −2.31443e7 | −0.314484 | ||||||||
\(57\) | −2.08330e8 | −2.61406 | ||||||||
\(58\) | 7.73421e7 | 0.897408 | ||||||||
\(59\) | −1.05493e8 | −1.13342 | −0.566710 | − | 0.823917i | \(-0.691784\pi\) | ||||
−0.566710 | + | 0.823917i | \(0.691784\pi\) | |||||||
\(60\) | 7.81416e7 | 0.778398 | ||||||||
\(61\) | 515476. | 0.00476677 | 0.00238338 | − | 0.999997i | \(-0.499241\pi\) | ||||
0.00238338 | + | 0.999997i | \(0.499241\pi\) | |||||||
\(62\) | −7.74022e7 | −0.665258 | ||||||||
\(63\) | 8.05546e7 | 0.644255 | ||||||||
\(64\) | −2.18710e8 | −1.62951 | ||||||||
\(65\) | 1.23988e7 | 0.0861528 | ||||||||
\(66\) | 3.07923e8 | 1.99754 | ||||||||
\(67\) | 2.84354e8 | 1.72394 | 0.861972 | − | 0.506956i | \(-0.169229\pi\) | ||||
0.861972 | + | 0.506956i | \(0.169229\pi\) | |||||||
\(68\) | −4.26589e8 | −2.41946 | ||||||||
\(69\) | −3.81130e8 | −2.02420 | ||||||||
\(70\) | −3.74677e7 | −0.186516 | ||||||||
\(71\) | 3.30668e8 | 1.54429 | 0.772147 | − | 0.635444i | \(-0.219183\pi\) | ||||
0.772147 | + | 0.635444i | \(0.219183\pi\) | |||||||
\(72\) | −3.23408e8 | −1.41825 | ||||||||
\(73\) | −1.87286e8 | −0.771885 | −0.385943 | − | 0.922523i | \(-0.626124\pi\) | ||||
−0.385943 | + | 0.922523i | \(0.626124\pi\) | |||||||
\(74\) | −5.58584e8 | −2.16544 | ||||||||
\(75\) | −4.07151e8 | −1.48587 | ||||||||
\(76\) | −7.04439e8 | −2.42205 | ||||||||
\(77\) | −8.91423e7 | −0.288985 | ||||||||
\(78\) | −2.36877e8 | −0.724600 | ||||||||
\(79\) | 4.60455e8 | 1.33004 | 0.665020 | − | 0.746825i | \(-0.268423\pi\) | ||||
0.665020 | + | 0.746825i | \(0.268423\pi\) | |||||||
\(80\) | −2.29805e7 | −0.0627271 | ||||||||
\(81\) | 7.78381e7 | 0.200914 | ||||||||
\(82\) | 9.52175e7 | 0.232570 | ||||||||
\(83\) | −1.63544e8 | −0.378253 | −0.189127 | − | 0.981953i | \(-0.560566\pi\) | ||||
−0.189127 | + | 0.981953i | \(0.560566\pi\) | |||||||
\(84\) | 4.32183e8 | 0.947134 | ||||||||
\(85\) | −2.37373e8 | −0.493227 | ||||||||
\(86\) | 1.19536e9 | 2.35644 | ||||||||
\(87\) | −4.96421e8 | −0.928995 | ||||||||
\(88\) | 3.57885e8 | 0.636168 | ||||||||
\(89\) | −8.24421e8 | −1.39282 | −0.696408 | − | 0.717646i | \(-0.745220\pi\) | ||||
−0.696408 | + | 0.717646i | \(0.745220\pi\) | |||||||
\(90\) | −5.23555e8 | −0.841146 | ||||||||
\(91\) | 6.85750e7 | 0.104828 | ||||||||
\(92\) | −1.28874e9 | −1.87551 | ||||||||
\(93\) | 4.96806e8 | 0.688674 | ||||||||
\(94\) | 1.64737e8 | 0.217629 | ||||||||
\(95\) | −3.91982e8 | −0.493753 | ||||||||
\(96\) | 1.57775e9 | 1.89591 | ||||||||
\(97\) | −6.27004e8 | −0.719113 | −0.359557 | − | 0.933123i | \(-0.617072\pi\) | ||||
−0.359557 | + | 0.933123i | \(0.617072\pi\) | |||||||
\(98\) | −2.07225e8 | −0.226947 | ||||||||
\(99\) | −1.24563e9 | −1.30326 | ||||||||
\(100\) | −1.37672e9 | −1.37672 | ||||||||
\(101\) | 8.53911e8 | 0.816520 | 0.408260 | − | 0.912866i | \(-0.366136\pi\) | ||||
0.408260 | + | 0.912866i | \(0.366136\pi\) | |||||||
\(102\) | 4.53499e9 | 4.14835 | ||||||||
\(103\) | −6.22026e8 | −0.544554 | −0.272277 | − | 0.962219i | \(-0.587777\pi\) | ||||
−0.272277 | + | 0.962219i | \(0.587777\pi\) | |||||||
\(104\) | −2.75312e8 | −0.230768 | ||||||||
\(105\) | 2.40486e8 | 0.193081 | ||||||||
\(106\) | −5.49652e8 | −0.422874 | ||||||||
\(107\) | 3.72891e8 | 0.275014 | 0.137507 | − | 0.990501i | \(-0.456091\pi\) | ||||
0.137507 | + | 0.990501i | \(0.456091\pi\) | |||||||
\(108\) | 2.49616e9 | 1.76549 | ||||||||
\(109\) | 1.62826e9 | 1.10485 | 0.552427 | − | 0.833562i | \(-0.313702\pi\) | ||||
0.552427 | + | 0.833562i | \(0.313702\pi\) | |||||||
\(110\) | 5.79370e8 | 0.377302 | ||||||||
\(111\) | 3.58528e9 | 2.24166 | ||||||||
\(112\) | −1.27100e8 | −0.0763247 | ||||||||
\(113\) | −2.54267e9 | −1.46702 | −0.733511 | − | 0.679678i | \(-0.762120\pi\) | ||||
−0.733511 | + | 0.679678i | \(0.762120\pi\) | |||||||
\(114\) | 7.48877e9 | 4.15278 | ||||||||
\(115\) | −7.17113e8 | −0.382338 | ||||||||
\(116\) | −1.67858e9 | −0.860757 | ||||||||
\(117\) | 9.58234e8 | 0.472754 | ||||||||
\(118\) | 3.79213e9 | 1.80059 | ||||||||
\(119\) | −1.31286e9 | −0.600146 | ||||||||
\(120\) | −9.65496e8 | −0.425045 | ||||||||
\(121\) | −9.79521e8 | −0.415413 | ||||||||
\(122\) | −1.85296e7 | −0.00757264 | ||||||||
\(123\) | −6.11154e8 | −0.240756 | ||||||||
\(124\) | 1.67988e9 | 0.638089 | ||||||||
\(125\) | −1.61396e9 | −0.591284 | ||||||||
\(126\) | −2.89567e9 | −1.02348 | ||||||||
\(127\) | −2.88641e9 | −0.984559 | −0.492279 | − | 0.870437i | \(-0.663836\pi\) | ||||
−0.492279 | + | 0.870437i | \(0.663836\pi\) | |||||||
\(128\) | 4.36068e9 | 1.43585 | ||||||||
\(129\) | −7.67243e9 | −2.43938 | ||||||||
\(130\) | −4.45695e8 | −0.136865 | ||||||||
\(131\) | −2.81188e9 | −0.834210 | −0.417105 | − | 0.908858i | \(-0.636955\pi\) | ||||
−0.417105 | + | 0.908858i | \(0.636955\pi\) | |||||||
\(132\) | −6.68294e9 | −1.91595 | ||||||||
\(133\) | −2.16796e9 | −0.600786 | ||||||||
\(134\) | −1.02216e10 | −2.73871 | ||||||||
\(135\) | 1.38898e9 | 0.359909 | ||||||||
\(136\) | 5.27082e9 | 1.32115 | ||||||||
\(137\) | 3.31457e9 | 0.803867 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(138\) | 1.37004e10 | 3.21570 | ||||||||
\(139\) | 5.32393e9 | 1.20967 | 0.604833 | − | 0.796352i | \(-0.293240\pi\) | ||||
0.604833 | + | 0.796352i | \(0.293240\pi\) | |||||||
\(140\) | 8.13171e8 | 0.178898 | ||||||||
\(141\) | −1.05737e9 | −0.225289 | ||||||||
\(142\) | −1.18864e10 | −2.45332 | ||||||||
\(143\) | −1.06039e9 | −0.212057 | ||||||||
\(144\) | −1.77604e9 | −0.344208 | ||||||||
\(145\) | −9.34037e8 | −0.175472 | ||||||||
\(146\) | 6.73231e9 | 1.22624 | ||||||||
\(147\) | 1.33008e9 | 0.234935 | ||||||||
\(148\) | 1.21231e10 | 2.07700 | ||||||||
\(149\) | −3.15502e9 | −0.524402 | −0.262201 | − | 0.965013i | \(-0.584448\pi\) | ||||
−0.262201 | + | 0.965013i | \(0.584448\pi\) | |||||||
\(150\) | 1.46357e10 | 2.36049 | ||||||||
\(151\) | −1.66845e9 | −0.261166 | −0.130583 | − | 0.991437i | \(-0.541685\pi\) | ||||
−0.130583 | + | 0.991437i | \(0.541685\pi\) | |||||||
\(152\) | 8.70386e9 | 1.32256 | ||||||||
\(153\) | −1.83453e10 | −2.70653 | ||||||||
\(154\) | 3.20437e9 | 0.459091 | ||||||||
\(155\) | 9.34762e8 | 0.130079 | ||||||||
\(156\) | 5.14102e9 | 0.695006 | ||||||||
\(157\) | 3.85793e9 | 0.506765 | 0.253382 | − | 0.967366i | \(-0.418457\pi\) | ||||
0.253382 | + | 0.967366i | \(0.418457\pi\) | |||||||
\(158\) | −1.65518e10 | −2.11294 | ||||||||
\(159\) | 3.52795e9 | 0.437759 | ||||||||
\(160\) | 2.96861e9 | 0.358107 | ||||||||
\(161\) | −3.96619e9 | −0.465219 | ||||||||
\(162\) | −2.79802e9 | −0.319178 | ||||||||
\(163\) | 1.14839e10 | 1.27422 | 0.637111 | − | 0.770772i | \(-0.280129\pi\) | ||||
0.637111 | + | 0.770772i | \(0.280129\pi\) | |||||||
\(164\) | −2.06653e9 | −0.223072 | ||||||||
\(165\) | −3.71869e9 | −0.390582 | ||||||||
\(166\) | 5.87885e9 | 0.600905 | ||||||||
\(167\) | −1.49406e10 | −1.48643 | −0.743213 | − | 0.669055i | \(-0.766699\pi\) | ||||
−0.743213 | + | 0.669055i | \(0.766699\pi\) | |||||||
\(168\) | −5.33994e9 | −0.517184 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 8.53277e9 | 0.783556 | ||||||||
\(171\) | −3.02941e10 | −2.70942 | ||||||||
\(172\) | −2.59433e10 | −2.26020 | ||||||||
\(173\) | 5.46601e9 | 0.463941 | 0.231971 | − | 0.972723i | \(-0.425483\pi\) | ||||
0.231971 | + | 0.972723i | \(0.425483\pi\) | |||||||
\(174\) | 1.78447e10 | 1.47583 | ||||||||
\(175\) | −4.23697e9 | −0.341495 | ||||||||
\(176\) | 1.96538e9 | 0.154397 | ||||||||
\(177\) | −2.43398e10 | −1.86396 | ||||||||
\(178\) | 2.96351e10 | 2.21267 | ||||||||
\(179\) | 2.22364e10 | 1.61892 | 0.809461 | − | 0.587173i | \(-0.199759\pi\) | ||||
0.809461 | + | 0.587173i | \(0.199759\pi\) | |||||||
\(180\) | 1.13629e10 | 0.806792 | ||||||||
\(181\) | −4.21143e9 | −0.291659 | −0.145830 | − | 0.989310i | \(-0.546585\pi\) | ||||
−0.145830 | + | 0.989310i | \(0.546585\pi\) | |||||||
\(182\) | −2.46504e9 | −0.166534 | ||||||||
\(183\) | 1.18932e8 | 0.00783918 | ||||||||
\(184\) | 1.59233e10 | 1.02413 | ||||||||
\(185\) | 6.74585e9 | 0.423413 | ||||||||
\(186\) | −1.78585e10 | −1.09405 | ||||||||
\(187\) | 2.03010e10 | 1.21403 | ||||||||
\(188\) | −3.57534e9 | −0.208740 | ||||||||
\(189\) | 7.68211e9 | 0.437928 | ||||||||
\(190\) | 1.40904e10 | 0.784392 | ||||||||
\(191\) | 1.11392e10 | 0.605627 | 0.302813 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302813 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(192\) | −5.04615e10 | −2.67981 | ||||||||
\(193\) | 2.91759e10 | 1.51362 | 0.756808 | − | 0.653637i | \(-0.226758\pi\) | ||||
0.756808 | + | 0.653637i | \(0.226758\pi\) | |||||||
\(194\) | 2.25387e10 | 1.14241 | ||||||||
\(195\) | 2.86070e9 | 0.141682 | ||||||||
\(196\) | 4.49747e9 | 0.217679 | ||||||||
\(197\) | −2.66926e10 | −1.26268 | −0.631338 | − | 0.775507i | \(-0.717494\pi\) | ||||
−0.631338 | + | 0.775507i | \(0.717494\pi\) | |||||||
\(198\) | 4.47763e10 | 2.07040 | ||||||||
\(199\) | 2.08728e10 | 0.943501 | 0.471751 | − | 0.881732i | \(-0.343622\pi\) | ||||
0.471751 | + | 0.881732i | \(0.343622\pi\) | |||||||
\(200\) | 1.70104e10 | 0.751761 | ||||||||
\(201\) | 6.56073e10 | 2.83511 | ||||||||
\(202\) | −3.06952e10 | −1.29715 | ||||||||
\(203\) | −5.16595e9 | −0.213510 | ||||||||
\(204\) | −9.84241e10 | −3.97893 | ||||||||
\(205\) | −1.14991e9 | −0.0454750 | ||||||||
\(206\) | 2.23597e10 | 0.865095 | ||||||||
\(207\) | −5.54217e10 | −2.09804 | ||||||||
\(208\) | −1.51191e9 | −0.0560070 | ||||||||
\(209\) | 3.35237e10 | 1.21533 | ||||||||
\(210\) | −8.64468e9 | −0.306734 | ||||||||
\(211\) | −2.72187e10 | −0.945358 | −0.472679 | − | 0.881235i | \(-0.656713\pi\) | ||||
−0.472679 | + | 0.881235i | \(0.656713\pi\) | |||||||
\(212\) | 1.19293e10 | 0.405604 | ||||||||
\(213\) | 7.62931e10 | 2.53967 | ||||||||
\(214\) | −1.34042e10 | −0.436896 | ||||||||
\(215\) | −1.44360e10 | −0.460759 | ||||||||
\(216\) | −3.08419e10 | −0.964048 | ||||||||
\(217\) | 5.16996e9 | 0.158277 | ||||||||
\(218\) | −5.85305e10 | −1.75520 | ||||||||
\(219\) | −4.32114e10 | −1.26940 | ||||||||
\(220\) | −1.25742e10 | −0.361893 | ||||||||
\(221\) | −1.56171e10 | −0.440386 | ||||||||
\(222\) | −1.28879e11 | −3.56117 | ||||||||
\(223\) | 3.81531e10 | 1.03314 | 0.516569 | − | 0.856246i | \(-0.327209\pi\) | ||||
0.516569 | + | 0.856246i | \(0.327209\pi\) | |||||||
\(224\) | 1.64187e10 | 0.435735 | ||||||||
\(225\) | −5.92054e10 | −1.54007 | ||||||||
\(226\) | 9.14003e10 | 2.33056 | ||||||||
\(227\) | −2.63924e10 | −0.659726 | −0.329863 | − | 0.944029i | \(-0.607002\pi\) | ||||
−0.329863 | + | 0.944029i | \(0.607002\pi\) | |||||||
\(228\) | −1.62531e11 | −3.98317 | ||||||||
\(229\) | 5.14334e10 | 1.23591 | 0.617953 | − | 0.786215i | \(-0.287962\pi\) | ||||
0.617953 | + | 0.786215i | \(0.287962\pi\) | |||||||
\(230\) | 2.57778e10 | 0.607394 | ||||||||
\(231\) | −2.05673e10 | −0.475250 | ||||||||
\(232\) | 2.07400e10 | 0.470017 | ||||||||
\(233\) | −6.10637e10 | −1.35732 | −0.678659 | − | 0.734454i | \(-0.737438\pi\) | ||||
−0.678659 | + | 0.734454i | \(0.737438\pi\) | |||||||
\(234\) | −3.44453e10 | −0.751032 | ||||||||
\(235\) | −1.98948e9 | −0.0425534 | ||||||||
\(236\) | −8.23016e10 | −1.72705 | ||||||||
\(237\) | 1.06238e11 | 2.18732 | ||||||||
\(238\) | 4.71928e10 | 0.953410 | ||||||||
\(239\) | −7.41233e10 | −1.46948 | −0.734741 | − | 0.678348i | \(-0.762696\pi\) | ||||
−0.734741 | + | 0.678348i | \(0.762696\pi\) | |||||||
\(240\) | −5.30216e9 | −0.103158 | ||||||||
\(241\) | 2.24805e10 | 0.429269 | 0.214634 | − | 0.976694i | \(-0.431144\pi\) | ||||
0.214634 | + | 0.976694i | \(0.431144\pi\) | |||||||
\(242\) | 3.52105e10 | 0.659938 | ||||||||
\(243\) | −4.50176e10 | −0.828236 | ||||||||
\(244\) | 4.02154e8 | 0.00726336 | ||||||||
\(245\) | 2.50259e9 | 0.0443755 | ||||||||
\(246\) | 2.19689e10 | 0.382473 | ||||||||
\(247\) | −2.57889e10 | −0.440856 | ||||||||
\(248\) | −2.07562e10 | −0.348429 | ||||||||
\(249\) | −3.77334e10 | −0.622056 | ||||||||
\(250\) | 5.80162e10 | 0.939333 | ||||||||
\(251\) | −2.53210e10 | −0.402669 | −0.201335 | − | 0.979523i | \(-0.564528\pi\) | ||||
−0.201335 | + | 0.979523i | \(0.564528\pi\) | |||||||
\(252\) | 6.28455e10 | 0.981684 | ||||||||
\(253\) | 6.13300e10 | 0.941089 | ||||||||
\(254\) | 1.03757e11 | 1.56410 | ||||||||
\(255\) | −5.47677e10 | −0.811136 | ||||||||
\(256\) | −4.47722e10 | −0.651522 | ||||||||
\(257\) | −7.30610e10 | −1.04469 | −0.522344 | − | 0.852735i | \(-0.674942\pi\) | ||||
−0.522344 | + | 0.852735i | \(0.674942\pi\) | |||||||
\(258\) | 2.75798e11 | 3.87527 | ||||||||
\(259\) | 3.73098e10 | 0.515198 | ||||||||
\(260\) | 9.67305e9 | 0.131275 | ||||||||
\(261\) | −7.21865e10 | −0.962883 | ||||||||
\(262\) | 1.01077e11 | 1.32525 | ||||||||
\(263\) | 1.14086e11 | 1.47038 | 0.735191 | − | 0.677860i | \(-0.237093\pi\) | ||||
0.735191 | + | 0.677860i | \(0.237093\pi\) | |||||||
\(264\) | 8.25726e10 | 1.04621 | ||||||||
\(265\) | 6.63798e9 | 0.0826855 | ||||||||
\(266\) | 7.79310e10 | 0.954427 | ||||||||
\(267\) | −1.90213e11 | −2.29055 | ||||||||
\(268\) | 2.21842e11 | 2.62686 | ||||||||
\(269\) | −1.48238e10 | −0.172613 | −0.0863067 | − | 0.996269i | \(-0.527506\pi\) | ||||
−0.0863067 | + | 0.996269i | \(0.527506\pi\) | |||||||
\(270\) | −4.99290e10 | −0.571763 | ||||||||
\(271\) | −2.59065e10 | −0.291775 | −0.145887 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145887 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(272\) | 2.89454e10 | 0.320641 | ||||||||
\(273\) | 1.58219e10 | 0.172395 | ||||||||
\(274\) | −1.19148e11 | −1.27705 | ||||||||
\(275\) | 6.55171e10 | 0.690809 | ||||||||
\(276\) | −2.97343e11 | −3.08437 | ||||||||
\(277\) | −3.70344e10 | −0.377961 | −0.188980 | − | 0.981981i | \(-0.560518\pi\) | ||||
−0.188980 | + | 0.981981i | \(0.560518\pi\) | |||||||
\(278\) | −1.91377e11 | −1.92171 | ||||||||
\(279\) | 7.22426e10 | 0.713796 | ||||||||
\(280\) | −1.00473e10 | −0.0976876 | ||||||||
\(281\) | −8.33411e10 | −0.797408 | −0.398704 | − | 0.917080i | \(-0.630540\pi\) | ||||
−0.398704 | + | 0.917080i | \(0.630540\pi\) | |||||||
\(282\) | 3.80088e10 | 0.357901 | ||||||||
\(283\) | −1.02296e11 | −0.948026 | −0.474013 | − | 0.880518i | \(-0.657195\pi\) | ||||
−0.474013 | + | 0.880518i | \(0.657195\pi\) | |||||||
\(284\) | 2.57974e11 | 2.35312 | ||||||||
\(285\) | −9.04396e10 | −0.812001 | ||||||||
\(286\) | 3.81174e10 | 0.336881 | ||||||||
\(287\) | −6.35991e9 | −0.0553327 | ||||||||
\(288\) | 2.29427e11 | 1.96507 | ||||||||
\(289\) | 1.80399e11 | 1.52122 | ||||||||
\(290\) | 3.35755e10 | 0.278760 | ||||||||
\(291\) | −1.44665e11 | −1.18262 | ||||||||
\(292\) | −1.46113e11 | −1.17616 | ||||||||
\(293\) | 4.44571e10 | 0.352400 | 0.176200 | − | 0.984354i | \(-0.443619\pi\) | ||||
0.176200 | + | 0.984354i | \(0.443619\pi\) | |||||||
\(294\) | −4.78118e10 | −0.373226 | ||||||||
\(295\) | −4.57964e10 | −0.352072 | ||||||||
\(296\) | −1.49790e11 | −1.13415 | ||||||||
\(297\) | −1.18790e11 | −0.885883 | ||||||||
\(298\) | 1.13412e11 | 0.833081 | ||||||||
\(299\) | −4.71797e10 | −0.341377 | ||||||||
\(300\) | −3.17643e11 | −2.26409 | ||||||||
\(301\) | −7.98423e10 | −0.560639 | ||||||||
\(302\) | 5.99752e10 | 0.414897 | ||||||||
\(303\) | 1.97018e11 | 1.34281 | ||||||||
\(304\) | 4.77985e10 | 0.320984 | ||||||||
\(305\) | 2.23776e8 | 0.00148069 | ||||||||
\(306\) | 6.59450e11 | 4.29968 | ||||||||
\(307\) | 4.96403e10 | 0.318942 | 0.159471 | − | 0.987203i | \(-0.449021\pi\) | ||||
0.159471 | + | 0.987203i | \(0.449021\pi\) | |||||||
\(308\) | −6.95453e10 | −0.440341 | ||||||||
\(309\) | −1.43516e11 | −0.895545 | ||||||||
\(310\) | −3.36015e10 | −0.206648 | ||||||||
\(311\) | 1.63025e10 | 0.0988170 | 0.0494085 | − | 0.998779i | \(-0.484266\pi\) | ||||
0.0494085 | + | 0.998779i | \(0.484266\pi\) | |||||||
\(312\) | −6.35211e10 | −0.379509 | ||||||||
\(313\) | 3.07617e10 | 0.181159 | 0.0905797 | − | 0.995889i | \(-0.471128\pi\) | ||||
0.0905797 | + | 0.995889i | \(0.471128\pi\) | |||||||
\(314\) | −1.38680e11 | −0.805062 | ||||||||
\(315\) | 3.49701e10 | 0.200124 | ||||||||
\(316\) | 3.59228e11 | 2.02665 | ||||||||
\(317\) | 6.00070e9 | 0.0333761 | 0.0166880 | − | 0.999861i | \(-0.494688\pi\) | ||||
0.0166880 | + | 0.999861i | \(0.494688\pi\) | |||||||
\(318\) | −1.26818e11 | −0.695437 | ||||||||
\(319\) | 7.98821e10 | 0.431908 | ||||||||
\(320\) | −9.49455e10 | −0.506173 | ||||||||
\(321\) | 8.60349e10 | 0.452274 | ||||||||
\(322\) | 1.42571e11 | 0.739061 | ||||||||
\(323\) | 4.93726e11 | 2.52391 | ||||||||
\(324\) | 6.07262e10 | 0.306142 | ||||||||
\(325\) | −5.04007e10 | −0.250589 | ||||||||
\(326\) | −4.12808e11 | −2.02427 | ||||||||
\(327\) | 3.75678e11 | 1.81698 | ||||||||
\(328\) | 2.55335e10 | 0.121809 | ||||||||
\(329\) | −1.10034e10 | −0.0517778 | ||||||||
\(330\) | 1.33674e11 | 0.620491 | ||||||||
\(331\) | −2.75688e11 | −1.26238 | −0.631192 | − | 0.775627i | \(-0.717434\pi\) | ||||
−0.631192 | + | 0.775627i | \(0.717434\pi\) | |||||||
\(332\) | −1.27590e11 | −0.576364 | ||||||||
\(333\) | 5.21349e11 | 2.32343 | ||||||||
\(334\) | 5.37064e11 | 2.36138 | ||||||||
\(335\) | 1.23443e11 | 0.535506 | ||||||||
\(336\) | −2.93250e10 | −0.125520 | ||||||||
\(337\) | −1.39653e11 | −0.589815 | −0.294907 | − | 0.955526i | \(-0.595289\pi\) | ||||
−0.294907 | + | 0.955526i | \(0.595289\pi\) | |||||||
\(338\) | −2.93228e10 | −0.122202 | ||||||||
\(339\) | −5.86654e11 | −2.41259 | ||||||||
\(340\) | −1.85189e11 | −0.751555 | ||||||||
\(341\) | −7.99442e10 | −0.320178 | ||||||||
\(342\) | 1.08897e12 | 4.30426 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | 3.20548e11 | 1.23418 | ||||||||
\(345\) | −1.65455e11 | −0.628773 | ||||||||
\(346\) | −1.96485e11 | −0.737031 | ||||||||
\(347\) | −4.96372e11 | −1.83791 | −0.918955 | − | 0.394363i | \(-0.870965\pi\) | ||||
−0.918955 | + | 0.394363i | \(0.870965\pi\) | |||||||
\(348\) | −3.87288e11 | −1.41556 | ||||||||
\(349\) | 4.34232e11 | 1.56678 | 0.783388 | − | 0.621533i | \(-0.213490\pi\) | ||||
0.783388 | + | 0.621533i | \(0.213490\pi\) | |||||||
\(350\) | 1.52305e11 | 0.542509 | ||||||||
\(351\) | 9.13823e10 | 0.321351 | ||||||||
\(352\) | −2.53886e11 | −0.881448 | ||||||||
\(353\) | 5.55167e11 | 1.90299 | 0.951496 | − | 0.307660i | \(-0.0995458\pi\) | ||||
0.951496 | + | 0.307660i | \(0.0995458\pi\) | |||||||
\(354\) | 8.74934e11 | 2.96115 | ||||||||
\(355\) | 1.43549e11 | 0.479702 | ||||||||
\(356\) | −6.43180e11 | −2.12230 | ||||||||
\(357\) | −3.02908e11 | −0.986968 | ||||||||
\(358\) | −7.99324e11 | −2.57187 | ||||||||
\(359\) | 1.82924e11 | 0.581227 | 0.290613 | − | 0.956841i | \(-0.406141\pi\) | ||||
0.290613 | + | 0.956841i | \(0.406141\pi\) | |||||||
\(360\) | −1.40397e11 | −0.440550 | ||||||||
\(361\) | 4.92617e11 | 1.52661 | ||||||||
\(362\) | 1.51387e11 | 0.463339 | ||||||||
\(363\) | −2.25999e11 | −0.683166 | ||||||||
\(364\) | 5.34994e10 | 0.159732 | ||||||||
\(365\) | −8.13040e10 | −0.239770 | ||||||||
\(366\) | −4.27522e9 | −0.0124536 | ||||||||
\(367\) | −1.84215e11 | −0.530064 | −0.265032 | − | 0.964240i | \(-0.585383\pi\) | ||||
−0.265032 | + | 0.964240i | \(0.585383\pi\) | |||||||
\(368\) | 8.74451e10 | 0.248554 | ||||||||
\(369\) | −8.88703e10 | −0.249539 | ||||||||
\(370\) | −2.42491e11 | −0.672647 | ||||||||
\(371\) | 3.67132e10 | 0.100610 | ||||||||
\(372\) | 3.87588e11 | 1.04937 | ||||||||
\(373\) | 4.08286e10 | 0.109213 | 0.0546065 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546065 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(374\) | −7.29753e11 | −1.92865 | ||||||||
\(375\) | −3.72378e11 | −0.972396 | ||||||||
\(376\) | 4.41759e10 | 0.113983 | ||||||||
\(377\) | −6.14513e10 | −0.156673 | ||||||||
\(378\) | −2.76146e11 | −0.695706 | ||||||||
\(379\) | −1.76701e11 | −0.439908 | −0.219954 | − | 0.975510i | \(-0.570591\pi\) | ||||
−0.219954 | + | 0.975510i | \(0.570591\pi\) | |||||||
\(380\) | −3.05809e11 | −0.752357 | ||||||||
\(381\) | −6.65964e11 | −1.61915 | ||||||||
\(382\) | −4.00418e11 | −0.962117 | ||||||||
\(383\) | −7.60004e11 | −1.80477 | −0.902384 | − | 0.430932i | \(-0.858185\pi\) | ||||
−0.902384 | + | 0.430932i | \(0.858185\pi\) | |||||||
\(384\) | 1.00611e12 | 2.36132 | ||||||||
\(385\) | −3.86982e10 | −0.0897670 | ||||||||
\(386\) | −1.04877e12 | −2.40458 | ||||||||
\(387\) | −1.11568e12 | −2.52836 | ||||||||
\(388\) | −4.89163e11 | −1.09575 | ||||||||
\(389\) | 3.59913e10 | 0.0796938 | 0.0398469 | − | 0.999206i | \(-0.487313\pi\) | ||||
0.0398469 | + | 0.999206i | \(0.487313\pi\) | |||||||
\(390\) | −1.02832e11 | −0.225081 | ||||||||
\(391\) | 9.03248e11 | 1.95439 | ||||||||
\(392\) | −5.55695e10 | −0.118864 | ||||||||
\(393\) | −6.48766e11 | −1.37190 | ||||||||
\(394\) | 9.59508e11 | 2.00593 | ||||||||
\(395\) | 1.99891e11 | 0.413148 | ||||||||
\(396\) | −9.71793e11 | −1.98584 | ||||||||
\(397\) | −5.85617e11 | −1.18319 | −0.591597 | − | 0.806234i | \(-0.701502\pi\) | ||||
−0.591597 | + | 0.806234i | \(0.701502\pi\) | |||||||
\(398\) | −7.50308e11 | −1.49888 | ||||||||
\(399\) | −5.00201e11 | −0.988021 | ||||||||
\(400\) | 9.34151e10 | 0.182451 | ||||||||
\(401\) | 9.17734e10 | 0.177242 | 0.0886211 | − | 0.996065i | \(-0.471754\pi\) | ||||
0.0886211 | + | 0.996065i | \(0.471754\pi\) | |||||||
\(402\) | −2.35836e12 | −4.50394 | ||||||||
\(403\) | 6.14990e10 | 0.116144 | ||||||||
\(404\) | 6.66187e11 | 1.24417 | ||||||||
\(405\) | 3.37908e10 | 0.0624095 | ||||||||
\(406\) | 1.85698e11 | 0.339188 | ||||||||
\(407\) | −5.76929e11 | −1.04219 | ||||||||
\(408\) | 1.21610e12 | 2.17270 | ||||||||
\(409\) | 3.83284e11 | 0.677276 | 0.338638 | − | 0.940917i | \(-0.390034\pi\) | ||||
0.338638 | + | 0.940917i | \(0.390034\pi\) | |||||||
\(410\) | 4.13355e10 | 0.0722430 | ||||||||
\(411\) | 7.64749e11 | 1.32200 | ||||||||
\(412\) | −4.85279e11 | −0.829764 | ||||||||
\(413\) | −2.53289e11 | −0.428392 | ||||||||
\(414\) | 1.99222e12 | 3.33301 | ||||||||
\(415\) | −7.09971e10 | −0.117496 | ||||||||
\(416\) | 1.95308e11 | 0.319742 | ||||||||
\(417\) | 1.22836e12 | 1.98935 | ||||||||
\(418\) | −1.20506e12 | −1.93071 | ||||||||
\(419\) | −1.50550e11 | −0.238625 | −0.119313 | − | 0.992857i | \(-0.538069\pi\) | ||||
−0.119313 | + | 0.992857i | \(0.538069\pi\) | |||||||
\(420\) | 1.87618e11 | 0.294207 | ||||||||
\(421\) | 1.08971e12 | 1.69061 | 0.845303 | − | 0.534287i | \(-0.179420\pi\) | ||||
0.845303 | + | 0.534287i | \(0.179420\pi\) | |||||||
\(422\) | 9.78421e11 | 1.50183 | ||||||||
\(423\) | −1.53756e11 | −0.233507 | ||||||||
\(424\) | −1.47395e11 | −0.221480 | ||||||||
\(425\) | 9.64914e11 | 1.43463 | ||||||||
\(426\) | −2.74248e12 | −4.03459 | ||||||||
\(427\) | 1.23766e9 | 0.00180167 | ||||||||
\(428\) | 2.90915e11 | 0.419053 | ||||||||
\(429\) | −2.44657e11 | −0.348738 | ||||||||
\(430\) | 5.18926e11 | 0.731976 | ||||||||
\(431\) | −4.54924e11 | −0.635025 | −0.317512 | − | 0.948254i | \(-0.602848\pi\) | ||||
−0.317512 | + | 0.948254i | \(0.602848\pi\) | |||||||
\(432\) | −1.69372e11 | −0.233973 | ||||||||
\(433\) | −8.89329e11 | −1.21581 | −0.607906 | − | 0.794009i | \(-0.707990\pi\) | ||||
−0.607906 | + | 0.794009i | \(0.707990\pi\) | |||||||
\(434\) | −1.85843e11 | −0.251444 | ||||||||
\(435\) | −2.15504e11 | −0.288572 | ||||||||
\(436\) | 1.27030e12 | 1.68352 | ||||||||
\(437\) | 1.49156e12 | 1.95648 | ||||||||
\(438\) | 1.55330e12 | 2.01661 | ||||||||
\(439\) | −1.19486e12 | −1.53541 | −0.767707 | − | 0.640801i | \(-0.778602\pi\) | ||||
−0.767707 | + | 0.640801i | \(0.778602\pi\) | |||||||
\(440\) | 1.55364e11 | 0.197612 | ||||||||
\(441\) | 1.93412e11 | 0.243506 | ||||||||
\(442\) | 5.61380e11 | 0.699612 | ||||||||
\(443\) | 7.07379e11 | 0.872640 | 0.436320 | − | 0.899791i | \(-0.356282\pi\) | ||||
0.436320 | + | 0.899791i | \(0.356282\pi\) | |||||||
\(444\) | 2.79709e12 | 3.41573 | ||||||||
\(445\) | −3.57895e11 | −0.432648 | ||||||||
\(446\) | −1.37148e12 | −1.64128 | ||||||||
\(447\) | −7.27938e11 | −0.862404 | ||||||||
\(448\) | −5.25122e11 | −0.615898 | ||||||||
\(449\) | −1.52186e12 | −1.76712 | −0.883558 | − | 0.468322i | \(-0.844859\pi\) | ||||
−0.883558 | + | 0.468322i | \(0.844859\pi\) | |||||||
\(450\) | 2.12823e12 | 2.44660 | ||||||||
\(451\) | 9.83446e10 | 0.111932 | ||||||||
\(452\) | −1.98369e12 | −2.23537 | ||||||||
\(453\) | −3.84951e11 | −0.429500 | ||||||||
\(454\) | 9.48719e11 | 1.04806 | ||||||||
\(455\) | 2.97695e10 | 0.0325627 | ||||||||
\(456\) | 2.00819e12 | 2.17502 | ||||||||
\(457\) | 4.30973e11 | 0.462197 | 0.231098 | − | 0.972930i | \(-0.425768\pi\) | ||||
0.231098 | + | 0.972930i | \(0.425768\pi\) | |||||||
\(458\) | −1.84886e12 | −1.96340 | ||||||||
\(459\) | −1.74950e12 | −1.83974 | ||||||||
\(460\) | −5.59463e11 | −0.582587 | ||||||||
\(461\) | −3.63737e11 | −0.375088 | −0.187544 | − | 0.982256i | \(-0.560053\pi\) | ||||
−0.187544 | + | 0.982256i | \(0.560053\pi\) | |||||||
\(462\) | 7.39323e11 | 0.754997 | ||||||||
\(463\) | 1.70614e12 | 1.72544 | 0.862721 | − | 0.505681i | \(-0.168759\pi\) | ||||
0.862721 | + | 0.505681i | \(0.168759\pi\) | |||||||
\(464\) | 1.13897e11 | 0.114072 | ||||||||
\(465\) | 2.15672e11 | 0.213922 | ||||||||
\(466\) | 2.19503e12 | 2.15628 | ||||||||
\(467\) | −8.23780e11 | −0.801466 | −0.400733 | − | 0.916195i | \(-0.631245\pi\) | ||||
−0.400733 | + | 0.916195i | \(0.631245\pi\) | |||||||
\(468\) | 7.47576e11 | 0.720359 | ||||||||
\(469\) | 6.82735e11 | 0.651590 | ||||||||
\(470\) | 7.15151e10 | 0.0676017 | ||||||||
\(471\) | 8.90117e11 | 0.833399 | ||||||||
\(472\) | 1.01690e12 | 0.943057 | ||||||||
\(473\) | 1.23462e12 | 1.13412 | ||||||||
\(474\) | −3.81889e12 | −3.47484 | ||||||||
\(475\) | 1.59339e12 | 1.43616 | ||||||||
\(476\) | −1.02424e12 | −0.914472 | ||||||||
\(477\) | 5.13012e11 | 0.453728 | ||||||||
\(478\) | 2.66448e12 | 2.33447 | ||||||||
\(479\) | 1.33355e12 | 1.15744 | 0.578722 | − | 0.815525i | \(-0.303552\pi\) | ||||
0.578722 | + | 0.815525i | \(0.303552\pi\) | |||||||
\(480\) | 6.84929e11 | 0.588925 | ||||||||
\(481\) | 4.43817e11 | 0.378052 | ||||||||
\(482\) | −8.08098e11 | −0.681950 | ||||||||
\(483\) | −9.15094e11 | −0.765074 | ||||||||
\(484\) | −7.64183e11 | −0.632985 | ||||||||
\(485\) | −2.72193e11 | −0.223377 | ||||||||
\(486\) | 1.61823e12 | 1.31576 | ||||||||
\(487\) | −3.46476e11 | −0.279121 | −0.139560 | − | 0.990214i | \(-0.544569\pi\) | ||||
−0.139560 | + | 0.990214i | \(0.544569\pi\) | |||||||
\(488\) | −4.96890e9 | −0.00396617 | ||||||||
\(489\) | 2.64961e12 | 2.09552 | ||||||||
\(490\) | −8.99598e10 | −0.0704963 | ||||||||
\(491\) | 2.15900e12 | 1.67643 | 0.838216 | − | 0.545338i | \(-0.183599\pi\) | ||||
0.838216 | + | 0.545338i | \(0.183599\pi\) | |||||||
\(492\) | −4.76798e11 | −0.366853 | ||||||||
\(493\) | 1.17648e12 | 0.896958 | ||||||||
\(494\) | 9.27025e11 | 0.700358 | ||||||||
\(495\) | −5.40750e11 | −0.404830 | ||||||||
\(496\) | −1.13985e11 | −0.0845632 | ||||||||
\(497\) | 7.93935e11 | 0.583689 | ||||||||
\(498\) | 1.35639e12 | 0.988218 | ||||||||
\(499\) | −1.08273e12 | −0.781749 | −0.390875 | − | 0.920444i | \(-0.627827\pi\) | ||||
−0.390875 | + | 0.920444i | \(0.627827\pi\) | |||||||
\(500\) | −1.25914e12 | −0.900969 | ||||||||
\(501\) | −3.44715e12 | −2.44450 | ||||||||
\(502\) | 9.10203e11 | 0.639693 | ||||||||
\(503\) | −2.04294e12 | −1.42298 | −0.711492 | − | 0.702694i | \(-0.751980\pi\) | ||||
−0.711492 | + | 0.702694i | \(0.751980\pi\) | |||||||
\(504\) | −7.76502e11 | −0.536050 | ||||||||
\(505\) | 3.70697e11 | 0.253634 | ||||||||
\(506\) | −2.20461e12 | −1.49504 | ||||||||
\(507\) | 1.88208e11 | 0.126504 | ||||||||
\(508\) | −2.25186e12 | −1.50022 | ||||||||
\(509\) | −2.96107e12 | −1.95533 | −0.977663 | − | 0.210178i | \(-0.932596\pi\) | ||||
−0.977663 | + | 0.210178i | \(0.932596\pi\) | |||||||
\(510\) | 1.96871e12 | 1.28860 | ||||||||
\(511\) | −4.49674e11 | −0.291745 | ||||||||
\(512\) | −6.23255e11 | −0.400822 | ||||||||
\(513\) | −2.88901e12 | −1.84171 | ||||||||
\(514\) | 2.62629e12 | 1.65962 | ||||||||
\(515\) | −2.70032e11 | −0.169154 | ||||||||
\(516\) | −5.98572e12 | −3.71700 | ||||||||
\(517\) | 1.70147e11 | 0.104741 | ||||||||
\(518\) | −1.34116e12 | −0.818459 | ||||||||
\(519\) | 1.26114e12 | 0.762974 | ||||||||
\(520\) | −1.19518e11 | −0.0716831 | ||||||||
\(521\) | −5.60548e11 | −0.333306 | −0.166653 | − | 0.986016i | \(-0.553296\pi\) | ||||
−0.166653 | + | 0.986016i | \(0.553296\pi\) | |||||||
\(522\) | 2.59486e12 | 1.52967 | ||||||||
\(523\) | 2.85263e12 | 1.66720 | 0.833599 | − | 0.552370i | \(-0.186276\pi\) | ||||
0.833599 | + | 0.552370i | \(0.186276\pi\) | |||||||
\(524\) | −2.19371e12 | −1.27113 | ||||||||
\(525\) | −9.77569e11 | −0.561604 | ||||||||
\(526\) | −4.10099e12 | −2.33589 | ||||||||
\(527\) | −1.17739e12 | −0.664925 | ||||||||
\(528\) | 4.53459e11 | 0.253913 | ||||||||
\(529\) | 9.27591e11 | 0.514998 | ||||||||
\(530\) | −2.38613e11 | −0.131357 | ||||||||
\(531\) | −3.53935e12 | −1.93196 | ||||||||
\(532\) | −1.69136e12 | −0.915448 | ||||||||
\(533\) | −7.56540e10 | −0.0406031 | ||||||||
\(534\) | 6.83753e12 | 3.63884 | ||||||||
\(535\) | 1.61878e11 | 0.0854273 | ||||||||
\(536\) | −2.74102e12 | −1.43440 | ||||||||
\(537\) | 5.13047e12 | 2.66240 | ||||||||
\(538\) | 5.32866e11 | 0.274219 | ||||||||
\(539\) | −2.14031e11 | −0.109226 | ||||||||
\(540\) | 1.08362e12 | 0.548411 | ||||||||
\(541\) | −3.07722e12 | −1.54444 | −0.772220 | − | 0.635355i | \(-0.780854\pi\) | ||||
−0.772220 | + | 0.635355i | \(0.780854\pi\) | |||||||
\(542\) | 9.31253e11 | 0.463522 | ||||||||
\(543\) | −9.71676e11 | −0.479648 | ||||||||
\(544\) | −3.73915e12 | −1.83053 | ||||||||
\(545\) | 7.06855e11 | 0.343199 | ||||||||
\(546\) | −5.68743e11 | −0.273873 | ||||||||
\(547\) | −2.99830e12 | −1.43196 | −0.715982 | − | 0.698119i | \(-0.754021\pi\) | ||||
−0.715982 | + | 0.698119i | \(0.754021\pi\) | |||||||
\(548\) | 2.58589e12 | 1.22489 | ||||||||
\(549\) | 1.72944e10 | 0.00812514 | ||||||||
\(550\) | −2.35512e12 | −1.09744 | ||||||||
\(551\) | 1.94275e12 | 0.897915 | ||||||||
\(552\) | 3.67389e12 | 1.68422 | ||||||||
\(553\) | 1.10555e12 | 0.502708 | ||||||||
\(554\) | 1.33126e12 | 0.600440 | ||||||||
\(555\) | 1.55643e12 | 0.696323 | ||||||||
\(556\) | 4.15351e12 | 1.84323 | ||||||||
\(557\) | 2.77410e12 | 1.22116 | 0.610581 | − | 0.791954i | \(-0.290936\pi\) | ||||
0.610581 | + | 0.791954i | \(0.290936\pi\) | |||||||
\(558\) | −2.59688e12 | −1.13396 | ||||||||
\(559\) | −9.49761e11 | −0.411397 | ||||||||
\(560\) | −5.51763e10 | −0.0237086 | ||||||||
\(561\) | 4.68392e12 | 1.99653 | ||||||||
\(562\) | 2.99583e12 | 1.26679 | ||||||||
\(563\) | −6.92492e11 | −0.290487 | −0.145244 | − | 0.989396i | \(-0.546397\pi\) | ||||
−0.145244 | + | 0.989396i | \(0.546397\pi\) | |||||||
\(564\) | −8.24915e11 | −0.343284 | ||||||||
\(565\) | −1.10381e12 | −0.455699 | ||||||||
\(566\) | 3.67720e12 | 1.50606 | ||||||||
\(567\) | 1.86889e11 | 0.0759383 | ||||||||
\(568\) | −3.18746e12 | −1.28492 | ||||||||
\(569\) | 4.26105e11 | 0.170417 | 0.0852083 | − | 0.996363i | \(-0.472844\pi\) | ||||
0.0852083 | + | 0.996363i | \(0.472844\pi\) | |||||||
\(570\) | 3.25100e12 | 1.28997 | ||||||||
\(571\) | −3.57448e12 | −1.40718 | −0.703591 | − | 0.710605i | \(-0.748421\pi\) | ||||
−0.703591 | + | 0.710605i | \(0.748421\pi\) | |||||||
\(572\) | −8.27273e11 | −0.323122 | ||||||||
\(573\) | 2.57008e12 | 0.995982 | ||||||||
\(574\) | 2.28617e11 | 0.0879033 | ||||||||
\(575\) | 2.91504e12 | 1.11209 | ||||||||
\(576\) | −7.33780e12 | −2.77757 | ||||||||
\(577\) | −3.13230e12 | −1.17645 | −0.588224 | − | 0.808698i | \(-0.700173\pi\) | ||||
−0.588224 | + | 0.808698i | \(0.700173\pi\) | |||||||
\(578\) | −6.48472e12 | −2.41666 | ||||||||
\(579\) | 6.73156e12 | 2.48922 | ||||||||
\(580\) | −7.28698e11 | −0.267375 | ||||||||
\(581\) | −3.92669e11 | −0.142966 | ||||||||
\(582\) | 5.20021e12 | 1.87874 | ||||||||
\(583\) | −5.67703e11 | −0.203523 | ||||||||
\(584\) | 1.80533e12 | 0.642244 | ||||||||
\(585\) | 4.15985e11 | 0.146851 | ||||||||
\(586\) | −1.59808e12 | −0.559834 | ||||||||
\(587\) | 7.18927e11 | 0.249927 | 0.124963 | − | 0.992161i | \(-0.460119\pi\) | ||||
0.124963 | + | 0.992161i | \(0.460119\pi\) | |||||||
\(588\) | 1.03767e12 | 0.357983 | ||||||||
\(589\) | −1.94426e12 | −0.665635 | ||||||||
\(590\) | 1.64623e12 | 0.559313 | ||||||||
\(591\) | −6.15861e12 | −2.07653 | ||||||||
\(592\) | −8.22592e11 | −0.275256 | ||||||||
\(593\) | 4.09447e12 | 1.35973 | 0.679864 | − | 0.733339i | \(-0.262039\pi\) | ||||
0.679864 | + | 0.733339i | \(0.262039\pi\) | |||||||
\(594\) | 4.27010e12 | 1.40734 | ||||||||
\(595\) | −5.69933e11 | −0.186422 | ||||||||
\(596\) | −2.46142e12 | −0.799057 | ||||||||
\(597\) | 4.81586e12 | 1.55163 | ||||||||
\(598\) | 1.69595e12 | 0.542322 | ||||||||
\(599\) | −9.86003e11 | −0.312938 | −0.156469 | − | 0.987683i | \(-0.550011\pi\) | ||||
−0.156469 | + | 0.987683i | \(0.550011\pi\) | |||||||
\(600\) | 3.92471e12 | 1.23631 | ||||||||
\(601\) | 3.62685e12 | 1.13395 | 0.566976 | − | 0.823735i | \(-0.308113\pi\) | ||||
0.566976 | + | 0.823735i | \(0.308113\pi\) | |||||||
\(602\) | 2.87006e12 | 0.890650 | ||||||||
\(603\) | 9.54021e12 | 2.93853 | ||||||||
\(604\) | −1.30166e12 | −0.397952 | ||||||||
\(605\) | −4.25226e11 | −0.129039 | ||||||||
\(606\) | −7.08212e12 | −2.13322 | ||||||||
\(607\) | 3.76025e12 | 1.12426 | 0.562131 | − | 0.827048i | \(-0.309982\pi\) | ||||
0.562131 | + | 0.827048i | \(0.309982\pi\) | |||||||
\(608\) | −6.17457e12 | −1.83249 | ||||||||
\(609\) | −1.19191e12 | −0.351127 | ||||||||
\(610\) | −8.04401e9 | −0.00235228 | ||||||||
\(611\) | −1.30890e11 | −0.0379945 | ||||||||
\(612\) | −1.43122e13 | −4.12407 | ||||||||
\(613\) | −2.13878e12 | −0.611780 | −0.305890 | − | 0.952067i | \(-0.598954\pi\) | ||||
−0.305890 | + | 0.952067i | \(0.598954\pi\) | |||||||
\(614\) | −1.78440e12 | −0.506681 | ||||||||
\(615\) | −2.65312e11 | −0.0747858 | ||||||||
\(616\) | 8.59283e11 | 0.240449 | ||||||||
\(617\) | 2.69179e12 | 0.747752 | 0.373876 | − | 0.927479i | \(-0.378028\pi\) | ||||
0.373876 | + | 0.927479i | \(0.378028\pi\) | |||||||
\(618\) | 5.15892e12 | 1.42269 | ||||||||
\(619\) | −7.17858e11 | −0.196531 | −0.0982654 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982654 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(620\) | 7.29264e11 | 0.198208 | ||||||||
\(621\) | −5.28530e12 | −1.42613 | ||||||||
\(622\) | −5.86019e11 | −0.156984 | ||||||||
\(623\) | −1.97943e12 | −0.526435 | ||||||||
\(624\) | −3.48835e11 | −0.0921062 | ||||||||
\(625\) | 2.74597e12 | 0.719840 | ||||||||
\(626\) | −1.10578e12 | −0.287796 | ||||||||
\(627\) | 7.73471e12 | 1.99867 | ||||||||
\(628\) | 3.00981e12 | 0.772183 | ||||||||
\(629\) | −8.49682e12 | −2.16435 | ||||||||
\(630\) | −1.25706e12 | −0.317923 | ||||||||
\(631\) | −4.59827e12 | −1.15468 | −0.577341 | − | 0.816503i | \(-0.695910\pi\) | ||||
−0.577341 | + | 0.816503i | \(0.695910\pi\) | |||||||
\(632\) | −4.43853e12 | −1.10665 | ||||||||
\(633\) | −6.28000e12 | −1.55469 | ||||||||
\(634\) | −2.15705e11 | −0.0530223 | ||||||||
\(635\) | −1.25304e12 | −0.305832 | ||||||||
\(636\) | 2.75236e12 | 0.667035 | ||||||||
\(637\) | 1.64648e11 | 0.0396214 | ||||||||
\(638\) | −2.87149e12 | −0.686143 | ||||||||
\(639\) | 1.10941e13 | 2.63231 | ||||||||
\(640\) | 1.89304e12 | 0.446016 | ||||||||
\(641\) | −5.40351e12 | −1.26420 | −0.632099 | − | 0.774888i | \(-0.717806\pi\) | ||||
−0.632099 | + | 0.774888i | \(0.717806\pi\) | |||||||
\(642\) | −3.09266e12 | −0.718497 | ||||||||
\(643\) | 2.49434e12 | 0.575449 | 0.287724 | − | 0.957713i | \(-0.407101\pi\) | ||||
0.287724 | + | 0.957713i | \(0.407101\pi\) | |||||||
\(644\) | −3.09426e12 | −0.708877 | ||||||||
\(645\) | −3.33073e12 | −0.757741 | ||||||||
\(646\) | −1.77478e13 | −4.00957 | ||||||||
\(647\) | 7.00912e12 | 1.57251 | 0.786257 | − | 0.617900i | \(-0.212016\pi\) | ||||
0.786257 | + | 0.617900i | \(0.212016\pi\) | |||||||
\(648\) | −7.50316e11 | −0.167169 | ||||||||
\(649\) | 3.91667e12 | 0.866594 | ||||||||
\(650\) | 1.81173e12 | 0.398093 | ||||||||
\(651\) | 1.19283e12 | 0.260294 | ||||||||
\(652\) | 8.95928e12 | 1.94160 | ||||||||
\(653\) | 6.91176e12 | 1.48758 | 0.743788 | − | 0.668416i | \(-0.233027\pi\) | ||||
0.743788 | + | 0.668416i | \(0.233027\pi\) | |||||||
\(654\) | −1.35044e13 | −2.88652 | ||||||||
\(655\) | −1.22068e12 | −0.259129 | ||||||||
\(656\) | 1.40221e11 | 0.0295628 | ||||||||
\(657\) | −6.28353e12 | −1.31571 | ||||||||
\(658\) | 3.95534e11 | 0.0822559 | ||||||||
\(659\) | 2.27667e12 | 0.470236 | 0.235118 | − | 0.971967i | \(-0.424452\pi\) | ||||
0.235118 | + | 0.971967i | \(0.424452\pi\) | |||||||
\(660\) | −2.90118e12 | −0.595150 | ||||||||
\(661\) | 2.29883e12 | 0.468383 | 0.234191 | − | 0.972190i | \(-0.424756\pi\) | ||||
0.234191 | + | 0.972190i | \(0.424756\pi\) | |||||||
\(662\) | 9.91004e12 | 2.00546 | ||||||||
\(663\) | −3.60323e12 | −0.724237 | ||||||||
\(664\) | 1.57647e12 | 0.314724 | ||||||||
\(665\) | −9.41149e11 | −0.186621 | ||||||||
\(666\) | −1.87407e13 | −3.69108 | ||||||||
\(667\) | 3.55418e12 | 0.695301 | ||||||||
\(668\) | −1.16560e13 | −2.26494 | ||||||||
\(669\) | 8.80283e12 | 1.69905 | ||||||||
\(670\) | −4.43736e12 | −0.850722 | ||||||||
\(671\) | −1.91382e10 | −0.00364459 | ||||||||
\(672\) | 3.78819e12 | 0.716588 | ||||||||
\(673\) | −5.78650e12 | −1.08730 | −0.543649 | − | 0.839313i | \(-0.682958\pi\) | ||||
−0.543649 | + | 0.839313i | \(0.682958\pi\) | |||||||
\(674\) | 5.02005e12 | 0.936998 | ||||||||
\(675\) | −5.64614e12 | −1.04685 | ||||||||
\(676\) | 6.36400e11 | 0.117212 | ||||||||
\(677\) | 8.97926e12 | 1.64283 | 0.821413 | − | 0.570334i | \(-0.193186\pi\) | ||||
0.821413 | + | 0.570334i | \(0.193186\pi\) | |||||||
\(678\) | 2.10882e13 | 3.83271 | ||||||||
\(679\) | −1.50544e12 | −0.271799 | ||||||||
\(680\) | 2.28815e12 | 0.410387 | ||||||||
\(681\) | −6.08936e12 | −1.08495 | ||||||||
\(682\) | 2.87372e12 | 0.508645 | ||||||||
\(683\) | 1.01954e13 | 1.79272 | 0.896358 | − | 0.443331i | \(-0.146203\pi\) | ||||
0.896358 | + | 0.443331i | \(0.146203\pi\) | |||||||
\(684\) | −2.36342e13 | −4.12847 | ||||||||
\(685\) | 1.43891e12 | 0.249704 | ||||||||
\(686\) | −4.97548e11 | −0.0857780 | ||||||||
\(687\) | 1.18669e13 | 2.03251 | ||||||||
\(688\) | 1.76033e12 | 0.299534 | ||||||||
\(689\) | 4.36720e11 | 0.0738272 | ||||||||
\(690\) | 5.94755e12 | 0.998889 | ||||||||
\(691\) | 2.79110e12 | 0.465720 | 0.232860 | − | 0.972510i | \(-0.425192\pi\) | ||||
0.232860 | + | 0.972510i | \(0.425192\pi\) | |||||||
\(692\) | 4.26436e12 | 0.706930 | ||||||||
\(693\) | −2.99076e12 | −0.492587 | ||||||||
\(694\) | 1.78429e13 | 2.91976 | ||||||||
\(695\) | 2.31120e12 | 0.375757 | ||||||||
\(696\) | 4.78522e12 | 0.772966 | ||||||||
\(697\) | 1.44839e12 | 0.232454 | ||||||||
\(698\) | −1.56092e13 | −2.48903 | ||||||||
\(699\) | −1.40888e13 | −2.23217 | ||||||||
\(700\) | −3.30551e12 | −0.520352 | ||||||||
\(701\) | −2.22264e12 | −0.347647 | −0.173824 | − | 0.984777i | \(-0.555612\pi\) | ||||
−0.173824 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(702\) | −3.28488e12 | −0.510509 | ||||||||
\(703\) | −1.40311e13 | −2.16666 | ||||||||
\(704\) | 8.12007e12 | 1.24590 | ||||||||
\(705\) | −4.59020e11 | −0.0699811 | ||||||||
\(706\) | −1.99564e13 | −3.02315 | ||||||||
\(707\) | 2.05024e12 | 0.308615 | ||||||||
\(708\) | −1.89889e13 | −2.84021 | ||||||||
\(709\) | −6.86568e12 | −1.02041 | −0.510206 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510206 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(710\) | −5.16009e12 | −0.762069 | ||||||||
\(711\) | 1.54485e13 | 2.26711 | ||||||||
\(712\) | 7.94696e12 | 1.15889 | ||||||||
\(713\) | −3.55694e12 | −0.515434 | ||||||||
\(714\) | 1.08885e13 | 1.56793 | ||||||||
\(715\) | −4.60332e11 | −0.0658710 | ||||||||
\(716\) | 1.73480e13 | 2.46683 | ||||||||
\(717\) | −1.71020e13 | −2.41663 | ||||||||
\(718\) | −6.57550e12 | −0.923355 | ||||||||
\(719\) | 1.08604e13 | 1.51553 | 0.757766 | − | 0.652526i | \(-0.226291\pi\) | ||||
0.757766 | + | 0.652526i | \(0.226291\pi\) | |||||||
\(720\) | −7.71007e11 | −0.106921 | ||||||||
\(721\) | −1.49348e12 | −0.205822 | ||||||||
\(722\) | −1.77079e13 | −2.42521 | ||||||||
\(723\) | 5.18679e12 | 0.705953 | ||||||||
\(724\) | −3.28559e12 | −0.444416 | ||||||||
\(725\) | 3.79683e12 | 0.510387 | ||||||||
\(726\) | 8.12389e12 | 1.08530 | ||||||||
\(727\) | 1.18416e13 | 1.57220 | 0.786098 | − | 0.618102i | \(-0.212098\pi\) | ||||
0.786098 | + | 0.618102i | \(0.212098\pi\) | |||||||
\(728\) | −6.61025e11 | −0.0872221 | ||||||||
\(729\) | −1.19187e13 | −1.56299 | ||||||||
\(730\) | 2.92260e12 | 0.380905 | ||||||||
\(731\) | 1.81830e13 | 2.35526 | ||||||||
\(732\) | 9.27864e10 | 0.0119449 | ||||||||
\(733\) | 5.16125e12 | 0.660369 | 0.330184 | − | 0.943916i | \(-0.392889\pi\) | ||||
0.330184 | + | 0.943916i | \(0.392889\pi\) | |||||||
\(734\) | 6.62192e12 | 0.842077 | ||||||||
\(735\) | 5.77408e11 | 0.0729776 | ||||||||
\(736\) | −1.12961e13 | −1.41899 | ||||||||
\(737\) | −1.05573e13 | −1.31810 | ||||||||
\(738\) | 3.19459e12 | 0.396425 | ||||||||
\(739\) | −9.11730e12 | −1.12452 | −0.562259 | − | 0.826961i | \(-0.690068\pi\) | ||||
−0.562259 | + | 0.826961i | \(0.690068\pi\) | |||||||
\(740\) | 5.26284e12 | 0.645175 | ||||||||
\(741\) | −5.95012e12 | −0.725010 | ||||||||
\(742\) | −1.31971e12 | −0.159832 | ||||||||
\(743\) | −1.58640e12 | −0.190969 | −0.0954843 | − | 0.995431i | \(-0.530440\pi\) | ||||
−0.0954843 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(744\) | −4.78894e12 | −0.573008 | ||||||||
\(745\) | −1.36965e12 | −0.162894 | ||||||||
\(746\) | −1.46765e12 | −0.173499 | ||||||||
\(747\) | −5.48697e12 | −0.644748 | ||||||||
\(748\) | 1.58380e13 | 1.84988 | ||||||||
\(749\) | 8.95312e11 | 0.103946 | ||||||||
\(750\) | 1.33857e13 | 1.54478 | ||||||||
\(751\) | 1.04973e13 | 1.20420 | 0.602100 | − | 0.798420i | \(-0.294331\pi\) | ||||
0.602100 | + | 0.798420i | \(0.294331\pi\) | |||||||
\(752\) | 2.42598e11 | 0.0276635 | ||||||||
\(753\) | −5.84215e12 | −0.662209 | ||||||||
\(754\) | 2.20897e12 | 0.248896 | ||||||||
\(755\) | −7.24302e11 | −0.0811257 | ||||||||
\(756\) | 5.99328e12 | 0.667292 | ||||||||
\(757\) | 5.39506e12 | 0.597125 | 0.298562 | − | 0.954390i | \(-0.403493\pi\) | ||||
0.298562 | + | 0.954390i | \(0.403493\pi\) | |||||||
\(758\) | 6.35179e12 | 0.698851 | ||||||||
\(759\) | 1.41503e13 | 1.54767 | ||||||||
\(760\) | 3.77849e12 | 0.410825 | ||||||||
\(761\) | 3.08992e12 | 0.333977 | 0.166988 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166988 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(762\) | 2.39392e13 | 2.57224 | ||||||||
\(763\) | 3.90945e12 | 0.417595 | ||||||||
\(764\) | 8.69038e12 | 0.922823 | ||||||||
\(765\) | −7.96398e12 | −0.840724 | ||||||||
\(766\) | 2.73196e13 | 2.86711 | ||||||||
\(767\) | −3.01299e12 | −0.314354 | ||||||||
\(768\) | −1.03300e13 | −1.07146 | ||||||||
\(769\) | −1.64177e13 | −1.69295 | −0.846473 | − | 0.532432i | \(-0.821278\pi\) | ||||
−0.846473 | + | 0.532432i | \(0.821278\pi\) | |||||||
\(770\) | 1.39107e12 | 0.142607 | ||||||||
\(771\) | −1.68569e13 | −1.71804 | ||||||||
\(772\) | 2.27618e13 | 2.30637 | ||||||||
\(773\) | −1.51411e13 | −1.52528 | −0.762640 | − | 0.646823i | \(-0.776097\pi\) | ||||
−0.762640 | + | 0.646823i | \(0.776097\pi\) | |||||||
\(774\) | 4.01049e13 | 4.01664 | ||||||||
\(775\) | −3.79977e12 | −0.378356 | ||||||||
\(776\) | 6.04397e12 | 0.598335 | ||||||||
\(777\) | 8.60825e12 | 0.847267 | ||||||||
\(778\) | −1.29377e12 | −0.126604 | ||||||||
\(779\) | 2.39177e12 | 0.232702 | ||||||||
\(780\) | 2.23180e12 | 0.215889 | ||||||||
\(781\) | −1.22768e13 | −1.18074 | ||||||||
\(782\) | −3.24687e13 | −3.10481 | ||||||||
\(783\) | −6.88408e12 | −0.654513 | ||||||||
\(784\) | −3.05167e11 | −0.0288480 | ||||||||
\(785\) | 1.67479e12 | 0.157416 | ||||||||
\(786\) | 2.33210e13 | 2.17944 | ||||||||
\(787\) | −1.10748e13 | −1.02908 | −0.514542 | − | 0.857465i | \(-0.672038\pi\) | ||||
−0.514542 | + | 0.857465i | \(0.672038\pi\) | |||||||
\(788\) | −2.08245e13 | −1.92400 | ||||||||
\(789\) | 2.63223e13 | 2.41811 | ||||||||
\(790\) | −7.18540e12 | −0.656341 | ||||||||
\(791\) | −6.10494e12 | −0.554482 | ||||||||
\(792\) | 1.20072e13 | 1.08437 | ||||||||
\(793\) | 1.47225e10 | 0.00132206 | ||||||||
\(794\) | 2.10509e13 | 1.87966 | ||||||||
\(795\) | 1.53154e12 | 0.135980 | ||||||||
\(796\) | 1.62841e13 | 1.43766 | ||||||||
\(797\) | −1.41284e13 | −1.24032 | −0.620158 | − | 0.784477i | \(-0.712931\pi\) | ||||
−0.620158 | + | 0.784477i | \(0.712931\pi\) | |||||||
\(798\) | 1.79805e13 | 1.56960 | ||||||||
\(799\) | 2.50587e12 | 0.217520 | ||||||||
\(800\) | −1.20673e13 | −1.04161 | ||||||||
\(801\) | −2.76597e13 | −2.37411 | ||||||||
\(802\) | −3.29894e12 | −0.281573 | ||||||||
\(803\) | 6.95340e12 | 0.590171 | ||||||||
\(804\) | 5.11842e13 | 4.32000 | ||||||||
\(805\) | −1.72179e12 | −0.144510 | ||||||||
\(806\) | −2.21068e12 | −0.184510 | ||||||||
\(807\) | −3.42020e12 | −0.283871 | ||||||||
\(808\) | −8.23123e12 | −0.679382 | ||||||||
\(809\) | −1.45772e13 | −1.19648 | −0.598239 | − | 0.801317i | \(-0.704133\pi\) | ||||
−0.598239 | + | 0.801317i | \(0.704133\pi\) | |||||||
\(810\) | −1.21467e12 | −0.0991457 | ||||||||
\(811\) | 8.28702e12 | 0.672674 | 0.336337 | − | 0.941742i | \(-0.390812\pi\) | ||||
0.336337 | + | 0.941742i | \(0.390812\pi\) | |||||||
\(812\) | −4.03026e12 | −0.325335 | ||||||||
\(813\) | −5.97725e12 | −0.479838 | ||||||||
\(814\) | 2.07387e13 | 1.65566 | ||||||||
\(815\) | 4.98535e12 | 0.395810 | ||||||||
\(816\) | 6.67839e12 | 0.527310 | ||||||||
\(817\) | 3.00262e13 | 2.35777 | ||||||||
\(818\) | −1.37778e13 | −1.07594 | ||||||||
\(819\) | 2.30072e12 | 0.178684 | ||||||||
\(820\) | −8.97116e11 | −0.0692925 | ||||||||
\(821\) | −1.34592e13 | −1.03389 | −0.516944 | − | 0.856019i | \(-0.672931\pi\) | ||||
−0.516944 | + | 0.856019i | \(0.672931\pi\) | |||||||
\(822\) | −2.74902e13 | −2.10017 | ||||||||
\(823\) | −1.12252e13 | −0.852892 | −0.426446 | − | 0.904513i | \(-0.640235\pi\) | ||||
−0.426446 | + | 0.904513i | \(0.640235\pi\) | |||||||
\(824\) | 5.99598e12 | 0.453094 | ||||||||
\(825\) | 1.51164e13 | 1.13607 | ||||||||
\(826\) | 9.10490e12 | 0.680558 | ||||||||
\(827\) | 1.18754e13 | 0.882821 | 0.441411 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441411 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(828\) | −4.32378e13 | −3.19688 | ||||||||
\(829\) | 1.79748e13 | 1.32181 | 0.660903 | − | 0.750471i | \(-0.270173\pi\) | ||||
0.660903 | + | 0.750471i | \(0.270173\pi\) | |||||||
\(830\) | 2.55211e12 | 0.186658 | ||||||||
\(831\) | −8.54472e12 | −0.621574 | ||||||||
\(832\) | −6.24657e12 | −0.451946 | ||||||||
\(833\) | −3.15217e12 | −0.226834 | ||||||||
\(834\) | −4.41553e13 | −3.16035 | ||||||||
\(835\) | −6.48595e12 | −0.461726 | ||||||||
\(836\) | 2.61538e13 | 1.85186 | ||||||||
\(837\) | 6.88943e12 | 0.485198 | ||||||||
\(838\) | 5.41175e12 | 0.379088 | ||||||||
\(839\) | −1.21225e13 | −0.844623 | −0.422312 | − | 0.906451i | \(-0.638781\pi\) | ||||
−0.422312 | + | 0.906451i | \(0.638781\pi\) | |||||||
\(840\) | −2.31816e12 | −0.160652 | ||||||||
\(841\) | −9.87785e12 | −0.680895 | ||||||||
\(842\) | −3.91715e13 | −2.68575 | ||||||||
\(843\) | −1.92288e13 | −1.31138 | ||||||||
\(844\) | −2.12349e13 | −1.44049 | ||||||||
\(845\) | 3.54122e11 | 0.0238945 | ||||||||
\(846\) | 5.52700e12 | 0.370957 | ||||||||
\(847\) | −2.35183e12 | −0.157011 | ||||||||
\(848\) | −8.09438e11 | −0.0537529 | ||||||||
\(849\) | −2.36021e13 | −1.55907 | ||||||||
\(850\) | −3.46854e13 | −2.27909 | ||||||||
\(851\) | −2.56692e13 | −1.67776 | ||||||||
\(852\) | 5.95208e13 | 3.86982 | ||||||||
\(853\) | −1.99327e13 | −1.28913 | −0.644564 | − | 0.764550i | \(-0.722961\pi\) | ||||
−0.644564 | + | 0.764550i | \(0.722961\pi\) | |||||||
\(854\) | −4.44896e10 | −0.00286219 | ||||||||
\(855\) | −1.31512e13 | −0.841622 | ||||||||
\(856\) | −3.59447e12 | −0.228824 | ||||||||
\(857\) | −1.82579e13 | −1.15621 | −0.578107 | − | 0.815961i | \(-0.696208\pi\) | ||||
−0.578107 | + | 0.815961i | \(0.696208\pi\) | |||||||
\(858\) | 8.79459e12 | 0.554017 | ||||||||
\(859\) | −6.62180e12 | −0.414961 | −0.207480 | − | 0.978239i | \(-0.566526\pi\) | ||||
−0.207480 | + | 0.978239i | \(0.566526\pi\) | |||||||
\(860\) | −1.12624e13 | −0.702082 | ||||||||
\(861\) | −1.46738e12 | −0.0909974 | ||||||||
\(862\) | 1.63530e13 | 1.00882 | ||||||||
\(863\) | 2.17631e12 | 0.133559 | 0.0667794 | − | 0.997768i | \(-0.478728\pi\) | ||||
0.0667794 | + | 0.997768i | \(0.478728\pi\) | |||||||
\(864\) | 2.18794e13 | 1.33574 | ||||||||
\(865\) | 2.37288e12 | 0.144113 | ||||||||
\(866\) | 3.19684e13 | 1.93148 | ||||||||
\(867\) | 4.16222e13 | 2.50172 | ||||||||
\(868\) | 4.03339e12 | 0.241175 | ||||||||
\(869\) | −1.70954e13 | −1.01693 | ||||||||
\(870\) | 7.74666e12 | 0.458435 | ||||||||
\(871\) | 8.12144e12 | 0.478136 | ||||||||
\(872\) | −1.56955e13 | −0.919288 | ||||||||
\(873\) | −2.10363e13 | −1.22576 | ||||||||
\(874\) | −5.36166e13 | −3.10812 | ||||||||
\(875\) | −3.87511e12 | −0.223484 | ||||||||
\(876\) | −3.37118e13 | −1.93425 | ||||||||
\(877\) | −1.95150e12 | −0.111396 | −0.0556981 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556981 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(878\) | 4.29511e13 | 2.43921 | ||||||||
\(879\) | 1.02573e13 | 0.579539 | ||||||||
\(880\) | 8.53202e11 | 0.0479601 | ||||||||
\(881\) | −1.04264e12 | −0.0583102 | −0.0291551 | − | 0.999575i | \(-0.509282\pi\) | ||||
−0.0291551 | + | 0.999575i | \(0.509282\pi\) | |||||||
\(882\) | −6.95249e12 | −0.386841 | ||||||||
\(883\) | 1.82714e13 | 1.01146 | 0.505730 | − | 0.862692i | \(-0.331223\pi\) | ||||
0.505730 | + | 0.862692i | \(0.331223\pi\) | |||||||
\(884\) | −1.21838e13 | −0.671039 | ||||||||
\(885\) | −1.05663e13 | −0.579000 | ||||||||
\(886\) | −2.54279e13 | −1.38630 | ||||||||
\(887\) | −2.54434e13 | −1.38012 | −0.690062 | − | 0.723750i | \(-0.742417\pi\) | ||||
−0.690062 | + | 0.723750i | \(0.742417\pi\) | |||||||
\(888\) | −3.45601e13 | −1.86516 | ||||||||
\(889\) | −6.93028e12 | −0.372128 | ||||||||
\(890\) | 1.28651e13 | 0.687319 | ||||||||
\(891\) | −2.88991e12 | −0.153615 | ||||||||
\(892\) | 2.97656e13 | 1.57424 | ||||||||
\(893\) | 4.13803e12 | 0.217752 | ||||||||
\(894\) | 2.61669e13 | 1.37004 | ||||||||
\(895\) | 9.65319e12 | 0.502883 | ||||||||
\(896\) | 1.04700e13 | 0.542700 | ||||||||
\(897\) | −1.08855e13 | −0.561411 | ||||||||
\(898\) | 5.47056e13 | 2.80730 | ||||||||
\(899\) | −4.63290e12 | −0.236556 | ||||||||
\(900\) | −4.61897e13 | −2.34668 | ||||||||
\(901\) | −8.36095e12 | −0.422663 | ||||||||
\(902\) | −3.53516e12 | −0.177819 | ||||||||
\(903\) | −1.84215e13 | −0.921999 | ||||||||
\(904\) | 2.45099e13 | 1.22063 | ||||||||
\(905\) | −1.82825e12 | −0.0905976 | ||||||||
\(906\) | 1.38377e13 | 0.682318 | ||||||||
\(907\) | 2.68870e13 | 1.31920 | 0.659598 | − | 0.751618i | \(-0.270726\pi\) | ||||
0.659598 | + | 0.751618i | \(0.270726\pi\) | |||||||
\(908\) | −2.05903e13 | −1.00526 | ||||||||
\(909\) | 2.86491e13 | 1.39179 | ||||||||
\(910\) | −1.07011e12 | −0.0517301 | ||||||||
\(911\) | 1.32637e13 | 0.638015 | 0.319008 | − | 0.947752i | \(-0.396650\pi\) | ||||
0.319008 | + | 0.947752i | \(0.396650\pi\) | |||||||
\(912\) | 1.10282e13 | 0.527873 | ||||||||
\(913\) | 6.07192e12 | 0.289206 | ||||||||
\(914\) | −1.54920e13 | −0.734260 | ||||||||
\(915\) | 5.16305e10 | 0.00243507 | ||||||||
\(916\) | 4.01263e13 | 1.88321 | ||||||||
\(917\) | −6.75131e12 | −0.315302 | ||||||||
\(918\) | 6.28887e13 | 2.92267 | ||||||||
\(919\) | −2.84043e13 | −1.31360 | −0.656801 | − | 0.754064i | \(-0.728091\pi\) | ||||
−0.656801 | + | 0.754064i | \(0.728091\pi\) | |||||||
\(920\) | 6.91257e12 | 0.318123 | ||||||||
\(921\) | 1.14532e13 | 0.524515 | ||||||||
\(922\) | 1.30751e13 | 0.595877 | ||||||||
\(923\) | 9.44422e12 | 0.428310 | ||||||||
\(924\) | −1.60457e13 | −0.724162 | ||||||||
\(925\) | −2.74216e13 | −1.23156 | ||||||||
\(926\) | −6.13300e13 | −2.74109 | ||||||||
\(927\) | −2.08692e13 | −0.928213 | ||||||||
\(928\) | −1.47131e13 | −0.651236 | ||||||||
\(929\) | −1.41616e12 | −0.0623796 | −0.0311898 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311898 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(930\) | −7.75267e12 | −0.339843 | ||||||||
\(931\) | −5.20528e12 | −0.227076 | ||||||||
\(932\) | −4.76394e13 | −2.06821 | ||||||||
\(933\) | 3.76137e12 | 0.162509 | ||||||||
\(934\) | 2.96121e13 | 1.27323 | ||||||||
\(935\) | 8.81300e12 | 0.377113 | ||||||||
\(936\) | −9.23685e12 | −0.393353 | ||||||||
\(937\) | 1.36000e13 | 0.576381 | 0.288191 | − | 0.957573i | \(-0.406946\pi\) | ||||
0.288191 | + | 0.957573i | \(0.406946\pi\) | |||||||
\(938\) | −2.45420e13 | −1.03514 | ||||||||
\(939\) | 7.09746e12 | 0.297926 | ||||||||
\(940\) | −1.55211e12 | −0.0648407 | ||||||||
\(941\) | 1.71397e13 | 0.712606 | 0.356303 | − | 0.934370i | \(-0.384037\pi\) | ||||
0.356303 | + | 0.934370i | \(0.384037\pi\) | |||||||
\(942\) | −3.19967e13 | −1.32396 | ||||||||
\(943\) | 4.37562e12 | 0.180193 | ||||||||
\(944\) | 5.58443e12 | 0.228878 | ||||||||
\(945\) | 3.33493e12 | 0.136033 | ||||||||
\(946\) | −4.43803e13 | −1.80169 | ||||||||
\(947\) | 1.72767e13 | 0.698050 | 0.349025 | − | 0.937113i | \(-0.386513\pi\) | ||||
0.349025 | + | 0.937113i | \(0.386513\pi\) | |||||||
\(948\) | 8.28825e13 | 3.33292 | ||||||||
\(949\) | −5.34908e12 | −0.214082 | ||||||||
\(950\) | −5.72771e13 | −2.28152 | ||||||||
\(951\) | 1.38450e12 | 0.0548886 | ||||||||
\(952\) | 1.26552e13 | 0.499348 | ||||||||
\(953\) | 2.53499e13 | 0.995540 | 0.497770 | − | 0.867309i | \(-0.334152\pi\) | ||||
0.497770 | + | 0.867309i | \(0.334152\pi\) | |||||||
\(954\) | −1.84411e13 | −0.720806 | ||||||||
\(955\) | 4.83572e12 | 0.188125 | ||||||||
\(956\) | −5.78280e13 | −2.23912 | ||||||||
\(957\) | 1.84307e13 | 0.710294 | ||||||||
\(958\) | −4.79367e13 | −1.83875 | ||||||||
\(959\) | 7.95828e12 | 0.303833 | ||||||||
\(960\) | −2.19062e13 | −0.832427 | ||||||||
\(961\) | −2.18031e13 | −0.824638 | ||||||||
\(962\) | −1.59537e13 | −0.600585 | ||||||||
\(963\) | 1.25107e13 | 0.468773 | ||||||||
\(964\) | 1.75384e13 | 0.654098 | ||||||||
\(965\) | 1.26657e13 | 0.470172 | ||||||||
\(966\) | 3.28945e13 | 1.21542 | ||||||||
\(967\) | 9.19232e12 | 0.338069 | 0.169035 | − | 0.985610i | \(-0.445935\pi\) | ||||
0.169035 | + | 0.985610i | \(0.445935\pi\) | |||||||
\(968\) | 9.44204e12 | 0.345642 | ||||||||
\(969\) | 1.13914e14 | 4.15070 | ||||||||
\(970\) | 9.78441e12 | 0.354864 | ||||||||
\(971\) | −2.88697e13 | −1.04221 | −0.521106 | − | 0.853492i | \(-0.674480\pi\) | ||||
−0.521106 | + | 0.853492i | \(0.674480\pi\) | |||||||
\(972\) | −3.51209e13 | −1.26202 | ||||||||
\(973\) | 1.27827e13 | 0.457211 | ||||||||
\(974\) | 1.24546e13 | 0.443420 | ||||||||
\(975\) | −1.16286e13 | −0.412105 | ||||||||
\(976\) | −2.72874e10 | −0.000962582 0 | ||||||||
\(977\) | −1.03809e13 | −0.364511 | −0.182255 | − | 0.983251i | \(-0.558340\pi\) | ||||
−0.182255 | + | 0.983251i | \(0.558340\pi\) | |||||||
\(978\) | −9.52445e13 | −3.32901 | ||||||||
\(979\) | 3.06084e13 | 1.06492 | ||||||||
\(980\) | 1.95242e12 | 0.0676172 | ||||||||
\(981\) | 5.46288e13 | 1.88327 | ||||||||
\(982\) | −7.76088e13 | −2.66323 | ||||||||
\(983\) | −7.46537e12 | −0.255012 | −0.127506 | − | 0.991838i | \(-0.540697\pi\) | ||||
−0.127506 | + | 0.991838i | \(0.540697\pi\) | |||||||
\(984\) | 5.89119e12 | 0.200320 | ||||||||
\(985\) | −1.15877e13 | −0.392223 | ||||||||
\(986\) | −4.22904e13 | −1.42494 | ||||||||
\(987\) | −2.53874e12 | −0.0851512 | ||||||||
\(988\) | −2.01195e13 | −0.671755 | ||||||||
\(989\) | 5.49316e13 | 1.82574 | ||||||||
\(990\) | 1.94381e13 | 0.643126 | ||||||||
\(991\) | 1.19731e13 | 0.394345 | 0.197173 | − | 0.980369i | \(-0.436824\pi\) | ||||
0.197173 | + | 0.980369i | \(0.436824\pi\) | |||||||
\(992\) | 1.47245e13 | 0.482769 | ||||||||
\(993\) | −6.36077e13 | −2.07605 | ||||||||
\(994\) | −2.85393e13 | −0.927266 | ||||||||
\(995\) | 9.06124e12 | 0.293078 | ||||||||
\(996\) | −2.94381e13 | −0.947858 | ||||||||
\(997\) | 3.43494e12 | 0.110101 | 0.0550504 | − | 0.998484i | \(-0.482468\pi\) | ||||
0.0550504 | + | 0.998484i | \(0.482468\pi\) | |||||||
\(998\) | 3.89205e13 | 1.24191 | ||||||||
\(999\) | 4.97186e13 | 1.57934 |
(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 | 91.10.a.a.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.a.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial |