Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,7,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.76064900344\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.50898483.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} - 10x^{3} + 64x^{2} - 40x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-1.55022 - 2.68505i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.7.d.a.7.2 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.12493 | − | 3.63805i | −0.890616 | − | 0.454757i | ||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | 37.5291 | + | 51.8417i | 0.586392 | + | 0.810027i | ||||
\(5\) | 172.232 | 1.37785 | 0.688927 | − | 0.724831i | \(-0.258082\pi\) | ||||
0.688927 | + | 0.724831i | \(0.258082\pi\) | |||||||
\(6\) | 56.7117 | − | 111.067i | 0.262554 | − | 0.514197i | ||||
\(7\) | 545.623i | 1.59074i | 0.606126 | + | 0.795369i | \(0.292723\pi\) | ||||
−0.606126 | + | 0.795369i | \(0.707277\pi\) | |||||||
\(8\) | −78.7890 | − | 505.901i | −0.153885 | − | 0.988089i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | −1227.14 | − | 626.588i | −1.22714 | − | 0.626588i | ||||
\(11\) | − | 147.793i | − | 0.111039i | −0.998458 | − | 0.0555195i | \(-0.982318\pi\) | ||
0.998458 | − | 0.0555195i | \(-0.0176815\pi\) | |||||||
\(12\) | −808.133 | + | 585.021i | −0.467669 | + | 0.338554i | ||||
\(13\) | 1198.44 | 0.545491 | 0.272746 | − | 0.962086i | \(-0.412068\pi\) | ||||
0.272746 | + | 0.962086i | \(0.412068\pi\) | |||||||
\(14\) | 1985.01 | − | 3887.52i | 0.723399 | − | 1.41674i | ||||
\(15\) | 2684.83i | 0.795504i | ||||||||
\(16\) | −1279.13 | + | 3891.15i | −0.312288 | + | 0.949987i | ||||
\(17\) | 319.429 | 0.0650170 | 0.0325085 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325085 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(18\) | 1731.36 | + | 884.047i | 0.296872 | + | 0.151586i | ||||
\(19\) | − | 5768.21i | − | 0.840970i | −0.907300 | − | 0.420485i | \(-0.861860\pi\) | ||
0.907300 | − | 0.420485i | \(-0.138140\pi\) | |||||||
\(20\) | 6463.70 | + | 8928.79i | 0.807963 | + | 1.11610i | ||||
\(21\) | −8505.42 | −0.918412 | ||||||||
\(22\) | −537.679 | + | 1053.01i | −0.0504958 | + | 0.0988931i | ||||
\(23\) | − | 8044.99i | − | 0.661214i | −0.943768 | − | 0.330607i | \(-0.892746\pi\) | ||
0.943768 | − | 0.330607i | \(-0.107254\pi\) | |||||||
\(24\) | 7886.22 | − | 1228.20i | 0.570473 | − | 0.0888454i | ||||
\(25\) | 14038.8 | 0.898481 | ||||||||
\(26\) | −8538.83 | − | 4360.01i | −0.485823 | − | 0.248066i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | −28286.0 | + | 20476.7i | −1.28854 | + | 0.932796i | ||||
\(29\) | −34198.9 | −1.40223 | −0.701114 | − | 0.713049i | \(-0.747314\pi\) | ||||
−0.701114 | + | 0.713049i | \(0.747314\pi\) | |||||||
\(30\) | 9767.55 | − | 19129.2i | 0.361761 | − | 0.708488i | ||||
\(31\) | − | 19886.7i | − | 0.667540i | −0.942655 | − | 0.333770i | \(-0.891679\pi\) | ||
0.942655 | − | 0.333770i | \(-0.108321\pi\) | |||||||
\(32\) | 23269.9 | − | 23070.6i | 0.710142 | − | 0.704059i | ||||
\(33\) | 2303.86 | 0.0641084 | ||||||||
\(34\) | −2275.90 | − | 1162.10i | −0.0579052 | − | 0.0295669i | ||||
\(35\) | 93973.5i | 2.19180i | ||||||||
\(36\) | −9119.57 | − | 12597.5i | −0.195464 | − | 0.270009i | ||||
\(37\) | 92346.8 | 1.82313 | 0.911563 | − | 0.411161i | \(-0.134877\pi\) | ||||
0.911563 | + | 0.411161i | \(0.134877\pi\) | |||||||
\(38\) | −20985.1 | + | 41098.1i | −0.382437 | + | 0.748981i | ||||
\(39\) | 18681.9i | 0.314940i | ||||||||
\(40\) | −13570.0 | − | 87132.3i | −0.212031 | − | 1.36144i | ||||
\(41\) | 19729.1 | 0.286257 | 0.143129 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143129 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(42\) | 60600.5 | + | 30943.2i | 0.817953 | + | 0.417654i | ||||
\(43\) | 10650.3i | 0.133954i | 0.997755 | + | 0.0669770i | \(0.0213354\pi\) | ||||
−0.997755 | + | 0.0669770i | \(0.978665\pi\) | |||||||
\(44\) | 7661.84 | − | 5546.54i | 0.0899446 | − | 0.0651124i | ||||
\(45\) | −41852.3 | −0.459285 | ||||||||
\(46\) | −29268.1 | + | 57320.0i | −0.300692 | + | 0.588888i | ||||
\(47\) | − | 145079.i | − | 1.39737i | −0.715429 | − | 0.698686i | \(-0.753769\pi\) | ||
0.715429 | − | 0.698686i | \(-0.246231\pi\) | |||||||
\(48\) | −60657.0 | − | 19939.7i | −0.548476 | − | 0.180300i | ||||
\(49\) | −180055. | −1.53044 | ||||||||
\(50\) | −100025. | − | 51073.8i | −0.800201 | − | 0.408590i | ||||
\(51\) | 4979.40i | 0.0375376i | ||||||||
\(52\) | 44976.5 | + | 62129.4i | 0.319872 | + | 0.441863i | ||||
\(53\) | 20665.9 | 0.138812 | 0.0694059 | − | 0.997589i | \(-0.477890\pi\) | ||||
0.0694059 | + | 0.997589i | \(0.477890\pi\) | |||||||
\(54\) | −13780.9 | + | 26989.2i | −0.0875180 | + | 0.171399i | ||||
\(55\) | − | 25454.6i | − | 0.152996i | ||||||
\(56\) | 276031. | − | 42989.1i | 1.57179 | − | 0.244790i | ||||
\(57\) | 89917.5 | 0.485534 | ||||||||
\(58\) | 243665. | + | 124418.i | 1.24885 | + | 0.637673i | ||||
\(59\) | − | 148313.i | − | 0.722142i | −0.932538 | − | 0.361071i | \(-0.882411\pi\) | ||
0.932538 | − | 0.361071i | \(-0.117589\pi\) | |||||||
\(60\) | −139186. | + | 100759.i | −0.644380 | + | 0.466478i | ||||
\(61\) | −97811.2 | −0.430922 | −0.215461 | − | 0.976512i | \(-0.569125\pi\) | ||||
−0.215461 | + | 0.976512i | \(0.569125\pi\) | |||||||
\(62\) | −72348.8 | + | 141691.i | −0.303568 | + | 0.594521i | ||||
\(63\) | − | 132586.i | − | 0.530246i | ||||||
\(64\) | −249729. | + | 79719.0i | −0.952639 | + | 0.304104i | ||||
\(65\) | 206410. | 0.751607 | ||||||||
\(66\) | −16414.9 | − | 8381.58i | −0.0570960 | − | 0.0291537i | ||||
\(67\) | 478892.i | 1.59226i | 0.605127 | + | 0.796129i | \(0.293122\pi\) | ||||
−0.605127 | + | 0.796129i | \(0.706878\pi\) | |||||||
\(68\) | 11987.9 | + | 16559.7i | 0.0381255 | + | 0.0526655i | ||||
\(69\) | 125409. | 0.381752 | ||||||||
\(70\) | 341881. | − | 669554.i | 0.996737 | − | 1.95205i | ||||
\(71\) | 137300.i | 0.383615i | 0.981433 | + | 0.191807i | \(0.0614349\pi\) | ||||
−0.981433 | + | 0.191807i | \(0.938565\pi\) | |||||||
\(72\) | 19145.7 | + | 122934.i | 0.0512949 | + | 0.329363i | ||||
\(73\) | −251405. | −0.646258 | −0.323129 | − | 0.946355i | \(-0.604735\pi\) | ||||
−0.323129 | + | 0.946355i | \(0.604735\pi\) | |||||||
\(74\) | −657964. | − | 335963.i | −1.62370 | − | 0.829079i | ||||
\(75\) | 218843.i | 0.518738i | ||||||||
\(76\) | 299034. | − | 216476.i | 0.681208 | − | 0.493138i | ||||
\(77\) | 80639.2 | 0.176634 | ||||||||
\(78\) | 67965.8 | − | 133107.i | 0.143221 | − | 0.280490i | ||||
\(79\) | − | 616099.i | − | 1.24959i | −0.780787 | − | 0.624797i | \(-0.785182\pi\) | ||
0.780787 | − | 0.624797i | \(-0.214818\pi\) | |||||||
\(80\) | −220307. | + | 670179.i | −0.430287 | + | 1.30894i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −140569. | − | 71775.7i | −0.254945 | − | 0.130177i | ||||
\(83\) | 746788.i | 1.30606i | 0.757333 | + | 0.653029i | \(0.226502\pi\) | ||||
−0.757333 | + | 0.653029i | \(0.773498\pi\) | |||||||
\(84\) | −319201. | − | 440936.i | −0.538550 | − | 0.743939i | ||||
\(85\) | 55015.7 | 0.0895839 | ||||||||
\(86\) | 38746.3 | − | 75882.5i | 0.0609165 | − | 0.119302i | ||||
\(87\) | − | 533109.i | − | 0.809577i | ||||||
\(88\) | −74768.7 | + | 11644.5i | −0.109716 | + | 0.0170872i | ||||
\(89\) | −406308. | −0.576348 | −0.288174 | − | 0.957578i | \(-0.593048\pi\) | ||||
−0.288174 | + | 0.957578i | \(0.593048\pi\) | |||||||
\(90\) | 298195. | + | 152261.i | 0.409046 | + | 0.208863i | ||||
\(91\) | 653899.i | 0.867733i | ||||||||
\(92\) | 417066. | − | 301922.i | 0.535602 | − | 0.387731i | ||||
\(93\) | 310003. | 0.385404 | ||||||||
\(94\) | −527806. | + | 1.03368e6i | −0.635464 | + | 1.24452i | ||||
\(95\) | − | 993469.i | − | 1.15873i | ||||||
\(96\) | 359635. | + | 362742.i | 0.406488 | + | 0.410001i | ||||
\(97\) | 1.11574e6 | 1.22250 | 0.611250 | − | 0.791438i | \(-0.290667\pi\) | ||||
0.611250 | + | 0.791438i | \(0.290667\pi\) | |||||||
\(98\) | 1.28288e6 | + | 655051.i | 1.36304 | + | 0.695980i | ||||
\(99\) | 35913.7i | 0.0370130i | ||||||||
\(100\) | 526862. | + | 727794.i | 0.526862 | + | 0.727794i | ||||
\(101\) | −853307. | −0.828211 | −0.414106 | − | 0.910229i | \(-0.635906\pi\) | ||||
−0.414106 | + | 0.910229i | \(0.635906\pi\) | |||||||
\(102\) | 18115.3 | − | 35477.8i | 0.0170705 | − | 0.0334316i | ||||
\(103\) | − | 1.08151e6i | − | 0.989738i | −0.868968 | − | 0.494869i | \(-0.835216\pi\) | ||
0.868968 | − | 0.494869i | \(-0.164784\pi\) | |||||||
\(104\) | −94424.3 | − | 606295.i | −0.0839428 | − | 0.538994i | ||||
\(105\) | −1.46490e6 | −1.26544 | ||||||||
\(106\) | −147243. | − | 75183.6i | −0.123628 | − | 0.0631256i | ||||
\(107\) | − | 219304.i | − | 0.179017i | −0.995986 | − | 0.0895087i | \(-0.971470\pi\) | ||
0.995986 | − | 0.0895087i | \(-0.0285297\pi\) | |||||||
\(108\) | 196376. | − | 142160.i | 0.155890 | − | 0.112851i | ||||
\(109\) | −913974. | −0.705756 | −0.352878 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352878 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(110\) | −92605.3 | + | 181362.i | −0.0695758 | + | 0.136260i | ||||
\(111\) | 1.43954e6i | 1.05258i | ||||||||
\(112\) | −2.12310e6 | − | 697923.i | −1.51118 | − | 0.496768i | ||||
\(113\) | 1.37579e6 | 0.953490 | 0.476745 | − | 0.879042i | \(-0.341816\pi\) | ||||
0.476745 | + | 0.879042i | \(0.341816\pi\) | |||||||
\(114\) | −640656. | − | 327125.i | −0.432424 | − | 0.220800i | ||||
\(115\) | − | 1.38560e6i | − | 0.911057i | ||||||
\(116\) | −1.28346e6 | − | 1.77293e6i | −0.822256 | − | 1.13584i | ||||
\(117\) | −291222. | −0.181830 | ||||||||
\(118\) | −539570. | + | 1.05672e6i | −0.328399 | + | 0.643151i | ||||
\(119\) | 174288.i | 0.103425i | ||||||||
\(120\) | 1.35826e6 | − | 211535.i | 0.786029 | − | 0.122416i | ||||
\(121\) | 1.74972e6 | 0.987670 | ||||||||
\(122\) | 696898. | + | 355843.i | 0.383786 | + | 0.195965i | ||||
\(123\) | 307547.i | 0.165271i | ||||||||
\(124\) | 1.03096e6 | − | 746329.i | 0.540725 | − | 0.391440i | ||||
\(125\) | −273201. | −0.139879 | ||||||||
\(126\) | −482356. | + | 944668.i | −0.241133 | + | 0.472245i | ||||
\(127\) | 3.46516e6i | 1.69166i | 0.533456 | + | 0.845828i | \(0.320893\pi\) | ||||
−0.533456 | + | 0.845828i | \(0.679107\pi\) | |||||||
\(128\) | 2.06932e6 | + | 340535.i | 0.986728 | + | 0.162380i | ||||
\(129\) | −166022. | −0.0773384 | ||||||||
\(130\) | −1.47066e6 | − | 750931.i | −0.669393 | − | 0.341798i | ||||
\(131\) | 2.11232e6i | 0.939608i | 0.882771 | + | 0.469804i | \(0.155675\pi\) | ||||
−0.882771 | + | 0.469804i | \(0.844325\pi\) | |||||||
\(132\) | 86462.0 | + | 119436.i | 0.0375927 | + | 0.0519296i | ||||
\(133\) | 3.14727e6 | 1.33776 | ||||||||
\(134\) | 1.74224e6 | − | 3.41207e6i | 0.724090 | − | 1.41809i | ||||
\(135\) | − | 652413.i | − | 0.265168i | ||||||
\(136\) | −25167.5 | − | 161599.i | −0.0100051 | − | 0.0642426i | ||||
\(137\) | −1.39131e6 | −0.541081 | −0.270541 | − | 0.962709i | \(-0.587202\pi\) | ||||
−0.270541 | + | 0.962709i | \(0.587202\pi\) | |||||||
\(138\) | −893530. | − | 456245.i | −0.339995 | − | 0.173604i | ||||
\(139\) | − | 647825.i | − | 0.241220i | −0.992700 | − | 0.120610i | \(-0.961515\pi\) | ||
0.992700 | − | 0.120610i | \(-0.0384850\pi\) | |||||||
\(140\) | −4.87175e6 | + | 3.52674e6i | −1.77542 | + | 1.28526i | ||||
\(141\) | 2.26156e6 | 0.806773 | ||||||||
\(142\) | 499505. | − | 978252.i | 0.174452 | − | 0.341653i | ||||
\(143\) | − | 177122.i | − | 0.0605708i | ||||||
\(144\) | 310829. | − | 945549.i | 0.104096 | − | 0.316662i | ||||
\(145\) | −5.89014e6 | −1.93207 | ||||||||
\(146\) | 1.79124e6 | + | 914626.i | 0.575567 | + | 0.293890i | ||||
\(147\) | − | 2.80678e6i | − | 0.883603i | ||||||
\(148\) | 3.46569e6 | + | 4.78742e6i | 1.06907 | + | 1.47678i | ||||
\(149\) | −617756. | −0.186749 | −0.0933744 | − | 0.995631i | \(-0.529765\pi\) | ||||
−0.0933744 | + | 0.995631i | \(0.529765\pi\) | |||||||
\(150\) | 796161. | − | 1.55924e6i | 0.235900 | − | 0.461996i | ||||
\(151\) | − | 3.16384e6i | − | 0.918931i | −0.888196 | − | 0.459466i | \(-0.848041\pi\) | ||
0.888196 | − | 0.459466i | \(-0.151959\pi\) | |||||||
\(152\) | −2.91815e6 | + | 454472.i | −0.830953 | + | 0.129412i | ||||
\(153\) | −77621.2 | −0.0216723 | ||||||||
\(154\) | −574548. | − | 293370.i | −0.157313 | − | 0.0803255i | ||||
\(155\) | − | 3.42512e6i | − | 0.919772i | ||||||
\(156\) | −968502. | + | 701115.i | −0.255110 | + | 0.184678i | ||||
\(157\) | −2.09075e6 | −0.540261 | −0.270131 | − | 0.962824i | \(-0.587067\pi\) | ||||
−0.270131 | + | 0.962824i | \(0.587067\pi\) | |||||||
\(158\) | −2.24140e6 | + | 4.38966e6i | −0.568261 | + | 1.11291i | ||||
\(159\) | 322149.i | 0.0801430i | ||||||||
\(160\) | 4.00782e6 | − | 3.97349e6i | 0.978472 | − | 0.970090i | ||||
\(161\) | 4.38953e6 | 1.05182 | ||||||||
\(162\) | −420720. | − | 214824.i | −0.0989573 | − | 0.0505285i | ||||
\(163\) | − | 449351.i | − | 0.103758i | −0.998653 | − | 0.0518792i | \(-0.983479\pi\) | ||
0.998653 | − | 0.0518792i | \(-0.0165211\pi\) | |||||||
\(164\) | 740417. | + | 1.02279e6i | 0.167859 | + | 0.231876i | ||||
\(165\) | 396798. | 0.0883320 | ||||||||
\(166\) | 2.71685e6 | − | 5.32081e6i | 0.593939 | − | 1.16320i | ||||
\(167\) | 1.79059e6i | 0.384456i | 0.981350 | + | 0.192228i | \(0.0615713\pi\) | ||||
−0.981350 | + | 0.192228i | \(0.938429\pi\) | |||||||
\(168\) | 670134. | + | 4.30290e6i | 0.141330 | + | 0.907473i | ||||
\(169\) | −3.39054e6 | −0.702439 | ||||||||
\(170\) | −391983. | − | 200150.i | −0.0797849 | − | 0.0407389i | ||||
\(171\) | 1.40168e6i | 0.280323i | ||||||||
\(172\) | −552129. | + | 399696.i | −0.108506 | + | 0.0785496i | ||||
\(173\) | −6.06946e6 | −1.17223 | −0.586114 | − | 0.810229i | \(-0.699343\pi\) | ||||
−0.586114 | + | 0.810229i | \(0.699343\pi\) | |||||||
\(174\) | −1.93948e6 | + | 3.79836e6i | −0.368161 | + | 0.721022i | ||||
\(175\) | 7.65987e6i | 1.42925i | ||||||||
\(176\) | 575084. | + | 189047.i | 0.105486 | + | 0.0346761i | ||||
\(177\) | 2.31197e6 | 0.416929 | ||||||||
\(178\) | 2.89491e6 | + | 1.47817e6i | 0.513305 | + | 0.262098i | ||||
\(179\) | − | 4.05372e6i | − | 0.706797i | −0.935473 | − | 0.353398i | \(-0.885026\pi\) | ||
0.935473 | − | 0.353398i | \(-0.114974\pi\) | |||||||
\(180\) | −1.57068e6 | − | 2.16970e6i | −0.269321 | − | 0.372033i | ||||
\(181\) | 6.32630e6 | 1.06688 | 0.533438 | − | 0.845839i | \(-0.320900\pi\) | ||||
0.533438 | + | 0.845839i | \(0.320900\pi\) | |||||||
\(182\) | 2.37892e6 | − | 4.65898e6i | 0.394608 | − | 0.772817i | ||||
\(183\) | − | 1.52473e6i | − | 0.248793i | ||||||
\(184\) | −4.06997e6 | + | 633857.i | −0.653338 | + | 0.101751i | ||||
\(185\) | 1.59050e7 | 2.51200 | ||||||||
\(186\) | −2.20874e6 | − | 1.12781e6i | −0.343247 | − | 0.175265i | ||||
\(187\) | − | 47209.3i | − | 0.00721943i | ||||||
\(188\) | 7.52116e6 | − | 5.44470e6i | 1.13191 | − | 0.819408i | ||||
\(189\) | 2.06682e6 | 0.306137 | ||||||||
\(190\) | −3.61429e6 | + | 7.07839e6i | −0.526942 | + | 1.03199i | ||||
\(191\) | 1.15014e7i | 1.65063i | 0.564674 | + | 0.825314i | \(0.309002\pi\) | ||||
−0.564674 | + | 0.825314i | \(0.690998\pi\) | |||||||
\(192\) | −1.24270e6 | − | 3.89288e6i | −0.175574 | − | 0.550006i | ||||
\(193\) | −8.78066e6 | −1.22139 | −0.610696 | − | 0.791865i | \(-0.709110\pi\) | ||||
−0.610696 | + | 0.791865i | \(0.709110\pi\) | |||||||
\(194\) | −7.94958e6 | − | 4.05913e6i | −1.08878 | − | 0.555940i | ||||
\(195\) | 3.21761e6i | 0.433941i | ||||||||
\(196\) | −6.75731e6 | − | 9.33438e6i | −0.897441 | − | 1.23970i | ||||
\(197\) | −9.77747e6 | −1.27887 | −0.639437 | − | 0.768843i | \(-0.720833\pi\) | ||||
−0.639437 | + | 0.768843i | \(0.720833\pi\) | |||||||
\(198\) | 130656. | − | 255882.i | 0.0168319 | − | 0.0329644i | ||||
\(199\) | 3.78391e6i | 0.480156i | 0.970754 | + | 0.240078i | \(0.0771730\pi\) | ||||
−0.970754 | + | 0.240078i | \(0.922827\pi\) | |||||||
\(200\) | −1.10610e6 | − | 7.10223e6i | −0.138263 | − | 0.887779i | ||||
\(201\) | −7.46519e6 | −0.919291 | ||||||||
\(202\) | 6.07975e6 | + | 3.10438e6i | 0.737618 | + | 0.376635i | ||||
\(203\) | − | 1.86597e7i | − | 2.23058i | ||||||
\(204\) | −258141. | + | 186872.i | −0.0304065 | + | 0.0220118i | ||||
\(205\) | 3.39798e6 | 0.394421 | ||||||||
\(206\) | −3.93461e6 | + | 7.70570e6i | −0.450090 | + | 0.881476i | ||||
\(207\) | 1.95493e6i | 0.220405i | ||||||||
\(208\) | −1.53297e6 | + | 4.66332e6i | −0.170350 | + | 0.518210i | ||||
\(209\) | −852501. | −0.0933805 | ||||||||
\(210\) | 1.04373e7 | + | 5.32940e6i | 1.12702 | + | 0.575467i | ||||
\(211\) | − | 2.78490e6i | − | 0.296458i | −0.988953 | − | 0.148229i | \(-0.952643\pi\) | ||
0.988953 | − | 0.148229i | \(-0.0473572\pi\) | |||||||
\(212\) | 775572. | + | 1.07135e6i | 0.0813982 | + | 0.112441i | ||||
\(213\) | −2.14030e6 | −0.221480 | ||||||||
\(214\) | −797840. | + | 1.56253e6i | −0.0814094 | + | 0.159436i | ||||
\(215\) | 1.83432e6i | 0.184569i | ||||||||
\(216\) | −1.91635e6 | + | 298452.i | −0.190158 | + | 0.0296151i | ||||
\(217\) | 1.08506e7 | 1.06188 | ||||||||
\(218\) | 6.51200e6 | + | 3.32509e6i | 0.628557 | + | 0.320947i | ||||
\(219\) | − | 3.91902e6i | − | 0.373117i | ||||||
\(220\) | 1.31961e6 | − | 955290.i | 0.123931 | − | 0.0897154i | ||||
\(221\) | 382817. | 0.0354662 | ||||||||
\(222\) | 5.23714e6 | − | 1.02566e7i | 0.478669 | − | 0.937446i | ||||
\(223\) | − | 9.97883e6i | − | 0.899839i | −0.893069 | − | 0.449920i | \(-0.851453\pi\) | ||
0.893069 | − | 0.449920i | \(-0.148547\pi\) | |||||||
\(224\) | 1.25878e7 | + | 1.26966e7i | 1.11997 | + | 1.12965i | ||||
\(225\) | −3.41142e6 | −0.299494 | ||||||||
\(226\) | −9.80239e6 | − | 5.00519e6i | −0.849193 | − | 0.433606i | ||||
\(227\) | 2.19292e7i | 1.87476i | 0.348313 | + | 0.937378i | \(0.386755\pi\) | ||||
−0.348313 | + | 0.937378i | \(0.613245\pi\) | |||||||
\(228\) | 3.37452e6 | + | 4.66148e6i | 0.284714 | + | 0.393296i | ||||
\(229\) | 1.11307e7 | 0.926865 | 0.463432 | − | 0.886132i | \(-0.346618\pi\) | ||||
0.463432 | + | 0.886132i | \(0.346618\pi\) | |||||||
\(230\) | −5.04090e6 | + | 9.87232e6i | −0.414309 | + | 0.811401i | ||||
\(231\) | 1.25704e6i | 0.101980i | ||||||||
\(232\) | 2.69450e6 | + | 1.73013e7i | 0.215782 | + | 1.38553i | ||||
\(233\) | −1.19630e7 | −0.945744 | −0.472872 | − | 0.881131i | \(-0.656783\pi\) | ||||
−0.472872 | + | 0.881131i | \(0.656783\pi\) | |||||||
\(234\) | 2.07493e6 | + | 1.05948e6i | 0.161941 | + | 0.0826886i | ||||
\(235\) | − | 2.49872e7i | − | 1.92537i | ||||||
\(236\) | 7.68879e6 | − | 5.56604e6i | 0.584954 | − | 0.423458i | ||||
\(237\) | 9.60403e6 | 0.721453 | ||||||||
\(238\) | 634068. | − | 1.24179e6i | 0.0470332 | − | 0.0921119i | ||||
\(239\) | − | 7.26061e6i | − | 0.531838i | −0.963995 | − | 0.265919i | \(-0.914325\pi\) | ||
0.963995 | − | 0.265919i | \(-0.0856754\pi\) | |||||||
\(240\) | −1.04471e7 | − | 3.43425e6i | −0.755719 | − | 0.248426i | ||||
\(241\) | 649330. | 0.0463889 | 0.0231945 | − | 0.999731i | \(-0.492616\pi\) | ||||
0.0231945 | + | 0.999731i | \(0.492616\pi\) | |||||||
\(242\) | −1.24666e7 | − | 6.36557e6i | −0.879635 | − | 0.449150i | ||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | −3.67077e6 | − | 5.07070e6i | −0.252690 | − | 0.349059i | ||||
\(245\) | −3.10112e7 | −2.10873 | ||||||||
\(246\) | 1.11887e6 | − | 2.19125e6i | 0.0751580 | − | 0.147193i | ||||
\(247\) | − | 6.91288e6i | − | 0.458742i | ||||||
\(248\) | −1.00607e7 | + | 1.56685e6i | −0.659588 | + | 0.102724i | ||||
\(249\) | −1.16413e7 | −0.754053 | ||||||||
\(250\) | 1.94654e6 | + | 993920.i | 0.124578 | + | 0.0636109i | ||||
\(251\) | 2.13158e7i | 1.34797i | 0.738744 | + | 0.673986i | \(0.235419\pi\) | ||||
−0.738744 | + | 0.673986i | \(0.764581\pi\) | |||||||
\(252\) | 6.87351e6 | − | 4.97585e6i | 0.429513 | − | 0.310932i | ||||
\(253\) | −1.18899e6 | −0.0734206 | ||||||||
\(254\) | 1.26064e7 | − | 2.46890e7i | 0.769292 | − | 1.50661i | ||||
\(255\) | 857610.i | 0.0517213i | ||||||||
\(256\) | −1.35049e7 | − | 9.95458e6i | −0.804952 | − | 0.593339i | ||||
\(257\) | 3.34616e7 | 1.97128 | 0.985638 | − | 0.168872i | \(-0.0540126\pi\) | ||||
0.985638 | + | 0.168872i | \(0.0540126\pi\) | |||||||
\(258\) | 1.18289e6 | + | 603995.i | 0.0688788 | + | 0.0351702i | ||||
\(259\) | 5.03865e7i | 2.90011i | ||||||||
\(260\) | 7.74639e6 | + | 1.07007e7i | 0.440737 | + | 0.608822i | ||||
\(261\) | 8.31034e6 | 0.467409 | ||||||||
\(262\) | 7.68475e6 | − | 1.50501e7i | 0.427293 | − | 0.836829i | ||||
\(263\) | − | 3.12778e7i | − | 1.71937i | −0.510825 | − | 0.859685i | \(-0.670660\pi\) | ||
0.510825 | − | 0.859685i | \(-0.329340\pi\) | |||||||
\(264\) | −181519. | − | 1.16553e6i | −0.00986531 | − | 0.0633448i | ||||
\(265\) | 3.55932e6 | 0.191262 | ||||||||
\(266\) | −2.24240e7 | − | 1.14499e7i | −1.19143 | − | 0.608356i | ||||
\(267\) | − | 6.33371e6i | − | 0.332755i | ||||||
\(268\) | −2.48266e7 | + | 1.79724e7i | −1.28977 | + | 0.933688i | ||||
\(269\) | 2.30534e7 | 1.18435 | 0.592174 | − | 0.805810i | \(-0.298270\pi\) | ||||
0.592174 | + | 0.805810i | \(0.298270\pi\) | |||||||
\(270\) | −2.37351e6 | + | 4.64839e6i | −0.120587 | + | 0.236163i | ||||
\(271\) | 1.74540e7i | 0.876974i | 0.898738 | + | 0.438487i | \(0.144485\pi\) | ||||
−0.898738 | + | 0.438487i | \(0.855515\pi\) | |||||||
\(272\) | −408591. | + | 1.24294e6i | −0.0203040 | + | 0.0617654i | ||||
\(273\) | −1.01933e7 | −0.500986 | ||||||||
\(274\) | 9.91299e6 | + | 5.06167e6i | 0.481896 | + | 0.246060i | ||||
\(275\) | − | 2.07483e6i | − | 0.0997664i | ||||||
\(276\) | 4.70649e6 | + | 6.50142e6i | 0.223857 | + | 0.309230i | ||||
\(277\) | −1.60256e7 | −0.754007 | −0.377003 | − | 0.926212i | \(-0.623046\pi\) | ||||
−0.377003 | + | 0.926212i | \(0.623046\pi\) | |||||||
\(278\) | −2.35682e6 | + | 4.61570e6i | −0.109696 | + | 0.214834i | ||||
\(279\) | 4.83246e6i | 0.222513i | ||||||||
\(280\) | 4.75414e7 | − | 7.40408e6i | 2.16570 | − | 0.337285i | ||||
\(281\) | 4.55471e6 | 0.205278 | 0.102639 | − | 0.994719i | \(-0.467271\pi\) | ||||
0.102639 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(282\) | −1.61135e7 | − | 8.22769e6i | −0.718524 | − | 0.366885i | ||||
\(283\) | − | 1.40790e7i | − | 0.621171i | −0.950545 | − | 0.310586i | \(-0.899475\pi\) | ||
0.950545 | − | 0.310586i | \(-0.100525\pi\) | |||||||
\(284\) | −7.11787e6 | + | 5.15275e6i | −0.310739 | + | 0.224949i | ||||
\(285\) | 1.54866e7 | 0.668995 | ||||||||
\(286\) | −644378. | + | 1.26198e6i | −0.0275450 | + | 0.0539453i | ||||
\(287\) | 1.07647e7i | 0.455360i | ||||||||
\(288\) | −5.65459e6 | + | 5.60615e6i | −0.236714 | + | 0.234686i | ||||
\(289\) | −2.40355e7 | −0.995773 | ||||||||
\(290\) | 4.19668e7 | + | 2.14287e7i | 1.72073 | + | 0.878620i | ||||
\(291\) | 1.73927e7i | 0.705810i | ||||||||
\(292\) | −9.43502e6 | − | 1.30333e7i | −0.378961 | − | 0.523486i | ||||
\(293\) | 7.00361e6 | 0.278432 | 0.139216 | − | 0.990262i | \(-0.455542\pi\) | ||||
0.139216 | + | 0.990262i | \(0.455542\pi\) | |||||||
\(294\) | −1.02112e7 | + | 1.99981e7i | −0.401824 | + | 0.786950i | ||||
\(295\) | − | 2.55442e7i | − | 0.995005i | ||||||
\(296\) | −7.27591e6 | − | 4.67184e7i | −0.280551 | − | 1.80141i | ||||
\(297\) | −559839. | −0.0213695 | ||||||||
\(298\) | 4.40146e6 | + | 2.24743e6i | 0.166321 | + | 0.0849253i | ||||
\(299\) | − | 9.64148e6i | − | 0.360687i | ||||||
\(300\) | −1.13452e7 | + | 8.21297e6i | −0.420192 | + | 0.304184i | ||||
\(301\) | −5.81104e6 | −0.213086 | ||||||||
\(302\) | −1.15102e7 | + | 2.25421e7i | −0.417890 | + | 0.818415i | ||||
\(303\) | − | 1.33017e7i | − | 0.478168i | ||||||
\(304\) | 2.24450e7 | + | 7.37830e6i | 0.798911 | + | 0.262625i | ||||
\(305\) | −1.68462e7 | −0.593748 | ||||||||
\(306\) | 553045. | + | 282390.i | 0.0193017 | + | 0.00985565i | ||||
\(307\) | − | 318209.i | − | 0.0109976i | −0.999985 | − | 0.00549879i | \(-0.998250\pi\) | ||
0.999985 | − | 0.00549879i | \(-0.00175033\pi\) | |||||||
\(308\) | 3.02632e6 | + | 4.18048e6i | 0.103577 | + | 0.143078i | ||||
\(309\) | 1.68591e7 | 0.571425 | ||||||||
\(310\) | −1.24608e7 | + | 2.44037e7i | −0.418273 | + | 0.819163i | ||||
\(311\) | − | 4.67977e7i | − | 1.55576i | −0.628412 | − | 0.777881i | \(-0.716295\pi\) | ||
0.628412 | − | 0.777881i | \(-0.283705\pi\) | |||||||
\(312\) | 9.45120e6 | − | 1.47193e6i | 0.311188 | − | 0.0484644i | ||||
\(313\) | −3.64905e7 | −1.19000 | −0.595000 | − | 0.803726i | \(-0.702848\pi\) | ||||
−0.595000 | + | 0.803726i | \(0.702848\pi\) | |||||||
\(314\) | 1.48965e7 | + | 7.60627e6i | 0.481165 | + | 0.245687i | ||||
\(315\) | − | 2.28356e7i | − | 0.730601i | ||||||
\(316\) | 3.19396e7 | − | 2.31216e7i | 1.01220 | − | 0.732752i | ||||
\(317\) | −4.96927e7 | −1.55996 | −0.779982 | − | 0.625801i | \(-0.784772\pi\) | ||||
−0.779982 | + | 0.625801i | \(0.784772\pi\) | |||||||
\(318\) | 1.17200e6 | − | 2.29529e6i | 0.0364456 | − | 0.0713766i | ||||
\(319\) | 5.05436e6i | 0.155702i | ||||||||
\(320\) | −4.30112e7 | + | 1.37301e7i | −1.31260 | + | 0.419010i | ||||
\(321\) | 3.41861e6 | 0.103356 | ||||||||
\(322\) | −3.12751e7 | − | 1.59694e7i | −0.936766 | − | 0.478322i | ||||
\(323\) | − | 1.84253e6i | − | 0.0546773i | ||||||
\(324\) | 2.21606e6 | + | 3.06120e6i | 0.0651547 | + | 0.0900030i | ||||
\(325\) | 1.68247e7 | 0.490113 | ||||||||
\(326\) | −1.63476e6 | + | 3.20159e6i | −0.0471848 | + | 0.0924088i | ||||
\(327\) | − | 1.42474e7i | − | 0.407468i | ||||||
\(328\) | −1.55444e6 | − | 9.98100e6i | −0.0440506 | − | 0.282848i | ||||
\(329\) | 7.91585e7 | 2.22285 | ||||||||
\(330\) | −2.82716e6 | − | 1.44357e6i | −0.0786699 | − | 0.0401696i | ||||
\(331\) | 4.59328e7i | 1.26660i | 0.773907 | + | 0.633299i | \(0.218300\pi\) | ||||
−0.773907 | + | 0.633299i | \(0.781700\pi\) | |||||||
\(332\) | −3.87148e7 | + | 2.80263e7i | −1.05794 | + | 0.765863i | ||||
\(333\) | −2.24403e7 | −0.607709 | ||||||||
\(334\) | 6.51427e6 | − | 1.27578e7i | 0.174834 | − | 0.342403i | ||||
\(335\) | 8.24804e7i | 2.19390i | ||||||||
\(336\) | 1.08795e7 | − | 3.30958e7i | 0.286809 | − | 0.872480i | ||||
\(337\) | 2.96501e7 | 0.774706 | 0.387353 | − | 0.921931i | \(-0.373389\pi\) | ||||
0.387353 | + | 0.921931i | \(0.373389\pi\) | |||||||
\(338\) | 2.41573e7 | + | 1.23350e7i | 0.625603 | + | 0.319439i | ||||
\(339\) | 2.14464e7i | 0.550498i | ||||||||
\(340\) | 2.06469e6 | + | 2.85211e6i | 0.0525313 | + | 0.0725654i | ||||
\(341\) | −2.93911e6 | −0.0741229 | ||||||||
\(342\) | 5.09937e6 | − | 9.98683e6i | 0.127479 | − | 0.249660i | ||||
\(343\) | − | 3.40503e7i | − | 0.843798i | ||||||
\(344\) | 5.38799e6 | − | 839126.i | 0.132359 | − | 0.0206135i | ||||
\(345\) | 2.15994e7 | 0.525999 | ||||||||
\(346\) | 4.32445e7 | + | 2.20810e7i | 1.04400 | + | 0.533078i | ||||
\(347\) | 3.19623e7i | 0.764980i | 0.923960 | + | 0.382490i | \(0.124933\pi\) | ||||
−0.923960 | + | 0.382490i | \(0.875067\pi\) | |||||||
\(348\) | 2.76373e7 | − | 2.00071e7i | 0.655779 | − | 0.474730i | ||||
\(349\) | 2.02402e7 | 0.476145 | 0.238073 | − | 0.971247i | \(-0.423484\pi\) | ||||
0.238073 | + | 0.971247i | \(0.423484\pi\) | |||||||
\(350\) | 2.78670e7 | − | 5.45760e7i | 0.649960 | − | 1.27291i | ||||
\(351\) | − | 4.53970e6i | − | 0.104980i | ||||||
\(352\) | −3.40967e6 | − | 3.43913e6i | −0.0781780 | − | 0.0788535i | ||||
\(353\) | −2.37115e7 | −0.539058 | −0.269529 | − | 0.962992i | \(-0.586868\pi\) | ||||
−0.269529 | + | 0.962992i | \(0.586868\pi\) | |||||||
\(354\) | −1.64726e7 | − | 8.41106e6i | −0.371323 | − | 0.189601i | ||||
\(355\) | 2.36474e7i | 0.528565i | ||||||||
\(356\) | −1.52484e7 | − | 2.10637e7i | −0.337966 | − | 0.466858i | ||||
\(357\) | −2.71687e6 | −0.0597124 | ||||||||
\(358\) | −1.47477e7 | + | 2.88825e7i | −0.321421 | + | 0.629484i | ||||
\(359\) | − | 3.50832e7i | − | 0.758255i | −0.925344 | − | 0.379128i | \(-0.876224\pi\) | ||
0.925344 | − | 0.379128i | \(-0.123776\pi\) | |||||||
\(360\) | 3.29750e6 | + | 2.11731e7i | 0.0706769 | + | 0.453814i | ||||
\(361\) | 1.37736e7 | 0.292770 | ||||||||
\(362\) | −4.50744e7 | − | 2.30154e7i | −0.950177 | − | 0.485169i | ||||
\(363\) | 2.72754e7i | 0.570232i | ||||||||
\(364\) | −3.38992e7 | + | 2.45402e7i | −0.702887 | + | 0.508832i | ||||
\(365\) | −4.33000e7 | −0.890449 | ||||||||
\(366\) | −5.54704e6 | + | 1.08636e7i | −0.113140 | + | 0.221579i | ||||
\(367\) | − | 1.82217e7i | − | 0.368630i | −0.982867 | − | 0.184315i | \(-0.940993\pi\) | ||
0.982867 | − | 0.184315i | \(-0.0590067\pi\) | |||||||
\(368\) | 3.13043e7 | + | 1.02906e7i | 0.628145 | + | 0.206489i | ||||
\(369\) | −4.79418e6 | −0.0954191 | ||||||||
\(370\) | −1.13322e8 | − | 5.78634e7i | −2.23723 | − | 1.14235i | ||||
\(371\) | 1.12758e7i | 0.220813i | ||||||||
\(372\) | 1.16341e7 | + | 1.60711e7i | 0.225998 | + | 0.312188i | ||||
\(373\) | 3.69902e7 | 0.712788 | 0.356394 | − | 0.934336i | \(-0.384006\pi\) | ||||
0.356394 | + | 0.934336i | \(0.384006\pi\) | |||||||
\(374\) | −171750. | + | 336363.i | −0.00328308 | + | 0.00642973i | ||||
\(375\) | − | 4.25878e6i | − | 0.0807591i | ||||||
\(376\) | −7.33958e7 | + | 1.14307e7i | −1.38073 | + | 0.215034i | ||||
\(377\) | −4.09855e7 | −0.764903 | ||||||||
\(378\) | −1.47259e7 | − | 7.51919e6i | −0.272651 | − | 0.139218i | ||||
\(379\) | − | 8.07965e7i | − | 1.48414i | −0.670322 | − | 0.742070i | \(-0.733844\pi\) | ||
0.670322 | − | 0.742070i | \(-0.266156\pi\) | |||||||
\(380\) | 5.15032e7 | − | 3.72840e7i | 0.938605 | − | 0.679472i | ||||
\(381\) | −5.40165e7 | −0.976678 | ||||||||
\(382\) | 4.18426e7 | − | 8.19463e7i | 0.750634 | − | 1.47007i | ||||
\(383\) | 1.84048e7i | 0.327594i | 0.986494 | + | 0.163797i | \(0.0523741\pi\) | ||||
−0.986494 | + | 0.163797i | \(0.947626\pi\) | |||||||
\(384\) | −5.30841e6 | + | 3.22575e7i | −0.0937499 | + | 0.569688i | ||||
\(385\) | 1.38886e7 | 0.243376 | ||||||||
\(386\) | 6.25616e7 | + | 3.19445e7i | 1.08779 | + | 0.555437i | ||||
\(387\) | − | 2.58802e6i | − | 0.0446514i | ||||||
\(388\) | 4.18728e7 | + | 5.78420e7i | 0.716864 | + | 0.990258i | ||||
\(389\) | 3.06205e7 | 0.520191 | 0.260096 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260096 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(390\) | 1.17059e7 | − | 2.29253e7i | 0.197337 | − | 0.386474i | ||||
\(391\) | − | 2.56980e6i | − | 0.0429902i | ||||||
\(392\) | 1.41864e7 | + | 9.10902e7i | 0.235512 | + | 1.51221i | ||||
\(393\) | −3.29279e7 | −0.542483 | ||||||||
\(394\) | 6.96638e7 | + | 3.55710e7i | 1.13899 | + | 0.581577i | ||||
\(395\) | − | 1.06112e8i | − | 1.72176i | ||||||
\(396\) | −1.86183e6 | + | 1.34781e6i | −0.0299815 | + | 0.0217041i | ||||
\(397\) | 4.82333e7 | 0.770860 | 0.385430 | − | 0.922737i | \(-0.374053\pi\) | ||||
0.385430 | + | 0.922737i | \(0.374053\pi\) | |||||||
\(398\) | 1.37661e7 | − | 2.69601e7i | 0.218354 | − | 0.427634i | ||||
\(399\) | 4.90611e7i | 0.772357i | ||||||||
\(400\) | −1.79574e7 | + | 5.46269e7i | −0.280585 | + | 0.853545i | ||||
\(401\) | 2.62250e6 | 0.0406708 | 0.0203354 | − | 0.999793i | \(-0.493527\pi\) | ||||
0.0203354 | + | 0.999793i | \(0.493527\pi\) | |||||||
\(402\) | 5.31889e7 | + | 2.71588e7i | 0.818735 | + | 0.418054i | ||||
\(403\) | − | 2.38331e7i | − | 0.364137i | ||||||
\(404\) | −3.20238e7 | − | 4.42369e7i | −0.485657 | − | 0.670873i | ||||
\(405\) | 1.01701e7 | 0.153095 | ||||||||
\(406\) | −6.78851e7 | + | 1.32949e8i | −1.01437 | + | 1.98659i | ||||
\(407\) | − | 1.36482e7i | − | 0.202438i | ||||||
\(408\) | 2.51909e6 | − | 392322.i | 0.0370905 | − | 0.00577647i | ||||
\(409\) | −1.29865e8 | −1.89812 | −0.949059 | − | 0.315098i | \(-0.897963\pi\) | ||||
−0.949059 | + | 0.315098i | \(0.897963\pi\) | |||||||
\(410\) | −2.42104e7 | − | 1.23620e7i | −0.351277 | − | 0.179365i | ||||
\(411\) | − | 2.16884e7i | − | 0.312393i | ||||||
\(412\) | 5.60675e7 | − | 4.05882e7i | 0.801715 | − | 0.580375i | ||||
\(413\) | 8.09228e7 | 1.14874 | ||||||||
\(414\) | 7.11216e6 | − | 1.39288e7i | 0.100231 | − | 0.196296i | ||||
\(415\) | 1.28620e8i | 1.79956i | ||||||||
\(416\) | 2.78877e7 | − | 2.76488e7i | 0.387376 | − | 0.384058i | ||||
\(417\) | 1.00986e7 | 0.139268 | ||||||||
\(418\) | 6.07401e6 | + | 3.10145e6i | 0.0831661 | + | 0.0424654i | ||||
\(419\) | − | 5.61116e6i | − | 0.0762799i | −0.999272 | − | 0.0381400i | \(-0.987857\pi\) | ||
0.999272 | − | 0.0381400i | \(-0.0121433\pi\) | |||||||
\(420\) | −5.49765e7 | − | 7.59431e7i | −0.742043 | − | 1.02504i | ||||
\(421\) | −1.62466e7 | −0.217729 | −0.108865 | − | 0.994057i | \(-0.534721\pi\) | ||||
−0.108865 | + | 0.994057i | \(0.534721\pi\) | |||||||
\(422\) | −1.01316e7 | + | 1.98422e7i | −0.134816 | + | 0.264030i | ||||
\(423\) | 3.52543e7i | 0.465790i | ||||||||
\(424\) | −1.62824e6 | − | 1.04549e7i | −0.0213610 | − | 0.137158i | ||||
\(425\) | 4.48438e6 | 0.0584165 | ||||||||
\(426\) | 1.52494e7 | + | 7.78651e6i | 0.197254 | + | 0.100720i | ||||
\(427\) | − | 5.33680e7i | − | 0.685484i | ||||||
\(428\) | 1.13691e7 | − | 8.23029e6i | 0.145009 | − | 0.104974i | ||||
\(429\) | 2.76105e6 | 0.0349706 | ||||||||
\(430\) | 6.67335e6 | − | 1.30694e7i | 0.0839341 | − | 0.164380i | ||||
\(431\) | 2.83367e7i | 0.353931i | 0.984217 | + | 0.176965i | \(0.0566280\pi\) | ||||
−0.984217 | + | 0.176965i | \(0.943372\pi\) | |||||||
\(432\) | 1.47397e7 | + | 4.84534e6i | 0.182825 | + | 0.0600998i | ||||
\(433\) | 1.20593e8 | 1.48545 | 0.742727 | − | 0.669595i | \(-0.233532\pi\) | ||||
0.742727 | + | 0.669595i | \(0.233532\pi\) | |||||||
\(434\) | −7.73099e7 | − | 3.94752e7i | −0.945727 | − | 0.482897i | ||||
\(435\) | − | 9.18182e7i | − | 1.11548i | ||||||
\(436\) | −3.43006e7 | − | 4.73820e7i | −0.413850 | − | 0.571681i | ||||
\(437\) | −4.64052e7 | −0.556061 | ||||||||
\(438\) | −1.42576e7 | + | 2.79227e7i | −0.169678 | + | 0.332304i | ||||
\(439\) | 4.16793e7i | 0.492637i | 0.969189 | + | 0.246318i | \(0.0792209\pi\) | ||||
−0.969189 | + | 0.246318i | \(0.920779\pi\) | |||||||
\(440\) | −1.28775e7 | + | 2.00555e6i | −0.151173 | + | 0.0235437i | ||||
\(441\) | 4.37534e7 | 0.510148 | ||||||||
\(442\) | −2.72755e6 | − | 1.39271e6i | −0.0315868 | − | 0.0161285i | ||||
\(443\) | 2.51566e7i | 0.289362i | 0.989478 | + | 0.144681i | \(0.0462155\pi\) | ||||
−0.989478 | + | 0.144681i | \(0.953784\pi\) | |||||||
\(444\) | −7.46284e7 | + | 5.40248e7i | −0.852620 | + | 0.617226i | ||||
\(445\) | −6.99790e7 | −0.794123 | ||||||||
\(446\) | −3.63035e7 | + | 7.10984e7i | −0.409208 | + | 0.801411i | ||||
\(447\) | − | 9.62986e6i | − | 0.107820i | ||||||
\(448\) | −4.34965e7 | − | 1.36258e8i | −0.483749 | − | 1.51540i | ||||
\(449\) | −1.15867e8 | −1.28003 | −0.640014 | − | 0.768363i | \(-0.721071\pi\) | ||||
−0.640014 | + | 0.768363i | \(0.721071\pi\) | |||||||
\(450\) | 2.43061e7 | + | 1.24109e7i | 0.266734 | + | 0.136197i | ||||
\(451\) | − | 2.91583e6i | − | 0.0317857i | ||||||
\(452\) | 5.16321e7 | + | 7.13232e7i | 0.559119 | + | 0.772353i | ||||
\(453\) | 4.93193e7 | 0.530545 | ||||||||
\(454\) | 7.97796e7 | − | 1.56244e8i | 0.852558 | − | 1.66969i | ||||
\(455\) | 1.12622e8i | 1.19561i | ||||||||
\(456\) | −7.08451e6 | − | 4.54894e7i | −0.0747163 | − | 0.479751i | ||||
\(457\) | 6.14718e7 | 0.644061 | 0.322031 | − | 0.946729i | \(-0.395635\pi\) | ||||
0.322031 | + | 0.946729i | \(0.395635\pi\) | |||||||
\(458\) | −7.93054e7 | − | 4.04941e7i | −0.825480 | − | 0.421498i | ||||
\(459\) | − | 1.20999e6i | − | 0.0125125i | ||||||
\(460\) | 7.18321e7 | − | 5.20005e7i | 0.737981 | − | 0.534237i | ||||
\(461\) | 9.60847e7 | 0.980734 | 0.490367 | − | 0.871516i | \(-0.336863\pi\) | ||||
0.490367 | + | 0.871516i | \(0.336863\pi\) | |||||||
\(462\) | 4.57318e6 | − | 8.95632e6i | 0.0463759 | − | 0.0908247i | ||||
\(463\) | 5.41563e7i | 0.545639i | 0.962065 | + | 0.272820i | \(0.0879562\pi\) | ||||
−0.962065 | + | 0.272820i | \(0.912044\pi\) | |||||||
\(464\) | 4.37449e7 | − | 1.33073e8i | 0.437899 | − | 1.33210i | ||||
\(465\) | 5.33923e7 | 0.531031 | ||||||||
\(466\) | 8.52357e7 | + | 4.35222e7i | 0.842294 | + | 0.430083i | ||||
\(467\) | 1.65365e8i | 1.62365i | 0.583902 | + | 0.811824i | \(0.301525\pi\) | ||||
−0.583902 | + | 0.811824i | \(0.698475\pi\) | |||||||
\(468\) | −1.09293e7 | − | 1.50975e7i | −0.106624 | − | 0.147288i | ||||
\(469\) | −2.61295e8 | −2.53286 | ||||||||
\(470\) | −9.09050e7 | + | 1.78032e8i | −0.875576 | + | 1.71477i | ||||
\(471\) | − | 3.25916e7i | − | 0.311920i | ||||||
\(472\) | −7.50316e7 | + | 1.16854e7i | −0.713540 | + | 0.111127i | ||||
\(473\) | 1.57404e6 | 0.0148741 | ||||||||
\(474\) | −6.84280e7 | − | 3.49400e7i | −0.642538 | − | 0.328086i | ||||
\(475\) | − | 8.09785e7i | − | 0.755595i | ||||||
\(476\) | −9.03537e6 | + | 6.54086e6i | −0.0837770 | + | 0.0606476i | ||||
\(477\) | −5.02181e6 | −0.0462706 | ||||||||
\(478\) | −2.64145e7 | + | 5.17313e7i | −0.241857 | + | 0.473663i | ||||
\(479\) | − | 1.68599e8i | − | 1.53408i | −0.641601 | − | 0.767039i | \(-0.721729\pi\) | ||
0.641601 | − | 0.767039i | \(-0.278271\pi\) | |||||||
\(480\) | 6.19405e7 | + | 6.24757e7i | 0.560082 | + | 0.564921i | ||||
\(481\) | 1.10672e8 | 0.994499 | ||||||||
\(482\) | −4.62643e6 | − | 2.36230e6i | −0.0413147 | − | 0.0210957i | ||||
\(483\) | 6.84260e7i | 0.607267i | ||||||||
\(484\) | 6.56654e7 | + | 9.07084e7i | 0.579162 | + | 0.800040i | ||||
\(485\) | 1.92166e8 | 1.68443 | ||||||||
\(486\) | 3.34877e6 | − | 6.55837e6i | 0.0291727 | − | 0.0571330i | ||||
\(487\) | 3.13794e6i | 0.0271680i | 0.999908 | + | 0.0135840i | \(0.00432405\pi\) | ||||
−0.999908 | + | 0.0135840i | \(0.995676\pi\) | |||||||
\(488\) | 7.70645e6 | + | 4.94828e7i | 0.0663124 | + | 0.425790i | ||||
\(489\) | 7.00469e6 | 0.0599049 | ||||||||
\(490\) | 2.20953e8 | + | 1.12821e8i | 1.87807 | + | 0.958959i | ||||
\(491\) | − | 2.16648e8i | − | 1.83025i | −0.403175 | − | 0.915123i | \(-0.632093\pi\) | ||
0.403175 | − | 0.915123i | \(-0.367907\pi\) | |||||||
\(492\) | −1.59438e7 | + | 1.15420e7i | −0.133874 | + | 0.0969135i | ||||
\(493\) | −1.09241e7 | −0.0911687 | ||||||||
\(494\) | −2.51494e7 | + | 4.92538e7i | −0.208616 | + | 0.408562i | ||||
\(495\) | 6.18548e6i | 0.0509985i | ||||||||
\(496\) | 7.73820e7 | + | 2.54377e7i | 0.634154 | + | 0.208465i | ||||
\(497\) | −7.49140e7 | −0.610231 | ||||||||
\(498\) | 8.29431e7 | + | 4.23516e7i | 0.671572 | + | 0.342911i | ||||
\(499\) | 8.66193e7i | 0.697129i | 0.937285 | + | 0.348564i | \(0.113331\pi\) | ||||
−0.937285 | + | 0.348564i | \(0.886669\pi\) | |||||||
\(500\) | −1.02530e7 | − | 1.41632e7i | −0.0820239 | − | 0.113306i | ||||
\(501\) | −2.79125e7 | −0.221966 | ||||||||
\(502\) | 7.75481e7 | − | 1.51874e8i | 0.612999 | − | 1.20052i | ||||
\(503\) | 8.57535e7i | 0.673826i | 0.941536 | + | 0.336913i | \(0.109383\pi\) | ||||
−0.941536 | + | 0.336913i | \(0.890617\pi\) | |||||||
\(504\) | −6.70756e7 | + | 1.04463e7i | −0.523930 | + | 0.0815968i | ||||
\(505\) | −1.46966e8 | −1.14115 | ||||||||
\(506\) | 8.47149e6 | + | 4.32562e6i | 0.0653895 | + | 0.0333885i | ||||
\(507\) | − | 5.28533e7i | − | 0.405554i | ||||||
\(508\) | −1.79640e8 | + | 1.30044e8i | −1.37029 | + | 0.991974i | ||||
\(509\) | −428408. | −0.00324866 | −0.00162433 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162433 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(510\) | 3.12003e6 | − | 6.11041e6i | 0.0235206 | − | 0.0460638i | ||||
\(511\) | − | 1.37172e8i | − | 1.02803i | ||||||
\(512\) | 6.00058e7 | + | 1.20057e8i | 0.447078 | + | 0.894495i | ||||
\(513\) | −2.18500e7 | −0.161845 | ||||||||
\(514\) | −2.38411e8 | − | 1.21735e8i | −1.75565 | − | 0.896451i | ||||
\(515\) | − | 1.86271e8i | − | 1.36371i | ||||||
\(516\) | −6.23064e6 | − | 8.60684e6i | −0.0453507 | − | 0.0626462i | ||||
\(517\) | −2.14417e7 | −0.155163 | ||||||||
\(518\) | 1.83309e8 | − | 3.59000e8i | 1.31885 | − | 2.58289i | ||||
\(519\) | − | 9.46135e7i | − | 0.676786i | ||||||
\(520\) | −1.62629e7 | − | 1.04423e8i | −0.115661 | − | 0.742655i | ||||
\(521\) | −1.15523e8 | −0.816872 | −0.408436 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408436 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(522\) | −5.92106e7 | − | 3.02335e7i | −0.416282 | − | 0.212558i | ||||
\(523\) | 2.33392e8i | 1.63147i | 0.578423 | + | 0.815737i | \(0.303668\pi\) | ||||
−0.578423 | + | 0.815737i | \(0.696332\pi\) | |||||||
\(524\) | −1.09507e8 | + | 7.92736e7i | −0.761108 | + | 0.550979i | ||||
\(525\) | −1.19406e8 | −0.825176 | ||||||||
\(526\) | −1.13790e8 | + | 2.22852e8i | −0.781895 | + | 1.53130i | ||||
\(527\) | − | 6.35237e6i | − | 0.0434014i | ||||||
\(528\) | −2.94694e6 | + | 8.96468e6i | −0.0200203 | + | 0.0609022i | ||||
\(529\) | 8.33140e7 | 0.562796 | ||||||||
\(530\) | −2.53599e7 | − | 1.29490e7i | −0.170341 | − | 0.0869778i | ||||
\(531\) | 3.60400e7i | 0.240714i | ||||||||
\(532\) | 1.18114e8 | + | 1.63160e8i | 0.784453 | + | 1.08362i | ||||
\(533\) | 2.36443e7 | 0.156151 | ||||||||
\(534\) | −2.30424e7 | + | 4.51272e7i | −0.151323 | + | 0.296357i | ||||
\(535\) | − | 3.77711e7i | − | 0.246660i | ||||||
\(536\) | 2.42272e8 | − | 3.77315e7i | 1.57329 | − | 0.245024i | ||||
\(537\) | 6.31912e7 | 0.408069 | ||||||||
\(538\) | −1.64254e8 | − | 8.38697e7i | −1.05480 | − | 0.538590i | ||||
\(539\) | 2.66109e7i | 0.169939i | ||||||||
\(540\) | 3.38222e7 | − | 2.44845e7i | 0.214793 | − | 0.155493i | ||||
\(541\) | 7.23945e6 | 0.0457208 | 0.0228604 | − | 0.999739i | \(-0.492723\pi\) | ||||
0.0228604 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(542\) | 6.34985e7 | − | 1.24358e8i | 0.398810 | − | 0.781046i | ||||
\(543\) | 9.86173e7i | 0.615961i | ||||||||
\(544\) | 7.43308e6 | − | 7.36941e6i | 0.0461713 | − | 0.0457758i | ||||
\(545\) | −1.57415e8 | −0.972428 | ||||||||
\(546\) | 7.26263e7 | + | 3.70837e7i | 0.446186 | + | 0.227827i | ||||
\(547\) | − | 2.10222e8i | − | 1.28444i | −0.766518 | − | 0.642222i | \(-0.778013\pi\) | ||
0.766518 | − | 0.642222i | \(-0.221987\pi\) | |||||||
\(548\) | −5.22147e7 | − | 7.21280e7i | −0.317286 | − | 0.438291i | ||||
\(549\) | 2.37681e7 | 0.143641 | ||||||||
\(550\) | −7.54834e6 | + | 1.47830e7i | −0.0453695 | + | 0.0888535i | ||||
\(551\) | 1.97267e8i | 1.17923i | ||||||||
\(552\) | −9.88086e6 | − | 6.34446e7i | −0.0587459 | − | 0.377205i | ||||
\(553\) | 3.36157e8 | 1.98778 | ||||||||
\(554\) | 1.14181e8 | + | 5.83021e7i | 0.671530 | + | 0.342890i | ||||
\(555\) | 2.47935e8i | 1.45030i | ||||||||
\(556\) | 3.35844e7 | − | 2.43123e7i | 0.195395 | − | 0.141450i | ||||
\(557\) | 2.09356e8 | 1.21149 | 0.605745 | − | 0.795659i | \(-0.292875\pi\) | ||||
0.605745 | + | 0.795659i | \(0.292875\pi\) | |||||||
\(558\) | 1.75808e7 | − | 3.44309e7i | 0.101189 | − | 0.198174i | ||||
\(559\) | 1.27638e7i | 0.0730708i | ||||||||
\(560\) | −3.65665e8 | − | 1.20205e8i | −2.08219 | − | 0.684474i | ||||
\(561\) | 735920. | 0.00416814 | ||||||||
\(562\) | −3.24520e7 | − | 1.65703e7i | −0.182823 | − | 0.0933514i | ||||
\(563\) | 2.84648e8i | 1.59508i | 0.603266 | + | 0.797540i | \(0.293866\pi\) | ||||
−0.603266 | + | 0.797540i | \(0.706134\pi\) | |||||||
\(564\) | 8.48744e7 | + | 1.17243e8i | 0.473085 | + | 0.653508i | ||||
\(565\) | 2.36954e8 | 1.31377 | ||||||||
\(566\) | −5.12200e7 | + | 1.00312e8i | −0.282482 | + | 0.553225i | ||||
\(567\) | 3.22185e7i | 0.176749i | ||||||||
\(568\) | 6.94603e7 | − | 1.08177e7i | 0.379046 | − | 0.0590325i | ||||
\(569\) | 3.14469e8 | 1.70703 | 0.853516 | − | 0.521067i | \(-0.174466\pi\) | ||||
0.853516 | + | 0.521067i | \(0.174466\pi\) | |||||||
\(570\) | −1.10341e8 | − | 5.63413e7i | −0.595817 | − | 0.304230i | ||||
\(571\) | 6.34099e6i | 0.0340603i | 0.999855 | + | 0.0170302i | \(0.00542113\pi\) | ||||
−0.999855 | + | 0.0170302i | \(0.994579\pi\) | |||||||
\(572\) | 9.18229e6 | − | 6.64722e6i | 0.0490640 | − | 0.0355183i | ||||
\(573\) | −1.79288e8 | −0.952990 | ||||||||
\(574\) | 3.91624e7 | − | 7.66974e7i | 0.207078 | − | 0.405551i | ||||
\(575\) | − | 1.12942e8i | − | 0.594088i | ||||||
\(576\) | 6.06840e7 | − | 1.93717e7i | 0.317546 | − | 0.101368i | ||||
\(577\) | −1.02190e8 | −0.531964 | −0.265982 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265982 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(578\) | 1.71251e8 | + | 8.74426e7i | 0.886851 | + | 0.452835i | ||||
\(579\) | − | 1.36877e8i | − | 0.705171i | ||||||
\(580\) | −2.21052e8 | − | 3.05355e8i | −1.13295 | − | 1.56503i | ||||
\(581\) | −4.07464e8 | −2.07760 | ||||||||
\(582\) | 6.32756e7 | − | 1.23922e8i | 0.320972 | − | 0.628606i | ||||
\(583\) | − | 3.05427e6i | − | 0.0154135i | ||||||
\(584\) | 1.98080e7 | + | 1.27186e8i | 0.0994493 | + | 0.638560i | ||||
\(585\) | −5.01577e7 | −0.250536 | ||||||||
\(586\) | −4.99002e7 | − | 2.54795e7i | −0.247976 | − | 0.126619i | ||||
\(587\) | 1.05154e8i | 0.519889i | 0.965624 | + | 0.259945i | \(0.0837043\pi\) | ||||
−0.965624 | + | 0.259945i | \(0.916296\pi\) | |||||||
\(588\) | 1.45509e8 | − | 1.05336e8i | 0.715742 | − | 0.518138i | ||||
\(589\) | −1.14711e8 | −0.561381 | ||||||||
\(590\) | −9.29310e7 | + | 1.82000e8i | −0.452486 | + | 0.886167i | ||||
\(591\) | − | 1.52416e8i | − | 0.738359i | ||||||
\(592\) | −1.18124e8 | + | 3.59335e8i | −0.569340 | + | 1.73195i | ||||
\(593\) | −3.73401e8 | −1.79065 | −0.895326 | − | 0.445412i | \(-0.853057\pi\) | ||||
−0.895326 | + | 0.445412i | \(0.853057\pi\) | |||||||
\(594\) | 3.98881e6 | + | 2.03672e6i | 0.0190320 | + | 0.00971791i | ||||
\(595\) | 3.00178e7i | 0.142504i | ||||||||
\(596\) | −2.31838e7 | − | 3.20255e7i | −0.109508 | − | 0.151272i | ||||
\(597\) | −5.89854e7 | −0.277218 | ||||||||
\(598\) | −3.50762e7 | + | 6.86948e7i | −0.164025 | + | 0.321233i | ||||
\(599\) | − | 9.24133e7i | − | 0.429986i | −0.976616 | − | 0.214993i | \(-0.931027\pi\) | ||
0.976616 | − | 0.214993i | \(-0.0689729\pi\) | |||||||
\(600\) | 1.10713e8 | − | 1.72424e7i | 0.512559 | − | 0.0798259i | ||||
\(601\) | −8.65606e7 | −0.398747 | −0.199373 | − | 0.979924i | \(-0.563891\pi\) | ||||
−0.199373 | + | 0.979924i | \(0.563891\pi\) | |||||||
\(602\) | 4.14032e7 | + | 2.11409e7i | 0.189777 | + | 0.0969022i | ||||
\(603\) | − | 1.16371e8i | − | 0.530753i | ||||||
\(604\) | 1.64019e8 | − | 1.18736e8i | 0.744359 | − | 0.538854i | ||||
\(605\) | 3.01357e8 | 1.36087 | ||||||||
\(606\) | −4.83924e7 | + | 9.47739e7i | −0.217450 | + | 0.425864i | ||||
\(607\) | − | 2.82004e8i | − | 1.26093i | −0.776219 | − | 0.630463i | \(-0.782865\pi\) | ||
0.776219 | − | 0.630463i | \(-0.217135\pi\) | |||||||
\(608\) | −1.33076e8 | − | 1.34226e8i | −0.592092 | − | 0.597208i | ||||
\(609\) | 2.90876e8 | 1.28782 | ||||||||
\(610\) | 1.20028e8 | + | 6.12874e7i | 0.528801 | + | 0.270011i | ||||
\(611\) | − | 1.73869e8i | − | 0.762254i | ||||||
\(612\) | −2.91305e6 | − | 4.02402e6i | −0.0127085 | − | 0.0175552i | ||||
\(613\) | 3.77812e8 | 1.64019 | 0.820095 | − | 0.572228i | \(-0.193921\pi\) | ||||
0.820095 | + | 0.572228i | \(0.193921\pi\) | |||||||
\(614\) | −1.15766e6 | + | 2.26721e6i | −0.00500122 | + | 0.00979462i | ||||
\(615\) | 5.29693e7i | 0.227719i | ||||||||
\(616\) | −6.35348e6 | − | 4.07955e7i | −0.0271813 | − | 0.174530i | ||||
\(617\) | −3.24962e8 | −1.38349 | −0.691747 | − | 0.722140i | \(-0.743159\pi\) | ||||
−0.691747 | + | 0.722140i | \(0.743159\pi\) | |||||||
\(618\) | −1.20120e8 | − | 6.13344e7i | −0.508920 | − | 0.259860i | ||||
\(619\) | 2.43629e8i | 1.02721i | 0.858028 | + | 0.513603i | \(0.171689\pi\) | ||||
−0.858028 | + | 0.513603i | \(0.828311\pi\) | |||||||
\(620\) | 1.77564e8 | − | 1.28542e8i | 0.745040 | − | 0.539347i | ||||
\(621\) | −3.04744e7 | −0.127251 | ||||||||
\(622\) | −1.70253e8 | + | 3.33430e8i | −0.707493 | + | 1.38559i | ||||
\(623\) | − | 2.21691e8i | − | 0.916818i | ||||||
\(624\) | −7.26940e7 | − | 2.38966e7i | −0.299189 | − | 0.0983518i | ||||
\(625\) | −2.66409e8 | −1.09121 | ||||||||
\(626\) | 2.59992e8 | + | 1.32755e8i | 1.05983 | + | 0.541161i | ||||
\(627\) | − | 1.32892e7i | − | 0.0539132i | ||||||
\(628\) | −7.84641e7 | − | 1.08388e8i | −0.316805 | − | 0.437626i | ||||
\(629\) | 2.94982e7 | 0.118534 | ||||||||
\(630\) | −8.30771e7 | + | 1.62702e8i | −0.332246 | + | 0.650685i | ||||
\(631\) | − | 3.50492e8i | − | 1.39505i | −0.716560 | − | 0.697526i | \(-0.754284\pi\) | ||
0.716560 | − | 0.697526i | \(-0.245716\pi\) | |||||||
\(632\) | −3.11685e8 | + | 4.85418e7i | −1.23471 | + | 0.192294i | ||||
\(633\) | 4.34124e7 | 0.171160 | ||||||||
\(634\) | 3.54057e8 | + | 1.80785e8i | 1.38933 | + | 0.709405i | ||||
\(635\) | 5.96810e8i | 2.33085i | ||||||||
\(636\) | −1.67008e7 | + | 1.20900e7i | −0.0649180 | + | 0.0469952i | ||||
\(637\) | −2.15786e8 | −0.834844 | ||||||||
\(638\) | 1.83881e7 | − | 3.60120e7i | 0.0708066 | − | 0.138671i | ||||
\(639\) | − | 3.33639e7i | − | 0.127872i | ||||||
\(640\) | 3.56402e8 | + | 5.86509e7i | 1.35957 | + | 0.223735i | ||||
\(641\) | 9.43200e7 | 0.358121 | 0.179061 | − | 0.983838i | \(-0.442694\pi\) | ||||
0.179061 | + | 0.983838i | \(0.442694\pi\) | |||||||
\(642\) | −2.43574e7 | − | 1.24371e7i | −0.0920503 | − | 0.0470017i | ||||
\(643\) | − | 2.45499e7i | − | 0.0923459i | −0.998933 | − | 0.0461730i | \(-0.985297\pi\) | ||
0.998933 | − | 0.0461730i | \(-0.0147025\pi\) | |||||||
\(644\) | 1.64735e8 | + | 2.27561e8i | 0.616778 | + | 0.852001i | ||||
\(645\) | −2.85942e7 | −0.106561 | ||||||||
\(646\) | −6.70323e6 | + | 1.31279e7i | −0.0248649 | + | 0.0486965i | ||||
\(647\) | − | 4.28314e8i | − | 1.58143i | −0.612186 | − | 0.790713i | \(-0.709710\pi\) | ||
0.612186 | − | 0.790713i | \(-0.290290\pi\) | |||||||
\(648\) | −4.65241e6 | − | 2.98730e7i | −0.0170983 | − | 0.109788i | ||||
\(649\) | −2.19196e7 | −0.0801859 | ||||||||
\(650\) | −1.19875e8 | − | 6.12091e7i | −0.436503 | − | 0.222882i | ||||
\(651\) | 1.69144e8i | 0.613077i | ||||||||
\(652\) | 2.32952e7 | − | 1.68638e7i | 0.0840471 | − | 0.0608431i | ||||
\(653\) | 2.33639e8 | 0.839084 | 0.419542 | − | 0.907736i | \(-0.362191\pi\) | ||||
0.419542 | + | 0.907736i | \(0.362191\pi\) | |||||||
\(654\) | −5.18330e7 | + | 1.01512e8i | −0.185299 | + | 0.362898i | ||||
\(655\) | 3.63809e8i | 1.29464i | ||||||||
\(656\) | −2.52362e7 | + | 7.67690e7i | −0.0893947 | + | 0.271941i | ||||
\(657\) | 6.10915e7 | 0.215419 | ||||||||
\(658\) | −5.63999e8 | − | 2.87983e8i | −1.97970 | − | 1.01086i | ||||
\(659\) | − | 1.05674e8i | − | 0.369244i | −0.982810 | − | 0.184622i | \(-0.940894\pi\) | ||
0.982810 | − | 0.184622i | \(-0.0591061\pi\) | |||||||
\(660\) | 1.48915e7 | + | 2.05707e7i | 0.0517972 | + | 0.0715513i | ||||
\(661\) | −1.65729e8 | −0.573846 | −0.286923 | − | 0.957954i | \(-0.592632\pi\) | ||||
−0.286923 | + | 0.957954i | \(0.592632\pi\) | |||||||
\(662\) | 1.67106e8 | − | 3.27268e8i | 0.575994 | − | 1.12805i | ||||
\(663\) | 5.96753e6i | 0.0204764i | ||||||||
\(664\) | 3.77801e8 | − | 5.88387e7i | 1.29050 | − | 0.200983i | ||||
\(665\) | 5.42059e8 | 1.84324 | ||||||||
\(666\) | 1.59885e8 | + | 8.16389e7i | 0.541235 | + | 0.276360i | ||||
\(667\) | 2.75130e8i | 0.927173i | ||||||||
\(668\) | −9.28273e7 | + | 6.71993e7i | −0.311420 | + | 0.225442i | ||||
\(669\) | 1.55554e8 | 0.519522 | ||||||||
\(670\) | 3.00068e8 | − | 5.87667e8i | 0.997690 | − | 1.95392i | ||||
\(671\) | 1.44558e7i | 0.0478492i | ||||||||
\(672\) | −1.97920e8 | + | 1.96225e8i | −0.652203 | + | 0.646616i | ||||
\(673\) | −5.75722e7 | −0.188872 | −0.0944359 | − | 0.995531i | \(-0.530105\pi\) | ||||
−0.0944359 | + | 0.995531i | \(0.530105\pi\) | |||||||
\(674\) | −2.11255e8 | − | 1.07869e8i | −0.689966 | − | 0.352303i | ||||
\(675\) | − | 5.31788e7i | − | 0.172913i | ||||||
\(676\) | −1.27244e8 | − | 1.75772e8i | −0.411905 | − | 0.568995i | ||||
\(677\) | 6.12762e7 | 0.197481 | 0.0987407 | − | 0.995113i | \(-0.468519\pi\) | ||||
0.0987407 | + | 0.995113i | \(0.468519\pi\) | |||||||
\(678\) | 7.80232e7 | − | 1.52804e8i | 0.250343 | − | 0.490282i | ||||
\(679\) | 6.08774e8i | 1.94468i | ||||||||
\(680\) | −4.33464e6 | − | 2.78325e7i | −0.0137856 | − | 0.0885169i | ||||
\(681\) | −3.41842e8 | −1.08239 | ||||||||
\(682\) | 2.09409e7 | + | 1.06926e7i | 0.0660151 | + | 0.0337079i | ||||
\(683\) | 1.02941e8i | 0.323092i | 0.986865 | + | 0.161546i | \(0.0516479\pi\) | ||||
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(684\) | −7.26653e7 | + | 5.26036e7i | −0.227069 | + | 0.164379i | ||||
\(685\) | −2.39628e8 | −0.745531 | ||||||||
\(686\) | −1.23877e8 | + | 2.42606e8i | −0.383723 | + | 0.751499i | ||||
\(687\) | 1.73511e8i | 0.535125i | ||||||||
\(688\) | −4.14418e7 | − | 1.36231e7i | −0.127255 | − | 0.0418322i | ||||
\(689\) | 2.47669e7 | 0.0757206 | ||||||||
\(690\) | −1.53894e8 | − | 7.85799e7i | −0.468463 | − | 0.239202i | ||||
\(691\) | − | 1.95567e8i | − | 0.592736i | −0.955074 | − | 0.296368i | \(-0.904225\pi\) | ||
0.955074 | − | 0.296368i | \(-0.0957755\pi\) | |||||||
\(692\) | −2.27781e8 | − | 3.14651e8i | −0.687385 | − | 0.949536i | ||||
\(693\) | −1.95953e7 | −0.0588780 | ||||||||
\(694\) | 1.16281e8 | − | 2.27729e8i | 0.347880 | − | 0.681303i | ||||
\(695\) | − | 1.11576e8i | − | 0.332366i | ||||||
\(696\) | −2.69701e8 | + | 4.20031e7i | −0.799934 | + | 0.124582i | ||||
\(697\) | 6.30205e6 | 0.0186116 | ||||||||
\(698\) | −1.44210e8 | − | 7.36351e7i | −0.424062 | − | 0.216530i | ||||
\(699\) | − | 1.86485e8i | − | 0.546025i | ||||||
\(700\) | −3.97101e8 | + | 2.87468e8i | −1.15773 | + | 0.838099i | ||||
\(701\) | 9.70844e6 | 0.0281835 | 0.0140918 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140918 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(702\) | −1.65157e7 | + | 3.23450e7i | −0.0477403 | + | 0.0934967i | ||||
\(703\) | − | 5.32676e8i | − | 1.53319i | ||||||
\(704\) | 1.17819e7 | + | 3.69081e7i | 0.0337674 | + | 0.105780i | ||||
\(705\) | 3.89513e8 | 1.11161 | ||||||||
\(706\) | 1.68943e8 | + | 8.62639e7i | 0.480094 | + | 0.245140i | ||||
\(707\) | − | 4.65584e8i | − | 1.31747i | ||||||
\(708\) | 8.67661e7 | + | 1.19856e8i | 0.244484 | + | 0.337724i | ||||
\(709\) | −3.85467e8 | −1.08155 | −0.540777 | − | 0.841166i | \(-0.681870\pi\) | ||||
−0.540777 | + | 0.841166i | \(0.681870\pi\) | |||||||
\(710\) | 8.60306e7 | − | 1.68486e8i | 0.240369 | − | 0.470748i | ||||
\(711\) | 1.49712e8i | 0.416531i | ||||||||
\(712\) | 3.20126e7 | + | 2.05552e8i | 0.0886912 | + | 0.569483i | ||||
\(713\) | −1.59988e8 | −0.441387 | ||||||||
\(714\) | 1.93575e7 | + | 9.88414e6i | 0.0531808 | + | 0.0271546i | ||||
\(715\) | − | 3.05060e7i | − | 0.0834577i | ||||||
\(716\) | 2.10152e8 | − | 1.52133e8i | 0.572525 | − | 0.414460i | ||||
\(717\) | 1.13182e8 | 0.307057 | ||||||||
\(718\) | −1.27634e8 | + | 2.49965e8i | −0.344822 | + | 0.675314i | ||||
\(719\) | 4.77343e8i | 1.28423i | 0.766607 | + | 0.642116i | \(0.221943\pi\) | ||||
−0.766607 | + | 0.642116i | \(0.778057\pi\) | |||||||
\(720\) | 5.35346e7 | − | 1.62854e8i | 0.143429 | − | 0.436315i | ||||
\(721\) | 5.90098e8 | 1.57441 | ||||||||
\(722\) | −9.81360e7 | − | 5.01092e7i | −0.260745 | − | 0.133139i | ||||
\(723\) | 1.01220e7i | 0.0267826i | ||||||||
\(724\) | 2.37420e8 | + | 3.27966e8i | 0.625608 | + | 0.864199i | ||||
\(725\) | −4.80111e8 | −1.25987 | ||||||||
\(726\) | 9.92294e7 | − | 1.94335e8i | 0.259317 | − | 0.507857i | ||||
\(727\) | 7.19080e8i | 1.87143i | 0.352753 | + | 0.935716i | \(0.385246\pi\) | ||||
−0.352753 | + | 0.935716i | \(0.614754\pi\) | |||||||
\(728\) | 3.30808e8 | − | 5.15200e7i | 0.857397 | − | 0.133531i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 3.08509e8 | + | 1.57528e8i | 0.793047 | + | 0.404938i | ||||
\(731\) | 3.40201e6i | 0.00870929i | ||||||||
\(732\) | 7.90444e7 | − | 5.72216e7i | 0.201529 | − | 0.145890i | ||||
\(733\) | −6.05981e7 | −0.153867 | −0.0769337 | − | 0.997036i | \(-0.524513\pi\) | ||||
−0.0769337 | + | 0.997036i | \(0.524513\pi\) | |||||||
\(734\) | −6.62915e7 | + | 1.29828e8i | −0.167637 | + | 0.328308i | ||||
\(735\) | − | 4.83417e8i | − | 1.21747i | ||||||
\(736\) | −1.85603e8 | − | 1.87206e8i | −0.465534 | − | 0.469556i | ||||
\(737\) | 7.07769e7 | 0.176803 | ||||||||
\(738\) | 3.41582e7 | + | 1.74415e7i | 0.0849817 | + | 0.0433925i | ||||
\(739\) | − | 2.69944e8i | − | 0.668868i | −0.942419 | − | 0.334434i | \(-0.891455\pi\) | ||
0.942419 | − | 0.334434i | \(-0.108545\pi\) | |||||||
\(740\) | 5.96902e8 | + | 8.24545e8i | 1.47302 | + | 2.03479i | ||||
\(741\) | 1.07761e8 | 0.264855 | ||||||||
\(742\) | 4.10219e7 | − | 8.03390e7i | 0.100416 | − | 0.196660i | ||||
\(743\) | 6.61552e8i | 1.61286i | 0.591327 | + | 0.806432i | \(0.298604\pi\) | ||||
−0.591327 | + | 0.806432i | \(0.701396\pi\) | |||||||
\(744\) | −2.44248e7 | − | 1.56831e8i | −0.0593078 | − | 0.380814i | ||||
\(745\) | −1.06397e8 | −0.257313 | ||||||||
\(746\) | −2.63553e8 | − | 1.34572e8i | −0.634820 | − | 0.324145i | ||||
\(747\) | − | 1.81469e8i | − | 0.435353i | ||||||
\(748\) | 2.44741e6 | − | 1.77172e6i | 0.00584793 | − | 0.00423342i | ||||
\(749\) | 1.19657e8 | 0.284770 | ||||||||
\(750\) | −1.54937e7 | + | 3.03435e7i | −0.0367258 | + | 0.0719253i | ||||
\(751\) | − | 5.41405e8i | − | 1.27821i | −0.769119 | − | 0.639105i | \(-0.779305\pi\) | ||
0.769119 | − | 0.639105i | \(-0.220695\pi\) | |||||||
\(752\) | 5.64525e8 | + | 1.85575e8i | 1.32748 | + | 0.436382i | ||||
\(753\) | −3.32281e8 | −0.778252 | ||||||||
\(754\) | 2.92019e8 | + | 1.49108e8i | 0.681235 | + | 0.347845i | ||||
\(755\) | − | 5.44913e8i | − | 1.26615i | ||||||
\(756\) | 7.75658e7 | + | 1.07147e8i | 0.179517 | + | 0.247980i | ||||
\(757\) | 6.06873e8 | 1.39898 | 0.699488 | − | 0.714644i | \(-0.253411\pi\) | ||||
0.699488 | + | 0.714644i | \(0.253411\pi\) | |||||||
\(758\) | −2.93942e8 | + | 5.75669e8i | −0.674923 | + | 1.32180i | ||||
\(759\) | − | 1.85346e7i | − | 0.0423894i | ||||||
\(760\) | −5.02597e8 | + | 7.82745e7i | −1.14493 | + | 0.178311i | ||||
\(761\) | −1.34482e8 | −0.305147 | −0.152574 | − | 0.988292i | \(-0.548756\pi\) | ||||
−0.152574 | + | 0.988292i | \(0.548756\pi\) | |||||||
\(762\) | 3.84863e8 | + | 1.96515e8i | 0.869844 | + | 0.444151i | ||||
\(763\) | − | 4.98685e8i | − | 1.12267i | ||||||
\(764\) | −5.96251e8 | + | 4.31636e8i | −1.33705 | + | 0.967916i | ||||
\(765\) | −1.33688e7 | −0.0298613 | ||||||||
\(766\) | 6.69578e7 | − | 1.31133e8i | 0.148975 | − | 0.291760i | ||||
\(767\) | − | 1.77745e8i | − | 0.393922i | ||||||
\(768\) | 1.55177e8 | − | 2.10520e8i | 0.342565 | − | 0.464740i | ||||
\(769\) | 8.02045e7 | 0.176368 | 0.0881839 | − | 0.996104i | \(-0.471894\pi\) | ||||
0.0881839 | + | 0.996104i | \(0.471894\pi\) | |||||||
\(770\) | −9.89554e7 | − | 5.05276e7i | −0.216754 | − | 0.110677i | ||||
\(771\) | 5.21615e8i | 1.13812i | ||||||||
\(772\) | −3.29530e8 | − | 4.55205e8i | −0.716215 | − | 0.989361i | ||||
\(773\) | −6.19810e8 | −1.34190 | −0.670950 | − | 0.741503i | \(-0.734114\pi\) | ||||
−0.670950 | + | 0.741503i | \(0.734114\pi\) | |||||||
\(774\) | −9.41536e6 | + | 1.84394e7i | −0.0203055 | + | 0.0397672i | ||||
\(775\) | − | 2.79184e8i | − | 0.599771i | ||||||
\(776\) | −8.79082e7 | − | 5.64456e8i | −0.188124 | − | 1.20794i | ||||
\(777\) | −7.85448e8 | −1.67438 | ||||||||
\(778\) | −2.18169e8 | − | 1.11399e8i | −0.463291 | − | 0.236561i | ||||
\(779\) | − | 1.13802e8i | − | 0.240734i | ||||||
\(780\) | −1.66807e8 | + | 1.20754e8i | −0.351504 | + | 0.254459i | ||||
\(781\) | 2.02920e7 | 0.0425962 | ||||||||
\(782\) | −9.34908e6 | + | 1.83096e7i | −0.0195501 | + | 0.0382877i | ||||
\(783\) | 1.29545e8i | 0.269859i | ||||||||
\(784\) | 2.30314e8 | − | 7.00622e8i | 0.477939 | − | 1.45390i | ||||
\(785\) | −3.60094e8 | −0.744401 | ||||||||
\(786\) | 2.34609e8 | + | 1.19793e8i | 0.483144 | + | 0.246698i | ||||
\(787\) | 1.14696e8i | 0.235301i | 0.993055 | + | 0.117651i | \(0.0375363\pi\) | ||||
−0.993055 | + | 0.117651i | \(0.962464\pi\) | |||||||
\(788\) | −3.66940e8 | − | 5.06881e8i | −0.749922 | − | 1.03592i | ||||
\(789\) | 4.87573e8 | 0.992678 | ||||||||
\(790\) | −3.86040e8 | + | 7.56038e8i | −0.782981 | + | 1.53342i | ||||
\(791\) | 7.50661e8i | 1.51675i | ||||||||
\(792\) | 1.81688e7 | − | 2.82960e6i | 0.0365721 | − | 0.00569574i | ||||
\(793\) | −1.17221e8 | −0.235064 | ||||||||
\(794\) | −3.43659e8 | − | 1.75475e8i | −0.686540 | − | 0.350554i | ||||
\(795\) | 5.54843e7i | 0.110425i | ||||||||
\(796\) | −1.96165e8 | + | 1.42007e8i | −0.388939 | + | 0.281560i | ||||
\(797\) | 6.07041e8 | 1.19907 | 0.599533 | − | 0.800350i | \(-0.295353\pi\) | ||||
0.599533 | + | 0.800350i | \(0.295353\pi\) | |||||||
\(798\) | 1.78487e8 | − | 3.49556e8i | 0.351235 | − | 0.687873i | ||||
\(799\) | − | 4.63425e7i | − | 0.0908529i | ||||||
\(800\) | 3.26681e8 | − | 3.23883e8i | 0.638049 | − | 0.632583i | ||||
\(801\) | 9.87327e7 | 0.192116 | ||||||||
\(802\) | −1.86851e7 | − | 9.54080e6i | −0.0362220 | − | 0.0184953i | ||||
\(803\) | 3.71559e7i | 0.0717598i | ||||||||
\(804\) | −2.80162e8 | − | 3.87009e8i | −0.539065 | − | 0.744650i | ||||
\(805\) | 7.56017e8 | 1.44925 | ||||||||
\(806\) | −8.67060e7 | + | 1.69809e8i | −0.165594 | + | 0.324306i | ||||
\(807\) | 3.59368e8i | 0.683783i | ||||||||
\(808\) | 6.72312e7 | + | 4.31689e8i | 0.127449 | + | 0.818346i | ||||
\(809\) | 4.94530e8 | 0.934001 | 0.467000 | − | 0.884257i | \(-0.345335\pi\) | ||||
0.467000 | + | 0.884257i | \(0.345335\pi\) | |||||||
\(810\) | −7.24613e7 | − | 3.69994e7i | −0.136349 | − | 0.0696209i | ||||
\(811\) | 2.71672e8i | 0.509310i | 0.967032 | + | 0.254655i | \(0.0819620\pi\) | ||||
−0.967032 | + | 0.254655i | \(0.918038\pi\) | |||||||
\(812\) | 9.67353e8 | − | 7.00283e8i | 1.80683 | − | 1.30799i | ||||
\(813\) | −2.72081e8 | −0.506321 | ||||||||
\(814\) | −4.96529e7 | + | 9.72424e7i | −0.0920601 | + | 0.180295i | ||||
\(815\) | − | 7.73925e7i | − | 0.142964i | ||||||
\(816\) | −1.93756e7 | − | 6.36931e6i | −0.0356602 | − | 0.0117225i | ||||
\(817\) | 6.14331e7 | 0.112651 | ||||||||
\(818\) | 9.25281e8 | + | 4.72457e8i | 1.69049 | + | 0.863182i | ||||
\(819\) | − | 1.58897e8i | − | 0.289244i | ||||||
\(820\) | 1.27523e8 | + | 1.76157e8i | 0.231285 | + | 0.319491i | ||||
\(821\) | −1.98822e8 | −0.359281 | −0.179640 | − | 0.983732i | \(-0.557493\pi\) | ||||
−0.179640 | + | 0.983732i | \(0.557493\pi\) | |||||||
\(822\) | −7.89036e7 | + | 1.54528e8i | −0.142063 | + | 0.278223i | ||||
\(823\) | 1.86806e8i | 0.335114i | 0.985862 | + | 0.167557i | \(0.0535878\pi\) | ||||
−0.985862 | + | 0.167557i | \(0.946412\pi\) | |||||||
\(824\) | −5.47139e8 | + | 8.52114e7i | −0.977949 | + | 0.152306i | ||||
\(825\) | 3.23434e7 | 0.0576002 | ||||||||
\(826\) | −5.76569e8 | − | 2.94402e8i | −1.02308 | − | 0.522396i | ||||
\(827\) | 3.36726e8i | 0.595332i | 0.954670 | + | 0.297666i | \(0.0962082\pi\) | ||||
−0.954670 | + | 0.297666i | \(0.903792\pi\) | |||||||
\(828\) | −1.01347e8 | + | 7.33669e7i | −0.178534 | + | 0.129244i | ||||
\(829\) | −5.87046e8 | −1.03041 | −0.515204 | − | 0.857068i | \(-0.672284\pi\) | ||||
−0.515204 | + | 0.857068i | \(0.672284\pi\) | |||||||
\(830\) | 4.67928e8 | − | 9.16411e8i | 0.818361 | − | 1.60271i | ||||
\(831\) | − | 2.49815e8i | − | 0.435326i | ||||||
\(832\) | −2.99286e8 | + | 9.55387e7i | −0.519656 | + | 0.165886i | ||||
\(833\) | −5.75148e7 | −0.0995049 | ||||||||
\(834\) | −7.19517e7 | − | 3.67392e7i | −0.124035 | − | 0.0633333i | ||||
\(835\) | 3.08396e8i | 0.529724i | ||||||||
\(836\) | −3.19936e7 | − | 4.41951e7i | −0.0547576 | − | 0.0756407i | ||||
\(837\) | −7.53306e7 | −0.128468 | ||||||||
\(838\) | −2.04137e7 | + | 3.99791e7i | −0.0346888 | + | 0.0679361i | ||||
\(839\) | 2.50547e8i | 0.424231i | 0.977245 | + | 0.212116i | \(0.0680354\pi\) | ||||
−0.977245 | + | 0.212116i | \(0.931965\pi\) | |||||||
\(840\) | 1.15418e8 | + | 7.41096e8i | 0.194732 | + | 1.25037i | ||||
\(841\) | 5.74745e8 | 0.966244 | ||||||||
\(842\) | 1.15756e8 | + | 5.91061e7i | 0.193913 | + | 0.0990138i | ||||
\(843\) | 7.10009e7i | 0.118517i | ||||||||
\(844\) | 1.44374e8 | − | 1.04515e8i | 0.240139 | − | 0.173841i | ||||
\(845\) | −5.83959e8 | −0.967859 | ||||||||
\(846\) | 1.28257e8 | − | 2.51184e8i | 0.211821 | − | 0.414840i | ||||
\(847\) | 9.54686e8i | 1.57112i | ||||||||
\(848\) | −2.64344e7 | + | 8.04140e7i | −0.0433492 | + | 0.131869i | ||||
\(849\) | 2.19469e8 | 0.358633 | ||||||||
\(850\) | −3.19509e7 | − | 1.63144e7i | −0.0520267 | − | 0.0265653i | ||||
\(851\) | − | 7.42929e8i | − | 1.20548i | ||||||
\(852\) | −8.03234e7 | − | 1.10957e8i | −0.129874 | − | 0.179405i | ||||
\(853\) | 9.93388e8 | 1.60056 | 0.800280 | − | 0.599627i | \(-0.204684\pi\) | ||||
0.800280 | + | 0.599627i | \(0.204684\pi\) | |||||||
\(854\) | −1.94156e8 | + | 3.80243e8i | −0.311729 | + | 0.610503i | ||||
\(855\) | 2.41413e8i | 0.386244i | ||||||||
\(856\) | −1.10946e8 | + | 1.72788e7i | −0.176885 | + | 0.0275481i | ||||
\(857\) | 1.08596e9 | 1.72532 | 0.862662 | − | 0.505781i | \(-0.168796\pi\) | ||||
0.862662 | + | 0.505781i | \(0.168796\pi\) | |||||||
\(858\) | −1.96723e7 | − | 1.00449e7i | −0.0311453 | − | 0.0159031i | ||||
\(859\) | − | 4.90420e8i | − | 0.773729i | −0.922137 | − | 0.386865i | \(-0.873558\pi\) | ||
0.922137 | − | 0.386865i | \(-0.126442\pi\) | |||||||
\(860\) | −9.50942e7 | + | 6.88403e7i | −0.149506 | + | 0.108230i | ||||
\(861\) | −1.67805e8 | −0.262902 | ||||||||
\(862\) | 1.03091e8 | − | 2.01897e8i | 0.160952 | − | 0.315216i | ||||
\(863\) | − | 9.42173e8i | − | 1.46588i | −0.680293 | − | 0.732940i | \(-0.738148\pi\) | ||
0.680293 | − | 0.732940i | \(-0.261852\pi\) | |||||||
\(864\) | −8.73913e7 | − | 8.81464e7i | −0.135496 | − | 0.136667i | ||||
\(865\) | −1.04535e9 | −1.61516 | ||||||||
\(866\) | −8.59217e8 | − | 4.38724e8i | −1.32297 | − | 0.675520i | ||||
\(867\) | − | 3.74677e8i | − | 0.574910i | ||||||
\(868\) | 4.07214e8 | + | 5.62515e8i | 0.622678 | + | 0.860152i | ||||
\(869\) | −9.10550e7 | −0.138754 | ||||||||
\(870\) | −3.34040e8 | + | 6.54198e8i | −0.507271 | + | 0.993463i | ||||
\(871\) | 5.73926e8i | 0.868563i | ||||||||
\(872\) | 7.20111e7 | + | 4.62381e8i | 0.108605 | + | 0.697349i | ||||
\(873\) | −2.71125e8 | −0.407500 | ||||||||
\(874\) | 3.30634e8 | + | 1.68825e8i | 0.495237 | + | 0.252873i | ||||
\(875\) | − | 1.49065e8i | − | 0.222510i | ||||||
\(876\) | 2.03169e8 | − | 1.47077e8i | 0.302235 | − | 0.218793i | ||||
\(877\) | −7.83937e8 | −1.16220 | −0.581102 | − | 0.813831i | \(-0.697378\pi\) | ||||
−0.581102 | + | 0.813831i | \(0.697378\pi\) | |||||||
\(878\) | 1.51632e8 | − | 2.96962e8i | 0.224030 | − | 0.438750i | ||||
\(879\) | 1.09175e8i | 0.160753i | ||||||||
\(880\) | 9.90478e7 | + | 3.25598e7i | 0.145344 | + | 0.0477787i | ||||
\(881\) | 3.53897e8 | 0.517546 | 0.258773 | − | 0.965938i | \(-0.416682\pi\) | ||||
0.258773 | + | 0.965938i | \(0.416682\pi\) | |||||||
\(882\) | −3.11740e8 | − | 1.59177e8i | −0.454346 | − | 0.231993i | ||||
\(883\) | − | 1.09742e9i | − | 1.59401i | −0.603974 | − | 0.797004i | \(-0.706417\pi\) | ||
0.603974 | − | 0.797004i | \(-0.293583\pi\) | |||||||
\(884\) | 1.43668e7 | + | 1.98459e7i | 0.0207971 | + | 0.0287286i | ||||
\(885\) | 3.98194e8 | 0.574467 | ||||||||
\(886\) | 9.15211e7 | − | 1.79239e8i | 0.131589 | − | 0.257710i | ||||
\(887\) | − | 9.70332e8i | − | 1.39043i | −0.718801 | − | 0.695216i | \(-0.755309\pi\) | ||
0.718801 | − | 0.695216i | \(-0.244691\pi\) | |||||||
\(888\) | 7.28267e8 | − | 1.13420e8i | 1.04004 | − | 0.161976i | ||||
\(889\) | −1.89067e9 | −2.69098 | ||||||||
\(890\) | 4.98595e8 | + | 2.54588e8i | 0.707259 | + | 0.361133i | ||||
\(891\) | − | 8.72703e6i | − | 0.0123377i | ||||||
\(892\) | 5.17320e8 | − | 3.74496e8i | 0.728894 | − | 0.527659i | ||||
\(893\) | −8.36848e8 | −1.17515 | ||||||||
\(894\) | −3.50340e7 | + | 6.86120e7i | −0.0490317 | + | 0.0960257i | ||||
\(895\) | − | 6.98179e8i | − | 0.973863i | ||||||
\(896\) | −1.85803e8 | + | 1.12907e9i | −0.258303 | + | 1.56963i | ||||
\(897\) | 1.50296e8 | 0.208243 | ||||||||
\(898\) | 8.25541e8 | + | 4.21529e8i | 1.14001 | + | 0.582101i | ||||
\(899\) | 6.80103e8i | 0.936043i | ||||||||
\(900\) | −1.28028e8 | − | 1.76854e8i | −0.175621 | − | 0.242598i | ||||
\(901\) | 6.60127e6 | 0.00902513 | ||||||||
\(902\) | −1.06079e7 | + | 2.07750e7i | −0.0144548 | + | 0.0283089i | ||||
\(903\) | − | 9.05851e7i | − | 0.123025i | ||||||
\(904\) | −1.08397e8 | − | 6.96013e8i | −0.146728 | − | 0.942133i | ||||
\(905\) | 1.08959e9 | 1.47000 | ||||||||
\(906\) | −3.51396e8 | − | 1.79426e8i | −0.472512 | − | 0.241269i | ||||
\(907\) | − | 4.60206e8i | − | 0.616780i | −0.951260 | − | 0.308390i | \(-0.900210\pi\) | ||
0.951260 | − | 0.308390i | \(-0.0997902\pi\) | |||||||
\(908\) | −1.13685e9 | + | 8.22983e8i | −1.51860 | + | 1.09934i | ||||
\(909\) | 2.07354e8 | 0.276070 | ||||||||
\(910\) | 4.09725e8 | − | 8.02424e8i | 0.543711 | − | 1.06483i | ||||
\(911\) | 1.30765e9i | 1.72956i | 0.502148 | + | 0.864782i | \(0.332543\pi\) | ||||
−0.502148 | + | 0.864782i | \(0.667457\pi\) | |||||||
\(912\) | −1.15016e8 | + | 3.49882e8i | −0.151626 | + | 0.461251i | ||||
\(913\) | 1.10370e8 | 0.145024 | ||||||||
\(914\) | −4.37982e8 | − | 2.23638e8i | −0.573611 | − | 0.292891i | ||||
\(915\) | − | 2.62606e8i | − | 0.342801i | ||||||
\(916\) | 4.17726e8 | + | 5.77035e8i | 0.543506 | + | 0.750785i | ||||
\(917\) | −1.15253e9 | −1.49467 | ||||||||
\(918\) | −4.40202e6 | + | 8.62112e6i | −0.00569016 | + | 0.0111439i | ||||
\(919\) | 4.64060e7i | 0.0597898i | 0.999553 | + | 0.0298949i | \(0.00951727\pi\) | ||||
−0.999553 | + | 0.0298949i | \(0.990483\pi\) | |||||||
\(920\) | −7.00979e8 | + | 1.09170e8i | −0.900205 | + | 0.140198i | ||||
\(921\) | 4.96038e6 | 0.00634946 | ||||||||
\(922\) | −6.84596e8 | − | 3.49561e8i | −0.873457 | − | 0.445996i | ||||
\(923\) | 1.64546e8i | 0.209259i | ||||||||
\(924\) | −6.51672e7 | + | 4.71756e7i | −0.0826063 | + | 0.0598001i | ||||
\(925\) | 1.29643e9 | 1.63804 | ||||||||
\(926\) | 1.97023e8 | − | 3.85859e8i | 0.248133 | − | 0.485955i | ||||
\(927\) | 2.62808e8i | 0.329913i | ||||||||
\(928\) | −7.95807e8 | + | 7.88990e8i | −0.995781 | + | 0.987251i | ||||
\(929\) | −7.13241e8 | −0.889588 | −0.444794 | − | 0.895633i | \(-0.646723\pi\) | ||||
−0.444794 | + | 0.895633i | \(0.646723\pi\) | |||||||
\(930\) | −3.80416e8 | − | 1.94244e8i | −0.472944 | − | 0.241490i | ||||
\(931\) | 1.03860e9i | 1.28706i | ||||||||
\(932\) | −4.48962e8 | − | 6.20184e8i | −0.554577 | − | 0.766078i | ||||
\(933\) | 7.29504e8 | 0.898220 | ||||||||
\(934\) | 6.01605e8 | − | 1.17821e9i | 0.738365 | − | 1.44605i | ||||
\(935\) | − | 8.13094e6i | − | 0.00994731i | ||||||
\(936\) | 2.29451e7 | + | 1.47330e8i | 0.0279809 | + | 0.179665i | ||||
\(937\) | 8.74097e7 | 0.106253 | 0.0531265 | − | 0.998588i | \(-0.483081\pi\) | ||||
0.0531265 | + | 0.998588i | \(0.483081\pi\) | |||||||
\(938\) | 1.86170e9 | + | 9.50604e8i | 2.25581 | + | 1.15184i | ||||
\(939\) | − | 5.68831e8i | − | 0.687047i | ||||||
\(940\) | 1.29538e9 | − | 9.37749e8i | 1.55960 | − | 1.12902i | ||||
\(941\) | 1.35628e9 | 1.62773 | 0.813863 | − | 0.581057i | \(-0.197361\pi\) | ||||
0.813863 | + | 0.581057i | \(0.197361\pi\) | |||||||
\(942\) | −1.18570e8 | + | 2.32213e8i | −0.141848 | + | 0.277801i | ||||
\(943\) | − | 1.58721e8i | − | 0.189277i | ||||||
\(944\) | 5.77107e8 | + | 1.89711e8i | 0.686026 | + | 0.225516i | ||||
\(945\) | 3.55971e8 | 0.421813 | ||||||||
\(946\) | −1.12149e7 | − | 5.72643e6i | −0.0132471 | − | 0.00676411i | ||||
\(947\) | 9.31247e8i | 1.09652i | 0.836309 | + | 0.548258i | \(0.184709\pi\) | ||||
−0.836309 | + | 0.548258i | \(0.815291\pi\) | |||||||
\(948\) | 3.60431e8 | + | 4.97889e8i | 0.423055 | + | 0.584397i | ||||
\(949\) | −3.01295e8 | −0.352528 | ||||||||
\(950\) | −2.94604e8 | + | 5.76966e8i | −0.343612 | + | 0.672945i | ||||
\(951\) | − | 7.74633e8i | − | 0.900646i | ||||||
\(952\) | 8.81723e7 | − | 1.37319e7i | 0.102193 | − | 0.0159155i | ||||
\(953\) | 9.78401e8 | 1.13042 | 0.565208 | − | 0.824949i | \(-0.308796\pi\) | ||||
0.565208 | + | 0.824949i | \(0.308796\pi\) | |||||||
\(954\) | 3.57800e7 | + | 1.82696e7i | 0.0412093 | + | 0.0210419i | ||||
\(955\) | 1.98090e9i | 2.27432i | ||||||||
\(956\) | 3.76403e8 | − | 2.72484e8i | 0.430803 | − | 0.311866i | ||||
\(957\) | −7.87897e7 | −0.0898946 | ||||||||
\(958\) | −6.13371e8 | + | 1.20125e9i | −0.697632 | + | 1.36627i | ||||
\(959\) | − | 7.59131e8i | − | 0.860718i | ||||||
\(960\) | −2.14032e8 | − | 6.70478e8i | −0.241916 | − | 0.757828i | ||||
\(961\) | 4.92024e8 | 0.554391 | ||||||||
\(962\) | −7.88533e8 | − | 4.02632e8i | −0.885716 | − | 0.452255i | ||||
\(963\) | 5.32909e7i | 0.0596725i | ||||||||
\(964\) | 2.43688e7 | + | 3.36624e7i | 0.0272021 | + | 0.0375763i | ||||
\(965\) | −1.51231e9 | −1.68290 | ||||||||
\(966\) | 2.48938e8 | − | 4.87530e8i | 0.276159 | − | 0.540842i | ||||
\(967\) | − | 848332.i | − | 0.000938180i | −1.00000 | 0.000469090i | \(-0.999851\pi\) | |||
1.00000 | 0.000469090i | \(-0.000149316\pi\) | ||||||||
\(968\) | −1.37859e8 | − | 8.85185e8i | −0.151987 | − | 0.975906i | ||||
\(969\) | 2.87222e7 | 0.0315680 | ||||||||
\(970\) | −1.36917e9 | − | 6.99111e8i | −1.50018 | − | 0.766004i | ||||
\(971\) | 2.01864e8i | 0.220496i | 0.993904 | + | 0.110248i | \(0.0351645\pi\) | ||||
−0.993904 | + | 0.110248i | \(0.964835\pi\) | |||||||
\(972\) | −4.77194e7 | + | 3.45449e7i | −0.0519633 | + | 0.0376171i | ||||
\(973\) | 3.53468e8 | 0.383718 | ||||||||
\(974\) | 1.14160e7 | − | 2.23576e7i | 0.0123548 | − | 0.0241962i | ||||
\(975\) | 2.62271e8i | 0.282967i | ||||||||
\(976\) | 1.25113e8 | − | 3.80598e8i | 0.134572 | − | 0.409371i | ||||
\(977\) | 3.23896e8 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(978\) | −4.99079e7 | − | 2.54835e7i | −0.0533523 | − | 0.0272422i | ||||
\(979\) | 6.00494e7i | 0.0639971i | ||||||||
\(980\) | −1.16382e9 | − | 1.60768e9i | −1.23654 | − | 1.70813i | ||||
\(981\) | 2.22096e8 | 0.235252 | ||||||||
\(982\) | −7.88176e8 | + | 1.54360e9i | −0.832317 | + | 1.63005i | ||||
\(983\) | − | 9.70682e8i | − | 1.02192i | −0.859605 | − | 0.510960i | \(-0.829290\pi\) | ||
0.859605 | − | 0.510960i | \(-0.170710\pi\) | |||||||
\(984\) | 1.55588e8 | − | 2.42313e7i | 0.163302 | − | 0.0254327i | ||||
\(985\) | −1.68399e9 | −1.76210 | ||||||||
\(986\) | 7.78335e7 | + | 3.97426e7i | 0.0811963 | + | 0.0414596i | ||||
\(987\) | 1.23396e9i | 1.28336i | ||||||||
\(988\) | 3.58376e8 | − | 2.59434e8i | 0.371593 | − | 0.269003i | ||||
\(989\) | 8.56815e7 | 0.0885723 | ||||||||
\(990\) | 2.25031e7 | − | 4.40710e7i | 0.0231919 | − | 0.0454201i | ||||
\(991\) | 2.58231e7i | 0.0265330i | 0.999912 | + | 0.0132665i | \(0.00422299\pi\) | ||||
−0.999912 | + | 0.0132665i | \(0.995777\pi\) | |||||||
\(992\) | −4.58797e8 | − | 4.62761e8i | −0.469987 | − | 0.474048i | ||||
\(993\) | −7.16021e8 | −0.731270 | ||||||||
\(994\) | 5.33757e8 | + | 2.72541e8i | 0.543481 | + | 0.277507i | ||||
\(995\) | 6.51710e8i | 0.661584i | ||||||||
\(996\) | −4.36886e8 | − | 6.03503e8i | −0.442171 | − | 0.610804i | ||||
\(997\) | −7.49027e8 | −0.755809 | −0.377904 | − | 0.925845i | \(-0.623355\pi\) | ||||
−0.377904 | + | 0.925845i | \(0.623355\pi\) | |||||||
\(998\) | 3.15126e8 | − | 6.17156e8i | 0.317024 | − | 0.620874i | ||||
\(999\) | − | 3.49809e8i | − | 0.350861i |
(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 | 12.7.d.a.7.1 | ✓ | 6 | |
3.2 | odd | 2 | 36.7.d.e.19.6 | 6 | |||
4.3 | odd | 2 | inner | 12.7.d.a.7.2 | yes | 6 | |
8.3 | odd | 2 | 192.7.g.e.127.4 | 6 | |||
8.5 | even | 2 | 192.7.g.e.127.1 | 6 | |||
12.11 | even | 2 | 36.7.d.e.19.5 | 6 | |||
16.3 | odd | 4 | 768.7.b.h.127.8 | 12 | |||
16.5 | even | 4 | 768.7.b.h.127.11 | 12 | |||
16.11 | odd | 4 | 768.7.b.h.127.5 | 12 | |||
16.13 | even | 4 | 768.7.b.h.127.2 | 12 | |||
24.5 | odd | 2 | 576.7.g.p.127.6 | 6 | |||
24.11 | even | 2 | 576.7.g.p.127.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.7.d.a.7.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
12.7.d.a.7.2 | yes | 6 | 4.3 | odd | 2 | inner | |
36.7.d.e.19.5 | 6 | 12.11 | even | 2 | |||
36.7.d.e.19.6 | 6 | 3.2 | odd | 2 | |||
192.7.g.e.127.1 | 6 | 8.5 | even | 2 | |||
192.7.g.e.127.4 | 6 | 8.3 | odd | 2 | |||
576.7.g.p.127.5 | 6 | 24.11 | even | 2 | |||
576.7.g.p.127.6 | 6 | 24.5 | odd | 2 | |||
768.7.b.h.127.2 | 12 | 16.13 | even | 4 | |||
768.7.b.h.127.5 | 12 | 16.11 | odd | 4 | |||
768.7.b.h.127.8 | 12 | 16.3 | odd | 4 | |||
768.7.b.h.127.11 | 12 | 16.5 | even | 4 |