Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,7,Mod(8,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.8");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.d (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.21146025774\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{14} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.5 | ||
Root | \(4.07727 + 7.06203i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.8 |
Dual form | 27.7.d.a.17.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.2318 | + | 7.06203i | 1.52898 | + | 0.882754i | 0.999405 | + | 0.0344882i | \(0.0109801\pi\) |
0.529570 | + | 0.848266i | \(0.322353\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 67.7447 | + | 117.337i | 1.05851 | + | 1.83339i | ||||
\(5\) | 103.839 | − | 59.9512i | 0.830709 | − | 0.479610i | −0.0233865 | − | 0.999726i | \(-0.507445\pi\) |
0.854095 | + | 0.520117i | \(0.174112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −128.891 | + | 223.245i | −0.375774 | + | 0.650860i | −0.990443 | − | 0.137926i | \(-0.955956\pi\) |
0.614668 | + | 0.788786i | \(0.289290\pi\) | |||||||
\(8\) | 1009.72i | 1.97211i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1693.51 | 1.69351 | ||||||||
\(11\) | −518.417 | − | 299.308i | −0.389495 | − | 0.224875i | 0.292447 | − | 0.956282i | \(-0.405531\pi\) |
−0.681941 | + | 0.731407i | \(0.738864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −968.088 | − | 1676.78i | −0.440641 | − | 0.763212i | 0.557096 | − | 0.830448i | \(-0.311915\pi\) |
−0.997737 | + | 0.0672356i | \(0.978582\pi\) | |||||||
\(14\) | −3153.13 | + | 1820.46i | −1.14910 | + | 0.663432i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2795.02 | + | 4841.12i | −0.682378 | + | 1.18191i | ||||
\(17\) | − | 4874.12i | − | 0.992085i | −0.868298 | − | 0.496043i | \(-0.834786\pi\) | ||
0.868298 | − | 0.496043i | \(-0.165214\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7688.70 | 1.12097 | 0.560483 | − | 0.828166i | \(-0.310616\pi\) | ||||
0.560483 | + | 0.828166i | \(0.310616\pi\) | |||||||
\(20\) | 14069.0 | + | 8122.75i | 1.75863 | + | 1.01534i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4227.45 | − | 7322.16i | −0.397018 | − | 0.687656i | ||||
\(23\) | 594.548 | − | 343.263i | 0.0488656 | − | 0.0282126i | −0.475368 | − | 0.879787i | \(-0.657685\pi\) |
0.524234 | + | 0.851574i | \(0.324352\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −624.198 | + | 1081.14i | −0.0399486 | + | 0.0691931i | ||||
\(26\) | − | 27346.7i | − | 1.55591i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −34926.6 | −1.59104 | ||||||||
\(29\) | −29972.2 | − | 17304.5i | −1.22892 | − | 0.709520i | −0.262119 | − | 0.965036i | \(-0.584421\pi\) |
−0.966805 | + | 0.255516i | \(0.917755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1387.88 | − | 2403.88i | −0.0465872 | − | 0.0806915i | 0.841791 | − | 0.539803i | \(-0.181501\pi\) |
−0.888379 | + | 0.459111i | \(0.848168\pi\) | |||||||
\(32\) | −12411.9 | + | 7166.00i | −0.378780 | + | 0.218689i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 34421.2 | − | 59619.2i | 0.875768 | − | 1.51687i | ||||
\(35\) | 30908.6i | 0.720900i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17175.3 | 0.339077 | 0.169539 | − | 0.985524i | \(-0.445772\pi\) | ||||
0.169539 | + | 0.985524i | \(0.445772\pi\) | |||||||
\(38\) | 94046.7 | + | 54297.9i | 1.71393 | + | 0.989537i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 60534.0 | + | 104848.i | 0.945843 | + | 1.63825i | ||||
\(41\) | −71583.2 | + | 41328.6i | −1.03863 | + | 0.599652i | −0.919444 | − | 0.393221i | \(-0.871361\pi\) |
−0.119183 | + | 0.992872i | \(0.538027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −63212.6 | + | 109487.i | −0.795056 | + | 1.37708i | 0.127747 | + | 0.991807i | \(0.459225\pi\) |
−0.922803 | + | 0.385271i | \(0.874108\pi\) | |||||||
\(44\) | − | 81106.2i | − | 0.952129i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9696.53 | 0.0996191 | ||||||||
\(47\) | 72025.6 | + | 41584.0i | 0.693734 | + | 0.400528i | 0.805009 | − | 0.593262i | \(-0.202160\pi\) |
−0.111275 | + | 0.993790i | \(0.535494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25599.0 | + | 44338.7i | 0.217588 | + | 0.376873i | ||||
\(50\) | −15270.1 | + | 8816.21i | −0.122161 | + | 0.0705297i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 131166. | − | 227185.i | 0.932846 | − | 1.61574i | ||||
\(53\) | 40017.8i | 0.268798i | 0.990927 | + | 0.134399i | \(0.0429103\pi\) | ||||
−0.990927 | + | 0.134399i | \(0.957090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −71775.6 | −0.431409 | ||||||||
\(56\) | −225415. | − | 130143.i | −1.28357 | − | 0.741068i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −244410. | − | 423330.i | −1.25266 | − | 2.16968i | ||||
\(59\) | 57614.7 | − | 33263.9i | 0.280529 | − | 0.161963i | −0.353134 | − | 0.935573i | \(-0.614884\pi\) |
0.633663 | + | 0.773609i | \(0.281551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −184662. | + | 319843.i | −0.813555 | + | 1.40912i | 0.0968060 | + | 0.995303i | \(0.469137\pi\) |
−0.910361 | + | 0.413815i | \(0.864196\pi\) | |||||||
\(62\) | − | 39205.0i | − | 0.164500i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 155336. | 0.592561 | ||||||||
\(65\) | −201050. | − | 116076.i | −0.732088 | − | 0.422671i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −127954. | − | 221623.i | −0.425432 | − | 0.736870i | 0.571029 | − | 0.820930i | \(-0.306545\pi\) |
−0.996461 | + | 0.0840603i | \(0.973211\pi\) | |||||||
\(68\) | 571915. | − | 330195.i | 1.81888 | − | 1.05013i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −218277. | + | 378068.i | −0.636377 | + | 1.10224i | ||||
\(71\) | 269837.i | 0.753923i | 0.926229 | + | 0.376961i | \(0.123031\pi\) | ||||
−0.926229 | + | 0.376961i | \(0.876969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 551862. | 1.41861 | 0.709303 | − | 0.704903i | \(-0.249010\pi\) | ||||
0.709303 | + | 0.704903i | \(0.249010\pi\) | |||||||
\(74\) | 210085. | + | 121292.i | 0.518441 | + | 0.299322i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 520869. | + | 902171.i | 1.18655 | + | 2.05517i | ||||
\(77\) | 133638. | − | 77156.0i | 0.292724 | − | 0.169004i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 355021. | − | 614915.i | 0.720068 | − | 1.24719i | −0.240905 | − | 0.970549i | \(-0.577444\pi\) |
0.960972 | − | 0.276645i | \(-0.0892226\pi\) | |||||||
\(80\) | 670259.i | 1.30910i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.16746e6 | −2.11738 | ||||||||
\(83\) | −301612. | − | 174136.i | −0.527490 | − | 0.304547i | 0.212503 | − | 0.977160i | \(-0.431838\pi\) |
−0.739994 | + | 0.672614i | \(0.765172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −292209. | − | 506121.i | −0.475814 | − | 0.824134i | ||||
\(86\) | −1.54641e6 | + | 892818.i | −2.43124 | + | 1.40368i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 302218. | − | 523456.i | 0.443478 | − | 0.768126i | ||||
\(89\) | − | 836103.i | − | 1.18601i | −0.805197 | − | 0.593007i | \(-0.797941\pi\) | ||
0.805197 | − | 0.593007i | \(-0.202059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 499109. | 0.662326 | ||||||||
\(92\) | 80554.9 | + | 46508.4i | 0.103450 | + | 0.0597266i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 587335. | + | 1.01729e6i | 0.707135 | + | 1.22479i | ||||
\(95\) | 798384. | − | 460947.i | 0.931196 | − | 0.537626i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47014.3 | + | 81431.2i | −0.0515128 | + | 0.0892227i | −0.890632 | − | 0.454725i | \(-0.849738\pi\) |
0.839119 | + | 0.543948i | \(0.183071\pi\) | |||||||
\(98\) | 723123.i | 0.768306i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −169144. | −0.169144 | ||||||||
\(101\) | 233315. | + | 134704.i | 0.226453 | + | 0.130743i | 0.608935 | − | 0.793220i | \(-0.291597\pi\) |
−0.382482 | + | 0.923963i | \(0.624930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 128429. | + | 222446.i | 0.117531 | + | 0.203569i | 0.918789 | − | 0.394750i | \(-0.129169\pi\) |
−0.801258 | + | 0.598319i | \(0.795835\pi\) | |||||||
\(104\) | 1.69308e6 | − | 977498.i | 1.50514 | − | 0.868992i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −282607. | + | 489490.i | −0.237282 | + | 0.410985i | ||||
\(107\) | 983414.i | 0.802759i | 0.915912 | + | 0.401379i | \(0.131469\pi\) | ||||
−0.915912 | + | 0.401379i | \(0.868531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.19797e6 | −0.925053 | −0.462526 | − | 0.886606i | \(-0.653057\pi\) | ||||
−0.462526 | + | 0.886606i | \(0.653057\pi\) | |||||||
\(110\) | −877945. | − | 506882.i | −0.659613 | − | 0.380828i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −720503. | − | 1.24795e6i | −0.512840 | − | 0.888264i | ||||
\(113\) | 246875. | − | 142533.i | 0.171097 | − | 0.0987827i | −0.412006 | − | 0.911181i | \(-0.635172\pi\) |
0.583103 | + | 0.812398i | \(0.301838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41158.0 | − | 71287.8i | 0.0270621 | − | 0.0468729i | ||||
\(116\) | − | 4.68914e6i | − | 3.00414i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 939643. | 0.571896 | ||||||||
\(119\) | 1.08812e6 | + | 628227.i | 0.645709 | + | 0.372800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −706609. | − | 1.22388e6i | −0.398863 | − | 0.690850i | ||||
\(122\) | −4.51749e6 | + | 2.60817e6i | −2.48781 | + | 1.43634i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 188043. | − | 325700.i | 0.0986261 | − | 0.170825i | ||||
\(125\) | 2.02316e6i | 1.03586i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 359846. | 0.175673 | 0.0878365 | − | 0.996135i | \(-0.472005\pi\) | ||||
0.0878365 | + | 0.996135i | \(0.472005\pi\) | |||||||
\(128\) | 2.69440e6 | + | 1.55561e6i | 1.28479 | + | 0.741775i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.63947e6 | − | 2.83964e6i | −0.746230 | − | 1.29251i | ||||
\(131\) | 1.24110e6 | − | 716547.i | 0.552066 | − | 0.318736i | −0.197889 | − | 0.980225i | \(-0.563408\pi\) |
0.749955 | + | 0.661489i | \(0.230075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −991001. | + | 1.71646e6i | −0.421230 | + | 0.729591i | ||||
\(134\) | − | 3.61447e6i | − | 1.50221i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.92149e6 | 1.95650 | ||||||||
\(137\) | −3.36619e6 | − | 1.94347e6i | −1.30911 | − | 0.755816i | −0.327164 | − | 0.944968i | \(-0.606093\pi\) |
−0.981948 | + | 0.189152i | \(0.939426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.53995e6 | + | 4.39933e6i | 0.945760 | + | 1.63810i | 0.754222 | + | 0.656620i | \(0.228014\pi\) |
0.191538 | + | 0.981485i | \(0.438652\pi\) | |||||||
\(140\) | −3.62673e6 | + | 2.09389e6i | −1.32169 | + | 0.763080i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.90560e6 | + | 3.30060e6i | −0.665529 | + | 1.15273i | ||||
\(143\) | 1.15903e6i | 0.396356i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.14970e6 | −1.36117 | ||||||||
\(146\) | 6.75027e6 | + | 3.89727e6i | 2.16902 | + | 1.25228i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.16353e6 | + | 2.01530e6i | 0.358917 | + | 0.621662i | ||||
\(149\) | 842550. | − | 486446.i | 0.254705 | − | 0.147054i | −0.367212 | − | 0.930137i | \(-0.619688\pi\) |
0.621917 | + | 0.783084i | \(0.286354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.13402e6 | − | 5.42828e6i | 0.910271 | − | 1.57663i | 0.0965886 | − | 0.995324i | \(-0.469207\pi\) |
0.813682 | − | 0.581310i | \(-0.197460\pi\) | |||||||
\(152\) | 7.76344e6i | 2.21067i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.17951e6 | 0.596757 | ||||||||
\(155\) | −288231. | − | 166410.i | −0.0774008 | − | 0.0446874i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 832183. | + | 1.44138e6i | 0.215040 | + | 0.372461i | 0.953285 | − | 0.302072i | \(-0.0976783\pi\) |
−0.738245 | + | 0.674533i | \(0.764345\pi\) | |||||||
\(158\) | 8.68510e6 | − | 5.01435e6i | 2.20193 | − | 1.27129i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −859221. | + | 1.48822e6i | −0.209771 | + | 0.363334i | ||||
\(161\) | 176973.i | 0.0424062i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.47297e6 | 0.571025 | 0.285513 | − | 0.958375i | \(-0.407836\pi\) | ||||
0.285513 | + | 0.958375i | \(0.407836\pi\) | |||||||
\(164\) | −9.69876e6 | − | 5.59958e6i | −2.19879 | − | 1.26947i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.45951e6 | − | 4.25999e6i | −0.537680 | − | 0.931289i | ||||
\(167\) | −5.00452e6 | + | 2.88936e6i | −1.07452 | + | 0.620373i | −0.929412 | − | 0.369044i | \(-0.879685\pi\) |
−0.145105 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 539017. | − | 933604.i | 0.111671 | − | 0.193421i | ||||
\(170\) | − | 8.25437e6i | − | 1.68011i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.71293e7 | −3.36630 | ||||||||
\(173\) | −6.80297e6 | − | 3.92770e6i | −1.31389 | − | 0.758577i | −0.331156 | − | 0.943576i | \(-0.607438\pi\) |
−0.982739 | + | 0.184999i | \(0.940772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −160906. | − | 278698.i | −0.0300233 | − | 0.0520019i | ||||
\(176\) | 2.89797e6 | − | 1.67315e6i | 0.531565 | − | 0.306899i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.90459e6 | − | 1.02270e7i | 1.04696 | − | 1.81339i | ||||
\(179\) | − | 1.71905e6i | − | 0.299730i | −0.988706 | − | 0.149865i | \(-0.952116\pi\) | ||
0.988706 | − | 0.149865i | \(-0.0478839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16259e6 | −0.701985 | −0.350993 | − | 0.936378i | \(-0.614156\pi\) | ||||
−0.350993 | + | 0.936378i | \(0.614156\pi\) | |||||||
\(182\) | 6.10501e6 | + | 3.52473e6i | 1.01268 | + | 0.584671i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 346599. | + | 600327.i | 0.0556383 | + | 0.0963684i | ||||
\(185\) | 1.78346e6 | − | 1.02968e6i | 0.281674 | − | 0.162625i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45886e6 | + | 2.52683e6i | −0.223095 | + | 0.386412i | ||||
\(188\) | 1.12684e7i | 1.69585i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.30209e7 | 1.89837 | ||||||||
\(191\) | 7.35905e6 | + | 4.24875e6i | 1.05614 | + | 0.609763i | 0.924362 | − | 0.381516i | \(-0.124598\pi\) |
0.131778 | + | 0.991279i | \(0.457931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.99176e6 | + | 3.44984e6i | 0.277055 | + | 0.479873i | 0.970651 | − | 0.240490i | \(-0.0773083\pi\) |
−0.693597 | + | 0.720364i | \(0.743975\pi\) | |||||||
\(194\) | −1.15014e6 | + | 664033.i | −0.157523 | + | 0.0909462i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.46839e6 | + | 6.00742e6i | −0.460638 | + | 0.797848i | ||||
\(197\) | − | 5.45308e6i | − | 0.713252i | −0.934247 | − | 0.356626i | \(-0.883927\pi\) | ||
0.934247 | − | 0.356626i | \(-0.116073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.95878e6 | 0.502345 | 0.251172 | − | 0.967942i | \(-0.419184\pi\) | ||||
0.251172 | + | 0.967942i | \(0.419184\pi\) | |||||||
\(200\) | −1.09165e6 | − | 630265.i | −0.136456 | − | 0.0787831i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.90257e6 | + | 3.29535e6i | 0.230827 | + | 0.399805i | ||||
\(203\) | 7.72627e6 | − | 4.46077e6i | 0.923596 | − | 0.533238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.95540e6 | + | 8.58300e6i | −0.575198 | + | 0.996272i | ||||
\(206\) | 3.62788e6i | 0.415003i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.08233e7 | 1.20273 | ||||||||
\(209\) | −3.98596e6 | − | 2.30129e6i | −0.436610 | − | 0.252077i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.70148e6 | − | 8.14320e6i | −0.500481 | − | 0.866858i | −1.00000 | 0.000555034i | \(-0.999823\pi\) | |
0.499519 | − | 0.866303i | \(-0.333510\pi\) | |||||||
\(212\) | −4.69558e6 | + | 2.71099e6i | −0.492812 | + | 0.284525i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.94490e6 | + | 1.20289e7i | −0.708639 | + | 1.22740i | ||||
\(215\) | 1.51587e7i | 1.52527i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 715538. | 0.0700251 | ||||||||
\(218\) | −1.46533e7 | − | 8.46010e6i | −1.41438 | − | 0.816594i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.86242e6 | − | 8.42195e6i | −0.456651 | − | 0.790942i | ||||
\(221\) | −8.17281e6 | + | 4.71857e6i | −0.757172 | + | 0.437153i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 795234. | − | 1.37739e6i | 0.0717101 | − | 0.124205i | −0.827941 | − | 0.560816i | \(-0.810488\pi\) |
0.899651 | + | 0.436610i | \(0.143821\pi\) | |||||||
\(224\) | − | 3.69452e6i | − | 0.328711i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.02630e6 | 0.348803 | ||||||||
\(227\) | 6.81870e6 | + | 3.93678e6i | 0.582940 | + | 0.336561i | 0.762301 | − | 0.647223i | \(-0.224070\pi\) |
−0.179361 | + | 0.983783i | \(0.557403\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.97961e6 | − | 3.42878e6i | −0.164844 | − | 0.285518i | 0.771756 | − | 0.635919i | \(-0.219379\pi\) |
−0.936600 | + | 0.350401i | \(0.886045\pi\) | |||||||
\(230\) | 1.00687e6 | − | 581319.i | 0.0827545 | − | 0.0477783i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.74727e7 | − | 3.02636e7i | 1.39925 | − | 2.42357i | ||||
\(233\) | 2.89646e6i | 0.228981i | 0.993424 | + | 0.114491i | \(0.0365236\pi\) | ||||
−0.993424 | + | 0.114491i | \(0.963476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.97205e6 | 0.768388 | ||||||||
\(236\) | 7.80618e6 | + | 4.50690e6i | 0.593885 | + | 0.342880i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.87313e6 | + | 1.53687e7i | 0.658182 | + | 1.14000i | ||||
\(239\) | −576101. | + | 332612.i | −0.0421992 | + | 0.0243637i | −0.520951 | − | 0.853586i | \(-0.674423\pi\) |
0.478752 | + | 0.877950i | \(0.341089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −413009. | + | 715353.i | −0.0295059 | + | 0.0511057i | −0.880401 | − | 0.474229i | \(-0.842727\pi\) |
0.850895 | + | 0.525335i | \(0.176060\pi\) | |||||||
\(242\) | − | 1.99604e7i | − | 1.40839i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00393e7 | −3.44462 | ||||||||
\(245\) | 5.31632e6 | + | 3.06938e6i | 0.361504 | + | 0.208714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.44334e6 | − | 1.28922e7i | −0.493943 | − | 0.855535i | ||||
\(248\) | 2.42724e6 | − | 1.40137e6i | 0.159132 | − | 0.0918751i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.42876e7 | + | 2.47469e7i | −0.914409 | + | 1.58380i | ||||
\(251\) | − | 1.12048e7i | − | 0.708568i | −0.935138 | − | 0.354284i | \(-0.884725\pi\) | ||
0.935138 | − | 0.354284i | \(-0.115275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −410965. | −0.0253772 | ||||||||
\(254\) | 4.40156e6 | + | 2.54124e6i | 0.268600 | + | 0.155076i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.70008e7 | + | 2.94463e7i | 1.01333 | + | 1.75514i | ||||
\(257\) | 6.71894e6 | − | 3.87918e6i | 0.395823 | − | 0.228529i | −0.288857 | − | 0.957372i | \(-0.593275\pi\) |
0.684680 | + | 0.728844i | \(0.259942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.21373e6 | + | 3.83429e6i | −0.127416 | + | 0.220692i | ||||
\(260\) | − | 3.14542e7i | − | 1.78961i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.02411e7 | 1.12546 | ||||||||
\(263\) | 1.56666e7 | + | 9.04514e6i | 0.861209 | + | 0.497219i | 0.864417 | − | 0.502776i | \(-0.167688\pi\) |
−0.00320789 | + | 0.999995i | \(0.501021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.39912e6 | + | 4.15539e6i | 0.128918 | + | 0.223293i | ||||
\(266\) | −2.42435e7 | + | 1.39970e7i | −1.28810 | + | 0.743685i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.73364e7 | − | 3.00276e7i | 0.900648 | − | 1.55997i | ||||
\(269\) | − | 2.74843e7i | − | 1.41198i | −0.708222 | − | 0.705990i | \(-0.750502\pi\) | ||
0.708222 | − | 0.705990i | \(-0.249498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.70982e6 | 0.186400 | 0.0931999 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0931999 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(272\) | 2.35962e7 | + | 1.36232e7i | 1.17256 | + | 0.676977i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.74497e7 | − | 4.75443e7i | −1.33440 | − | 2.31125i | ||||
\(275\) | 647190. | − | 373655.i | 0.0311196 | − | 0.0179669i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.29022e7 | − | 2.23472e7i | 0.607049 | − | 1.05144i | −0.384675 | − | 0.923052i | \(-0.625687\pi\) |
0.991724 | − | 0.128387i | \(-0.0409801\pi\) | |||||||
\(278\) | 7.17489e7i | 3.33950i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.12090e7 | −1.42169 | ||||||||
\(281\) | −1.85887e7 | − | 1.07322e7i | −0.837781 | − | 0.483693i | 0.0187281 | − | 0.999825i | \(-0.494038\pi\) |
−0.856509 | + | 0.516131i | \(0.827372\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.29799e6 | + | 7.44434e6i | 0.189630 | + | 0.328448i | 0.945127 | − | 0.326704i | \(-0.105938\pi\) |
−0.755497 | + | 0.655152i | \(0.772605\pi\) | |||||||
\(284\) | −3.16620e7 | + | 1.82800e7i | −1.38224 | + | 0.798035i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.18509e6 | + | 1.41770e7i | −0.349885 | + | 0.606019i | ||||
\(287\) | − | 2.13074e7i | − | 0.901334i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 380565. | 0.0157665 | ||||||||
\(290\) | −5.07583e7 | − | 2.93053e7i | −2.08120 | − | 1.20158i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.73857e7 | + | 6.47540e7i | 1.50161 | + | 2.60086i | ||||
\(293\) | 2.62704e6 | − | 1.51672e6i | 0.104439 | − | 0.0602980i | −0.446871 | − | 0.894599i | \(-0.647462\pi\) |
0.551310 | + | 0.834301i | \(0.314128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.98842e6 | − | 6.90815e6i | 0.155359 | − | 0.269089i | ||||
\(296\) | 1.73422e7i | 0.668697i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.37412e7 | 0.519249 | ||||||||
\(299\) | −1.15115e6 | − | 664617.i | −0.0430644 | − | 0.0248632i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.62950e7 | − | 2.82238e7i | −0.597523 | − | 1.03494i | ||||
\(302\) | 7.66693e7 | − | 4.42651e7i | 2.78356 | − | 1.60709i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.14901e7 | + | 3.72219e7i | −0.764922 | + | 1.32488i | ||||
\(305\) | 4.42827e7i | 1.56076i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.14414e7 | 0.395426 | 0.197713 | − | 0.980260i | \(-0.436649\pi\) | ||||
0.197713 | + | 0.980260i | \(0.436649\pi\) | |||||||
\(308\) | 1.81065e7 | + | 1.04538e7i | 0.619703 | + | 0.357786i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.35039e6 | − | 4.07100e6i | −0.0788960 | − | 0.136652i | ||||
\(311\) | −2.38167e7 | + | 1.37506e7i | −0.791771 | + | 0.457129i | −0.840586 | − | 0.541679i | \(-0.817789\pi\) |
0.0488146 | + | 0.998808i | \(0.484456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.26080e7 | + | 2.18377e7i | −0.411163 | + | 0.712155i | −0.995017 | − | 0.0997035i | \(-0.968211\pi\) |
0.583854 | + | 0.811858i | \(0.301544\pi\) | |||||||
\(314\) | 2.35076e7i | 0.759311i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.62032e7 | 3.04880 | ||||||||
\(317\) | 2.38960e7 | + | 1.37964e7i | 0.750150 | + | 0.433099i | 0.825748 | − | 0.564039i | \(-0.190753\pi\) |
−0.0755979 | + | 0.997138i | \(0.524087\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.03587e7 | + | 1.79419e7i | 0.319106 | + | 0.552708i | ||||
\(320\) | 1.61299e7 | − | 9.31260e6i | 0.492245 | − | 0.284198i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.24979e6 | + | 2.16470e6i | −0.0374343 | + | 0.0648381i | ||||
\(323\) | − | 3.74756e7i | − | 1.11209i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41711e6 | 0.0704120 | ||||||||
\(326\) | 3.02488e7 | + | 1.74642e7i | 0.873083 | + | 0.504075i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.17303e7 | − | 7.22790e7i | −1.18258 | − | 2.04829i | ||||
\(329\) | −1.85668e7 | + | 1.07196e7i | −0.521375 | + | 0.301016i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.48940e7 | + | 4.31176e7i | −0.686452 | + | 1.18897i | 0.286527 | + | 0.958072i | \(0.407499\pi\) |
−0.972978 | + | 0.230897i | \(0.925834\pi\) | |||||||
\(332\) | − | 4.71871e7i | − | 1.28946i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.16191e7 | −2.19055 | ||||||||
\(335\) | −2.65732e7 | − | 1.53420e7i | −0.706820 | − | 0.408083i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.25640e7 | + | 2.17615e7i | 0.328275 | + | 0.568589i | 0.982170 | − | 0.187997i | \(-0.0601994\pi\) |
−0.653895 | + | 0.756586i | \(0.726866\pi\) | |||||||
\(338\) | 1.31863e7 | − | 7.61311e6i | 0.341486 | − | 0.197157i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.95912e7 | − | 6.85740e7i | 1.00731 | − | 1.74471i | ||||
\(341\) | 1.66162e6i | 0.0419052i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.35255e7 | −1.07860 | ||||||||
\(344\) | −1.10552e8 | − | 6.38270e7i | −2.71575 | − | 1.56794i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.54751e7 | − | 9.60857e7i | −1.33927 | − | 2.31969i | ||||
\(347\) | −6.77305e7 | + | 3.91042e7i | −1.62105 | + | 0.935912i | −0.634408 | + | 0.772999i | \(0.718756\pi\) |
−0.986640 | + | 0.162914i | \(0.947911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.64391e6 | − | 2.84733e6i | 0.0386724 | − | 0.0669826i | −0.846041 | − | 0.533117i | \(-0.821020\pi\) |
0.884714 | + | 0.466135i | \(0.154354\pi\) | |||||||
\(350\) | − | 4.54530e6i | − | 0.106013i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.57938e6 | 0.196711 | ||||||||
\(353\) | 5.41484e7 | + | 3.12626e7i | 1.23101 | + | 0.710724i | 0.967241 | − | 0.253861i | \(-0.0817006\pi\) |
0.263770 | + | 0.964586i | \(0.415034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.61771e7 | + | 2.80195e7i | 0.361589 | + | 0.626290i | ||||
\(356\) | 9.81060e7 | − | 5.66415e7i | 2.17443 | − | 1.25541i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.21400e7 | − | 2.10271e7i | 0.264588 | − | 0.458279i | ||||
\(359\) | 2.74347e7i | 0.592949i | 0.955041 | + | 0.296475i | \(0.0958110\pi\) | ||||
−0.955041 | + | 0.296475i | \(0.904189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.20703e7 | 0.256564 | ||||||||
\(362\) | −5.09160e7 | − | 2.93964e7i | −1.07332 | − | 0.619680i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.38120e7 | + | 5.85641e7i | 0.701078 | + | 1.21430i | ||||
\(365\) | 5.73046e7 | − | 3.30848e7i | 1.17845 | − | 0.680378i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.15329e7 | − | 3.72960e7i | 0.435616 | − | 0.754509i | −0.561730 | − | 0.827321i | \(-0.689864\pi\) |
0.997346 | + | 0.0728120i | \(0.0231973\pi\) | |||||||
\(368\) | 3.83770e6i | 0.0770066i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.90865e7 | 0.574231 | ||||||||
\(371\) | −8.93377e6 | − | 5.15791e6i | −0.174950 | − | 0.101007i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92734e7 | + | 3.33826e7i | 0.371392 | + | 0.643270i | 0.989780 | − | 0.142603i | \(-0.0455472\pi\) |
−0.618388 | + | 0.785873i | \(0.712214\pi\) | |||||||
\(374\) | −3.56891e7 | + | 2.06051e7i | −0.682214 | + | 0.393876i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.19882e7 | + | 7.27257e7i | −0.789884 | + | 1.36812i | ||||
\(377\) | 6.70090e7i | 1.25057i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.90700e7 | −1.26874 | −0.634369 | − | 0.773030i | \(-0.718740\pi\) | ||||
−0.634369 | + | 0.773030i | \(0.718740\pi\) | |||||||
\(380\) | 1.08173e8 | + | 6.24534e7i | 1.97136 | + | 1.13817i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00096e7 | + | 1.03940e8i | 1.07654 | + | 1.86463i | ||||
\(383\) | −1.05696e7 | + | 6.10238e6i | −0.188132 | + | 0.108618i | −0.591108 | − | 0.806592i | \(-0.701309\pi\) |
0.402976 | + | 0.915211i | \(0.367976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.25120e6 | − | 1.60235e7i | 0.162112 | − | 0.280787i | ||||
\(386\) | 5.62636e7i | 0.978285i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.27399e7 | −0.218107 | ||||||||
\(389\) | −4.23039e7 | − | 2.44242e7i | −0.718674 | − | 0.414926i | 0.0955907 | − | 0.995421i | \(-0.469526\pi\) |
−0.814264 | + | 0.580494i | \(0.802859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.67310e6 | − | 2.89790e6i | −0.0279893 | − | 0.0484789i | ||||
\(392\) | −4.47697e7 | + | 2.58478e7i | −0.743235 | + | 0.429107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.85098e7 | − | 6.67010e7i | 0.629626 | − | 1.09054i | ||||
\(395\) | − | 8.51359e7i | − | 1.38141i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.99924e7 | −0.319516 | −0.159758 | − | 0.987156i | \(-0.551071\pi\) | ||||
−0.159758 | + | 0.987156i | \(0.551071\pi\) | |||||||
\(398\) | 4.84230e7 | + | 2.79570e7i | 0.768073 | + | 0.443447i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.48929e6 | − | 6.04362e6i | −0.0545201 | − | 0.0944316i | ||||
\(401\) | 3.74023e7 | − | 2.15942e7i | 0.580049 | − | 0.334892i | −0.181104 | − | 0.983464i | \(-0.557967\pi\) |
0.761153 | + | 0.648572i | \(0.224634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.68718e6 | + | 4.65433e6i | −0.0410565 | + | 0.0711119i | ||||
\(404\) | 3.65020e7i | 0.553570i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26008e8 | 1.88287 | ||||||||
\(407\) | −8.90396e6 | − | 5.14071e6i | −0.132069 | − | 0.0762499i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.84954e7 | + | 3.20349e7i | 0.270329 | + | 0.468224i | 0.968946 | − | 0.247272i | \(-0.0795341\pi\) |
−0.698617 | + | 0.715496i | \(0.746201\pi\) | |||||||
\(410\) | −1.21227e8 | + | 6.99904e7i | −1.75893 | + | 1.01552i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.74008e7 | + | 3.01390e7i | −0.248815 | + | 0.430960i | ||||
\(413\) | 1.71496e7i | 0.243447i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.17586e7 | −0.584255 | ||||||||
\(416\) | 2.40316e7 | + | 1.38746e7i | 0.333812 | + | 0.192727i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.25036e7 | − | 5.62979e7i | −0.445044 | − | 0.770839i | ||||
\(419\) | 2.11639e7 | − | 1.22190e7i | 0.287709 | − | 0.166109i | −0.349199 | − | 0.937049i | \(-0.613546\pi\) |
0.636908 | + | 0.770939i | \(0.280213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.26175e7 | − | 9.11362e7i | 0.705154 | − | 1.22136i | −0.261482 | − | 0.965208i | \(-0.584211\pi\) |
0.966636 | − | 0.256154i | \(-0.0824554\pi\) | |||||||
\(422\) | − | 1.32808e8i | − | 1.76721i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.04068e7 | −0.530099 | ||||||||
\(425\) | 5.26961e6 | + | 3.04241e6i | 0.0686454 | + | 0.0396325i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.76022e7 | − | 8.24495e7i | −0.611426 | − | 1.05902i | ||||
\(428\) | −1.15391e8 | + | 6.66210e7i | −1.47177 | + | 0.849728i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.07051e8 | + | 1.85418e8i | −1.34644 | + | 2.33210i | ||||
\(431\) | − | 1.45082e8i | − | 1.81210i | −0.423166 | − | 0.906052i | \(-0.639081\pi\) | ||
0.423166 | − | 0.906052i | \(-0.360919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53388e8 | 1.88941 | 0.944706 | − | 0.327920i | \(-0.106347\pi\) | ||||
0.944706 | + | 0.327920i | \(0.106347\pi\) | |||||||
\(434\) | 8.75232e6 | + | 5.05316e6i | 0.107067 | + | 0.0618150i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.11561e7 | − | 1.40566e8i | −0.979178 | − | 1.69599i | ||||
\(437\) | 4.57130e6 | − | 2.63924e6i | 0.0547767 | − | 0.0316253i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.50547e6 | + | 4.33960e6i | −0.0296139 | + | 0.0512928i | −0.880453 | − | 0.474134i | \(-0.842761\pi\) |
0.850839 | + | 0.525427i | \(0.176094\pi\) | |||||||
\(440\) | − | 7.24733e7i | − | 0.850785i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.33291e8 | −1.54360 | ||||||||
\(443\) | 5.63189e7 | + | 3.25157e7i | 0.647803 | + | 0.374009i | 0.787614 | − | 0.616169i | \(-0.211316\pi\) |
−0.139811 | + | 0.990178i | \(0.544650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.01254e7 | − | 8.68197e7i | −0.568824 | − | 0.985232i | ||||
\(446\) | 1.94543e7 | − | 1.12319e7i | 0.219286 | − | 0.126605i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00214e7 | + | 3.46780e7i | −0.222669 | + | 0.385674i | ||||
\(449\) | 7.25149e7i | 0.801103i | 0.916274 | + | 0.400551i | \(0.131181\pi\) | ||||
−0.916274 | + | 0.400551i | \(0.868819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.94800e7 | 0.539386 | ||||||||
\(452\) | 3.34489e7 | + | 1.93117e7i | 0.362215 | + | 0.209125i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.56033e7 | + | 9.63078e7i | 0.594201 | + | 1.02919i | ||||
\(455\) | 5.18268e7 | − | 2.99222e7i | 0.550200 | − | 0.317658i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.85809e7 | − | 4.95036e7i | 0.299452 | − | 0.518667i | −0.676558 | − | 0.736389i | \(-0.736529\pi\) |
0.976011 | + | 0.217722i | \(0.0698627\pi\) | |||||||
\(458\) | − | 5.59202e7i | − | 0.582066i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.11529e7 | 0.114582 | ||||||||
\(461\) | −1.35879e8 | − | 7.84499e7i | −1.38692 | − | 0.800736i | −0.393950 | − | 0.919132i | \(-0.628892\pi\) |
−0.992966 | + | 0.118396i | \(0.962225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63223e7 | + | 8.02325e7i | 0.466710 | + | 0.808365i | 0.999277 | − | 0.0380229i | \(-0.0121060\pi\) |
−0.532567 | + | 0.846388i | \(0.678773\pi\) | |||||||
\(464\) | 1.67546e8 | − | 9.67327e7i | 1.67718 | − | 0.968321i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.04549e7 | + | 3.54289e7i | −0.202134 | + | 0.350107i | ||||
\(467\) | 1.48541e8i | 1.45846i | 0.684269 | + | 0.729230i | \(0.260122\pi\) | ||||
−0.684269 | + | 0.729230i | \(0.739878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.59683e7 | 0.639465 | ||||||||
\(470\) | 1.21976e8 | + | 7.04229e7i | 1.17485 | + | 0.678298i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.35872e7 | + | 5.81748e7i | 0.319410 | + | 0.553234i | ||||
\(473\) | 6.55410e7 | − | 3.78401e7i | 0.619340 | − | 0.357576i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.79927e6 | + | 8.31258e6i | −0.0447811 | + | 0.0775631i | ||||
\(476\) | 1.70236e8i | 1.57845i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.39567e6 | −0.0860288 | ||||||||
\(479\) | 9.81933e7 | + | 5.66919e7i | 0.893460 | + | 0.515839i | 0.875073 | − | 0.483992i | \(-0.160813\pi\) |
0.0183874 | + | 0.999831i | \(0.494147\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.66272e7 | − | 2.87991e7i | −0.149411 | − | 0.258788i | ||||
\(482\) | −1.01037e7 | + | 5.83337e6i | −0.0902275 | + | 0.0520929i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.57380e7 | − | 1.65823e8i | 0.844400 | − | 1.46254i | ||||
\(485\) | 1.12743e7i | 0.0988241i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.72741e8 | −1.49558 | −0.747789 | − | 0.663937i | \(-0.768884\pi\) | ||||
−0.747789 | + | 0.663937i | \(0.768884\pi\) | |||||||
\(488\) | −3.22952e8 | − | 1.86456e8i | −2.77894 | − | 1.60442i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.33521e7 | + | 7.50881e7i | 0.368487 | + | 0.638238i | ||||
\(491\) | −1.40807e8 | + | 8.12949e7i | −1.18954 | + | 0.686782i | −0.958202 | − | 0.286092i | \(-0.907644\pi\) |
−0.231339 | + | 0.972873i | \(0.574311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.43440e7 | + | 1.46088e8i | −0.703904 | + | 1.21920i | ||||
\(494\) | − | 2.10260e8i | − | 1.74412i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.55166e7 | 0.127160 | ||||||||
\(497\) | −6.02398e7 | − | 3.47795e7i | −0.490698 | − | 0.283305i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.94818e7 | − | 1.03026e8i | −0.478721 | − | 0.829169i | 0.520981 | − | 0.853568i | \(-0.325566\pi\) |
−0.999702 | + | 0.0243990i | \(0.992233\pi\) | |||||||
\(500\) | −2.37392e8 | + | 1.37058e8i | −1.89914 | + | 1.09647i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.91285e7 | − | 1.37055e8i | 0.625492 | − | 1.08338i | ||||
\(503\) | − | 5.21107e7i | − | 0.409471i | −0.978817 | − | 0.204736i | \(-0.934367\pi\) | ||
0.978817 | − | 0.204736i | \(-0.0656334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.23028e7 | 0.250822 | ||||||||
\(506\) | −5.02685e6 | − | 2.90225e6i | −0.0388011 | − | 0.0224018i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.43776e7 | + | 4.22233e7i | 0.185952 | + | 0.322078i | ||||
\(509\) | 1.99506e8 | − | 1.15185e8i | 1.51287 | − | 0.873458i | 0.512987 | − | 0.858397i | \(-0.328539\pi\) |
0.999887 | − | 0.0150611i | \(-0.00479427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.11298e7 | + | 1.23200e8i | −0.533076 | + | 0.923314i | ||||
\(512\) | 2.81123e8i | 2.09453i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.09580e8 | 0.806938 | ||||||||
\(515\) | 2.66718e7 | + | 1.53990e7i | 0.195268 | + | 0.112738i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.48929e7 | − | 4.31157e7i | −0.180137 | − | 0.312007i | ||||
\(518\) | −5.41558e7 | + | 3.12669e7i | −0.389633 | + | 0.224955i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.17204e8 | − | 2.03004e8i | 0.833554 | − | 1.44376i | ||||
\(521\) | 2.01324e8i | 1.42358i | 0.702392 | + | 0.711790i | \(0.252115\pi\) | ||||
−0.702392 | + | 0.711790i | \(0.747885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.15112e8 | 0.804669 | 0.402334 | − | 0.915493i | \(-0.368199\pi\) | ||||
0.402334 | + | 0.915493i | \(0.368199\pi\) | |||||||
\(524\) | 1.68155e8 | + | 9.70844e7i | 1.16874 | + | 0.674770i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.27754e8 | + | 2.21277e8i | 0.877845 | + | 1.52047i | ||||
\(527\) | −1.17168e7 | + | 6.76469e6i | −0.0800528 | + | 0.0462185i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.37823e7 | + | 1.27795e8i | −0.498408 | + | 0.863268i | ||||
\(530\) | 6.77706e7i | 0.455212i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.68540e8 | −1.78350 | ||||||||
\(533\) | 1.38598e8 | + | 8.00194e7i | 0.915323 | + | 0.528462i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.89569e7 | + | 1.02116e8i | 0.385011 | + | 0.666859i | ||||
\(536\) | 2.23777e8 | − | 1.29198e8i | 1.45319 | − | 0.838998i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.94095e8 | − | 3.36183e8i | 1.24643 | − | 2.15888i | ||||
\(539\) | − | 3.06480e7i | − | 0.195720i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.95684e8 | −1.23584 | −0.617921 | − | 0.786241i | \(-0.712025\pi\) | ||||
−0.617921 | + | 0.786241i | \(0.712025\pi\) | |||||||
\(542\) | 4.53778e7 | + | 2.61989e7i | 0.285001 | + | 0.164545i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.49279e7 | + | 6.04969e7i | 0.216958 | + | 0.375783i | ||||
\(545\) | −1.24396e8 | + | 7.18198e7i | −0.768449 | + | 0.443664i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.66519e7 | − | 2.88419e7i | 0.101742 | − | 0.176222i | −0.810660 | − | 0.585517i | \(-0.800892\pi\) |
0.912402 | + | 0.409294i | \(0.134225\pi\) | |||||||
\(548\) | − | 5.26639e8i | − | 3.20016i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.05551e7 | 0.0634414 | ||||||||
\(551\) | −2.30448e8 | − | 1.33049e8i | −1.37758 | − | 0.795347i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.15178e7 | + | 1.58513e8i | 0.541166 | + | 0.937326i | ||||
\(554\) | 3.15634e8 | − | 1.82231e8i | 1.85632 | − | 1.07175i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.44136e8 | + | 5.96062e8i | −2.00219 | + | 3.46790i | ||||
\(557\) | 2.14530e7i | 0.124143i | 0.998072 | + | 0.0620716i | \(0.0197707\pi\) | ||||
−0.998072 | + | 0.0620716i | \(0.980229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44781e8 | 1.40134 | ||||||||
\(560\) | −1.49632e8 | − | 8.63901e7i | −0.852041 | − | 0.491926i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.51582e8 | − | 2.62548e8i | −0.853965 | − | 1.47911i | ||||
\(563\) | 5.21863e7 | − | 3.01297e7i | 0.292436 | − | 0.168838i | −0.346604 | − | 0.938012i | \(-0.612665\pi\) |
0.639040 | + | 0.769174i | \(0.279332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.70901e7 | − | 2.96009e7i | 0.0947543 | − | 0.164119i | ||||
\(566\) | 1.21410e8i | 0.669586i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.72460e8 | −1.48682 | ||||||||
\(569\) | −2.39117e8 | − | 1.38054e8i | −1.29800 | − | 0.749398i | −0.317938 | − | 0.948112i | \(-0.602990\pi\) |
−0.980058 | + | 0.198714i | \(0.936324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49346e8 | − | 2.58675e8i | −0.802204 | − | 1.38946i | −0.918162 | − | 0.396205i | \(-0.870327\pi\) |
0.115958 | − | 0.993254i | \(-0.463006\pi\) | |||||||
\(572\) | −1.35997e8 | + | 7.85179e7i | −0.726677 | + | 0.419547i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.50474e8 | − | 2.60628e8i | 0.795656 | − | 1.37812i | ||||
\(575\) | 857055.i | 0.00450822i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.68320e7 | 0.504071 | 0.252035 | − | 0.967718i | \(-0.418900\pi\) | ||||
0.252035 | + | 0.967718i | \(0.418900\pi\) | |||||||
\(578\) | 4.65499e6 | + | 2.68756e6i | 0.0241066 | + | 0.0139179i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.81120e8 | − | 4.86914e8i | −1.44081 | − | 2.49556i | ||||
\(581\) | 7.77499e7 | − | 4.48889e7i | 0.396435 | − | 0.228882i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.19777e7 | − | 2.07459e7i | 0.0604458 | − | 0.104695i | ||||
\(584\) | 5.57226e8i | 2.79765i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.28446e7 | 0.212913 | ||||||||
\(587\) | 8.25319e7 | + | 4.76498e7i | 0.408044 | + | 0.235585i | 0.689949 | − | 0.723858i | \(-0.257633\pi\) |
−0.281905 | + | 0.959442i | \(0.590966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.06710e7 | − | 1.84827e7i | −0.0522227 | − | 0.0904523i | ||||
\(590\) | 9.75712e7 | − | 5.63328e7i | 0.475079 | − | 0.274287i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.80052e7 | + | 8.31475e7i | −0.231379 | + | 0.400760i | ||||
\(593\) | − | 5.27042e7i | − | 0.252744i | −0.991983 | − | 0.126372i | \(-0.959667\pi\) | ||
0.991983 | − | 0.126372i | \(-0.0403333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.50652e8 | 0.715194 | ||||||||
\(596\) | 1.14156e8 | + | 6.59083e7i | 0.539215 | + | 0.311316i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.38709e6 | − | 1.62589e7i | −0.0438963 | − | 0.0760305i | ||||
\(599\) | −2.56013e8 | + | 1.47809e8i | −1.19119 | + | 0.687733i | −0.958576 | − | 0.284836i | \(-0.908061\pi\) |
−0.232613 | + | 0.972569i | \(0.574728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.74992e7 | − | 1.68874e8i | 0.449136 | − | 0.777926i | −0.549194 | − | 0.835695i | \(-0.685065\pi\) |
0.998330 | + | 0.0577686i | \(0.0183986\pi\) | |||||||
\(602\) | − | 4.60303e8i | − | 2.10986i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.49252e8 | 3.85412 | ||||||||
\(605\) | −1.46747e8 | − | 8.47242e7i | −0.662677 | − | 0.382597i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.29203e7 | + | 1.26302e8i | 0.326049 | + | 0.564733i | 0.981724 | − | 0.190310i | \(-0.0609493\pi\) |
−0.655675 | + | 0.755043i | \(0.727616\pi\) | |||||||
\(608\) | −9.54313e7 | + | 5.50973e7i | −0.424600 | + | 0.245143i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.12726e8 | + | 5.41658e8i | −1.37776 | + | 2.38636i | ||||
\(611\) | − | 1.61028e8i | − | 0.705955i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.48295e8 | −1.94618 | −0.973089 | − | 0.230431i | \(-0.925986\pi\) | ||||
−0.973089 | + | 0.230431i | \(0.925986\pi\) | |||||||
\(614\) | 1.39949e8 | + | 8.07997e7i | 0.604596 | + | 0.349064i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.79060e7 | + | 1.34937e8i | 0.333295 | + | 0.577284i | ||||
\(617\) | −1.11067e8 | + | 6.41247e7i | −0.472857 | + | 0.273004i | −0.717435 | − | 0.696625i | \(-0.754684\pi\) |
0.244578 | + | 0.969630i | \(0.421351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.15337e6 | − | 3.72975e6i | 0.00907919 | − | 0.0157256i | −0.861450 | − | 0.507842i | \(-0.830443\pi\) |
0.870529 | + | 0.492117i | \(0.163777\pi\) | |||||||
\(620\) | − | 4.50936e7i | − | 0.189208i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.88427e8 | −1.61413 | ||||||||
\(623\) | 1.86656e8 | + | 1.07766e8i | 0.771929 | + | 0.445673i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.11538e8 | + | 1.93189e8i | 0.456860 | + | 0.791304i | ||||
\(626\) | −3.08438e8 | + | 1.78077e8i | −1.25732 | + | 0.725912i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.12752e8 | + | 1.95292e8i | −0.455245 | + | 0.788508i | ||||
\(629\) | − | 8.37143e7i | − | 0.336394i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.51870e6 | 0.0100251 | 0.00501255 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501255 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(632\) | 6.20892e8 | + | 3.58472e8i | 2.45960 | + | 1.42005i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.94861e8 | + | 3.37509e8i | 0.764641 | + | 1.32440i | ||||
\(635\) | 3.73659e7 | − | 2.15732e7i | 0.145933 | − | 0.0842545i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.95641e7 | − | 8.58475e7i | 0.191756 | − | 0.332131i | ||||
\(638\) | 2.92615e8i | 1.12677i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.73044e8 | 1.42305 | ||||||||
\(641\) | 1.94736e8 | + | 1.12431e8i | 0.739387 | + | 0.426885i | 0.821846 | − | 0.569709i | \(-0.192944\pi\) |
−0.0824597 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.85392e8 | + | 3.21108e8i | 0.697360 | + | 1.20786i | 0.969378 | + | 0.245572i | \(0.0789756\pi\) |
−0.272018 | + | 0.962292i | \(0.587691\pi\) | |||||||
\(644\) | −2.07655e7 | + | 1.19890e7i | −0.0777473 | + | 0.0448874i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.64654e8 | − | 4.58394e8i | 0.981705 | − | 1.70036i | ||||
\(647\) | − | 1.34128e8i | − | 0.495230i | −0.968858 | − | 0.247615i | \(-0.920353\pi\) | ||
0.968858 | − | 0.247615i | \(-0.0796468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.98246e7 | −0.145686 | ||||||||
\(650\) | 2.95656e7 | + | 1.70697e7i | 0.107658 | + | 0.0621565i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.67530e8 | + | 2.90171e8i | 0.604436 | + | 1.04691i | ||||
\(653\) | 1.53586e8 | − | 8.86727e7i | 0.551583 | − | 0.318457i | −0.198177 | − | 0.980166i | \(-0.563502\pi\) |
0.749760 | + | 0.661710i | \(0.230169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.59157e7 | − | 1.48810e8i | 0.305738 | − | 0.529553i | ||||
\(656\) | − | 4.62057e8i | − | 1.63676i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.02808e8 | −1.06289 | ||||||||
\(659\) | 1.53754e8 | + | 8.87701e7i | 0.537243 | + | 0.310177i | 0.743961 | − | 0.668223i | \(-0.232945\pi\) |
−0.206718 | + | 0.978401i | \(0.566278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.74792e8 | − | 4.75953e8i | −0.951479 | − | 1.64801i | −0.742228 | − | 0.670148i | \(-0.766231\pi\) |
−0.209251 | − | 0.977862i | \(-0.567103\pi\) | |||||||
\(662\) | −6.08996e8 | + | 3.51604e8i | −2.09914 | + | 1.21194i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.75828e8 | − | 3.04544e8i | 0.600600 | − | 1.04027i | ||||
\(665\) | 2.37647e8i | 0.808104i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.37599e7 | −0.0800695 | ||||||||
\(668\) | −6.78059e8 | − | 3.91478e8i | −2.27477 | − | 1.31334i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.16692e8 | − | 3.75321e8i | −0.720474 | − | 1.24790i | ||||
\(671\) | 1.91463e8 | − | 1.10541e8i | 0.633751 | − | 0.365896i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.22468e8 | + | 2.12121e8i | −0.401770 | + | 0.695886i | −0.993940 | − | 0.109927i | \(-0.964938\pi\) |
0.592170 | + | 0.805813i | \(0.298272\pi\) | |||||||
\(674\) | 3.54909e8i | 1.15914i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.46062e8 | 0.472821 | ||||||||
\(677\) | −4.25927e8 | − | 2.45909e8i | −1.37268 | − | 0.792518i | −0.381416 | − | 0.924404i | \(-0.624563\pi\) |
−0.991265 | + | 0.131886i | \(0.957897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.21194e7 | − | 2.09914e7i | −0.0387143 | − | 0.0670552i | ||||
\(680\) | 5.11041e8 | − | 2.95050e8i | 1.62528 | − | 0.938357i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.17344e7 | + | 2.03246e7i | −0.0369920 | + | 0.0640720i | ||||
\(683\) | 5.92974e8i | 1.86112i | 0.366143 | + | 0.930559i | \(0.380678\pi\) | ||||
−0.366143 | + | 0.930559i | \(0.619322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.66054e8 | −1.44999 | ||||||||
\(686\) | −5.32396e8 | − | 3.07379e8i | −1.64916 | − | 0.952142i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.53361e8 | − | 6.12038e8i | −1.08506 | − | 1.87937i | ||||
\(689\) | 6.71009e7 | − | 3.87407e7i | 0.205150 | − | 0.118443i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.74226e8 | − | 3.01769e8i | 0.528056 | − | 0.914620i | −0.471409 | − | 0.881915i | \(-0.656254\pi\) |
0.999465 | − | 0.0327051i | \(-0.0104122\pi\) | |||||||
\(692\) | − | 1.06432e9i | − | 3.21185i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.10462e9 | −3.30472 | ||||||||
\(695\) | 5.27490e8 | + | 3.04546e8i | 1.57130 | + | 0.907192i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.01440e8 | + | 3.48905e8i | 0.594906 | + | 1.03041i | ||||
\(698\) | 4.02159e7 | − | 2.32187e7i | 0.118258 | − | 0.0682765i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.18011e7 | − | 3.77606e7i | 0.0635600 | − | 0.110089i | ||||
\(701\) | − | 5.37432e8i | − | 1.56016i | −0.625679 | − | 0.780080i | \(-0.715178\pi\) | ||
0.625679 | − | 0.780080i | \(-0.284822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.32056e8 | 0.380094 | ||||||||
\(704\) | −8.05290e7 | − | 4.64934e7i | −0.230799 | − | 0.133252i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.41555e8 | + | 7.64796e8i | 1.25479 | + | 2.17336i | ||||
\(707\) | −6.01441e7 | + | 3.47242e7i | −0.170190 | + | 0.0982594i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.46671e7 | + | 1.29327e8i | −0.209503 | + | 0.362870i | −0.951558 | − | 0.307469i | \(-0.900518\pi\) |
0.742055 | + | 0.670339i | \(0.233851\pi\) | |||||||
\(710\) | 4.56972e8i | 1.27678i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.44230e8 | 2.33895 | ||||||||
\(713\) | −1.65032e6 | − | 952815.i | −0.00455303 | − | 0.00262869i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.94851e7 | + | 1.20352e8i | 0.190096 | + | 0.329256i | ||||
\(716\) | 2.01709e8 | − | 1.16457e8i | 0.549522 | − | 0.317267i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.93745e8 | + | 3.35576e8i | −0.523429 | + | 0.906605i | ||||
\(719\) | − | 7.89635e7i | − | 0.212442i | −0.994343 | − | 0.106221i | \(-0.966125\pi\) | ||
0.994343 | − | 0.106221i | \(-0.0338751\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.62132e7 | −0.176660 | ||||||||
\(722\) | 1.47641e8 | + | 8.52407e7i | 0.392280 | + | 0.226483i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.81993e8 | − | 4.88427e8i | −0.743059 | − | 1.28702i | ||||
\(725\) | 3.74172e7 | − | 2.16028e7i | 0.0981877 | − | 0.0566887i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.83494e7 | + | 8.37436e7i | −0.125831 | + | 0.217946i | −0.922057 | − | 0.387053i | \(-0.873493\pi\) |
0.796226 | + | 0.604999i | \(0.206826\pi\) | |||||||
\(728\) | 5.03961e8i | 1.30618i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.34585e8 | 2.40243 | ||||||||
\(731\) | 5.33654e8 | + | 3.08105e8i | 1.36618 | + | 0.788764i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.61563e7 | − | 1.14586e8i | −0.167981 | − | 0.290951i | 0.769729 | − | 0.638371i | \(-0.220391\pi\) |
−0.937710 | + | 0.347420i | \(0.887058\pi\) | |||||||
\(734\) | 5.26771e8 | − | 3.04132e8i | 1.33209 | − | 0.769083i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.91964e6 | + | 8.52107e6i | −0.0123396 | + | 0.0213728i | ||||
\(737\) | 1.53191e8i | 0.382676i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.72581e7 | −0.0675401 | −0.0337700 | − | 0.999430i | \(-0.510751\pi\) | ||||
−0.0337700 | + | 0.999430i | \(0.510751\pi\) | |||||||
\(740\) | 2.41639e8 | + | 1.39511e8i | 0.596311 | + | 0.344280i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.28507e7 | − | 1.26181e8i | −0.178329 | − | 0.308875i | ||||
\(743\) | −1.77637e7 | + | 1.02559e7i | −0.0433078 | + | 0.0250038i | −0.521498 | − | 0.853253i | \(-0.674626\pi\) |
0.478190 | + | 0.878257i | \(0.341293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.83261e7 | − | 1.01024e8i | 0.141057 | − | 0.244318i | ||||
\(746\) | 5.44439e8i | 1.31139i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.95321e8 | −0.944594 | ||||||||
\(749\) | −2.19542e8 | − | 1.26753e8i | −0.522483 | − | 0.301656i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.15842e8 | − | 5.47054e8i | −0.745676 | − | 1.29155i | −0.949878 | − | 0.312620i | \(-0.898793\pi\) |
0.204202 | − | 0.978929i | \(-0.434540\pi\) | |||||||
\(752\) | −4.02626e8 | + | 2.32456e8i | −0.946778 | + | 0.546622i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.73220e8 | + | 8.19641e8i | −1.10395 | + | 1.91210i | ||||
\(755\) | − | 7.51553e8i | − | 1.74630i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.20833e8 | 1.43116 | 0.715578 | − | 0.698533i | \(-0.246163\pi\) | ||||
0.715578 | + | 0.698533i | \(0.246163\pi\) | |||||||
\(758\) | −8.44851e8 | − | 4.87775e8i | −1.93987 | − | 1.11998i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.65428e8 | + | 8.06144e8i | 1.06026 | + | 1.83642i | ||||
\(761\) | −7.24053e8 | + | 4.18032e8i | −1.64292 | + | 0.948540i | −0.663130 | + | 0.748504i | \(0.730772\pi\) |
−0.979789 | + | 0.200035i | \(0.935894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.54407e8 | − | 2.67441e8i | 0.347611 | − | 0.602080i | ||||
\(764\) | 1.15132e9i | 2.58176i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.72381e8 | −0.383533 | ||||||||
\(767\) | −1.11552e8 | − | 6.44047e7i | −0.247225 | − | 0.142735i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.70941e7 | − | 1.16210e8i | −0.147538 | − | 0.255544i | 0.782779 | − | 0.622300i | \(-0.213802\pi\) |
−0.930317 | + | 0.366756i | \(0.880468\pi\) | |||||||
\(770\) | 2.26318e8 | − | 1.30665e8i | 0.495731 | − | 0.286211i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.69863e8 | + | 4.67416e8i | −0.586531 | + | 1.01590i | ||||
\(773\) | − | 5.46031e8i | − | 1.18217i | −0.806611 | − | 0.591083i | \(-0.798701\pi\) | ||
0.806611 | − | 0.591083i | \(-0.201299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.46525e6 | 0.00744439 | ||||||||
\(776\) | −8.22227e7 | − | 4.74713e7i | −0.175957 | − | 0.101589i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.44969e8 | − | 5.97503e8i | −0.732556 | − | 1.26882i | ||||
\(779\) | −5.50382e8 | + | 3.17763e8i | −1.16427 | + | 0.672189i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.07646e7 | − | 1.39888e8i | 0.169538 | − | 0.293649i | ||||
\(782\) | − | 4.72620e7i | − | 0.0988307i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.86198e8 | −0.593908 | ||||||||
\(785\) | 1.72826e8 | + | 9.97809e7i | 0.357272 | + | 0.206271i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03958e8 | + | 1.80060e8i | 0.213272 | + | 0.369397i | 0.952736 | − | 0.303798i | \(-0.0982548\pi\) |
−0.739465 | + | 0.673195i | \(0.764921\pi\) | |||||||
\(788\) | 6.39849e8 | − | 3.69417e8i | 1.30767 | − | 0.754984i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.01233e8 | − | 1.04137e9i | 1.21944 | − | 2.11214i | ||||
\(791\) | 7.34847e7i | 0.148480i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.15074e8 | 1.43394 | ||||||||
\(794\) | −2.44543e8 | − | 1.41187e8i | −0.488533 | − | 0.282055i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.68186e8 | + | 4.64512e8i | 0.531737 | + | 0.920996i | ||||
\(797\) | 6.08306e8 | − | 3.51206e8i | 1.20157 | − | 0.693724i | 0.240662 | − | 0.970609i | \(-0.422635\pi\) |
0.960903 | + | 0.276885i | \(0.0893021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.02685e8 | − | 3.51061e8i | 0.397358 | − | 0.688244i | ||||
\(800\) | − | 1.78920e7i | − | 0.0349453i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.09996e8 | 1.18251 | ||||||||
\(803\) | −2.86095e8 | − | 1.65177e8i | −0.552540 | − | 0.319009i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.06098e7 | + | 1.83766e7i | 0.0203385 | + | 0.0352272i | ||||
\(806\) | −6.57381e7 | + | 3.79539e7i | −0.125549 | + | 0.0724855i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.36014e8 | + | 2.35583e8i | −0.257839 | + | 0.446590i | ||||
\(809\) | 8.20042e8i | 1.54878i | 0.632707 | + | 0.774392i | \(0.281944\pi\) | ||||
−0.632707 | + | 0.774392i | \(0.718056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.91041e8 | −1.29551 | −0.647756 | − | 0.761848i | \(-0.724292\pi\) | ||||
−0.647756 | + | 0.761848i | \(0.724292\pi\) | |||||||
\(812\) | 1.04683e9 | + | 6.04386e8i | 1.95527 | + | 1.12888i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.26077e7 | − | 1.25760e8i | −0.134620 | − | 0.233169i | ||||
\(815\) | 2.56789e8 | − | 1.48257e8i | 0.474356 | − | 0.273869i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.86023e8 | + | 8.41816e8i | −0.891231 | + | 1.54366i | ||||
\(818\) | 5.22459e8i | 0.954537i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.34281e9 | −2.43541 | ||||||||
\(821\) | −6.01769e8 | − | 3.47432e8i | −1.08743 | − | 0.627827i | −0.154538 | − | 0.987987i | \(-0.549389\pi\) |
−0.932891 | + | 0.360160i | \(0.882722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.18960e7 | − | 1.24528e8i | −0.128975 | − | 0.223391i | 0.794305 | − | 0.607519i | \(-0.207835\pi\) |
−0.923280 | + | 0.384128i | \(0.874502\pi\) | |||||||
\(824\) | −2.24608e8 | + | 1.29677e8i | −0.401461 | + | 0.231784i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.21111e8 | + | 2.09770e8i | −0.214904 | + | 0.372224i | ||||
\(827\) | − | 6.36987e8i | − | 1.12620i | −0.826390 | − | 0.563098i | \(-0.809609\pi\) | ||
0.826390 | − | 0.563098i | \(-0.190391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.52328e7 | 0.167156 | 0.0835782 | − | 0.996501i | \(-0.473365\pi\) | ||||
0.0835782 | + | 0.996501i | \(0.473365\pi\) | |||||||
\(830\) | −5.10784e8 | − | 2.94901e8i | −0.893311 | − | 0.515753i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.50379e8 | − | 2.60464e8i | −0.261106 | − | 0.452250i | ||||
\(833\) | 2.16112e8 | − | 1.24772e8i | 0.373890 | − | 0.215866i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.46442e8 | + | 6.00055e8i | −0.595074 | + | 1.03070i | ||||
\(836\) | − | 6.23601e8i | − | 1.06730i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.45164e8 | 0.586534 | ||||||||
\(839\) | 2.46672e8 | + | 1.42416e8i | 0.417671 | + | 0.241143i | 0.694081 | − | 0.719897i | \(-0.255811\pi\) |
−0.276409 | + | 0.961040i | \(0.589144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.01478e8 | + | 5.22175e8i | 0.506836 | + | 0.877866i | ||||
\(842\) | 1.28721e9 | − | 7.43173e8i | 2.15633 | − | 1.24496i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.37000e8 | − | 1.10332e9i | 1.05953 | − | 1.83516i | ||||
\(845\) | − | 1.29259e8i | − | 0.214235i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.64301e8 | 0.599529 | ||||||||
\(848\) | −1.93731e8 | − | 1.11851e8i | −0.317695 | − | 0.183422i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.29712e7 | + | 7.44283e7i | 0.0699715 | + | 0.121194i | ||||
\(851\) | 1.02115e7 | − | 5.89563e6i | 0.0165692 | − | 0.00956625i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.56817e7 | − | 7.91230e7i | 0.0736029 | − | 0.127484i | −0.826875 | − | 0.562386i | \(-0.809884\pi\) |
0.900478 | + | 0.434902i | \(0.143217\pi\) | |||||||
\(854\) | − | 1.34467e9i | − | 2.15895i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.92973e8 | −1.58313 | ||||||||
\(857\) | 4.56487e8 | + | 2.63553e8i | 0.725247 | + | 0.418721i | 0.816681 | − | 0.577090i | \(-0.195812\pi\) |
−0.0914341 | + | 0.995811i | \(0.529145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.81645e8 | + | 3.14618e8i | 0.286578 | + | 0.496368i | 0.972991 | − | 0.230845i | \(-0.0741489\pi\) |
−0.686413 | + | 0.727212i | \(0.740816\pi\) | |||||||
\(860\) | −1.77868e9 | + | 1.02692e9i | −2.79642 | + | 1.61451i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.02458e9 | − | 1.77462e9i | 1.59964 | − | 2.77066i | ||||
\(863\) | 9.96932e8i | 1.55108i | 0.631300 | + | 0.775538i | \(0.282522\pi\) | ||||
−0.631300 | + | 0.775538i | \(0.717478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.41881e8 | −1.45528 | ||||||||
\(866\) | 1.87621e9 | + | 1.08323e9i | 2.88886 | + | 1.66789i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.84739e7 | + | 8.39593e7i | 0.0741223 | + | 0.128384i | ||||
\(869\) | −3.68099e8 | + | 2.12522e8i | −0.560925 | + | 0.323850i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.47742e8 | + | 4.29101e8i | −0.374925 | + | 0.649390i | ||||
\(872\) | − | 1.20961e9i | − | 1.82430i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.45537e7 | 0.111670 | ||||||||
\(875\) | −4.51661e8 | − | 2.60766e8i | −0.674199 | − | 0.389249i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.01845e8 | − | 6.96015e8i | −0.595744 | − | 1.03186i | −0.993441 | − | 0.114342i | \(-0.963524\pi\) |
0.397698 | − | 0.917517i | \(-0.369809\pi\) | |||||||
\(878\) | −6.12928e7 | + | 3.53874e7i | −0.0905578 | + | 0.0522836i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00614e8 | − | 3.47474e8i | 0.294384 | − | 0.509888i | ||||
\(881\) | 1.05052e8i | 0.153630i | 0.997045 | + | 0.0768151i | \(0.0244751\pi\) | ||||
−0.997045 | + | 0.0768151i | \(0.975525\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.90921e7 | −0.129407 | −0.0647034 | − | 0.997905i | \(-0.520610\pi\) | ||||
−0.0647034 | + | 0.997905i | \(0.520610\pi\) | |||||||
\(884\) | −1.10733e9 | − | 6.39316e8i | −1.60295 | − | 0.925463i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.59254e8 | + | 7.95452e8i | 0.660316 | + | 1.14370i | ||||
\(887\) | −8.98422e8 | + | 5.18704e8i | −1.28739 | + | 0.743274i | −0.978188 | − | 0.207722i | \(-0.933395\pi\) |
−0.309201 | + | 0.950997i | \(0.600062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.63807e7 | + | 8.03337e7i | −0.0660134 | + | 0.114339i | ||||
\(890\) | − | 1.41595e9i | − | 2.00853i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.15491e8 | 0.303623 | ||||||||
\(893\) | 5.53783e8 | + | 3.19727e8i | 0.777652 | + | 0.448978i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.03059e8 | − | 1.78504e8i | −0.143753 | − | 0.248988i | ||||
\(896\) | −6.94566e8 | + | 4.01008e8i | −0.965582 | + | 0.557479i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.12103e8 | + | 8.86988e8i | −0.707177 | + | 1.22487i | ||||
\(899\) | 9.60662e7i | 0.132218i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.95051e8 | 0.266670 | ||||||||
\(902\) | 6.05229e8 | + | 3.49429e8i | 0.824708 | + | 0.476145i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.43919e8 | + | 2.49274e8i | 0.194810 | + | 0.337421i | ||||
\(905\) | −4.32238e8 | + | 2.49552e8i | −0.583145 | + | 0.336679i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.83227e8 | + | 4.90564e8i | −0.379589 | + | 0.657467i | −0.991002 | − | 0.133844i | \(-0.957268\pi\) |
0.611414 | + | 0.791311i | \(0.290601\pi\) | |||||||
\(908\) | 1.06678e9i | 1.42501i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.45247e8 | 1.12166 | ||||||||
\(911\) | −7.72892e8 | − | 4.46229e8i | −1.02227 | − | 0.590205i | −0.107506 | − | 0.994204i | \(-0.534286\pi\) |
−0.914759 | + | 0.403999i | \(0.867620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.04241e8 | + | 1.80550e8i | 0.136970 | + | 0.237239i | ||||
\(914\) | 6.99193e8 | − | 4.03679e8i | 0.915711 | − | 0.528686i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.68216e8 | − | 4.64563e8i | 0.348978 | − | 0.604447i | ||||
\(917\) | 3.69424e8i | 0.479090i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.10427e8 | 0.271116 | 0.135558 | − | 0.990769i | \(-0.456717\pi\) | ||||
0.135558 | + | 0.990769i | \(0.456717\pi\) | |||||||
\(920\) | 7.19807e7 | + | 4.15581e7i | 0.0924385 | + | 0.0533694i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.10803e9 | − | 1.91917e9i | −1.41371 | − | 2.44861i | ||||
\(923\) | 4.52457e8 | − | 2.61226e8i | 0.575403 | − | 0.332209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.07208e7 | + | 1.85689e7i | −0.0135457 | + | 0.0234618i | ||||
\(926\) | 1.30852e9i | 1.64796i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.96016e8 | 0.620657 | ||||||||
\(929\) | 7.86889e8 | + | 4.54310e8i | 0.981445 | + | 0.566638i | 0.902706 | − | 0.430257i | \(-0.141577\pi\) |
0.0787392 | + | 0.996895i | \(0.474911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.96823e8 | + | 3.40907e8i | 0.243908 | + | 0.422462i | ||||
\(932\) | −3.39863e8 | + | 1.96220e8i | −0.419813 | + | 0.242379i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.04900e9 | + | 1.81692e9i | −1.28746 | + | 2.22995i | ||||
\(935\) | 3.49843e8i | 0.427994i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.34303e9 | 1.63255 | 0.816275 | − | 0.577663i | \(-0.196035\pi\) | ||||
0.816275 | + | 0.577663i | \(0.196035\pi\) | |||||||
\(938\) | 8.06912e8 | + | 4.65871e8i | 0.977727 | + | 0.564491i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.75553e8 | + | 1.17009e9i | 0.813347 | + | 1.40876i | ||||
\(941\) | 8.97969e8 | − | 5.18443e8i | 1.07769 | − | 0.622202i | 0.147415 | − | 0.989075i | \(-0.452905\pi\) |
0.930271 | + | 0.366872i | \(0.119571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.83731e7 | + | 4.91437e7i | −0.0338354 | + | 0.0586047i | ||||
\(944\) | 3.71893e8i | 0.442081i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.06891e9 | 1.26261 | ||||||||
\(947\) | −2.00750e8 | − | 1.15903e8i | −0.236377 | − | 0.136472i | 0.377133 | − | 0.926159i | \(-0.376910\pi\) |
−0.613510 | + | 0.789687i | \(0.710243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.34251e8 | − | 9.25350e8i | −0.625096 | − | 1.08270i | ||||
\(950\) | −1.17407e8 | + | 6.77852e7i | −0.136938 | + | 0.0790613i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.34334e8 | + | 1.09870e9i | −0.735202 | + | 1.27341i | ||||
\(953\) | − | 2.56619e8i | − | 0.296490i | −0.988951 | − | 0.148245i | \(-0.952638\pi\) | ||
0.988951 | − | 0.148245i | \(-0.0473625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.01887e9 | 1.16979 | ||||||||
\(956\) | −7.80555e7 | − | 4.50654e7i | −0.0893367 | − | 0.0515785i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00720e8 | + | 1.38689e9i | 0.910719 | + | 1.57741i | ||||
\(959\) | 8.67739e8 | − | 5.00990e8i | 0.983860 | − | 0.568032i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.39899e8 | − | 7.61928e8i | 0.495659 | − | 0.858507i | ||||
\(962\) | − | 4.69687e8i | − | 0.527574i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.11917e8 | −0.124929 | ||||||||
\(965\) | 4.13644e8 | + | 2.38817e8i | 0.460304 | + | 0.265757i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62366e8 | + | 2.81225e8i | 0.179562 | + | 0.311010i | 0.941731 | − | 0.336368i | \(-0.109199\pi\) |
−0.762169 | + | 0.647379i | \(0.775865\pi\) | |||||||
\(968\) | 1.23578e9 | − | 7.13478e8i | 1.36243 | − | 0.786601i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.96192e7 | + | 1.37905e8i | −0.0872374 | + | 0.151100i | ||||
\(971\) | − | 1.01485e9i | − | 1.10852i | −0.832342 | − | 0.554262i | \(-0.813001\pi\) | ||
0.832342 | − | 0.554262i | \(-0.186999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.30950e9 | −1.42157 | ||||||||
\(974\) | −2.11293e9 | − | 1.21990e9i | −2.28670 | − | 1.32023i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.03226e9 | − | 1.78794e9i | −1.11030 | − | 1.92310i | ||||
\(977\) | −3.71703e8 | + | 2.14603e8i | −0.398578 | + | 0.230119i | −0.685870 | − | 0.727724i | \(-0.740578\pi\) |
0.287292 | + | 0.957843i | \(0.407245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.50253e8 | + | 4.33450e8i | −0.266705 | + | 0.461946i | ||||
\(980\) | 8.31736e8i | 0.883705i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.29643e9 | −2.42504 | ||||||||
\(983\) | −1.36423e9 | − | 7.87641e8i | −1.43624 | − | 0.829216i | −0.438658 | − | 0.898654i | \(-0.644546\pi\) |
−0.997586 | + | 0.0694381i | \(0.977879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.26919e8 | − | 5.66240e8i | −0.342083 | − | 0.592505i | ||||
\(986\) | −2.06336e9 | + | 1.19128e9i | −2.15250 | + | 1.24275i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.00849e9 | − | 1.74676e9i | 1.04569 | − | 1.81118i | ||||
\(989\) | 8.67940e7i | 0.0897224i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.55480e9 | −1.59755 | −0.798774 | − | 0.601631i | \(-0.794518\pi\) | ||||
−0.798774 | + | 0.601631i | \(0.794518\pi\) | |||||||
\(992\) | 3.44524e7 | + | 1.98911e7i | 0.0352927 | + | 0.0203762i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.91228e8 | − | 8.50831e8i | −0.500177 | − | 0.866332i | ||||
\(995\) | 4.11074e8 | − | 2.37334e8i | 0.417302 | − | 0.240930i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.50335e8 | − | 9.53207e8i | 0.555317 | − | 0.961838i | −0.442561 | − | 0.896738i | \(-0.645930\pi\) |
0.997879 | − | 0.0650998i | \(-0.0207366\pi\) | |||||||
\(998\) | − | 1.68025e9i | − | 1.69037i | ||||||
\(999\) | 0 | 0 |
(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 | 27.7.d.a.8.5 | 10 | ||
3.2 | odd | 2 | 9.7.d.a.2.1 | ✓ | 10 | ||
4.3 | odd | 2 | 432.7.q.a.305.4 | 10 | |||
9.2 | odd | 6 | 81.7.b.a.80.10 | 10 | |||
9.4 | even | 3 | 9.7.d.a.5.1 | yes | 10 | ||
9.5 | odd | 6 | inner | 27.7.d.a.17.5 | 10 | ||
9.7 | even | 3 | 81.7.b.a.80.1 | 10 | |||
12.11 | even | 2 | 144.7.q.a.65.2 | 10 | |||
36.23 | even | 6 | 432.7.q.a.17.4 | 10 | |||
36.31 | odd | 6 | 144.7.q.a.113.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.7.d.a.2.1 | ✓ | 10 | 3.2 | odd | 2 | ||
9.7.d.a.5.1 | yes | 10 | 9.4 | even | 3 | ||
27.7.d.a.8.5 | 10 | 1.1 | even | 1 | trivial | ||
27.7.d.a.17.5 | 10 | 9.5 | odd | 6 | inner | ||
81.7.b.a.80.1 | 10 | 9.7 | even | 3 | |||
81.7.b.a.80.10 | 10 | 9.2 | odd | 6 | |||
144.7.q.a.65.2 | 10 | 12.11 | even | 2 | |||
144.7.q.a.113.2 | 10 | 36.31 | odd | 6 | |||
432.7.q.a.17.4 | 10 | 36.23 | even | 6 | |||
432.7.q.a.305.4 | 10 | 4.3 | odd | 2 |