Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,7,Mod(26,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, 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("81.26");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.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: | \(18.6343807732\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.53 |
Dual form | 81.7.d.b.26.2 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.19615 | − | 3.00000i | 0.649519 | − | 0.375000i | −0.138753 | − | 0.990327i | \(-0.544309\pi\) |
0.788272 | + | 0.615327i | \(0.210976\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −14.0000 | + | 24.2487i | −0.218750 | + | 0.378886i | ||||
\(5\) | 207.846 | + | 120.000i | 1.66277 | + | 0.960000i | 0.971384 | + | 0.237513i | \(0.0763322\pi\) |
0.691384 | + | 0.722487i | \(0.257001\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −149.500 | − | 258.942i | −0.435860 | − | 0.754932i | 0.561505 | − | 0.827473i | \(-0.310222\pi\) |
−0.997365 | + | 0.0725413i | \(0.976889\pi\) | |||||||
\(8\) | 552.000i | 1.07812i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1440.00 | 1.44000 | ||||||||
\(11\) | −540.400 | + | 312.000i | −0.406010 | + | 0.234410i | −0.689074 | − | 0.724691i | \(-0.741983\pi\) |
0.283064 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1247.50 | + | 2160.73i | −0.567820 | + | 0.983493i | 0.428961 | + | 0.903323i | \(0.358880\pi\) |
−0.996781 | + | 0.0801699i | \(0.974454\pi\) | |||||||
\(14\) | −1553.65 | − | 897.000i | −0.566199 | − | 0.326895i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 760.000 | + | 1316.36i | 0.185547 | + | 0.321377i | ||||
\(17\) | 1872.00i | 0.381030i | 0.981684 | + | 0.190515i | \(0.0610158\pi\) | ||||
−0.981684 | + | 0.190515i | \(0.938984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2509.00 | −0.365797 | −0.182898 | − | 0.983132i | \(-0.558548\pi\) | ||||
−0.182898 | + | 0.983132i | \(0.558548\pi\) | |||||||
\(20\) | −5819.69 | + | 3360.00i | −0.727461 | + | 0.420000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1872.00 | + | 3242.40i | −0.175808 | + | 0.304508i | ||||
\(23\) | 12429.2 | + | 7176.00i | 1.02155 | + | 0.589792i | 0.914552 | − | 0.404467i | \(-0.132543\pi\) |
0.106997 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20987.5 | + | 36351.4i | 1.34320 | + | 2.32649i | ||||
\(26\) | 14970.0i | 0.851730i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8372.00 | 0.381378 | ||||||||
\(29\) | 20535.2 | − | 11856.0i | 0.841986 | − | 0.486121i | −0.0159529 | − | 0.999873i | \(-0.505078\pi\) |
0.857939 | + | 0.513752i | \(0.171745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2665.00 | + | 4615.92i | −0.0894565 | + | 0.154943i | −0.907282 | − | 0.420524i | \(-0.861846\pi\) |
0.817825 | + | 0.575467i | \(0.195180\pi\) | |||||||
\(32\) | −22696.8 | − | 13104.0i | −0.692651 | − | 0.399902i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5616.00 | + | 9727.20i | 0.142886 | + | 0.247486i | ||||
\(35\) | − | 71760.0i | − | 1.67370i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32591.0 | 0.643417 | 0.321708 | − | 0.946839i | \(-0.395743\pi\) | ||||
0.321708 | + | 0.946839i | \(0.395743\pi\) | |||||||
\(38\) | −13037.1 | + | 7527.00i | −0.237592 | + | 0.137174i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −66240.0 | + | 114731.i | −1.03500 | + | 1.79267i | ||||
\(41\) | −57282.4 | − | 33072.0i | −0.831131 | − | 0.479854i | 0.0231087 | − | 0.999733i | \(-0.492644\pi\) |
−0.854240 | + | 0.519879i | \(0.825977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 35315.0 | + | 61167.4i | 0.444175 | + | 0.769333i | 0.997994 | − | 0.0633035i | \(-0.0201636\pi\) |
−0.553820 | + | 0.832637i | \(0.686830\pi\) | |||||||
\(44\) | − | 17472.0i | − | 0.205109i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 86112.0 | 0.884688 | ||||||||
\(47\) | 3450.25 | − | 1992.00i | 0.0332320 | − | 0.0191865i | −0.483292 | − | 0.875459i | \(-0.660559\pi\) |
0.516524 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14124.0 | − | 24463.5i | 0.120052 | − | 0.207936i | ||||
\(50\) | 218108. | + | 125925.i | 1.74487 | + | 1.00740i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −34930.0 | − | 60500.5i | −0.248421 | − | 0.430278i | ||||
\(53\) | 190944.i | 1.28256i | 0.767306 | + | 0.641281i | \(0.221597\pi\) | ||||
−0.767306 | + | 0.641281i | \(0.778403\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −149760. | −0.900135 | ||||||||
\(56\) | 142936. | − | 82524.0i | 0.813911 | − | 0.469912i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 71136.0 | − | 123211.i | 0.364591 | − | 0.631489i | ||||
\(59\) | −205560. | − | 118680.i | −1.00088 | − | 0.577858i | −0.0923717 | − | 0.995725i | \(-0.529445\pi\) |
−0.908509 | + | 0.417866i | \(0.862778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30900.5 | + | 53521.2i | 0.136137 | + | 0.235796i | 0.926031 | − | 0.377447i | \(-0.123198\pi\) |
−0.789894 | + | 0.613243i | \(0.789865\pi\) | |||||||
\(62\) | 31980.0i | 0.134185i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −254528. | −0.970947 | ||||||||
\(65\) | −518576. | + | 299400.i | −1.88831 | + | 1.09021i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 215130. | − | 372617.i | 0.715282 | − | 1.23891i | −0.247568 | − | 0.968871i | \(-0.579631\pi\) |
0.962850 | − | 0.270035i | \(-0.0870353\pi\) | |||||||
\(68\) | −45393.6 | − | 26208.0i | −0.144367 | − | 0.0833503i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −215280. | − | 372876.i | −0.627638 | − | 1.08710i | ||||
\(71\) | − | 251712.i | − | 0.703281i | −0.936135 | − | 0.351640i | \(-0.885624\pi\) | ||
0.936135 | − | 0.351640i | \(-0.114376\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 251615. | 0.646797 | 0.323398 | − | 0.946263i | \(-0.395175\pi\) | ||||
0.323398 | + | 0.946263i | \(0.395175\pi\) | |||||||
\(74\) | 169348. | − | 97773.0i | 0.417912 | − | 0.241281i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 35126.0 | − | 60840.0i | 0.0800180 | − | 0.138595i | ||||
\(77\) | 161580. | + | 93288.0i | 0.353927 | + | 0.204340i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −330414. | − | 572293.i | −0.670157 | − | 1.16075i | −0.977859 | − | 0.209263i | \(-0.932893\pi\) |
0.307702 | − | 0.951483i | \(-0.400440\pi\) | |||||||
\(80\) | 364800.i | 0.712500i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −396864. | −0.719781 | ||||||||
\(83\) | 690964. | − | 398928.i | 1.20843 | − | 0.697686i | 0.246012 | − | 0.969267i | \(-0.420880\pi\) |
0.962416 | + | 0.271580i | \(0.0875462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −224640. | + | 389088.i | −0.365789 | + | 0.633565i | ||||
\(86\) | 367004. | + | 211890.i | 0.577000 | + | 0.333131i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −172224. | − | 298301.i | −0.252724 | − | 0.437730i | ||||
\(89\) | − | 270576.i | − | 0.383813i | −0.981413 | − | 0.191906i | \(-0.938533\pi\) | ||
0.981413 | − | 0.191906i | \(-0.0614670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 746005. | 0.989960 | ||||||||
\(92\) | −348018. | + | 200928.i | −0.446928 | + | 0.258034i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11952.0 | − | 20701.5i | 0.0143899 | − | 0.0249240i | ||||
\(95\) | −521486. | − | 301080.i | −0.608235 | − | 0.351165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −110364. | − | 191155.i | −0.120923 | − | 0.209445i | 0.799209 | − | 0.601054i | \(-0.205252\pi\) |
−0.920132 | + | 0.391608i | \(0.871919\pi\) | |||||||
\(98\) | − | 169488.i | − | 0.180078i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.17530e6 | −1.17530 | ||||||||
\(101\) | 250746. | − | 144768.i | 0.243371 | − | 0.140510i | −0.373354 | − | 0.927689i | \(-0.621792\pi\) |
0.616725 | + | 0.787179i | \(0.288459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 297102. | − | 514597.i | 0.271891 | − | 0.470929i | −0.697455 | − | 0.716628i | \(-0.745684\pi\) |
0.969346 | + | 0.245700i | \(0.0790177\pi\) | |||||||
\(104\) | −1.19272e6 | − | 688620.i | −1.06033 | − | 0.612181i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 572832. | + | 992174.i | 0.480961 | + | 0.833049i | ||||
\(107\) | − | 1.99368e6i | − | 1.62744i | −0.581259 | − | 0.813718i | \(-0.697440\pi\) | ||
0.581259 | − | 0.813718i | \(-0.302560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.51135e6 | 1.16704 | 0.583521 | − | 0.812098i | \(-0.301674\pi\) | ||||
0.583521 | + | 0.812098i | \(0.301674\pi\) | |||||||
\(110\) | −778176. | + | 449280.i | −0.584655 | + | 0.337551i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 227240. | − | 393591.i | 0.161745 | − | 0.280150i | ||||
\(113\) | 1.42936e6 | + | 825240.i | 0.990617 | + | 0.571933i | 0.905459 | − | 0.424435i | \(-0.139527\pi\) |
0.0851580 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.72224e6 | + | 2.98301e6i | 1.13240 | + | 1.96138i | ||||
\(116\) | 663936.i | 0.425356i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.42416e6 | −0.866788 | ||||||||
\(119\) | 484739. | − | 279864.i | 0.287652 | − | 0.166076i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −691092. | + | 1.19701e6i | −0.390104 | + | 0.675679i | ||||
\(122\) | 321127. | + | 185403.i | 0.176847 | + | 0.102103i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −74620.0 | − | 129246.i | −0.0391372 | − | 0.0677877i | ||||
\(125\) | 6.32400e6i | 3.23789i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41135e6 | 0.689005 | 0.344502 | − | 0.938785i | \(-0.388048\pi\) | ||||
0.344502 | + | 0.938785i | \(0.388048\pi\) | |||||||
\(128\) | 130029. | − | 75072.0i | 0.0620024 | − | 0.0357971i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.79640e6 | + | 3.11146e6i | −0.817660 | + | 1.41623i | ||||
\(131\) | 279927. | + | 161616.i | 0.124518 | + | 0.0718903i | 0.560965 | − | 0.827839i | \(-0.310430\pi\) |
−0.436447 | + | 0.899730i | \(0.643764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 375096. | + | 649684.i | 0.159436 | + | 0.276152i | ||||
\(134\) | − | 2.58157e6i | − | 1.07292i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.03334e6 | −0.410798 | ||||||||
\(137\) | −1.85195e6 | + | 1.06922e6i | −0.720224 | + | 0.415822i | −0.814835 | − | 0.579693i | \(-0.803173\pi\) |
0.0946111 | + | 0.995514i | \(0.469839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 55614.5 | − | 96327.1i | 0.0207083 | − | 0.0358678i | −0.855486 | − | 0.517827i | \(-0.826741\pi\) |
0.876194 | + | 0.481959i | \(0.160075\pi\) | |||||||
\(140\) | 1.74009e6 | + | 1.00464e6i | 0.634143 | + | 0.366122i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −755136. | − | 1.30793e6i | −0.263730 | − | 0.456794i | ||||
\(143\) | − | 1.55688e6i | − | 0.532411i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.69088e6 | 1.86670 | ||||||||
\(146\) | 1.30743e6 | − | 754845.i | 0.420107 | − | 0.242549i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −456274. | + | 790290.i | −0.140747 | + | 0.243782i | ||||
\(149\) | −2.97619e6 | − | 1.71830e6i | −0.899708 | − | 0.519447i | −0.0226029 | − | 0.999745i | \(-0.507195\pi\) |
−0.877106 | + | 0.480298i | \(0.840529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.96966e6 | + | 3.41156e6i | 0.572086 | + | 0.990881i | 0.996352 | + | 0.0853436i | \(0.0271988\pi\) |
−0.424266 | + | 0.905538i | \(0.639468\pi\) | |||||||
\(152\) | − | 1.38497e6i | − | 0.394375i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.11946e6 | 0.306510 | ||||||||
\(155\) | −1.10782e6 | + | 639600.i | −0.297491 | + | 0.171757i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −215533. | + | 373314.i | −0.0556948 | + | 0.0964663i | −0.892529 | − | 0.450991i | \(-0.851071\pi\) |
0.836834 | + | 0.547457i | \(0.184404\pi\) | |||||||
\(158\) | −3.43376e6 | − | 1.98248e6i | −0.870559 | − | 0.502618i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.14496e6 | − | 5.44723e6i | −0.767813 | − | 1.32989i | ||||
\(161\) | − | 4.29125e6i | − | 1.02827i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.94353e6 | −1.83422 | −0.917109 | − | 0.398637i | \(-0.869483\pi\) | ||||
−0.917109 | + | 0.398637i | \(0.869483\pi\) | |||||||
\(164\) | 1.60391e6 | − | 926016.i | 0.363620 | − | 0.209936i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.39357e6 | − | 4.14578e6i | 0.523265 | − | 0.906321i | ||||
\(167\) | 3.06428e6 | + | 1.76916e6i | 0.657928 | + | 0.379855i | 0.791487 | − | 0.611186i | \(-0.209307\pi\) |
−0.133559 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −699108. | − | 1.21089e6i | −0.144839 | − | 0.250868i | ||||
\(170\) | 2.69568e6i | 0.548683i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.97764e6 | −0.388653 | ||||||||
\(173\) | 1.53149e6 | − | 884208.i | 0.295785 | − | 0.170772i | −0.344763 | − | 0.938690i | \(-0.612041\pi\) |
0.640548 | + | 0.767918i | \(0.278707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.27526e6 | − | 1.08691e7i | 1.17089 | − | 2.02805i | ||||
\(176\) | −821408. | − | 474240.i | −0.150668 | − | 0.0869882i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −811728. | − | 1.40595e6i | −0.143930 | − | 0.249294i | ||||
\(179\) | 3.82637e6i | 0.667156i | 0.942722 | + | 0.333578i | \(0.108256\pi\) | ||||
−0.942722 | + | 0.333578i | \(0.891744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.32721e6 | −0.392464 | −0.196232 | − | 0.980558i | \(-0.562871\pi\) | ||||
−0.196232 | + | 0.980558i | \(0.562871\pi\) | |||||||
\(182\) | 3.87636e6 | − | 2.23802e6i | 0.642998 | − | 0.371235i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.96115e6 | + | 6.86092e6i | −0.635870 | + | 1.10136i | ||||
\(185\) | 6.77391e6 | + | 3.91092e6i | 1.06985 | + | 0.617680i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −584064. | − | 1.01163e6i | −0.0893173 | − | 0.154702i | ||||
\(188\) | 111552.i | 0.0167882i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.61296e6 | −0.526747 | ||||||||
\(191\) | 4.47073e6 | − | 2.58118e6i | 0.641620 | − | 0.370440i | −0.143618 | − | 0.989633i | \(-0.545874\pi\) |
0.785238 | + | 0.619193i | \(0.212540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.73777e6 | − | 3.00990e6i | 0.241724 | − | 0.418678i | −0.719481 | − | 0.694512i | \(-0.755620\pi\) |
0.961205 | + | 0.275833i | \(0.0889538\pi\) | |||||||
\(194\) | −1.14693e6 | − | 662181.i | −0.157084 | − | 0.0906925i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 395472. | + | 684978.i | 0.0525228 | + | 0.0909721i | ||||
\(197\) | − | 7.36920e6i | − | 0.963877i | −0.876205 | − | 0.481939i | \(-0.839933\pi\) | ||
0.876205 | − | 0.481939i | \(-0.160067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.43100e6 | 1.06984 | 0.534921 | − | 0.844902i | \(-0.320341\pi\) | ||||
0.534921 | + | 0.844902i | \(0.320341\pi\) | |||||||
\(200\) | −2.00660e7 | + | 1.15851e7i | −2.50825 | + | 1.44814i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 868608. | − | 1.50447e6i | 0.105383 | − | 0.182528i | ||||
\(203\) | −6.14002e6 | − | 3.54494e6i | −0.733976 | − | 0.423761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.93728e6 | − | 1.37478e7i | −0.921319 | − | 1.59577i | ||||
\(206\) | − | 3.56523e6i | − | 0.407836i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.79240e6 | −0.421429 | ||||||||
\(209\) | 1.35586e6 | − | 782808.i | 0.148517 | − | 0.0857465i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.05006e6 | + | 3.55081e6i | −0.218233 | + | 0.377990i | −0.954268 | − | 0.298953i | \(-0.903362\pi\) |
0.736035 | + | 0.676943i | \(0.236696\pi\) | |||||||
\(212\) | −4.63015e6 | − | 2.67322e6i | −0.485945 | − | 0.280560i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.98104e6 | − | 1.03595e7i | −0.610289 | − | 1.05705i | ||||
\(215\) | 1.69512e7i | 1.70563i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.59367e6 | 0.155962 | ||||||||
\(218\) | 7.85323e6 | − | 4.53406e6i | 0.758016 | − | 0.437641i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.09664e6 | − | 3.63149e6i | 0.196905 | − | 0.341049i | ||||
\(221\) | −4.04489e6 | − | 2.33532e6i | −0.374740 | − | 0.216356i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.26818e6 | + | 1.25889e7i | 0.655407 | + | 1.13520i | 0.981792 | + | 0.189962i | \(0.0608363\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(224\) | 7.83619e6i | 0.697206i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.90288e6 | 0.857899 | ||||||||
\(227\) | −5.12266e6 | + | 2.95757e6i | −0.437943 | + | 0.252847i | −0.702725 | − | 0.711462i | \(-0.748033\pi\) |
0.264782 | + | 0.964308i | \(0.414700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.58496e6 | + | 1.66016e7i | −0.798149 | + | 1.38243i | 0.122671 | + | 0.992447i | \(0.460854\pi\) |
−0.920820 | + | 0.389988i | \(0.872479\pi\) | |||||||
\(230\) | 1.78980e7 | + | 1.03334e7i | 1.47103 | + | 0.849301i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.54451e6 | + | 1.13354e7i | 0.524099 | + | 0.907766i | ||||
\(233\) | − | 7.40563e6i | − | 0.585456i | −0.956196 | − | 0.292728i | \(-0.905437\pi\) | ||
0.956196 | − | 0.292728i | \(-0.0945631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 956160. | 0.0736762 | ||||||||
\(236\) | 5.75567e6 | − | 3.32304e6i | 0.437885 | − | 0.252813i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.67918e6 | − | 2.90843e6i | 0.124557 | − | 0.215739i | ||||
\(239\) | 1.28766e7 | + | 7.43434e6i | 0.943212 | + | 0.544563i | 0.890966 | − | 0.454071i | \(-0.150029\pi\) |
0.0522459 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.11498e6 | + | 3.66325e6i | 0.151097 | + | 0.261707i | 0.931631 | − | 0.363406i | \(-0.118386\pi\) |
−0.780534 | + | 0.625113i | \(0.785053\pi\) | |||||||
\(242\) | 8.29311e6i | 0.585156i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.73043e6 | −0.119120 | ||||||||
\(245\) | 5.87124e6 | − | 3.38976e6i | 0.399237 | − | 0.230500i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12998e6 | − | 5.42128e6i | 0.207707 | − | 0.359758i | ||||
\(248\) | −2.54799e6 | − | 1.47108e6i | −0.167048 | − | 0.0964453i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.89720e7 | + | 3.28605e7i | 1.21421 | + | 2.10307i | ||||
\(251\) | − | 1.32500e7i | − | 0.837906i | −0.908008 | − | 0.418953i | \(-0.862397\pi\) | ||
0.908008 | − | 0.418953i | \(-0.137603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.95565e6 | −0.553013 | ||||||||
\(254\) | 7.33357e6 | − | 4.23404e6i | 0.447522 | − | 0.258377i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.59533e6 | − | 1.48875e7i | 0.512321 | − | 0.887367i | ||||
\(257\) | −2.78576e7 | − | 1.60836e7i | −1.64114 | − | 0.947510i | −0.980431 | − | 0.196865i | \(-0.936924\pi\) |
−0.660705 | − | 0.750646i | \(-0.729743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.87235e6 | − | 8.43917e6i | −0.280440 | − | 0.485736i | ||||
\(260\) | − | 1.67664e7i | − | 0.953937i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.93939e6 | 0.107835 | ||||||||
\(263\) | −2.52540e7 | + | 1.45804e7i | −1.38823 | + | 0.801497i | −0.993116 | − | 0.117134i | \(-0.962629\pi\) |
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.29133e7 | + | 3.96870e7i | −1.23126 | + | 2.13260i | ||||
\(266\) | 3.89811e6 | + | 2.25057e6i | 0.207114 | + | 0.119577i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.02365e6 | + | 1.04333e7i | 0.312936 | + | 0.542021i | ||||
\(269\) | − | 1.84710e7i | − | 0.948930i | −0.880274 | − | 0.474465i | \(-0.842642\pi\) | ||
0.880274 | − | 0.474465i | \(-0.157358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.27473e7 | −1.14294 | −0.571468 | − | 0.820624i | \(-0.693626\pi\) | ||||
−0.571468 | + | 0.820624i | \(0.693626\pi\) | |||||||
\(272\) | −2.46422e6 | + | 1.42272e6i | −0.122454 | + | 0.0706989i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.41534e6 | + | 1.11117e7i | −0.311866 | + | 0.540168i | ||||
\(275\) | −2.26833e7 | − | 1.30962e7i | −1.09071 | − | 0.629720i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08882e7 | + | 1.88590e7i | 0.512293 | + | 0.887317i | 0.999898 | + | 0.0142530i | \(0.00453704\pi\) |
−0.487606 | + | 0.873064i | \(0.662130\pi\) | |||||||
\(278\) | − | 667374.i | − | 0.0310624i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.96115e7 | 1.80446 | ||||||||
\(281\) | 2.61503e7 | − | 1.50979e7i | 1.17858 | − | 0.680451i | 0.222891 | − | 0.974843i | \(-0.428451\pi\) |
0.955685 | + | 0.294393i | \(0.0951173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.88938e6 | − | 1.71289e7i | 0.436325 | − | 0.755736i | −0.561078 | − | 0.827763i | \(-0.689613\pi\) |
0.997403 | + | 0.0720265i | \(0.0229466\pi\) | |||||||
\(284\) | 6.10369e6 | + | 3.52397e6i | 0.266463 | + | 0.153843i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.67064e6 | − | 8.08979e6i | −0.199654 | − | 0.345811i | ||||
\(287\) | 1.97771e7i | 0.836596i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.06332e7 | 0.854816 | ||||||||
\(290\) | 2.95707e7 | − | 1.70726e7i | 1.21246 | − | 0.700014i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.52261e6 | + | 6.10134e6i | −0.141487 | + | 0.245062i | ||||
\(293\) | 1.72782e7 | + | 9.97558e6i | 0.686904 | + | 0.396584i | 0.802451 | − | 0.596718i | \(-0.203529\pi\) |
−0.115547 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.84832e7 | − | 4.93343e7i | −1.10949 | − | 1.92169i | ||||
\(296\) | 1.79902e7i | 0.693684i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.06196e7 | −0.779170 | ||||||||
\(299\) | −3.10108e7 | + | 1.79041e7i | −1.16011 | + | 0.669791i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.05592e7 | − | 1.82890e7i | 0.387196 | − | 0.670643i | ||||
\(302\) | 2.04693e7 | + | 1.18180e7i | 0.743161 | + | 0.429064i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.90684e6 | − | 3.30274e6i | −0.0678724 | − | 0.117559i | ||||
\(305\) | 1.48322e7i | 0.522766i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.43404e7 | 0.841226 | 0.420613 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420613 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(308\) | −4.52423e6 | + | 2.61206e6i | −0.154843 | + | 0.0893988i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.83760e6 | + | 6.64692e6i | −0.128817 | + | 0.223118i | ||||
\(311\) | 4.60253e7 | + | 2.65727e7i | 1.53009 | + | 0.883395i | 0.999357 | + | 0.0358529i | \(0.0114148\pi\) |
0.530728 | + | 0.847542i | \(0.321919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.58934e6 | + | 2.75282e6i | 0.0518303 | + | 0.0897728i | 0.890777 | − | 0.454442i | \(-0.150161\pi\) |
−0.838946 | + | 0.544214i | \(0.816828\pi\) | |||||||
\(314\) | 2.58640e6i | 0.0835422i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.85032e7 | 0.586387 | ||||||||
\(317\) | −3.20922e7 | + | 1.85284e7i | −1.00745 | + | 0.581649i | −0.910443 | − | 0.413635i | \(-0.864259\pi\) |
−0.0970027 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.39814e6 | + | 1.28140e7i | −0.227903 | + | 0.394740i | ||||
\(320\) | −5.29027e7 | − | 3.05434e7i | −1.61446 | − | 0.932109i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.28737e7 | − | 2.22980e7i | −0.385600 | − | 0.667879i | ||||
\(323\) | − | 4.69685e6i | − | 0.139380i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04728e8 | −3.05078 | ||||||||
\(326\) | −4.12758e7 | + | 2.38306e7i | −1.19136 | + | 0.687832i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.82557e7 | − | 3.16199e7i | 0.517342 | − | 0.896063i | ||||
\(329\) | −1.03162e6 | − | 595608.i | −0.0289690 | − | 0.0167253i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.73374e6 | − | 4.73497e6i | −0.0753829 | − | 0.130567i | 0.825870 | − | 0.563861i | \(-0.190685\pi\) |
−0.901253 | + | 0.433294i | \(0.857351\pi\) | |||||||
\(332\) | 2.23400e7i | 0.610476i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.12299e7 | 0.569782 | ||||||||
\(335\) | 8.94281e7 | − | 5.16313e7i | 2.37870 | − | 1.37334i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.04610e7 | − | 3.54394e7i | 0.534609 | − | 0.925971i | −0.464573 | − | 0.885535i | \(-0.653792\pi\) |
0.999182 | − | 0.0404357i | \(-0.0128746\pi\) | |||||||
\(338\) | −7.26534e6 | − | 4.19465e6i | −0.188151 | − | 0.108629i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.28992e6 | − | 1.08945e7i | −0.160033 | − | 0.277185i | ||||
\(341\) | − | 3.32592e6i | − | 0.0838781i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.36232e7 | −1.08102 | ||||||||
\(344\) | −3.37644e7 | + | 1.94939e7i | −0.829437 | + | 0.478876i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.30525e6 | − | 9.18896e6i | 0.128079 | − | 0.221839i | ||||
\(347\) | −4.64593e7 | − | 2.68233e7i | −1.11195 | − | 0.641983i | −0.172614 | − | 0.984990i | \(-0.555221\pi\) |
−0.939333 | + | 0.343007i | \(0.888554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.04437e6 | − | 1.39333e7i | −0.189241 | − | 0.327775i | 0.755756 | − | 0.654853i | \(-0.227269\pi\) |
−0.944997 | + | 0.327078i | \(0.893936\pi\) | |||||||
\(350\) | − | 7.53032e7i | − | 1.75634i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.63538e7 | 0.374965 | ||||||||
\(353\) | 3.56049e6 | − | 2.05565e6i | 0.0809441 | − | 0.0467331i | −0.458982 | − | 0.888446i | \(-0.651786\pi\) |
0.539926 | + | 0.841713i | \(0.318452\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.02054e7 | − | 5.23174e7i | 0.675150 | − | 1.16939i | ||||
\(356\) | 6.56112e6 | + | 3.78806e6i | 0.145421 | + | 0.0839590i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.14791e7 | + | 1.98824e7i | 0.250184 | + | 0.433331i | ||||
\(359\) | 1.41496e7i | 0.305816i | 0.988240 | + | 0.152908i | \(0.0488638\pi\) | ||||
−0.988240 | + | 0.152908i | \(0.951136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.07508e7 | −0.866193 | ||||||||
\(362\) | −1.20925e7 | + | 6.98163e6i | −0.254913 | + | 0.147174i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.04441e7 | + | 1.80897e7i | −0.216554 | + | 0.375082i | ||||
\(365\) | 5.22972e7 | + | 3.01938e7i | 1.07547 | + | 0.620925i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.06695e7 | − | 3.58006e7i | −0.418150 | − | 0.724257i | 0.577603 | − | 0.816317i | \(-0.303988\pi\) |
−0.995753 | + | 0.0920605i | \(0.970655\pi\) | |||||||
\(368\) | 2.18150e7i | 0.437736i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.69310e7 | 0.926520 | ||||||||
\(371\) | 4.94433e7 | − | 2.85461e7i | 0.968247 | − | 0.559018i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.91690e7 | + | 5.05222e7i | −0.562076 | + | 0.973545i | 0.435239 | + | 0.900315i | \(0.356664\pi\) |
−0.997315 | + | 0.0732299i | \(0.976669\pi\) | |||||||
\(374\) | −6.06977e6 | − | 3.50438e6i | −0.116027 | − | 0.0669880i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.09958e6 | + | 1.90454e6i | 0.0206854 | + | 0.0358282i | ||||
\(377\) | 5.91614e7i | 1.10412i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.49065e7 | 1.37595 | 0.687974 | − | 0.725735i | \(-0.258500\pi\) | ||||
0.687974 | + | 0.725735i | \(0.258500\pi\) | |||||||
\(380\) | 1.46016e7 | − | 8.43024e6i | 0.266103 | − | 0.153635i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.54871e7 | − | 2.68244e7i | 0.277830 | − | 0.481215i | ||||
\(383\) | 2.46336e7 | + | 1.42222e7i | 0.438461 | + | 0.253146i | 0.702945 | − | 0.711244i | \(-0.251868\pi\) |
−0.264483 | + | 0.964390i | \(0.585201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.23891e7 | + | 3.87791e7i | 0.392333 | + | 0.679541i | ||||
\(386\) | − | 2.08532e7i | − | 0.362586i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.18036e6 | 0.105808 | ||||||||
\(389\) | −5.29457e7 | + | 3.05682e7i | −0.899460 | + | 0.519303i | −0.877025 | − | 0.480445i | \(-0.840475\pi\) |
−0.0224348 | + | 0.999748i | \(0.507142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34335e7 | + | 2.32675e7i | −0.224728 | + | 0.389241i | ||||
\(392\) | 1.35038e7 | + | 7.79645e6i | 0.224181 | + | 0.129431i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.21076e7 | − | 3.82915e7i | −0.361454 | − | 0.626057i | ||||
\(395\) | − | 1.58598e8i | − | 2.57340i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.70144e7 | −0.591561 | −0.295780 | − | 0.955256i | \(-0.595580\pi\) | ||||
−0.295780 | + | 0.955256i | \(0.595580\pi\) | |||||||
\(398\) | 4.38087e7 | − | 2.52930e7i | 0.694883 | − | 0.401191i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.19010e7 | + | 5.52542e7i | −0.498453 | + | 0.863346i | ||||
\(401\) | 1.80800e7 | + | 1.04385e7i | 0.280391 | + | 0.161884i | 0.633600 | − | 0.773660i | \(-0.281576\pi\) |
−0.353209 | + | 0.935544i | \(0.614910\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.64918e6 | − | 1.15167e7i | −0.101590 | − | 0.175960i | ||||
\(404\) | 8.10701e6i | 0.122947i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.25393e7 | −0.635642 | ||||||||
\(407\) | −1.76122e7 | + | 1.01684e7i | −0.261234 | + | 0.150824i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.55265e7 | + | 7.88542e7i | −0.665418 | + | 1.15254i | 0.313754 | + | 0.949504i | \(0.398413\pi\) |
−0.979172 | + | 0.203033i | \(0.934920\pi\) | |||||||
\(410\) | −8.24866e7 | − | 4.76237e7i | −1.19683 | − | 0.690989i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.31887e6 | + | 1.44087e7i | 0.118952 | + | 0.206031i | ||||
\(413\) | 7.09706e7i | 1.00746i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.91485e8 | 2.67912 | ||||||||
\(416\) | 5.66285e7 | − | 3.26945e7i | 0.786602 | − | 0.454145i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.69685e6 | − | 8.13518e6i | 0.0643099 | − | 0.111388i | ||||
\(419\) | −9.97756e7 | − | 5.76055e7i | −1.35638 | − | 0.783108i | −0.367249 | − | 0.930123i | \(-0.619700\pi\) |
−0.989134 | + | 0.147014i | \(0.953034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.57948e7 | + | 1.13960e8i | 0.881750 | + | 1.52724i | 0.849394 | + | 0.527759i | \(0.176967\pi\) |
0.0323553 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(422\) | 2.46007e7i | 0.327349i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.05401e8 | −1.38276 | ||||||||
\(425\) | −6.80499e7 | + | 3.92886e7i | −0.886463 | + | 0.511799i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.23925e6 | − | 1.60028e7i | 0.118673 | − | 0.205548i | ||||
\(428\) | 4.83442e7 | + | 2.79115e7i | 0.616613 | + | 0.356002i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.08536e7 | + | 8.80810e7i | 0.639612 | + | 1.10784i | ||||
\(431\) | 7.15543e7i | 0.893725i | 0.894603 | + | 0.446863i | \(0.147459\pi\) | ||||
−0.894603 | + | 0.446863i | \(0.852541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83937e7 | 0.226572 | 0.113286 | − | 0.993562i | \(-0.463862\pi\) | ||||
0.113286 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(434\) | 8.28095e6 | − | 4.78101e6i | 0.101300 | − | 0.0584858i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.11590e7 | + | 3.66484e7i | −0.255291 | + | 0.442176i | ||||
\(437\) | −3.11849e7 | − | 1.80046e7i | −0.373680 | − | 0.215744i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.95305e7 | + | 8.57894e7i | 0.585436 | + | 1.01400i | 0.994821 | + | 0.101643i | \(0.0324100\pi\) |
−0.409385 | + | 0.912362i | \(0.634257\pi\) | |||||||
\(440\) | − | 8.26675e7i | − | 0.970458i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.80238e7 | −0.324534 | ||||||||
\(443\) | −1.17257e8 | + | 6.76984e7i | −1.34874 | + | 0.778695i | −0.988071 | − | 0.154000i | \(-0.950784\pi\) |
−0.360668 | + | 0.932694i | \(0.617451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.24691e7 | − | 5.62382e7i | 0.368460 | − | 0.638192i | ||||
\(446\) | 7.55332e7 | + | 4.36091e7i | 0.851399 | + | 0.491555i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.80519e7 | + | 6.59079e7i | 0.423197 | + | 0.732999i | ||||
\(449\) | 6.85948e7i | 0.757796i | 0.925438 | + | 0.378898i | \(0.123697\pi\) | ||||
−0.925438 | + | 0.378898i | \(0.876303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.12739e7 | 0.449930 | ||||||||
\(452\) | −4.00220e7 | + | 2.31067e7i | −0.433395 | + | 0.250221i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.77454e7 | + | 3.07359e7i | −0.189635 | + | 0.328457i | ||||
\(455\) | 1.55054e8 | + | 8.95206e7i | 1.64607 | + | 0.950361i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.56324e7 | − | 6.17172e7i | −0.373334 | − | 0.646633i | 0.616743 | − | 0.787165i | \(-0.288452\pi\) |
−0.990076 | + | 0.140532i | \(0.955119\pi\) | |||||||
\(458\) | 1.15020e8i | 1.19722i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.64454e7 | −0.990851 | ||||||||
\(461\) | 1.35584e8 | − | 7.82797e7i | 1.38391 | − | 0.798999i | 0.391287 | − | 0.920269i | \(-0.372030\pi\) |
0.992620 | + | 0.121270i | \(0.0386966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 276906. | − | 479616.i | 0.00278991 | − | 0.00483227i | −0.864627 | − | 0.502414i | \(-0.832445\pi\) |
0.867417 | + | 0.497582i | \(0.165779\pi\) | |||||||
\(464\) | 3.12135e7 | + | 1.80211e7i | 0.312456 | + | 0.180396i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.22169e7 | − | 3.84808e7i | −0.219546 | − | 0.380265i | ||||
\(467\) | − | 3.14739e7i | − | 0.309030i | −0.987990 | − | 0.154515i | \(-0.950619\pi\) | ||
0.987990 | − | 0.154515i | \(-0.0493815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.28648e8 | −1.24705 | ||||||||
\(470\) | 4.96835e6 | − | 2.86848e6i | 0.0478541 | − | 0.0276286i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.55114e7 | − | 1.13469e8i | 0.623004 | − | 1.07907i | ||||
\(473\) | −3.81684e7 | − | 2.20366e7i | −0.360679 | − | 0.208238i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.26576e7 | − | 9.12057e7i | −0.491338 | − | 0.851023i | ||||
\(476\) | 1.56724e7i | 0.145316i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.92120e7 | 0.816845 | ||||||||
\(479\) | 5.78365e7 | − | 3.33919e7i | 0.526254 | − | 0.303833i | −0.213236 | − | 0.977001i | \(-0.568400\pi\) |
0.739490 | + | 0.673168i | \(0.235067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.06573e7 | + | 7.04205e7i | −0.365345 | + | 0.632796i | ||||
\(482\) | 2.19795e7 | + | 1.26899e7i | 0.196280 | + | 0.113322i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.93506e7 | − | 3.35162e7i | −0.170670 | − | 0.295610i | ||||
\(485\) | − | 5.29745e7i | − | 0.464346i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00508e8 | 1.73598 | 0.867992 | − | 0.496579i | \(-0.165411\pi\) | ||||
0.867992 | + | 0.496579i | \(0.165411\pi\) | |||||||
\(488\) | −2.95437e7 | + | 1.70571e7i | −0.254218 | + | 0.146773i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.03386e7 | − | 3.52274e7i | 0.172875 | − | 0.299428i | ||||
\(491\) | −7.46373e7 | − | 4.30919e7i | −0.630538 | − | 0.364042i | 0.150422 | − | 0.988622i | \(-0.451937\pi\) |
−0.780961 | + | 0.624580i | \(0.785270\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.21944e7 | + | 3.84419e7i | 0.185227 | + | 0.320822i | ||||
\(494\) | − | 3.75597e7i | − | 0.311560i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.10160e6 | −0.0663935 | ||||||||
\(497\) | −6.51787e7 | + | 3.76309e7i | −0.530929 | + | 0.306532i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.33365e6 | + | 9.23816e6i | −0.0429263 | + | 0.0743505i | −0.886690 | − | 0.462364i | \(-0.847001\pi\) |
0.843764 | + | 0.536714i | \(0.180335\pi\) | |||||||
\(500\) | −1.53349e8 | − | 8.85360e7i | −1.22679 | − | 0.708288i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.97500e7 | − | 6.88491e7i | −0.314215 | − | 0.544236i | ||||
\(503\) | − | 1.07893e8i | − | 0.847790i | −0.905711 | − | 0.423895i | \(-0.860663\pi\) | ||
0.905711 | − | 0.423895i | \(-0.139337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.94886e7 | 0.539560 | ||||||||
\(506\) | −4.65349e7 | + | 2.68669e7i | −0.359193 | + | 0.207380i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.97588e7 | + | 3.42233e7i | −0.150720 | + | 0.261054i | ||||
\(509\) | −1.33397e8 | − | 7.70167e7i | −1.01156 | − | 0.584025i | −0.0999128 | − | 0.994996i | \(-0.531856\pi\) |
−0.911648 | + | 0.410971i | \(0.865190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.76164e7 | − | 6.51536e7i | −0.281913 | − | 0.488288i | ||||
\(512\) | − | 9.35347e7i | − | 0.696888i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.93003e8 | −1.42127 | ||||||||
\(515\) | 1.23503e8 | − | 7.13046e7i | 0.904183 | − | 0.522030i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.24301e6 | + | 2.15295e6i | −0.00899502 | + | 0.0155798i | ||||
\(518\) | −5.06350e7 | − | 2.92341e7i | −0.364302 | − | 0.210330i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.65269e8 | − | 2.86254e8i | −1.17539 | − | 2.03583i | ||||
\(521\) | − | 1.85442e8i | − | 1.31128i | −0.755074 | − | 0.655640i | \(-0.772399\pi\) | ||
0.755074 | − | 0.655640i | \(-0.227601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.46950e7 | −0.102723 | −0.0513613 | − | 0.998680i | \(-0.516356\pi\) | ||||
−0.0513613 | + | 0.998680i | \(0.516356\pi\) | |||||||
\(524\) | −7.83796e6 | + | 4.52525e6i | −0.0544765 | + | 0.0314520i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.74823e7 | + | 1.51524e8i | −0.601122 | + | 1.04117i | ||||
\(527\) | −8.64099e6 | − | 4.98888e6i | −0.0590380 | − | 0.0340856i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.89720e7 | + | 5.01810e7i | 0.195709 | + | 0.338979i | ||||
\(530\) | 2.74959e8i | 1.84689i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.10053e7 | −0.139507 | ||||||||
\(533\) | 1.42920e8 | − | 8.25146e7i | 0.943865 | − | 0.544941i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.39242e8 | − | 4.14379e8i | 1.56234 | − | 2.70605i | ||||
\(536\) | 2.05685e8 | + | 1.18752e8i | 1.33570 | + | 0.771164i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.54131e7 | − | 9.59783e7i | −0.355849 | − | 0.616348i | ||||
\(539\) | 1.76268e7i | 0.112566i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.03570e7 | −0.0654098 | −0.0327049 | − | 0.999465i | \(-0.510412\pi\) | ||||
−0.0327049 | + | 0.999465i | \(0.510412\pi\) | |||||||
\(542\) | −1.18198e8 | + | 6.82419e7i | −0.742359 | + | 0.428601i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.45307e7 | − | 4.24884e7i | 0.152375 | − | 0.263921i | ||||
\(545\) | 3.14129e8 | + | 1.81362e8i | 1.94052 | + | 1.12036i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.01598e7 | − | 6.95589e7i | −0.245375 | − | 0.425002i | 0.716862 | − | 0.697215i | \(-0.245578\pi\) |
−0.962237 | + | 0.272213i | \(0.912244\pi\) | |||||||
\(548\) | − | 5.98765e7i | − | 0.363844i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.57154e8 | −0.944579 | ||||||||
\(551\) | −5.15228e7 | + | 2.97467e7i | −0.307996 | + | 0.177821i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.87936e7 | + | 1.71116e8i | −0.584189 | + | 1.01185i | ||||
\(554\) | 1.13154e8 | + | 6.53294e7i | 0.665488 | + | 0.384220i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.55721e6 | + | 2.69716e6i | 0.00905986 | + | 0.0156921i | ||||
\(557\) | − | 3.87935e7i | − | 0.224488i | −0.993681 | − | 0.112244i | \(-0.964196\pi\) | ||
0.993681 | − | 0.112244i | \(-0.0358038\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.76222e8 | −1.00884 | ||||||||
\(560\) | 9.44619e7 | − | 5.45376e7i | 0.537889 | − | 0.310550i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.05872e7 | − | 1.56902e8i | 0.510338 | − | 0.883932i | ||||
\(563\) | −2.12726e8 | − | 1.22818e8i | −1.19205 | − | 0.688233i | −0.233282 | − | 0.972409i | \(-0.574946\pi\) |
−0.958772 | + | 0.284177i | \(0.908280\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.98058e8 | + | 3.43046e8i | 1.09811 | + | 1.90198i | ||||
\(566\) | − | 1.18673e8i | − | 0.654487i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.38945e8 | 0.758225 | ||||||||
\(569\) | −2.91854e7 | + | 1.68502e7i | −0.158427 | + | 0.0914677i | −0.577117 | − | 0.816661i | \(-0.695822\pi\) |
0.418691 | + | 0.908129i | \(0.362489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.18485e8 | − | 2.05222e8i | 0.636435 | − | 1.10234i | −0.349774 | − | 0.936834i | \(-0.613742\pi\) |
0.986209 | − | 0.165504i | \(-0.0529250\pi\) | |||||||
\(572\) | 3.77523e7 | + | 2.17963e7i | 0.201723 | + | 0.116465i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.93312e7 | + | 1.02765e8i | 0.313724 | + | 0.543385i | ||||
\(575\) | 6.02425e8i | 3.16883i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.09015e6 | 0.0212918 | 0.0106459 | − | 0.999943i | \(-0.496611\pi\) | ||||
0.0106459 | + | 0.999943i | \(0.496611\pi\) | |||||||
\(578\) | 1.07213e8 | − | 6.18996e7i | 0.555219 | − | 0.320556i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.96723e7 | + | 1.37997e8i | −0.408341 | + | 0.707268i | ||||
\(581\) | −2.06598e8 | − | 1.19279e8i | −1.05341 | − | 0.608187i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.95745e7 | − | 1.03186e8i | −0.300646 | − | 0.520734i | ||||
\(584\) | 1.38891e8i | 0.697328i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.19707e8 | 0.594876 | ||||||||
\(587\) | −3.15888e8 | + | 1.82378e8i | −1.56178 | + | 0.901692i | −0.564699 | + | 0.825297i | \(0.691008\pi\) |
−0.997078 | + | 0.0763950i | \(0.975659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.68648e6 | − | 1.15813e7i | 0.0327229 | − | 0.0566778i | ||||
\(590\) | −2.96006e8 | − | 1.70899e8i | −1.44127 | − | 0.832116i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.47692e7 | + | 4.29014e7i | 0.119384 | + | 0.206779i | ||||
\(593\) | − | 3.38297e8i | − | 1.62231i | −0.584832 | − | 0.811154i | \(-0.698840\pi\) | ||
0.584832 | − | 0.811154i | \(-0.301160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.34335e8 | 0.637731 | ||||||||
\(596\) | 8.33333e7 | − | 4.81125e7i | 0.393622 | − | 0.227258i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.07425e8 | + | 1.86065e8i | −0.502343 | + | 0.870084i | ||||
\(599\) | 2.18701e8 | + | 1.26267e8i | 1.01758 | + | 0.587502i | 0.913403 | − | 0.407056i | \(-0.133445\pi\) |
0.104181 | + | 0.994558i | \(0.466778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33928e8 | − | 2.31971e8i | −0.616949 | − | 1.06859i | −0.990039 | − | 0.140792i | \(-0.955035\pi\) |
0.373090 | − | 0.927795i | \(-0.378298\pi\) | |||||||
\(602\) | − | 1.26710e8i | − | 0.580794i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.10301e8 | −0.500575 | ||||||||
\(605\) | −2.87282e8 | + | 1.65862e8i | −1.29730 | + | 0.748999i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.36076e8 | − | 2.35691e8i | 0.608438 | − | 1.05385i | −0.383060 | − | 0.923724i | \(-0.625130\pi\) |
0.991498 | − | 0.130122i | \(-0.0415370\pi\) | |||||||
\(608\) | 5.69463e7 | + | 3.28779e7i | 0.253370 | + | 0.146283i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.44967e7 | + | 7.70706e7i | 0.196037 | + | 0.339546i | ||||
\(611\) | 9.94008e6i | 0.0435779i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.91383e7 | −0.213323 | −0.106662 | − | 0.994295i | \(-0.534016\pi\) | ||||
−0.106662 | + | 0.994295i | \(0.534016\pi\) | |||||||
\(614\) | 1.26476e8 | − | 7.30212e7i | 0.546392 | − | 0.315460i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.14950e7 | + | 8.91919e7i | −0.220304 | + | 0.381578i | ||||
\(617\) | −1.07978e8 | − | 6.23412e7i | −0.459706 | − | 0.265412i | 0.252214 | − | 0.967671i | \(-0.418841\pi\) |
−0.711921 | + | 0.702260i | \(0.752174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.26787e8 | + | 3.92806e8i | 0.956193 | + | 1.65617i | 0.731615 | + | 0.681718i | \(0.238767\pi\) |
0.224578 | + | 0.974456i | \(0.427900\pi\) | |||||||
\(620\) | − | 3.58176e7i | − | 0.150287i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.18873e8 | 1.32509 | ||||||||
\(623\) | −7.00634e7 | + | 4.04511e7i | −0.289752 | + | 0.167289i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.30950e8 | + | 7.46428e8i | −1.76517 | + | 3.05737i | ||||
\(626\) | 1.65169e7 | + | 9.53604e6i | 0.0673296 | + | 0.0388727i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.03492e6 | − | 1.04528e7i | −0.0243665 | − | 0.0422040i | ||||
\(629\) | 6.10104e7i | 0.245161i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.31523e7 | −0.211560 | −0.105780 | − | 0.994390i | \(-0.533734\pi\) | ||||
−0.105780 | + | 0.994390i | \(0.533734\pi\) | |||||||
\(632\) | 3.15906e8 | − | 1.82388e8i | 1.25143 | − | 0.722513i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.11171e8 | + | 1.92553e8i | −0.436237 | + | 0.755584i | ||||
\(635\) | 2.93343e8 | + | 1.69362e8i | 1.14566 | + | 0.661445i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.52394e7 | + | 6.10364e7i | 0.136336 | + | 0.236141i | ||||
\(638\) | 8.87777e7i | 0.341855i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.60346e7 | 0.137461 | ||||||||
\(641\) | 3.16482e8 | − | 1.82721e8i | 1.20164 | − | 0.693768i | 0.240721 | − | 0.970594i | \(-0.422616\pi\) |
0.960920 | + | 0.276826i | \(0.0892827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.62806e7 | + | 1.32122e8i | −0.286933 | + | 0.496983i | −0.973076 | − | 0.230484i | \(-0.925969\pi\) |
0.686143 | + | 0.727467i | \(0.259303\pi\) | |||||||
\(644\) | 1.04057e8 | + | 6.00775e7i | 0.389596 | + | 0.224933i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.40905e7 | − | 2.44055e7i | −0.0522673 | − | 0.0905296i | ||||
\(647\) | − | 1.22990e7i | − | 0.0454107i | −0.999742 | − | 0.0227054i | \(-0.992772\pi\) | ||
0.999742 | − | 0.0227054i | \(-0.00722796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.48113e8 | 0.541824 | ||||||||
\(650\) | −5.44181e8 | + | 3.14183e8i | −1.98154 | + | 1.14404i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.11209e8 | − | 1.92620e8i | 0.401235 | − | 0.694960i | ||||
\(653\) | 4.95449e7 | + | 2.86048e7i | 0.177934 | + | 0.102730i | 0.586322 | − | 0.810078i | \(-0.300575\pi\) |
−0.408387 | + | 0.912809i | \(0.633909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.87878e7 | + | 6.71825e7i | 0.138029 | + | 0.239074i | ||||
\(656\) | − | 1.00539e8i | − | 0.356141i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.14730e6 | −0.0250879 | ||||||||
\(659\) | 1.99266e8 | − | 1.15046e8i | 0.696269 | − | 0.401991i | −0.109687 | − | 0.993966i | \(-0.534985\pi\) |
0.805956 | + | 0.591975i | \(0.201652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.40523e7 | + | 4.16598e7i | −0.0832822 | + | 0.144249i | −0.904658 | − | 0.426138i | \(-0.859874\pi\) |
0.821376 | + | 0.570388i | \(0.193207\pi\) | |||||||
\(662\) | −2.84098e7 | − | 1.64024e7i | −0.0979253 | − | 0.0565372i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.20208e8 | + | 3.81412e8i | 0.752193 | + | 1.30284i | ||||
\(665\) | 1.80046e8i | 0.612235i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.40315e8 | 1.14684 | ||||||||
\(668\) | −8.57997e7 | + | 4.95365e7i | −0.287843 | + | 0.166187i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.09788e8 | − | 5.36568e8i | 1.03001 | − | 1.78402i | ||||
\(671\) | −3.33973e7 | − | 1.92819e7i | −0.110546 | − | 0.0638238i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.15326e8 | − | 1.99751e8i | −0.378341 | − | 0.655305i | 0.612480 | − | 0.790486i | \(-0.290172\pi\) |
−0.990821 | + | 0.135181i | \(0.956839\pi\) | |||||||
\(674\) | − | 2.45532e8i | − | 0.801914i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.91500e7 | 0.126734 | ||||||||
\(677\) | 4.88652e8 | − | 2.82123e8i | 1.57483 | − | 0.909228i | 0.579265 | − | 0.815139i | \(-0.303340\pi\) |
0.995564 | − | 0.0940888i | \(-0.0299938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.29987e7 | + | 5.71554e7i | −0.105411 | + | 0.182578i | ||||
\(680\) | −2.14777e8 | − | 1.24001e8i | −0.683062 | − | 0.394366i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.97776e6 | − | 1.72820e7i | −0.0314543 | − | 0.0544804i | ||||
\(683\) | − | 2.05363e8i | − | 0.644555i | −0.946645 | − | 0.322278i | \(-0.895552\pi\) | ||
0.946645 | − | 0.322278i | \(-0.104448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.13228e8 | −1.59675 | ||||||||
\(686\) | −2.26673e8 | + | 1.30870e8i | −0.702145 | + | 0.405384i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.36788e7 | + | 9.29744e7i | −0.164830 | + | 0.285495i | ||||
\(689\) | −4.12579e8 | − | 2.38203e8i | −1.26139 | − | 0.728264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.43345e7 | + | 9.41101e7i | 0.164680 | + | 0.285234i | 0.936542 | − | 0.350556i | \(-0.114007\pi\) |
−0.771861 | + | 0.635791i | \(0.780674\pi\) | |||||||
\(692\) | 4.95156e7i | 0.149425i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.21879e8 | −0.962974 | ||||||||
\(695\) | 2.31185e7 | − | 1.33475e7i | 0.0688661 | − | 0.0397599i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.19108e7 | − | 1.07233e8i | 0.182839 | − | 0.316686i | ||||
\(698\) | −8.35995e7 | − | 4.82662e7i | −0.245831 | − | 0.141931i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.75707e8 | + | 3.04334e8i | 0.512266 | + | 0.887271i | ||||
\(701\) | 1.08271e8i | 0.314310i | 0.987574 | + | 0.157155i | \(0.0502321\pi\) | ||||
−0.987574 | + | 0.157155i | \(0.949768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.17708e7 | −0.235360 | ||||||||
\(704\) | 1.37547e8 | − | 7.94127e7i | 0.394215 | − | 0.227600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.23339e7 | − | 2.13629e7i | 0.0350498 | − | 0.0607081i | ||||
\(707\) | −7.49729e7 | − | 4.32856e7i | −0.212152 | − | 0.122486i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.42675e7 | − | 1.45956e8i | −0.236440 | − | 0.409527i | 0.723250 | − | 0.690586i | \(-0.242647\pi\) |
−0.959690 | + | 0.281060i | \(0.909314\pi\) | |||||||
\(710\) | − | 3.62465e8i | − | 1.01272i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.49358e8 | 0.413798 | ||||||||
\(713\) | −6.62476e7 | + | 3.82481e7i | −0.182769 | + | 0.105522i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.86826e8 | − | 3.23591e8i | 0.511115 | − | 0.885276i | ||||
\(716\) | −9.27845e7 | − | 5.35692e7i | −0.252776 | − | 0.145940i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.24488e7 | + | 7.35234e7i | 0.114681 | + | 0.198633i | ||||
\(719\) | − | 6.10328e8i | − | 1.64201i | −0.570918 | − | 0.821007i | \(-0.693413\pi\) | ||
0.570918 | − | 0.821007i | \(-0.306587\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.77667e8 | −0.474025 | ||||||||
\(722\) | −2.11747e8 | + | 1.22252e8i | −0.562609 | + | 0.324822i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.25809e7 | − | 5.64318e7i | 0.0858515 | − | 0.148699i | ||||
\(725\) | 8.61965e8 | + | 4.97656e8i | 2.26191 | + | 1.30591i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.07962e8 | − | 5.33407e8i | −0.801483 | − | 1.38821i | −0.918640 | − | 0.395096i | \(-0.870711\pi\) |
0.117156 | − | 0.993113i | \(-0.462622\pi\) | |||||||
\(728\) | 4.11795e8i | 1.06730i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.62326e8 | 0.931388 | ||||||||
\(731\) | −1.14505e8 | + | 6.61097e7i | −0.293139 | + | 0.169244i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.82521e8 | + | 3.16136e8i | −0.463449 | + | 0.802716i | −0.999130 | − | 0.0417037i | \(-0.986721\pi\) |
0.535681 | + | 0.844420i | \(0.320055\pi\) | |||||||
\(734\) | −2.14804e8 | − | 1.24017e8i | −0.543193 | − | 0.313612i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.88069e8 | − | 3.25744e8i | −0.471718 | − | 0.817040i | ||||
\(737\) | 2.68483e8i | 0.670678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.10760e8 | −1.76112 | −0.880562 | − | 0.473931i | \(-0.842835\pi\) | ||||
−0.880562 | + | 0.473931i | \(0.842835\pi\) | |||||||
\(740\) | −1.89670e8 | + | 1.09506e8i | −0.468061 | + | 0.270235i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.71277e8 | − | 2.96660e8i | 0.419263 | − | 0.726185i | ||||
\(743\) | 1.83073e8 | + | 1.05697e8i | 0.446331 | + | 0.257689i | 0.706279 | − | 0.707933i | \(-0.250372\pi\) |
−0.259949 | + | 0.965622i | \(0.583706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.12393e8 | − | 7.14286e8i | −0.997338 | − | 1.72744i | ||||
\(746\) | 3.50028e8i | 0.843115i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.27076e7 | 0.0781526 | ||||||||
\(749\) | −5.16247e8 | + | 2.98055e8i | −1.22860 | + | 0.709335i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.53126e7 | − | 1.65086e8i | 0.225025 | − | 0.389754i | −0.731302 | − | 0.682054i | \(-0.761087\pi\) |
0.956327 | + | 0.292299i | \(0.0944203\pi\) | |||||||
\(752\) | 5.24437e6 | + | 3.02784e6i | 0.0123322 | + | 0.00711999i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.77484e8 | + | 3.07412e8i | 0.414043 | + | 0.717144i | ||||
\(755\) | 9.45438e8i | 2.19681i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.27405e8 | 1.44631 | 0.723153 | − | 0.690688i | \(-0.242692\pi\) | ||||
0.723153 | + | 0.690688i | \(0.242692\pi\) | |||||||
\(758\) | 3.89226e8 | − | 2.24720e8i | 0.893704 | − | 0.515980i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.66196e8 | − | 2.87860e8i | 0.378600 | − | 0.655754i | ||||
\(761\) | −6.91991e7 | − | 3.99521e7i | −0.157017 | − | 0.0906537i | 0.419433 | − | 0.907786i | \(-0.362229\pi\) |
−0.576450 | + | 0.817133i | \(0.695562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.25947e8 | − | 3.91352e8i | −0.508667 | − | 0.881038i | ||||
\(764\) | 1.44546e8i | 0.324135i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.70666e8 | 0.379719 | ||||||||
\(767\) | 5.12872e8 | − | 2.96107e8i | 1.13664 | − | 0.656239i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.32237e8 | + | 5.75452e8i | −0.730583 | + | 1.26541i | 0.226052 | + | 0.974115i | \(0.427418\pi\) |
−0.956634 | + | 0.291291i | \(0.905915\pi\) | |||||||
\(770\) | 2.32675e8 | + | 1.34335e8i | 0.509656 | + | 0.294250i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.86575e7 | + | 8.42773e7i | 0.105754 | + | 0.183172i | ||||
\(773\) | 6.85987e6i | 0.0148517i | 0.999972 | + | 0.00742587i | \(0.00236375\pi\) | ||||
−0.999972 | + | 0.00742587i | \(0.997636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.23727e8 | −0.480632 | ||||||||
\(776\) | 1.05518e8 | − | 6.09207e7i | 0.225808 | − | 0.130371i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.83409e8 | + | 3.17674e8i | −0.389477 | + | 0.674595i | ||||
\(779\) | 1.43722e8 | + | 8.29776e7i | 0.304025 | + | 0.175529i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.85341e7 | + | 1.36025e8i | 0.164856 | + | 0.285539i | ||||
\(782\) | 1.61202e8i | 0.337093i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.29370e7 | 0.0891011 | ||||||||
\(785\) | −8.95954e7 | + | 5.17279e7i | −0.185215 | + | 0.106934i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.52795e8 | − | 2.64648e8i | 0.313462 | − | 0.542932i | −0.665648 | − | 0.746266i | \(-0.731845\pi\) |
0.979109 | + | 0.203335i | \(0.0651779\pi\) | |||||||
\(788\) | 1.78694e8 | + | 1.03169e8i | 0.365200 | + | 0.210848i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.75795e8 | − | 8.24102e8i | −0.965026 | − | 1.67147i | ||||
\(791\) | − | 4.93494e8i | − | 0.997131i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.54193e8 | −0.309205 | ||||||||
\(794\) | −1.92332e8 | + | 1.11043e8i | −0.384230 | + | 0.221835i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.18034e8 | + | 2.04441e8i | −0.234028 | + | 0.405348i | ||||
\(797\) | −1.74456e8 | − | 1.00722e8i | −0.344597 | − | 0.198953i | 0.317706 | − | 0.948189i | \(-0.397087\pi\) |
−0.662303 | + | 0.749236i | \(0.730421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.72902e6 | + | 6.45886e6i | 0.00731063 | + | 0.0126624i | ||||
\(800\) | − | 1.10008e9i | − | 2.14860i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.25262e8 | 0.242826 | ||||||||
\(803\) | −1.35973e8 | + | 7.85039e7i | −0.262606 | + | 0.151616i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.14950e8 | − | 8.91919e8i | 0.987137 | − | 1.70977i | ||||
\(806\) | −6.91003e7 | − | 3.98950e7i | −0.131970 | − | 0.0761928i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.99119e7 | + | 1.38412e8i | 0.151488 | + | 0.262385i | ||||
\(809\) | 1.11534e8i | 0.210650i | 0.994438 | + | 0.105325i | \(0.0335882\pi\) | ||||
−0.994438 | + | 0.105325i | \(0.966412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.72124e8 | −0.322685 | −0.161343 | − | 0.986898i | \(-0.551582\pi\) | ||||
−0.161343 | + | 0.986898i | \(0.551582\pi\) | |||||||
\(812\) | 1.71921e8 | − | 9.92584e7i | 0.321115 | − | 0.185396i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.10104e7 | + | 1.05673e8i | −0.113118 | + | 0.195925i | ||||
\(815\) | −1.65103e9 | − | 9.53224e8i | −3.04988 | − | 1.76085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.86053e7 | − | 1.53469e8i | −0.162478 | − | 0.281420i | ||||
\(818\) | 5.46318e8i | 0.998126i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.44488e8 | 0.806154 | ||||||||
\(821\) | −7.46933e8 | + | 4.31242e8i | −1.34975 | + | 0.779276i | −0.988213 | − | 0.153084i | \(-0.951080\pi\) |
−0.361532 | + | 0.932360i | \(0.617746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.94505e6 | − | 5.10097e6i | 0.00528315 | − | 0.00915068i | −0.863372 | − | 0.504568i | \(-0.831652\pi\) |
0.868655 | + | 0.495418i | \(0.164985\pi\) | |||||||
\(824\) | 2.84057e8 | + | 1.64001e8i | 0.507720 | + | 0.293132i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.12912e8 | + | 3.68774e8i | 0.377798 | + | 0.654366i | ||||
\(827\) | − | 7.60618e8i | − | 1.34478i | −0.740199 | − | 0.672388i | \(-0.765269\pi\) | ||
0.740199 | − | 0.672388i | \(-0.234731\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06302e9 | −1.86585 | −0.932926 | − | 0.360067i | \(-0.882754\pi\) | ||||
−0.932926 | + | 0.360067i | \(0.882754\pi\) | |||||||
\(830\) | 9.94988e8 | − | 5.74456e8i | 1.74014 | − | 1.00467i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.17524e8 | − | 5.49967e8i | 0.551323 | − | 0.954920i | ||||
\(833\) | 4.57956e7 | + | 2.64401e7i | 0.0792299 | + | 0.0457434i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.24598e8 | + | 7.35426e8i | 0.729321 | + | 1.26322i | ||||
\(836\) | 4.38372e7i | 0.0750282i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.91266e8 | −1.17466 | ||||||||
\(839\) | −4.04427e8 | + | 2.33496e8i | −0.684786 | + | 0.395361i | −0.801656 | − | 0.597786i | \(-0.796047\pi\) |
0.116870 | + | 0.993147i | \(0.462714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62822e7 | + | 2.82016e7i | −0.0273732 | + | 0.0474117i | ||||
\(842\) | 6.83760e8 | + | 3.94769e8i | 1.14543 | + | 0.661312i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.74017e7 | − | 9.94227e7i | −0.0954767 | − | 0.165371i | ||||
\(845\) | − | 3.35572e8i | − | 0.556180i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.13273e8 | 0.680122 | ||||||||
\(848\) | −2.51351e8 | + | 1.45117e8i | −0.412185 | + | 0.237975i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.35732e8 | + | 4.08299e8i | −0.383850 | + | 0.664847i | ||||
\(851\) | 4.05080e8 | + | 2.33873e8i | 0.657282 | + | 0.379482i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.10268e8 | + | 8.83809e8i | 0.822150 | + | 1.42400i | 0.904078 | + | 0.427367i | \(0.140559\pi\) |
−0.0819289 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(854\) | − | 1.10871e8i | − | 0.178010i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.10051e9 | 1.75458 | ||||||||
\(857\) | −5.46885e7 | + | 3.15744e7i | −0.0868867 | + | 0.0501641i | −0.542814 | − | 0.839853i | \(-0.682641\pi\) |
0.455927 | + | 0.890017i | \(0.349308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17778e8 | + | 8.96818e8i | −0.816892 | + | 1.41490i | 0.0910701 | + | 0.995844i | \(0.470971\pi\) |
−0.907962 | + | 0.419053i | \(0.862362\pi\) | |||||||
\(860\) | −4.11045e8 | − | 2.37317e8i | −0.646240 | − | 0.373107i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.14663e8 | + | 3.71807e8i | 0.335147 | + | 0.580492i | ||||
\(863\) | − | 4.60575e8i | − | 0.716585i | −0.933609 | − | 0.358292i | \(-0.883359\pi\) | ||
0.933609 | − | 0.358292i | \(-0.116641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.24420e8 | 0.655764 | ||||||||
\(866\) | 9.55765e7 | − | 5.51811e7i | 0.147163 | − | 0.0849643i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.23114e7 | + | 3.86444e7i | −0.0341167 | + | 0.0590919i | ||||
\(869\) | 3.57111e8 | + | 2.06178e8i | 0.544181 | + | 0.314183i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.36751e8 | + | 9.29679e8i | 0.812303 | + | 1.40695i | ||||
\(872\) | 8.34267e8i | 1.25822i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.16055e8 | −0.323616 | ||||||||
\(875\) | 1.63755e9 | − | 9.45438e8i | 2.44438 | − | 1.41127i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.52290e8 | − | 7.83389e8i | 0.670530 | − | 1.16139i | −0.307224 | − | 0.951637i | \(-0.599400\pi\) |
0.977754 | − | 0.209754i | \(-0.0672664\pi\) | |||||||
\(878\) | 5.14736e8 | + | 2.97183e8i | 0.760504 | + | 0.439077i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.13818e8 | − | 1.97138e8i | −0.167017 | − | 0.289282i | ||||
\(881\) | 1.06708e9i | 1.56051i | 0.625460 | + | 0.780257i | \(0.284912\pi\) | ||||
−0.625460 | + | 0.780257i | \(0.715088\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.52780e7 | −0.123867 | −0.0619334 | − | 0.998080i | \(-0.519727\pi\) | ||||
−0.0619334 | + | 0.998080i | \(0.519727\pi\) | |||||||
\(884\) | 1.13257e8 | − | 6.53890e7i | 0.163949 | − | 0.0946559i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.06190e8 | + | 7.03542e8i | −0.584021 | + | 1.01155i | ||||
\(887\) | −2.10625e8 | − | 1.21604e8i | −0.301814 | − | 0.174252i | 0.341444 | − | 0.939902i | \(-0.389084\pi\) |
−0.643258 | + | 0.765650i | \(0.722418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.10996e8 | − | 3.65456e8i | −0.300310 | − | 0.520152i | ||||
\(890\) | − | 3.89629e8i | − | 0.552690i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.07018e8 | −0.573481 | ||||||||
\(893\) | −8.65667e6 | + | 4.99793e6i | −0.0121562 | + | 0.00701836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.59164e8 | + | 7.95296e8i | −0.640470 | + | 1.10933i | ||||
\(896\) | −3.88785e7 | − | 2.24465e7i | −0.0540488 | − | 0.0312051i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.05784e8 | + | 3.56429e8i | 0.284174 | + | 0.492203i | ||||
\(899\) | 1.26385e8i | 0.173947i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.57447e8 | −0.488695 | ||||||||
\(902\) | 2.14465e8 | − | 1.23822e8i | 0.292238 | − | 0.168724i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.55532e8 | + | 7.89005e8i | −0.616615 | + | 1.06801i | ||||
\(905\) | −4.83701e8 | − | 2.79265e8i | −0.652577 | − | 0.376765i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.31213e8 | − | 7.46882e8i | −0.577922 | − | 1.00099i | −0.995717 | − | 0.0924497i | \(-0.970530\pi\) |
0.417795 | − | 0.908541i | \(-0.362803\pi\) | |||||||
\(908\) | − | 1.65624e8i | − | 0.221241i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.07425e9 | 1.42554 | ||||||||
\(911\) | −9.92770e8 | + | 5.73176e8i | −1.31309 | + | 0.758111i | −0.982606 | − | 0.185702i | \(-0.940544\pi\) |
−0.330480 | + | 0.943813i | \(0.607211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.48931e8 | + | 4.31161e8i | −0.327090 | + | 0.566536i | ||||
\(914\) | −3.70303e8 | − | 2.13795e8i | −0.484974 | − | 0.280000i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.68379e8 | − | 4.64846e8i | −0.349190 | − | 0.604815i | ||||
\(917\) | − | 9.66464e7i | − | 0.125336i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.23240e8 | 1.06067 | 0.530335 | − | 0.847788i | \(-0.322066\pi\) | ||||
0.530335 | + | 0.847788i | \(0.322066\pi\) | |||||||
\(920\) | −1.64662e9 | + | 9.50676e8i | −2.11461 | + | 1.22087i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.69678e8 | − | 8.13506e8i | 0.599249 | − | 1.03793i | ||||
\(923\) | 5.43883e8 | + | 3.14011e8i | 0.691672 | + | 0.399337i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.84004e8 | + | 1.18473e9i | 0.864238 | + | 1.49690i | ||||
\(926\) | − | 3.32288e6i | − | 0.00418486i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.21444e8 | −0.777603 | ||||||||
\(929\) | 6.31105e8 | − | 3.64369e8i | 0.787144 | − | 0.454458i | −0.0518119 | − | 0.998657i | \(-0.516500\pi\) |
0.838956 | + | 0.544199i | \(0.183166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.54371e7 | + | 6.13789e7i | −0.0439146 | + | 0.0760624i | ||||
\(932\) | 1.79577e8 | + | 1.03679e8i | 0.221821 | + | 0.128069i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.44218e7 | − | 1.63543e8i | −0.115886 | − | 0.200721i | ||||
\(935\) | − | 2.80351e8i | − | 0.342978i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.88557e8 | 0.715434 | 0.357717 | − | 0.933830i | \(-0.383555\pi\) | ||||
0.357717 | + | 0.933830i | \(0.383555\pi\) | |||||||
\(938\) | −6.68475e8 | + | 3.85944e8i | −0.809984 | + | 0.467645i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.33862e7 | + | 2.31856e7i | −0.0161167 | + | 0.0279149i | ||||
\(941\) | −8.43199e8 | − | 4.86821e8i | −1.01196 | − | 0.584253i | −0.100192 | − | 0.994968i | \(-0.531946\pi\) |
−0.911764 | + | 0.410715i | \(0.865279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.74649e8 | − | 8.22117e8i | −0.566028 | − | 0.980389i | ||||
\(944\) | − | 3.60787e8i | − | 0.428879i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.64439e8 | −0.312357 | ||||||||
\(947\) | −3.38266e8 | + | 1.95298e8i | −0.398299 | + | 0.229958i | −0.685750 | − | 0.727838i | \(-0.740525\pi\) |
0.287451 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.13890e8 | + | 5.43673e8i | −0.367264 | + | 0.636120i | ||||
\(950\) | −5.47234e8 | − | 3.15946e8i | −0.638267 | − | 0.368504i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.54485e8 | + | 2.67576e8i | 0.179050 | + | 0.310124i | ||||
\(953\) | 4.41062e7i | 0.0509590i | 0.999675 | + | 0.0254795i | \(0.00811125\pi\) | ||||
−0.999675 | + | 0.0254795i | \(0.991889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.23896e9 | 1.42249 | ||||||||
\(956\) | −3.60546e8 | + | 2.08161e8i | −0.412655 | + | 0.238247i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.00352e8 | − | 3.47019e8i | 0.227875 | − | 0.394691i | ||||
\(959\) | 5.53733e8 | + | 3.19698e8i | 0.627834 | + | 0.362480i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.29547e8 | + | 7.43998e8i | 0.483995 | + | 0.838304i | ||||
\(962\) | 4.87887e8i | 0.548017i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.18439e8 | −0.132209 | ||||||||
\(965\) | 7.22377e8 | − | 4.17064e8i | 0.803863 | − | 0.464110i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.81689e8 | − | 8.34310e8i | 0.532705 | − | 0.922673i | −0.466565 | − | 0.884487i | \(-0.654509\pi\) |
0.999271 | − | 0.0381861i | \(-0.0121580\pi\) | |||||||
\(968\) | −6.60748e8 | − | 3.81483e8i | −0.728467 | − | 0.420581i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.58923e8 | − | 2.75263e8i | −0.174130 | − | 0.301601i | ||||
\(971\) | 7.36207e8i | 0.804160i | 0.915605 | + | 0.402080i | \(0.131713\pi\) | ||||
−0.915605 | + | 0.402080i | \(0.868287\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.32575e7 | −0.0361036 | ||||||||
\(974\) | 1.04187e9 | − | 6.01525e8i | 1.12755 | − | 0.650994i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.69688e7 | + | 8.13523e7i | −0.0505196 | + | 0.0875025i | ||||
\(977\) | 1.39341e9 | + | 8.04484e8i | 1.49415 | + | 0.862648i | 0.999977 | − | 0.00671600i | \(-0.00213779\pi\) |
0.494172 | + | 0.869364i | \(0.335471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.44197e7 | + | 1.46219e8i | 0.0899696 | + | 0.155832i | ||||
\(980\) | 1.89827e8i | 0.201687i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.17103e8 | −0.546062 | ||||||||
\(983\) | 3.87093e8 | − | 2.23488e8i | 0.407526 | − | 0.235285i | −0.282200 | − | 0.959356i | \(-0.591064\pi\) |
0.689726 | + | 0.724070i | \(0.257731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.84304e8 | − | 1.53166e9i | 0.925322 | − | 1.60270i | ||||
\(986\) | 2.30651e8 | + | 1.33167e8i | 0.240616 | + | 0.138920i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.76394e7 | + | 1.51796e8i | 0.0908716 | + | 0.157394i | ||||
\(989\) | 1.01368e9i | 1.04788i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.40384e9 | −1.44244 | −0.721220 | − | 0.692706i | \(-0.756418\pi\) | ||||
−0.721220 | + | 0.692706i | \(0.756418\pi\) | |||||||
\(992\) | 1.20974e8 | − | 6.98443e7i | 0.123924 | − | 0.0715478i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.25786e8 | + | 3.91072e8i | −0.229899 | + | 0.398197i | ||||
\(995\) | 1.75235e9 | + | 1.01172e9i | 1.77890 | + | 1.02705i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.65711e8 | − | 1.15304e9i | −0.671738 | − | 1.16348i | −0.977411 | − | 0.211348i | \(-0.932215\pi\) |
0.305673 | − | 0.952137i | \(-0.401119\pi\) | |||||||
\(998\) | 6.40038e7i | 0.0643894i | ||||||||
\(999\) | 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 | 81.7.d.b.53.2 | 4 | ||
3.2 | odd | 2 | inner | 81.7.d.b.53.1 | 4 | ||
9.2 | odd | 6 | inner | 81.7.d.b.26.2 | 4 | ||
9.4 | even | 3 | 27.7.b.b.26.2 | yes | 2 | ||
9.5 | odd | 6 | 27.7.b.b.26.1 | ✓ | 2 | ||
9.7 | even | 3 | inner | 81.7.d.b.26.1 | 4 | ||
36.23 | even | 6 | 432.7.e.d.161.2 | 2 | |||
36.31 | odd | 6 | 432.7.e.d.161.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.7.b.b.26.1 | ✓ | 2 | 9.5 | odd | 6 | ||
27.7.b.b.26.2 | yes | 2 | 9.4 | even | 3 | ||
81.7.d.b.26.1 | 4 | 9.7 | even | 3 | inner | ||
81.7.d.b.26.2 | 4 | 9.2 | odd | 6 | inner | ||
81.7.d.b.53.1 | 4 | 3.2 | odd | 2 | inner | ||
81.7.d.b.53.2 | 4 | 1.1 | even | 1 | trivial | ||
432.7.e.d.161.1 | 2 | 36.31 | odd | 6 | |||
432.7.e.d.161.2 | 2 | 36.23 | even | 6 |